Mathematics College

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: $_.

Answers

Answer 1

Answer: $77

Step-by-step explanation:

Using the given expression, we can find the total cost for all the tickets.

The question asks for the cost of 3 adults and 4 children.

Let's substitute the values for the variables(again).

We'll get

15*3+8*4(since there's 3 adults and 4 children)

= 45+32

= 77

Total: $77

Nice airpods, btw

Related Questions

Determine the interval(s) on which the given function is decreasing?

Answers

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, ∞).

Geometry question! Help!

Answers

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]

a solid sphere is cut into 12 equal wedges. the volume of each wedge is V=1/9πr^3. solve the formula for r.

Answers

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

Subject of formula

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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please help me!! i don’t understand this like at all this is algebra btw

Answers

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).

How to determine the fence's dimension?

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

P = 2(L + W)

Where:

P is the perimeter of a rectangle.L is the length of a rectangle.W is the width of a rectangle.

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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A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a function of time, in seconds, is given by
h(t) = −4.9t(squared) + 20t + 12.
How long does it take to reach maximum height? (Round your answer to three decimal places.)

Answers

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

What time does the ball take to reach 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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A cylinder and a cone have the same radius and height. The volume of the
cylinder is 639 ft3. What is the volume of the cone?

Answers

26282 because you need to cancel cancel or cancel cancel pay rent money bill pay rent pay pay for your bill card info

According to the graph, what is the value of the constant in the equation
below?
Height =
Constant
Width
A. 0.3
B. 2.2
C. 0.4
D. 1.3
Height
1.8
1.6-
1.4
0.8
0.6 +
0.4+
0.2 +
(0.5, 0.8)
(0.8, 0.5)
(1.6, 0.25)
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Width
(2,0.2)

Answers

Answer: 0.4

Step-by-step explanation:

Consider the point (0.5, 0.8).

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

You are training to compete in a 10-kilometer race, and you know the circular running trail at
your park is one mile long. How many times will you need to run this trail in order to run 10
kilometers? (round to the nearest whole number) 1 Kilometer=0.62
.

Answers

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

write an inequality to represent the graph:

Answers

Answer:

Step-by-step explanation:

PreCalc work, Need help with writing piece wise functions with graphs level 2. Giving branliest.

Answers

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

[tex]f(x) = -0.5x + 3, x < 5[/tex].[tex]f(x) = -5, x = 5[/tex][tex]f(x) = -x + 9, x > 5[/tex].

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

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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What kind of multi step do I have to do to prove a is parallel to b and m parallel to n.

Answers

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

How to prove Perpendicular and Parallel Lines?

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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What is the perimeter of a yard with length = 4 x + 6 2 x + 1 feet and width = x − 3 2 x + 1 feet? 4 x − 3 4 x + 12 feet 4 x − 3 2 x + 6 feet 8 x − 6 4 x + 12 feet 8 x − 6 2 x + 6 feet

Answers

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

Perimeter of a rectangle

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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(c) Use a calculator to verify that Σ(x) = 64, Σ(x2) = 1118, Σ(y) = 628, Σ(y2) = 87,982, and Σ(x y) = 9,627.

Compute r. (Enter a number. Round your answer to three decimal places.)

Answers

The correlation based on the computation is 0.97.

How to compute the value?

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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You are buying a house and you are financing the purchase with a mortgage of $130,000. The mortgage has a 30 year term and requires monthly payments. The mortgage charges an interest rate of 0.3% every month. What is the total interest payment over the life of the mortgage?

Answers

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)

Use the graph of the polynomial function to find the factored form of the
related polynomial. Assume it has no constant factor.

Answers

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

How to determine the factored form of the related polynomial?

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)

Answers

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.

What is the interpretation of a x% confidence interval?

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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Which graph shows the solution to the inequality lx+3l≥2 ?

Answers

Choice B

When solving absolute value equations, we solve for two conditions, positive and negative.

You need 30 quarts of water based paint to paint the interior of a house. If the price ofa gallon of paint is $22, how much will cost the paint for the interior of the house?

Answers

$164

4 quarts in a gallon

Divide 30 by 4 to get how many gallons you need

Multiply that by 22 to get the price

If in a one tail hypothesis test where H0 is not only rejected in the upper tail, the oval he = 0.0739 and Zstat = + 1.45, what is the statistical decision if the null hypothesis is tested at the .10 level of significance?
What is the statistical decision?
Reject or do not reject?

Answers

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].

What is the relation between the p-value and the conclusion of the test hypothesis?

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

If it is more, the null hypothesis is not rejected.If it is less, it is rejected.

In this problem, we have that:

The p-value is of 0.0739.The significance level is of 0.1.

Hence:

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

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Add.

−5/6+(−2 5/8)

Enter your answer as a simplified fraction by filling in the boxes.
pllzzzzz helppppp

Answers

Answer is -3 11/24
We know we have
-5/6 added to -2 5/8
First we have to make the denominator the same for both fractions. 24 is a number that is divisible by both 6 and 8. See attachment for the math.
Now we have -20/24 and -2 15/24
Combine negative numbers to add them together.
Now we have -2 35/24, you need to reduce to simplest terms. Your fraction -35/24 is an improper fraction so divide -35/24 and you get -1 11/24 so combine that with your -2 for a total of
-3 11/24

Howard and Jane are surveying their neighbors about the community garden. Their questions, written on the survey, are below:

Howard: Did you visit the garden this month?
Jane: How many times do you visit the garden in a month?

Who wrote a statistical question and why?

Jane, because there will be variability in the responses collected
Jane, because there can be only one answer to the question
Howard, because every neighbor will give the same answer
Howard, because there can be many answers to the question

Answers

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).

How to identify the statistical question?

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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Identify a pair of factors of −35 that has a sum of −2.

Answers

Answer:

-7 and 5

Step-by-step explanation:

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

Add them, and you get -2.

c= 0.99, x= 14.6, s=0.75, n = 13

Answers

Answer:

sorry accidentally posted

Step-by-step explanation:

will update when question comes out

Rewrite without parentheses.
−6w x5 (2w³ +7w¹x² – 5x²)
-
Simplify your answer as much as possible.
0

Answers

Step-by-step explanation:

Help me am lost somewhere

A theater group made appearances in two cities. The hotel charge before tax in the second city was $1500 higher than in the first. The tax in the first city was 8%, and the tax in the second city was 5%. The total hotel tax paid for the two cities was $692.50. How much was the hotel charge in each city before tax?

Answers

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

Here are the gold medal times for the women’s 100-meter freestyle (swimming) in every other Summer Olympics:

Answers

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

The scatter plot of the data

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

Describe the relationship between the variables in the graph.

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

Find the correlation coefficient.

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

X Values

∑ = 21608Mean = 1964.364∑(X - Mx)2 = SSx = 10062.545

Y Values

∑ = 686.41Mean = 62.401∑(Y - My)2 = SSy = 842.83

X and Y Combined

N = 11∑(X - Mx)(Y - My) = -2806.684

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

Find the least-squares regression line.

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

Sum of X = 21608Sum of Y = 686.41Mean X = 1964.3636Mean Y = 62.4009Sum of squares (SSX) = 10062.5455Sum of products (SP) = -2806.6836

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

The estimated gold medal time for 1924 and for 1976.

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

Why are your answers in Question 5 different than the times given in the table?

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

Find the estimated gold medal time for 2022 and for 2200.

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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Normandin Inc. has an unfunded pension liability of $575 million that must be paid in 20 years. To assess the value of the firm’s stock, financial analysts want to discount this liability back to the present. If the relevant discount rate is 6.8%, what is the present value of this liability?

Answers

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.

What is the present value?

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:

Data and Calculations:

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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does this represent quntitites that are proportional

Answers

Answer:

Step-by-step explanation:

Not all of the pairs represent the same ratio

Find x and simplify completely

Answers

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

Given the similar hexagon-based prisms pictured below, if prism 2 has a surface area of 256 cm, what is the surface area prism 1? Hint : the ratio of surface areas is the scale factor squared.

Answers

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

How to determine the surface area prism 1 using the hint that the ratio of surface areas is the scale factor squared?

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