Answer:
13112221
Step-by-step explanation:
Each sequence of numbers is a verbal representation of the sequence before it. Thus, starting with 1, the next sequence would be "one one," or "11." That sequence is followed by "two one," or "21," and so on and so forth.
This may also be a good explanation:
The first number is just ONE (amount) "1" (0-9 numeral). So if you say there's ONE "1" (seriously just say it aloud) the next number would be an 11. Then there are TWO "1's", creating 21. Then ONE "2" and ONE "1" which creates 1,211. Then ONE "1", ONE "2", and TWO "1's" creating 111,221 ... and so on.
The first number 1 is read as one one, so the second number is written as 11, this is read as two ones, so the next number is written as 21 ( two ones)
This continues throughout the sequence.
The last number written is 312211 which is read as one three, one one, two twos, two ones
This gets written as 13112221
A water sprinkler sprays water over a distance of 36 yards while rotating through an angle of 125°. What area of lawn receives water? Round to the nearest integer as needed.
Answer:
1413 square yards of lawn receives water.
Step-by-step explanation:
We are given the following in the question:
Radius of garden, r = 36 yards
Rotating angle, [tex]\theta[/tex] = [tex]125^\circ[/tex]
First converts the given angle measure in radians.
[tex]\text{Radians} = \dfrac{\pi}{180}\times \theta[/tex]
Thus, the rotating angle in radians is:
[tex]\dfrac{\pi}{180}\times 125 = 2.18\text{ Radians}[/tex]
Area of lawn =
[tex]\displaystyle\frac{1}{2}r^2 \times \text{Radian measure of angle}\\\\=\frac{1}{2}(36)^2\times 2.18 = 1412.64 \approx 1413\text{ square yards}[/tex]
Thus, 1413 square yards of lawn receives water.
Final answer:
1413 square yards of lawn receives water.
Explanation:
1413 square yards of lawn receives water.
Step-by-step explanation:
We are given the following in the question:
Radius of garden, r = 36 yards
[tex]Rotating angle, \theta = 125^\circ[/tex]
First converts the given angle measure in radians.
[tex]\text{Radians} = (\pi)/(180)* \theta[/tex]
Thus, the rotating angle in radians is:
[tex](\pi)/(180)* 125 = 2.18\text{ Radians}[/tex]
Area of lawn =
[tex]\displaystyle(1)/(2)r^2 * \text{Radian measure of angle}\n\n=(1)/(2)(36)^2* 2.18 = 1412.64 \approx 1413\text{ square yards}[/tex]
Thus, 1413 square yards of lawn receives water.
Determine if each scenario is either a permutation or combination. Do NOT solve these scenarios. a) An art gallery displays 125 different pieces of artwork at a time. However, 15 pieces are selected to be displayed prominently throughout in the gallery. For instance, the most popular piece is displayed in a location that can be seen as soon as you walk in the door. Determine how many ways these more popular 15 pieces can be displayed throughout the gallery. b) An art gallery has a total of 320 different pieces of art. However, only 125 pieces can be displayed at a time. Determine how many ways those 125 pieces can be selected.
Answer:
a) Permutations
b) combination
Step-by-step explanation:
a)
Since the order of 15 most important artwork pieces matter, with most popular at first and then at N0.2, 3,4, and so on. Whenever we are dealing with "order of placement" the question at hand is of permutations.
b)
Out of 320 pieces, 125 pieces are to be "selected" and displayed, the process of selection incurs Combinations in which the order in which we select does not matter.
Scenario a) represents a permutation and the 15 popular pieces can be arranged in 15! ways.
Scenario b) represents a combination and the 125 pieces can be selected in 320 choose 125 ways.
Explanation:a) This scenario is an example of a permutation. In a permutation, the order of the items matters. In this case, the 15 popular pieces can be arranged in 15! (15 factorial) ways.
b) This scenario is an example of a combination. In a combination, the order of the items does not matter. In this case, the 125 pieces can be selected from the total of 320 pieces in a total of 320 choose 125 ways.
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In the following triangle,what is the length of the hypotenuse?
Step-by-step explanation:
using trigonometric ratios,
sin theta= opposite ÷ hypoteneus (h)
sin 45°= 3 root 2 ÷ h
1/root 2= 3 root 2 ÷h
h= 3× root 2 × root 2
= 3×2
= 6 unit
Answer:
Step-by-step explanation:
The given triangle is a right angle triangle and also an isosceles triangle.
The hypotenuse is the longest side of the right angle triangle. To determine the hypotenuse, we will apply trigonometric ratio
Sin θ = opposite side/hypotenuse
Looking at the triangle.
θ = 45 degrees = 1/√2
opposite side = 3√2
Therefore,
Sin 45 = 3√2/hypotenuse
1/√2 = 3√2/hypotenuse
hypotenuse × 1 = √2 × 3√2
hypotenuse = 3√2 × √2
hypotenuse = 3 × 2 = 6
Alternatively,
We can apply Pythagoras theorem since both sides are equal
Since the length of one side is 3√2, then the length of the other side is also 3√2
Hypotenuse^2 = opposite side^2 + adjacent side^2
Hypotenuse^2 = (3√2)^2 + (3√2)^2
Hypotenuse^2 = 18 + 18 = 36
Hypotenuse = √36 = 6
The Denver Police Department wants to know if Hispanic residents of Denver believe that the police use racial profiling when making traffic stops. A sociologist prepares several questions about the police. The police department chooses an SRS of 300 mailing addresses in predominantly Hispanic neighborhoods and sends a uniformed Hispanic police officer to each address to ask the questions of an adult living there.
a. What are the population and the sample?
b. Why are the results likely to be biased even though the sample is an SRS?
Answer:
a) The population is all the Hispanic residents of Denver.
The sample is 300 adults which very visited by the officer.
b) The results are likely to be biased because the adults may be fearful of the Hispanic officer, may be intimidated by their presence and not want to tell how they really feel about this question.
Step-by-step explanation:
This is a common statistic method.
If you want to estimate something about a big population, you select a random sample of the population, and estimate for the entire population.
For example, if you want to estimate the proportion of residents of Buffalo, New York, that are Buffalo Bills fans, you are going to ask, for example, 1000 Buffalo residents. The population is all the residents of Buffalo, New York. and the sample are the 1000 Buffalo residents.
However, if you send a Bills player to ask this question, people will try to make him happy, which could lead to a biased answer.
So, for this question
a. What are the population and the sample?
The population is all the Hispanic residents of Denver.
The sample is 300 adults which very visited by the officer.
b. Why are the results likely to be biased even though the sample is an SRS?
The results are likely to be biased because the adults may be fearful of the Hispanic officer, may be intimidated by their presence and not want to tell how they really feel about this question.
Suppose that after computing based on n sample observations , another observation becomes available.
(i) What is the relationship between the mean of the first n observations, the new observation, and the mean of all n+1 observations?
(ii) For the strength observations given below: 22.2 40.4 16.4 73.7 36.6 109.9 30.0 4.4 33.1 66.7 81.5, the mean of the first 10 observations is 43.34. What is the mean of all 11 observations?
Answer:
Mean of the 11th observations = 46.809
Step-by-step explanation:
The step by step explanations is given in the attached file.
What is appled is mean or average which is the total number of observation divided by the sum of the frequencies of each observaton .
Let u = (1,2), v = (−3,4), and w = (5,0)
a) Draw these vectors in ℝ2 .
b) Find scalars λ1 and λ2 such that w = λ1u + λ2v.
Vectors u, v, and w are represented graphically in ℝ². Scalars λ₁ and λ₂ for w = λ₁u + λ₂v are found as λ₁ = 3/2t + 5 and λ₂ = t, where t is any real number.
a) Vector Representation:
To draw vectors u, v, and w in ℝ², we can use their respective components. Vector u = (1, 2) starts at the origin and extends to the point (1, 2). Vector v = (-3, 4) starts at the origin and extends to the point (-3, 4). Vector w = (5, 0) starts at the origin and extends to the point (5, 0).
b) Scalar Representation:
We want to find scalars λ₁ and λ₂ such that w = λ₁u + λ₂v. This can be expressed as a system of equations:
w₁ = λ₁u₁ + λ₂v₁
w₂ = λ₁u₂ + λ₂v₂
Substitute the values:
5 = λ₁(1) + λ₂(-3)
0 = λ₁(2) + λ₂(4)
Solve the system of equations to find λ₁ and λ₂. Multiplying the first equation by 2 and adding it to the second equation:
10 = 2λ₁ - 3λ₂ + 0
10 = 2λ₁ - 3λ₂
Solving for λ₁:
2λ₁ = 3λ₂ + 10
λ₁ = 3/2λ₂ + 5
Now, let λ₂ = t, then λ₁ = 3/2t + 5.
So, the scalars λ₁ and λ₂ are λ₁ = 3/2t + 5 and λ₂ = t, where t is any real number.
Solve for the vector x + 2a - b in terms of the vectors a and b. (If needed, use BOLD vector form on calcPad Vector menu.) x + 2a - b = 5(x + a) - 2(3a - b) x =
Answer:
x+2a-b=5x+5a-2*3a+2*b
x+2a-b=5x+5a-6a+2b
x+2a-b=5x-a+2b
5x-x=2a-b+a-2b
4x=3a-3b
4 x=3(a-b)
x=3/4(a-b)
The answer of the vector x in the form of a and b is 3/4(a-b).
What is vector ?"A vector is an object that has both a magnitude and a direction. Geometrically, we can picture a vector as a directed line segment, whose length is the magnitude of the vector and with an arrow indicating the direction. The direction of the vector is from its tail to its head."
Here,
[tex]x + 2a - b = 5(x + a) - 2(3a - b) x[/tex]
[tex]x+2a-b=5x+5a-6a+2b\\\\x+2a-b=5x-a+2b\\\\5x-x=2a-b+a-2b\\\\4x=3a-3b\\\\4 x=3(a-b)\\\\x=3/4(a-b)\\[/tex]
Hence the vector x = 3/4(a-b)
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You have made it to the final round of a game show. The announcer asks you the final multiple choicequestion, which has four possible answers, (a), (b), (c), and (d). If you answer the question correctly,you win $1,000,000. After considering the question, you realize you are not sure, but you have yoursuspicions. You think the answer is either choice (a) with probability 60%, or choice (b) with probability40%. You are certain the answer is not choice (c) or (d).
a. Choose not to answer the question. You walk away with $500,000.b. Select an answer (a or b). If you are correct, you win $1,000,000. If you are incorrect, you win only$32,000.c. Phone a friend. In this option, the announcer allows you to call a friend for help.After listening to your friend’s response, you must then answer the question. You know that: * Given thecorrect answer is (a), your friend will say "a" with probability 80%. * Given the correct answer is (b), yourfriend will say "b" with probability 80%.d. Make a decision tree to find your best strategy. In words, what should your strategy be? How muchmoney do you expect to win?
Answer:
The best option is to phone a friend which will yield a total earnings of $ 806,400
Step-by-step explanation:
From the analysis of the question, there is the probability of success and failure.
if he choose not to answer which is the probability of success, his earnings = $500,000.
if he he answers the question correctly, his earnings = $1,000,000 which in the end, is still a success for him
if he answers the question wrongly, his earnings = $32,000
the last option is to phone a friend and he will either choose option a or option b
Probability of choosing option A = 0.6
Probability of choosing option B = 0.4
For the second option ( option a) ; If he chooses to answer the question by going with option aexpected earnings = P(choosing A) x his earnings if correct + P(choosing B) x his earnings if wrong
= 0.6 x 1,000,000 + 0.4 x 32,000
= $612,000 will be his earning by second option
if he picks the option b = P (choosing B) x his earnings if correct + P(choosing A) x earnings if wrong = 0.4 x 1,000,000 + 0.6 x 32,000
= $419,000
if he chooses the third option of phoning his friend; since his probability of either a or b is like 80% (o.8) if correct and 0.2 (20%) if wrong =from the P(success) + P( failure) =1
His earnings = Probability of success x earnings if correct + Probability of failure x earnings if incorrect = 0.8 x 1,000,000 + 0.2 x 32,000
= $806,400
from the calculation done, it is apparent that his best option is to go by phoning a friend since that will yield more earnings for him which is greater than his earnings by going for the second options hence the best option is phoning a friend as this will accrue his expected earning to be $ 806,400
The best strategy is to select an answer (a or b). The expected payout for this option is $600,000.
Explanation:To find the best strategy, we can create a decision tree. The decision tree will consider the options of not answering, selecting an answer, and phoning a friend. The expected payout for each option can be calculated by multiplying the probability of that option with the payout associated with that outcome. After calculating the expected payout for each option, we can compare them to determine the best strategy.
The decision tree shows that the best strategy is to Select an answer (a or b).
The expected payout for this option is calculated by multiplying the probability of choosing (a) and winning with the payout of $1,000,000, and adding it to the probability of choosing (b) and winning with the payout of $32,000.
The expected payout for this option is $600,000.
Therefore, by selecting an answer, you can expect to win $600,000 on average.
In finding the areas under the normal curve, if we wish to determine the area between A and B, and both A and B are greater than the mean (with A further away from the mean than B)
a)We find the area between the mean and A and subtract the area between the mean and B
b)We find the area between the mean and A and add the area between the mean and B
c)We find the area between the mean and A and subtract it from .50
d)We find the area between the mean and A and add it to .50
Answer:
a.
Step-by-step explanation:
A and B both are greater than mean and so A and B lies on the right side of mean. Further it is stated that A is more away from the mean than B. It means that A is greater than B. So, in order to find the area between A and B we have to subtract the area of mean to B from area of mean to A. It can be explain in the notations as
P(B<X<A)=P((B-μ)/σ<z<(A-μ)/σ)
P(B<X<A)=P(z<(A-μ)/σ)-P(z<(B-μ)/σ)
Hence, we find the area from mean to A and subtract the area from mean to B.
A football team gained 7 2/5 yards and then lost 1 3/5 yards.
Answer:
there a bad football team probably the raiders
Step-by-step explanation:
but take 72.5 and take away 13.5
72.5
- 13.5
-----------
59
Answer: [tex]5\frac{4}{5}[/tex]
Step-by-step explanation:
The first step is to make 7&2/5 a improper fraction, using the rule [tex]a\frac{b}{c}= \frac{ac+b}{c}[/tex].
Earth is approximately a sphere of radius 6.37 × 106 m. What are (a) its circumference, (b) its surface area, and (c) its volume?
Answer:
(a) 4.00×10^7 m
(b) 5.10×10^14 m^2
(c) 1.083×10^21 m^3
Step-by-step explanation:
Put the given value of radius into the various formulas and do the arithmetic. Your scientific calculator can show you the results in scientific notation.
C = 2πr = 2π·6.37×10^6 m ≈ 4.00×10^7 m* . . . circumference
A = 4πr^2 = 4π(6.37×10^6 m)^2 ≈ 5.10×10^14 m^2 . . . area
V = (4/3)πr^3 = (4/3)π(6.37×10^6 m)^3 ≈ 1.083×10^21 m^3 . . . volume
_____
* An early definition of the meter was 10^-7 times the distance from the North Pole to the Equator as measured through Paris, France.
When Helen Mirren won the Oscar for Best Actress, she was 61 years old. The Oscar-winning Best Actresses had a mean age of 35.8 years and a standard deviation of 11.3 years. What is the difference between Helen Mirren's age and the mean age?
Answer:
a) [tex] 61-35.8=25.3[/tex]
b) [tex] \frac{25.2}{11.3}=2.23[/tex] deviations
c) [tex] z = \frac{61- 35.8}{11.3}= 2.23[/tex]
d) For this case since we have that z>2 we can consider this value as unusual, since is outside of the interval considered usual.
Step-by-step explanation:
Assuming this complete question : "Helen Mirren was 61 when she earned her Oscar-winning Best Actress award. The Oscar-winning Best Actresses have a mean age of 35.8 years and a standard deviation of 11.3 years"
a) What is the difference between Helen Mirren’s age and the mean age?
For this case we can do this:
[tex] 61-35.8=25.2[/tex]
b) How many standard deviations is that?
We just need to take the difference and divide by the deviation and we got:
[tex] \frac{25.2}{11.3}=2.23[/tex] deviations
c) Convert Helen Mirren’s age to a z score.
The z score is defined as:
[tex] z = \frac{x- \mu}{\sigma}[/tex]
And if we replace the values given we got:
[tex] z = \frac{61- 35.8}{11.3}= 2.23[/tex]
d) If we consider “usual” ages to be those that convert to z scores between –2 and 2, is Helen Mirren’s age usual or unusual?
For this case since we have that z>2 we can consider this value as unusual, since is outside of the interval considered usual.
find the lateral area for the prism.
L.A. =
Answer:
L.A. = 80 + 16√13
Step-by-step explanation:
the lateral area is the area of the vertical faces.
So, for the given prism = The sum of the area of the vertical rectangles.
= height * perimeter of the right triangle.
The hypotenuse of the right triangle = [tex]\sqrt{6^2+4^2} = \sqrt{36+16} =\sqrt{52} =\sqrt{4*13} =2\sqrt{13}[/tex]
So, the sides of the triangle are 4 , 6 and 2√13
The perimeter of the right triangle = 4 + 6 + 2√13 = 10 + 2√13
Height = 8
The lateral area for the prism = 8 * ( 10 + 2√13 ) = 80 + 16√13
Answer:
The correct answer is 80 + 16√13 feet²
Step-by-step explanation:
Like we can see in the plot, the prism has three rectangular sides, that are its lateral area. For calculating the area, we need to add up the three sides, this way:
Height of the prism (h) = 8 ' or 8 feet
Area of the first side = 8 * 4 = 32 feet²
Area of the third side = 8 * 6 = 48 feet²
Area of the third side = 8 * Hypotenuse of the triangle
Hypotenuse of the triangle² = 4² + 6² = 52
Hypotenuse of the triangle =√52 = √13 * 4 = 2√13 feet
Area of the third side = 8 * 2√13 feet = 16√13 feet²
Area lateral of the prism = 32 + 48 + 16√13 = 80 + 16√13 feet²
How much is the product of thirty-two and five? Write the answer in numeric form.
Answer:
160/100+60+0/one hundred sixty
OR JUST 160 LIKE YOU ASKED
The product of thirty-two and five will be equal to 160.
What is multiplication?A product is the result of multiplication or an expression that indicates factors that are to be multiplied, in mathematics.
The multiplication will be given as:-
32 x 5 = 160
Or we can also do it like the addition of 32 five times:-
32 + 32 + 32 + 32 + 32 = 160
Therefore products of thirty-two and five will be equal to 160.
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Suppose that a fungal disease originates in the middle of an orchard, initially affecting only one tree. The disease spreads out radially at a constant speed of 45 feet per day.
(a) What area will be affected after 2 days?
(b) What area will be affected after 4 days?
(c) What area will be affected after 8 days?
(d) Write a formula for the affected area as a function of time, measured in days. Use t as your variable for time, in days.
Answer:
a) 25446.90 ft²
b) 101787.60 ft²
c) 407150.41 ft²
d) 2025πt²
Step-by-step explanation:
Data provided in the question:
Rate of spread radially = 45 feet per day
a) Radius of spread after 2 days
= 45 × 2
= 90 feet
Therefore,
Area affected = πr²
= π(90)²
= 25446.90 ft²
b) Radius of spread after 2 days
= 45 × 4
= 180 feet
Therefore,
Area affected = πr²
= π(180)²
= 101787.60 ft²
c) Radius of spread after 2 days
= 45 × 8
= 360 feet
Therefore,
Area affected = πr²
= π(360)²
= 407150.41 ft²
a) Radius of spread after t days
= 45 × t ft
Therefore,
Area affected = πr²
= π(45t)²
= 2025πt²
The area affected by the fungal disease, which spreads radially at a constant speed, can be calculated by using the formula for the area of a circle, where the radius is the product of the spread speed and time. After 2, 4, and 8 days, the areas affected are 25,446 square feet, 101,784 square feet, and 407,150 square feet, respectively.
Explanation:The given scenario represents a real-world application of the mathematical concept involving growth in a circular pattern where the growth happens at a constant rate. Here, the representation of the disease spread through the farm is in form of a circle increasing in radius over time. To calculate the area affected on any given day (t), we apply the formula for the area of a circle (πr^2) where the radius is the rate of spread multiplied by the number of days.
(a) After 2 days, the radius of the spread will be 2*45 = 90 feet. So, the area affected will be π(90)^2 = 25,446 square feet.(b) After 4 days, the radius is 4*45 = 180 feet. Hence, the affected area in this case will be π(180)^2 = 101,784 square feet.(c) After 8 days, the radius is 8*45 = 360 feet. Therefore, the affected area will be π(360)^2 = 407,150 square feet.(d) The general formula relating the disease spread (the affected area) with the time will be: A = π[(45*t)]^2.Learn more about Circular Growth here:https://brainly.com/question/31924921
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Consider a value to be significantly low if its z score less than or equal to minus−2 or consider a value to be significantly high if its z score is greater than or equal to 2.
A test is used to assess readiness for college. In a recentyear, the mean test score was 20.8 an the standard deviation was 5.3. Identify the test scores that are significantly low or significantly high.
What test scores are significantly low? Select the correct answer below and fill in the answer box(es) to complete your choice.
Answer:
Test scores of 10.2 or lower are significantly low.
Test scores of 31.4 or higher are significantly high.
Step-by-step explanation:
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.
In this problem, we have that:
[tex]\mu = 20.8, \sigma = 5.3[/tex]
Identify the test scores that are significantly low or significantly high.
Significantly low
Z = -2 and lower.
So the significantly low scores are thoses values that are lower or equal than X when Z = -2. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-2 = \frac{X - 20.8}{5.3}[/tex]
[tex]X - 20.8 = -2*5.3[/tex]
[tex]X = 10.2[/tex]
Test scores of 10.2 or lower are significantly low.
Significantly high
Z = 2 and higher.
So the significantly high scores are thoses values that are higherr or equal than X when Z = 2. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2 = \frac{X - 20.8}{5.3}[/tex]
[tex]X - 20.8 = 2*5.3[/tex]
[tex]X = 31.4[/tex]
Test scores of 31.4 or higher are significantly high.
Final answer:
Using the z-score formula, test scores below 10.2 are significantly low, and scores above 31.4 are significantly high for the college readiness test with a mean of 20.8 and a standard deviation of 5.3.
Explanation:
To identify test scores that are considered significantly high or low based on their z-scores, we use the provided mean score (μ = 20.8) and standard deviation (σ = 5.3) of the college readiness test. According to the criteria, a z-score less than or equal to -2 is significantly low, while a z-score greater than or equal to 2 is significantly high. To find the actual test scores corresponding to these z-scores, we apply the formula:
Z = (x - μ) / σ
For a significantly low score (Z = -2):
-2 = (x - 20.8) / 5.3
x = -2 × 5.3 + 20.8 = -10.6 + 20.8 = 10.2
For a significantly high score (Z = 2):
2 = (x - 20.8) / 5.3
x = 2 × 5.3 + 20.8 = 10.6 + 20.8 = 31.4
Thus, test scores below 10.2 are considered significantly low, and scores above 31.4 are considered significantly high.
A salesman has a base salary $2600 per month and makes 3 commission on each unit sold. If his total annual compensation is $48,000 and he sold 2000 units, how much does each unit cost
Answer:
Each unit cost $800
Step-by-step explanation:
Annual compensation = $48,000
Annual number of units sold = 2000
Commission on each item sold = 3%
Compensation for 2000 units = $48,000
Compensation for 1 unit = $48,000/2000 = $24
Cost of one unit = compensation for one unit ÷ commission on one unit = $24 ÷ 3% = $24 ÷ 0.03 = $800
Answer: cost of one unit = $280
Question:
A salesman has a base salary $2600 per month and makes 3% commission on each unit sold. If his total annual compensation is $48,000 and he sold 2000 units, how much does each unit cost
Step-by-step explanation:
Given;
base salary = $2600 per month
Total annual compensation = $48,000 per annum
Number of units sold = 2000
Commission = 3% per unit
Salesman's Salary per annum = $2600 × 12 = $31,200
Total commission earned = total compensation - total yearly salary
Total commission = $48,000 - $31,200 = $16,800
Commission on each unit = total commission/number of units
Unit commission = $16800/2000 = $8.4
Given that the commission per unit is 3% per unit
That is $8.4 is 3% of the cost of each unit.
Cost of each unit = $8.4/3% = $8.4/0.03 = $280
In order to take a sample of 1200 people from a population, I first divide the population into men and women, and then take a simple random sample of 500 men and a separate simple random sample of 700 women. This is an example of a:
A. randomized comparative experiment.
B. stratified random sample.
C. a simple random sample.
D. a multistage sample.
E. convenience sampling
Answer:
B. stratified random sample.
Step-by-step explanation:
The Stratified sampling is a type of sampling method in which the observer divides the whole sample population in the different or the separate groups.
These separated different groups are known as strata.
And from these, probability sample also called as simple random sample is taken out from each group.
The sampling method used in this scenario is defined as stratified random sampling, where the population is divided into groups (or strata) and random samples are taken from each group.
Explanation:The technique described in your question is an example of a stratified random sample. This sampling method is characterized by dividing a population into smaller groups, known as 'strata', and then selecting a simple random sample from each group. In your example, the population is first divided into men and women, these are your strata. Then, a simple random sample is chosen from each group: 500 men and 700 women. This method ensures representation from all sections of the population and can often lead to more accurate results compared to a simple random sample.
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(a) Find z such that the proportion of observations that are less than z in a standard normal distribution is 0.36. (Enter your answer rounded to two decimal places.)
(b) Find z such that 36% of all observations from a standard normal distribution are greater than z. (Enter your answer rounded to two decimal places.)
Finding the z-value in a standard normal distribution for certain proportions involves using a standard normal (Z-score) table. For (a) the z-value is -0.36, and for (b), the z-value is 0.36.
Explanation:To find the value of z that allows for a proportion of observations less or greater than it in a standard normal distribution, you need to use a standard normal (Z-score) table, or use an online calculator that allows you to find the Z-score associated with a specific proportion.
(a) For the proportion of observations that are less than z = 0.36, you would look up this proportion in the body of a standard normal table to find the associated Z-score. Alternatively, using a Z-score calculator, the z value is approximately -0.36.
(b) For the proportion of observations that are greater than Z = 0.36, it would be equivalent to looking for the proportion that is less than Z = 1 - 0.36 = 0.64 in the standard normal table. The z value here is approximately 0.36.
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Let the distribution of X be Binomial(150,0.8). The next 4 questions correspond to this information. The answer may be rounded up to 3 decimal places of the actual value:
Answer:
Step-by-step explanation:
Hello!
Missing Questions:
1) The probabylity of P(121 < X ≤ 129) is:
You can rewrite it as:
P(X ≤ 129) - P(X < 121)
Now the expression " P(X < 121)" does not include 121 so to calculate this interval you have to substract the cummulative probability to the previoous value of the variable " P(X ≤ 120)"
Then the interval is
P(X ≤ 129) - P(X ≤ 120)= 0.978 - 0.533= 0.445
2) The approximation to normal (without correction of continuity) of P(121 < X ≤ 129) is:
To use the normal approximation you have to calculate the mean and variance of the variable.
E(X)= np= 150*0.8= 120
V(X)= np(1-p)= 150*0.8*0.2= 24
Now you can standardize the given interval:
P(X ≤ 129) - P(X < 121)= P(Z ≤ (129-120)/√24) - P(Z < (121-120)/√24)
P(Z ≤ 1.84) - P(Z < 0.20) = 0.967 - 0.579= 0.388
3) The approximation to normal (with correction of continuity) of P(121 < X ≤ 129) is:
P(121 < X ≤ 129)
Applying the correction of continuity:
For X ≤ n + 0.5
For X > n + 0.5
P(121.5 < X ≤ 129.5) = P(X ≤ 129.5) - P(X < 121.5)
P(Z ≤ (129.5-120)/√24) - P(Z < (121.5-120)/√24)
P(Z ≤ 1.94) - P(Z < 0.31) = 0.974 - 0.622= 0.352
4) The approximation of poisson of P(121 < X ≤ 129) is:
First define the rate of successes of the distribution λ= np= 150*0.8= 120
Then you look at the individual cummulative probabilities using the tables of the distribution:
P(X ≤ 129; λ= 120)= 0.808
P(X < 121; λ= 120)= P(X ≤ 120; λ= 120)= 0.524
P(121 < X ≤ 129) = P(120 ≤ X ≤ 129)= P(X ≤ 129) - ≤ 129)= 0.808 - 0.524= 0.284
I hope it helps!
Find the amount of each payment to be made into a sinking fund which earns 5â% compounded quarterly and produces â$55 comma 000 at the end of 4.5 years. Payments are made at the end of each period. The payment size is $?
Answer:
$2743.66
Step-by-step explanation:
Data provided in the question:
Interest rate = 5%
Future value = $55,000
Time, t = 4.5 years
Now,
Since the interest is compounded quarterly
therefore,
Number of periods in a year = 4
Interest rate per period = 5% ÷ 4 = 1.25% = 0.0125
Total number of periods in 4.5 years = 4.5 × 4 = 18
also,
PMT = Future value × [ r × (( 1 + r )ⁿ - 1)⁻¹ ]
therefore,
PMT = $55,000 × [ 0.125 × ( ( 1 + 0.0125 )¹⁸ - 1 )⁻¹ ]
or
PMT = $55,000 × 0.0498
or
PMT = $2743.66
Compare these rational numbers. Which of the following are true?
i -4.3<-3.7
ii -3.7<-2.6
iii -4.3 > -2.6
iv -1.8 > -0.9
A. i,ii,iii,iv
B. iii and iv
C. ii,iii
D. i and iii
Answer:
none of the above (only i and ii are correct)
Step-by-step explanation:
The given numbers appear on the number line left-to-right in this order:
-4.3 -3.7 -2.6 -1.8 -0.9
The "<" relationship is true if the number on the left is to the left on the number line. That is the case for -4.3 < -3.7, and for -3.7 < -2.6.
The ">" relationship is true if the number on the left is to the right on the number line. That is NOT THE CASE for -4.3 > -2.6 or -1.8 > -0.9.
Hence, only options i and ii are true. None of the answer choices A, B, C, or D lists only these two options.
When comparing these negative rational numbers remember that on the number line numbers get smaller as you move to the left. This means -4.3 is less than -3.7, -3.7 is less than -2.6, and -4.3 is certainly not greater than -2.6. Similarly, -1.8 is not 'greater' than -0.9. So the correct answer is D. i and iii.
Explanation:In Mathematics, a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Here, we are comparing some negative rational numbers. To interpret these, remember that on the number line, numbers become smaller as you move to the left. So, -4.3 is less than -3.7, -3.7 is less than -2.6, -4.3 is not greater than -2.6 because it is more to the left on the number line, and -1.8 is not greater than -0.9 for the same reason. So option A. i,ii,iii,iv is not correct, option B. iii and iv is not correct, option C. ii,iii is not correct but option D. i and iii is correct according to the comparison results of the rational numbers.
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Either use technology to find the P-value or use
table to find a range of values for the P-value. The claim is that for the widths (yd) of tornadoes, the mean is μ, < 140 yd. The
sample size is n = 21 and the test statistic is t = -0.024.
Answer:
The first step is calculate the degrees of freedom, on this case:
[tex]df=n-1=21-1=20[/tex]
Since is a one side left tailed test the p value would be:
[tex]p_v =P(t_{(20)}<-0.024)=0.4905[/tex]
And we can use the following excel code to find it: "=T.DIST(-0.024,20,TRUE)"
Step-by-step explanation:
Data given and notation
[tex]\bar X[/tex] represent the mean
[tex]s[/tex] represent the sample standard deviation
[tex]n=21[/tex] sample size
[tex]\mu_o =140[/tex] represent the value that we want to test
[tex]\alpha[/tex] represent the significance level for the hypothesis test.
t=-0.024 would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean for the widths of tornadoes is lower than 140 yd, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 140[/tex]
Alternative hypothesis:[tex]\mu < 140[/tex]
If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
The statistic is given by: [tex] t = -0.024[/tex]
P-value
The first step is calculate the degrees of freedom, on this case:
[tex]df=n-1=21-1=20[/tex]
Since is a one side left tailed test the p value would be:
[tex]p_v =P(t_{(20)}<-0.024)=0.4905[/tex]
And we can use the following excel code to find it: "=T.DIST(-0.024,20,TRUE)"
Based on the p value obtained we can conclude that we FAIL to reject the null hypothesis at any significance level selected [tex]\alpah=0.01,0.05,0.1[/tex]
The temperature adjusted for wind-chill is a temperature which tells you how cold it feels, as a result of the combination of wind and temperature.
Temperature (F)
35 30 25 20 15 10 5 0
5 31 25 19 13 7 -1 -5 -11
10 27 21 15 9 31 -41 -10 -16 Wind Speed (mph)
15 25 19 13 6 0 -7 -13 -19
20 24 17 11 4 -2 -9 -15 -22
25 23 16 9 3 -4 -11 -17 -24
(a) If the temperature is 0°F and the wind speed is 10 mph, how cold does it feel?
(b) If the temperature is 35°F, what wind speed makes it feel like 25°F?
(c) If the wind is blowing at 10 mph, approximately what temperature feels like 0°F?
Final answer:
The wind chill table can be used to determine how cold it feels at different combinations of temperature and wind speed.
Explanation:
Wind chill is a measure of how cold it feels when the temperature is combined with wind speed. To determine how cold it feels when the temperature is 0°F and the wind speed is 10 mph, we can look at the table provided. At 0°F and 10 mph wind speed, the temperature adjusted for wind chill is -10°F.
If the temperature is 35°F and we want to know the wind speed that makes it feel like 25°F, we can look at the table and find that at 35°F, a wind speed of 15 mph makes it feel like 25°F.
If the wind speed is 10 mph and we want to know the approximate temperature that feels like 0°F, we can look at the table and find that at 10 mph wind speed, a temperature of 5°F feels like 0°F.
(a) At 0°F with a wind speed of 10 mph, it feels like -11°F.
(b) To make 35°F feel like 25°F, a wind speed of 15 mph is needed.
(c) With a wind speed of 10 mph, a temperature of 5°F feels like 0°F.
To find the adjusted temperature for wind-chill, we can use the given table which provides adjustments based on both temperature and wind speed.
(a) If the temperature is 0°F and the wind speed is 10 mph, we can find the adjusted temperature from the table:
Temperature: 0°F
Wind speed: 10 mph
From the table:
Adjusted temperature: -11°F
So, it feels like -11°F when the temperature is 0°F with a wind speed of 10 mph.
(b) If the temperature is 35°F, and we want it to feel like 25°F, we need to find the wind speed that corresponds to this adjusted temperature from the table:
Temperature: 35°F
Adjusted temperature desired: 25°F
From the table, look for the entry where the adjusted temperature is 25°F:
Adjusted temperature: 25°F
Wind speed corresponding to this adjusted temperature: 15 mph
So, a wind speed of 15 mph would make a temperature of 35°F feel like 25°F.
(c) If the wind speed is 10 mph and we want to find the temperature that feels like 0°F, we can find this from the table:
Wind speed: 10 mph
Adjusted temperature desired: 0°F
From the table, look for the entry where the adjusted temperature is 0°F:
Adjusted temperature: 0°F
Corresponding temperature: 5°F
So, approximately, a temperature of 5°F would feel like 0°F with a wind speed of 10 mph.
Briefly discuss the three combinations of variable types that can form bivariate data.
Answer:
Step-by-step explanation:
from the word Bi "meaning two"
Bivariate data are two different variables obtained from the same population element. Bivariate data are used if the sampled data cannot be graphically displayed using a single variable.
To form a bivariate data, there are three combinations of variable
1. Both variables are qualitative i.e attribute in nature
2. Both variables are quantitative i.e numerical
3. One of them is qualitative whilee the other is quantitative
Qualitative data are data that are measure of type which could represent a name, colour,symbol. traits or characteristics
Quantitative data are data that can be counted, measured and expressed using numbers/
We are going to approximate f by three polynomials, of degrees 1, 2, and 3. Let's call them p1, p2, and p3, respectively. p1 will be determined by the requirement that p1(1)
Answer:7
Step-by-step explanation:
A University of Florida student earns $10 per day delivering advertising brochures door-to-door, plus $1.50 for each person he interviews. How many people did he interview on a day when he earned $52?
Answer:
28
Step-by-step explanation:
People he interviewed on that day (x)
1.50x + 10 = 52
1.50x = 42
x = 42/1.50
x = 28
The number of people is 28 if the University of Florida student earns $10 per day delivering advertising brochures door-to-door.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
A University of Florida student earns $10 per day delivering advertising brochures door-to-door, plus $1.50 for each person he interviews.
Let's suppose the people he interviewed on that day x
The linear equation can be framed as per the question:
1.50x + 10 = 52
After solving:
x = 42/1.50
x = 28
Thus, the number of people is 28 if the University of Florida student earns $10 per day delivering advertising brochures door-to-door, plus $1.50 for each person he interviews.
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Refer to the accompanying TI-83/84 Plus calculator display of a 95% confidence interval. The sample display results from using a simple random sample of the amounts of tar (in milligrams) in cigarettes that are all king size, nonfiltered, nonmenthol, and non-light. Express the confidence interval in the format of x overbarplus or minusE. ZInterval (21.182,23.958) x overbarequals22.57 nequals25 The confidence interval is nothingplus or minus nothing.
Answer:
[22.57 ± 2.776]
Step-by-step explanation:
Hello!
You have the 95% Confidence Z-interval (21.182;23.958), the mean X[bar]= 22.57 and the sample size n=25.
The formula for the Z interval is
[X[bar] ± [tex]Z_{1-\alpha /2} *( \frac{Sigma}{\sqrt{n} } )[/tex]]
The value of Z comes from tha standard normal table:
[tex]Z_{1-\alpha /2} = Z_{0.975}= 1.96[/tex]
The semiamplitude (d) or margin of error (E) of the interval is:
E or d= (Upperbond- Lowerbond)/2 = (23.958-21.182)/2 = 2.776
[X[bar] ± E]
[22.57 ± 2.776]
I hope it helps!
You have 8 friends, of whom 5 will be invited to your big party in IV on Friday night. (a) How many choices are there if 2 of the friends are feuding and will not attend together
Answer:
36
Step-by-step explanation:
We have been given that you have 8 friends, of whom 5 will be invited to your big party in IV on Friday night. We are asked to find the number of choices if 2 of the friends are feuding and will not attend together.
We can choose 5 friends from 8 friends in [tex]^8C_5[/tex] ways.
[tex]^8C_5=\frac{8!}{5!(8-5)!}=\frac{8!}{5!(3)!}=\frac{8*7*6*5!}{5!*3*2*1}=8*7=56[/tex]
Therefore, we can choose 5 friends from 8 friends in 56 ways.
Since two friends are feuding, so we need to choose 3 friends from 6 friends and subtract them from total ways.
We can choose 3 friends from 6 friends in [tex]^6C_3[/tex] ways.
[tex]^6C_3=\frac{6!}{3!(6-3)!}=\frac{6!}{3!(3)!}=\frac{6*5*4*3!}{3!*3*2*1}=5*4=20[/tex]
[tex]56-20=36[/tex]
Therefore, we have 36 choices, if 2 of the friends are feuding and will not attend together.
Final answer:
The number of different choices for inviting friends to the party without the feuding friends attending together is 41 different choices.
Explanation:
The student's question deals with a combinatorial problem where they have 8 friends but can only invite 5 to a party. However, there is a constraint: 2 of the friends are feuding and cannot attend together. To solve this, we calculate the number of ways to choose 5 friends out of 8 without the feuding friends both attending.
Calculating Combinations with Restrictions
First, we find the total number of ways to invite 5 friends out of 8 without any restrictions, which is calculated using the combination formula C(n, k) = n! / (k!(n - k)!), where n is the total number of friends and k is the number of friends to be invited.
C(8, 5) = 8! / (5!(8 - 5)!) = (8 × 7 × 6) / (3 × 2 × 1) = 56 ways.
Next, we calculate the number of combinations where the feuding friends would attend together. We treat them as a single entity and find combinations of the remaining 6 friends to invite 4 plus the 'unit' of feuding friends.
C(6, 4) = 6! / (4!(6 - 4)!) = (6 × 5) / (2 × 1) = 15 ways.
To get the total number of combinations without the feuding friends attending together, we subtract the 15 'restricted' combinations from the total 56 combinations.
56 - 15 = 41.
Therefore, there are 41 different choices for inviting friends to the party without the feuding friends attending together.
Compare the graphs below of the logarithmic functions. Write the equation to represent g(x).
Answer:
The equation to represent g(x) will be [tex]g(x)=log(x)+4[/tex]
Step-by-step explanation:
Considering the logarithmic function
[tex]f(x)=log(x)[/tex]
As we know that when a constant c gets added to the parent function, the result would be a vertical shift c units in the direction of the sign of c.
So,
[tex]g(x)=log(x)+4[/tex] is basically the shift up by 4 units, and the graph also showing the same situation.
Therefore, the equation to represent g(x) will be [tex]g(x)=log(x)+4[/tex]
Also, the graphs of both [tex]f(x)=log(x)[/tex] and [tex]g(x)=log(x)+4[/tex] is attached where black mark graph represents [tex]f(x)=log(x)[/tex] and red mark graph represents [tex]g(x)=log(x)+4[/tex].
Keywords: transformation, vertical shift, graph
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