Answer:
a) Range = 25.6
b) Variance = 48.1446
c) s = 6.9386
d) See below
Step-by-step explanation:
(a) the sample range
To obtain the sample range, we must sort the data increasingly :
23.7, 26.3, 28.3, 28.7, 29.6, 29.8, 30.1, 31, 33.5, 49.3
Then, find the distance between the largest and the lowest
Range = 49.3 - 23.7 = 25.6
(b) the sample variance [tex]s^2[/tex] from the definition
In order to find the variance from the definition, we need first the mean. The mean is defined as the average
[tex]\bar x=\displaystyle\frac{\displaystyle\sum_{i=1}^{n}x_i}{n}[/tex]
where the [tex]x_i[/tex] are the values of the data collected and n=10 the size of the sample.
So, the mean is
[tex]\bar x=31.03[/tex]
Now, the variance of the sample is defined as
[tex]s^2=\displaystyle\frac{\displaystyle\sum_{i=1}^n(x_i-\bar x)^2}{n-1}[/tex]
and we have that the variance is
[tex]s^2=48.1446[/tex]
(c) the sample standard deviation
The sample standard deviation is nothing but the square root of the variance
[tex]s=\sqrt{48.1446}=6.9386[/tex]
d) [tex]s^2[/tex] using the shortcut method
The shortcut method figures out the variance without having to compute the mean. The formula is
[tex]s^2=\frac{n\sum x_i^2-(\sum x_i)^2}{n(n-1)}[/tex]
where n=10 is the sample size .
So, using the shortcut method,
[tex]s^2=\frac{10*10,061.91-96,286.09}{10*9}=48.1446[/tex]
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.
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 .
Use inductive reasoning to predict the next line in the pattern. Then perform the arithmetic to determine whether your conjecture is correct. 8(5) = 10(5 - 1) 8(5) + 8(25) = 10(25 - 1) 8(5) + 8(25) + 8(125) = 10(125 - 1) 8(5) + 8(25) + 8(125) + 8(625) = 10(625 - 1)
Answer:
8(5) + 8(25) + 8(125) + 8(625) +8(3125)= 10(3125 - 1)=31240
Hence proved Conjecture is correct
L.H.S=R.H.S
Step-by-step explanation:
Consider the pattern:
8(5)=10(5-1)=40
8(5) + 8(25) = 10(25 - 1) =240
8(5) + 8(25) + 8(125) = 10(125 - 1) =1240
8(5) + 8(25) + 8(125) + 8(625) = 10(625 - 1)=6240
According to inductive reasoning next term of pattern will become:
8(5) + 8(25) + 8(125) + 8(625) +8(3125)= 10(3125 - 1)=31240
Checking whether conjecture is correct or not:
Consider L.H.S:
8(5) + 8(25) + 8(125) + 8(625) +8(3125)
40+200+1000+5000+25000
31240
R.H.S:
31240
Hence proved Conjecture is correct
L.H.S=R.H.S
Determine whether the distribution is a discrete probability distribution. x âP(x) 0 0.21 1 0.28 2 0.02 3 0.28 4 0.21 Is the distribution a discrete probabilityâ distribution? Why? Choose the correct answer below. A. No comma because the total probability is not equal to 1. B. No comma because some of the probabilities have values greater than 1 or less than 0. C. Yes comma because the distribution is symmetric. D. Yes comma because the probabilities sum to 1 and are all between 0 and 1 comma inclusive.
Answer:
D. Yes, because the probabilities sum to 1 and are all between 0 and 1, inclusive.
Step-by-step explanation:
0.21 + 0.28 + 0.02 + 0.28 + 0.21 = 1
All individual data are between 0 and 1. Data added up = 1
The true statement is (d) Yes, because the probabilities sum to 1 and are all between 0 and 1, inclusive.
For a distribution to be a discrete probability distribution, the following must be true
[tex]\sum P(x) =1[/tex]
So, we have:
[tex]\sum P(x) = 0.21 + 0.28 + 0.02 + 0.28 + 0.21[/tex]
Evaluate the sum
[tex]\sum P(x) =1[/tex]
The above statement shows that the distribution is a discrete probability distribution
Hence, the true statement is (d) Yes, because the probabilities sum to 1 and are all between 0 and 1, inclusive.
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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].
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]
A statistic refers to:
a fixed unknown number that describes the entire group of interest.
an entire group of interest.
a subset that includes all elements in the group of interest.
a number produced from a subset of the group of interest.
a subset of the entire group of interest.
Answer:
a number produced from a subset of the group of interest.
Step-by-step explanation:
This problems is, basically, about the difference of concepts between a statistic and a parameter.
When something is taken from a sample and estimated to the entire population, it is a statistic. For example, if you survey 200 Central New York residents, an 60% of them say they are Buffalo Bills fans, the 60% is a statistic.
When something is true to the entire population, it is a parameter. If i study the voting preference of all 53 players on the Buffalo Bills active roster, and 83% are Democrats, the 83% is an parameter.
So the correct answer is:
a number produced from a subset of the group of interest.
This subset is the sample, for example, and the group of interest is the population.
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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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.
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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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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A single card is drawn from a standard deck. Find the probability of the following event. Drawing a jack or a face card
Answer:
16/52 or 4/13 when reduced.
Step-by-step explanation:
4/52 is for the Jack card since there are 4 jack cards out of a total of 52 cards.
12/52 is for the face cards since there are 12 face cards out of a total of 52 cards.
Since the problem says OR, this means one or the other, so you will be adding those two fractions together. If the problem said AND, this would mean that you have to multiply since both would have to occur.
The probability of selecting a heart or a face card from a standard deck of cards is 22/52.
To calculate the probability of selecting a heart or a face card from a standard deck of cards, we must consider the total number of heart cards and face cards in the deck, mindful not to double-count any cards that are both. A standard deck has 52 cards, 12 of which are face cards (3 face cards per suit, and there are 4 suits in total). Besides these 12 face cards, there are 13 heart cards, but since three of them are face cards, which we have already counted, we subtract those, leaving us with 10 additional heart cards. Thus, the total number of favorable outcomes is 12 (face cards) + 10 (non-face-card hearts) = 22.
The probability of drawing a heart or face card is then 22 favorable outcomes divided by 52 possible outcomes, which simplifies to 11/26 or about 42.31%.
To understand if this outcome is more or less likely than selecting a heart suit face card, we consider that there are only 3 face cards in the hearts suit. Hence, the probability of drawing a heart suit face card is 3/52 or about 5.77%. Clearly, drawing a heart or a face card is more likely than drawing a heart suit face card alone, as 42.31% > 5.77%.
(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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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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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.
Suppose that in a certain metric geometry satisfying Axioms D-1-D-3, points A, B, C, and D are collinear and AB = AC = 3,BC = 6,BD = 2,and AD = 1. If the Ruler Postulate is also valid, find CD
Answer:
We calculate that is CD=4.
Step-by-step explanation:
From Exercise we have that
AB=AC=3
BC=6
BD=2
AD=1.
From Axioms D-1 and D-3, we have
D-1: ∀ A, B∈ S, there is a unique AB ∈ R
D-3: ∀ A, B∈ S, AB=BA.
We use the Axioms D-1 and D-3, and we get that
AC=CA=3
AD=1
because are the points is collinear, we get
CA+AD=CD
3+1=CD
CD=4
We calculate that is CD=4.
Final answer:
To find the length of segment CD, we assume points on a collinear path as A-D-B-C, and subtract the length of BD from BC, resulting in CD = 4 units.
Explanation:
The student has asked for the length of segment CD when given a set of collinear points A, B, C, and D, with various distances between them. Since we have point B between points A and C, and points A and D, and knowing AB, AC, BC, and BD, we can determine the length of AD by subtracting from AC the length of BC, since AB equals AC. Therefore, AD = AC - BC = 3 - 6 = -3, which does not make sense geometrically since lengths cannot be negative. This might imply a typo or a misinterpretation of the points' arrangement. If assuming points in a line segment: A-D-B-C, CD can be found by subtracting BD from BC, CD = BC - BD = 6 - 2 = 4.
Bruno listens to podcasts for
two and a half hours a day.
Write an equation where x is
the number of days and y is
the total number of hours.
What is the constant of
proportionality? 25 points brainiest
Answer:the constant of proportionality is 2.5 hours per day.
The equation is y = 2.5x
Step-by-step explanation:
Let x represent the number of days that Bruno listens to podcasts.
Let y represent the total number of hours that Bruno listens to podcasts.
Bruno listens to podcasts for
two and a half hours a day.
Let k represent the constant of proportionality. Therefore,
y = kx
k = y/x
So k = 2.5/1 = 2.5 hours/day
The equation is expressed as
y = 2.5x
Jimmy decides to mow lawns to earn money. The initial cost of his lawnmower is %350. Gasoline and maintenance costs a $6 per lawn. a) Formulate a function C(x) for the total cost of mowing x lawns. b) Jimmy determines that the total-profit function for the lawn mowing business is given by p(x) = 9x - 350. Find a function for the total revenue from mowing x lawns. How much does jimmy charge per lawn? c) How many lawns must jimmy mow before he begins making a profit? a) Formulate a function C(x) for the total cost of mowing x lawns. b) Find a function for the total revenue from mowing x lawns R(x) = How much does Jimmy charge per lawn?
Answer:
Step-by-step explanation:
a) C(x) = 6x+350
b) Function for total revenue, R(x) = 15x & charge per lawn is $15.
c) Jimmy must mow approx 39 lawns before he begins making a profit.
How to formulate a function ?
Consider the initial cost of lawnmower is $350,
Gasoline and maintenance cost are $6 per lawn.
(a) To formulate a function C(x) for the total revenue of mowing x lawn, we use the given values than the function C(x) will be given by
C(x) = 6x+350
How to find the total revenue ?Find the function for the total revenue from moving x lawns.
Recollect: P(x) = R(x)-C(x)
So, R(x) = P(x)+C(x) ..............(1)
Substitute, P(x) = 9x-350 & C(x) = 6x+350 in (1) we get,
R(x) = 9x-350+6x+350
= 15x
So, the total revenue = 15x
∴ Charge per lawn = R(x)/x = 15x/x = $15
How much lawn jimmy needs to mow before make profit ?To find the number of lawn jimmy must mow before begins making a profit, we use P(x) = 0
∴ 9x-350=0
⇒x = 350/9
⇒x ≈ 39
Hence, the solution is x = 39 (approx)
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We flip a fair coin five times. For every heads you pay me $1 and for every tails I pay you $1. Let X denote the my net winning at the end of the flips. Find the possible values and the probability mass function of X.
The possible values of net winnings in this coin flipping game range from -5 to 5 dollars. The individual probabilities of these outcomes can be calculated using a binomial probability distribution. The game is symmetric because of the fairness of the coin, resulting in the probability of winning and losing $5 being equal.
Explanation:In this coin flipping game
, we have five independent trials (flips) each having two possible outcomes (heads or tails). This implies
a binomial distribution
is expected. In each trial, 'success' can be defined as getting heads, and 'failure' as getting tails. Number of successes (X) can range from 0 to 5, that is your net winnings can be from -5 to 5 dollars.
The Probability Mass Function (PMF) of X can be calculated using the binomial distribution formula, which is: P(X=k) = (5 choose k) * (0.5)^k * (0.5)^(5-k), where k represents number of 'successes' (heads), (5 choose k) is the number of combinations of getting k successful outcomes in 5 trials, and (0.5) is the probability of getting heads or tails.
PMF will give you the probability of each possible outcome (from -5 to 5 dollars), which in this specific scenario is symmetric due to the coin being fair. So for instance, winning $5 and losing $5 both have a probability of (0.5)^5 = 0.03125.
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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.
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.
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.
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!
Make a substitution to express the integrand as a rational function and then evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) x + 25 x dx
Answer:
∫(x+25x)dx=13x²
Step-by-step explanation:
From Exercise, we want calculate integral for x + 25 x dx.
But this not required a substitution to express the integrand as a rational function. We can calculte integral, and we get
∫(x+25x)dx= ∫x dx+25∫x dx=x²/2+ \frac{25}{2} · x^2=\frac{26}{2}·x^2=13x²
Therefore, we get that is
∫(x+25x)dx=13x².
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 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
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.
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:
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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Evaluate each of the following to three significant figures, and express each answer in SI units using an appropriate prefix: (a) [4.86(10 6 )] 2 mm, (b) (348 mm) 3 , (c) (83 700 mN) 2 .
Answer:
a). [tex]4.86\times 10^{-15}[/tex] m
b). [tex]4.21\times 10^{-2}[/tex] m³
c). [tex]7.00\times 10^{3}[/tex] N²
Step-by-step explanation:
In this question we have to convert each option into SI units.
a). [tex]4.86(10^{-6})^{2}[/tex] mm
= [tex]4.86\times (10^{-12})\times (10^{-3} )[/tex] m
= [tex]4.86\times 10^{-15}[/tex] m
b). (348 mm)³
= [tex](348)^{3}\times (10^{-3})^{3}[/tex] m³
= [tex]42144192\times 10^{-9}[/tex] m³
= [tex]4.21\times 10^{-2}[/tex] m³
c). [tex](83700)^{2}\times (10^{-3})^{2}[/tex] N²
= [tex]700569\times 10^{4}\times 10^{-6}[/tex] N²
= [tex]7.00\times 10^{9}\times 10^{-6}N^{2}[/tex]
= [tex]7.00\times 10^{3}[/tex] N²