if another line is perpendicular to the line shown on the graph, what must be its slope

Answer:

Step-by-step explanation:

First, add each number in the set of data. Then, divide the sum by the count of numbers in the data set.

example:

DATA SET:

5 4 7 6

MEAN STEP 1:

5 + 4 + 7 + 6 = 22

MEAN STEP 2:

Since there are four numbers in the data set, divide 22 by four.

Answer:

Sample Answer: First, find the mean of the data set by averaging. Next, find the absolute deviations for each data point. That is, find the distance each point is from the mean. Then find the mean of the absolute deviations.

Which did you include in your explanation? Check all that apply.

Find the mean of the set of data.

Find the absolute deviations for each point.

Absolute deviation is a data point’s distance from the data set’s mean.

Find the mean of the absolute deviations.

Your parents would need to save approximately $4,467.56 each year to reach their goal of $160,000 by your 18th birthday. your parents would need to save approximately $40,079.89 each year to reach their new goal of $200,000, assuming a five-year saving period.

a. To calculate the amount your parents would have to save each year to reach a goal of $160,000 by your 18th birthday, we can use the future value of an ordinary annuity formula:

FV = P * [(1 + r)^n - 1] / r

Where:

FV = future value ($160,000)

P = annual savings amount

r = interest rate per period (9.5% or 0.095)

n = number of periods (number of years, in this case, 17 since they start saving on your first birthday until your 18th birthday)

Plugging in the values, we have: $160,000 = P * [(1 + 0.095)^17 - 1] / 0.095

Simplifying the equation and solving for P, we find: P ≈ $4,467.56

b. If your parents decide to save for five years instead of four and aim to have $200,000 saved, we can use the same formula to calculate the new annual savings amount: $200,000 = P * [(1 + 0.095)^5 - 1] / 0.095

Simplifying the equation and solving for P, we find: P ≈ $40,079.89

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See your Question is not clear .I am writing steps to do .

Answer:

Step-by-step explanation:

The diagram does not define r. Nor is it spoken of anywhere else.

So my guess is that r multiplied by P gives Q.

r = 12/8 =   1 4/8 = 1 1/2 = 3/2

Oh! x

8/12 = 5/x             Cross multiply

8x = 12 * 5           Combine on the right

8x = 60                Divide by 8

x = 60/8 = 7 4/8 = 7 1/2 = 7.5

The new image would be smaller in sample size than the original image.

For example, if the scale factor is 0.5, the new image will be half the size of the original image. To determine the exact size of the new image, the scale factor is multiplied with the width and height of the original image. For example, if the original image is 200 x 100 pixels, and the scale factor is 0.5, the new image will be

(200 x 0.5) = 100 x (100 x 0.5)

= 50 pixels.

The same concept applies when the scale factor is a decimal. For example, if the scale factor is 0.75, the new image will be three-quarters the size of the original image. In this case, the new image would be

(200 x 0.75) = 150 x (100 x 0.75)

= 75 pixels.

In summary, when the scale factor is less than 1, the new image will always be smaller than the original image, depending on the scale factor. The exact size of the new image can be determined by multiplying the width and height of the original image with the scale factor.

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When rotating 180 degrees counterclockwise the sign of the numbers change. A positive becomes a negative and a negative becomes a positive.

(5.1) becomes (-5,-1)

answer: (-5,-1)

The rotation, the coordinates of the resulting point G' are (-5, -1).

To rotate a point 180° counter clockwise around the origin, you simply negate both the x and y coordinates of the original point.

Given the point G(5, 1), to find the resulting point G' after a 180° counter clockwise rotation, you negate both the x and y coordinates:

G'(-5, -1)

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Answer:

B 9

Step-by-step explanation:

one side is 3 units long, to find the area the square is 3x3

The area of the square DEFG, given D(0,0) and E(3,0) is 9 square units.

Area of a two dimensional shape is the total region which is bounded by the object's shape.

We have that all the four sides of a square are equal.

Area of a square = a², where "a" is the side length.

Given are two vertices of the square, D(0,0) and E(3,0).

Using the distance formula,

DE = √(3 - 0)² + (0 - 0)² = √9 = 3 units

Area = 3² = 9 units²

Hence the area of the square is 9 square units.

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a. the deposit payable for the apartment is $35,250. b. The total amount paid for the house would be $716,610. This includes the deposit payable and the total amount repaid to the bank over the loan term.

a) To find the deposit payable, we need to calculate 15% of the total price of the apartment. The deposit is the amount that the buyer needs to pay upfront before obtaining the mortgage.

15% of $235,000 can be calculated as:

Deposit = 0.15 * $235,000

Deposit = $35,250

Therefore, the deposit payable for the apartment is $35,250.

b) The mortgage needed is the remaining amount that the buyer needs to borrow from the bank to cover the rest of the apartment's price. To find this, we subtract the deposit from the total price.

Mortgage Needed = Total Price - Deposit

Mortgage Needed = $235,000 - $35,250

Mortgage Needed = $199,750

Therefore, the mortgage needed is $199,750.

c) The total amount of money repaid to the bank can be calculated by multiplying the monthly payment by the number of months in the loan term. In this case, the loan term is 20 years, which is equal to 240 months.

Total Amount Repaid = Monthly Payment * Number of Months

Total Amount Repaid = $2,839 * 240

Total Amount Repaid = $681,360

Therefore, the total amount of money repaid to the bank would be $681,360 if each monthly payment was $2,839.

d) The total amount paid for the house includes both the deposit payable and the total amount repaid to the bank. It represents the overall cost of purchasing the house.

Total Amount Paid = Deposit + Total Amount Repaid

Total Amount Paid = $35,250 + $681,360

Total Amount Paid = $716,610

Therefore, the total amount paid for the house would be $716,610. This includes the deposit payable and the total amount repaid to the bank over the loan term.

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Answer:

Step-by-step explanation:

This is a GP as :

Answer:

35 x 14 = 490

Step-by-step explanation:

Therefore, the long dimension of the quilt is (26x + 60)/(x + 6) cm longer than the short dimension.

Area is the measure of the extent of a 2-dimensional surface or region, usually measured in square units such as square meters (m²), square feet (ft²), or square centimeters (cm²). It is the amount of space inside the boundary of a flat shape or the surface of an object.

Here,

The area of the original square is x^2 cm². Maria adds some fabric to one side of the square, which increases the length of the rectangle by a certain amount, and adds a different amount of fabric to the adjacent side, which increases the width of the rectangle by a certain amount. Let's say Maria adds y cm of fabric to one side and z cm of fabric to the other side. Then the length of the rectangle is x + y cm and the width is x + z cm. The area of the rectangle is given by:

(x + y)(x + z) = x^2 + xy + xz + yz

We know that the area of the rectangle is x² + 13x + 30 cm². So we can set these two expressions equal to each other:

x² + xy + xz + yz = x² + 13x + 30

Simplifying this equation, we get:

xy + xz + yz = 13x + 30

We want to find the difference between the length and the width of the rectangle, which is (x + y) - (x + z) = y - z. To solve for y - z, we need to express yz in terms of y - z. We can do this by factoring the left side of the equation above:

xy + xz + yz = y(x + z) + xz = (y - z)(x + y + z)

Substituting this expression for yz in the equation above, we get:

(y - z)(x + y + z) = 13x + 30

We want to solve for y - z, so let's focus on the left side of the equation:

(y - z)(x + y + z) = y(x + y + z) - z(x + y + z)

= xy + y² + yz - xz - z² - yz

= y² - z² + xy - xz

Substituting the expression we found earlier for xy - xz, we get:

(y - z)(x + y + z) = y² - z² + (y - z)(x + z)

(y - z)[x + y + z - (x + z)] = y² - z²

y - z = (y² - z²)/(y - z) = y + z

= (13x + 30)/(x + 6)

So the difference between the length and the width of the rectangle is:

y - z = (13x + 30)/(x + 6)

Therefore, the long dimension of the quilt is (x + y) = x + (13x + 30)/(x + 6) cm, and the short dimension is (x + z) = x + (30 - 13x)/(x + 6) cm. The difference between the long and short dimensions is:

[x + (13x + 30)/(x + 6)] - [x + (30 - 13x)/(x + 6)]

= (13x + 30)/(x + 6) - (30 - 13x)/(x + 6)

= (26x + 60)/(x + 6)

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The items in order from the greatest thickness to the least is

Item                    Thickness

Folder                 1.9 * 10⁻²

Ruler                   1.2 * 10⁻²

Dollar bill            1.0 * 10⁻⁴

Sheet of paper   8.0 * 10⁻⁵

From the question, we have the following parameters that can be used in our computation:

Item                    Thickness

Sheet of paper   8.0 * 10⁻⁵

Folder                 1.9 * 10⁻²

Dollar bill            1.0 * 10⁻⁴

Ruler                   1.2 * 10⁻²

By definition, the smaller the power; the smaller the thickness

Since -5 is less than -4, then -4 is thicker than -5

So, we have the following order

Item                    Thickness

Folder                 1.9 * 10⁻²

Ruler                   1.2 * 10⁻²

Dollar bill            1.0 * 10⁻⁴

Sheet of paper   8.0 * 10⁻⁵

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To sketch the root locus for the system with the transfer function G(s)H(s) = K(s + 1) / s(s + 4)(s² + 2s + 2), we can follow some steps.

Step 1: Determine the number of poles and zeros.

The given transfer function has one zero at s = -1 and three poles at s = 0, s = -4, and s = -1 ± j.

Step 2: Find the angles and magnitudes of the poles and zeros.

For the poles and zeros, we have:

Zero: z = -1

Poles: p₁ = 0, p₂ = -4, p₃ = -1 ± j

Step 3: Determine the branches of the root locus.

The root locus branches originate from the poles and terminate at the zeros. In this case, since we have three poles and one zero, there will be three branches starting from the poles and converging towards the zero.

Step 4: Determine the asymptotes.

The number of asymptotes is given by the formula: N = P - Z, where P is the number of poles and Z is the number of zeros. In this case, N = 3 - 1 = 2. Thus, there will be two asymptotes.

Step 5: Calculate the angles of the asymptotes.

The angles of the asymptotes are given by the formula: θ = (2k + 1)π / N, where k = 0, 1, 2, ..., (N - 1). In this case, N = 2, so we have k = 0, 1.

θ₁ = (2 × 0 + 1)π / 2 = π / 2

θ₂ = (2 × 1 + 1)π / 2 = 3π / 2

Step 6: Calculate the departure and arrival angles.

The departure angles are the angles at which the root locus branches leave the poles, and the arrival angles are the angles at which the branches arrive at the zeros. The angles can be calculated using the formula: θᵈ = (Σp - Σz) / (2n + 1), where Σp is the sum of the angles from the poles and Σz is the sum of the angles from the zeros, and n is the index of the point along the root locus.

For this transfer function, let's calculate the departure and arrival angles for a few points along the root locus:

Point 1: Along the real-axis

Σp = 0 + (-4) + (-1) + (-1) = -6

Σz = -1

θᵈ = (-6 - (-1)) / (2 × 0 + 1) = -5 / 1 = -5

Point 2: On the imaginary axis

Σp = 0 + (-4) + (-1) + (-1) = -6

Σz = -1

θᵈ = (-6 - (-1)) / (2 × 1 + 1) = -5 / 3

Repeat these calculations for additional points along the root locus to obtain the departure and arrival angles.

Step 7: Sketch the root locus.

Using the information obtained from the previous steps, sketch the root locus on the complex plane. Plot the branches originating from the poles and converging towards the zeros. Indicate the asymptotes and the departure/arrival angles at various points along the root locus.

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The trigonometric ratios that would be affected are given as follows:

D) sin A, cos A and tan A.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

Enlarging side AB, the hypotenuse AC would also be enlarged, as it depends on both side lengths AB and BC according to the Pythagorean Theorem.

Then all the three trigonometric ratios will be affected, as they depend either on AB or on the hypotenuse.

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Answer:

7 - 2 = 5

Step-by-step explanation:

if c = 7, then 7 - 2 = 5.

The two positive numbers are 6 and 11

From the question, we understand that:

There are two positive numbers

Represent these numbers with x and y

So, we have the following equations

x = y - 5

6x - 3y = 3

Substitute x = y - 5 in 6x - 3y = 3

6(y - 5) - 3y = 3

Open the brackets

6y - 30 - 3y = 3

Evaluate the like terms

3y = 33

Divide by 3

y = 11

Substitute y = 11 in x = y - 5

x = 11 - 5

So, we have

x = 6

hence, the numbers are 6 and 11

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The number of calories that Darrell will burn in 1 minute while kayaking is given as follows:

4 calories.

The number of calories that Darrell will burn in 1 minute while kayaking is obtained applying the proportions in the context of the problem.

For each input-output pair in the table, the constant of proportionality is of 4, hence the number of calories that Darrell will burn in 1 minute while kayaking is given as follows:

4 calories.

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The variable assigned to strgrade when intscore equals 90 would likely be 'A'.

When the variable intscore equals 90, the corresponding value assigned to the variable strgrade would typically be 'A'. This suggests that a score of 90 is associated with the highest grade achievable in the given context. The specific mapping between integer scores and letter grades may vary depending on the grading system or criteria in place. It is important to note that without further information about the grading scale or specific rules defined within the system, it is difficult to determine the exact value of strgrade assigned to intscore of 90.

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Based on given details  i would say a reasonable expectation would be about 6 children .

Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.

For the question above, we will use probability.

after 4 children, there is 37.5% chance you have 2 boys/2 girls

after 5 children, there is 62.5% chance you have at least 2boys/2 girls

after 6 children, there is 78% chance you have at least 2boys/2 girls

after 8 children, there is 93% chance you have at least 2boys/2 girls ...

based on this i would say a reasonable expectation would be about 6 children

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The weight of the last child is 36 lbs.

The average weight of the three children is 60 lbs. The total weight will be:

= 60 × 3

= 180 lbs.

When another child is added, the weight is 54lb. The total weight will be:

= 54 × 4

= 216 lbs

The weight of the last child will be:

= 216 - 180

= 36 lbs.

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Step-by-step explanation:

1. -3x+7x=18

    x(-3+7)=18

      x=\(\frac{18}{(-3+7)}\)

2. 4x+7x=-5

    x(4+7)=-5

     x=\(\frac{-5}{(4+7)}\)

I hope this helped, may be wrong but ive done it my way

Answer:

Week0=20 W1=25 W2=30 W3=35 W4=40 W5=45 W6=50 W7=55 W8=60 W9=65

Step-by-step explanation:

W means week im just lazy:)

And just for every week you will add 5 to each week ig

Replace x with 1/4 and solve:

12(1/4) - 2

3-2 =1

The answer is 1

Answer:

the answer is 1

Step-by-step explanation:

g(1/4)=12(1/4)-2

=12/4-2

=3-2

=1

The probability that the mean of a month's reviews will take Yoonie from 3.5 to 4.25 hours is 0.7492.

The random variable X is defined as the time it takes her to complete one review.

The random variable X follows a Normal distribution with parameters μ = 4 hours and σ = 1.2 hours.

A random sample of n = 16 reviews are selected as a set.

Compute the probability that the mean of a month’s reviews will take Yoonie from 3.5 to 4.25 hours as follows:

P(3.5 < X < 4.25) = P(3.5-4/1.2√16 < x- μ /σ/√n < 4.25-4/1.2/√16)

=P(-1.67 < Z < 0.83)

= P(Z < 0.83) - (P(Z < -1.67)

= 0.7967 - 0.0475

= 0.7492

Thus, the probability that the mean of a month’s reviews will take Yoonie from 3.5 to 4.25 hours is 0.7492.

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In this case, the mean is 5.5 cm and the standard deviation is 0.1 cm. So, one standard deviation below the mean is 5.4 cm and one standard deviation above the mean is 5.6 cm. Therefore, about 68% of the data falls between 5.4 cm and 5.6 cm, which includes the range of 5.3 cm to 5.7 cm.

Your question involves a normal distribution with a mean (µ) of 5.5 cm and a standard deviation (σ) of 0.1 cm. You want to find the percentage of data between 5.3 cm and 5.7 cm.

First, we need to standardize the scores using the z-score formula: z = (x - µ) / σ

For 5.3 cm: z1 = (5.3 - 5.5) / 0.1 = -2
For 5.7 cm: z2 = (5.7 - 5.5) / 0.1 = 2

Now, referring to a standard normal distribution table or using a calculator, we find the area between these z-scores:

This can be determined using the empirical rule, also known as the 68-95-99.7 rule, which states that for a normal distribution:
- About 68% of the data falls within one standard deviation of the mean
- About 95% of the data falls within two standard deviations of the mean
- About 99.7% of the data falls within three standard deviations of the mean

P(-2 < z < 2) = P(z < 2) - P(z < -2) = 0.9772 - 0.0228 = 0.9544

Converting it to a percentage, we get 95.44%, which is approximately 95%.

So, the answer is A. 95%.

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The LCM of A = a^3× b^2×c and B=a^5 ×b×c^4×d in exponential form is a^5 × b^2 × c^4 × d^1.

To find the LCM (Least Common Multiple) of two numbers, we need to find the greatest power of each prime factor that occurs in either number.

The prime factors in the given expressions are a, b, c, and d. For each prime factor, we need to find the greatest power that occurs in either A or B.

For a: The highest power of a that occurs in A is a^3, and the highest power that occurs in B is a^5. Therefore, the LCM must include a^5.

For b: The highest power of b that occurs in A is b^2, and the highest power that occurs in B is b^1. Therefore, the LCM must include b^2.

For c: The highest power of c that occurs in A is c^1, and the highest power that occurs in B is c^4. Therefore, the LCM must include c^4.

For d: The highest power of d that occurs in A is d^0, and the highest power that occurs in B is d^1. Therefore, the LCM must include d^1.

Putting all of this together, we have:

LCM(A,B) = a^5 × b^2 × c^4 × d^1

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to properly examine the effect of a categorical independent variable in a multiple linear regression model we use an interaction term then it is a true statement

we have given that the by which method we use the different levels of a qualitative independent variable and we have to explain about it.

So, For his purpose, we know that the

A dummy variable is a variable that takes values of 0 and 1, where the values indicate the presence or absence of something.

And in the multiple regression method there are a lot of different variables which are used for a qualitative and for this a variable is used which is called the dummy variables.

By this variables we show the analysis between the given data. it gives the output in the 0 and 1 numbers.

So, For the levels of qualitative, the variable called dummy variables is used in the multiple regression method.

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