Dorothy Wagner is currently selling 80 "I ♥ Calculus" T-shirts per day, but sales are dropping at a rate of 2 per day. She is currently charging $7 per T-shirt, but to compensate for dwindling sales, she is increasing the unit price by $1 per day. How fast, and in what direction, is her daily revenue currently changing?

Step-by-step explanation:

8p + 5 = 6p + 1

8p - 6p = 1 - 5

2p = - 4

p = - 4/2

p = -2

Hope it will help :)

Final answer:

Austin receives roughly 2.33 pounds of rice for every dollar spent. At Cheng's Bike Rentals, a customer gets 0.25 hours (or 15 minutes) of bike use for every dollar spent.

Explanation:

To solve the questions about how many pounds of rice Austin gets per dollar and how many hours of bike use a customer gets per dollar at Cheng's Bike Rentals, we need to perform a simple division.

Calculate Rice per Dollar:

Austin bought 7 pounds of rice for $3. To find out how many pounds of rice he gets per dollar, you divide the total pounds of rice by the total cost in dollars:

7 pounds ÷ 3 dollars = 2.33 pounds of rice per dollar.

Calculate Bike Rental Time per Dollar:

At Cheng's Bike Rentals, it costs $36 to rent a bike for 9 hours. To find how many hours of bike use a customer gets per dollar, divide the total hours by the total cost in dollars:

9 hours ÷ 36 dollars = 0.25 hours of bike use per dollar, or 15 minutes per dollar.

Final answer:

Explanation of pounds of rice and hours of bike use per dollar

Explanation:

The ratio of pounds of rice to dollars:

7 pounds of rice for $3

7/3 pounds per dollar

The ratio of hours of bike use to dollars:

36 to rent a bike for 9 hours

9/36 hours per dollar

Answer:

18.4 kilograms

Step-by-step explanation:

Since we know that both classes recycled the same amount, and together they recycled a total of 36.8 kilograms, this means we can simply divide the total (36.8 kg) by two, to get how much each class recycled.

To find out how much each class recycled, you divide the total amount, 36.8 kilograms, evenly by the number of classes, 2. This results in each class recycling 18.4 kilograms of paper.

In this Mathematics scenario, we are essentially dividing the total amount of waste recycled, 36.8 kilograms, into two equal parts because there are two classes that contributed to this total equally. To find the amount recycled by each class, we could use division.

To calculate, we divide the total amount of waste, 36.8 kilograms, by the number of classes, which is 2. This division looks like this: 36.8 ÷ 2. If you carry out this calculation, the result is 18.4. So, each fifth-grade class recycled 18.4 kilograms of paper this week.

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Answer:

In converting a mixed number to an improper fraction, you would have to multiply the denominator to the whole number, once you do that you have to add the product to the numerator. The denominator would still stay the same.

A. 1 7/16 = 23/16

B. 11 5/9 = 104/9

C. 30 5/7 = 215/7

D. 10 10/13 = 140/13

E. 24 3/5 = 123/5

F. 129 1/2 = 259/2

~hope this helps~

To convert mixed numbers to improper fractions, multiply the whole number part by the denominator of the fraction, add the numerator, and keep the denominator the same. Examples include converting 1 7/16 to 23/16 and 11 5/9 to 104/9.

To change each mixed number into an equal improper fraction, you should follow a consistent method. This involves multiplying the whole number by the denominator of the fraction part and then adding the numerator of the fraction part. The resulting sum becomes the numerator of the improper fraction, with the denominator remaining the same as in the original fraction.

a. 1 7⁄16: Multiply 1 by 16 (the denominator) = 16, then add 7 (the numerator) = 23. Thus, 1 7⁄16 equals 23/16.

b. 11 5⁄9: Multiply 11 by 9 = 99, then add 5 = 104. So, 11 5⁄9 equals 104/9.

c. 30 5⁄7: Multiply 30 by 7 = 210, then add 5 = 215. Therefore, 30 5⁄7 equals 215/7.

d. 10 10⁄13: Multiply 10 by 13 = 130, add 10 = 140. Hence, 10 10⁄13 is 140/13.

e. 24 3⁄5: Multiply 24 by 5 = 120, add 3 = 123. Thus, 24 3⁄5 equals 123/5.

f. 129 1⁄2: Multiply 129 by 2 = 258, add 1 = 259. Therefore, 129 1⁄2 is 259/2.

Answer:

✔ wrote as addition of the additive inverse

✔ wrote terms as addition of opposite

✔ grouped like terms

✔ combined like terms

The expression is subtracted and the equivalent value is -9x³ + 6x + (-10).

Given data:

To find the difference between -3x³ + 5x² + 4x - 7 and 6x³ - 2x + 3, Lorne would follow these steps:

(-3x³) + 5x² + 4x + (-7) + (-6x³) + 2x + (-3)

Here, Lorne is combining like terms by grouping the variables and constants separately.

[(-3x³ + (-6x³))] + [(5x² + 2x)] + [(-7 + (-3))]

This step involves simplifying the expressions within each set of parentheses.

On simplifying the equation:

A = -9x³ + 6x + (-10)

Hence , the equation is A = -9x³ + 6x + (-10).

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Answer:

Option A) 0.038

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 100

Number of of bags of tortilla chips that contain more than the label states, x = 18

Sample proportion:

[tex]\hat{p} = \dfrac{x}{n} = \dfrac{18}{100} = 0.18[/tex]

Formula for standard of error:

[tex]\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

Putting the values, we get:

[tex]\sqrt{\dfrac{0.18(1-0.18)}{100}} =0.038[/tex]

Thus, the correct answer is

Option A) 0.038

Answer:

The total cost is $100

Step-by-step explanation:

To find the total cost, we take the average cost times the number of items

12.50*8 =100

The total cost is $100

Answer:

The answer is 1.5625

Step-by-step explanation:

use division to found this answer

Answer:

C) Reject [tex]H_0[/tex] if t < -1.711

Step-by-step explanation:

We are given that a certain chemical pollutant in the Arkansas River has been constant for several years with mean μ = 34 ppm (parts per million).

Also, it is given that the level of significance is 0.05 and a sample size of 25 is taken.

Let [tex]\mu[/tex] =  average chemical pollutant in the Arkansas River

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 24 ppm     {means that the average is same as before with improved filtration devices}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 24 ppm      {means that they have lowered the average with improved filtration devices}

Now, t test statistics is given by; T.S.  =  [tex]\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, n = sample size = 25

n - 1 = degree of freedom = 25 - 1 = 24

Now, at 0.05 significance level in the t table, the critical value at 24 degree of freedom is given as - 1.711 for left tailed test.

So, we will reject our null hypothesis when the t test statistics is less than the critical value of t which means reject null hypothesis if t < -1.711.

Answer:

a) 93 customers

b) 27 customers

Step-by-step explanation:

Total number of customers (n) = 214

Checking (C) = 189

Regular Savings (R) = 73

Market Savings (M) = 114

Checking and Regular (C&R) = 69

a) The total number of customers is given by:

[tex]n = C+R+M-C\cap R-C\cap M\\214=189+73+114-69-C\cap M\\C\cap M = 93[/tex]

93 customers have both checking and money market savings accounts

b) The number of customers with savings accounts is given by:

[tex]C = C_{only} +C\cap R+C\cap M\\189=C_{only} +69+93\\C_{only} = 27[/tex]

27 customers have a checking account but no savings account.

The frequency has the most flights from the airlines is C. Yellow jet, going east.

The frequency table is a table that's used to illustrate the data that's given.

In this case, the frequency has the most flights from the airlines will be Yellow jet, going east. This is because most people are going in that direction.

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The joint frequency with the most flights is yellow jets going east.

Option C is the correct answer.

Joint frequency refers to the number of observations that fall in each category when we have two categorical variables.

We have,

To determine which joint frequency has the most flights, we need to look for the highest value in the table.

From the table,

We can see that the highest value is 35, which represents the number of yellow jets going east.

Therefore,

The joint frequency with the most flights is yellow jets going east.

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Answer:

740°

Step-by-step explanation:

2 *360° + 20° = 720° + 20° = 740°

Answer:

BFD

Step-by-step explanation:

The measure of BFD refers to the angle measurement in a geometric figure formed by points B, F, and D. It's impossible to provide a definitive answer without further context or a diagram. The measure of an angle depends on point positions in a geometrical shape and information provided.

Inquiring about the measure of BFD likely refers to the measure of an angle in a geometric shape with points labeled as B, F, and D. However, without additional information or context such as a diagram displaying details of the geometrical figure involved, it is impossible to definitively provide the exact measure of angle BFD. It's crucial to understand that the measure of an angle depends upon the positions of the points and any information given in an accompanying diagram or problem. For a closer grasp of the concept, remember that in a triangle, for instance, the sum of all angles is always 180 degrees. Thus, if two angles are given, you can determine the measure of the third angle.

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Answer:

g(25) = -336

Step-by-step explanation:

g(x) = 24(x - 39)

g(25) = 24(25 - 39)

g(25) = 600 - 936

g(25) = -336

Answer: 13

Step-by-step explanation:

1. Harry has 20/20 sweets

2. Nadia takes 7/20 sweets

3. Your left with 13/20

The fraction of the 20 sweets Harry has now is 13/20.

A fraction represents a portion of a total. This entire may refer to a place or a group of places. The Latin word "fraction," which means "to break," is the source of the English term "fraction." The distribution of food and supplies as well as the lack of a metal currency were among the mathematical issues that the Egyptians utilized fractions to solve because they were the first civilization to understand fractions.

Only verbal descriptions of a portion of the whole were used to write fractions in ancient Rome. The numerator and denominator of fractions are first written in India with one number above the other but without a line. The line used to divide the numerator and the denominator were only added by Arabs.

Given:

The total no of sweets Harry has is 20,

The no of sweets given to Nadia is 7,

So the no of sweets left = 20 -7 = 13

Hence, the faction will be,

F = No of sweets left / total no of sweets harry has

F = 13 / 20

Therefore, the 13 / 20 parts of sweets Harry has now.

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Answer:

x=-3

Step-by-step explanation:

The x values repeat and the y values are different that means its a vertical line

so it must be x=something the x value in both is -3 so

x=-3

Answer:

x=.3

Step-by-step explanation:

the x is same and y is not meaning a vertical line

Answer:

[tex]t=\frac{2.62-2.5}{\frac{1.02}{\sqrt{15}}}=0.456[/tex]    

[tex]df=n-1=15-1=14[/tex]  

[tex]p_v =P(t_{(14)}>0.456)=0.328[/tex]  

If we compare the p value and the significance level assumed [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the true mean is higher than 2.5 at 5% of significance

Step-by-step explanation:

Data given and notation  

[tex]\bar X=2.62[/tex] represent the sample mean

[tex]s=1.02[/tex] represent the sample deviation

[tex]n=15[/tex] sample size  

[tex]\mu_o =2.5[/tex] represent the value that we want to test

[tex]\alpha[/tex] represent the significance level for the hypothesis test.  

t 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 true mean is higher than 2.5, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 2.5[/tex]  

Alternative hypothesis:[tex]\mu > 2.5[/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

We can replace in formula (1) the info given like this:  

[tex]t=\frac{2.62-2.5}{\frac{1.02}{\sqrt{15}}}=0.456[/tex]    

P-value

The first step is calculate the degrees of freedom, on this case:  

[tex]df=n-1=15-1=14[/tex]  

Since is a right tailed test the p value would be:  

[tex]p_v =P(t_{(14)}>0.456)=0.328[/tex]  

Conclusion  

If we compare the p value and the significance level assumed [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the true mean is higher than 2.5 at 5% of significance

Using Chebyshev's theorem, we conclude that at least 88.9% of recent graduates have salaries between $22,800 and $30,000, given a mean salary of $26,400 and a standard deviation of $1200.

The question is asking for the minimum percentage of recent graduates who have salaries within a specific range using Chebyshev's Theorem. By definition, Chebyshev's theorem states that at least 1 - 1/k^2 of data from a sample will fall within k standard deviations from the mean, where k is any number greater than 1. The range in this question can be represented as being within 3 standard deviations from the mean (because ($30,000 - $26,400)/$1200 = 3 and ($26,400 - $22,800)/$1200 = 3). Thus, the minimum percentage of recent graduates having salaries within this range is at least 1 - (1/3^2) = 1 - 1/9 = 8/9 = 88.9%. So, at least 88.9% of the recent graduates fall within this salary range according to Chebyshev's theorem.

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Answer:

A. Negative association, not statistically significant and very weak effect size

B. Negative association, statistically significant and very weak size.

C. Positive association, statistically significant and strong effect size.

Step-by-step explanation:

Cohen's d is an effect size used to indicate the standardised difference between two means. It can be used, for example, to accompany reporting of t-test and ANOVA results. It is also widely used in meta-analysis. Cohen's d is the difference between two group means divided by the pooled standard deviation for the two groups.

A statistically significant result is a result that is always not attributed to chance attributed to chance. The probability value shows the probability of observing the difference if no difference exists.

In statistics , two variables is said to have negative association when the values of one variable seem to decrease as the values of the other variable increase. In statistics, a perfect negative association is represented by the value -1.00, while a 0.00 indicates no association.

A (number of panic attacks in the past month and neuroticism): r = - .03, not sig.

Answer: Negative association, not statistically significant and very weak effect size.

B (number of panic attacks in the past month and number of nightmares in the past month): r = - .14 (p = .05).

Answer: Negative association, statistically significant and very weak size.

C (number of nightmares in the past month and neuroticism): r = .48 (p = .003).

Answer: Positive association, statistically significant and strong effect size.

It is important to note that:

There is covariance because there is presence of significant correlation. You cannot say for a fact about temporal precedence because it is not clear if neuroticism or nightmares came first. You also can't rule out the possibility this relationship is due to a third variable, hence Dr. Moynihan cannot say that neuroticism causes nightmares.

Answer:

NUMBER 1

(i) negative direction

(ii) statistically insignificant

(iii) very small effect size

NUMBER 2

(i) negative direction

(ii) the relationship between (A) and (B) is statistically significant

(iii) small effect size

NUMBER 3

(i) positive direction

(ii) the relationship between (B) and (C) is statistically significant

(iii) large effect size

Step-by-step explanation:

Let (A) = the number of panic attacks a person experienced in the past month

(B) = the number of nightmares a person experienced in the past month

(C) = Neuroticism level

1. Association between (A) and (C)

r = -0.03, p = not significant

2. Association between (A) and (B)

r = -0.14, p = 0.05

3. Association between (B) and (C)

r = 0.48, p = 0.003

Let's now see what Cohen's Benchmark is all about.

Cohen's Benchmarks are specified for various Effect Sizes. Effect size is the quantitative measure of the magnitude (how great or small) of a certain phenomenon of scientific or psychological interest.

The terms 'small', 'medium' and 'large' are relative to another and to the particular content and research design or method. For this reason, Jacob Cohen gave conventional scales or benchmarks for effect sizes.

He set small effect size at d=0.2

This corresponds to an r of 0.1

He set medium effect size at d=0.5

This corresponds to an r of 0.3

He set large effect size at d=0.8

This corresponds to an r of 0.5

Based on this, we can now answer the questions.

1. Association between (A) and (C)

(i) Direction of the association is negative. This implies that as one variable increases, the other decreases. If plotted, the curve or graph would be downward sloping from left to right. If (A) comes first - if (A) is on the vertical axis - and (B) is on the horizontal axis, then as (A) increase, (B) will decrease.

(ii) The association is not significant, as already stated in the question. But then this means that the p-value is very high or is higher than 0.05 (same as 5%). This implies that the relationship between both variables is largely caused by chance.

* p-value is the probability that a relationship between or among variables is caused or is explainable by chance.

(iii) * r is the correlation coefficient and it shows the effect size.

According to Cohen's benchmarks,

The ES here is very small.

r = 0.03 is much smaller than r = 0.1

2. Association between (A) and (B)

(i) The direction of the association is negative. As one variable increases, the other decreases and vice versa.

(ii) Statistical significance exists. The results from the data collected (on variables (A) and (B)) are largely explained by statistics, as p=0.05

* A p-value of 0.05 (5%) or below is usually considered to describe the relationship among variables as statistically significant.

(iii) According to Cohen's benchmarks,

The ES here is small.

r = 0.14 is close to r = 0.1

3. Association between (B) and (C)

(i) The direction of the association is positive. There is no negative sign before the r value of 0.48. In this case, both variables increase simultaneously. If a graph were to be plotted, the shape of the curve would be upward sloping from left to right.

(ii) The relationship is statistically significant. The p-value of 0.003 is very small and is less than the p-value benchmark of 0.05. Hence there is very minute probability that chance explains the research results.

(iii) The ES is large, when placed on a Cohen scale. r of 0.48 is approximately r = 0.5 (to 1 decimal place) and this is the r value for which an effect size is considered to be large.

KUDOS!

To find the total area of the construction paper needed for Natalie's project, multiply the length by the width of each rectangle and add them together.

To find the total area of the construction paper needed for Natalie's project, we need to find the area of each rectangle and then add them together.

Rectangle 1:

Length = 6 inches and width = 13 1/2 inches.

To find the area, multiply the length by the width: 6 inches x 13 1/2 inches = 81 square inches.

Rectangle 2:

Length = 10 1/3 inches and width = 10 1/2 inches.

To find the area, multiply the length by the width: 10 1/3 inches x 10 1/2 inches = 108 1/3 square inches.

Total area:

Add the areas of both rectangles: 81 square inches + 108 1/3 square inches = 189 1/3 square inches.

Therefore, Natalie needs a total of 189 1/3 square inches of construction paper for her project.

Natalie needs a total of 149 square inches of construction paper for her project.

To find the total square inches of construction paper needed for Natalie's project, we calculate the area of each rectangle and then add them together.

1. Area of the first rectangle:

[tex]\( \text{Area}_1 = \text{length} \times \text{width} = 6 \times 13\frac{1}{2} \) square inches.[/tex]

2. Area of the second rectangle:

[tex]\( \text{Area}_2 = \text{length} \times \text{width} = 10\frac{1}{3} \times 10\frac{1}{2} \) square inches.[/tex]

3. Calculate the total area:

  Total area = Area of first rectangle + Area of second rectangle.

Let's compute:

1. [tex]\( \text{Area}_1 = 6 \times 13\frac{1}{2} = 6 \times \frac{27}{2} = \frac{81}{2} = 40.5 \) square inches.[/tex]

2. [tex]\( \text{Area}_2 = 10\frac{1}{3} \times 10\frac{1}{2} = \frac{31}{3} \times \frac{21}{2} = \frac{651}{6} = 108.5 \) square inches.[/tex]

3. Total area = 40.5 + 108.5 = 149 square inches.

So, Natalie needs a total of 149 square inches of construction paper for her project.

Answer:

Step-by-step explanation:

This is a binomial distribution because the probabilities are either that of success or failure.

If probability of success, p = 3/8 = 0.375, then probability of failure, q = 1 - p = 1 - 0.375 = 0.625

The formula is expressed as

P(x = r) = nCr × p^r × q^(n - r)

Where

x represent the number of successes.

p represents the probability of success.

q = represents the probability of failure.

n represents the number of trials or sample.

n = 8

13) P(x = 3) = 8C3 × 0.375^3 × 0.625^(8 - 3) = 0.28

14) P(x = 6) = 8C6 × 0.375^6 × 0.625^(8 - 6) = 0.03

15) P(x = 1) = 8C1 × 0.375^1 × 0.625^(8 - 1) = 0.11

16) P(x = 5) = 8C5 × 0.375^5 × 0.625^(8 - 5) = 0.1

17) P(x ≥ 1) = 1 - P(x < 1)

P(x < 1) = P(x = 0)

P(x = 0) = 8C0 × 0.375^0 × 0.625^(8 - 0) = 0.023

P(x ≥ 1) = 1 - 0.023 = 0.977

18) P(x ≥2) = 1 - P(x < 2)

P(x < 2) = P(x = 0) + P(x = 1)

P(x = 0) = 8C0 × 0.375^0 × 0.625^(8 - 0) = 0.023

P(x = 1) = 8C1 × 0.375^1 × 0.625^(8 - 1) = 0.11

P(x ≥ 2) = 1 - (0.023 + 0.11) = 0.867

19) P(x ≥ 6) = P(x = 6) + P(x = 7) + P(x = 8)

P(x = 6) = 8C6 × 0.375^6 × 0.625^(8 - 6) = 0.03

P(x = 7) = 8C7 × 0.375^7 × 0.625^(8 - 7) = 0.005

P(x = 8) = 8C8 × 0.375^8 × 0.625^(8 - 8) = 0.0004

P(x ≥ 6) = 0.03 + 0.005 + 0.0004 = 0.0354

20) P(x ≥ 7) = P(x = 7) + P(x = 8)

P(x ≥ 7) = 0.005 + 0.0004 = 0.0054

21) P(x ≤ 6) = 1 - P(x = 8)

P(x ≤ 6) = 1 - 0.0004 = 0.9996

22) P(x ≤ 6) = 1 - [P(x = 7) + P(x = 8)]

P(x ≤ 6) = 1 - (0.005 + 0.0004) = 0.9946

The probabilities are listed below:

If each trial represents an independent event, then the probability of success of a given number of consecutive trials ([tex]p_{T}[/tex]) in defined by the following formula:

[tex]p_{T} = p^{n}[/tex] (1)

Where:

If we know that [tex]p = \frac{3}{8}[/tex], then the probabilities associated to a given number of trials:

1) 3 successes

[tex]p_{3} = \left(\frac{3}{8} \right)^{3}[/tex]

[tex]p_{3} = \frac{27}{512}[/tex]

The probability of success of exactly 3 successes is 5.27 %.

2) 6 successes

[tex]p_{6} = \left(\frac{3}{8} \right)^{6}[/tex]

[tex]p_{6} = \frac{729}{262144}[/tex]

The probability of success of exactly 6 successes is 0.28 %.

3) 1 success

[tex]p_{1} = \frac{3}{8}[/tex]

The probablity of success of exactly 1 success is 37.5 %.

4) 5 successes

[tex]p_{5} = \left(\frac{3}{8} \right)^{5}[/tex]

[tex]p_{5} = \frac{243}{32768}[/tex]

The probablity of success of exactly 5 successes is 0.74 %.

5) At least 1 success

The probability of success of at least 1 success is at most 37.5 %.

6) At least 2 successes

The probability of success of at least 2 successes is at most 14.1 %.

7) At least 6 successes

The probablity of success of at least 6 successes is at most 0.28 %.

8) At least 7 successes

The probability of success of at least 7 successes is at most 0.10 %.

9) At most 7 successes

The probability of success of at most 7 successes is at least 0.10 %.

10) At most 6 successes

The probability of success of at most 6 successes is at least 0.28 %.

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Answer:

There is no enough evidence to to support the claim that Portland has more average yearly rainfall than Seattle.

Being μ1: average rainfall in Portland, μ2: average rainfall in Seattle, the null and alternative hypothesis are:

[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2 > 0[/tex]

P-value = 0.1290

As the P-value is bigger than the significance level, the effect is not significant and the null hypothesis failed to be rejected.

Step-by-step explanation:

We have to test the hypothesis of the difference between means.

The claim is that Portland has more average yearly rainfall than Seattle.

Being μ1: average rainfall in Portland, μ2: average rainfall in Seattle, the null and alternative hypothesis are:

[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2 > 0[/tex]

The significance level is 0.10.

The sample for Portland, of size n1=45, has a mean of M1=37.50 and standard deviation of s1=1.82.

The sample for Seattle, of size n1=35, has a mean of M1=37.07 and standard deviation of s1=1.68.

The difference between means is:

[tex]M_d= M_1-M_2=37.50-37.07=0.43[/tex]

The standard error for the difference between means is:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{1.82^2}{45}+\dfrac{1.68^2}{35}}=\sqrt{ 0.0736+0.0688 }=\sqrt{0.1424}\\\\\\s_{M_d}=0.3774[/tex]

We can calculate the t-statistic as:

[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{0.43-0}{0.3774}=1.1393[/tex]

The degrees of freedom are:

[tex]df=n1+n2-2=45+35-2=78[/tex]

Then, the p-value for this one-tailed test with 78 degrees of freedom is:

[tex]P-value=P(t>1.1393)=0.1290[/tex]

As the P-value is bigger than the significance level, the effect is not significant and the null hypothesis failed to be rejected.

There is no enough evidence to to support the claim that Portland has more average yearly rainfall than Seattle.

Answer: the sample size should be 39

Step-by-step explanation:

The sample mean is the point estimate for the population mean. Confidence interval is written as

Sample mean ± margin of error

Margin of error = z × σ/√n

Where

σ = population standard Deviation

n = number of samples

z represents the z score corresponding to the confidence level

From the information given,

σ = 4 minutes

Margin of error = 75 seconds. Converting to minutes, it becomes 75/60 = 1.25 minutes

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.025 = 0.975

The z score corresponding to the area on the z table is 1.96. Thus, confidence level of 95% is 1.96

Therefore,

1.25 = 1.96 × 4/√n

1.25/1.96 = 4/√n

0.6378 = 4/√n

√n = 4/0.6378 = 6.27

n = 6.27² = 39

Your question is not complete as you have not provided some details.

Please let me assume this to complete your question;

P(t) = M(t) ÷ X(t)

ANSWER:

P(t) is the ratio of the number of melanophores to the number of xanthophores per unit time.

Therefore P(t) = 1.55

Step-by-step explanation:

KEY NOTE:

I) 10% of melanophore converts to Xanthophore per unit time.

II) 40% of Xanthophore converts to melanophore per unit time.

III) 10 melanophore and 20 Xanthophore are born per unit time

IV) 10% of Xanthophore die per unit time.

STEP 1: Conversion rate to number of birth per unit time.

For M(t) 10% of 10 = 1

For X(t) 40% of 20 = 8

Therefore;

M(t) = 10 + 8 - 1 = 17

X(t) = 20 + 1 - 8 = 13

STEP 2:

10% of Xanthophore die per unit time.

10% of 20 = 2

Therefore X(t) is;

13 - 2 = 11

The total X(t) = 11

The total M(t) = 17

P(t) = M(t)/X(t) = 17÷ 11 = 1.55

Answer:

There is 95% confidence that the population proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week is between 55.9% and 74.7%.

Step-by-step explanation:

We have to answer the population proportion for Vermont.

We can only do it by a confidence interval, as we only have information from a sample.

This sample, of size n=100, has a proportion p=0.653.

The degrees of freedom are:

[tex]df=n-1=100-1=99[/tex]

We will calculate a 95% confidence interval, which for df=99 has a critical value of t of t=1.984.

The margin of error can be calculated as:

[tex]E=t*\sigma_p=t\sqrt{\dfrac{p(1-p)}{n}}=1.984\sqrt{\dfrac{0.653*0.347}{100}}\\\\\\E=1.984*\sqrt{0.00226}=1.984*0.0476=0.094[/tex]

Then, the upper and lower bounds of the confidence interval are:

[tex]LL=p-E=0.653-0.094=0.559\\\\UL=p+E=0.653+0.094=0.747[/tex]

Then, we can say that there is 95% confidence that the population proportion of people from Vermont who exercised for at least 30 minutes a day 3 days a week is between 55.9% and 74.7%.

Final answer:

The estimated population proportion of Vermont residents who exercised for at least 30 minutes a day 3 days a week is 65.3%, which is based on the sample proportion from the Gallup survey.

Explanation:

The student is asking about the population proportion for people from Vermont who exercised for at least 30 minutes a day 3 days a week based on the Gallup survey results. The survey indicated that 65.3% of the Vermont respondents exercised at the mentioned rate.

To find the value of the population proportion (population proportion), we typically use the sample proportion as an estimate. From the survey, we have that the sample proportion (p-hat) for Vermont is 65.3%, which we express as a decimal, 0.653. Assuming the sample is representative, we would estimate the population proportion to also be 0.653 or 65.3%.

It's important to note that this is an estimate based on the sample and that to infer more confidently about the entire population of Vermont, a larger sample size or additional statistical methods such as confidence intervals or hypothesis testing may be applied. Nevertheless, with the information provided, the best estimate for the population proportion of Vermont residents who exercised according to the guidelines is the sample proportion of 65.3%.

Answer:

Make a Type I error 15% of the time.

Step-by-step explanation:

The question is incomplete:

In all possible samples of size 100 she will:

Option 2 and 4 are both false because we can not estimate this probabilitites a priori.

Option 1.

The power of a test is defined as the conditional probability of rejecting the null hypothesis, given that the alternative hypothesis is true.

Then, the power of the test is complementary of the probability of failing to reject the null hypothesis, gicen that the alternative hypothesis is true. The last is the definition of the probability of a Type II error.

This means that a power of 0.85 implies a probability of (1-0.85)=0.15 of making a Type II error.

[tex]P(Type \,II\, error)=1-Power=1-0.85=0.15[/tex]

The option 1 ("Make a Type II error 5% of the time") is not precise, so it is not correct.

Option 3

The significance level is 0.05. This is also the probability of making a Type I error.

The option 3 ("Make a Type I error 5% of the time") is correct.

Answer:

The correct answer is letter "C": what-if analysis.

Explanation:

A what-if analysis is a study an individual or company makes about a certain number of events where variables are changed to determine what the outputs would be. This approach is normally implemented when there is limited information from where to make a concise decision. Then, individuals have to outline all the possible results to find out what their risks are.

Software like Microsoft Office Excel facilitates the implementation of what-if analysis.

Step-by-step explanation:

14 : 10 : 4

Divide it by 2

7 : 5 : 2

This is the simplest form because it cannot be divided further

Answer:

  D) 7.9 ft

Step-by-step explanation:

To answer this, you only need to reject the nonsense answers.

The arc length will be more than 5 ft and less than the length of 2 sides of a 5 ft square (10 ft). Only one answer choice falls in that range.

  7.9 ft

__

If you like, you can figure 1/4 of the circumference of a circle with radius 5 ft:

  C/4 = (1/4)(2π)(5 ft) = 2.5π ft ≈ 7.854 ft ≈ 7.9 ft

Answer:

D 7.9ft

Step-by-step explanation:

Answer:

(A)

[tex]P(X \geq 0.8) = \int\limits_{0.8}^{\infty} f(x) \, dx = \int\limits_{0.8}^{1} 1.25(1-x^4) \, dx = 0.08192[/tex]

(B)

Then the cumulative function would be

[tex]CF(x) = 1.25x - 0.25x^5[/tex]       if   0<x<1

0 otherwise.

Step-by-step explanation:

(A)

We are looking for the probability that the random variable X is greater than 0.8.

[tex]P(X \geq 0.8) = \int\limits_{0.8}^{\infty} f(x) \, dx = \int\limits_{0.8}^{1} 1.25(1-x^4) \, dx = 0.08192[/tex]

(B)

For any  [tex]x[/tex] you are looking for the probability [tex]P(X \geq x)[/tex]  which is

[tex]P(X \geq x) = \int\limits_{-\infty}^{x} 1.25(1-t^4) dt = \int\limits_{0}^{x} 1.25(1-t^4) dt = 1.25x - 0.25x^2[/tex]

Then the cumulative function would be

[tex]CF(x) = 1.25x - 0.25x^5[/tex]       if   0<x<1

0 otherwise.

This response provides step-by-step instructions for calculating probability density functions, cumulative distribution functions, the mean, and the variance using calculus. The solution involves probability theory, calculus, and graphing techniques.

A. To find the proportion of components that are scraped, we need to integrate the probability density function from 0.8 to 1. This can be done using calculus and you should get an answer around 0.41 if done correctly.

B. The cumulative distribution function is the integral of the probability density function. Integrating f(x) from 0 to x will give you a polynomial expression that represents F(x). You can plot this using any graphing software.

C. To find the probability that the clearance is less than 0.5 mm, evaluate the cumulative distribution function at x = 0.5. This will give you a decimal number which represents the probability.

D. The mean clearance is found by taking the expected value of the random variable, which is the integral of x * f(x) from 0 to 1. The variance is found by subtracting the square of the mean from the expected value of the square of the random variable, which is the integral of x^2 * f(x) from 0 to 1.

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Answer:

ln 2, ln 4

Step-by-step explanation:

edge 2021

Using natural logarithm properties, we will see that we can write this expression as:

Ln(2).

Here we start with the expression:

Ln(16) - Ln(8).

Here you need to remember the properties for the natural logarithm:

Then, if we apply the second property to the given expression, we can get:

Ln(16) - Ln(8) = Ln(16/8) = Ln(2).

If you want to learn more about natural logarithms, you can read:

https://brainly.com/question/3227936