5. A ramp is to be built using a 20 foot long board and an 18 foot long board. To make die stable, the builders would like to add a third board to create a right triangle. How longed that board be, to the nearest hundredth of a foot?

The values of a, b, and c that represent the perimeter of the pool are a = 80, b = 0, and c = 100.

Step 1: Add the three dimensions together to find the total length of one side of the perimeter:
(4x^2 + 15) + (8x^2 + 10) + (8x^2) = 20x^2 + 25

Step 2: Since the perimeter has 4 equal sides (it's a rectangle), multiply the total length of one side by 4:
Perimeter = 4(20x^2 + 25) = 80x^2 + 100

Now, compare the perimeter polynomial with the general form ax^2 + bx + c:
80x^2 + 100 = ax^2 + bx + c

From this comparison, you can see that:
a = 80
b = 0 (since there is no term with x)
c = 100

So, the values of a, b, and c that represent the perimeter of the pool are a = 80, b = 0, and c = 100.

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Answer:

The correct answer is ** x(y+12) or f.

We can simplify the expression 1/5x(5y+60) by multiplying the factors in the parentheses and then dividing by 5. This gives us:

```

1/5x(5y+60) = 1/5 * 5xy + 1/5 * 60x = x(y+12)

```

The unit rate of the linear equation y = 8x is 8.

A linear equation of a function illustrates the straight line on a coordinate plane. It can be expressed in a slope intercept form y = mx + b, where:

The slope shows steep the gradient is and it is the change in the rise over the run. For a unit rate which is usually the ratio between two different quantities. We can say in the linear equation, the unit rate represents the slope of the function.

Given that:
y = 8x

To find the unit rate(slope) which is the change in the y-axis(rise) over the change in the x-axis(run) by using slope-intercept form. Then, we can conclude that the unit rate is 8.

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The difference between the costs of a hovercraft and a boat in the year 2010 was approximately $1,558.

(a) The difference in costs between a hovercraft and a boat can be expressed as follows:

Cost difference = Hovercraft cost - Boat cost

Cost difference = (-1012 + 350t + 400) - (30 + 140t)

Cost difference = -1012 + 350t + 400 - 30 - 140t

Cost difference = 220t - 642

Therefore, the difference in costs between a hovercraft and a boat can be expressed as 220t - 642.

(b) To find the difference in the year 2010, we need to substitute t = 10 in the expression we derived in part (a):

Cost difference = 220t - 642

Cost difference = 220(10) - 642

Cost difference = 2200 - 642

Cost difference = 1558

Therefore, the difference between the costs of a hovercraft and a boat in the year 2010 was approximately $1,558.

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I apologize, but I am having trouble understanding your question. Can you please provide more context and clarity? Specifically, what do you mean by "carbon monoxide wel wat" and "arts permitin"? Additionally, what city or population are you referring to? Once I have a better understanding of your question, I will do my best to provide a helpful response.
Hi! It seems like the question is asking about the prediction of carbon monoxide levels in relation to population growth. Unfortunately, the text is a bit unclear, so I'll try my best to answer based on the provided information.

The given equation for carbon monoxide levels (CO) is: CO = 0.02(2 + P), where P is the population in thousands. To find the predicted increase in CO levels after 2 years, you would need to know the population growth rate or the population for those years. Please provide more information or clarify the question, and I'll be happy to help further

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The rotation used in this problem is given as follows:

90º clockwise rotation.

The five more known rotation rules are given as follows:

A vertex and it's equivalent is given as follows:

A(1,3) and A'(3, -1).

Hence the rule is:

(x,y) -> (y, -x).

Which is the rule for a 90° clockwise rotation = 270º counterclockwise rotation.

The image is presented at the end of the answer.

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Answer:

90° clockwise rotation

Step-by-step explanation:

I did the exam and got it correct

The equation would be written as: y = $85,000(1 + 0.12/1)^5

Then the predicted earning would be y = $132,559

y=a(b)x

where y = income

a =  $85,000

b = (1 + r = percent increase)

then x = time period = 5 years

When we put in the values we would have y = $85,000(1 + 0.12/1) ^5

The exponential function of the form y = a(b)^x is: y = $85,000(1 + 0.12/1) ^5

When we solve the above, we would have the income = y = $132,559

Therefore the predicted earnings that Dans small business would have in a period of five years is equal to $132,559

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Answer:

ChatGPT

To find the balances for each type of investment after one year, we can use the formula for compound interest:

Treasury bond: A = P(1 + r/n)^(nt)

A = 0.4(30000)(1 + 0.0535/1)^(1*1) = $12,912.00

CD: A = P(1 + r/n)^(nt)

A = 0.1(30000)(1 + 0.0475/1)^(1*1) = $10,316.25

Stock plan: After the first year, 30% is still in the savings account. The other 70% is in the stock plan, which increased by 9%, so the new value is:

0.7(30000)(1 + 0.09) = $23,940.00

Savings account: A = P(1 + r/n)^(nt)

A = 0.2(30000)(1 + 0.039/1)^(1*1) = $6,351.00

To find the total gain from all of the investments combined, we need to add up the gains from each investment:

Treasury bond: $12,912.00 - $12,000.00 = $912.00 gain

CD: $10,316.25 - $9,000.00 = $1,316.25 gain

Stock plan: After the second year, the stock plan decreased in value by 5%, so the new value is:

0.7($23,940.00)(1 - 0.05) = $19,149.00

After the third year, the stock plan increased by 7%, so the final value is:

0.7($19,149.00)(1 + 0.07) = $20,129.57

The gain from the stock plan is:

$20,129.57 - $21,000.00 = -$870.43 loss (since the stock plan decreased in value overall)

Savings account: $6,351.00 - $6,000.00 = $351.00 gain

Total gain = $912.00 + $1,316.25 - $870.43 + $351.00 = $708.82

If you had invested 40% in stock and 30% in Treasury bonds, the calculations would be:

Treasury bond: A = P(1 + r/n)^(nt)

A = 0.3(30000)(1 + 0.0535/1)^(1*3) = $12,853.81

Stock plan: After the first year, 40% is still in the savings account. The other 60% is in the stock plan, which increased by 9%, so the new value is:

0.6(30000)(1 + 0.09) = $16,200.00

After the second year, the stock plan decreased in value by 5%, so the new value is:

0.6($16,200.00)(1 - 0.05) = $15,390.00

After the third year, the stock plan increased by 7%, so the final value is:

0.6($15,390.00)(1 + 0.07) = $16,019.16

Total gain = ($12,853.81 - $12,000.00) + (-$981.84) + ($1,019.16) = $890.13

Therefore, investing 40% in stock and 30% in Treasury bonds

Critical numbers: 0, -3, 3
Increasing intervals: (-∞, -3), (3, ∞)
Decreasing intervals: (-3, 0), (0, 3)

Let's analyze the given function and find the critical numbers, as well as the intervals where it is increasing or decreasing.

Function: f(x) = x^2 / (x^2 - 9)

1. Find the critical numbers:
To find the critical numbers, we need to compute the first derivative of the function and set it equal to zero or identify where it's undefined.

f'(x) = (2x(x^2 - 9) - x^2(2x)) / (x^2 - 9)^2 = (2x^3 - 18x - 2x^3) / (x^2 - 9)^2 = -18x / (x^2 - 9)^2

Setting f'(x) equal to zero:
-18x = 0
x = 0

Now, let's check where f'(x) is undefined:
x^2 - 9 = 0
x = ±3

Thus, the critical numbers are 0, -3, and 3.

2. Find the open intervals where the function is increasing or decreasing:
To determine the intervals, we will examine the sign of f'(x) in the intervals determined by the critical numbers: (-∞, -3), (-3, 0), (0, 3), (3, ∞).

Interval (-∞, -3): Choose x = -4, then f'(-4) > 0. So, f(x) is increasing on this interval.

Interval (-3, 0): Choose x = -1, then f'(-1) < 0. So, f(x) is decreasing on this interval.

Interval (0, 3): Choose x = 1, then f'(1) < 0. So, f(x) is decreasing on this interval.

Interval (3, ∞): Choose x = 4, then f'(4) > 0. So, f(x) is increasing on this interval.

Your answer:
Critical numbers: 0, -3, 3
Increasing intervals: (-∞, -3), (3, ∞)
Decreasing intervals: (-3, 0), (0, 3)

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Answer:20 feet by 10 feet

Step-by-step explanation:

If a scale model of the plane is 40.6 cm long, the scale factor used to create the model is approximately 1:142.857 or 0.007 rounded to the nearest thousandth.

To determine the scale factor used to create the model, we need to divide the length of the actual airplane by the length of the model airplane:

58 m / 40.6 cm

To perform this calculation, we need to convert the units so that they match. We can convert 58 m to cm by multiplying by 100:

58 m = 58 × 100 cm = 5800 cm

Now we can divide:

5800 cm / 40.6 cm = 142.857...

Rounding to the nearest thousandth, we get:

142.857... ≈ 142.857

Therefore, the scale factor used to create the model is approximately 1:142.857 or 0.007 rounded to the nearest thousandth.

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She is incorrect when she said that her rate increased each hour from 8 to 12 to 16 miles per hour. Her jogging rate was actually a steady 5 miles per hour.

You asked if Christy is correct when she said that her rate increased each hour, from 8 to 12 to 16 miles per hour. Let's analyze the data given in the table and see if she's right.

The table shows the distance Christy jogged and the corresponding time:
- 10 miles in 2 hours
- 15 miles in 3 hours
- 20 miles in 4 hours

To find her jogging rate for each time period, we need to divide the distance by the time.

1. For the first 2 hours:
Jogging rate = distance / time = 10 miles / 2 hours = 5 miles per hour

2. For the first 3 hours:
Jogging rate = distance / time = 15 miles / 3 hours = 5 miles per hour

3. For the first 4 hours:
Jogging rate = distance / time = 20 miles / 4 hours = 5 miles per hour

Christy's jogging rate remained constant at 5 miles per hour throughout her run. Therefore, she is incorrect when she said that her rate increased each hour from 8 to 12 to 16 miles per hour. Her jogging rate was actually a steady 5 miles per hour.

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Answer: As the Integers being positive or negative depends on the 0 As it is reference present on  the centre of the number line

Numbers on the left side are negative while that on right side being positive

Step-by-step explanation:

Since we need to round our answer to the nearest whole number, the insect population after 5 days will be approximately 367 insects.

Given the rate at which the insect population increases, we can determine the population after 5 days using the given formula: 280 + 64 + 0.9t^2 insects per day.
First, we need to substitute t with the number of days, which is 5:

280 + 64 + 0.9(5)^2

Now, calculate the value of the equation:

280 + 64 + 0.9(25) = 280 + 64 + 22.5 = 366.5

OR,

The population of insects after 5 days can be found by plugging in t = 5 into the given equation:

Population = 280 + 64 + 0.9(5)^2
Population = 280 + 64 + 22.5
Population = 366.5

Rounding to the nearest insect, the population after 5 days is 367 insects.

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a The purpose of this report is to investigate the advantages and limitations of the annual budgeting system to determine whether the elimination of the system is a good idea.

b Report on the Advantages and Limitations of an Annual Budgeting System This report investigates the advantages and limitations of an annual budgeting system. The purpose is to assess the feasibility of eliminating the annual budgeting system at Brooklane Ltd. By analyzing academic sources, we can gain insights into the potential benefits and drawbacks of such a decision.

The annual budgeting system has several advantages. Firstly, it allows organizations to set financial goals and targets for the coming year. This helps organizations to allocate resources and prioritize their spending to achieve their goals.

Limitations of an Annual Budgeting System is that despite its advantages, the annual budgeting system also has limitations. Firstly, it can be time-consuming and costly to prepare, especially for larger organizations. This can divert resources from other important areas of the organization.

In conclusion, the annual budgeting system has both advantages and limitations.

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The area of the table is approximately 651 square inches.

What is Area ?

Area is a measure of the size of a two-dimensional shape or surface, such as a rectangle, circle, or triangle. It is expressed in square units, such as square inches, square feet, or square meters.

Let's use the Pythagorean theorem to find the length of the table top:

Substituting the given values, we get:

40*40 = [tex]length^{2}[/tex] + 21*21

Simplifying and solving for length, we get:

[tex]length^{2}[/tex]= 1600 - 441

[tex]length^{2}[/tex] = 961

length = 31 inches (rounded to the nearest inch)

Now that we know the length and width of the table, we can find the area by multiplying them together:

area = length x width

area = 31 x 21

area = 651 square inches (rounded to the nearest inch)

Therefore, the area of the table is approximately 651 square inches.

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The length of the diagonal of Stacy's ceiling using the Pythagorean Theorem and trigonometry is 35.36 ft.

(a) Using the Pythagorean Theorem:

Since the ceiling is a square, we can treat it as two right triangles. Let's call the length of the diagonal 'd'. Now, we can apply the Pythagorean Theorem (a² + b² = c²) to one of the right triangles:

a² + b² = d²
25² + 25² = d²
625 + 625 = d²
1250 = d²

Now, take the square root of both sides:

√1250 = d
d ≈ 35.36 ft

(b) Using trigonometry:

In one of the right triangles, the angle between the two sides of the square (25 ft each) is 45 degrees. We can use the tangent function (tan) to relate the angle to the side lengths:

tan(45) = opposite side / adjacent side
tan(45) = 25 / 25

Since tan(45) = 1, we have 1 = 1, which confirms the angle is 45 degrees. Now, we can use the sine or cosine function to find the diagonal:

sin(45) = opposite side / hypotenuse
sin(45) = 25 / d

OR

cos(45) = adjacent side / hypotenuse
cos(45) = 25 / d

Both functions give us the same result since the angles are 45 degrees. Solving for 'd':

d = 25 / sin(45)
d ≈ 35.36 ft

So, the length of the diagonal of Stacy's ceiling is approximately 35.36 ft using both methods.

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You should choose Account 1 to obtain the greater amount in 10 years. Account 1 will have a higher balance after 10 years.

Account 1 pays 6% annual interest compounded quarterly, which means the interest is calculated and added to the principal four times a year. You can use the formula A = P(1 + r/n)^(nt) to calculate the future value, where A is the final amount, P is the principal ($2500), r is the annual interest rate (0.06), n is the number of times compounded per year (4), and t is the number of years (10).

Account 2 pays 4% annual interest compounded continuously. You can use the formula A = Pe^(rt) to calculate the future value, where A is the final amount, P is the principal ($2500), e is the base of the natural logarithm (approximately 2.71828), r is the annual interest rate (0.04), and t is the number of years (10).

When you compare the final amounts for both accounts, Account 1 will have a higher balance after 10 years.

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Answer:

Step-by-step explanation:

The Pythagorean theorem has the formula a squared(leg) + b squared(leg) = c squared(longest leg). This means [tex]12^{2} +16^{2} =20^{2} -- > 144+256=400[/tex] which is true meaning number 1 is a right triangle. [tex]10^{2} +49.5^{2} = 50.5^{2} -- > 100+2450.25=2550.25[/tex] is true meaning number 2 is also a right triangle because the sum of the shortest legs squared are equal to the longest leg (hypotenuse) squared.

The given statement:

(x + 2) + 5 = x + (2 + 5)

illustrates the associative property of addition.

There are three properties of addition : Associative, commutative and identity.

The associative property of addition states that : (a+b)+c = a + (b+c)

The commutative property of addition states that : a + b = b + a

The identity property of addition states that : a + 0 = a.

Therefore, the statement is illustrating the associative property of addition.

Answer:

Sarah will have $937.28 and Claire will have $928.

Step-by-step explanation:

All my work is provided in the screenshots that are attached to my answer! Drop questions in the comments and I'll try to respond if I remember/see them lol.

Have a great day!

Normal Distribution: Finding Values

Press the "2nd" key, then press the "vars" key to access the DISTR menu.

Scroll down to "Normalcdf" and press enter.

Enter the lower bound, upper bound, mean, and standard deviation. For example, if you want to find the probability that X is between 60 and 70, given that the mean is 65 and the standard deviation is 5, you would enter "60, 70, 65, 5".

Press enter to get the result. The calculator will give you the probability that X falls between the two values you entered.

Press the "2nd" key, then press the "vars" key to access the DISTR menu.

Scroll down to "InvNorm" and press enter.

Enter the probability you want to find. For example, if you want to find the z-score that corresponds to the 90th percentile, you would enter "0.9".

Enter the mean and standard deviation. For example, if the mean is 65 and the standard deviation is 5, you would enter "65, 5".

Press enter to get the result. The calculator will give you the z-score that corresponds to the probability you entered.

Sampling Distributions and the Central Limit Theorem: Press the "2nd" key, then press the "vars" key to access the DISTR menu.

Scroll down to "1-PropZTest" or "2-PropZTest" and press enter, depending on the type of test you want to perform.

Enter the sample statistics and the population parameters, if known. The calculator will use these values to calculate the test statistic and p-value.

Press enter to get the result. The calculator will give you the test statistic and the p-value, which you can use to make inferences about the population.

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The value of c is 21.8.

We can solve for c by simplifying the expression on the right side of the equation and equating it to the expression on the left side.

Starting with the right side, we distribute the 3 across the parentheses:

5 * 3 * (4x - 2.6) = 60x - 13

Now, we can set this equal to the expression on the left and solve for c:

21.2x + c = 60x - 13

c = 60x - 13 - 21.2x

c = 38.8x - 13

However, we are asked to find the value of c, not in terms of x. Since we were not given a specific value for x, we cannot solve for c exactly. Therefore, we can only express the value of c in terms of x, which is c = 38.8x - 13.

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There are different ways a person can make up a story about a word problem. The square root of 81 - 7 is 2. Hence the story is given below.

The hypothetical story goes like this: Mia was trying to figure out the length of the missing side of a square garden bed. She knew that the total area of the garden bed was 81 square feet. She also knew that she had already planted in a section of the garden bed that was 7 feet wide.

So, what will be the length of the missing side of the garden bed if Mia wants to make sure it is completely filled with soil. In order to solve this problem, Mia used the equation: the square root of 81-7=2. She plugged in the values she knew and solved for the missing side length. Therefore, The solution will be:= ✓81 - 7= 9 - 7= 2

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A story for the word problem is that what will be the length of the missing side of a square garden when the total area is 81 feet² and the width was 7 feet wide?

From the information, we are seeking a story problem that has the equation had the square root of 81 - 7 = 2.

This will be written as story for the word problem is that what will be the length of the missing side of a square garden when the total area is 81 feet ² and the width was 7 feet wide?

The length will be calculated thus :

= √ 81 - 7

= 9 - 7

= 2

The length of the missing side is 2 feet.

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The volume of the solid enclosed by the paraboloids z = 4 (x² + y²) and z = 50 – 4 (x² + y²) is approximately 164.93 cubic units.

To find the volume of the solid enclosed by the two paraboloids, we need to first find the intersection of the two surfaces. Setting the equations of the paraboloids equal to each other, we get:

4(x² + y²) = 50 - 4(x² + y²)

Simplifying this equation, we get:

8x² + 8y² = 50

Dividing by 8, we get:

x² + y² = 6.25

This equation represents a circle of radius 2.5 centered at the origin in the xy-plane.

To find the volume of the solid, we can use a double integral in cylindrical coordinates:

V = ∫∫R (50 - 4r²) - 4r² r dr dθ

where R is the region enclosed by the circle x² + y² = 6.25.

Evaluating the integral, we get:

V = ∫0^2π ∫0^2.5 (50 - 8r²) r dr dθ

= 2π [25r² - (4/3)r^4]0^2.5

= 2π [156.25/3]

≈ 164.93 cubic units

Therefore, the volume of the solid enclosed by the paraboloids z = 4 (x² + y²) and z = 50 – 4 (x² + y²) is approximately 164.93 cubic units.

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The volume of the cone is approximately 26.1 cubic inches.

The formula used to calculate the volume of a cone is:

V = (1/3) × π ×[tex]r^2[/tex] × h

where V is the volume of the cone, r is the radius of the base of the cone, h is the height of the cone, and π is a mathematical constant that is approximately equal to 3.14.

Part b. Plugging in the given values, we get:

V = (1/3) × 3.14 ×[tex]2.5^2[/tex]× 4.2

V = (1/3) × 3.14 × 6.25 × 4.2

V = 26.125 cubic inches (rounded to the nearest tenth)

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Answer:

Solution: (x-3)(x+1)

Step-by-step explanation:

1) Using Mid term break:

x²-2x-3

x²+x-3x-3

2) Take Common Factors from the two pairs

(x²+x) + (-3x-3)

x(x+1) -3(x+1)

3) Rewrite in Factored Form:

(x-3)(x+1)