A 12 cm by 12 cm square piece of paper has 5 holes punched out of it. 4 of the holes are circles of radius 3 cm and 1 of the holes is a circle of radius 1 cm. The paper and punched holes can be visually interpreted as below. Determine the area of paper remaining after the holes have been punched out.

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 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].

More can be learned about linear functions at https://brainly.com/question/25537936

#SPJ1

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.

More can be learned about confidence intervals at https://brainly.com/question/25890103

#SPJ1

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.

Learn more about determining the present value at https://brainly.com/question/15904086

#SPJ1

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

Learn more on perimeter of a rectangle here: https://brainly.com/question/19819849

#SPJ1

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].

More can be learned about p-values at https://brainly.com/question/13873630

#SPJ1

Step-by-step explanation:

Help me am lost somewhere

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

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

Learn more about computations on:

brainly.com/question/4658834

#SPJ1

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

Answer:

B

Step-by-step explanation:

Not all of the pairs represent the same ratio

Answer:

Step-by-step explanation:

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.

Read more on perimeter of a rectangle here: https://brainly.com/question/17107023

#SPJ1

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:

-7 and 5

Step-by-step explanation:

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

Add them, and you get -2.

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

Read more about least-squares regression line at:

https://brainly.com/question/14563186

#SPJ1

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.

To learn more on quadratic equations: https://brainly.com/question/1863222

#SPJ1

Answer:

sorry accidentally posted

Step-by-step explanation:

will update when question comes out

The couple are owning income tax of $22,996.

What is tax?

Tax is the obligatory payment payable to the government on earnings.

In this case, the amount of tax to be paid is the sum of $9,235 plus 22% of the excess of the combined taxable income of the couple over $80,250.

Excess over $80,250=$142,800-$80,250

Excess over $80,250=$62,550

Initial tax amount=$9,235

extra tax amount=$62,550*22%

extra tax= 13,761

total tax amount=initial tax amount+ extra tax

total tax amount=$9,235+$13,761

total tax amount=$22,996

In essence, the couple would pay an initial tax of $9,235 plus an extra tax of $13,761 which gives a total tax liability of $22,996

Find out more about tax deduction and tax credit on:https://brainly.com/question/17395659

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.

Learn more about statical question in: https://brainly.com/question/11043497

#SPJ1

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)

Read more about polynomial at:

https://brainly.com/question/4142886

#SPJ1

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)

Learn more on Subject of formula here: https://brainly.com/question/1463152

#SPJ1

Answer: 0.4

Step-by-step explanation:

Consider the point (0.5, 0.8).

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

Answer:

for what lol

Step-by-step explanation:

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)

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, ∞).