simplify each expression 4(x+2)+(8+2x)

In a sample of 5000 students, the mean GPA is 2.80 and their standard deviation is 0.35 and 1428 students score below 2.60.

To find the number of students scoring below 2.60, we need to calculate the area under the normal distribution curve to the left of this value.

First, we need to standardize the value of 2.60 using the z-score formula: z = (x - μ) / σ, where x is the value (2.60), μ is the mean (2.80), and σ is the standard deviation (0.35). Plugging in the values, we get z = (2.60 - 2.80) / 0.35 = -0.57.

Now, we can use a standard normal distribution table or a statistical calculator to find the area to the left of -0.57. Consulting a standard normal distribution table, we find that the area to the left of -0.57 is approximately 0.2857.

To calculate the number of students scoring below 2.60, we multiply this area by the total number of students in the sample: 0.2857 * 5000 ≈ 1428.5.

Since the number of students must be a whole number, we round down to 1428 students.

Therefore, approximately 1428 students score below 2.60 in the sample of 5000 students, assuming a normal distribution with a mean of 2.80 and a standard deviation of 0.35.

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Answer:

[tex]\textsf{The parabola has a vertex at $\left(\:\boxed{-3}\:,\boxed{-7}\:\right)$, has a p-value of $\boxed{-1}$ and it}[/tex]

[tex]\textsf{$\boxed{\sf op\:\!ens\;to\;the\;left}$\:.}[/tex]

Step-by-step explanation:

The given directrix of the parabola is x = -2, which is a vertical line.

The directrix is perpendicular to the axis of symmetry. Therefore, this means that the parabola has a horizontal axis of symmetry.

The focus of a parabola is a fixed point located inside the curve. The x-coordinate of the given focus is x = -4. As this is to the left of the directrix, it means that the parabola opens to the left.

The standard form of a horizontal parabola is:

[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]

where:

As the focus is (-4, -7), then:

[tex]\begin{aligned}(h+p, k)&=(-4,-7)\\\\\implies k&=-7\\\implies h+p&=-4\end{aligned}[/tex]

As the directrix is x = -2, then:

[tex]h - p=-2[/tex]

To find the value of h, sum the equations involved h and p to eliminate p:

[tex]\begin{array}{crcccr}&h &+& p& =& -4\\+&h& -& p& = &-2\\\cline{2-6}&2h&&& =& -6\\\cline{2-6}\\\implies &h&&&=&-3\end{array}[/tex]

To find the value of p, substitute the found value of h into one of the equations:

[tex]\begin{aligned}-3 - p&=-2\\p&=-3+2\\p&=-1\end{aligned}[/tex]    

Therefore, the values of h, k and p are:

The parabola has a vertex at (-3, -7), has a p-value of -1 and it opens to the left.

The parabola has a vertex at (-3, y), has p-value of 1 and it equation is

(x + 3)² = 4y.

To find the equation of the parabola with the given focus and directrix, we can use the standard form equation of a parabola:

(x - h)² = 4p(y - k)

where (h, k) is the vertex of the parabola and "p" is the distance from the vertex to the focus (and also from the vertex to the directrix).

Given:

Focus: (-4, -7)

Directrix: x = -2

1. Finding the vertex:

Since the directrix is a vertical line, the vertex lies on the line that is equidistant from the focus and directrix. In this case, it lies on the line x = (-4 + (-2))/2 = -3.

Therefore, the vertex of the parabola is (-3, y).

2. Finding the p-value:

The distance from the vertex to the focus (and also to the directrix) is the same. In this case, the distance is |-3 - (-4)| = 1.

Therefore, the value of "p" is 1.

3. Writing the equation of the parabola:

Using the vertex (-3, y) and the p-value of 1, we can write the equation of the parabola:

(x - h)² = 4p(y - k)

(x - (-3))² = 4(1)(y - y)

Simplifying, we get:

(x + 3)² = 4(y - y)

(x + 3)² = 4y

So, the equation of the parabola is (x + 3)² = 4y.

The vertex of the parabola is (-3, y) and the p-value is 1.

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a) The least squares regression line for the given data is y = -3.5358x + 87.2857.

b) The slope of -3.5358 indicates that for each additional day absent, the final grade is expected to decrease by approximately 3.5358 points on average.

c) The y-intercept of 87.2857 represents the estimated final grade when the number of absences is zero, implying that a student who did not miss any classes is expected to have a final grade of approximately 87.2857.

a) To find the least squares regression line, we need to determine the equation of the line in the form y = mx + b, where m represents the slope and b represents the y-intercept.

Let's calculate the necessary sums:

∑x = 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45

∑y = 89.2 + 86.4 + 83.5 + 81.1 + 78.2 + 73.9 + 64.3 + 71.8 + 65.5 + 66.2 = 759.9

∑xy = (0 * 89.2) + (1 * 86.4) + (2 * 83.5) + (3 * 81.1) + (4 * 78.2) + (5 * 73.9) + (6 * 64.3) + (7 * 71.8) + (8 * 65.5) + (9 * 66.2) = 5079.6

∑[tex]x^2[/tex] = [tex](0^2) + (1^2) + (2^2) + (3^2) + (4^2) + (5^2) + (6^2) + (7^2) + (8^2) + (9^2)[/tex] = 285

[tex]\sum y^2 = (89.2^2) + (86.4^2) + (83.5^2) + (81.1^2) + (78.2^2) + (73.9^2) + (64.3^2) + (71.8^2) + (65.5^2) + (66.2^2) = 59718.63[/tex]

Using the formulas for the slope (m) and y-intercept (b):

m = (n∑xy - (∑x)(∑y)) / (n∑x^2 - (∑x)^2)

b = (∑y - m(∑x)) / n

Substituting the calculated values:

m = (10 * 5079.6 - (45 * 759.9)) / (10 * 285 - (45)^2)

b = (759.9 - m(45)) / 10

Calculating the values:

m ≈ -3.5358

b ≈ 87.2857

Therefore, the least squares regression line is y = -3.5358x + 87.2857.

b) The slope (-3.5358) represents the change in the final grade (y) for each additional day absent (x). This means that on average, for each additional day a student is absent, their final grade is expected to decrease by approximately 3.5358 points.

c) The y-intercept (87.2857) represents the estimated final grade when the number of absences (x) is zero. In other words, it is the predicted final grade for a student who did not miss any classes.

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Question

The following data represents the number of days absent, x, and the final grade, y, for a sample of college students at a community college.

No.of absences, x | 0 1 2 3 4 5 6 7 8 9

Final Grade, y | 89.2 86.4 83.5 81.1 78.2 73.9 64.3 71.8 65.5 66.2

a) Find the least squares regression line treating the number of absences as the explanatory variable and the final grade as the response variable.

b) Interpret the slope using complete sentences.

c) Interpret the y intercept using complete sentences.

Answer:

180 meters

Step-by-step explanation:

To find the perimeter of the actual swimming pool, you need to first find the length and width of the actual swimming pool by multiplying the length and width of the pictured swimming pool by the scale factor of 1200 cm.

Now that we know that the perimeter of the actual pool is 18000 centimeters, we need to convert that to meters! Keep in mind that:

Now we can divide 18000 by 100:

18000 cm ÷ 100 = 180 m

Therefore, the perimeter of the actual swimming pool is 180 m.

Answer:

Step-by-step explanation:

Let's denote the length of the rectangle as 3x and the width as 2x, based on the given ratio.

The perimeter of a rectangle is given by the formula P = 2(length + width). In this case, we have:

P = 2(3x + 2x)

40 = 2(5x)

Now, let's solve for x:

40 = 10x

x = 40/10

x = 4

Now that we have the value of x, we can find the length of the rectangle:

Length = 3x = 3(4) = 12

Therefore, the length of the rectangle is 12.

The function f(x) = -0.5(x + 5)³(x + 3)(x - 3) satisfies the specified conditions of decreasing at x = -5, having a local minimum at x = -3, and a local maximum at x = 3.

One possible function that satisfies the given properties is:

f(x) = -0.5(x + 5)³(x + 3)(x - 3)

Check as follows:

Decreasing at x = -5:

Taking the derivative of f(x) and evaluating it at x = -5, we have:

f'(x) = -1.5(x + 5)²(x + 3)(x - 3) - 0.5(x + 5)³

f'(-5) = -1.5(0)²(-2)(-8) - 0.5(0)³ = 0 - 0 = 0

The derivative is zero at x = -5, therefore the function has a critical point at that location. To check if it is a maximum or minimum, we can examine the second derivative.

Taking the second derivative:

f''(x) = -3(x + 5)(x + 3)(x - 3) - 3(x + 5)²(x - 3)

f''(-5) = -3(0)(-2)(-8) - 3(0)²(-8) = 0 - 0 = 0

The second derivative is also zero at x = -5. However, since the first derivative is negative for x < -5 and positive for x > -5, this means that f(x) is decreasing at x = -5.

Local minimum at x = -3:

To check if f(x) has a local minimum at x = -3, we can examine the first and second derivatives at that point.

Taking the first derivative:

f'(-3) = -1.5(2)²(0)(-6) - 0.5(2)³ = 0

The first derivative is zero at x = -3, indicating a critical point.

Taking the second derivative:

f''(-3) = -3(2)(0)(-6) - 3(2)²(-6) = 0 - 72 = -72

Since the second derivative is negative at x = -3, this confirms the presence of a local minimum.

Local maximum at x = 3:

To check if f(x) has a local maximum at x = 3, we can again examine the first and second derivatives at that point.

Taking the first derivative:

f'(3) = -1.5(8)²(6)(0) - 0.5(8)³ = 0

The first derivative is zero at x = 3, indicating a critical point.

Taking the second derivative:

f''(3) = -3(8)(6)(0) - 3(8)²(0) = 0 - 0 = 0

The second derivative is zero at x = 3, indicating that the test is inconclusive. However, since the first derivative is positive for x < 3 and negative for x > 3, this means that f(x) is decreasing at x = 3.

Therefore, the function f(x) = -0.5(x + 5)³(x + 3)(x - 3) satisfies all the given conditions.

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The statement which is not true include the following: (2) AABM is isosceles.

In Mathematics and Geometry, an isosceles triangle simply refers to a type of triangle with two (2) sides that are equal in length and two (2) equal angles.

By critically observing circle M shown above, we can reasonably infer and logically deduce the following true statements:

ΔABC is a right triangle.

BM = MC (radius of circle M).

mBC = m∠BMC

mAB = 1/2m∠ACB (intersecting secant theorem).

In this context, we can logically conclude that triangle ABM does not represent an isosceles triangle because it does not have two (2) sides that are equal in length.

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The true statement about the transformation is that the second trapezoid is a dilation of the first trapezoid with a scale factor of 2.

The given transformation involves two trapezoids with identical angle measures but different side lengths. Let's analyze the two trapezoids and determine the statement that is true about the transformation.

First Trapezoid:

Side lengths: 4, 2, 6, 2

Second Trapezoid:

Side lengths: 8, 4, 12, 4

To determine the relationship between the side lengths of the two trapezoids, we can compare the corresponding sides.

Comparing the corresponding sides:

4 / 8 = 2 / 4 = 6 / 12 = 2 / 4

We can observe that the corresponding sides of the two trapezoids have the same ratio. This indicates that the side lengths of the second trapezoid are twice the lengths of the corresponding sides of the first trapezoid. Therefore, the statement that is true about the transformation is:

The second trapezoid is a dilation of the first trapezoid with a scale factor of 2.

A dilation is a type of transformation that produces an image that is the same shape as the original figure but a different size. In this case, the second trapezoid is obtained by scaling up the first trapezoid by a factor of 2 in all directions.

This transformation preserves the shape and angle measures of the trapezoid but changes its size. The corresponding sides of the second trapezoid are twice as long as the corresponding sides of the first trapezoid.

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The systematic sample would be A. The city manager takes a list of the residents and selects every 6th resident until 54 residents are selected.

The random sample would be C. The botanist assigns each plant a different number. Using a random number table, he draws 80 of those numbers at random. Then, he selects the plants assigned to the drawn numbers. Every set of 80 plants is equally likely to be drawn using the random number table.

The cluster sample is C. The host forms groups of 13 passengers based on the passengers' ages. Then, he randomly chooses 6 groups and selects all of the passengers in these groups.

A systematic sample involves selecting items from a larger population at uniform intervals. A random sample involves selecting items such that every individual item has an equal chance of being chosen.

A cluster sample involves dividing the population into distinct groups (clusters), then selecting entire clusters for inclusion in the sample.

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The tangent line at that point is:

y = (-3/25)*x + 6/5

so m = -3/25, and b = 6/5

To find the slope at that point, we need to evaluate the derivative at that point.

y = 3/x

The derivative is:

y' = -3/x²

When x = 5, we have:

y' = -3/5² = -3/25

So that is the slope, m.

Now let's find the line.

The line must pass trhough the point (5, 3/5), then:

3/5 = (-3/25)*5 + b

3/5 = -3/5 + b

3/5 + 3/5 = b

6/5 = b

The equation of the line is:

y = (-3/25)*x + 6/5

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The correct statement is the first one:

f(0) = 2

g(-2) = 0

Here we can see the graph of two quadratic equations.

The orange one is g(x), and we can see that it has the vertex at (-2, 0).

And the blue one is f(x), we can see that the vertex is at (2, 0)

From, that, we coclude that:

g(-2) = 0

f(2) = 0

We also can see that the two have the sa,me y-intercept (0, 2), so:

f(0) = g(0) = 2

Then the correct statement is the first one:

f(0) = 2

g(-2) = 0

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Answer:

8

Step-by-step explanation:

The value of x in the right triangle using pthagorean theorem is 3√41.

The figure in the image is that of a right triangle with of its interior angle at 90 degrees.

Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

c² = a² + b²

From the figure:

Hypotenuse c = 25

Leg a = 16

Leb b = x

Plug these values into the above formula and solve for x:

c² = a² + b²

25² = 16² + x²

625 = 256 + x²

x² = 625 - 256

x² = 369

Take the square root( we use the positive value because its dimension ).

x = √369

x = 3√41

Therefore, the value of x is 3√41.

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The ordered pair given in the first row of the table can be written using function notation as (x, f(x)) = (-6, 8).

f(x) = -5 when x is 4.

In function notation, we represent the input value as 'x' and the corresponding output value as 'f(x)'.

Looking at the first row of the table, we see that when x is -6, the corresponding value of f(x) is 8.

Therefore, we can write this ordered pair as (-6, 8) in function notation.

Similarly, we can determine that f(x) = -5 when x is 4 by examining the second row of the table.

The value of f(x) is -5 when x is 4, so we can express it as f(4) = -5.

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The distance from point A to point B is approximately 16.64 units. None of the given options (A, B, C, D) match this value exactly, so there seems to be an error in the options provided.

To find the distance from point A to point B, we can use the distance formula in Euclidean geometry. The distance formula between two points (x1, y1) and (x2, y2) is given by:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, point A is (-8, -3) and point B is (6, 6). Plugging these values into the distance formula, we have:

distance = sqrt((6 - (-8))^2 + (6 - (-3))^2)

= sqrt((6 + 8)^2 + (6 + 3)^2)

= sqrt(14^2 + 9^2)

= sqrt(196 + 81)

= sqrt(277)

≈ 16.64

Thus, the distance between points A and B is roughly 16.64 units. Since none of the available options (A, B, C, or D) exactly match this value, there appears to be a problem with the options.

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Answer:

17.5

Step-by-step explanation:

The triangle is an equilateral triangle since all sides are equal

Area of a equilateral triangle is:

[tex]ar(triangle) = \frac{a^2\sqrt{3} x}{4}[/tex]

[tex]=\frac{5^2\sqrt{3} }{4} \\\\=\frac{25\sqrt{3} }{4} \\[/tex]

the sde of the square = diameterof the circle(d)

d = 6

r = d/2 = 3

ar(circle) = πr²

= π * 3²

= 9π

= 9*22/7

= 198/7

ar(shaded region) = ar(circle)-ar(triangle)

[tex]= \frac{198}{7} - \frac{25\sqrt{3} }{4}[/tex]

= 17.5

(a) Starting at 12 and making 1/2 revolution clockwise, the hand stops at 6.

(b) Starting at 2 and making 1/2 revolution clockwise, the hand stops at 8.

(c) Starting at 5 and making 1/4 revolution clockwise, the hand stops at 8.

(d) Starting at 5 and making 3/4 revolution clockwise, the hand stops at 11.

To determine where the hand of a clock will stop, we need to consider the fractions of a revolution made by the hand starting from different positions.

(a) If the hand starts at 12 and makes 1/2 of a revolution clockwise, it will stop at 6.

This is because a half revolution corresponds to the hand moving from 12 to 6 on the clock face.

(b) If the hand starts at 2 and makes 1/2 of a revolution clockwise, it will stop at 8.

Again, a half revolution corresponds to the hand moving from 2 to 8 on the clock face.

(c) If the hand starts at 5 and makes 1/4 of a revolution clockwise, it will stop at 8.

A quarter revolution corresponds to the hand moving from 5 to 8 on the clock face.

(d) If the hand starts at 5 and makes 3/4 of a revolution clockwise, it will stop at 11.

A three-quarter revolution corresponds to the hand moving from 5 to 11 on the clock face.

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The direct labor cost included in the Preble Company's flexible budget for March is $819,000.

To find the direct labor cost included in the company's flexible budget for March, we shall estimate the actual direct labor cost incurred during the period.

Given:

Actual production and sales =n26,600 units

Actual direct labor rate = $13.00 per hour

Actual direct labor hours worked = 63,000 hours

Direct labor cost = Actual direct labor rate × Actual direct labor hours worked

Direct labor cost = $13.00/hour × 63,000 hours

Direct labor cost = $819,000

Hence, the direct labor cost included in the company's flexible budget for March would be $819,000.

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Answer:

  f(x +h) = 4x² +4h² +8xh +5x +5h +3

  (f(x+h) -f(x))/h = 4h +8x +5

  f'(x) = 8x +5

Step-by-step explanation:

For f(x) = 4x² +5x +3, you want the simplified expression f(x+h), the difference quotient (f(x+h) -f(x))/h, and the value of that at h=0.

Put (x+h) where h is in the function, and simplify:

  f(x+h) = 4(x+h)² +5(x+h) +3

  = 4(x² +2xh +h²) +5x +5h +3

  f(x +h) = 4x² +4h² +8xh +5x +5h +3

The difference quotient is ...

  (f(x+h) -f(x))/h = ((4x² +4h² +8xh +5x +5h +3) - (4x² +5x +3))/h

  = (4h² +8xh +5h)/h

  (f(x+h) -f(x))/h = 4h +8x +5

When h=0, the value of this is ...

  f'(x) = 4·0 +8x +5

  f'(x) = 8x +5

__

Additional comment

Technically, the difference quotient is undefined at h=0, because h is in the denominator, and we cannot divide by 0. The limit as h→0 will be the value of the simplified rational expression that has h canceled from every term of the difference. This will always be the case for difference quotients for polynomial functions.

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The width of the house on the plan is 0.615 meters.

To find the scale of the plan in the form 1:n, we can compare the measurements on the plan to the actual measurements of the house.

Length of the rectangle on the plan = 78.5 cm

Actual length of the house = 15.7 m

We need to convert the actual length of the house to the same unit as the length on the plan, which is centimeters.

1 meter = 100 centimeters

So, the actual length of the house in centimeters = 15.7 m [tex]\times[/tex] 100 cm/m = 1570 cm

Now, we can find the scale of the plan by dividing the length on the plan by the actual length of the house:

Scale = Length on the plan / Actual length of the house

= 78.5 cm / 1570 cm

Simplifying this fraction, we get:

Scale = 1/20

Therefore, the scale of the plan is 1:20.

To find the width of the house on the plan, we can use the same scale.

Width of the house in actual measurements = 12.3 m.

Width of the house on the plan = (Width of the house in actual measurements) / Scale

= 12.3 m / 20

= 0.615 m.

So, the width of the house on the plan is 0.615 meters.

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(a) To find the assets in 2011 using the given information: A. To find the assets in 2011, substitute 11 for x and evaluate to find A(x).

In 2011 the assets are about $669.6 billion

(b) To find the assets in 2016 using the given information: B. To find the assets in 2016, substitute 16 for x and evaluate to find A(x).

In 2016 the assets are about $931.5 billion.

(c) To find the assets in 2019 using the given information: B. To find the assets in 2019, substitute 19 for x and evaluate to find A(x).

In 2019 the assets are about $1135.4 billion.

Based on the information provided, we can logically deduce that the assets for a financial firm can be approximately represented by the following exponential function:

[tex]A(x)=324e^{0.066x}[/tex]

where:

For the year 2011, the cost (in billions of dollars) is given by;

x = (2011 - 2007) + 7

x = 4 + 7

x = 11 years.

Next, we would substitute 11 for x in the exponential function:

[tex]A(11)=324e^{0.066 \times 11}[/tex]

A(11) = $669.6 billions.

Part b.

For the year 2016, the cost (in billions of dollars) is given by;

x = (2016 - 2007) + 7

x = 9 + 7

x = 16 years.

Next, we would substitute 16 for x in the exponential function:

[tex]A(16)=324e^{0.066 \times 16}[/tex]

A(16) = $931.5 billions.

Part c.

For the year 2019, the cost (in billions of dollars) is given by;

x = (2019 - 2007) + 7

x = 12 + 7

x = 19 years.

Next, we would substitute 19 for x in the exponential function:

[tex]A(19)=324e^{0.066 \times 19}[/tex]

A(19) = $1135.4 billions.

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Answer:

$6240

Step-by-step explanation:

given likelihoods:

sunny day = 14% = 0.14

cloudy day = 26% = 0.26

rainy day = 60% = 0.60

profits:

profit on a sunny day = $40,000

profit on a cloudy day = $14,000

Loss on a rainy day = -$5,000

expected profit = (probability of sunny day * profit on sunny day) + (probability of cloudy day * profit on cloudy day) + (probability of rainy day * loss on rainy)

expected profit = (0.14 * $40,000) + (0.26 * $14,000) + (0.60 * -$5,000)

=6240

Answer:

The volume of the cylinder is 628.318530718

Step-by-step explanation:

The formula used to find the volume of a cylinder (v) is [tex]v = \pi r^2h[/tex], where r = radius and h = height. As the question says to keep the answer exact, we will be using pi as opposed to 3.14.

The radius is 5, and the height is 8. Plug these values into the equation and solve:

[tex]v =\pi *5^2*8[/tex]

[tex]v = 628.318530718[/tex]

So, the exact volume of the cylinder is 628.318530718. Rounded is 628.32

Answer:

200π or 628

Step-by-step explanation:

Note: your picture is not clear so I am assuming the height to be 8.

r = 5

h = 8

Volume = πr²h

= π * 5² * 8

= (25*8) π

= 200π

= 200*3.14

= 628

a) Brooke's monthly income is $3,166.67 from her full-time job as a cook, and an additional $532.59 from her part-time job, resulting in a total monthly income of $3,699.26.

b) Yes, the rent of $975 per month for the new apartment falls within the housing guideline of spending 30% or less of her monthly income on housing.

a) To determine Brooke's monthly income, we need to calculate her earnings from both her full-time and part-time jobs.

Full-time job income: Brooke earns $38,000 per year as a cook.

To find her monthly income from this job, we divide her annual salary by 12:

Monthly income from full-time job = $38,000 / 12 = $3,166.67

Part-time job income: Brooke earns $10.25 per hour and works 12 hours per week.

To find her weekly income from this job, we multiply her hourly rate by the number of hours she works:

Weekly income from part-time job = $10.25/hour x 12 hours/week = $123

To find her monthly income, we multiply her weekly income by the average number of weeks in a month (approximately 4.33):

Monthly income from part-time job = $123/week x 4.33 weeks/month = $532.59 (rounded to the nearest cent)

To calculate Brooke's total monthly income, we add her full-time and part-time job incomes:

Total monthly income = $3,166.67 + $532.59 = $3,699.26 (rounded to the nearest cent)

b) The rent for the new apartment is $975 per month, including utilities. To determine if it falls within the housing guidelines, we need to compare it to a percentage of Brooke's monthly income.

Typically, a common guideline is to spend no more than 30% of your monthly income on housing.

Percentage of monthly income for housing = 30% of total monthly income

= 30/100 x $3,699.26

= $1,109.78 (rounded to the nearest cent)

Since the rent of $975 is lower than the guideline of $1,109.78, if Brooke takes this apartment, it will fall within the housing guidelines.

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Answer:

It's A and B: Opposite sides are parallel and Corresponding parts of congruent triangles are congruent.

Step-by-step explanation:

The inverse of the original statement is: "If the sum of the interior angles of a polygon is not more than 180°, then the polygon is a triangle."

The inverse of the conditional statement "If the sum of interior angles of a polygon is more than 180°, then the polygon is not a triangle" is: "If the sum of the interior angles of a polygon is not more than 180°, then the polygon is a triangle."
To find the inverse, we need to negate both the hypothesis and the conclusion of the original statement.
The hypothesis of the original statement is "the sum of the interior angles of a polygon is more than 180°". To negate this, we say "the sum of the interior angles of a polygon is not more than 180°".
The conclusion of the original statement is "the polygon is not a triangle". To negate this, we say "the polygon is a triangle".
In summary, the inverse of the original statement is "If the sum of the interior angles of a polygon is not more than 180°, then the polygon is a triangle."

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The correct statement about the mean is:

The mean equals the sum of all observations divided by the number of observations.

The mean is a commonly used measure of central tendency. It is calculated by summing up all the observations and then dividing the sum by the total number of observations. It provides an average value that represents the typical value of the data set.

To calculate the mean, it is not necessary to order the observations from least to most. The order of the observations does not affect the mean calculation.

The mean is not necessarily a whole number. It can be a decimal or a fraction, depending on the data set and the values of the observations. The mean represents the balance point of the data set and can take on any real number value.

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33.) The volume of the given triangular prism would be= 36. That is option E.(NOTA)

To calculate the volume of a triangular prism, the formula that should be used is given as follows;

Volume= BH

where;

B= area of base = 1/2 × base×height

= 1/2×4×3

= 6

H= 6

Volume= 6×6= 36.

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