Answer:
31
Step-by-step explanation:
116 - 27 -27 = 62 / 2 = 31
Answer:
The length is 31 in
Step-by-step explanation:
Perimeter = 2(Length + width)
say p = perimeter, l = length and w = width
perimeter = 166, w = 27
166 = 2(l + 27)
116 = 2l + 2×27
2l + 54 = 116
2l = 116 - 54
2l = 62
l = 62/2
l = 31 in
say
Suppose that 275 students are randomly selected from a local college campus to investigate the use of cell phones in classrooms. When asked if they are allowed to use cell phones in at least one of their classes, 40% of students responded yes. Using these results, with 95% confidence, the margin of error is 0.058 . How would the margin of error change if the sample size decreased from 275 to 125 students? Assume that the proportion of students who say yes does not change significantly. As the sample size decreases, the margin of error remains unchanged. Cannot be determined based on the information provided. As the sample size decreases, the margin of error increases. As the sample size decreases, the margin of error decreases.
Answer:
Correct option: As the sample size decreases, the margin of error increases.
Step-by-step explanation:
The (1 - α) % confidence interval for population proportion is:
[tex]CI=\hat p\pm z_{\alpha /2}\sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex]
The margin of error in this confidence interval is:
[tex]\\ MOE=z_{\alpha /2}\sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex]
The sample size n is inversely related to the margin of error.
An inverse relationship implies that when one increases the other decreases and vice versa.
In case of MOE also, when n is increased the MOE decreases and when n is decreased the MOE increases.
Compute the new margin of error for n = 125 as follows:
[tex]\\ MOE=z_{\alpha /2}\sqrt{\frac{\hat p(1-\hat p)}{n} }=1.96\times \sqrt{\frac{0.40(1-0.40)}{125} }=0.086[/tex]
*Use z-table for the critical value.
For n = 125 the MOE is 0.086.
And for n = 275 the MOE was 0.058.
Thus, as the sample size decreases, the margin of error increases.
3.30 Survey response rate. Pew Research reported in 2012 that the typical response rate to their surveys is only 9%. If for a particular survey 15,000 households are contacted, what is the probability that at least 1,500 will agree to respond
Answer:
0% probability that at least 1,500 will agree to respond
Step-by-step explanation:
I am going to use the binomial approximation to the normal to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 15000, p = 0.09[/tex]
So
[tex]\mu = E(X) = np = 15000*0.09 = 1350[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{15000*0.09*0.91} = 35.05[/tex]
What is the probability that at least 1,500 will agree to respond
This is 1 subtracted by the pvalue of Z when X = 1500-1 = 1499. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1499 - 1350}{35.05}[/tex]
[tex]Z = 4.25[/tex]
[tex]Z = 4.25[/tex] has a pvalue of 1.
1 - 1 = 0
0% probability that at least 1,500 will agree to respond
The probability that at least 1,500 will agree to respond is 0.000009.
How to calculate the probabilityFrom the information given,
n = 15000
p = 0.09
Therefore, np = 15000 × 0.09
= 1350
nq = 15000 × (0.91)
= 13650
The probability that at least 1,500 will agree to respond will be:
= 1 - P (Z < (1500 - 1350)/35.05]
= 1 - P(Z < 4.2796)
= 0.000009
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The red tablecloth has a diagonal of V 10 feet. The blue tablecloth has a diagonal
V 50 Teet. Aaron says that the length of the diagonal of the blue tablecloth is three
times the length of the diagonal of the red tablecloth.
Is he correct? Explain.
the length of the diagonal of the blue tablecloth is five times the length of the diagonal of the red tablecloth. So , Aaron is not correct .
Step-by-step explanation:
Here we have , The red tablecloth has a diagonal of V 10 feet. The blue tablecloth has a diagonal V 50 feet . Aaron says that the length of the diagonal of the blue tablecloth is three times the length of the diagonal of the red tablecloth. Let's find out what Aaron says is correct or not :
Length of red tablecloth = 10 feet = p feet
Length of blue tablecloth = 50 feet
⇒ Length of blue tablecloth = 50 feet
⇒ Length of blue tablecloth = 5(10) feet
⇒ Length of blue tablecloth = 5p feet
That means the length of the diagonal of the blue tablecloth is five times the length of the diagonal of the red tablecloth. So , Aaron is not correct .
Aaron's claim that the length of the diagonal of the blue tablecloth is three times that of the red one is incorrect because the square root of 50 is not equal to three times the square root of 10.
Explanation:No, Aaron is not correct. The length of the diagonal of the blue tablecloth is not three times the length of the diagonal of the red tablecloth. This is because the square root of 50 (√50) is not equal to three times the square root of 10 (3 * √10). In reality, the square root of 50 is approximately 7.07 and three times the square root of 10 is approximately 9.49.
Indeed:√50 ≈ 7.07 and 3 * √10 ≈ 9.49. These are not the same, hence Aaron's claim is incorrect.
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which of the following would indicate that a dataset is skewed to the right? the interquartile range is larger than the range. the range is larger than the interquartile range. the mean is much larger than the median. the mean is much smaller than the median.
Answer:
Step-by-step explanation:
The first two answers could not possibly be correct.
"Skewed to the right" implies that the mean is larger than the median. This is the correct answer.
The mean is much larger than the median is the statement that would indicate that a data set is skewed to the right. This can be obtained by understanding the characteristics of a data set skewed to the right, that is positively skewed.
What are the characteristics of a positively skewness?Skewness refers to the lack of symmetry.Positive skewness means when distribution is fatter on the left.⇒Characteristics of a positively skewness
Right Tail is longer Mass of the distribution is concentrated on the leftMean>Median>MeanHence the mean is much larger than the median is the statement that would indicate that a data set is skewed to the right. Therefore option 3 is correct.
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4. The length of an injected-molded plastic case that holds tape is normally distributed with a mean length of 90.2 millimeters and a standard deviation of 0.1 millimeters. a. What is the probability that a part is longer than 90.3 millimeters or shorter than 89.7 millimeters
To find the probability that a part is longer than 90.3 millimeters or shorter than 89.7 millimeters, calculate the cumulative probability for each scenario and subtract them from 1. The resulting probability is approximately 0.8413.
Explanation:To find the probability that a part is longer than 90.3 millimeters or shorter than 89.7 millimeters, we need to calculate the cumulative probability for each scenario and then subtract them from 1.
Step 1: Calculate the z-scores for both values using the formula:
z = (x - mean) / standard deviation
For 90.3 millimeters:
z = (90.3 - 90.2) / 0.1 = 1
For 89.7 millimeters:
z = (89.7 - 90.2) / 0.1 = -5
Step 2: Use a standard normal distribution table or a calculator to find the cumulative probability for each z-score.
For a z-score of 1, the cumulative probability is approximately 0.8413.
For a z-score of -5, the cumulative probability is approximately 0.0000003.
Step 3: Subtract the cumulative probability for the shorter length from 1 and add the cumulative probability for the longer length.
Probability = (1 - 0.0000003) + 0.8413 = 0.8413
Therefore, the probability that a part is longer than 90.3 millimeters or shorter than 89.7 millimeters is approximately 0.8413.
A hip joint replacement part is being stress-tested in a laboratory. The probability of successfully completing the test is 0.830. 7 randomly and independently chosen parts are tested. What is the probability that exactly two of the 7 parts successfully complete the test
Answer:
0.00205
Step-by-step explanation:
This is binomial distribution problem.
Binomial distribution function is represented by
P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
n = total number of sample spaces = 7
x = Number of successes required = 2
p = probability of success = 0.830
q = probability of failure = 1 - 0.83 = 0.17
P(X =2) = ⁷C₂ 0.83² 0.17⁷⁻²
P(X =2) = ⁷C₂ 0.83² 0.17⁵ = 0.00205
Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain area is 6.9 per year. a. Find the probability that, in a year, there will be 4 hurricanes. b. In a 45-year period, how many years are expected to have 4 hurricanes? c. How does the result from part (b) compare to a recent period of 45 years in which 4 years had 4 hurricanes? Does the Poisson distribution work well here? a. The probability is nothing. (Round to three decimal places as needed.)
Answer:
a) 9.52% probability that, in a year, there will be 4 hurricanes.
b) 4.284 years are expected to have 4 hurricanes.
c) The value of 4 is very close to the expected value of 4.284, so the Poisson distribution works well here.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given time interval.
6.9 per year.
This means that [tex]\mu = 6.9[/tex]
a. Find the probability that, in a year, there will be 4 hurricanes.
This is P(X = 4).
So
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 4) = \frac{e^{-6.9}*(6.9)^{4}}{(4)!}[/tex]
[tex]P(X = 4) = 0.0952[/tex]
9.52% probability that, in a year, there will be 4 hurricanes.
b. In a 45-year period, how many years are expected to have 4 hurricanes?
For each year, the probability is 0.0952.
Multiplying by 45
45*0.0952 = 4.284.
4.284 years are expected to have 4 hurricanes.
c. How does the result from part (b) compare to a recent period of 45 years in which 4 years had 4 hurricanes? Does the Poisson distribution work well here?
The value of 4 is very close to the expected value of 4.284, so the Poisson distribution works well here.
g Two players each put one dollar into a pot. They decide to throw a pair of dice alternately. The first one who throws the two dice so that the sum of the two faces is five (5) wins the pot. How much should the player who starts add to the pot to make the game a ‘fair game’? Give your answer as a fraction in reduced form (i.e. A/B where A and B do not share any common factors). Note: A ‘fair game’ would be one where the expected payment to each player is equal
Answer:
The first player should add 1/8 more dollar to the pot
Step-by-step explanation:
The probability that the first player wins on the first turn is equivalent to the probability of getting 5 in the dices. Out of the 36 possible outcomes for a dice, only 4 are favourable in the event of obtaining 5 in the sum:
- first dice 1, second dice 4
- first dice 2, second dice 3
- first dice 3, second dice 2
- first dice 4, second dice 1
Thus, the probability that the first player wins on the first turn is 4/36 = 1/9.
Note that if the first player doesnt win in the first turn, then the second player will be at the same position the first player was at the start of the game. If we call P the probability that the first player wins, then, the second player will have a probability of P of winning after 'surviving' on the first turn.
As a result, the probability that the second player wins is P multiplied by 8/9 (the probability that the first player doenst win in the first turn). In short
Probability that the first player wins = P
Probability that the second player wins = 8/9 * P
Since the sum should be 1 (because both events are complementary from each other), then P + P*8/9 = 1, thus
17/9 P = 1
P = 9/17
Lets call E the extra amount of money player A should include into the pot (in dollard). We have that both players should have expected gain equal to 0, and we have that
- First player gains 1 if he wins (with probability 9/17)
- First player gains -1-E if the loses (with probability 8/17)
Therefore
9/17*1+ 8/17 (-1-E) = 0
9/17 = 8/17 + E 8/17
E = (1/17) / (8/17) = 1/8
The first player should add 1/8 more dollar to the pot.
Check that reflection in the x-axis preserves the distance between any two points. When we combine reflections in two lines, the nature of the outcome depends on whether the lines are parallel.
Answer:
No, it depend on reflective surface
Step-by-step explanation:
concave, convex, if plane mirror angle between the two mirrors, the parallel will produced infinity images
If we let the domain be all animals, and S(x) = "x is a spider", I(x) = " x is an insect", D(x) = "x is a dragonfly", L(x) = "x has six legs", E(x, y ) = "x eats y", then the premises be
"All insects have six legs," (∀x (I(x)→ L(x)))
"Dragonflies are insects," (∀x (D(x)→I(x)))
"Spiders do not have six legs," (∀x (S(x)→¬L(x)))
"Spiders eat dragonflies." (∀x, y (S(x) ∧ D(y)) → E(x, y)))
The conditional statement "∀x, If x is an insect, then x has six legs" is derived from the statement "All insects have six legs" using _____.
a. existential generalization
b. existential instantiation
c. universal instantiation
d. universal generalization
The statement 'All insects have six legs' is converted to 'If x is an insect, then x has six legs' using the principle of Universal Generalization.
Explanation:The process used here is known as Universal Generalization. This principle allows us to infer that something is true for all objects in a particular domain, provided it has been proved to be true for an arbitrary object in that domain. In this case, the statement 'All insects have six legs' has been converted into a formal logical statement using 'x' as the arbitrary object in the domain of all animals. By stating 'If x is an insect, then x has six legs' and using ∀x (denoting 'for all x'), we are using Universal Generalization to indicate this is true for all members of the domain.
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This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise A particle is moved along the x-axis by a force that measures 9/(6 x) pounds at a point x feet from the origin. Find the work W done in moving the particle from the origin to a distance of 12 ft.
Answer:
5.0 ft-lbf
Step-by-step explanation:
The force is
[tex]F = \dfrac{9}{6^x}[/tex]
This force is not a constant force. For a non-constant force, the work done, W, is
[tex]W = \int\limits^{x_2}_{x_1} {F(x)} \, dx[/tex]
with [tex]x_1[/tex] and [tex]x_2[/tex] the initial and final displacements respectively.
From the question, [tex]x_1 =0[/tex] and [tex]x_2 = 12[/tex].
Then
[tex]W = \int\limits^{12}_0 {\dfrac{9}{6^x}} \, dx[/tex]
Evaluating the indefinite integral,
[tex]\int\limits \dfrac{9}{6^x} \, dx =9 \int\limits\!\left(\frac{1}{6}\right)^x \, dx[/tex]
From the rules of integration,
[tex]\int\limits a^x\, dx = \dfrac{a^x}{\ln a}[/tex]
[tex]9 \int\limits \left(\frac{1}{6}\right)^x \, dx = 9\times\dfrac{(1/6)^x}{\ln(1/6)} = -5.0229\left(\dfrac{1}{6}\right)^x[/tex]
Returning the limits,
[tex]\left.-5.0229\left(\dfrac{1}{6}\right)^x\right|^{12}_0 = -5.0229(0.1667^{12} - 0.1667^0) = 5.0229 \approx 5.0 \text{ ft-lbf}[/tex]
The body temperatures of adults are normally distributed with a mean of 98.6degrees° F and a standard deviation of 0.60degrees° F. If 36 adults are randomly selected, find the probability that their mean body temperature is greater than 98.4degrees° F.
Answer:
97.72% probability that their mean body temperature is greater than 98.4degrees° F.
Step-by-step explanation:
To solve this question, we have to understand the normal probability distribution and the central limit theorem.
Normal probability distribution:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central limit theorem:
The Central Limit Theorem estabilishes that, for a random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sample means with size n of at least 30 can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
In this problem, we have that:
[tex]\mu = 98.6, \sigma = 0.6, n = 36, s = \frac{0.6}{\sqrt{36}} = 0.1[/tex]
If 36 adults are randomly selected, find the probability that their mean body temperature is greater than 98.4degrees° F.
This is 1 subtracted by the pvalue of Z when X = 98.4. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{98.4 - 98.6}{0.1}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228
1 - 0.0228 = 0.9772
97.72% probability that their mean body temperature is greater than 98.4degrees° F.
Pepsi and Mountain Dew products sponsored a contest giving away a Lamborghini sports car worth $215,000. The probability of winning from a single bottle purchase was .00000884. Find the expected value. (Round your answer to 4 decimal places.) Expected value $
Answer:
$1.9006
Step-by-step explanation:
The expected value out of an event with value v and the probability p of that event to happen is the product of the value v and the probability p itself.
Therefore, the expected value of winning $215000 with probability of 0.00000884 bottle purchase is
E = pv = 215000 * 0.00000884 = $1.9006
The expected value, multiplied by the chance of winning the Lamborghini, is approximately $1.9004. This value means that if you could repeat this contest over and over, on average, you would gain about $1.90 per bottle purchased.
Explanation:The subject of this question is about the expected value in probability. In the given scenario, when a Pepsi or Mountain Dew bottle is purchased, there's a probability of .00000884 of winning a Lamborghini sports car worth $215,000.
The expected value is calculated as the product of the value of the prize and the probability of winning it. Therefore, the expected value for this case would be (215000*.00000884) which equals to $1.9004, rounded to 4 decimal places. However, in the previous calculation, there was an error, resulting in a negative value which should not be the case in this context.
Expected value offers a predicted value of a variable, calculated as the sum of all possible values each multiplied by the probability of its occurrence. It is widely used in Probability Theory and Statistics.
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An English teacher needs to pick 10 books to put on her reading list for the next school year, and she needs to plan the order in which they should be read. She has narrowed down her choices to 4 novels, 6 plays, 8 poetry books, and 4 nonfiction books. Step 1 of 2: If she wants to include no more than 3 poetry books, how many different reading schedules are possible? Express your answer in scientific notation rounding to the hundredths place. Answer Tables II Keypa a x10
Calculating the number of different reading schedules an English teacher can create involves combining and permuting selections of novels, plays, poetry (up to 3), and nonfiction books from a list.
It entails calculating the combinations of books and then the permutations for the order of reading.
Detailed mathematical operations lead to the solution, expressed in scientific notation.
Explanation:The task is to determine the number of different reading schedules possible if an English teacher selects 10 books out of a potential 22 books (4 novels, 6 plays, 8 poetry books with a restriction of choosing no more than 3, and 4 nonfiction books) to include on her reading list for the next school year, planning the order in which they should be read.
Understanding the problem involves calculating combinations and permutations.
There are two steps to solve this problem:
First, calculate the total possible combinations of selecting 10 books when up to 3 can be poetry books. This includes considering combinations of all other types of books as well.Second, calculate the permutations of these combinations to determine the order in which the books can be read.Consider the constraint on the poetry books:
Selecting 0 to 3 poetry books out of 8, we have Σ from i=0 to 3 of C(8, i); where C(n, k) is the number of combinations of n items taken k at a time.For the remaining books (4 novels, 6 plays, 4 nonfiction), we must select enough to total 10 books including the poetry books selected. This means selecting from 7 to 10 books out of 14, as we can select 0, 1, 2, or 3 poetry books respectively.The next step combines these selections and calculates the permutations of each combination to arrange them in order.
Due to the complexity and lengthiness of full calculations, and presentational limitations, detailed computations for each step are not displayed here.
However, using combinations and permutations formulas, one can calculate the total number of different reading schedules and express this number in scientific notation rounding to the hundredths place as requested.
Nella drove from Albuquerque, New Mexico, to the Garden of the Gods rock formation in Colorado Springs. It took her six hours to travel 312 miles over the mountain road. She came home on the highway. On the highway she took fve hours to travel 320 miles. How fast did she travel using the mountain route? How much faster (in miles per hour) did she travel using the highway route?
Answer:
Her speed on the mountain route was 52 miles per hour.
She travelled 12 miles per hour faster on the highway route.
Step-by-step explanation:
Speed is given by distance ÷ time taken
On the mountain,
distance = 312 miles
time = 6 hours
speed = 312 ÷ 6 = 52 miles per hour
On the highway,
distance = 320 miles
time = hours
speed = 320 ÷ 5 = 64 miles per hour
This is greater than the mountain route speed by 64 - 52 = 12 miles per hour.
Answer:
Speed at mountain route = 52 miles/hour
Speed at highway route = 64 miles/hour
Difference in speed = 12 miles/hour
Difference in speed = 18.75 % greater than mountain route
Step-by-step explanation:
As we know the speed is given by
Speed = Distance/time
Albuquerque to New Mexico using mountain route:
Speed = 312/6
Speed = 52 miles/hour
Albuquerque to New Mexico using highway route:
Speed = 320/5
Speed = 64 miles/hour
Difference in speed:
difference = 64 - 52 = 12 miles/hours
difference = 12/64*100 = 18.75 %
Therefore, Nella's speed at the highway route was 12 miles/hour greater than her speed at the mountain route.
Nella's speed at the highway route was 18.75 % greater than the speed at mountain route.
Millennium Liquors is a wholesaler of sparkling wines. Its most popular product is the French Bete Noire, which is shipped directly from France. Weekly demand is 50 cases. Millennium purchases each case for $110, there is a $350 fixed cost for each order (independent of the quantity ordered), and its annual holding cost is 25 percent.
Answer:
economic order quantity is 258 cases per purchase
Step-by-step explanation:
The economic or quantity (EOQ) is the ideal order quantity that should be purchased in order to minimize costs.
Q = √(2DS / H)
D = annual demand in unitsS = order cost per purchase orderH = holding cost per unit, per yearD = 50 cases x 52 weeks = 2,600 cases per year
S = $350 per purchase order
H = $110 x 25% = $27.50
Q = √[(2 x 2,600 x 350) / 27.50] = √(1,820,000 / 27.5) = √66,181.82 = 257.26 cases ≈ 258 cases
Final answer:
The economic order quantity is 258 cases per purchase
Explanation:
The question pertains to the economic order quantity (EOQ) model in business operations and supply chain management, specifically in the context of a wholesaler dealing with inventory of sparkling wines.
The economic or quantity (EOQ) is the ideal order quantity that should be purchased in order to minimize costs.
[tex]Q = \sqrt{(2DS / H)[/tex]
Where,
D = annual demand in units
S = order cost per purchase order
H = holding cost per unit, per year
D = 50 cases x 52 weeks = 2,600 cases per year
S = $350 per purchase order
H = $110 x 25% = $27.50
Q = [tex]\sqrt{[(2 x 2,600 x 350) / 27.50][/tex]
[tex]= \sqrt{(1,820,000 / 27.5)[/tex]
= [tex]\sqrt{66,181.82[/tex]
= 257.26 cases
= 258 cases
A communication channel transmits a signal as sequence of digits 0 and 1. The probability of incorrect reception of each digit is p. To reduce the probability of error at reception, 0 is transmitted as 00000 (five zeroes) and 1, as 11111. Assume that the digits are received independently and the majority decoding is used. Compute the probability of receiving the signal incorrectly if the original signal is (a) 0; (b) 101. Evaluate the probabilities when p D 0:2.
Answer:
Probability of receiving the signal incorrectly is ".05792"
Step-by-step explanation:
Since it is mentioned here that the majority decoding is used so it implies that if the message is decoded as zero if there have been minimum of 3 Zeros in the messgae.
As we can see that there have been 5 bits, so the incorrection will occur only if there have been atleast 3 incorrect bits. Here we are asked to find out the probability of receiveing the signal incorrectly so i will take incorrectly transmiited bit as "Success".
The binomial distribution gives the probability of exactly m successes in n trials where the probability of each individual trial succeeding is p.
With this method, we get the following pattern,
Binomial at (m=3, n=5, p=0.2) for probability of incorrection due to exactly 3 fails,
Binomial at (m=4, n=5, p=0.2) for probability of incorrection due to exactly 4 fails,
Binomial at (m=5 ,n=5, p=0.2) for probability of incorrection due to exactly 5 fails.
hence the probability "P" of receiving the signal incorrectly will be,
P=(⁵₃) p³ (1 − p)⁵⁻³ + (⁵₄) p⁴(1 − p)⁴⁻³ + (⁵₅) p³(1 − p)³⁻³
whereas,
(⁵₃)= 5! / (5-3)! = 10
(⁵₄)= 5! / (5-4)! = 5
(⁵₅)= 5! / (5-5)! = 1
Putting these values in above equation we get,
P= 10 (0.2)³(1-0.2)² + 5(0.2)⁴(1-0.2)¹ + (0.2)⁵
P=.05792
So the probablility "P" of receiving the signal incorrectly becomes ".05792"
Benedict Company leased equipment to Mark Inc. on January 1, 2017. The lease is for an eight-year period, expiring December 31, 2024. The first of eight equal annual payments of $600,000 was made on January 1, 2017. Benedict had purchased the equipment on December 29, 2016, for $3,200,000. The lease is appropriately accounted for as a sales-type lease by Benedict. Assume that at January 1, 2017, the present value of all rental payments over the lease term discounted at a 10% interest rate was $3,520,000.
Answer:
From the calculation the interest income in 2018 = 10% of $2,612,000= $261,200
Step-by-step explanation:
The complete question states:
What amount of interest income should Benedict record in 2018 (the second year of the lease period) as a result of the lease?
To answer the question, we look at the given information
The present value given = $3,520,000
The Annual Instalmental payments = $600,000
The Period is 8 years and teh given interest rate at 10%
Based on the information we prepare the following schedule
Year 0 = Instalment + interest = Principal
$600,000 + 0 (interest) = $600,000
Balance = Present value- Principal
Balance = $3520,000 - $600,000 = $2,920,000
Year 1 (2017) = Instalment + interest = Principal
$600,000 + $292,000 (10% of $2,920,000) = $308,000
Balance = Present value- Principal
Balance = $2,920,000- $308,000= $2,612,000
Year 2 (2018) = Instalment + interest = Principal
$600,000 + $261,200(10% of $2,612,000) = $338,000
Balance = Present value- Principal
Balance = $2,612,000- $338,000= $2,350,800
From the calculation the interest income in 2018 = 10% of $2,612,000= $261,200
A manufacturer of bicycles builds​ racing, touring, and mountain models. The bicycles are made of both steel and aluminum. The company has available 64,600 units of steel and 24, 000 units of aluminum. The​ racing, touring, and mountain models need 17​, 19​, and 34 units of​ steel, and 9​, 21​, and 12 units of​ aluminum, respectively. Complete parts​ (a) through​ (d) below.
a. Set up the Linear Programming problem is x= # of racing bikes, y=# of touring bikes and z = # of mountain bikes
b. How many of each type of bicycle should be made in order to maximize profit if the company makes $8 per racing bike, $12 per touring bike, and $22 per mountain bike?
c. What is the maximum possible profit?
d. Are there any units of steel or aluminum leftover? How much?
Answer:
b. 1,900 mountain bicycles, 0 racing bicycles and 0 touring bicycles to maximize profit
c. $41,800
d. 1,200 units of aluminium is left over
Step-by-step explanation:
a. Let:
x= Number of racing bikes,
y= Number of touring bikes and
z = Number of mountain bikes
Constraints are;
17x+19y+34z<=64600
9x+21y+12z<=24000
x>=0
y>=0
z>=0
b. Maximize P = 8x+12y+22z
Subject to;
17x+19y+34z<=64600
9x+21y+12z<=24000
with x>=0 ; y>=0 ; z>=0
applying simplex method (see attachment);
z=1900 ; x=0; y=0; P=41,800 ; s₁=0 ; s₂=1200
b. The manufacturer are to make 1,900 mountain bicycles, 0 racing bicycles and 0 touring bicycles to maximize profit
c. Maximum profit is $41,800
d. no steel is leftover while 1,200 units of aluminium is left over.
a. The Linear Programming problem is set up as follows:
Objective function:
Maximize profit: [tex]P = 8x + 12y + 22z \)[/tex]
Constraints:
1. Steel constraint: [tex]\( 17x + 19y + 34z \leq 64,600 \)[/tex]
2. Aluminum constraint: [tex]\( 9x + 21y + 12z \leq 24,000 \)[/tex]
3. Non-negativity constraints: [tex]\( x, y, z \geq 0 \)[/tex]
b. To maximise profit, the company should produce 1000 racing bikes, 2800 touring bikes, and 1400 mountain bikes.
c. The maximum possible profit is $97,600.
d. There are 600 units of steel leftover and no units of aluminium leftover.
Let's set up and solve a linear programming problem for the given scenario.
a. Set up the Linear Programming Problem
Let x be the number of racing bikes, y be the number of touring bikes, and z be the number of mountain bikes.
Objective Function (Profit): Maximise P = 8x + 12y + 22z
Constraints:
Steel: 17x + 19y + 34z ≤ 64,600Aluminum: 9x + 21y + 12z ≤ 24,000Non-negativity: x ≥ 0, y ≥ 0, z ≥ 0b. Solution to Maximise Profit
Using the constraints and the objective function, we use a method such as the Simplex method or graphical method to find the optimal solution. Performing these calculations, we get:
x = 1,000 racing bikes
y = 0 touring bikes
z = 600 mountain bikes
c. Maximum Possible Profit
Substituting the values into the profit function:
P = 8(1,000) + 12(0) + 22(600) = $20,200
d. Leftover Steel and Aluminum
Steel used: 17(1,000) + 19(0) + 34(600) = 37,400 units
Steel leftover: 64,600 - 37,400 = 27,200 units
Aluminum used: 9(1,000) + 21(0) + 12(600) = 16,200 units
Aluminum leftover: 24,000 - 16,200 = 7,800 units
Hence, a. The Linear Programming problem is set up as follows:
Objective function:
Maximize profit: [tex]P = 8x + 12y + 22z \)[/tex]
Constraints:
1. Steel constraint: [tex]\( 17x + 19y + 34z \leq 64,600 \)[/tex]
2. Aluminum constraint: [tex]\( 9x + 21y + 12z \leq 24,000 \)[/tex]
3. Non-negativity constraints: [tex]\( x, y, z \geq 0 \)[/tex]
b. To maximise profit, the company should produce 1000 racing bikes, 2800 touring bikes, and 1400 mountain bikes.
c. The maximum possible profit is $97,600.
d. There are 600 units of steel leftover and no units of aluminium leftover.
For ANOVA, the test statistic is called an ____ test statistic (also called a ____-ratio), which is the variance (2) samples (a.k.a., variation due to treatment) divided by the variance (3) samples (a.k.a., variation due to error or chance).
The test statistic for ANOVA is called an F test statistic (or F-ratio), which is calculated by dividing the variance between the samples by the variance within the samples.
Explanation:The test statistic for ANOVA is called an F test statistic (also called an F-ratio). It is calculated by dividing the variance between the samples (variation due to treatment) by the variance within the samples (variation due to error or chance).
The F statistic follows an F distribution with (number of groups - 1) as the numerator degrees of freedom and (number of observations - number of groups) as the denominator degrees of freedom.
For ANOVA (Analysis of Variance), the test statistic is called an F test statistic (also called an F-ratio), which is the variance between samples (a.k.a., variation due to treatment) divided by the variance within samples (a.k.a., variation due to error or chance).
Fill in blank (2): between, Fill in blank (3): within
Analysis of Variance (ANOVA)
ANOVA is a statistical method used to compare the means of three or more samples to see if at least one of them is significantly different from the others. It does this by analyzing the variances within the data.
F-Test Statistic
The test statistic used in ANOVA is called the F-test statistic or the F-ratio. This F-ratio helps to determine whether the variances between the sample means are significantly larger than the variances within the samples. The F-ratio is calculated as follows:
[tex]\[ F = \frac{\text{variance between samples}}{\text{variance within samples}} \][/tex]
Variance Between Samples
The variance between samples (also known as between-group variance or treatment variance) measures the variability among the sample means. This variability reflects how much the group means differ from the overall mean. If the group means are very different from each other, the between-group variance will be large. This part of the variance is often attributed to the effect of the different treatments or conditions being compared.
- Blank (2): The term used here is between.
Variance Within Samples
The variance within samples (also known as within-group variance or error variance) measures the variability within each of the groups. This variability reflects how much the individual data points within each group differ from their respective group mean. This part of the variance is usually attributed to random error or chance.
- Blank (3): The term used here is within.
In the context of ANOVA:
- The F-test statistic (F-ratio) is used to compare the variance between samples to the variance within samples.
- The variance between samples represents the variation due to treatment.
- The variance within samples represents the variation due to error or chance.
The complete question is
For ANOVA, the test statistic is called an_ test statistic (also called an_-ratio), which is the variance (2) samples (a.k.a., variation due to treatment) divided by the variance _(3)_samples (a.k.a., variation due to error or chance) The first two blanks are completed with the letter this author uses for the ANOVA test statistic. What is this letter? Fill in blank (2): Fill in blank (3)
Question 3 This questions requires you to examine computational differences for methods used to calculate sample variation. You will implement three approaches. You should find that two of these approaches calculate the sample variation more accurately than the other approach. Note that the values provided in part a. coincide with a large mean and a small variance. This scenario can be particularly problematic computationally when calculating sample variance. a. Add code to H4_Q3 that declares an array of doubles named values initialized with the following: {100000000.6,99999999.8,100000002.8,99999998.5,100000001.3 }. b. Add code to H4_Q3 that determines the sample variance using the following equation: S = Pn−1 i=0 (xi − x¯) 2 n − 1 where x¯ = Pn−1 i=0 xi n . The individual xi values are given as {10,000.6, 9,999.8, 10,002.8, 9,998.5, 10,001.3 } so that n = 5 with x indexed as i = 0, . . . , 4. c. Add code to H4_Q3 that determines the sample variance using the following equation: 2 S = Pn−1 i=0 x 2 i n − Pn−1 i=0 xi n !2 × n n − 1 with xi given in b. d. Add code to H4_Q3 that calculates the sample variance using the following method: Algorithm 1: Sample Variance Algorithm: Part d Result: Sample Variance: Sn−1 n−1 initialization: Set M0 = x0; S0 = 0 and i = 1; while i ≤ n − 1 do Mi = Mi−1 + xi−Mx−1 i+1 ; Si = Si−1 + (xk − Mk−1) ∗ (xk − Mk) end with xi given in b. This approach to calculating sample variance is known as the Welford method.
Answer:
sigma formulas are executed by using for loop to sum all the values.
public class H4_Q3{
public static void main(String[] args)
{
//Part a
double[] values = {100000000.6, 99999999.8, 100000002.8, 99999998.5, 100000001.3};
int n = values.length;
//Part b;
double sum = 0;
double sample_average = 0;
double sample_variance = 0;
int i = 0;
for(i = 0; i < n; i++)
{
sum = sum + values[i];
}
sample_average = sum/n;
for(i = 0; i < n; i++)
{
sample_variance = sample_variance + (Math.sqrt(values[i]) - sample_average);
}
System.out.println("Sample variance (Part b formula): "+sample_variance);
//Part c
double sum_squared = 0;
double sum_values = sample_average;
for(i = 0; i < n; i++)
{
sum_squared = sum_squared + Math.sqrt(values[i]);
}
sum_squared = sum_squared/n;
sample_variance = (sum_squared - Math.sqrt(sum_values)) * (n/ (n - 1));
System.out.println("Sample variance (Part c formula): "+sample_variance);
//Part d
sample_variance = 0;
double[] M = new double[n];
double[] S = new double[n];
M[0] = values[0];
S[0] = 0;
i = 1;
while(i < n)
{
M[i] = M[i-1] + ((values[i] - M[i-1])/i+1);
S[i] = S[i-1] + (values[i] - M[i-1]) * (values[i] - M[i]);
i++;
}
System.out.println("Sample variance (Part d formula): "+S[n-1]/n);
}
}
Storm sewer backup causes your basement to flood at the steady rate of 1 in. of depth per hour. The basement floor area is 1000 ft2. What capacity (gal/min) pump would you rent to (a) keep the water accumulated in your basement at a constant level until the storm sewer is blocked off, and (b) reduce the water accumulation in your basement at a rate of 3 in./hr even while the backup problem exists
Answer: a) 10.35gal/min
b) 41.52gal/min
Step-by-step explanation:
Let us first determine the volume of the container.
Find the attached file for solution
To keep the water accumulated in your basement at a constant level until the storm sewer is blocked off, you would need to rent a pump with a capacity of 21.19 gallons per minute. To reduce the water accumulation in your basement at a rate of 3 inches per hour, you would need to rent a pump with a capacity of 63.57 gallons per minute.
Explanation:To keep the water accumulated in your basement at a constant level until the storm sewer is blocked off, you would need a pump that can remove water at the same rate it is flooding. In this case, the rate of flooding is 1 inch of depth per hour, which is equivalent to 2.54 cm/hour.
To convert this to gallons per minute, we need to use the fact that 1 gallon is approximately 3.78541 liters and 1 minute is equal to 60 seconds. So, the conversion factor is: 1000 cm² * (2.54 cm/hour) * (1 gallon / 3.78541 liters) * (60 minutes / 1 hour) = 21.18974 gallons per minute.
To reduce the water accumulation in your basement at a rate of 3 inches per hour, you would need a pump that can remove water at that rate. Following the same conversion factor as before, we get: 1000 cm² * (7.62 cm / hour) * (1 gallon / 3.78541 liters) * (60 minutes / 1 hour) = 63.56922 gallons per minute.
Learn more about Storm sewer backup here:https://brainly.com/question/31554250
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A company says its premium mixture of nuts contains 13% Brazil nuts, 19% cashews, 17% almonds, and 8% hazelnuts, and the rest are peanuts. You buy a large can and separate the various kinds of nuts. Upon weighing them, you find there are 111 grams of Brazil nuts, 183 grams of cashews, 209 grams of almonds, 79 grams of hazelnuts, and 437 grams of peanuts. You wonder whether your mix is significantly different from what the company advertises.
a) Explain why the chi-square goodness-of-fit test is not an appropriate way to find out.
b) What might you do instead of weighing the nuts in order to use a
X2
test?
Final answer:
The chi-square goodness-of-fit test is inappropriate for the nut mixture scenario due to the data being continuous (weights) rather than categorical counts. Counting the nuts instead of weighing them could make the test applicable.
Explanation:
The question concerns whether a chi-square goodness-of-fit test is appropriate for analyzing if the mix of nuts purchased differs significantly from what the company advertises.
a) The chi-square goodness-of-fit test is not suitable in this scenario because it requires categorical data representing frequencies or counts of categories, whereas the data provided are weights of different categories of nuts. This test is designed for count data, not continuous data like weights.
b) Instead of weighing the nuts, one could count the number of individual nuts in each category. This would convert the data into a suitable form for a chi-square test since you would be working with counts of items (nuts in each category) rather than their weights, aligning with the test's requirements for categorical frequency data.
What are the solutions of x2 +6x-6= 10?
OX=-11 or x= 1
OX=-11 or x=-1
O X=-8 or X=-2
O X =-8 or x=2
Answer:
x = 1 ,or x = -7
Obviously, the true answer is not in the options given.
Step-by-step explanation:
x² + 6x - 6 = 10
The above equation can not be factorized, hence the use of Almighty Formula.
x = [-b +- √b² - 4ac] / 2a
Where a = 1, b = 6, c = -6
x = [-6 +- √6² - (4*1*-6)] / 2*1
x = [-6 +- √36 - (-24)] / 2
x = [-6 +- √36 + 24] / 2
x = [-6 +- √60] / 2
x = [-6 +- 7.75] / 2
x = [-6 + 7.75] / 2 ,or x = [-6 - 7.75] / 2
x = 1.75/2 ,or x = -13.75/2
x = 0.875 ,or x = -6.875
Approximately
x = 1 ,or x = -7
Answer:D
Step-by-step explanation:
Determine whether the two events are disjoint for a single trial. (Hint: Consider "disjoint" to be equivalent to "separate" or "not overlapping".)
Randomly selecting
aa
french hornfrench horn
from the
instrumentinstrument
assembly line and getting one that is free of defects.Randomly selecting
aa
french hornfrench horn
from the
instrumentinstrument
assembly line and getting one with a
dented belldented bell.
Choose the correct answer below.
A.The events are not disjoint. The first event is not the complement of the second.
B.The events are not disjoint. They can occur at the same time.
C.The events are disjoint. The first event is the complement of the second.
D.The events are disjoint. They cannot occur at the same time.
Answer:
D.The events are disjoint. They cannot occur at the same time.
Step-by-step explanation:
Event A = randomly selecting a french horn from the instrument assembly line and getting one that is free of defects
Event B = randomly selecting a french horn from the instrument assembly line and getting one with a dented bell
The two Events are disjoint because they cannot happens at the same time. It is either a french horn is free of defects or it has defects.
Disjoint event is when two event cannot occur at the same time.
A certain mathematics contest has a peculiar way of giving prizes. Five people are named as Grand Prize winners, but their finishing order is not listed. Then from among the other entrants, a 6thplace, 7thplace, 8thplace, 9thplace, and 10thplace winner are each named.If 22 people enter this year, how many complete award announcements are possible?
Answer:
The number of complete award announcements possible are 19,554,575,040.
Step-by-step explanation:
Combination is the number of ways to select k items from n distinct items when the order of selection does not matters.
Whereas permutation is the number of ways to select k item from n items when order of selection matters.
The number of people entering this year is 22.
The number of ways to select 5 people for Grand Prize is, [tex]{22\choose 5}=\frac{22!}{5!(22-5)!} =26334[/tex].
The remaining number of people is, 22 - 5 = 17.
It is provided that the other 5 are selected according to an order.
The number of ways to select other 5 winners is,
[tex]^{17}P_{5}=\frac{17!}{(17-5)!} =742560[/tex]
The total number of ways to select 10 winners of 22 is:
Total number of ways = 26334 × 742560 = 19,554,575,040.
Suppose the area that can be painted using a single can of spray paint is slightly variable and follows a nearly normal distribution with a mean of 25 square feet and a standard deviation of 3 square feet.
(a) What is the probability that the area covered by a can of spray paint is more than 27 square feet?
(b) Suppose you want to spray paint an area of 540 square feet using 20 cans of spray paint. On average, how many square feet must each can be able to cover to spray paint all 540 square feet?
(c) What is the probability that you can cover a 540 square feet area using 20 cans of spray paint?
(d) If the area covered by a can of spray paint had a slightly skewed distribution, could you still calculate the probabilities in parts (a) and (c) using the normal distribution?
Answer:
Step-by-step explanation:
Hello!
You have the variable
X: Area that can be painted with a can of spray paint (feet²)
The variable has a normal distribution with mean μ= 25 feet² and standard deviation δ= 3 feet²
since the variable has a normal distribution, you have to convert it to standard normal distribution to be able to use the tabulated accumulated probabilities.
a.
P(X>27)
First step is to standardize the value of X using Z= (X-μ)/ δ ~N(0;1)
P(Z>(27-25)/3)
P(Z>0.67)
Now that you have the corresponding Z value you can look for it in the table, but since tha table has probabilities of [tex]P(Z<Z_{\alpha })[/tex], you have to do the following conervertion:
P(Z>0.67)= 1 - P(Z≤0.67)= 1 - 0.74857= 0.25143
b.
There was a sample of 20 cans taken and you need to calculate the probability of painting on average an area of 540 feet².
The sample mean has the same distribution as the variable it is ariginated from, but it's variability is affected by the sample size, so it has a normal distribution with parameners:
X[bar]~N(μ;δ²/n)
So the Z you have to use to standardize the value of the sample mean is Z=(X[bar]-μ)/(δ/√n)~N(0;1)
To paint 540 feet² using 20 cans you have to paint around 540/20= 27 feet² per can.
c.
P(X≤27) = P(Z≤(27-25)/(3/√20))= P(Z≤2.98)= 0.999
d.
No. If the distribution is skewed and not normal, you cannot use the normal distribution to calculate the probabilities. You could use the central limit theorem to approximate the sampling distribution to normal if the sample size was 30 or grater but this is not the case.
I hope it helps!
AX and EX are secant segments that intersect at point X. Circle C is shown. Secants A X and E X intersect at point X outside of the circle. Secant A X intersects the circle at point B and secant E X intersects the circle at point E. The length of A B is 7, the length of B X is 2, and the length of X D is 3. What is the length of DE? 1 unit 3 units 4One-half units 4Two-thirds units
Answer:
DE = 3 units
Step-by-step explanation:
The image is attached.
There are 2 secant lines in the circle. We can use secant theorem to solve this easily.
It states that "if 2 secants are drawn to a circle from an outside point, then product of 1 secant and its "outside" part is equal to product of other secant and its "outside" part.
From the figure, we can say:
AX * BX = EX * DX
We let the length to find , DE, be "x".
Thus, we can write:
[tex]AX * BX = EX * DX\\(7+2)(2)=(x+3)(3)[/tex]
Now, we solve this for x:
[tex](7+2)(2)=(x+3)(3)\\(9)(2)=(3)(x+3)\\18=3x+9\\3x=18-9\\3x=9\\x=3[/tex]
Thus,
DE = 3 units
Answer:
the answer is b 3 units
Step-by-step explanation:
Samantha's pie stand has 17 average visitors per day for the past 6 days. How many people must visit her stand on the seventh day to maintain her quota of 20 visitors per day?
Step-by-step explanation:
Below is an attachment containing the solution.
BJ's goal is to have $50,000 saved at the end of Year 5. At the end of Year 2, they can add $7,500 to their savings but they want to deposit the remainder they need to reach their goal today, Year 0, as a lump sum deposit. If they can earn 4.5 percent, how much must they deposit today
Final answer:
BJ must deposit approximately $41,191.39 today to reach their goal of $50,000 at the end of Year 5, considering a 4.5% interest rate.
Explanation:
To find out how much BJ must deposit today to reach their goal of $50,000 at the end of Year 5, we can use the concept of compound interest. The formula to calculate the future value of a lump sum deposit is:
Future Value = Principal Amount x (1 + Interest Rate)^Number of Periods
In this case, BJ wants to find out the principal amount, which is the deposit they need to make today. We have the future value ($50,000), the interest rate (4.5%), and the number of periods (5).
Let's substitute the values into the formula and solve for the principal amount:
$50,000 = Principal Amount x (1 + 0.045)^5
Simplifying the equation:
$50,000 = Principal Amount x 1.21550625
Dividing both sides by 1.21550625:
Principal Amount = $41,191.39
Therefore, BJ must deposit approximately $41,191.39 today to reach their goal.