To the nearest tenth of a second, how much time would it take the penny to hit the ground?

0.5 seconds
0.6 seconds
0.7 seconds
0.8 seconds

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:360 miles per minute , and 1080 in 3 minutes

Step-by-step explanation:

Final answer:

To factor a composite number into primes, divide it by its smallest divisor that is not 1, then continue dividing the quotient until all factors are prime. An example is the number 60, which factors into 2 x 2 x 3 x 5, or 2² x 3 x 5 when using exponents for the repeated factor of 2.

Explanation:

The subject of the question is to select a composite number and break down its factors until all the factors are prime. As an example, let's choose the composite number 60. Here's how you can factor it into primes:

First, note that 60 is an even number, so it is divisible by 2. Start by dividing 60 by 2 to get 30.

Now, 30 is still even, so we can divide by 2 again to get 15.

15 is divisible by 3, so when we divide it by 3, we get 5, which is a prime number.

So, the prime factorization of 60 is 2 x 2 x 3 x 5, often written using exponents for any repeated factors as 22 x 3 x 5.

Through factorization, we have converted the composite number into a product of prime factors. Each factor multiplication is a step that requires one to find two numbers that multiply to the number we are factoring and continuing this process until we reach numbers that are prime.

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:

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:

m=log 100s/S

Step-by-step explanation:

howdy!

answer is in the attachment below :)

Answer:

4 y x '  −  9 x y  −  7 y r '  +  4 x y?  +  12

Step-by-step explanation:

Simplified the expression.

<3

Answer:

4 y x ' − 9 x y − 7 y r ' + 4 x y ? + 12

Answer:

J

Step-by-step explanation:

Answer:

The height that cuts off the top 5% is 74.83 inches.

Step-by-step explanation:

We are given that in the survey, respondents were grouped by age. In the 20-29 age group, the heights were normally distributed, with a mean of 69.9 inches and a standard deviation of 3.0 inches.

Let X = heights of respondents

So, X ~ N([tex]\mu=69.9,\sigma^{2} =3^{2}[/tex])

The z-score probability distribution for normal distribution is given by;

               Z = [tex]\frac{ X -\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean height = 69.9 inches

            [tex]\sigma[/tex] = standard deviation = 3.0 inches

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, we have to find the height that cuts off the top 5%, that means;

           P(X > [tex]x[/tex]) = 0.05   {where [tex]x[/tex] is the height that cuts off top 5%}

           P( [tex]\frac{ X -\mu}{\sigma}[/tex] > [tex]\frac{ x -69.9}{3}[/tex] ) = 0.05

           P(Z > [tex]\frac{ x -69.9}{3}[/tex] ) = 0.05

Now, in the z table the critical value of X that gives the area of top 5% is given as 1.6449.

So,         [tex]\frac{ x -69.9}{3} = 1.6449[/tex]

              [tex]x -69.9= 1.6449 \times 3[/tex]

                 [tex]x[/tex] = 69.9 + 4.9347 = 74.83

Hence, the height that cuts off the top 5% is 74.83 inches.

Answer:

A

Step-by-step explanation:

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

Uta initially invest $353, if she withdraws $500 after six years with compound interest of 6% a year.

Step-by-step explanation:

The given is,

                 After six years she withdraws her total balance of $500

                 Interest rate 6 % a year ( compounded )

Step:1

          Formula to calculate the future amount with an compound interest rate,

                                      [tex]F=P(1+r)^{t}[/tex].............................(1)

        Where, F - Future worth amount

                     P - Initial investment

                      r - Rate of interest

                      t - No. of years

Step:2

        From the given,

                   F = $500

                   r = 6%

                   t = 6 years

       Equation (1) becomes,

                           [tex]500 = P(1+0.06)^{6}[/tex]

                                  = [tex]P(1.06)^{6}[/tex]

                                  = P (1.41852)

                              [tex]P= \frac{500}{1.41852}[/tex]

                                  = 352.48

                                  ≅ 353

                              P = $353

Result:

         Uta initially invest $353, if she withdraws $500 after six years with compound interest of 6% a year.

Answer:

C- $352.48

Step-by-step explanation:

Just took test :]

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:

https://brainly.com/question/11503532

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:

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.

https://brainly.com/question/35182200

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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).

A similar problem is given at https://brainly.com/question/15297663

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:

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

X + 3 < 9

Subtract 3 from both sides:

X < 6

The answer is x < 6

Answer:

The 90% confidence interval for the mean score of all such subjects is between 39.7 and 112.7

Step-by-step explanation:

We have the standard deviation of the sample, so we use the t-distribution to build the confidence interval.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 27 - 1 = 26

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 26 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95([tex]t_{95}[/tex]). So we have T = 1.7056

The margin of error is:

M = T*s = 1.7056*21.4 = 36.50.

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 76.2 - 36.5 = 39.7

The upper end of the interval is the sample mean added to M. So it is 76.2 + 36.5 = 112.7

The 90% confidence interval for the mean score of all such subjects is between 39.7 and 112.7

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:

4/6 > 3/10

Step-by-step explanation:

4/6 < 3/10

First get a common denominator of 30

4/6 *5/5   < 3/10 *3/3

20/30 < 9/30

This is false since 20 > 9

Answer:

  17 points

Step-by-step explanation:

20% × 85 = 0.20 × 85 = 17

Jayla scored 17 points.

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:

1/2

Step-by-step explanation:

Since they have the same denominator, you can just subtract the numerators. So, 8-2=6.

6/12 can be simplified to 1/2.

Answer:

the answer is 1/2 or 0.5

Step-by-step explanation:

hope this helps!

Answer: The final answer in proper fraction is 169/9

Step-by-step explanation:

Given the expression

-6 4/9-3 2/9-82/9

Firstly let us convert all mixed fraction to proper fraction to further simplify the expression

-58/9 - 29/9 - 82/9

We now have all terms in proper fraction, we can continue by finding the LCM which is 9

= (- 58-29-82)/9

= 169/9

Answer:

a =8

Step-by-step explanation:

-5(a + 3) = -55

Distribute

-5a -15 = -55

Add 15 to each side

-5a-15+15 = -55+15

-5a = -40

Divide each side by -5

-5a/-5 = -40/-5

a = 8

Answer:

p=population of Floridians that would support the amendment

Step-by-step explanation:

we are given parameters are,

n = Sample size = 500

and p = Population proportion = 60% = 0.6  

p = the population proportion of Floridians that would the amendment.

Answer:

A

Step-by-step explanation:

The complete question is:

In order for a constitutional amendment to the Florida constitution to pass 60% of the popular vote must support the amendment. A researcher is interested in determining if the more than sixty percent of the voters would support a new amendment about higher education. The researcher asks 500 random selected potential voters if they would support the amendment. Define the parameter.

A) phat= sample proportion of 500 Floridans that would support the ammendment

B) p= population proportion of Floridans that would support the ammendment

C) phat= population proportion of Floridans that would support the ammendment

D) p= sample proportion of 500 Floridans that would support the ammendment

p is the actual probability of an event which is 0.6

phat is the value calculated from the sample observation

here a sample of 500 Floridans is taken and probability from sample is being observed.  So phat is the parameter which is the population proportion of 500 Floridans that would support the ammendment

The number in question is found by setting up the equation (x + 13) / -7 = -4, and solving for 'x'. Following order of operations and sign rules, we determine that the number is 15.

The question asks us to find a number when given that the quotient of that number increased by 13 and -7 is -4. To solve this, we set up an equation and follow the multiplication and division rules for signs and the order of operations.

Let the unknown number be 'x'. According to the problem, (x + 13) / -7 = -4. Multiplying both sides by -7 to eliminate the denominator, we get x + 13 = (-7)(-4). Applying the rule that the product of two negative numbers is positive, we simplify the right side to get x + 13 = 28. Now, we subtract 13 from both sides to isolate 'x': x = 28 - 13, which gives us x = 15.

The number in question is therefore 15.

Answer:

  a = 1

Step-by-step explanation:

The problem is written as a linear equation:

  ((1/8)^-3)a = 512

  512a = 512 . . . . simplify

  a = 1 . . . . . . . . . divide by the coefficient of a

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We suspect you might intend the exponential equation:

  (1/8)^(-3a) = 512

  512^a = 512 . . . . . simplify

  a = 1 . . . . . . . . . . . compare bases and exponents

equivalently, take the log to the base 512:

  a·1 = 1

  a = 1

Question: The question is incomplete. What need to be calculated is not included in the question. Below is the question requirement and the answer.

a) Suppose X1, X2, and X3 are independent. All three repairs must be completed on a given object. What is the mean and variance of the total repair time for this object?

Answer:

Mean = 50 minutes

Variance = 725 minutes

Step-by-step explanation:

X₁ = 50

X₂ = 60

X₃ = 40

σ₁ = 15

σ₂ = 20

σ₃ = 10

Calculating the mean E(Y) using the formula;

E(Y) = E(X₁ +X₂ +X₃)/3

        = (EX₁ + EX₂ + EX₃)/3

        = (50 + 60 + 40)/3

       = 50 minutes

Therefore, the mean of the total repair time for this object is 50 minutes

Calculating the variance V(Y) using the formula;

V(Y) = V(X₁ +X₂ +X₃)

       = E(X₁) +E(X₂) + E(X₃)

       = σ₁² + σ₂² + σ₃²

        = 15² + 20² + 10²

        = 225 + 400 + 100

         = 725 minutes

Therefore, the variance of the total repair time for this object is 725 minutes