a.) The probability that Kevin will get exactly five questions correct is 0.2461 or 24.61%. b.) The probability of Kevin passing the test is 0.828125 or 82.81%.
Explanation:
Given data:
Kevin is not prepared for a 10 question true-false questions on a test.Let X be the random variable representing the number of questions that Kevin gets correct out of 10. Then X has a binomial distribution with parameters n=10 and p=0.5 (since each question is true-false and Kevin is guessing the answers without any knowledge).a.) To find the probability that Kevin will get exactly five questions correct, we need to use the binomial probability formula:
P(X = k) = (n C k) * p^k * q^(n-k)
where n C k is the number of ways to choose k items from n (also known as the binomial coefficient),
p is the probability of success (getting a true answer),
and q is the probability of failure (getting a false answer).
In this case, we have:
k = 5 (since we want exactly 5 questions correct)
n = 10 (since there are 10 questions)
p = 0.5 (since each question is true-false and Kevin is guessing)
q = 1 - p = 0.5 (since there are only two options: true or false)
So, using the formula:
P(X = 5) = (10 C 5) * (0.5)^5 * (0.5)^(10-5)= 252 * 0.03125 * 0.03125= 0.2461 or 24.61%
Therefore, the probability that Kevin will get exactly five questions correct is 0.2461 or 24.61%.
b.) To find the probability of Kevin passing the test, we need to find the probability of getting at least four questions correct. That is,P(X ≥ 4) = P(X = 4) + P(X = 5) + ... + P(X = 10)
This is a bit cumbersome to calculate directly, so we can use the complement rule:
Prob(Kevin passes) = 1 - Prob(Kevin fails)Prob(Kevin fails) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
Now, using the binomial probability formula:
P(X = k) = (n C k) * p^k * q^(n-k)we get:P(X = 0) = (10 C 0) * (0.5)^0 * (0.5)^(10-0) = 0.0009765625P(X = 1) = (10 C 1) * (0.5)^1 * (0.5)^(10-1) = 0.009765625P(X = 2) = (10 C 2) * (0.5)^2 * (0.5)^(10-2) = 0.0439453125P(X = 3) = (10 C 3) * (0.5)^3 * (0.5)^(10-3) = 0.1171875So,Prob(Kevin fails) = 0.0009765625 + 0.009765625 + 0.0439453125 + 0.1171875= 0.171875And therefore,Prob(Kevin passes) = 1 - Prob(Kevin fails) = 1 - 0.171875= 0.828125 or 82.81%
Therefore, the probability of Kevin passing the test is 0.828125 or 82.81%.
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a.) The probability that Kevin will get exactly five questions correct is 0.246.
b.) To find the probability that Kevin passes the test, we need to find the probability that he gets at least four questions correct. This means we need to find the probability of him getting 4, 5, 6, 7, 8, 9, or 10 questions correct and add them up. The probability that he passes is 0.427.
Explanation: Let P(True) = P(T)
= P(False) = P(F)
= 0.5Kevin is not prepared for a 10 question true-false questions on a test. So, he is going to guess the answers. The probability of getting exactly n answers correct out of a total of 10 questions is given by the Binomial Distribution. The formula for the Binomial Probability is as follows:
[tex]P(X = n) = C(n, r) \times p^r \times q^{(n-r)}[/tex]
where n is the total number of trials (10), r is the number of successes (in this case, the number of questions that Kevin gets correct), p is the probability of success on one trial (0.5), and q is the probability of failure (0.5). We want to find the probability of Kevin getting exactly 5 questions correct. So, we substitute n = 10,
r = 5,
p = 0.5,
and q = 0.5 into the formula:
P(X = 5) = C(10, 5) * 0.5^5 * 0.5^5
= 252 * 0.03125 * 0.03125
= 0.246
Hence, the probability that Kevin will get exactly five questions correct is 0.246.
To find the probability that Kevin passes the test, we need to find the probability of him getting at least four questions correct. This means we need to find the probability of him getting 4, 5, 6, 7, 8, 9, or 10 questions correct and add them up. We can find this probability using the Binomial Distribution as well:
P(X >= 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)
P(X >= 4) = C(10, 4) * 0.5^4 * 0.5^6 + C(10, 5) * 0.5^5 * 0.5^5 + C(10, 6) * 0.5^6 * 0.5^4 + C(10, 7) * 0.5^7 * 0.5^3 + C(10, 8) * 0.5^8 * 0.5^2 + C(10, 9) * 0.5^9 * 0.5^1 + C(10, 10) * 0.5^10 * 0.5^0
P(X >= 4) = 0.205 + 0.246 + 0.205 + 0.117 + 0.0439 + 0.0107 + 0.00195
= 0.427
Therefore, the probability that Kevin passes the test is 0.427.
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PLEASE HELP FAST!!!!! I’ll mark brainliest
Please help me I need to answer this question
Answer:
.........
it is -7
Write a quadratic equation in standard form with [tex]\frac{3}{4}[/tex] an -5 as its roots
Knowing the roots first write the equation in factored form:
(X - 3/4)(x +5) = 0
Now use the FOIL method ( multiply each term in one set of parentheses by each term the other set:
X•x + x•5 -3/4•x -3/4•5
Simplify:
X^2 + 5x -3/4x -3 3/4
Combine like terms:
X^2+ 4 1/4x - 3 3/4
Based on the following new information. Given it is raining, what is the what is the probability of Sunshine delight winning ?
Storm Chaser Sunshine delight
Given Raining 0.79 Given not raining 0.64
Based on the following information collected from emails. What is the probability that if the word "llwws" is in a document, it is spam ?
Spam Not spam
Word "aabbdd" 0.71 Word "llwws" 0.5
ROUND TO 2 DECIMAL PLACES
The probability of Sunshine Delight winning given that it is raining is approximately 0.79. The probability that a document is spam if it contains the word "llwws" is approximately 0.50.
In the case of Sunshine Delight winning, given that it is raining, the probability is directly provided as 0.79.
For the probability of a document being spam if it contains the word "llwws," the information shows that the probability of the word "llwws" appearing in a spam document is 0.50. However, without further information about the overall prevalence of spam and non-spam documents, we cannot directly determine the probability that a document containing "llwws" is spam. Additional context about the overall occurrence of spam and non-spam documents is required to calculate the requested probability.
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How long is 75% of a 24-hour day? How far is 75% of a 2,000-kilometer trip? How much is 75% of 10 liters of milk?
A consumer's utility is described by U(x, y) = xy. Marginal utilities then are described as MUX = y and MUy=x. Suppose the price of x is 1 and the price of y is 2. Consumer's income is 40. Then price of y falls to 1. When graphing, make sure to put x on the horizontal axis, and y on the vertical axis.
(a) Calculate the optimal consumption choice before the price change. Illustrate that choice on a graph. Label that choice A
(b) Calculate the optimal consumption choice the consumer would buy at the new price of y, if they wanted to get the same amount of utility as before the price change. Mustrate that choice on the same graph. Label that choice B
(c) What is the substitution effect of the price change? Illustrate on the graph.
(d) What is the optimal consumption choice after the price change? Illustrate on the graph and label that choice C (e) What is the income effect of the price change? Illustrate on the graph.
Before the price change, the optimal consumption choice (A) is determined by equalizing the marginal utilities of x and y.
Using the utility function U(x, y) = xy, and considering prices of Px = 1 and Py = 2, along with an income of 40, we find that the utility equalization condition leads to y = x/2.
With the budget constraint of x + 2y = 40, we solve for x = 20 and y = 10, giving the optimal consumption choice (20, 10) labeled as point A on the graph.
After the price change, with the price of y falling to 1, the consumer aims to maintain the same utility level. Setting MUX/Px = MUY/Py, we find x = y, and using the budget constraint x + y = 40, we get x = y = 20, resulting in the optimal consumption choice (20, 20) labeled as point B.
The substitution effect is illustrated by a movement from A to B along the budget constraint. The new optimal consumption choice (C) after the price change is determined by the new budget constraint x + y = 40, where x = 30 and y = 10, labeled as point C on the graph.
The income effect is depicted by the parallel shift of the budget constraint line outward from the origin.
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Jennifer is buying party supplies. She is planning on buying twice as many balloons as noisemakers. The number of napkins Jennifer is planning on buying is one-quarter of the number of noisemakers. If Jennifer buys 65 items, how many noisemakers does Jennifer buy? Write and solve an equation using a variable for this problem. <3
Answer:
808 over 25 as a faraction
Step-by-step explanation
a quarter of 65 is 16 4 over 25
16 4 over 25 times 2 808 over 25 as a fraction
An engine additive is being tested to see whether it can effectively increase gas mileage for a number of vehicles. Twenty assorted vehicles had their gas mileage, in miles per gallon, measured. Then, the engine additive was placed into each of the engines, and the gas mileage was measured again. Let
The calculated t-value is greater than 1.734, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.
An engine additive is being tested to see whether it can effectively increase gas mileage for a number of vehicles. Twenty assorted vehicles had their gas mileage, in miles per gallon, measured. Then, the engine additive was placed into each of the engines, and the gas mileage was measured again. Let µd be the true mean difference in the gas mileage before and after the engine additive is placed into the engines. We want to test the hypothesis that the engine additive has no effect. The null hypothesis is: H0: µd = 0The alternative hypothesis is: Ha: µd > 0 (one-tailed test)Assuming that the difference in gas mileage before and after the engine additive is approximately normally distributed, we can use a one-sample t-test. The test statistic is given by: $$t=\frac{\bar{x}-\mu}{s/\sqrt{n}}$$Where, $\bar{x}$ is the sample mean difference in gas mileage, μ is the hypothesized population mean difference, s is the sample standard deviation of the differences, and n is the sample size. We can use a significance level of α = 0.05.To determine the critical value of the t-distribution, we need to find the degrees of freedom (df). Since we have a sample size of n = 20, we have n - 1 = 19 degrees of freedom. Using a t-distribution table with 19 degrees of freedom and a significance level of 0.05 for a one-tailed test, we get a critical value of t = 1.734. If the calculated t-value is greater than 1.734, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.
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In a recent tennis tournament, women playing singles matches used challenges on 133 calls made by the line judges. Among those challenges, 35 were found to be successful with the call overturned.
a. Construct a 99% confidence interval for the percentage of successful challenges.
b. Compare the results from part (a) to this 99% confidence interval for the percentage of successful challenges made by the men playing singles matches: 21.7%
Required correct option is Since the two confidence intervals overlap, neither gender appears to be substantially more successful in their challenges.
a) In order to find the 99% confidence interval for the percentage of successful challenges, the formula is given below: Lower limit of CI: upper limit of CI: The confidence interval for the percentage of successful challenges is (19.68%, 34.97%).b) In part (a), we found the confidence interval for the percentage of successful challenges among women playing singles matches. 99% confidence interval for the percentage of successful challenges made by the men playing singles matches is 21.7%± 4.93%.Here, the two confidence intervals overlap, therefore, neither gender appears to be substantially more successful in their challenges.Therefore, option (C) is the correct answer.
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What is the product of the binomials below?
(3x + 6)(4x+2)
A. 7x2 +30x+12
B. 12x2 + 30x + 12
C. 7x2 + 30x + 8
D. 12x2 + 30x+8
SUM
PREVIOUS
Answer:
12x^2 + 30x+12
Step-by-step explanation:
3x+6) (4x+2)
3x 6
12x^2 24x 4x
6x 12 2
use a punnet square type deal here.
12x^2 + 24x + 6x + 12
12x^2 + 30x+12
And so your answer should be: 12x^2 + 30x+12
Find x.
30
20
Need help with this question asap
Answer:
x = 10[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using the cosine ratio in the right triangle and the exact value
cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] , then
cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{20}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2x = 20[tex]\sqrt{3}[/tex] ( divide both sides by 2 )
x = 10[tex]\sqrt{3}[/tex]
pls help immediately!!! i’ll be giving brainiest to those who provide the write answer and who don’t leave a link!
Answer:
trapazoid
Step-by-step explanation:
.....
-2021
English
g
p
Which angles are corresponding angles? Select all that
apply.
o 21 and 23
5
3
7
6
4
8
26 and 28
22 and 28
25 and 27
22 and 27
23 and 26
Answer:
I'm not too sure what you mean but since there was no image I tried to look up how to tell if angles are corresponding based on angle degree and the most I got was the angles will be equal but only if there is a transversal cur but none of the answers equal each other
Step-by-step explanation:
so what advice I can give you is corresponding angles are usually the same degree but on a different level. like on the first parallel line there is an angle and on the second (or whatever) there is another angle (on the same side of the first) -meaning they will both be on the right or the left- and yeah there you go
if you have any questions comment and I'll try my best to help
PLEASE HELP ASAP
Find the surface area and volume of the figure below:
Answer:
What I think it might be is 62.3
Hello! I was wondering can anyone help me?
Answer:
$86.94
Step-by-step explanation:
All we need to do is subtract his weekly play from his pay after taxes and his other taxes.
$625
$499.61
_ $38.45
____________
$86.94
Have a nice day, fam. Spread The Love.
6 STUP1D QUESTIONS FOR 100 POINTS
1. Why do British people never sound British when they sing?
2. Why do they call it 'head over heels in love if our head is always over our heels?
3. Can a hearse driver drive a corpse in the carpool lane?
4. Why is the name of the phobia for the fear of long words Hippopotomonstrosesquippedaliophobia?
5. If someone can't see, they're blind and if someone can't hear, they're deaf, so what do you call people who can't smell?
6. How do they get those boats in those glass bottles?
What correction does Petri need to make? BRAINLIEST I WILL CROWN
(15 points !!!) What is the measure of
A. 25°
B. 75°
C. 90°
D. 105°
Answer:
D. 105°
Step-by-step explanation:
If the cumulative distribution of a random variable X is given as: (7) 4 2 0 X FIX) 5 72-51 12 then K= (A) WIM. (B) 3 (C) 12 1 (D) 6 K+ (E)
The value of K is given as follows:
K = 1/12.
How to obtain the value of K?A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
For a distribution, we have that the sum of all the probabilities in the distribution must be of 1.
This means that the cumulative distribution at the least value is of 1, hence the equation is given as follows:
17/12 - 5K = 1
Then the value of K is obtained as follows:
5K = 17/12 - 1
5K = 17/12 - 12/12
5K = 5/12
K = 1/12.
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Which of the expressions below is equal to 8x+4? Select all that apply
Answer:
C and D.
Step-by-step explanation:
For C, 4 * 2x = 8x and 4*1 = 4.
For D, 5x+3x = 8x and 2+2 = 4.
Answer:
A) 8( x + 2 ) is the only equal expression.
2. A (simplified representation of) the 2019 British parliament was as a weighted voting system (326 : 316, 259, 35, 12, 12, 10,6). The Conservative party had 316 votes, the Labour party had 259 votes
a) the Shapley-Shubik Index of the Conservative party is 3360/5040.
b) the Shapley-Shubik Index of the Labour party is 82.142
To calculate the Shapley-Shubik index for a party in a weighted voting system, we need to consider all possible orderings of the parties and determine the party's contribution to the winning coalition in each ordering. The Shapley-Shubik index represents the average contribution across all possible orderings.
(a) The Shapley-Shubik Index of the Conservative party is 3360/5040. Justify this calculation:
To calculate the Shapley-Shubik Index of the Conservative party, we consider all possible orderings of the parties and determine the Conservative party's contribution to the winning coalition in each ordering.
The total number of possible orderings of the parties is given by the factorial of the total number of parties: 7! = 5040.
In each ordering, we examine the cumulative votes of the parties in the order until the winning threshold of 326 votes is reached. The Conservative party, with 316 votes, does not reach the threshold alone.
However, if we consider the cumulative votes of the Conservative party and the Labour party (316 + 259 = 575), we reach the winning threshold. Therefore, the Conservative party's contribution to the winning coalition is 575 votes.
Since there are 6 other parties, we need to distribute the remaining votes among them. We can do this in 6! = 720 different ways.
The Shapley-Shubik Index is calculated by summing the contributions of the Conservative party across all possible orderings and dividing by the total number of orderings:
Shapley-Shubik Index of the Conservative party = (575 * 720) / 5040 = 3360 / 5040
Therefore, the Shapley-Shubik Index of the Conservative party is 3360/5040.
(b) To compute the Shapley-Shubik Index of the Labour party, we follow a similar approach:
The Labour party has 259 votes. We consider all possible orderings of the parties and determine the Labour party's contribution to the winning coalition in each ordering.
In each ordering, we examine the cumulative votes of the parties in the order until the winning threshold of 326 votes is reached. The Labour party alone does not reach the threshold.
However, if we consider the cumulative votes of the Labour party and the Conservative party (259 + 316 = 575), we reach the winning threshold. Therefore, the Labour party's contribution to the winning coalition is 575 votes.
Similar to the previous calculation, we distribute the remaining votes among the 6 other parties in 6! = 720 different ways.
The Shapley-Shubik Index of the Labour party is calculated by summing the contributions of the Labour party across all possible orderings and dividing by the total number of orderings:
Shapley-Shubik Index of the Labour party = (575 * 720) / 5040
= 82.142
Therefore, the Shapley-Shubik Index of the Labour party is 82.142.
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Given question is incomplete, the complete question is below
A (simplified representation of) the 2019 British parliament was as a weighted voting system [326 : 316,259,35,12,12,10,6]. The Conservative party had 316 votes, the Labour party had 259 votes, and various other parties had the remaining votes.
(a) The Shapley-Shubik Index of the Conservative party is 3360/5040. Justify this calculation.
(b) Compute the Shapley-Shubik Index of the Labour party.
Mr. D. decided to invest $2,500 into a share of his friend's company because his
friend guaranteed that his money would increase at a rate of 14% every month.
How much money should Mr. D have after 7 months?
hhheeelllppp.........
p(s) = 40 + 12d Rewrite the equation for 8a function notation .
Answer:
Function notation means to replace y= into f(x)=. So I think that it would be f(x) = 40 +12d.
Step-by-step explanation:
A spinner has 10 congruent sections labeled with colors as shown. If the spinner is spun twice, what is the probability that the first spin will land on
yellow and the second spin will land on green?
The congruent 10 - labeled color spinner isn't attached and could not be found.
However, we could solve the problem hypothetically.
Answer:
Kindly check explanation
Step-by-step explanation:
The events here are independent events :
Probability = required outcome / Total possible outcomes
Total possible outcomes = number of divisions on spinner = 10
Required outcome = number of specified color
Therefore, Probability that first spin lands on yellow :
Number of yellow divisions on spinner / total number of divisions
Let number of yellow divisions = 3
Therefore. Probability that first spin lands in yellow = 3 / 10
Probability that second spin lands on green :
Number of green divisions on spinner / total number of divisions
Let number of green divisions = 2
Therefore. Probability that first spin lands on green = 2 / 10
P(first) * P(second)
3/10 * 2/10 = 3/10 * 1/5 = 3/50
Recall ; this is an hypothetical situation and not the original problem.
The probability that the first spin will land on yellow and the second spin will land on green is; 2/5
Conditional Probability Problem
The spinner is missing but from online search, it is discovered that from the 10 congruent sections labeled, the colors are as follows;
Yellow - 2 sections
Green - 2 sections
Red - 3 sections
Blue - 3 sections
Thus, probability of getting yellow on first spin is;
P(yellow on first spin) = 2/10
Probability of getting green on second spin is;
P(green on second spin) = 2/10
Thus, probability that the first spin will land on yellow and the second spin will land on green is;
P(1st on yellow and 2nd on green) = 2/10 + 2/10
P(1st on yellow and 2nd on green) = 2/5
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Solve the system of equations given below.
Answer:
The system of this equation is ( -1, 10) which is Option A.
Step-by-step explanation:
Solve for y in the first equation.
[tex]y = - 5x + 5 \\ - 2y = - x - 21[/tex]
Replace all occurrences of yy with -5x+5 in each equation.
[tex]10x - 10 = - x - 21 \\ y = - 5x + 5[/tex]
Solve for x in the first equation.
[tex]x = - 1 \\ y = - 5x + 5[/tex]
Replace all occurrences of x with -1 in each equation.
[tex]y = 10 \\ x = - 1[/tex]
The solution to the system is the complete set of ordered pairs that are valid solutions.
(−1, 10)
Hence, the system of this equation is (-1, 10).
Option A.
(a) Suppose there are two classes into which we can classify a new value of the item. The probability that a classifier correctly allocates a new object is p = 0.7, and therefore 0.3 is the probability of making an error. To improve the classification accuracy, several independent classifiers may be used to classify the new value.
(i) Suppose there are three classifiers used to allocate a new object. If a majority deci- sion is made, what is the probability that the new object will be correctly classified?
(ii) By increasing the number of classifiers, the classification accuracy can be further improved. Use R to calculate the probabilities of correct classifications when the number of classifiers are 3,5,7,..., 29 (odd numbers from 3 to 29). Graph these probabilities.
(i) When using three classifiers with a majority decision, the probability of correctly classifying the new object is 0.973.
(ii) The probability of correct classification increases as the number of classifiers increases
How to calculate the probability(i) All three classifiers make the correct classification: p * p * p = 0.7 * 0.7 * 0.7 = 0.343.
Two classifiers make the correct classification and one classifier makes an error:
(p * p * q) + (p * q * p) + (q * p * p) = 3 * (0.7 * 0.7 * 0.3) = 0.441.
One classifier makes the correct classification and two classifiers make errors:
(p * q * q) + (q * p * q) + (q * q * p) = 3 * (0.7 * 0.3 * 0.3)
= 0.189.
The probability of the new object being correctly classified is the sum of these probabilities:
0.343 + 0.441 + 0.189
= 0.973.
(ii) The probability of correct classification increases as the number of classifiers increases. This is because the probability of a majority decision being correct is the probability that at least two of the classifiers make the correct decision. The more classifiers there are, the more likely it is that at least two of them will make the correct decision.
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If Erwin makes $23,440 a year, what does
he make each month?
Answer: 1,953
Step-by-step explanation:
23,440 divided by 12
{67, 68, 68, 71, 73, 73, 73, 74, 74, 74, 74, 75, 75, 77, 78, 79, 79, 80, 80}
What is the mean of the data?
1,412
862
79
74
Answer:
the answer is 1,412
Step-by-step explanation:
all you do is add all the numbers together
I will mark branlist if you give a full explanation