Short RESPONSE
5. To enter an aquarium adult tickets, a cost $15 each and children tickets, c cost $8
each. The expression 15a + 8c can be used to determine the total cost (in dollars)
for a adult tickets and c children.
How much will it cost for 3 adults and 4 children to enter the aquarium
Show your work
Answer: $_.

Step-by-step explanation:

Help me am lost somewhere

Considering the p-value, the decision is described as follows:

Since the p-value is less than [tex]\alpha[/tex], we reject [tex]H_0[/tex].

Depends on if the p-value is less or more than the significance level:

In this problem, we have that:

Hence:

Since the p-value is less than [tex]\alpha[/tex], we reject [tex]H_0[/tex].

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Answer:

Step-by-step explanation:

The ball takes approximately a time of 2.041 seconds to reach its maximum height.

The height of the ball as a function of time is modelled by a quadratic equation, the required information can be found by transforming the expression into vertex form:

h = - 4.9 · t² + 20 · t + 12

h = - 4.9 · (t² - 4.082 · t - 2.449)

h + (- 4.9) · (6.615) = - 4.9 · (t² - 4.082 · t + 4.166)

h - 32.414 = - 4.9 · (t - 2.041)²

The ball takes approximately a time of 2.041 seconds to reach its maximum height.

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The correlation based on the computation is 0.97.

It should be noted that the question is that we should simply calculate the correlation which is r.

The correlation will be:

= Σ(x y) / (Σ(x²) × Σ(y²)

= 9627/✓(1118 × 87982)

= 9627 ✓98363876

= 9627/9917.86

= 0.97

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The least-squares regression line equation is y = -0.28x + 610.31

To plot the scatter plot of the data, we represent the x-axis with year and we represent the y-axis with time

Next, we plot the scatter plot using the dataset

See attachment for the scatter plot

From the attached scatter plot, we can see that the relationship between the variables in the graph is approximately linear.

This is so because the points appear to be on a straight line

To do this, we make use of a graphing calculator, with the following summary:

X Values

Y Values

X and Y Combined

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -2806.684 / √((10062.545)(842.83)) = -0.9638

Hence, the correlation coefficient is -0.9638

To do this, we make use of a graphing calculator, with the following summary:

The least-squares regression line equation is

y = bx + a

Where

b = SP/SSX = -2806.68/10062.55 = -0.27892

a = MY - bMX = 62.4 - (-0.28*1964.36) = 610.30872

So, we have

y = -0.27892x + 610.30872

Approximate

y = -0.28x + 610.31

Hence, the least-squares regression line equation is y = -0.28x + 610.31

We have:

y = -0.28x + 610.31

Substitute 1924 and 1976 for x

y = -0.28 * 1924 + 610.31 = 71.59

y = -0.28 * 1976 + 610.31 = 57.03

Are these estimates reliable?

Yes, the estimates are reliable

Are they reasonable?

Yes, the estimates are reasonable

The results are different because the answers in 5 are estimated from the formula while the table are the actual values

We have:

y = -0.28x + 610.31

Substitute 2022 and 2200 for x

y = -0.28 * 2022 + 610.31 = 44.15

y = -0.28 * 2200 + 610.31 = -5.69

Are these estimates reliable?

No, the estimates are not reliable

Are they reasonable?

The estimate in 2022 is reasonable, while the estimate in 2200 is not reasonable

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Step-by-step explanation:

x = hotel charge before tax in 1st city

y = hotel charge before tax in 2nd city

y = x + 1500

x×0.08 + y×0.05 = 692.5

why ?

a% of b = b×a/100

why ?

b = 100%

1% = 100%/100 = b/100

a% = a×1% = a×b/100 = b×a/100

so, e.g. 8% of something is that something multiplied by 8/100 or 0.08

now, we are using the first equation in the second equation :

x×0.08 + (x + 1500)×0.05 = 692.5

x×0.08 + x×0.05 + 1500×0.05 = 692.5

x×0.13 + 75 = 692.5

x×0.13 = 617.5

x = 617.5 / 0.13 = $4,750

y = x + 1500 = 4750 + 1500 = $6,250

the hotel charge before tax in the first city : $4,750

the hotel charge before tax in the second city : $6,250

Using the interpretation of the confidence interval, the correct option is:

We are 95% confident that those who studied had a higher passing rate than those who did not study.

It means that we are x% confident that the population parameter(mean/proportion/standard deviation) is between a and b.

The confidence interval of the difference is:

(0.005, 0.125).

Since the entire interval is positive, the correct option is:

We are 95% confident that those who studied had a higher passing rate than those who did not study.

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According to the information, it can be inferred that Jane's question is the one that classifies as statistical because there will be variability in the answers (option A).

A statistical question is a type of question that is used to obtain information about a specific population and its trends or preferences.

In this case the statistical question is Jane's question because there will be variability in the answers, for example you will find that some people go to the garden once and others ten times a month.

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The perimeter of the given yard is P = 10x + 6

The formula for calculating the perimeter of a rectangle is expressed as:

P = 2(l + w)

where

l is the length

w is the width

Given the following parameters

length = 4x+6

width = x-3

Substitute

P = 2(4x+6+x-3)

P = 2(5x + 3)

P = 10x + 6

Hence the perimeter of the given yard is P = 10x + 6

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The present value of this unfunded pension liability of $575 million in 20 years at a discount rate of 6.8% is $154,256,257.63.

The present value of an asset or liability refers to its future value discounted from a future period to the present period.

The present value can be computed using the PV table or formula.

We can also use an online finance calculator to determine the present value of the unfunded pension liability, as follows:

N (# of periods) = 20 years

I/Y (Interest per year) = 6.8%

PMT (Periodic Payment) = $0

FV (Future Value) = $575,000,000

Results:

PV = $154,256,257.63

Total Interest $420,743,742.37

Thus, the present value of this unfunded pension liability of $575 million in 20 years at a discount rate of 6.8% is $154,256,257.63.

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The factored form of the related polynomial is (x - 1)(x - 9)

In this question, the given parameter is the attached graph

From the graph, we can see that the curve crosses the x-axis at two different points

These points are the zeros of the polynomial function.

From the graph, the points are

x = 1 and x = 9

Set these points to 0

x - 1 = 0 and x - 9 = 0

Multiply the above equations

(x - 1)(x - 9) = 0

Remove the equation

(x - 1)(x - 9)

Hence, the factored form of the related polynomial is (x - 1)(x - 9)

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The formula, solved for r is r = ∛(9V/π)

From the question, we are to solve for r is the given formula

The given formula is

V = 1/9πr³

Multiply both sides of the equation by 9 to get

9V = πr³

Now, divide both sides by π

∴ r³ = 9V/π

r = ∛(9V/π)

Hence, the formula, solved for r is r = ∛(9V/π)

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Answer:

(-∞, -1) U (0, ∞)

Step-by-step explanation:

To figure out which parts of the function are decreasing, we need to read the graph left to right.

Given this information, we can figure out that the first part of the graph is decreasing, starts to go up a little bit, and then starts to decrease again.

How do we write this in mathematical terms, however? We simply take the x-values for which parts it decreases.

The graph started on negative infinity, and kept decreasing until -1 on the x-axis. We can write this as (-∞, -1). The graph starts to increase, which is not relevant to the question. As it starts to decrease again, it starts on 0, and slowly decreases to the right, meaning that it is going towards positive infinity. We can write this as (0,∞).

Now that we have both parts of the decreasing function, we can combine them using the union symbol (∪).

Therefore, our final answer is (-∞, -1) U (0, ∞).  

The piece-wise linear functions can be written as follows:

A linear function is modeled by:

y = mx + b

In which:

For x less than 5, the y-intercept is of b = 3 and the function also gos through (2,2), hence the slope is:

m = (2 - 3)/(2 - 0) = -0.5.

Hence the rule is:

[tex]f(x) = -0.5x + 3, x < 5[/tex].

When x = 5, the function is constant at -5, hence:

[tex]f(x) = -5, x = 5[/tex]

For x less than 5, the function goes through points (6,3) and (7,2), hence the slope is:

m = (2 - 3)/(7 - 6) = -1.

Then:

y = -x + b

When x = 6, y = 3, hence the y-intercept is given as follows:

3 = -6 + b

b = 9.

Hence the rule is:

[tex]f(x) = -x  + 9, x > 5[/tex].

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Answer: [tex]2\sqrt{2}[/tex]

Step-by-step explanation:

The inradius is given by the area of the triangle divided by the semiperimeter.

The semiperimeter is [tex]\frac{12+12+8}{2}=16[/tex].

Thus, by Heron's formula, the area is [tex]\sqrt{16(16-12)(16-12)(16-8)}=32\sqrt{2}[/tex].

Therefore, the radius is [tex]\frac{32\sqrt{2}}{16}=2\sqrt{2}}[/tex]

Answer:

130,000 -:- by 30 x 0.3 x 12 = 15,600.

Step-by-step explanation:

(I hope its right, Im not good at math)

The length and width of the fence should be made 76.25 feet and 23.75 feet respectively. Also, the expression for the length is L = 3W + 5 and the perimeter is P = 2(4W + 5).

Mathematically, the perimeter of a rectangle can be calculated by using this formula;

P = 2(L + W)

Where:

Since the length of this fence is 5 more than 3 times the width, we have:

L = 3W + 5

Substituting the given parameters into the formula, we have;

200 = 2(3W + 5 + W)

200 = 2(4W + 5)

200 = 8W + 10

8W = 190

W = 190/8

W = 23.75 feet.

For the length, we have:

L = 3W + 5

L = 3(23.75) + 5

L = 76.25 feet.

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Answer:

x = [tex]6\sqrt{3}[/tex] i

Step-by-step explanation:

We can write the following equation according to Euclidian Theorem to find the value of x:

[tex]x^{2}[/tex] = 12*9 multiply 9 and 12

[tex]x^{2}[/tex] = 108 find the root of both sides

x = [tex]6\sqrt{3}[/tex] is the value of x

Answer:

-7 and 5

Step-by-step explanation:

If you multiply -7 and 5, you get -35

Add them, and you get -2.

Answer:

6.2 rounds

Step-by-step explanation:

since 1 kilometer is 0.62 miles

10 kilometers is 6.2 miles

so about 6 and 1/5 rounds

The proof that line n is perpendicular to both a and b is proved below using definition of right angle and perpendicular transversal theorem.

We are given that;

Line a is parallel to line b

Line m is parallel to line n.

A) We want to prove that line a is perpendicular to n.

From the image, we see that there is a right angle sign on the opposite side of ∠1 facing m.

Now, we know that by definition of a right angle that ∠1 will also be a right angle.

Since angle 1 is a right angle, then we can say the line transversal a is perpendicular to line m.

B) We want to prove that line b is perpendicular to n.

The definition of the perpendicular transversal theorem, states that if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.

Thus, b will be perpendicular to n.

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Answer:

B

Step-by-step explanation:

Not all of the pairs represent the same ratio

Answer: 0.4

Step-by-step explanation:

Consider the point (0.5, 0.8).

Constant = (height)(width), which for this point, is 0.4.

Using the hint that the ratio of surface areas is the scale factor squared, the surface area of prism 1 is 36 square cm

From the figure, we have the following parameters

Prism 1 = 3 cm

Prism 2 = 8 cm

Calculate the scale ratio of dilation from prism 2 to prism 1 using the following equation

Scale ratio = Prism 1/Prism 2

Substitute the known values in the above equation

Scale ratio = 3m/8m

This gives

Scale ratio = 0.375

The surface area of prism 1 is then calculated using the following equation

Area of prism 2 = Scale ratio^2 * Area of prism 1

Substitute the known values in the above equation

Area of prism 2 = 0.375^2 * 256 square cm

Evaluate the product

Area of prism 2 = 36 square cm

Hence, the surface area of prism 1 is 36 square cm

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Answer:

sorry accidentally posted

Step-by-step explanation:

will update when question comes out