Therefore, William needs to score a 97 on the third quiz to get an average of 90.
Average: The arithmetic mean is calculated by adding a set of integers, dividing by their count, and then taking the result. For instance, the result of 30 divided by 6 is 5, which is the average of 2, 3, 3, 5, 7, and 10.
The average test score is calculated by dividing the total score on an assessment by the total number of test-takers. As an illustration, if three students each obtained test scores of 69, 87, and 92, their combined scores would be totaled together and divided by three to yield an average of 82.6.
William needs to score "x" on the third quiz to get an average of 90.
The average of three quizzes can be calculated using the formula:
average = (sum of scores) / (number of scores)
To get an average of 90, William's total score on all three quizzes needs to be:
90 x 3 = 270
His current total score from the first two quizzes is:
85 + 88 = 173
So, to reach a total score of 270, William needs to score:
270 - 173 = 97
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In the country of Apexico, 6% of the population was unemployed in February of 2008. If there were 168,000,000 people willing and able to work in Apexico
during that month, how many people were unemployed?
A. 10,080,000
B. 28,000,000
C. 178,080,000
D. 157,920,000
The number of unemployed people in Apexico in February 2008 was 10,080,000. So, correct option is A.
To calculate the number of unemployed people in Apexico in February 2008, we can use the following formula:
Number of Unemployed = Total Population x Unemployment Rate
Substituting the given values:
Number of Unemployed = 168,000,000 x 0.06 = 10,080,000
Option A is the correct answer.
This calculation is based on the assumption that the unemployment rate is constant across the entire population of Apexico.
This calculation provides a rough estimate of the number of unemployed people in Apexico in February 2008, but it should be interpreted with caution.
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find the median of upper half
17,18,19,20,21,24,25,27
Answer: Whole thing=20.5
First half (17,18,19,20)=18.5
Second half (21,24,25,27) = 24.5
Step-by-step explanation:
eliminate numbers on both sides till you get to the middle if there is an even number add up the two numbers in the middle and divide them by 2
For example, In the whole thing, you are left with 20 and 21 so
20+21 =41/2= 20.5
For example, In the first part, you are left with 18 and 19 so
18+19 =37/2= 18.5
For example, In the first part, you are left with 24 and 25 so
24+25 =49/2= 24.5
The area of a square is defined by, A(x) = x2 - 6x + 9. What is the length of a side of the square?
The length of one side of the square is 3, as solving for "x" in the equation A(x) = x² - 6x + 9 yields (x - 3)² = 0, which has a solution of x = 3.
The area of a square is typically calculated using the formula A = s², where "s" represents the length of one side of the square.
In this problem, we are given the area of the square as A(x) = x² - 6x + 9.
To find the length of one side of the square, we need to solve for "x" in the equation A(x) = x² - 6x + 9.
Setting A(x) equal to zero
x² - 6x + 9 = 0
Factoring the quadratic
(x - 3)² = 0
Expanding the squared term
x - 3 = 0
Solving for "x"
x = 3
Therefore, the length of one side of the square is 3.
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Garret had 1/2 of pizza. He split the pizza into 5 equal pieces. What fraction of pizza was left?
Answer:Garret had 1/10 of the pizza left.
Step-by-step explanation:thats good
What is the domain of the function y = 2(x + 3)2 + 42? . a. C. { {x € Rl x > 3} b. {x € R} {x € RI* 53} {x € R| X <3} d. ER
The domain of a function y = 2(x + 3)2 + 42 is {x € R | x < 3} option d. {x € R | x < 3} means "the set of all real numbers x such that x is less than 3."
To determine the domain of the function, we need to find the set of all possible values of x that will give us a real number for y. The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the value that the function shoots out after we plug an x value in.In this case, there are no restrictions on the value of x except that the expression inside the square root (x + 3)^2 must not be negative, as taking the square root of a negative number would result in an imaginary number. Therefore, the domain of the function is all real numbers less than 3, represented as {x € R | x < 3}. The "€" symbol represents the element of or belonging to a set, so {x € R | x < 3} means "the set of all real numbers x such that x is less than 3."
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I'm
curious about why dx/dy becomes -e^-y.
how should I calculate this??
dx/dy = d/dy(-e^(-y)) = -(-e^(-y)) * 1 = e^(-y). Therefore, dx/dy is equal to e^(-y).
The derivative of a function tells you the rate at which the function is changing with respect to its independent variable. In the case of dx/dy = -e^(-y), x is a function of y, and you're trying to find the derivative of x with respect to y.
To find dx/dy, you need to use the chain rule of differentiation. The chain rule states that if y is a function of t and x is a function of y, then dx/dt = dx/dy * dy/dt.
In this case, you have x as a function of y given by x = -e^(-y). So, you can rewrite dx/dy as d/dy(-e^(-y)).
To differentiate -e^(-y) with respect to y, you can use the chain rule again. The derivative of e^(-y) with respect to y is -e^(-y) (since the derivative of e^u with respect to u is e^u), and then you need to multiply by the derivative of -y with respect to y, which is -1.
So, dx/dy = d/dy(-e^(-y)) = -(-e^(-y)) * 1 = e^(-y). Therefore, dx/dy is equal to e^(-y).
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Imagine that you are taking a multiple-choice quiz written in Icelandic and must guess randomly. Each question has 4 choices and 1 correct answer. Calculate the probability that you... answer the first question incorrectly. answer the first 2 questions incorrectly. answer the first 5 questions incorrectly. answer at least 1 of the first 5 questions correctly. (Note: Enter each answer as a fraction or as a decimal rounded to the nearest thousandth.)
The probabilities are:
- Answer the first question incorrectly: 0.750
- Answer the first 2 questions incorrectly: 0.5625
- Answer the first 5 questions incorrectly: 0.237
- Answer at least 1 of the first 5 questions correctly: 0.763
1. The probability of answering the first question incorrectly: Since there are 4 choices and only 1 is correct, the probability of choosing an incorrect answer is 3 incorrect choices out of 4 total choices. So, the probability is 3/4 or 0.750.
2. The probability of answering the first 2 questions incorrectly: For each question, the probability of answering incorrectly is 3/4. To find the combined probability, multiply the individual probabilities: (3/4) * (3/4) = 9/16 or 0.5625.
3. The probability of answering the first 5 questions incorrectly: Similarly, the combined probability is (3/4) * (3/4) * (3/4) * (3/4) * (3/4) = 243/1024 or approximately 0.237.
4. The probability of answering at least 1 of the first 5 questions correctly: Instead of calculating the probability of each possible correct scenario, it's easier to calculate the probability of answering all 5 questions incorrectly (which we've already done in step 3) and subtract that from 1. So, the probability is 1 - 0.237 = 0.763 or 763/1000.
So, the probabilities are:
- Answer the first question incorrectly: 0.750
- Answer the first 2 questions incorrectly: 0.5625
- Answer the first 5 questions incorrectly: 0.237
- Answer at least 1 of the first 5 questions correctly: 0.763
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Write x/5 = y/3 in standard form
Answer:
3x-5y=0
The standard form for linear equations in two variables is Ax+By=C, so just plug it in.
Answer:
Step-by-step explanation:
Standard form is ax+by=c
[tex]\frac{x}{5} =\frac{y}{3} \\[/tex] cross multiply to get rid of fractions
3x=5y now bring the 5y to the other side, by subtracting both sides by 5y
3x-5y=0
For a certain drug, based on standards set by the United States Pharmacopeia (USP) - an official public standards-setting authority for all prescription and over-the-counter medicines and other health care products manufactured or sold in the United States, a standard deviation of capsule weights of less than 0.8 mg is acceptable. A sample of 20 capsules was taken and the weights are provided below:
120.3 120.8 120.1 119.7 120.8
119.4 119.1 120.9 118.9 119.5
120.4 121.1 118.6 119.4 119.3
119.8 120.2 119.5 118.9 119.8
(Note: The average and the standard deviation of the data are respectively 119.8 g and 0.73 g.)
At 5% significance level, test the claim that the standard deviation of capsule weights of the drug is different from 0.8 g.
Procedure: Select an answer One mean Z Hypothesis Test One mean T Hypothesis Test One proportion Z Hypothesis Test One variance χ² Hypothesis Test
Assumptions: (select everything that applies)
Normal population
Sample size is greater than 30
The number of positive and negative responses are both greater than 10
Population standard deviation is unknown
Population standard deviation is known
Simple random sample
Step 1. Hypotheses Set-Up:
H0:H0: Select an answer p σ² μ = , where ? p μ σ is the Select an answer population proportion population standard deviation population mean and the units are ? lbs g mg kg
Ha:Ha: Select an answer μ p σ² ? > ≠ < , and the test is Select an answer Right-Tail Left-Tail Two-Tail
Step 2. The significance level α=α= %
Step 3. Compute the value of the test statistic: Select an answer z₀ f₀ χ²₀ t₀ = (Round the answer to 3 decimal places)
Step 4. Testing Procedure: (Round the answers to 3 decimal places)
CVA PVA
Provide the critical value(s) for the Rejection Region: Compute the P-value of the test statistic:
left CV is and right CV is P-value is
Step 5. Decision:
CVA PVA
Is the test statistic in the rejection region? Is the P-value less than the significance level?
? yes no ? yes no
Conclusion: Select an answer Do not reject the null hypothesis in favor of the alternative. Reject the null hypothesis in favor of the alternative.
Step 6. Interpretation:
At 5% significance level we Select an answer DO DO NOT have sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.
We cannot conclude that the standard deviation of capsule weights of the drug is different from 0.8 g.
Procedure: One variance χ² Hypothesis Test
Assumptions:
Normal population
Population standard deviation is unknown
Simple random sample
Step 1. Hypotheses Set-Up:
H0: σ² = 0.64 (null hypothesis)
Ha: σ² ≠ 0.64 (alternative hypothesis)
Step 2. The significance level α= 0.05
Step 3. Compute the value of the test statistic:
The test statistic is calculated as follows:
χ² = (n - 1) * s² / σ²
where n = 20 is the sample size, s² = 0.73² = 0.5329 is the sample variance, and σ² = 0.64 is the hypothesized population variance.
χ² = (20 - 1) * 0.5329 / 0.64 = 10.93
Step 4. Testing Procedure:
We need to find the critical value(s) for the rejection region and compute the P-value of the test statistic.
Since we are conducting a two-tailed test at a 5% significance level with 19 degrees of freedom (df = n - 1 = 20 - 1 = 19), the critical values are:
χ²(0.025, 19) = 9.24 and χ²(0.975, 19) = 32.85
The P-value for the test statistic of 10.93 with 19 degrees of freedom can be found using a chi-square distribution table or calculator. The P-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. The P-value for a two-tailed test is calculated as follows:
P-value = P(χ² > 10.93) + P(χ² < 0.417)
where P(χ² > 10.93) is the probability of obtaining a chi-square value greater than 10.93, and P(χ² < 0.417) is the probability of obtaining a chi-square value less than 0.417 (the minimum possible value for a chi-square distribution with 19 degrees of freedom).
Using a chi-square distribution table or calculator, we find:
P-value = 0.270 + 0.001 = 0.271
Step 5. Decision:
Since the test statistic of 10.93 is greater than the critical value of 9.24, we reject the null hypothesis. Alternatively, since the P-value of 0.271 is greater than the significance level of 0.05, we fail to reject the null hypothesis.
Conclusion:
At 5% significance level, we do not have sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis. Therefore, we cannot conclude that the standard deviation of capsule weights of the drug is different from 0.8 g.
Complete question: 0.8 mg is acceptable. A sample of 20 capsules was taken and the weights are provided below:
120.3 120.8 120.1 119.7 120.8
119.4 119.1 120.9 118.9 119.5
120.4 121.1 118.6 119.4 119.3
119.8 120.2 119.5 118.9 119.8
(Note: The average and the standard deviation of the data are respectively 119.8 g and 0.73 g.)
At 5% significance level, test the claim that the standard deviation of capsule weights of the drug is different from 0.8 g.
Procedure: Select an answer One mean Z Hypothesis Test One mean T Hypothesis Test One proportion Z Hypothesis Test One variance χ² Hypothesis Test
Assumptions: (select everything that applies)
Normal population
Sample size is greater than 30
The number of positive and negative responses are both greater than 10
Population standard deviation is unknown
Population standard deviation is known
Simple random sample
Step 1. Hypotheses Set-Up:
H0:H0: Select an answer p σ² μ = , where ? p μ σ is the Select an answer population proportion population standard deviation population mean and the units are ? lbs g mg kg
Ha:Ha: Select an answer μ p σ² ? > ≠ < , and the test is Select an answer Right-Tail Left-Tail Two-Tail
Step 2. The significance level α=α= %
Step 3. Compute the value of the test statistic: Select an answer z₀ f₀ χ²₀ t₀ = (Round the answer to 3 decimal places)
Step 4. Testing Procedure: (Round the answers to 3 decimal places)
CVA PVA
Provide the critical value(s) for the Rejection Region: Compute the P-value of the test statistic:
left CV is and right CV is P-value is
Step 5. Decision:
CVA PVA
Is the test statistic in the rejection region? Is the P-value less than the significance level?
? yes no ? yes no
Conclusion: Select an answer Do not reject the null hypothesis in favor of the alternative. Reject the null hypothesis in favor of the alternative.
Step 6. Interpretation:
At 5% significance level we Select an answer DO DO NOT have sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.
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shat is % of 80 = 4 ?
Answer:
5% is the answer I think
Step-by-step explanation:
I hope this helps
Answer:
5
Step-by-step explanation:
Y= 4/80
4/80 * 100/100 = 5/100
Y= 5
In a certain county in 2013, it was thought that 50% of men 50 years old or older had never been screened for prostate cancer. Suppose a random sample of 200 of these men shows that 160 of them had never been screened. What is the observed proportion of men who said they had not been screened?
The observed proportion of men who said they had not been screened is 0.8 or 80%.
Proportion calculationThe observed proportion of men who had not been screened can be calculated by dividing the number of men who had not been screened (160) by the total sample size (200):
Observed proportion of yet-to-be-screened men = number of unscreened men/ total sample size.
Observed proportion = 160/200 = 0.8
Therefore, the observed proportion of men who said they had not been screened is 0.8 or 80%.
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Ava has a collection of 48 fiction books and 22 nonfiction books. She has 18 total books that are signed by their author. There are 40 fiction books
that are unsigned.
Complete the two-way frequency table to show the number of each type of book in Ava's collection.
The required two-way frequency table is given below:
How to solveGiven, the number of fiction books
, number of non-fiction books
, number of signed books
, and number of unsigned fiction books
.
We need to construct the two-way frequency table based on the above information.
The required two-way frequency table is obtained as follows:
Fiction
Non-fiction
Total
Signed
(48-40)=8
(22-12)=10
18
Unsigned
40
(52-40)=12
(70-18)=52
Total
48
22
70
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(1 point) Let T be the linear transformation defined by T(x, y) = (62 - 8y, 2x – 7y,5y, Iz 9x – 3y) . Find its associated matrix A. A=
The associated matrix A of the linear transformation T is:
A =
[ 0 -8 0 62 ]
[ 2 -7 0 0 ]
[ 0 5 0 0 ]
[ 9 -3 1 0 ]
To find the associated matrix A, we need to apply T to the standard basis vectors e1 = (1,0,0,0), e2 = (0,1,0,0), e3 = (0,0,1,0), and e4 = (0,0,0,1), and write the resulting vectors in terms of the standard basis.
T(e1) = (62, 0, 0, 9)
T(e2) = (-8, 2, 5, -3)
T(e3) = (0, 0, 0, 0)
T(e4) = (0, 0, 0, 0)
Thus, the first column of A is T(e1) written in terms of the standard basis, which is (62, 0, 0, 9), the second column is T(e2) written in terms of the standard basis, which is (-8, 2, 5, -3), the third and fourth columns are T(e3) and T(e4) written in terms of the standard basis, which are (0, 0, 0, 0) and (0, 0, 0, 0) respectively.
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