The triangular prism below has a height of 13.4 units3 and a volume of 536 units

Find the area of one of its bases.

Step-by-step explanation:

You have to study the f'(x)

f'(x)= (e^x - 2)÷(e^x-2x)

it has to be = 0

(c.e.: e^x > 2x)

e^x - 2=0

e^x = 2

x= ln 2

The value of k is 18.

If x + 2 is a factor of f(x) = x^3 + 5x + k, it means that when x = -2, the expression f(x) becomes zero.

Substituting x = -2 into f(x), we have:

f(-2) = (-2)³ + 5(-2) + k

= -8 - 10 + k

= -18 + k

Since f(-2) should equal zero, we have:

-18 + k = 0

k = 18

Therefore, the value of k is 18.

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How to compare fractions is explained in the solution below.

One way to compare fractions is to convert them into their decimal form and decide which is the smaller of the two.

Example: 7/10 and 3/5 become 0.7 and 0.6.

Hence 3/5 is smaller than 7/10.

The other way is to convert them into fractions with identical denominator.

For that multiply the denominator of one fraction with the numerator and denominator of the other.

Do the same with the other denominator and the other fraction. Then decide which fraction is the smaller of the two.

Example: 7/8 and 13/15 become (7*15)/(8*15) = 105/120 and

(13*8)/(15*8) = 104/120.

Hence 13/15 is smaller than 7/8.

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The system of linear equations has no solution

The system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1.

In this problem, we have two equations which are;

x = 10 + 6y ...eq(i)

x - 6y = 5 ...eq(ii)

From eq(i)

x = 10 + 6y;

We can substitute this into eq(ii)

10 + 6y - 6y = 5

10 +0 = 5

Since y is already canceled out, we don't have solution to this equations.

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By completing the flexible budget performance report, Milano Pizza's owner can identify areas for improvement and make informed decisions to optimize the pizzeria's performance.

The flexible budget performance report for Milano Pizza for November will include revenue and spending variances, as well as activity variances. The two major cost drivers are the number of pizzas sold and the number of deliveries made.

1. Revenue variances: Calculate the difference between the actual revenue and the budgeted revenue for both in-store dining and delivery services. Label the variances as "F" for favorable (actual revenue higher than budgeted) or "U" for unfavorable (actual revenue lower than budgeted).

2. Spending variances: Analyze the costs related to pizza production and delivery person wages. Compare the actual costs to the budgeted costs, and label the variances as "F" for favorable (actual costs lower than budgeted) or "U" for unfavorable (actual costs higher than budgeted).

3. Activity variances: Assess the differences in the number of pizzas sold and deliveries made compared to the budgeted activity levels. Label these variances as "F" for favorable (higher activity than budgeted), "U" for unfavorable (lower activity than budgeted), or "None" for no effect (zero variance).

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The reduced row echelon form of the matrix is given as follows:

[tex]\left[\begin{array}{cccc}-1&0&0&8\\0&1&0&-2\\0&0&1&-6\end{array}\right][/tex]

The reduced row echelon form of a matrix is matrix in which the matrix except the last column has the format of an identity matrix, that is, a matrix in which the principal diagonal elements are of 1 and the rest of the elements are of 0.

Hence we can use a mix of row operations, along with the solution of a system of equations, to obtain the reduced row echelon form of a matrix.

The matrix in the context of this problem is defined as follows:

[tex]\left[\begin{array}{cccc}-1&5&-3&6\\0&3&6&-42\\0&-6&-1&18\end{array}\right][/tex]

First we want a value of 1 at line 1, column 1, hence we multiply the first line by -1, that is:

R1 -> -R1.

Hence:

[tex]\left[\begin{array}{cccc}1&-5&3&-6\\0&3&6&-42\\0&-6&-1&18\end{array}\right][/tex]

Then we want a value of 1 at line 2 column 2, thus:

R2 -> R2/3.

Hence:

[tex]\left[\begin{array}{cccc}1&-5&3&-6\\0&1&2&-14\\0&-6&-1&18\end{array}\right][/tex]

Then we want a value of 0 at line 3, column 2, hence:

L3 -> L3 + 6L2

[tex]\left[\begin{array}{cccc}1&-5&3&-6\\0&1&2&-14\\0&0&11&-66\end{array}\right][/tex]

Then the solution to the system of equations is given as follows:

Hence the row echelon form of the matrix is given as follows:

[tex]\left[\begin{array}{cccc}-1&0&0&8\\0&1&0&-2\\0&0&1&-6\end{array}\right][/tex]

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Answer: 32.493 maybe, dont quite understand the question

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer: n = 412

Step-by-step explanation:

If the last two digits of a number are divisible by 4, the whole number is divisible by 4 since any multiple of 100 is divisible by 4. The largest number that can be created is 421 since the largest number is in the hundreds place and then the second largest number is in the tens place, but 21 is not divisible by 4. The second largest number, 412, still has the greatest number as the hundreds place, but the tens place is now smaller. 12 is divisible by 4, so 412 is divisible by 4. We know that 412 is the largest possible number for n because there is only one larger number than 412, which is 421 and it is not divisible by 4.

Answer:

-----------------------------

Divisibility rule for 4:

We have 3 digits and the greatest number can be made by these digits is 421. But it has to be divisible by 4, hence we rearrange it to 412. Since 12 is divisible by 4, the number is divisible by 4.

Now, we choose 9 as the fourth digit. It will be a first digit from left and form the largest possible number n:

The expression in algebraic notation is 3 * (k - p²)

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

Three times the difference between k and the square of p​

Three times means 3*

So, we have

3 * the difference between k and the square of p​

the difference between k and the square of p​ means

k - p²

So, we have

3 * (k - p²)

So, we can conclude that

The expression"Three times the difference between k and the square of p​" in algebraic notation is 3 * (k - p²)

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Answer:

A. 6

Step-by-step explanation:

We know that 12% can be written in fraction form as [tex]\frac{12}{100}[/tex]. So, 12% of 100 is [tex]100\cdot\frac{12}{100} = 12[/tex].

We also know that 50 is half of 100. Therefore, 12% of 50 is exactly half of 12% of 100:

[tex]12\% \cdot 50[/tex]

[tex]= \frac{1}{2}(12\% \cdot 100)[/tex]

[tex]= \frac{1}{2}(12)[/tex]

[tex]\boxed{=6}[/tex]

The quadratic equation can be written as follows:

y = 5(x - 3)² + 50.

The quadratic function in the context of this problem is defined as follows:

y = 5x² - 30x + 95

The coefficients of the quadratic function are given as follows:

a = 5, b = -30 and c = 95.

Then the x-coordinate of the vertex is given as follows:

h = -b/2a

h = 30/10

h = 3.

The y-coordinate of the vertex is given as follows:

h = 5(3)² - 30(3) + 95

h = 50.

Hence the equation is:

y = 5(x - 3)² + 50.

The quadratic function in the context of this problem is defined as follows:

y = 5x² - 30x + 95

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Answer:

  85 1/3 cubic units

Step-by-step explanation:

You want the volume of a solid whose base is the ellipse in the x-y plane with axes 16 and 8 units and whose cross sections perpendicular to the major axis are isosceles triangles with height equal to 1/4 of the cross section dimension parallel to the minor axis.

The isosceles triangle cross section has base 2y and height (2y)/4, so area of ...

  A = 1/2bh

  A = (1/2)(2y)(2y/4) = y²/2

A differential of volume is the product of the area of a slice and its thickness:

  dV = A·dx = (1/2)y²·dx

The total volume is the integral of this differential of volume over the interval x ∈ [-8, 8]. That integral will be twice the integral on the interval [0, 8}, so we have ...

  [tex]\displaystyle V=2\int_0^8{\dfrac{y^2}{2}}\,dx=16\int_0^8{\left(1-\dfrac{x^2}{64}\right)}\,dx=16\left((8-0)-\dfrac{8^3-0^3}{3\cdot64}\right)\\\\\boxed{V=85\dfrac{1}{3}\text{ cubic units}}[/tex]

__

Alternate computation

The volume of half an ellipsoid with semi-axes 2, 4, and 8 is ...

  V = (1/2)(4/3)π(abc)

  V = (1/2)(4/3)π(2)(4)(8) = 128π/3

The area of half an ellipse with semi-axes 2 and 4 is ...

  A = (1/2)π(ab)

  A = (1/2)π(2)(4) = 4π

The area of a triangle with the same semi-axes is ...

  A = 1/2bh = (1/2)(2)(2·4) = 8

Then the ratio of triangle area to ellipse area at each cross section is ...

  triangle / ellipse = 8/(4π) = 2/π

The volume of the solid of interest is estimated to be this factor multiplied by the volume of the half-ellipsoid:

  (2/π)(128π/3) = 256/3 = 85 1/3 . . . . same as above

Triangle A''B''C'' is given by the image presented at the end of the answer.

The five more known rotation rules are given as follows:

The coordinates of triangle ABC are given as follows:

A(-5, 2), B(-3, 6), C(-1, 3).

Hence the coordinates after the rotation 90º clockwise are given as follows:

A'(2, 5), B'(6, 3), C'(3, 1).

y = 2 is an horizontal line, hence after the reflection, the x-coordinates remain constant, while the y-coordinates move in the opposite direction, hence:

A''(2, -1), B''(6,1), C''(3,3).

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The measure of the angles ∠1, ∠2, and ∠4 will be 133°, 47°, and 47°, respectively.

Given that:

Angle, ∠3 = 133°

Two angles are said to be supplementary angles if their sum is 180 degrees. Then we have

∠3 + ∠4 = 180°

133° + ∠4 = 180°

∠4 = 47°

When two lines intersect, then their opposite angles are equal. Then we have

∠4 = ∠2

∠2 = 47°

∠1 = ∠3

∠1 = 133°

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Answer:

Step-by-step explanation:

To find the median we first need to arrange the data points from smallest to largest:-

[tex]\sf 12, 13, 16, 5, 8, 18, 14, 19, 2[/tex]

Arranged:- 2, 5, 8, 12, 13, 14, 16, 18, 19.

Now, if the  number of data points is even, the median is the average of the two middle data points in the list. Since the numbers are odd, the median is the middle data point. which, in this case, it's 13.

2, 5, 8, 12, 13, 14, 16, 18, 19

______________________

Hope this helps!

The mass of the pipe is 254 grams.

First, The volume of the outer cylinder (V1) can be calculated using the formula for the volume of a cylinder:

V1 = π (radius_outer)² x  height

V1 = 3.14 (6)² (8)

and, the volume of inner cylinder

V2 = π(inner radius)² height

V2= 3.14 (5)² (8)

Now, let's calculate the volume of the plastic pipe:

Volume = V1 - V2

= 3.14 (6)² (8) - 3.14 (5)² (8)

= 3.14 x 8 (36- 25)

= 276.32 cm³

Now, Mass = Volume x density

Mass = 276.32 x 0.92

Mass = 254.19 grams

Thus, the mass of the pipe is 254 grams.

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The family's monthly payment should be $504.70.

We can use the following formula:

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

where

In this instance, the total loan amount is $43,008, the total number of payments is 9 years * 12 months/year = 108 months . The yearly interest rate must first be divided by 12 to determine the monthly interest rate. Assume that there is a 5% yearly interest rate.

[tex]r = 0.05 / 12 = 0.00417[/tex]

Now we can substitute the values into the formula and solve for P:

[tex]P = (0.00417 * $43,008) / (1 - (1 + 0.00417)^(-108))[/tex]

= $504.70

Therefore, the family's monthly payment should be $504.70.

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Answer:

----------------------

Martin has 1/4 of a bag of chocolate chip cookies.

Since the bag weights 4 pounds, Martin has:

Answer:

1.25

Step-by-step explanation:

Convert 1-half to a decimal by dividing 1 by 2:

1 ÷ 2 = 0.5

Add the two decimals:

0.5 + 0.75 = 1.25

Therefore, the sum of 1-half and 0.75 is 1.25.

The value of the cosine of angle B is,

⇒ cos B = 5 √89 / 89

We have to given that;

A triangle is shown in image.

Now, By trigonometry formula we get;

⇒ cos B = Base / Hypotenuse

Here, We can find the c as;

c² = 8² + 5²

c² = 64 + 25

c² = 89

c = √89

Hence, The value of the cosine of angle B is,

⇒ cos B = Base / Hypotenuse

⇒ cos B = 5 / √89

⇒ cos B = 5 √89 / 89

Thus, Option B; cos B = 5 √89 / 89 is correct.

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The cost each of one of the bag of windflower bulbs and one package of crocus bulbs is $14 and $16 respectively.

Let

cost each of one of the bag of windflower bulbs = x

Cost of each one package of crocus bulbs = y

4x + 9y = 200

2x + 6y = 124

Multiply (2) by 2

4x + 12y = 148

So,

4x + 9y = 200

4x + 12y = 248

Subtract to eliminate x

12y - 9y = 248 - 200

3y = 48

divide both sides by 3

y = 48/3

y = 16

Substitute y = 16 into (1)

4x + 9y = 200

4x + 9(16) = 200

4x + 144 = 200

4x = 200 - 144

4x = 56

x = 56/4

x = 14

Therefore, each one bag of windflower bulbs and one package of crocus bulbs is $14 and $16 respectively.

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The correct answer is B. Wages will increase.

When the Long-Run Aggregate Supply (LRAS) curve begins to slope upward in the second phase, it indicates that as the economy moves towards full employment and productive capacity, wages will increase.

The upward slope of the LRAS curve suggests that as the economy expands and approaches its maximum potential output, the demand for labor increases, leading to higher wages.

This is because firms need to pay higher wages to attract and retain workers in a tightening labor market, where the supply of labor becomes relatively scarce compared to the demand.

The right answer is B. Wages will increase.

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Answer:

------------------------

The graph has no intersection with the x-axis, therefore it has no zeros.

The matching choice is D.

Answer:

15 + x is the expression for 6 added to sum of 9 and x

The confidence interval based on the given values (x = 45, n = 96, Confidence level = 95%.

The confidence level (95%), sample size (n = 96), and sample mean (x = 45), we can calculate the margin of error and the confidence interval. Here's how:

1. Margin of Error:

The margin of error represents the maximum expected difference between the true population parameter and the sample estimate. It depends on the confidence level and the standard deviation (which we don't have in this case).

Since the standard deviation is unknown, we can use the t-distribution to estimate it. With a sample size of n = 96, the degrees of freedom are (n - 1) = 95. Considering a 95% confidence level, the critical value for a two-tailed test is approximately 1.984 (referencing a t-distribution table or calculator).

The margin of error (E) can be calculated using the following formula:

E = critical value * (standard deviation / sqrt(n))

However, since we don't have the standard deviation, we can't compute the margin of error in this case.

2. Confidence Interval:

The confidence interval represents a range of values within which the true population parameter is likely to fall.

The confidence interval can be calculated using the formula:

CI = x ± (critical value * standard deviation / sqrt(n))

The confidence interval based on the given values (x = 45, n = 96, confidence level = 95%.

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The perimeter of the figure is 17cm. Option (a) is the correct answer.

The rectangle has a length of 5 centimeters and a width of 3 centimeters. So, the rectangle has two sides of length 5 cm and two sides of length 3 cm. Therefore, the total perimeter of the rectangle is:

The Triangle and the rectangle ae sharing a side of length 5 cm Therefore perimeter of the figure is sum of two other sides of triangle+ sum of three sides of rectangle

Perimeter of rectangle = 2(Length + Width) = 2(5 + 3) = 2(8) = 16 cm

The triangle has side lengths of 5 centimeters, 3 centimeters, and 3 centimeters. The sum of the lengths of the sides of the triangle is:

Perimeter of triangle = sum of two other sides = 3+3=6cm

To find the total perimeter of the figure, we add the perimeters of the rectangle and the triangle:

Total perimeter =  The sum of two other sides of triangle sum of three sides of rectangle (3+5+3)

=3+3 +(3+5+3)

= 17cm

Therefore, Option (a) is the correct answer

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