Which of the following scale factors represents an enlargement of the original dimension?
A- 1/2
B- 1/12
C- 3/4
D- 16/1

Answer:

$100

Step-by-step explaine:

My house cleaners charge $25 per hour and they spend about 4 hour cleaning the house how much money will they make in the 4 hours spent cleaning the house?

Take 4 and multiply it by 25

The examples of unit rate are given below and this can be determined by using the definition of unit rate.

The unit rate is nothing but a ratio that represents the rate of something per unit.

Examples  --

1) A car is driving at a speed of 50 kilometers per hour. The 50 km/hr represents the unit rate.

2) The cost of the potatoes is $2 per pound. The $2/pound represents the unit rate.

3) The density of a substance is 4 Kg per liter. The 4kg/lt represents the unit rate.

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The maximum amount you can earn is $540

a. y = 13.50x , 10 <= x <= 40
b. x = 10, y = 135; x = 20, y= 270; x = 30, y = 405; x = 40, y = 540
c. Domain: 10 <= x <= 40; Range: 0 <= y <= 540
d. The minimum amount you can earn in a week with this job is $135. The maximum amount you can earn is $540.

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\(1+(0.2)^2=1+0.04=\boxed{1.04}\)

Answer:

1.44

Step-by-step explanation:

1 2/10 squared = 1.44

Answer:

6

Step-by-step explanation:

*sum of interior angles

1. x+x+x=180

2. 3x=180

3. x=6

The resulting equation is c = -b(a - d).

To multiply both sides of the equation ×(a−d)=×(−bc) by the same expression, we apply the distributive property. This allows us to multiply each term on both sides of the equation by the expression ×.

Starting with the left side of the equation:

×(a−d) simplifies to ×a - ×d.

Next, we move to the right side of the equation:

×(−bc) simplifies to -b×c.

Now, we have the equation ×a - ×d = -b×c.

To find the resulting equation in terms of c, we can divide both sides of the equation by -b. This gives us:

(×a - ×d) / -b = c.

Simplifying further, we have:

c = -b(a - d).

Therefore, the resulting equation is c = -b(a - d).

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Answer:

The given initial value problem's solution is y(t) = e^(-2t)(2cos(4t) + (1/8)sin(4t))

To solve the given initial value problem, we can use the method of solving second-order homogeneous linear differential equations with constant coefficients.

The characteristic equation corresponding to the given differential equation is:

r^2 + 4r + 20 = 0

To solve this quadratic equation, we can use the quadratic formula:

r = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = 4, and c = 20. Substituting these values into the quadratic formula, we get:

r = (-4 ± √(4^2 - 4(1)(20))) / (2(1))

r = (-4 ± √(-64)) / 2

r = (-4 ± 8i) / 2

r = -2 ± 4i

The roots of the characteristic equation are complex conjugates: -2 + 4i and -2 - 4i.

The general solution of the differential equation can be written as:

y(t) = e^(-2t)(c1cos(4t) + c2sin(4t))

To find the particular solution that satisfies the initial conditions, we substitute the initial values into the general solution and solve for the constants c1 and c2.

Given y(0) = 2:

2 = e^(-2(0))(c1cos(4(0)) + c2sin(4(0)))

2 = c1

Given y'(0) = -1:

-1 = -2e^(-2(0))(c1sin(4(0)) + 4c2cos(4(0)))

-1 = -2(1)(0 + 4c2)

-1 = -8c2

c2 = 1/8

Therefore, the particular solution that satisfies the initial conditions is:

y(t) = e^(-2t)(2cos(4t) + (1/8)sin(4t))

This is the solution to the given initial value problem.

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1. The break-even point in unit sales and in dollar sales is 4,500 units and $324,000 respectively.

2. If the variable expenses per stove increase as a percentage of the selling price, will it result in a higher break-even point.

3. Income statements before and after changes are implement net income of $36,000 and $(28,000) respectively.

4. The company has to sell 5,401 units to achieve the target profit of $35,000 per month.

1. The break-even point in unit sales and dollar sales is computed as follows:

Break-Even Point in Unit Sales = Fixed Costs / Contribution Margin per Unit = $108,000 / ($50 - $32) = 4,500 units

Break-Even Point in Dollar Sales = Fixed Costs / Contribution Margin Ratio = $108,000 / ($50 / $18) = $324,000

2. If variable expenses per stove increase as a percentage of selling price, it will result in a higher break-even point. Since variable expenses would have a higher percentage of revenue, contribution margin would be lower, making it more challenging to cover fixed costs.

3. Present Income Statement

Sales (8,000*$50) $400,000

Less variable expenses (8,000*$32) (256,000)

Contribution Margin $144,000

Less fixed expenses 108,000

Net Income $36,000

Income Statement if Changes are Implemented

Sales (8,000*$45) $360,000

Less variable expenses (8,000*$35) (280,000)

Contribution Margin $80,000

Less fixed expenses 108,000

Net Loss $(28,000)

4. The contribution margin ratio is 36% ($18/$50). So, the sales revenue required to achieve the target profit is:

$35,000 / 0.36 = $97,222

The number of units required to be sold is:

$97,222 / $18 = 5,401 units

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The preparation of the Sales section of the income statement for Blue Spruce Corp. is as follows:

BLUE SPRUCE CORP.

For the year ended October 31, 2022

Sales Revenue                         $908,400

Sales Returns and Allowances  (20,900)

Sales Discounts                           (14,700)

Net sales revenue                  $872,800

The net sales revenue represents the gross revenue minus sales returns and allowances and sales discounts.

In most jurisdictions, the sales discount account is reported on the income statement as a contra revenue account.  This implies that sales discounts are directly deducted from the gross sales and do not appear in the expense section nor the notes to the sales or revenue.

Sales Revenue $908,400

Freight-Out $12,600

Sales Returns and Allowances $20,900

Sales Discounts $14,700

Thus, the preparation of the sales section of the income statement for Blue Spruce Corp. shows a net sales revenue of $872,800.

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The function that has a greater maximum value is: A. function 1 has the larger maximum at (1, 4).

In this exercise, you are required to determine the maximum value of the given quadratic functions that is shown in the graph and written in standard form.

In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:

y = a(x - h)² + k

Where:

Function 1 = f(x) = -x² + 8x - 15

Function 2 = f(x) = -x² + 2x - 3

By critically observing the given quadratic functions shown in the image attached below, we can logically deduce that function 1 f(x) = -x² + 8x - 15 has the larger maximum at (1, 4) because the maximum of function 2 f(x) = -x² + 2x - 3 is at (1, -2).

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The linear regression equation that represents the correlation between homework grade (x) and test grade (y) is y = 0.6x + 18.5. Using this equation, the estimated homework grade for a student with a test grade of 32 is 38.

To find the linear regression equation, we need to calculate the slope and the y-intercept using the given data:

1: Calculate the mean of the homework grades (x) and test grades (y) from the table.

  Mean of x: (50 + 70 + 80 + 90) / 4 = 72.5

  Mean of y: (60 + 85 + 95 + 100) / 4 = 85

2: Calculate the differences between each homework grade (x) and the mean of x, and each test grade (y) and the mean of y.

  Difference for x: (50 - 72.5), (70 - 72.5), (80 - 72.5), (90 - 72.5) = -22.5, -2.5, 7.5, 17.5

  Difference for y: (60 - 85), (85 - 85), (95 - 85), (100 - 85) = -25, 0, 10, 15

3: Calculate the sum of the product of the differences for x and y, as well as the sum of the squared differences for x.

  Sum of (x - mean of x) * (y - mean of y): (-22.5 * -25) + (-2.5 * 0) + (7.5 * 10) + (17.5 * 15) = 162.5

  Sum of (x - mean of x)^2: (-22.5)^2 + (-2.5)^2 + (7.5)^2 + (17.5)^2 = 1050

4: Calculate the slope (b) using the formula:

  b = Sum of (x - mean of x) * (y - mean of y) / Sum of (x - mean of x)^2

  b = 162.5 / 1050 ≈ 0.155

5: Calculate the y-intercept (a) using the formula:

  a = mean of y - (b * mean of x)

  a = 85 - (0.155 * 72.5) ≈ 85 - 11.24 ≈ 73.76

6: Write the linear regression equation by rounding the coefficients to the nearest tenth:

  y = 0.2x + 73.8

7: Substitute the given test grade (y = 32) into the equation to estimate the homework grade (x):

  32 = 0.2x + 73.8

  0.2x = 32 - 73.8

  0.2x = -41.8

  x ≈ -209 (rounded to the nearest integer)

Therefore, the estimated homework grade for a student with a test grade of 32 is 38.

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Answer:

cubic polynomial, monomial

Step-by-step explanation:

Answer:

I have no idea and I'm not that smart

Hey there!

x + (-8) = 2

x - 8 = 2

x = 2 + 8

x = 10 (option c)

Hope it helps ya!

the correct answer is.x+-8+8=2-8

x= -6

So the probability that the number of U.S. adults who oppose taxes on junk food and soda is less than or equal to 210 is 0.188.

To solve this problem, we can use the binomial distribution. Let X be the number of U.S. adults who oppose taxes on junk food and soda. Then X follows a binomial distribution with n = 320 trials and p = 0.65 probability of success. We can use the binomial probability formula to find the probability that X takes on a specific value k:

\(P(X = k) = (^{n} Cx_{k} ) * p^k * (1-p)^{(n-k)}\)

where (n choose k) = n! / (k! * (n-k)!) is the binomial coefficient.

To find the probability that X is less than or equal to some value, we can use the cumulative distribution function (CDF) of the binomial distribution:

\(P(X < = k) = sum_{i=0}^k P(X = i)\)

Using a calculator or a computer, we can find the probabilities directly. Here are the probabilities for some values of k:

\(P(X = 208) = (320 choose 208) * 0.65^{208} * 0.35^{112}\)

= 0.051

\(P(X = 209) = (320 choose 209) * 0.65^{209} * 0.35^{111}\)

= 0.062

\(P(X = 210) = (320 choose 210) * 0.65^{210} * 0.35^{110}\)

= 0.075

\(P(X = 211) = (320 choose 211) * 0.65^{211} * 0.35^{109}\)

= 0.088

To find the probability that X is less than or equal to 210, we can add up the probabilities for k = 208, 209, 210:

P(X <= 210) = P(X = 208) + P(X = 209) + P(X = 210)

= 0.051 + 0.062 + 0.075

= 0.188

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Answer:

x = -1 and y = 3     x = 3 and y = -1

Step-by-step explanation:

Answer:

i believe the answer is f(x)=6

Step-by-step explanation:

Yes, an 11, 60, 61 triangle has a right angle. This is because the Pythagorean theorem applies to right triangles, stating that the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse).

In this case, we can apply the theorem and see that 11^2 + 60^2 = 3721 + 3600 = 7321. Taking the square root of 7321 gives us approximately 85.4, which is the length of the hypotenuse.

Now, if we compare the square of the hypotenuse (85.4^2 = 7291.16) to the sum of the squares of the legs (11^2 + 60^2 = 3721 + 3600 = 7321), we can see that they are not equal. Therefore, the 11, 60, 61 triangle is not a right triangle.

However, if we compare the square of the hypotenuse (61^2 = 3721) to the sum of the squares of the legs (11^2 + 60^2 = 3721), we can see that they are equal. Therefore, the 11, 60, 61 triangle is a right triangle.

In conclusion, the 11, 60, 61 triangle has a right angle because it satisfies the Pythagorean theorem, which applies only to right triangles.

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Answer:

The answer to the question is A

x=2/3

6(2/3) + 4 9/10 =4 + 4 9/10 = 8 9/10

Answer:

2x-1=y,2y+3=x

Step-by-step explanation:

no explanation

Answer:

it will be more wildfires longer periods of droughts

The value of the iterated integral is 0.5.

To evaluate the iterated integral ∫(3, 2)∫(4, 3)(3xy - 2)dydx, we will first integrate with respect to y, then with respect to x:

1. Integrate with respect to y: ∫(3xy - 2)dy

∫(3xy)dy = (3x/2)y²
∫(-2)dy = -2y

Now combine the two results: (3x/2)y^² - 2y

2. Evaluate the integral for y from 3 to 4:

[((3x/2)(4²) - 2(4)) - ((3x/2)(3²) - 2(3))]

[12x - 8 - (9x - 6)]

3. Integrate with respect to x: ∫(3, 2)(3x - 8)dx

∫(3x)dx = (3/2)x²
∫(-8)dx = -8x

Now combine the two results: (3/2)x² - 8x

4. Evaluate the integral for x from 2 to 3:

[((3/2)(3²) - 8(3)) - ((3/2)(2^²) - 8(2))]

[(13.5 - 24) - (6 - 16)]

5. Calculate the final result:

(-10.5) - (-10) = 0.5

The value of the iterated integral is 0.5.

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Answer:

A and B cost the same, so you could say either. and it's already arranged in order from top (lowest price) to bottom (highest price)

Step-by-step explanation:

When the color component is kept in the center and allowed to vary, it means that the color remains the same but its intensity or brightness changes. This can result in different shades or tints of the color

When the color component is pushed to the left, kept in the center, and allowed to increase between 0 and 127.5, it implies that the color's saturation is changing. Saturation refers to the purity or vividness of the color. By increasing the saturation, the color becomes more intense and vibrant, while decreasing the saturation makes it less vivid and more towards a shade of gray.

To create black in this color model, you need to set all the color components (red, green, and blue) to their minimum values, usually 0. This absence of color results in black.

To create white, you need to set all the color components (red, green, and blue) to their maximum values, usually 255. This combination of full intensity in all colors results in white.

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After substituting the given time of 8.91 seconds into the equation, we found that the car is going approximately 30.8 mph to the nearest tenth.

To find the speed of the car after 8.91 seconds, we need to substitute the value of t into the equation t = \(0.001(0.732x^2 + 15.417x + 605.738).\)

\(t = 8.91\) seconds
Plugging this value into the equation, we get:

\(8.91 = 0.001(0.732x^2 + 15.417x + 605.738)\)
Now, we can solve for x by isolating it:

\(0.732x^2 + 15.417x + 605.738 = 8.91 / 0.001\)
\(0.732x^2 + 15.417x + 605.738 = 8910\)

Next, we can rearrange the equation to a quadratic form:

\(0.732x^2 + 15.417x + 605.738 - 8910 = 0\)

\(0.732x^2 + 15.417x - 8304.262 = 0\)

To solve the quadratic equation,

we can use the quadratic formula:

\(x = (-b ± √(b^2 - 4ac)) / (2a)\)

In this case,

\(a = 0.732,\)

\(b = 15.417,\)

and\(c = -8304.262.\)

Plugging these values into the formula, we get:

\(x = (-15.417 ± √(15.417^2 - 4 * 0.732 * -8304.262)) / (2 * 0.732)\)

Simplifying the equation gives us two possible solutions for x.

However, only one of them is relevant in this case since we are looking for the speed of the car:

\(x ≈ 53.1\)

the car is going approximately 53.1 mph after 8.91 seconds.

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Answer: 45

Step-by-step explanation:

Answer:

1/6*2 = 1/12

Step-by-step explanation:

This is a fair die, so the chance of any side is 1/6th. We are rolling it twice,  and if we are looking for a specific result both times, that creates a 1/6 * 2 equation. The result of this is 1/12.

Answer:

for the first the answer is 280 and for the second the answer is 0 because there's no number to be rounded up

The approximate area of the trapezoid is determined as  13.95 unit².

The approximate area of the trapezoid is calculated as follows;

Area = ¹/₂(b₁ + b₂)h

Where;

The y-coordinates of the points on the curve at x=3/2 and x=4 is calculated as follows;

y(3/2) = - (3/2)²/2 + 3/2 + 5

y(3/2) = -9/8 + 3/2 + 5

y(3/2) = 5.375

y(4) = -4²/2 + 4 + 5

y(4) = -8 + 9

y(4) = 1

h = 5.375 - 1 = 4.375

The approximate area of the trapezoid is calculated as;

Area = ¹/₂(5.375 + 1) x 4.375

Area = 13.95 unit²

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