If you borrow $800 for 8 years at anannual interest rate of 11%, howmuch will you pay altogether?Enter

The surface area of the pyramid is given by the equation A = 170.4 inches²

The total surface area is the summation of the areas of the base and the three other sides. A = B + ( 1/2 ) ( P x h ), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid

Surface Area of Pyramid = B + ( 1/2 ) ( P x h )

Given data ,

Let the surface area of the pyramid be represented as A

Now , the equation will be

The slant height of the pyramid h = 6 inches

The side of the equilateral triangle = 12 inches

So , the perimeter of the triangle = 3 x side length

Substituting the values in the equation , we get

The perimeter of the triangle = 36 inches

The area of the base = 62.4 inches²

So , Surface Area of Pyramid = B + ( 1/2 ) ( P x h )

Substituting the values in the equation , we get

Surface Area of Pyramid = 62.4 + ( 1/2 ) ( 36 x 6 )

On simplifying the equation , we get

Surface Area of Pyramid = 62.4 + ( 108 )

Surface Area of Pyramid = 170.4 inches²

Hence , the surface area of pyramid is 170.4 inches²

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Explanation

The question wants us to determine the number of different ID cards that can be made if there are 3 digits on a car.

To do so, let us first list out all the possible outcomes. These are:

We can see that there are 10 possible digits

For the first case where no digit can be used more than once, we will have

Therefore, there are

For the second case, if the digits can be repeated, then, we will have

Then, since the numbers can be repeated, we will have

Answer:

B

Step-by-step explanation:

if you cannot recognize the right equation, just start evaluating some points... try 5, 6, 4

Answer: -24x^2+28x

Step-by-step explanation: -4x*6x-(-4x)*7 to -24x^2+28x

Answer:

Calculate the area of the right triangle that has vertices at A(626, 200), B(726, 200), and (025,10)

The predicted value of y when x = 3, based on the least-squares regression line equation y = 50 - 15x, is y = 50 - 15(3) = 5.

The given least-squares regression line equation y = 50 - 15x represents a linear relationship between the variables x and y. In this equation, the coefficient of x (-15) represents the slope of the line, and the constant term (50) represents the y-intercept.

To find the predicted value of y when x = 3, we substitute x = 3 into the equation and solve for y. Plugging in x = 3, we have y = 50 - 15(3). Simplifying this expression, we get y = 50 - 45 = 5.

Therefore, when x = 3, the predicted value of y based on the least-squares regression line is 5. This means that according to the regression line, when x is 3, the expected or estimated value of y is 5.

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Answer: Sample D is most representative.

Step-by-step explanation:

Sample D is most representative as the percentage per shape stays the same within the sample and the population.

Answer:

sample D is most representative

Answer:

4 (2×-2)+3(5×5)

4 (-4)+3 (25)

-16+75

=59ans

Answer:

Drinks = $1.5

Pizza = $10.50

Step-by-step explanation:

let d = drinks

p = pizza

p = 7d  equation 1

2p + 8d = 33 equation 2

from equation 1, we know the price of one pizza, the price of two pizzas can be determined by multiplying by 2

2p = 7d x 2 = 14d  eqn 3

Substitute for 2p in equation 2  

14d + 8d = 33

22d = 33

Divide both sides of the equation by 22

d = $1.5

Substitute for d in equation 1

p = 1.5 x 7 = $10.5

The solution to the given system of equations using the Gaussian method is: x = 29/2, y = -25/2, and z = -19/2.

To solve the system of equations using the Gaussian method:

1. Write the augmented matrix:

  \(\[ \begin{bmatrix} 2 & 1 & 1 & | & 10 \\ 3 & 3 & 0 & | & 9 \\ 5 & 4 & 1 & | & 19 \\ \end{bmatrix} \]\)

2. Perform row operations to transform the matrix into row-echelon form:

  - R2 = R2 - (3/2)R1

  - R3 = R3 - (5/2)R1

  The new matrix becomes:

  \(\[ \begin{bmatrix} 2 & 1 & 1 & | & 10 \\ 0 & 3/2 & -3/2 & | & -6/2 \\ 0 & 5/2 & -3/2 & | & 14/2 \\ \end{bmatrix} \]\)

3. Multiply R2 by 2/3 to make the leading coefficient of R2 equal to 1:

  - R2 = (2/3)R2

  The new matrix becomes:

  \(\[ \begin{bmatrix} 2 & 1 & 1 & | & 10 \\ 0 & 1 & -1 & | & -3 \\ 0 & 5/2 & -3/2 & | & 14/2 \\ \end{bmatrix} \]\)

4. Perform row operations to eliminate the coefficient in R3:

  - R3 = R3 - (5/2)R2

  The new matrix becomes:

  \(\[ \begin{bmatrix} 2 & 1 & 1 & | & 10 \\ 0 & 1 & -1 & | & -3 \\ 0 & 0 & -1 & | & 19/2 \\ \end{bmatrix} \]\)

5. Multiply R3 by -1 to make the leading coefficient of R3 equal to 1:

  - R3 = -R3

  The new matrix becomes:

  \(\[ \begin{bmatrix} 2 & 1 & 1 & | & 10 \\ 0 & 1 & -1 & | & -3 \\ 0 & 0 & 1 & | & -19/2 \\ \end{bmatrix} \]\)

6. Perform row operations to eliminate the coefficients in R1 and R2:

  - R1 = R1 - R3

  - R2 = R2 + R3

  The new matrix becomes:

  \(\[ \begin{bmatrix} 2 & 1 & 0 & | & 29/2 \\ 0 & 1 & 0 & | & -25/2 \\ 0 & 0 & 1 & | & -19/2 \\ \end{bmatrix} \]\)

7. Finally, read the values of x, y, and z from the augmented matrix:

  x = 29/2, y = -25/2, z = -19/2

Therefore, the solution to the given system of equations is x = 29/2, y = -25/2, and z = -19/2.

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Answer:

Answer Expert Verified y = (slope) x + (y-intercept) . Right away, you know that this line goes through the origin ...

Simplifying

2x + 9 + -10 = -5

Reorder the terms:

9 + -10 + 2x = -5

Combine like terms: 9 + -10 = -1

-1 + 2x = -5

Solving

-1 + 2x = -5

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.

-1 + 1 + 2x = -5 + 1

Combine like terms: -1 + 1 = 0

0 + 2x = -5 + 1

2x = -5 + 1

Combine like terms: -5 + 1 = -4

2x = -4

Divide each side by '2'.

x = -2

Simplifying

x = -2

I hope it helps you

When a question asks for an exponential model, the answer should have at least two variables, typically denoted as y and x.

The exponential model is a type of mathematical equation that represents the relationship between two variables, where one variable (y) changes exponentially with respect to changes in the other variable (x).

In its general form, an exponential model can be written as:

y = ab^x

where y is the dependent variable, x is the independent variable, a is a constant (representing the value of y when x=0), and b is the base of the exponential function (representing the rate of change of y with respect to x).

It is important to note that there can be variations of this general form of the exponential model, depending on the specific context of the problem and the type of data being analyzed.

For example, some exponential models may have additional parameters or modifications to better fit the data. However, the fundamental characteristic of an exponential model is that it represents an exponential relationship between two variables.

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Answer:

5 + (x * 10) = y

Step-by-step explanation:

The list starts off as 5

Then every hour(X), 10 dollars is being added to the total cost(Y).

Answer:

I would say 32 but I'm so sorry if it's wrong

When there is a multiplication between a term with parenthesis and another term we apply the distributive property:

It says that the parenthesis indicates that the term outside will multiply each of the terms inside it.

For the first parethesis:

- 3(2x + 4) = (-3) · 2x + (-3) · 4

since

(-3) · 2x = -6x

(-3) · 4 = -12

then

- 3(2x + 4) = (-3) · 2x + (-3) · 4

- 3(2x + 4) = -6 x - 12

For the second

– (2x + 4) ​= – 1 (2x + 4)

= ​(-1) · 2x + (-1) · 4

=-2x -4

We can see in this case that both parenthesis are the same, then it is the common factor of - 3(2x + 4) and – (2x + 4) ​,

We can factor it by separating it of each term and letting the remaining terms inside a parenthesis

- 3(2x + 4) – (2x + 4) ​= (2x + 4) ( -3 -1)

= (2x + 4) ( -4)

= -4 (2x + 4)

Answer:

I found 6 answers

Step-by-step explanation:

The linear equations are x + y = 679, 4x + 7y = 3370 and  586 non-students attended the play.

What is a linear equation, exactly?

A linear equation is a mathematical equation that describes a straight line when plotted on a graph. It is an equation in which the highest power of the variable is one. Linear equations are commonly written in the form of y = mx + b, where "x" and "y" are variables, "m" is the slope of the line, and "b" is the y-intercept. Linear equations can be used to model many real-world situations, such as distance and speed, cost and revenue, and temperature and time.

Now,

a) Let x = student tickets sold and y = number of non-student tickets sold. Then we have the following system of linear equations:

x + y = 679 (the total number of tickets sold is 679)

4x + 7y = 3370 (the total revenue from ticket sales is $3370)

b) To solve for y, we can use the first equation to get:

y = 679 - x

then,

4x + 7(679 - x) = 3370

Simplifying and solving for x, we get:

3x = 2363

x = 787

So 787 student tickets were sold. To find the number of non-student tickets sold, we can use the equation y = 679 - x:

y = 679 - 787 = -108

Since it doesn't make sense to have a negative number of non-student tickets sold, we made an error somewhere. Looking at the problem again, we realize that the equation should be:

x + y = 679 (the total number of tickets sold is 679)

4x + 7y = 3370 (the total revenue from ticket sales is $3370)

where y represents the number of student tickets sold and x represents the number of non-student tickets sold. With this correction, we get:

y = 679 - x

4(679 - x) + 7x = 3370

Simplifying and solving for x, we get:

3x = 1759

x = 586.33

x = 586

So 586 non-student tickets were sold.

Which means 586 non-students attended the play.

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Answer:

∠3 and ∠10 are;

B. Alternate exterior angles

Step-by-step explanation:

From the given diagram, we have;

∠3 and ∠10 are angles on the same transversal

The location of ∠3 and ∠10 are on the outer (exterior) part of the two lines crossed by the transversal that forms ∠3 and ∠10 such that the two lines comes between the angles

∠3 and ∠10 are on the alternate sides of the transversal such that ∠3 is below the transversal and ∠10 is above the transversal

Therefore, ∠3 and ∠10 are alternate exterior angles.

Giovanna deposited $1600 into two accounts, half in First Oak and half in West United.

Interest earned in First Oak account after 5 years at 6% simple interest:

= 0.06 x $800 x 5

= $240

Interest earned in West United account after 5 years at 5% compounded annually:

= $800 x (1 + 0.05)^5 - $800

= $800 x 1.27628 - $800

= $221.02

Total interest earned in both accounts:

= $240 + $221.02

= $461.02

Therefore, Giovanna will have earned $461.02 in interest from both accounts at the end of 5 years.

Answer:

B

Step-by-step explanation:

y = 8√x (square both of side)

y² = 64x

x = y²/64

f-¹(x) = x²/64

The inverse is B.) f-¹(x) = x²/64 for, x≥0

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

Here, given that, f(x) = 8√x for x ≥ 0

Let, f(x)=y

Then, we get,

y = 8√x (square both of side)

y² = 64x

x = y²/64

i.e. f-¹(x) = x²/64

Hence, The inverse is B.) f-¹(x) = x²/64 for, x≥0

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Answer:

2 1/4

Step-by-step explanation:

ANOVA is a more appropriate and efficient method for evaluating mean differences when an experiment consists of three or more treatment conditions, as it provides a more robust and reliable analysis than multiple t-tests, while also reducing the risk of Type I errors.

The principal reason why you should use ANOVA (Analysis of Variance) instead of several t-tests to evaluate mean differences when an experiment consists of three or more treatment conditions is that multiple t-tests accumulate the risk of a Type I error.

A Type I error is the rejection of a true null hypothesis, which means that you have falsely concluded that there is a significant difference between the treatment groups when there is actually no difference. When conducting multiple t-tests, the probability of making a Type I error increases with the number of tests performed. In other words, if you perform multiple t-tests, the overall probability of making at least one Type I error increases, and this can lead to incorrect conclusions.

ANOVA is a statistical technique that allows you to compare the means of three or more treatment groups simultaneously while controlling the probability of making a Type I error. ANOVA compares the variance between groups to the variance within groups to determine if the differences between the treatment groups are statistically significant. By using ANOVA instead of multiple t-tests, you can reduce the overall risk of making a Type I error while still evaluating the mean differences between the treatment groups.

Therefore, ANOVA is a more appropriate and efficient method for evaluating mean differences when an experiment consists of three or more treatment conditions, as it provides a more robust and reliable analysis than multiple t-tests, while also reducing the risk of Type I errors.

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The formula used to calculate the likely size of the chance error is SE = s/√n where SE is the standard error, s is the standard deviation, and n is the sample size. In this problem, there are eight students, so n = 8.

The standard deviation can be calculated using the formula σ = √(Σ(x - µ)² / n), where σ is the standard deviation, x is each data point, µ is the mean, and n is the sample size. Using the given data, the mean can be calculated as follows:

Mean = (9.93 + 9.96 + 10.10 + 10.02 + 10.02 + 9.90 + 9.93 + 9.92) / 8 = 9.985Next, calculate the sum of the squared deviations from the mean:Σ(x - µ)² = (9.93 - 9.985)² + (9.96 - 9.985)² + (10.10 - 9.985)² + (10.02 - 9.985)² + (10.02 - 9.985)² + (9.90 - 9.985)² + (9.93 - 9.985)² + (9.92 - 9.985)²Σ(x - µ)² = 0.0211.

Then, calculate the variance by dividing the sum of squared deviations by the sample size:

Variance = Σ(x - µ)² / n

Variance = 0.0211 / 8Variance = 0.00264Finally, calculate the standard deviation by taking the square root of the variance:

Standard deviation = √(Σ(x - µ)² / n)Standard deviation = √(0.00264)Standard deviation = 0.05134The standard error can now be calculated by dividing the standard deviation by the square root of the sample size:

Standard error = s/√nStandard error = 0.05134/√8Standard error = 0.01813

Given the measurements of eight students to determine the correct length of a ruler in a laboratory, we can calculate the size of the chance error using the formula SE = s/√n. This formula calculates the standard error, where s is the standard deviation and n is the sample size. To find the standard deviation, we use the formula σ = √(Σ(x - µ)² / n), where x is each data point, µ is the mean, and n is the sample size. Using the given measurements, the mean of the data is calculated to be 9.985. Using this mean, we can calculate the sum of the squared deviations from the mean, which is equal to 0.0211. Then, we can calculate the variance by dividing the sum of squared deviations by the sample size, which is equal to 0.00264. Finally, the standard deviation can be calculated by taking the square root of the variance, which is equal to 0.05134. By dividing the standard deviation by the square root of the sample size, we can find the standard error, which is equal to 0.01813. Therefore, we would expect the likely size of the chance error to be about 0.018 inches or so.

Given the measurements of eight students, we used the formulas SE = s/√n and σ = √(Σ(x - µ)² / n) to calculate the size of the chance error. The mean of the data was found to be 9.985, and the sum of the squared deviations from the mean was equal to 0.0211. We used these values to calculate the variance, which was equal to 0.00264, and the standard deviation, which was equal to 0.05134. Finally, we found the standard error to be equal to 0.01813. Therefore, we would expect the likely size of the chance error to be about 0.018 inches or so.

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The risk of explosion in the process industry is 6.6594e-06 per year.

To calculate the risk of explosion, we need to consider the probability of a gas release, the probability of ignition, and the probability of fatal injury.

Step 1: Calculate the probability of an explosion.

The probability of a gas release per year is given as\(1.23 * 10^-^5\).

The probability of ignition is 0.54.

The probability of fatal injury is 0.32.

To calculate the risk of explosion, we multiply these probabilities:

Risk of explosion = Probability of gas release * Probability of ignition * Probability of fatal injury

Risk of explosion = 1.23 * \(10^-^5\) * 0.54 * 0.32

Risk of explosion = 6.6594 *\(10^-^6\) per year

Therefore, the risk of explosion in the process industry is approximately 6.6594 * 10^-6 per year.

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The first five nonzero terms of the Taylor series for\(f(x) = \frac{7 \cdot \arctan(x)}{\frac{\pi}{24}}\) about the point a = 1 are \(7 + \frac{84}{\pi}(x - 1) - \frac{84}{\pi}(x - 1)^2 + 0 + 0\)

The first five nonzero terms of the Taylor series generated by the function \(f(x) = \frac{7 \cdot \arctan(x)}{\frac{\pi}{24}}\) about the point a = 1 can be found using the definition of the Taylor series.

The general form of the Taylor series expansion is given by:

\(f(x) = f(a) + f'(a)(x - a) + (f''(a)(x - a)^2)/2! + (f'''(a)(x - a)^3)/3! + (f''''(a)(x - a)^4)/4! + ...\)

To find the first five nonzero terms, we need to evaluate the function f(x) and its derivatives up to the fourth derivative at the point a = 1.

First, let's find the function and its derivatives:

\(f(x) = \frac{7 \cdot \arctan(x)}{\frac{\pi}{24}}\)

\(f'(x) = \frac{7}{\frac{\pi}{24} \cdot (1 + x^2)}\)

\(f''(x) = \frac{-7 \cdot (2x)}{\frac{\pi}{24} \cdot (1 + x^2)^2}\)

\(f'''(x) = \frac{-7 \cdot (2 \cdot (1 + x^2) - 4x^2)}{\frac{\pi}{24} \cdot (1 + x^2)^3}\)

\(f''''(x) = \frac{-7 \cdot (8x - 12x^3)}{\frac{\pi}{24} \cdot (1 + x^2)^4}\)

Now, let's substitute the value of a = 1 into these expressions and simplify:

\(f(1) = \frac{7 \cdot \arctan(1)}{\frac{\pi}{24}} = 7\)

\(f'(1) = \frac{7}{\frac{\pi}{24} \cdot (1 + 1^2)} = \frac{84}{\pi}\)

\(f''(1) = \frac{-7 \cdot (2 \cdot 1)}{\frac{\pi}{24} \cdot (1 + 1^2)^2} = \frac{-84}{\pi}\)

\(f'''(1) = \frac{-7 \cdot (2 \cdot (1 + 1^2) - 4 \cdot 1^2)}{\frac{\pi}{24} \cdot (1 + 1^2)^3} = 0\)

\(f''''(1) = \frac{-7 \cdot (8 \cdot 1 - 12 \cdot 1^3)}{\frac{\pi}{24} \cdot (1 + 1^2)^4} = 0\)

Now we can write the first five nonzero terms of the Taylor series:

\(f(x) = 7 + \frac{84}{\pi}(x - 1) - \frac{84}{\pi}(x - 1)^2 + \dots\)

These terms provide an approximation of the function f(x) near the point a = 1, with increasing accuracy as more terms are added to the series.

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Answer:

b= 2\(\sqrt{66}\) or 16.248

Step-by-step explanation:

5^2 +b^2= 17^2

25 + b^2 = 289

-25              -25

b^2=264

b= 2\(\sqrt{66}\) or 16.248

The answer is e. none of the above/can’t be determined with info given.

Based on the information given, we have:

P(A) = 0.46

P(B) = 0.17

P(A U B) = 0.63

Note that P(A U B) represents the probability of either event A or event B occurring, or both.

If events A and B are mutually exclusive, it means they cannot occur at the same time. In other words, if event A occurs, event B cannot occur, and vice versa. In this case, the probability of both events occurring would be zero.

On the other hand, if events A and B are collectively exhaustive, it means that together they account for all possible outcomes. In other words, either event A or event B (or both) must occur, and there are no other possibilities.

Using these definitions, we can see that events A and B are neither mutually exclusive nor collectively exhaustive. This is because the probability of both events occurring (i.e., the intersection of A and B) is not zero, which means they are not mutually exclusive. Additionally, the probability of either A or B occurring (i.e., the union of A and B) is not equal to one, which means they are not collectively exhaustive.

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The above prompt has to do with linear functions. The answers to same are given below.

12-14) the graph of the functions are attached accordingly.

15) a) The cost of buying s songs can be calculated using the following function:

C(s) = 0.9s

b) To find the cost of buying 5 songs, we can substitute s = 5 into the function:

C(5) = 0.9(5) = 4.5

So the cost of buying 5 songs is $4.50.

16) he linear function that relates y to x. y = (1/3)x + 3

We can see that the x-coordinates increase by 3 as we move from one point to the next, and the y-coordinates increase by 1 as we move from one point to the next. This suggests that the slope of the line connecting these points is:

slope = (change in y) / (change in x) = 1/3

We can then use the point-slope form of the equation of a line, using one of the points, say (-6,1), as the reference point:

y - y1 = m(x - x1)

where y1 = 1, x1 = -6, and m = 1/3. Substituting in these values, we get:

y - 1 = (1/3)(x + 6)

Expanding and simplifying, we get:

y = (1/3)x + 3

This is the linear function that relates y to x.

17) Since all values of y are constant (-7) regardless of the value of x, we cannot write a linear function that relates y to x. Instead, we can say that y is a constant function with a value of -7. In other words, y = -7 for all values of x.

18) a. To write the linear function that relates y to x, we need to find the slope and y-intercept of the line that passes through the given points. Using the formula for slope, we have:

slope = (change in y) / (change in x)

= (y2 - y1) / (x2 - x1)

= (15 - 12) / (8 - 6)

= 1.5

Using the slope-intercept form of a linear function (y = mx + b), where m is the slope and b is the y-intercept, we can write:

y = 1.5x + b

To find the value of b, we can use any of the given points. Let's use (6, 12):

12 = 1.5(6) + b

b = 3

Therefore, the linear function that relates y to x is:

y = 1.5x + 3

b. The slope of the linear function is 1.5. This means that for every increase of one week in the puppy's age, its weight increases by 1.5 pounds on average. The y-intercept of the function is 3, which means that when the puppy is born (at 0 weeks), its weight is estimated to be 3 pounds.

c. To find out after how many weeks the puppy will weigh 33 pounds, we can use the linear function we found in part (a):

y = 1.5x + 3

Substitute y = 33 and solve for x:

33 = 1.5x + 3

30 = 1.5x

x = 20

Therefore, the puppy will weigh 33 pounds after 20 weeks.

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Answer:

for example lets say: (x+2)(x-2)(

x

4

+4

x

2

+16)

Rewrte the given terms as perfect cubes as follows and use the algebraic identity for the factorisation of difference of two cubes.

x

6

-64 =  

(

x

2

)

3

-  

(

4

)

3

=(

x

2

-4) (

x

4

+4

x

2

+16)

=(x+2)(x-2)(

x

4

+4

x

2

+16)

Step-by-step explanation:

do u think its correct?