A fuel-anker's tank is long and has a diameter of seven feet. Determine the surface area of the fuel tank.

Answer:

The minimum cost of installing the cable is $156.

Step-by-step explanation:

We have an optimization problem.

We have to minimize the cost of the cable.

We will use the variable x to express the the length of cable CP and PM, accordingly to the attache picture.

The length of the cable that goes from C to P (let's call it CP) is x.

[tex]\bar{CP}=x[/tex]

Then, the length of the cable that goes from P to M (PM) can be calcualted usign the Pithagorean theorem:

[tex]\bar{PM}=\sqrt{(33-x)^2+9^2}[/tex]

The cost function Y is:

[tex]Y=4*\bar{CP}+5*\bar{PM}=4x+5\sqrt{(33-x)^2+9^2}[/tex]

To optimize this cost funtion we have to derive and equal to 0:

[tex]\dfrac{dY}{dx}=0\\\\\\\dfrac{dY}{dx}=4+5(\dfrac{1}{2})((33-x)^2+9^2)^{-1/2} *(-2)(33-x)\\\\\\\dfrac{dY}{dx}=4+5\dfrac{x-33}{\sqrt{(33-x)^2+81}}=0\\\\\\\dfrac{x-33}{\sqrt{(33-x)^2+81}}=-\dfrac{4}{5}\\\\\\(x-33)=-\dfrac{4}{5}\sqrt{(33-x)^2+81}\\\\\\(x-33)^2=(-\dfrac{4}{5})^2[(x-33)^2+81]\\\\\\(x-33)^2=\dfrac{16}{25}(x-33)^2+\dfrac{1296}{25}\\\\\\\dfrac{25-16}{25} (x-33)^2=\dfrac{1296}{25}\\\\\\9(x-33)^2=1296\\\\\\x-33=\sqrt{\dfrac{1296}{9}}=\sqrt{144}=\pm12\\\\\\x=33\pm12\\\\\\x_1=33-12=21\\\\x_2=33+12=45[/tex]

The valid solution is x=21, as x can not phisically larger than 33.

The cost then becomes:

[tex]Y=4*\bar{CP}+5*\bar{PM}=4x+5\sqrt{(33-x)^2+9^2}\\\\\\Y=4*21+5\sqrt{(33-21)^2+81}\\\\Y=81+5\sqrt{144+81}\\\\Y=81+5\sqrt{225}\\\\Y=81+5*15\\\\Y=81+75\\\\Y=156[/tex]

This optimization problem in calculus can be solved by setting up a cost function for the total cable installation, taking its derivative, setting it equal to 0 to find the critical points, which will give you the distance from C to P that minimizes cost, check this point for being minimal and calculating the minimal cost by substituting the found distance into the originally defined cost function.

The problem can be solved using the calculus principle of optimization. The situation described in your question makes a right triangle AMP. In this triangle, the vertical side (AP) measures 9 meters, and the hypotenuse (PM) represents cable installation that costs $5 per meter. The distance PC along the wall is $4 per meter. The cost of total cable installation from C -> P -> M is given as follows:

Cost = 4 * length CP + 5 * length PM

By the Pythagorean theorem, we know that [tex]PM = \sqrt{AP^2 + (33 - CP)^2}[/tex] Substituting PM into the equation, we get[tex]\text{Cost} = 4CP + 5 \cdot \sqrt{9^2 + (33-CP)^2}[/tex]

To minimize the cost, we take the derivative of the cost function and set it equal to 0 to find the critical points. Solving this equation will give you the value of CP that minimizes cost. Hence, by substituting found CP back to the original cost formula, we can find the minimal cost of installing the cable.

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Answer:

2 1/2 cups

Step-by-step explanation:

You are doubling your recipe. You would do 1 1/4 × 2. First, 1 × 2 = 2 and then 1/4 × 2 = 1/2. Put them together for your answer. I hope this helped.

Final answer:

Parker will need 2 1/2 cups of dip.

Explanation:

To find out how many cups of dip Parker will need, we can set up a proportion using the given information.

The snack mix recipe calls for 1 1/4 cups of dip and 1/2 cups of veggies.

Let's call the number of cups of dip Parker needs x.

The proportion will be: 1 1/4 cups / 1/2 cups = x cups / 1 cup.

To solve for x, we can cross multiply and then divide: (1 1/4) * 1 = (1/2) * x.

Simplifying both sides gives us 5/4 = 1/2 * x.

To isolate x, we can multiply both sides by the reciprocal of 1/2, which is 2/1: (5/4) * (2/1) = x.

Multiplying gives us x = 10/4, which simplifies to x = 2 1/2 cups.

Answer:

J

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello!

To test if calcium reduces the symptoms of PMS two independent groups of individuals are compared, the first group, control, is treated with the placebo, and the second group is treated with calcium.

The parameter to be estimated is the difference between the mean symptom scores of the placebo and calcium groups, symbolically: μ₁ - μ₂

There is no information about the distribution of both populations X₁~? and X₂~? but since both samples are big enough, n₁= 228 and n₂= 212, you can apply the central limit theorem and approximate the sampling distribution to normal X[bar]₁≈N(μ₁;δ₁²/n) and X[bar]₂≈N(μ₂;δ₂²/n)

The formula for the CI is:

[(X[bar]₁-X[bar]₂) ± [tex]Z_{1-\alpha /2}[/tex] * [tex]\sqrt{\frac{S^2_1}{n_1} +\frac{S^2_2}{n_2} }[/tex]]

95% confidence level [tex]Z_{1-\alpha /2}= Z_{0.975}= 1.96[/tex]

(a) mood swings: placebo = 0.70 ± 0.78; calcium = 0.50 ± 0.53

X₁: Mood swings score of a participant of the placebo group.

X₂: Mood swings score of a participant of the calcium group.

[(0.70-0.50) ± 1.96 * [tex]\sqrt{\frac{0.78^2}{228} +\frac{0.53^2}{212} }[/tex]]

[0.076; 0.324]

(b) crying spells: placebo = 0.39 + 0.57; calcium = 0.21 + 0.40

X₁: Crying spells score of a participant of the placebo group.

X₂: Crying spells score of a participant of the calcium group.

[(0.39-0.21) ± 1.96 * [tex]\sqrt{\frac{0.57^2}{228} +\frac{0.40^2}{212} }[/tex]]

[0.088; 0.272]

(c) aches and pains: placebo = 0.45 + 0.60; calcium = 0.37 + 0.45

X₁: Aches and pains score of a participant of the placebo group.

X₂: Aches and pains score of a participant of the calcium group.

[(0.45-0.37) ± 1.96 * [tex]\sqrt{\frac{0.60^2}{228} +\frac{0.45^2}{212} }[/tex]]

[-0.019; 0.179]

(d) craving sweets or salts: placebo = 0.60 + 0.75; calcium = 0.44 + 0.61

X₁: Craving for sweets or salts score of a participant of the placebo group.

X₂: Craving for sweets or salts score of a participant of the calcium group.

[(0.60-0.44) ± 1.96 * [tex]\sqrt{\frac{0.75^2}{228} +\frac{0.61^2}{212} }[/tex]]

[0.032; 0.287]

I hope this helps!

Using the z-distribution, the 95% confidence intervals are:

a) (0.08, 0.32).

b) (0.09, 0.27).

c) (-0.02, 0.18).

d) (0.03, 0.29).

We have to find the critical value, which is z with a p-value of [tex]\frac{1 + \alpha}{2}[/tex], in which [tex]\alpha[/tex] is the confidence level.

In this problem, [tex]\alpha = 0.95[/tex], thus, z with a p-value of [tex]\frac{1 + 0.95}{2} = 0.975[/tex], which means that it is z = 1.96.

Item a:

The standard errors are:

[tex]s_P = \frac{0.78}{\sqrt{228}} = 0.0517[/tex]

[tex]s_C = \frac{0.53}{\sqrt{212}} = 0.0364[/tex]

For the distribution of the differences, we have that:

[tex]\overline{x} = \mu_P - \mu_C = 0.7 - 0.5 = 0.2[/tex]

[tex]s = \sqrt{s_P^2 + s_C^2} = \sqrt{0.0517^2 + 0.0364^2} = 0.0632[/tex]

The interval is:

[tex]\overline{x} \pm zs[/tex]

Hence:

[tex]\overline{x} - zs = 0.2 - 1.96(0.0632) = 0.08[/tex]

[tex]\overline{x} + zs = 0.2 + 1.96(0.0632) = 0.32[/tex]

The interval is (0.08, 0.32).

Item b:

The standard errors are:

[tex]s_P = \frac{0.57}{\sqrt{228}} = 0.03775[/tex]

[tex]s_C = \frac{0.4}{\sqrt{212}} = 0.02747[/tex]

For the distribution of the differences, we have that:

[tex]\overline{x} = \mu_P - \mu_C = 0.39 - 0.21 = 0.18[/tex]

[tex]s = \sqrt{s_P^2 + s_C^2} = \sqrt{0.03775^2 + 0.02747^2} = 0.0467[/tex]

Hence:

[tex]\overline{x} - zs = 0.18 - 1.96(0.0467) = 0.09[/tex]

[tex]\overline{x} + zs = 0.18 + 1.96(0.0467) = 0.27[/tex]

The interval is (0.09, 0.27).

Item c:

The standard errors are:

[tex]s_P = \frac{0.6}{\sqrt{228}} = 0.0397[/tex]

[tex]s_C = \frac{0.45}{\sqrt{212}} = 0.0309[/tex]

For the distribution of the differences, we have that:

[tex]\overline{x} = \mu_P - \mu_C = 0.45 - 0.37 = 0.08[/tex]

[tex]s = \sqrt{s_P^2 + s_C^2} = \sqrt{0.0397^2 + 0.0309^2} = 0.0503[/tex]

Hence:

[tex]\overline{x} - zs = 0.08 - 1.96(0.0503) = -0.02[/tex]

[tex]\overline{x} + zs = 0.08 + 1.96(0.0503) = 0.18[/tex]

The interval is (-0.02, 0.18).

Item d:

The standard errors are:

[tex]s_P = \frac{0.75}{\sqrt{228}} = 0.0497[/tex]

[tex]s_C = \frac{0.61}{\sqrt{212}} = 0.0419[/tex]

For the distribution of the differences, we have that:

[tex]\overline{x} = \mu_P - \mu_C = 0.60 - 0.44 = 0.16[/tex]

[tex]s = \sqrt{s_P^2 + s_C^2} = \sqrt{0.0497^2 + 0.0419^2} = 0.065[/tex]

Hence:

[tex]\overline{x} - zs = 0.16 - 1.96(0.065) = 0.03[/tex]

[tex]\overline{x} + zs = 0.16 + 1.96(0.065) = 0.29[/tex]

The interval is (0.03, 0.29).

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Answer:

The probability is 0.503

Step-by-step explanation:

If the ghost appearances occur in the house according to a Poisson process with mean m, the time between appearances follows a exponential distribution with mean 1/m. so, the probability that the next ghost appearance happens before x hours is equal to:

[tex]P(X\leq x)=1-e^{-xm}[/tex]

Then, replacing m by 1.4 ghosts per hour we get:

[tex]P(X\leq x)=1-e^{-1.4x}[/tex]

Additionally, The exponential distribution have a memoryless property, so if it is now 1:00 p.m. and we want the probability that ghost appear before 1:30 p.m., we need to find the difference in hours from 1:00 p.m and 1:30 p.m. no matter that the last ghost appearance was at 12:35 p.m.

Therefore, there are 0.5 hours between 1:00 p.m. and 1:30 p.m, so the probability that the 7th ghost will appear before 1:30 p.m is calculated as:

[tex]P(x\leq 0.5)=1-e^{-1.4*0.5} =0.503[/tex]

Final answer:

The probability that the 7th ghost will appear before 1:30 p.m. in an old house in Pomona, CA can be calculated as approximately 0.5034, or 50.34%. This calculation is based on the Poisson distribution, with a rate of 1.4 ghosts per hour and the last ghost appearance occurring at 12:35 p.m.

Explanation:

The probability of the 7th ghost appearing before 1:30 p.m. can be calculated using the Poisson distribution. We know that the rate of ghost appearances is 1.4 ghosts per hour, which means the average time between ghost appearances is 1/1.4 hours. From 12:35 p.m. to 1:00 p.m., there are 25 minutes, or 25/60 hours. So, the probability that the 7th ghost will appear before 1:30 p.m. is equal to the probability that there will be at least 1 ghost in the remaining time, i.e., the probability that at least one ghost appears in the next 30 minutes.

We can use the complementary probability method to calculate this. The complementary probability is the probability that none of the ghosts appears in the next 30 minutes. Since the time follows a Poisson process, we can use the Poisson probability formula. Let's calculate:

Therefore, the probability that the 7th ghost will appear before 1:30 p.m. is approximately 0.5034, or 50.34%.

Answer:

Step-by-step explanation:

In statistics, linear regression is a analysis we do to describe the relationship between two variables. With this study, we pretend to know if there's a positive or negative correlation between those variables, if that correlation is strong or weak.

In a linear regression analysis, we modeled the data set using a regression equation, which is basically the line that best fits to the data set, this line is like the average where the majority of data falls. That means choice A is right.

When we use linear equations, we need to know its characteristics, and the most important one is the slope, which is the ratio between the dependent variable and the independent variable. Basically, the slope states the unit rate between Y and X, in other words, it states the amount of Y per unit of X. That means choice B is correct.

Therefore, the correct answers are A and B.

The options that are true about regression with one predictor variable include:

Regression simply refers to a statistical measurement which attempts to determine the strength that exists between a dependent variable and the independent variables.

It should be noted that in one predictor variable, the slope describes the amount of change in Y for a one-unit increase in X and the regression equation is the line that best fits a set of data as determined by having the least squared error.

Read related link on:

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Answer:

6y+8

Step-by-step explanation:

You should apply distributive property of the product, and multiply 2 by 3y and then add to that result the product of 2 times 4: [tex](3y+4)\times2= 2\times3y+2\times4=6y+8[/tex].

Answer:

m=log 100s/S

Step-by-step explanation:

howdy!

answer is in the attachment below :)

Answer:

A

Step-by-step explanation:

If you plug in the numbers to the formula, A is the correct answer.

Answer:

[tex]P(\frac{F}{E}) =\frac{0.3}{0.5} =0.6[/tex]

Step-by-step explanation:

Step 1:-

Suppose that E and F are two events and that P(E n F) = 0.3

also given P(E) =0.5

Conditional probability:-

if E₁ and E₂ are two events in a Sample S and P(E₁)≠ 0, then the probability of E₂ , after the event E₁ has occurred, is called the Conditional probability

of the event E₂ given  E₁ and is denoted by

[tex]P(\frac{F}{E}) = \frac{P(EnF)}{P(E)}[/tex]

[tex]P(\frac{F}{E}) =\frac{0.3}{0.5} =0.6[/tex]

Answer:

Read the explanation for the answers

Step-by-step explanation:

To find the midpoint, you simply need to find the average of the two endpoints. The average of 10.5 and 5.5 is 8, and the average of 4 and 4 is 4. Therefore, the center of the circle is at (4,8). The radius is the distance from the center to either of these points, or 8-5.5=2.5 units. And finally, the formula for the circle in standard form is [tex](y-8)^2+(x-4)^2=6.25[/tex]. Hope this helps!

Answer:

Check the explanation

Step-by-step explanation:

Total utility is the overall satisfaction that a particular consumer received from consuming a given overall quantity of a good or service, To calculate the value of total utility economists utilize the following basic total utility formula: TU = U1 + MU2 + MU3

Kindly check the attached image below to see the step by step explanation to the question above.

Answer: x = 10 y=20

Step-by-step explanation:

You can answer this question by plugging in each equation:

2x=y, x+y=30. Let us plug y as 2x in the second equation x+y=30

x+2x= 30

3x= 30

x=10

After we found x we can then find y by plugging the 10 for x.

2(10) = y

y =20

or you could plug in the other equation

10+y=30

subtract 10 from 30 and we get 20

to double check we can plug in both numbers

2(10) = 20 which is correct

and 10 + 20 = 30 which is correct

Answer: x^2+9 and x^2+3x+9

Step-by-step explanation:

A polynomial is prime if it cannot be factored into polynomials of lower degree. In this case, x² +9 and x² + 3x + 9 are prime polynomials while x² -9 and -2x² +8 are not.

In mathematics, a polynomial is said to be prime if it cannot be factored into polynomials of lower degree, at least one of which must be non-constant. To determine if a polynomial is prime, we try to factor it. In our case:

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Answer:

-1024

Step-by-step explanation:

Moivre's theorem allows to easily obtain trigonometric formulas that express the sine and cosine of a multiple angle as a function of the sine and cosine of a simple angle.

De Moivre's theorem can be applied to any complex number [tex]z[/tex]

Where:

[tex]z\in Z[/tex]

Let:

[tex](1+i)=z\\n=20[/tex]

According to Demoivres Theorem, If:

[tex]z=||z||(cos(\theta)+isin(\theta))[/tex]

Then:

[tex]z^n=||z||^n(cos(n\theta)+isin(n\theta))[/tex]

For a complex number [tex]z[/tex]:

[tex]z=a+bi[/tex]

Its magnitude and angle are given by:

[tex]||z||=\sqrt{a^2+b^2} \\\\\theta=arctan(\frac{b}{a} )[/tex]

So:

[tex]||z||=\sqrt{1^2+1^2} =\sqrt{2}[/tex]

[tex]\theta=arctan(\frac{1}{1} )=45^{\circ}[/tex]

Therefore, using De Moivre's theorem:

[tex]z^n=(\sqrt{2} )^{20}(cos(20*45)+isin(20*45))\\\\z^n=(\sqrt{2} )^{20}(cos(900)+isin(900))\\\\z^n=1024(-1+i(0))\\\\z^n=1024(-1)\\\\z^n=(1+i)^{20}=-1024[/tex]

C on e2020

i did it *dab*

Based on the experimental design and the data collected the statistical test that should be used is the correlation coefficient.

The statistical tests are tests that are used by researchers to determine the progress of a set process and make a quantitative decision during analysis of test results.

Example of statistical tests include the following:

The correlation coefficient which is a type of statistical test is used to assess the strength and direction of the linear relationships between pairs of variables.

Therefore, the relationship between cognitive reflectivity and cognitive impulsivity in human data can be statistically analysed using correlation coefficient.

Learn more about statistical tests here:

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Answer:

The best point estimate for the mean monthly food budget for all residents of the local apartment complex is $419.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem:

The mean of the sample is $419.

What is the best point estimate for the mean monthly food budget for all residents of the local apartment complex?

By the Central Limit Theorem(inverse, that is, sample to the population), $419.

The best point estimate for the mean monthly food budget for all residents of the local apartment complex is $419.

Answer:

[tex]n(S\cap F \cap R)=7[/tex]

Step-by-step explanation:

The Universal Set, n(U)=2092

[tex]n(S)=1232\\n(F)=879\\n(R)=114[/tex]

[tex]n(S\cap R)=23\\n(S\cap F)=103\\n(F\cap R)=14[/tex]

Let the number who take all three subjects, [tex]n(S\cap F \cap R)=x[/tex]

Note that in the Venn Diagram, we have subtracted [tex]n(S\cap F \cap R)=x[/tex] from each of the intersection of two sets.

The next step is to determine the number of students who study only each of the courses.

[tex]n(S\:only)=1232-[103-x+x+23-x]=1106+x\\n(F\: only)=879-[103-x+x+14-x]=762+x\\n(R\:only)=114-[23-x+x+14-x]=77+x[/tex]

These values are substituted in the second Venn diagram

Adding up all the values

2092=[1106+x]+[103-x]+x+[23-x]+[762+x]+[14-x]+[77+x]

2092=2085+x

x=2092-2085

x=7

The number of students who have taken courses in all three subjects, [tex]n(S\cap F \cap R)=7[/tex]

Using the principle of Inclusion-Exclusion, we find that 7 students have taken courses in all three languages: Spanish, French, and Russian.

Finding the Number of Students Taking All Three Language Courses

We can solve this problem using the principle of Inclusion-Exclusion. Let:
S = number of students taking Spanish
F = number of students taking French
R = number of students taking Russian
SF = number of students taking both Spanish and French
SR = number of students taking both Spanish and Russian
FR = number of students taking both French and Russian
SFR = number of students taking all three languages.

From the given data:

The principle of Inclusion-Exclusion states:

Total = S + F + R - SF - SR - FR + SFR
2092 = 1232 + 879 + 114 - 103 - 23 - 14 + SFR

Solving for SFR:

2092 = 2085 + SFR

Thus, SFR = 2092 - 2085 = 7

Therefore, 7 students have taken courses in all three languages: Spanish, French, and Russian.

Answer:

[tex]t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{4.94 -0}{\frac{3.901}{\sqrt{5}}}=2.832[/tex]

[tex]df=n-1=5-1=4[/tex]

[tex]p_v =P(t_{(4)}>2.832) =0.0236[/tex]

We see that the p value is lower than the significance level of 0.05 so then we have enough evidence to reject the null hypothesis and we can conclude that the average net sales improved

Step-by-step explanation:

Let put some notation  

x=test value before , y = test value after

x: 57.1 94.6 49.2 77.4 43.2

y: 63.5 101.8 57.8 81.2 41.9

The system of hypothesis for this case are:

Null hypothesis: [tex]\mu_y- \mu_x \leq 0[/tex]

Alternative hypothesis: [tex]\mu_y -\mu_x >0[/tex]

The first step is calculate the difference [tex]d_i=y_i-x_i[/tex] and we obtain this:

d: 6.4, 7.2, 8.6, 3.8, -1.3

The second step is calculate the mean difference  

[tex]\bar d= \frac{\sum_{i=1}^n d_i}{n}=4.94[/tex]

The third step would be calculate the standard deviation for the differences, and we got:

[tex]s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =3.901[/tex]

The next step is calculate the statistic given by :

[tex]t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{4.94 -0}{\frac{3.901}{\sqrt{5}}}=2.832[/tex]

The next step is calculate the degrees of freedom given by:

[tex]df=n-1=5-1=4[/tex]

Now we can calculate the p value, since we have a right tailed test the p value is given by:

[tex]p_v =P(t_{(4)}>2.832) =0.0236[/tex]

We see that the p value is lower than the significance level of 0.05 so then we have enough evidence to reject the null hypothesis and we can conclude that the average net sales improved

Answer:

-4.4m-3.2

Step-by-step explanation:

-6.4m+4(0.5m-0.8)

-6.4m+4*0.5+4*0.8

-6.4m+2m-3.2

-4.4m-3.2

Answer:

-4.4m-3.2

Step-by-step explanation:

multiply everything in the parentheses by 4 and then add.

Answer:

Null hypothesis:[tex]\mu_{A} \leq \mu_{B}[/tex]

Alternative hypothesis:[tex]\mu_{A} > \mu_{B}[/tex]

Since we dpn't know the population deviations for each group, for this case is better apply a t test to compare means, and the statistic is given by:

[tex]t=\frac{\bar X_{A}-\bar X_{B}}{\sqrt{\frac{\sigma^2_{A}}{n_{A}}+\frac{\sigma^2_{B}}{n_{B}}}}[/tex] (1)

Now we need to find the degrees of freedom given by:

[tex] df = n_A + n_B -2= 13+10-2=21[/tex]

And now since we are conducting a right tailed test we are looking ofr a value who accumulates 0.05 of the are on the right tail fo the t distribution with df =21 and we got:

[tex] t_{cric}= 1.721[/tex]

And for this case the rejection zone would be:

E. Reject H0 if t > 1.721

Step-by-step explanation:

Data given and notation

[tex]\bar X_{A}=12[/tex] represent the mean for 1

[tex]\bar X_{B}=9[/tex] represent the mean for 2

[tex]s_{A}=5[/tex] represent the sample standard deviation for 1

[tex]s_{2}=3[/tex] represent the sample standard deviation for 2

[tex]n_{1}=13[/tex] sample size for the group 1

[tex]n_{2}=10[/tex] sample size for the group 2

t would represent the statistic (variable of interest)

[tex]\alpha=0.05[/tex] significance level provided

Develop the null and alternative hypotheses for this study

We need to conduct a hypothesis in order to check if the mean for group A is higher than the mean for B:

Null hypothesis:[tex]\mu_{A} \leq \mu_{B}[/tex]

Alternative hypothesis:[tex]\mu_{A} > \mu_{B}[/tex]

Since we dpn't know the population deviations for each group, for this case is better apply a t test to compare means, and the statistic is given by:

[tex]t=\frac{\bar X_{A}-\bar X_{B}}{\sqrt{\frac{\sigma^2_{A}}{n_{A}}+\frac{\sigma^2_{B}}{n_{B}}}}[/tex] (1)

Now we need to find the degrees of freedom given by:

[tex] df = n_A + n_B -2= 13+10-2=21[/tex]

And now since we are conducting a right tailed test we are looking ofr a value who accumulates 0.05 of the are on the right tail fo the t distribution with df =21 and we got:

[tex] t_{cric}= 1.721[/tex]

And for this case the rejection zone would be:

E. Reject H0 if t > 1.721

Answer:

Test statistics = 3.74

P-value = 0.0001

Step-by-step explanation:

We are given that an experiment to compare the tension bond strength of polymer latex modified mortar to that of unmodified mortar resulted in x = 18.11 kg f/[tex]cm^{2}[/tex] for the modified mortar (m = 42) and y = 16.83 kg f/[tex]cm^{2}[/tex] for the unmodified mortar (n = 30).

Assume that the bond strength distributions are both normal and assuming that σ1 = 1.6 and σ2 = 1.3.

Let [tex]\mu_1[/tex] = true average tension bond strengths for the modified mortars

      [tex]\mu_2[/tex] = true average tension bond strengths for the unmodified mortars

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1-\mu_2=0[/tex]  or  [tex]\mu_1=\mu_2[/tex]    {means that true average tension bond strengths for the modified and unmodified mortars are same}

Alternate Hypothesis, [tex]H_a[/tex] : [tex]\mu_1-\mu_2>0[/tex]  or  [tex]\mu_1>\mu_2[/tex]    {means that the true average tension bond strengths for the modified mortars is greater than that for unmodified mortars}

The test statistics that will be used here is Two-sample z test statistics as we know about population standard deviations;

               T.S.  =  [tex]\frac{(x-y)-(\mu_1-\mu_2)}{\sqrt{\frac{\sigma_1^{2} }{m}+\frac{\sigma_2^{2} }{n} } }[/tex]  ~ N(0,1)

where, x = sample mean tension bond strengths for the modified mortars = 18.11 kg f/[tex]cm^{2}[/tex]

         y = sample mean tension bond strengths for the unmodified mortars = 16.83 kg f/[tex]cm^{2}[/tex]

         [tex]\sigma_1[/tex] = population standard deviation for modified mortars = 1.6

         [tex]\sigma_2[/tex] = population standard deviation for unmodified mortars = 1.3

         m = sample of modified mortars = 42

         n = sample of unmodified mortars = 30

So, test statistics  =  [tex]\frac{(18.11-16.83)-(0)}{\sqrt{\frac{1.6^{2} }{42}+\frac{1.3^{2} }{30} } }[/tex]

                               =  3.74

Now, P-value is given by the following formula;

         P-value = P(Z > 3.74) = 1 - P(Z [tex]\leq[/tex] 3.74)  

                                            = 1 - 0.9999 = 0.0001

Here, the above probability is calculated by looking at the value of x = 3.74 in the z table which gives an area of 0.9999.

To test the hypothesis H0: μ1 − μ2 = 0 versus Ha: μ1 − μ2 > 0 at level 0.01, calculate the test statistic and the P-value. The test statistic is Z = (x - y) / √((σ1² / m) + (σ2² / n)). Substituting the values gives Z = 1.278. The P-value is approximately 0.1019.

To test the hypothesis H0: μ1 − μ2 = 0 versus Ha: μ1 − μ2 > 0 at level 0.01, we calculate the test statistic and the P-value. The test statistic is given by:

Z = (x - y) / √((σ1² / m) + (σ2² / n))

where x = 18.11, y = 16.83, σ1 = 1.6, σ2 = 1.3, m = 42, and n = 30.

Substituting the values, we get Z = (18.11 - 16.83) / √((1.6² / 42) + (1.3² / 30)).

Calculating Z gives Z = 1.278. To determine the P-value, we find the area to the right of Z in the standard normal distribution. The P-value is the probability that Z > 1.278. Consulting a Z-table or using a calculator, we find the P-value to be approximately 0.1019.

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Answer:

H₀: p₁ - p₂ < 0.

Hₐ: p₁ - p₂ > 0.

Step-by-step explanation:

In this case, we need to determine if there is a higher incidence of smoking among women than among men in a neighborhood.

An experiment can be performed involving collecting two samples of men and women and computing the proportion of men and women smokers in the neighborhood. Then these two sample proportions can be used to determine which proportion is higher.

We are computing proportions of men and women smokers instead of the mean number of men and women smokers because the we need to determine the  incidence of smoking among men and women, i.e. the occurrence or frequency or rate of men and women smokers.

So, a two proportion test can be applied to determine whether the proportion of women smokers is higher than men.

The population proportion of women in the neighborhood is represented by p₁ and the  population proportion of men in the neighborhood is represented by p₂.

The hypothesis can be defined as:

H₀: The proportion of women smokers is not higher than men, i.e. p₁ - p₂ < 0.

Hₐ: The proportion of women smokers is higher than men, i.e. p₁ - p₂ > 0.

Final answer:

The null hypothesis (H0) should be P1 - P2 ≥ 0, indicating no higher incidence of smoking among women, and the alternative hypothesis (Ha) should be P1 - P2 < 0, suggesting a higher incidence of smoking among women.

Explanation:

When conducting a hypothesis test to determine if there's a higher incidence of smoking among women than among men in a neighborhood, you would use two hypotheses: the null hypothesis (H0) and the alternative hypothesis (Ha). Since we are looking to find if the incidence is higher in women, the null hypothesis should reflect there is no difference or that the incidence in women is less than or equal to the incidence in men. Therefore, the correct setup using population proportions (P1 for men and P2 for women) would be:

The null hypothesis statement is that the proportion of women who smoke is less than or equal to the proportion of men who smoke. The alternative hypothesis is what you intend to prove, which is that more women smoke than men in the neighborhood, hence P1 - P2 < 0. This would be considered a left-tailed test.

Answer:

C. 150 pages

Step-by-step explanation:

204 divided by 136 = 1.5

1.5 * 100 = 150

Hope it helps! :)

Answer:

Attached

Step-by-step explanation:

On a cartessian plane, we take four points as shown. Point A has coordinates as (4, 0) while point B is (32, 0). Since the y cordinates are zero, don't change, only x change. Change in x coordinates is 32-4=28 units.

Point C is (32, 12) where x has not changed when compared to point B but y changes by 12-0=12 units

Therefore, the diagram is triangle whose length is 28 units while width is 12 units.

Answer:

The amount of change he should received is

$100 - $56.875

= $43.125

= $43.13

Step-by-step explanation:

Length of window trim = 32 and 1/2 ft

Cost per foot = $1.75

Amount paid = $100

Total cost of window trim = 32.5×1.75 = $56.875

The amount of change he should received is

$100 - $56.875

= $43.125

= $43.13

Answer:

-3y=-2x+9

Step-by-step explanation:

flip the value

when flipping a value remember to invert its sign

Answer:

The relationship between price and the number of empanadas is PROPORTIONAL.

1 Empanada = 50 cent = $0.5

Constant of PROPORTIONALITY = ½

Step-by-step explanation:

From the given table:

2 Empanadas = $1

6 Empanadas = $3

We see that, as the number of Empanadas increases, the amount in Dollars also increases. Such that:

Let E = Empanadas

$ = dollar

~ = sign of PROPORTIONALITY.

Therefore:

$ ~ E

$ = KE

Where K = constant of proportionality.

When E = 4; $ = 2

$2 = K4

K= 2/4

K = ½

$ = ½E (Binding formula)

This applies for all the number of Empanadas bought.

Answer:

.50

Step-by-step explanation:

I ready