A stack of 4 identical books is 6.28 inches high. What is the heigh of 30 of these books?

Sally's average annual percentage gain is approximately 5.26%.

To calculate Sally's average annual percentage gain, we can use the formula:

Average Annual Percentage Gain = (Profit / Initial Investment) * (1 / Time) * 100

Profit = $2500

Initial Investment = $19000

Time = 2.5 years

Substituting the values into the formula:

Average Annual Percentage Gain = (2500 / 19000) * (1 / 2.5) * 100

= (0.1316) * (0.4) * 100

= 5.26

Therefore, Sally's average annual percentage gain is approximately 5.26%.

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The mean absolute deviation is 0.75

To calculate the mean absolute deviation (M.A.D.), you need to find the average of the absolute differences between each data point and the mean of the data set

From the information given, we have that the data set is;

8 9 9 7 8 6 9 8

Let's calculate the mean, we get;

Mean = (8 + 9 + 9 + 7 + 8 + 6 + 9 + 8) / 8

Mean = 64 / 8

Divide the values

Mean = 8

Let's determine the absolute difference, we get;

Absolute differences=

|8 - 8| = 0

|9 - 8| = 1

|9 - 8| = 1

|7 - 8| = 1

|8 - 8| = 0

|6 - 8| = 2

|9 - 8| = 1

|8 - 8| = 0

Find the mean of the absolute differences:

Average of absolute differences = (0 + 1 + 1 + 1 + 0 + 2 + 1 + 0) / 8

Absolute difference = 6 / 8 = 0.75

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Answer:$ 24,679.20 or 514.15 a month

Step-by-step explanation: 565(.09) is 50.85 which needs to be deducted from the payment of 565 because he needs to be able to pay for interest. 514.15 is then multiplied by 48 months which will bring you to 24,679.20

If Astrid says the function being graphed is y=-4+1/3. Matt is correct, while Astrid is incorrect.

Astrid's equation y = -4 + 1/3 is incorrect because it is missing the variable x. The equation is missing a term that represents the x variable, so the equation does not represent a line.

On the other hand, Matt's equation y = 1/3x is correct, and the slope of the line represented by this equation is indeed 1/3. This can be seen from the fact that the equation is in the form y = mx, where m is the slope of the line. In this case, m = 1/3, so Matt is correct.

Therefore, Matt is correct, while Astrid is incorrect.

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Answer:

A parallel line has the same slope, but is translated away from the line it is parallel to. Let's create an equation using what we have:

−

1

=

−

3

(

−

2

)

+

b

−

1

=

6

+

b

−

7

=

b

y

=

−

3

x

−

7

Hope this helped!!

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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Answer:

132 square feet

Step-by-step explanation:

The formula for the area of a triangle is 1/2 * b * h. B stands for base and h stands for height. 1/2 multiplied by the base, 10, is 5. We then multiply 5 by 12 which is 60. Let's look at the rectangle now. The area of a rectangle is length by width. The length is 12ft and the width is 6ft. 12 * 6 = 72. 72+60=132 square feet.

Answer:

Width: 22.53 in.

Length: 28.35 in.

Step-by-step explanation:

If the perimeter is 101.76 in, we can create an equation of 2l + 2w = 101.76 in (length is l, and width is w). We also have that the rectangular painting is 5.82 in taller than it is wide. We can create a new equation stating that l = w + 5.82. We can now substitute l for w + 5.82 into our original equation, 2l + 2w = 101.76, and we get 2(w + 5.82) + 2w = 101.76. Now simplify and get 4w + 11.64 = 101.76. Simplifying this the whole way, we get w = 22.53. Now plug this value of w back into the equation, l = w + 5.82, and we get l = 22.53 + 5.82 = 28.35. We now have width: 22.53 in. and length: 28.35 in.

The solution to the system of equations is (x, y) = (-261/47, 44/47) as an ordered pair.

To solve the given system of equations:

Equation 1: 8x + 9y = -36

Equation 2: x + 7y = 1

We can use the method of substitution or elimination to find the values of x and y. Let's use the method of substitution:

From Equation 2, we can solve for x:

x = 1 - 7y

Substituting this value of x into Equation 1:

8(1 - 7y) + 9y = -36

8 - 56y + 9y = -36

-47y = -44

y = 44/47

Substituting the value of y back into Equation 2 to find x:

x + 7(44/47) = 1

x + 308/47 = 1

x = 1 - 308/47

x = (47 - 308)/47

x = -261/47

Therefore, as an ordered pair, the solution to the system of equations is (x, y) = (-261/47, 44/47).

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Answer:

2923 is your p is equal to 2 and n

Step-by-step explanation:

√z is defined only when z >= 0

Therefore √x - 1 is defined only when (x - 1) >= 0, x >= 1.

The only graph that shows the domain x >= 1 is graph Y.

Answer:

\(P(X\cap Y\cap Z)=0.05\)

Step-by-step explanation:

From the question we are told that:

Percentage of audience in first concert \(P(X)=0.28\)

Percentage of audience in second concert \(P(Y)=0.42\)

Percentage of audience in third concert \(P(Z)=0.30\)

Audience Percentage at at-least one concert \(P(X \cup Y \cup Z)=0.80\)

Percentage of audience at first & second concert \(P(X \cap Y)=0.10\)

Percentage of audience in first & third concert \(P(X \cap Z)=0.08\)

Percentage of audience in second & third concert \(P(Y\cap Z)=0.07\)

Generally the equation for probability of attending all concerts \(P(X\cap Y\cap Z)\)is mathematically given by

\(P(X \cup Y \cup Z)=P(X)+P(Y)+P(Z)-P(X \cap Y)-P(X \cap Z)-P(Y\cap Z)+P(X\cap Y\cap Z)\)

\(P(X\cap Y\cap Z)=P(X \cup Y \cup Z)-P(X)-P(Y)-P(Z)+P(X \cap Y)+P(X \cap Z)+P(Y\cap Z)\)

\(P(X\cap Y\cap Z)=0.80-0.28-0.42-0.30+0.10+0.80+0.70\)

\(P(X\cap Y\cap Z)=0.05\)

Therefore the probability that a randomly selected audient attended all the concerts

\(P(X\cap Y\cap Z)=0.05\)

The number of adult and children in the group is given as follows:

The amounts are obtained by a system of equations, for which the variables are given as follows:

There were a total of 28 people, hence:

x + y = 28

y = 28 - x.

They spent a total of $308, hence:

15x + 8y = 308.

Replacing the second equation into the first, the value of x is given as follows:

15x + 8(28 - x) = 308

7x = 84

x = 84/7

x = 12.

Then the value of y is given as follows:

y = 28 - x = 28 - 12 = 16.

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Answer:

7m

Step-by-step explanation:

product means multiplication

7×m = 7m

Answer:

the answer is

Step-by-step explanation:

So 12 more than N would be 12 + N.

Answer:

b) 12 + n

Step-by-step explanation:

The statement is,

→ 12 more than a number.

Now equation will be,

→ 12 + n

≈ (or) n + 12

So, option (b) is correct.

Formula for circumference that involves the radius ⇒ C = 2πr

Since we are given that the circumference is 86 cm, substitute it in.

86 = 2πr

Now, π is equal to approximately 3.14 so we can

plug 3.14 in for π and we have 86 cm = 2(3.14)r.

Now solve the equation.

2(3.14) is 6.28 and we have 86 cm = 6.28r.

Now divide both sides by 6.28 and we have 13.6942 = r.

So the radius of the hula hoop is 13.6942 cm.

Answer:

43

Step-by-step explanation:

The transformation of a function may involve any change in the function. The value of the function g(x) will be 6|x|+10.

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units, y=f(x+c) (same output, but c units earlier)

Right shift by c units, y=f(x-c)(same output, but c units late)

Vertical shift

Up by d units:

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k \times f(x)

Horizontal stretch by a factor k: y = f(\dfrac{x}{k})

Given the function f(x)=3|x|+5, therefore, if the function is vertically stretched by a factor of 2, then the function g(x) can be written as,

g(x) = 2[f(x)]

g(x) = 2(3|x|+5)

g(x) = 6|x| + 10

Hence, the value of the function g(x) will be 6|x|+10.

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The area of the triangle FGH is equal to  13√10 unit²

Given that the vertices;

F(-5,-7), G(-2,-5), and H(-6,-2)

We have to find the area of the triangle as;

Area of triangle = 1/2bh²

Here,

Area of triangle FGH = 1/2 (GH) (FG)²

Now,

Length of FG =  √26

Length of GH =  √10

Then,

Area of triangle FGH = 1/2 (GH) (FG)²

Area of triangle = 1/2 × √10 × √26²

Area of triangle = 1/2 × √10 × 26

Area of triangle FGH = 13√10

Therefore,

The area of the triangle FGH = 13√10 unit²

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Answer:

23.87

Step-by-step explanation:

Answer:

  $4918

Step-by-step explanation:

You want the tax owed on $90,000 using the given tax rate table.

The tax is the sum of the amounts of tax due in each income range.

  tax = 0.0575(90,000 -17,000) +0.05(17,000 -5000) +0.03(5000 -3000) +0.02(3000)

  = 0.0575(90,000) -(17000(.0575 -.05) +5000(.05 -.03) +3000(.03 -.02))

  = 0.0575(90,000) -(127.50 +100 +30)

  = 5175 -257.50 = 4917.50

Rounded to the nearest dollar, the tax due is $4,918.

__

Additional comment

The tax will be the maximum of ...

You can compute them all and find the maximum, or you can choose the function applicable to the income amount. The result is the same.

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Answer:

b)  geometric

Step-by-step explanation:

Notice that each new term is derived by multiplying the previous term by 2.  Thus:  the first term is -2 and the common ratio is 2.  This is a geometric sequence.

Answer:

1  3/15 - 5/15

Step-by-step explanation:

Hope this helps. PS the / sign is supposed to be for the fraction.

Step-by-step explanation:

1 1/5 - 1/3 = 0.86

Hope I helped. The only way I know how to dot this is in decimal form sorry.

Answer:

$3.77 is the tax. Total is $57.62 is you buy it.

Step-by-step explanation:

Answer:

3.77

Step-by-step explanation:

Sales price x sales tax rate = sales tax

53.85 x .07 (7%) =  3.77

Answer: 6.

Step-by-step explanation: We can solve this problem by using the combination formula:

C(n, r) = n! / (r! * (n - r)!)

In this case, n is the number of choices (the digits 2, 3, 4, 5, 6, and 9) and r is the number of items in each combination (4 digits).

Plugging in the values, we get:

C(6, 4) = 6! / (4! * 2!) = (6 * 5 * 4 * 3) / (4 * 3 * 2) = 30

Therefore, there are 30 four-digit odd numbers that can be formed using the digits 2, 3, 4, 5, 6, and 9. However, not all of these numbers will be less than 5000, so we need to further filter the list to only include those that meet this requirement.

The four-digit odd numbers that can be formed using these digits are:

2359, 2395, 2539, 2593, 2935, 2953, 3259, 3295, 3529, 3592,

3925, 3952, 5239, 5293, 5329, 5392, 5923, 5932, 9235, 9253,

9352, 9523, 9532

Out of these numbers, only 2359, 2539, 2935, 3925, 5239, and 9523 are less than 5000. Therefore, there are 6 four-digit odd numbers less than 5000 that can be formed using the digits 2, 3, 4, 5, 6, and 9.

Therefore, the final answer is 6.

1.) The probability that the sample mean will be greater than 48 minutes is 0.9332.

2.) The probability of the sample mean being between 44 and 49 minutes is 0.6687.

3.) The z-score of 10 indicates that the sample mean of 65 minutes is 10 standard deviations above the population mean.

To solve this problem, we can use the Central Limit Theorem (CLT), which states that the distribution of sample means tends to be approximately normally distributed, regardless of the shape of the original population, when the sample size is large enough.

1.) Probability of sample mean > 48 minutes:

To calculate this probability, we need to standardize the sample mean using the formula: z = (x - μ) / (σ / √n), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, the population mean (μ) is 45 minutes, the population standard deviation (σ) is 12 minutes, and the sample size (n) is 36. We want to find the probability of the sample mean being greater than 48 minutes.

Calculating the z-score:

z = (48 - 45) / (12 / √36) = 3 / 2 = 1.5

Using a standard normal distribution table or calculator, we find that the probability corresponding to a z-score of 1.5 is approximately 0.9332. Therefore, the probability that the sample mean will be greater than 48 minutes is approximately 0.9332.

2.) Probability of sample mean between 44 and 49 minutes:

To calculate this probability, we need to find the z-scores for both 44 and 49 minutes and then calculate the area between those z-scores.

Calculating the z-scores:

For 44 minutes:

z1 = (44 - 45) / (12 / √36) = -1 / 2 = -0.5

For 49 minutes:

z2 = (49 - 45) / (12 / √36) = 4 / 2 = 2

Using the standard normal distribution table or calculator, we find the probabilities corresponding to z1 and z2:

P(z < -0.5) ≈ 0.3085

P(z < 2) ≈ 0.9772

The probability of the sample mean being between 44 and 49 minutes is approximately P(-0.5 < z < 2) = P(z < 2) - P(z < -0.5) ≈ 0.9772 - 0.3085 = 0.6687.

3.)Conclusion from 100 samples with a mean of 65 minutes:

If 100 samples were collected, and the sample mean was 65 minutes, we would need to assess whether this value is significantly different from the population mean of 45 minutes.

To make this assessment, we can calculate the z-score for the sample mean of 65 minutes:

z = (65 - 45) / (12 / √36) = 20 / 2 = 10

The z-score of 10 indicates that the sample mean of 65 minutes is 10 standard deviations above the population mean. This is an extremely large deviation, suggesting that the sample mean of 65 minutes is highly unlikely to occur by chance.

Given this, we can conclude that the sample mean of 65 minutes is significantly different from the population mean. It may indicate that there is a systematic difference in the delivery times between the sample and the population, possibly due to factors such as increased demand, traffic, or other external variables

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Complete question:

If sum of squares due to regression (SSR) is found to be 14,200 and sum of squares error (SSE) is 1525, then what is the value of total sum of squares (SST) ?

Answer:

The value of total sum of squares (SST) is 15,725.

Step-by-step explanation:

Given;

sum of squares due to regression (SSR) = 14,200

sum of squares error (SSE) =  1525

sum of squares (SST) = ?

The total sum of squares (SST) is given as the summation of the sum of squares due to regression (SSR) and sum of squares error (SSE);

SST = SSR + SSE

Substitute the given values and solve for SST.

SST = 14,200 + 1525

SST = 15,725

Therefore, the value of total sum of squares (SST) is 15,725.

The value of the total sum of square (SST) is the sum of the sum of square Regression (SSR) and the Sum of Square Error (SSE). Hence, the Total sum of Square , SST is 15725

Given the Parameters :

The Total Sum of Square (SST) is defined thus :

SST = 1525 + 14200

SST = 15,725

Therefore, the Total Sum of Square for the analysis of variance relationship ls 15,725.

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