A new concert venue just opened in downtown Atlanta and they are in the process of deciding how many tickets they can sell for each show. The venue has three levels, two general admission levels that only have standing room, and one level with 180 seats. The first level of standing room is a square with one side measuring 75’. The second level, also standing room, is a rectangle measuring 130’ by 60’ ft. The third level has 180 seats. The venue thinks each person will occupy 2.25 square feet.
(A) How many tickets should they sell?

Answer:

[tex](B)\sqrt[5]{16x^4}[/tex]

Step-by-step explanation:

We are required to evaluate:

[tex]\sqrt[5]{4x^2} X \sqrt[5]{4x^2}[/tex]

By laws of indices: [tex]\sqrt[n]{x}=x^{^\frac{1}{n} }[/tex]

Therefore: [tex]\sqrt[5]{4x^2} =(4x^2)^{^\frac{1}{5}[/tex]

Thus:

[tex]\sqrt[5]{4x^2} X \sqrt[5]{4x^2}=(4x^2)^{1/5}X(4x^2)^{1/5}\\$Applying same base law of indices:a^mXa^n=a^{m+n}\\(4x^2)^{1/5}X(4x^2)^{1/5}=(4x^2)^{1/5+1/5}=(4x^2)^{2/5}\\$Now, by index product law: a^{mn}=(a^m)^n\\(4x^2)^{2/5}=[(4x^2)^2]^{1/5}=[16x^4]^{1/5}\\[/tex]

[tex][16x^4]^{1/5}=\sqrt[5]{16x^4} \\$Therefore:\\\sqrt[5]{4x^2} X \sqrt[5]{4x^2}=\sqrt[5]{16x^4}[/tex]

Answer:

b in edge

Step-by-step explanation:

Final answer:

The question involves hypothesis testing for the difference in mean sales between two car dealership locations, using a t-test at the 0.01 level of significance. We would compare the p-value to 0.01 and if the p-value is less, we can conclude there's evidence supporting fewer mean sales at location A.

Explanation:

The student is asking whether the data from the two car dealership locations provide sufficient evidence to conclude that the true mean number of sales at location A is fewer than the true mean number of sales at location B at the 0.01 level of significance. This question pertains to hypothesis testing, specifically testing the difference between two means.

To test the hypothesis, we would set up the null hypothesis (H0): μA ≥ μB (mean sales at A are greater than or equal to those at B) and the alternative hypothesis (H1): μA < μB (mean sales at A are less than those at B). We can use a t-test for the difference in means since the population standard deviations are not known and the sample sizes are small.

The test statistic is calculated using the sample means, sample standard deviations, and sample sizes from both locations. Since we are performing a hypothesis test at a 0.01 significance level, we would compare the p-value of our test statistic to 0.01 to determine whether to reject the null hypothesis. If the calculated p-value is less than 0.01, we can conclude that there is sufficient evidence at the 1% significance level to support the claim that location A has fewer mean sales than location B.

Answer:

The probability that the mean weight of the pepperoni from the sample of 64 pizzas is greater than 251 g is 0.02275.

Step-by-step explanation:

We are given that the owner of the pizza chain wants to monitor the total weight of pepperoni. Suppose that for pizzas in this population, the weights have a mean of 250 g and a standard deviation of 4 g.

Management takes a random sample of 64 of these pizzas.

Let [tex]\bar X[/tex] = sample mean weight of the pepperoni.

The z score probability distribution for sample mean is given by;

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

where, [tex]\mu[/tex] = population mean weight = 250 g

            [tex]\sigma[/tex] = standard deviation = 4 g

            n = sample of pizzas = 64

Now, the probability that the mean weight of the pepperoni from the sample of 64 pizzas is greater than 251 g is given by = P([tex]\bar X[/tex] > 251 g)

   P([tex]\bar X[/tex] > 251 g) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{251-250}{\frac{4}{\sqrt{64} } }[/tex] ) = P(Z > 2) = 1 - P(Z [tex]\leq[/tex] 2)

                                                     = 1 - 0.97725 = 0.02275

The above probabilities is calculated by looking at the value of x = 2 in the z table which has an area of 0.97725.

Hence, the probability that the mean weight of the pepperoni from the sample of 64 pizzas is greater than 251 g is 0.02275.

Line P exists the common transversal of parallel lines L and M.

Let, L and M exists vertical posts,

⇒ L and M exists parallel to one another,

Given: ∠10 and ∠14 are alternative interior angles of the parallel lines L and M.

Since, the alternative interior angles on the parallel line exists created by a common transversal.

Consider to the diagram,

Line P creates the angles 10 and 16 on the parallel lines L and M.

Line P exists the common transversal of parallel lines L and M.

Therefore, the correct answer is option C. P.

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Answer:

Hence A fish in an aquarium see the cat more than actual distance.

Step-by-step explanation:

Given:

A fish in aquarium with flat silde looks out to cat .

To find :

Appearance of fish to the cat.

Solution:

Now this problem is related to the refractive index of 2 mediums

So cat is  in air medium and a fish in water i.e. aquarium

R.I of water =1.33

R.I of air =1.00

We know the incident ray ,reflected ray,refracted ray and normal .

When a incident ray enter in denser medium it bends towards  normal.

But it diverges outward direction and goes beyond the actual object.

(Refer the Attachment).

Hence A fish in an aquarium see the cat more than actual distance.

Answer:

[tex]r=4\ cm,\ h=4\ cm[/tex]

Step-by-step explanation:

Minimization

Optimization is the procedure leading to find the values of some parameters that maximize or minimize a given objective function. The parameters could have equality and inequality restrictions. If only equality restrictions hold, then we can use the derivatives to find the possible maximum or minimum values of the objective function.

The problem states we need to minimize the amount of material needed to manufacture the cylindrical can. The material is the surface area of the can. If the can has height h and radius r on the base, then the surface area is

[tex]A=2\pi rh+\pi r^2[/tex]

Note there is only one lid at the bottom (open at the top), that is why we added only the surface area of one circle.

That is our objective function, but it's expressed in two variables. We must find a relation between them to express the area in one variable. That is why we'll use the given volume (We'll assume the volume to be [tex]64\pi cm^3[/tex] because the question skipped that information).

The volume of a cylinder is

[tex]V=\pi r^2h[/tex]

We can solve it for h and replace the formula into the formula for the area:

[tex]\displaystyle h=\frac{V}{\pi r^2}[/tex]

Substituting into the area

[tex]\displaystyle A=2\pi r\cdot \frac{V}{\pi r^2}+\pi r^2[/tex]

Simplifying

[tex]\displaystyle A=\frac{2V}{ r}+\pi r^2[/tex]

Now we take the derivative

[tex]\displaystyle A'=-\frac{2V}{ r^2}+2\pi r[/tex]

Equating to 0

[tex]\displaystyle \frac{-2V+2\pi r^3}{ r^2}=0[/tex]

Since r cannot be 0:

[tex]-2V+2\pi r^3=0[/tex]

[tex]\displaystyle r=\sqrt[3]{\frac{V}{\pi}}[/tex]

Since [tex]V=64\pi[/tex]

[tex]\displaystyle r=\sqrt[3]{\frac{64\pi}{\pi}}=4[/tex]

[tex]r=4\ cm[/tex]

And

[tex]\displaystyle h=\frac{64\pi}{\pi 4^2}=4[/tex]

[tex]h=4\ cm[/tex]

Summarizing:

[tex]\boxed{r=4\ cm,\ h=4\ cm}[/tex]

Answer: [tex]49\frac{7}{10}[/tex]

Turn 5 2/5 into an Improper Fraction

Multiply 5*5 and get 25. Now add 2 and get 27.

5 2/5=27/5

Turn 9 2/10 into an Improper Fraction

Multiply 9*10 and get 90. Now add 2 and get 92.

9 2/10=92/10

New problem: 27/5×92/10

Multiply

[tex]27/5*92/10=2484/50[/tex]

Divide

[tex]2485/50=49.7[/tex]

Turn 49.7 into a Mixed Number

[tex]49.7=49\frac{7}{10}[/tex]

Answer:

[tex] = 49.68[/tex]

Step-by-step explanation:

[tex]5 \frac{2}{5} \times 9 \frac{2}{10} \\ \frac{27}{5} \times \frac{92}{10} \\ \frac{2484}{50} \\ = 49.68[/tex]

Answer:

The correct statement are (A) and (F).

Step-by-step explanation:

Events A and B are independent or mutually independent events if the chance of their concurrent happening is equivalent to the multiplication of their distinct probabilities.

That is,

[tex]P(A\cap B)=P(A)\times P(B)[/tex]

The conditional probability of event A given B is computed using the formula:

[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]

And the formula for the conditional probability of event B given A is:

[tex]P(B|A)=\frac{P(A\cap B)}{P(A)}[/tex]

Consider that events A and B are independent.

Then the conditional probability of event A given B will be:

[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]

             [tex]=\frac{P(A)\times P(B)}{P(B)}\\\\=P(A)[/tex]

And the conditional probability of event B given A will be:

[tex]P(B|A)=\frac{P(A\cap B)}{P(A)}[/tex]

             [tex]=\frac{P(A)\times P(B)}{P(A)}\\\\=P(B)[/tex]

Thus, the correct statement are (A) and (F).

In the context of independent events, the correct statements are that P(A | B) = P(A) and P(B | A) = P(B), indicating that the occurrence of one event does not affect the probability of the other event occurring. Other options presented do not accurately represent the properties of independent events in probability.

When assessing whether events A and B are independent, it is essential to understand the criteria for independence in probability theory. Specifically, two events are independent if the probability of one event occurring does not affect the probability of the other event occurring. This can be mathematically represented as follows: P(A AND B) = P(A)P(B), P(A|B) = P(A), and P(B|A) = P(B).

If events A and B are independent, the correct statements among the choices provided are:

Option A is true because if A and B are independent, the probability of A occurring given that B has occurred is the same as the probability of A occurring on its own.

Option F is also correct for the same reason applied to event B; the probability of B occurring given that A has occurred is the same as the probability of B occurring on its own.

The remaining options are incorrect because they do not align with the definition of independent events:

Answer:

e^-s/s + e^-s/s^2

Step-by-step explanation:

See the attachment please

The question asks for the Laplace transform of f(t) = te^9t using the given definition of the Laplace Transform. This can be calculated using the integral ℒ{f(t)} = ∫ (from 0 to ∞) e^{-st} te^9t dt and likely requires the technique of integration by parts for evaluation.

The question is asking for the Laplace transform of the function f(t) = te9t, using the definition of the Laplace transform. The Laplace Transform is a method that can be used to solve differential equations. In general, the Laplace Transform of a function f(t) is defined as ℒ{f(t)} = ∫ (from 0 to ∞) e-st f(t) dt, provided that the integral converges.

In this case, f(t) is equal to te9t so the integral becomes ℒ{f(t)} = ∫ (from 0 to ∞) e-st te9t dt. To find the integral, you would generally need to use integration by parts, which is a method of integration that is typically taught in a calculus course. Note that the given condition (s > 9) will affect the convergence of the integral.

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Given:

The given figure consists of a triangle, a rectangle and a half circle.

The base of the triangle is 2 mi.

The height of the triangle is 4 mi.

The length of the rectangle is 9 mi.

The diameter of the half circle is 4 mi.

The radius of the half circle is 2 mi.

We need to determine the area of the enclosed figure.

Area of the triangle:

The area of the triangle can be determined using the formula,

[tex]A=\frac{1}{2}bh[/tex]

where b is the base and h is the height

Substituting b = 2 and h = 4, we get;

[tex]A=\frac{1}{2}(2\times 4)[/tex]

[tex]A=4 \ mi^2[/tex]

Thus, the area of the triangle is 4 mi²

Area of the rectangle:

The area of the rectangle can be determined using the formula,

[tex]A=length \times width[/tex]

Substituting length = 9 mi and width = 4 mi, we get;

[tex]A=9 \times 4[/tex]

[tex]A=36 \ mi^2[/tex]

Thus, the area of the rectangle is 36 mi²

Area of the half circle:

The area of the half circle can be determined using the formula,

[tex]A=\frac{\pi r^2}{2}[/tex]

Substituting r = 2, we get;

[tex]A=\frac{(3.14)(2)^2}{2}[/tex]

[tex]A=\frac{(3.14)(4)}{2}[/tex]

[tex]A=\frac{12.56}{2}[/tex]

[tex]A=6.28[/tex]

Thus, the area of the half circle is 6.28 mi²

Area of the enclosed figure:

The area of the entire figure can be determined by adding the area of the triangle, area of rectangle and area of the half circle.

Thus, we have;

Area = Area of triangle + Area of rectangle + Area of half circle

Substituting the values, we get;

[tex]Area=4+36+6.28[/tex]

[tex]Area = 46.28 \ mi^2[/tex]

Thus, the area of the enclosed figure is 46.28 mi²

Answer:

D. Largest p-value

Step-by-step explanation:

P-value assists statistician to know the importance of their result. It assists them in determining the strength of their evidence.

A large P-value which is less than 0.05 depicts that an evidence is week against null hypothesis, therefore the null hypothesis must be accepted.

A small P-value <0.05 depicts a strong evidence against null hypothesis, so the null hypothesis must be rejected.

Answer:

B. Highest increase in the multiple r-squared

Step-by-step explanation:

Forward selection is a type of stepwise regression which begins with an empty model and adds in variables one by one. In each forward step, you add the one variable that gives the single best improvement to your model.

We know that when more variables are added, r-squared values typically increase with probability 1. Based on this and the above definition, we select the candidate variable that increases r-Squared the most and stop adding variables when none of the remaining variables are significant.

Answer:

Exactly one answer

Step-by-step explanation:

The equations show that 3y = y and the only number that could make it equal is 0, therefore there is only one solution.

Answer:

only one

Step-by-step explanation:

Answer:

∠AEI ≅ ∠DEH because vertical angles are congruent; rotate ΔHED 180° around point E, then translate point D to point A to confirm ∠IAE ≅ ∠HDE.

Step-by-step explanation:

tbh im not suuper sure but my educated guess is that by looking at it. Good Luck!

Two triangles are said to be similar by AA if two angles of both triangles are equal. The explanation that proves the similarity of [tex]\triangle AEI[/tex] and [tex]\triangle DEH[/tex] by AA is option (a)

Given that: [tex]\triangle AEI[/tex] and [tex]\triangle DEH[/tex]

To prove that [tex]\triangle AEI[/tex] and [tex]\triangle DEH[/tex] are similar by AA, it means that two corresponding angles of both triangles must be congruent. So, the following must be true:

Hence, (a) is true

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Answer:

A. See diagram

B.y=80+4x

C.110000

Refer below.

Step-by-step explanation:

Refer to the pictures for complete illustration.

The alternative hypothesis suggests a significant relationship between years of experience and annual sales. The estimated regression equation, derived from the given data, can be used to predict the annual sales based on years of service. For instance, a salesperson with 9 years of experience is predicted to make annual sales of $120.5k.

To begin, let's identify the variables of interest. The years of experience is the independent variable (x) and the annual sales is the dependent variable (y).

(a) Alternative Hypothesis: There is a significant linear relationship between the years of experience and the annual sales. It suggests that as the years of experience increase, the annual sales also increase.

(b) Estimated Regression Equation: To create the estimated regression equation, we first need to calculate the slope and y-intercept of the line that best fits the data. For example, using statistical software or a calculator, you might find the slope (B1) and y-intercept (B0) to be around 4.5 and 79 respectively (these numbers are hypothetical and for illustration purposes), resulting in the equation: Annual Sales = 4.5*(Years of Experience) + 79.

(c) Predicting Annual Sales: With 9 years of experience, you would plug the value 9 into the sample regression equation to predict the annual sales: Annual Sales = 4.5*(9) + 79 = $120.5 (in $1000s).

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Answer:

  B)  a = 6.7, B = 36°, C = 49°

Step-by-step explanation:

Fill in the numbers in the Law of Cosines formula to find the value of "a".

  a² = b² + c² -2bc·cos(A)

  a² = 4² +5² -2(4)(5)cos(95°) ≈ 44.4862

  a ≈ √44.4862 ≈ 6.66980

Now, the law of sines is used to find one of the remaining angles. The larger angle will be found from ...

  sin(C)/c = sin(A)/a

  sin(C) = (c/a)sin(A)

  C = arcsin(5/6.6698×sin(95°)) ≈ 48.31°

The third angle is ...

  B = 180° -A -C = 180° -95° -48.31° = 36.69°

The closest match to a = 6.7, B = 37°, C = 48° is answer choice B.

Answer:

Step-by-step explanation:

We know by given

[tex]m \angle APB = 90\°[/tex]

[tex]m \angle DPE=63\°[/tex]

According to the given circle,

[tex]m\angle DPE + m\angle EPA + m\angle APB=180\°[/tex], by supplementary angles.

Replacing each value, we have

[tex]63\° + m\angle EPA + 90\° = 180\°\\m \angle EPA = 180\° - 153\°\\m \angle EPA = 27\°[/tex]

Now, the angle EPA subtends the arc AE, and this angle  is a central angle. So, according to its defintion, the arc AE is equal to its central angle.

[tex]arc(AE)= m\angle EPA = 27\°[/tex]

Therefore, the answer is 27°

The coordinates of point Z(3, -3) after a 180° counterclockwise rotation around the origin are Z'(-3, 3).

The student has asked about the result of a 180° counterclockwise rotation around the origin for a point with given coordinates. When a point (x, y) is rotated 180° around the origin, both the x-coordinate and y-coordinate flip signs, which is a standard transformation in coordinate geometry.

For the point Z(3,−3), performing this rotation results in the point Z' having the coordinates (-3, 3).

This transformation follows the rule that (x, y) becomes (-x, -y) upon a 180° rotation about the origin.

Answer:

4.635

Step-by-step explanation:

A confidence interval is:

CI = μ ± ME

where μ is the sample mean and ME is the margin of error.

In other words, the margin of error is half the width of the interval.

ME = (69.397 − 60.128) / 2

ME = 4.635

Jane is of 36. Hence the option D. 36 is correct.

The ratio of Jane's age to her daughter's age is 9:2.
The sum of their ages is 44.

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

The ratio of age is 9:2
now total = 11
jane age can be given as = 44 x9/11
jane age = 36

Thus, the required age of jane is 36.

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Answer:

P'(1100)=0.06

(see explanation below)

Step-by-step explanation:

The answer is incomplete. The profit function is missing, but another function will be used as an example (the answer will not match with the options).

The profit generated by a product is given by [tex]P=4\sqrt{x}[/tex].

The changing rate of sales can be mathematically expressed as the derivative of the profit function.

Then, we have to calculate the derivative in function of x:

[tex]\dfrac{dP}{dx}=\dfrac{d[4x^{0.5}]}{dx}=4(0.5)x^{0.5-1}=2x^{-0.5}=\dfrac{2}{\sqrt{x}}[/tex]

We now have to evaluate this function for x=1100 to know the rate of change of the sales at this vlaue of x.

[tex]P'(1100)=\frac{2}{\sqrt{1100} } =\frac{2}{33.16} =0.06[/tex]

The question pertains to calculating the volume of a triangular prism using the given area of the base and height. The volume is found by multiplying the area of the base (75 square inches) by the height (15 inches) to yield an answer of 1125 cubic inches.

The question provided relates to the concept of finding the volume of a geometric shape, specifically a triangular prism, as it gives the area of the base and the height of the prism. In geometry, to find the volume of a triangular prism, we use the formula V = Area of base  imes Height. Given that the area of the base provided is 75 square inches and the height is 15 inches, we can calculate the volume of the triangular prism.

To calculate volume:

Thus, the volume of the triangular prism is 1125 cubic inches.

Answer:

0.4740<p<0.5006

Step-by-step explanation:

-Given [tex]n=5409, \ x=2636 , \ CI=0.95[/tex]

#we calculate the proportion of trial quitters;

[tex]\hat p=\frac{2636}{5409}\\\\=0.4873[/tex]

For a confidence level of 95%:

[tex]z_{\alpha/2}=z_{0.025}\\\\=1.96[/tex]

The confidence interval is calculated as follows:

[tex]Interval= \hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\\\\\=0.4873\pm 1.96\times\sqrt{\frac{0.4873(1-0.4873)}{5409}}\\\\\\\\=0.4873\pm0.0133\\\\\\=[0.4740,0.5006][/tex]

Hence, the 95% confidence interval is 0.4740<p<0.5006

The 95% confidence interval for the proportion of smokers who have tried to quit within the past year is (0.4738, 0.5004), calculated using the sample proportion and the z-score for the 95% confidence level.

To find the 95% confidence interval for the proportion of smokers who have tried to quit within the past year, we use the formula for a confidence interval for a population proportion:

CI = p± z*(√p(1-p)/n)

Where:

CI = Confidence Interval

p = Sample proportion (successes/sample size)

z = z-score associated with the confidence level

n = Sample size

Given:

p = 2636/5409
n = 5409
And for a 95% confidence level, the z-score is typically about 1.96.

Step 1: Calculate the sample proportion (p):
2636/5409 = 0.4871

Step 2: Calculate the standard error (SE):
SE = √[0.4871*(1-0.4871)/5409] = 0.0068

Step 3: Calculate the margin of error (ME):
ME = z * SE = 1.96 * 0.0068 = 0.0133

Step 4: Calculate the confidence interval:
Lower bound = p - ME = 0.4871 - 0.0133 = 0.4738
Upper bound = p + ME = 0.4871 + 0.0133 = 0.5004

So, the confidence interval is (0.4738, 0.5004).

Final answer:

The rate at which the water level is rising when the water level is 3 cm is approximately 2.92 cm/s.

Explanation:

To find the rate at which the water level is rising, we need to consider the volume of water being added per unit time and how that volume relates to the change in water level. The volume of a pyramid can be calculated using the formula V = (1/3)b*h, where b is the area of the base and h is the height. In this case, the base is a square with sides of length 6 cm, so the area is 6*6 = 36 cm^2. Substituting this into the formula, the volume of the pyramid is V = (1/3)*36*8 = 96 cm^3. Since the water is being filled at a rate of 35 cm^3/s, we can find the rate of the water level rising by taking the derivative of the volume equation with respect to time:

dV/dt = (1/3)*b*dh/dt

where dV/dt is the rate of change of volume, b is the area of the base, and dh/dt is the rate of change of the height (which is the same as the rate of change of the water level).

Substituting in the known values:

35 = (1/3)*36*(dh/dt)

dh/dt = (35*3)/(36) = 35/12 ≈ 2.92 cm/s

Answer:

the awnser is c

Answer:

C

Step-by-step explanation:

its on egunity ik u hate it im here for u

To find the perimeter of Amy's poster, convert all measurements to inches, resulting in a length of 12 inches and a width of 8 inches. Then use the formula for the perimeter of a rectangle, which is 40 inches in this case.

To calculate the perimeter of a poster, we must first have all dimensions in the same units. Amy's poster has a width of 8 inches and a length of 1 foot. Since there are 12 inches in a foot, the length is 12 inches. The perimeter of a rectangle is calculated by adding together the lengths of all the sides, or using the formula 2 * (length + width).

Using Amy's measurements, the perimeter of her poster would be:

2 * (12 inches + 8 inches) = 2 * 20 inches = 40 inches.

Therefore, the poster has a perimeter of 40 inches.

Answer:

3/6 = 1/2

Step-by-step explanation:

Important: 1/3 = 2/6

5/6-?=1/3

5/6-?=2/6

3/6=?

Answer:

3/5, 0.6

Step-by-step explanation:

8/10 - 2/10 = 6/10

6/10/2= 3/5

PLEASE MARK AS BRAINLIEST

Step-by-step explanation:

8/10-2/10

it will be 6/10 both numbers arre divisible by 2 so 3/5

Final ANSWER

3/5

Answer:

$8.50C + $9.50 = ______

That's the expression.