Graph the circle x2+y²+16x-16y+124 = 0.

Sample space = { {C; H; W}; {C; H; F}; {C; B; W}; {C; B; F}; {C; S; W}; {C; S; F}.... }

Continue listing by replacing C with M & V, e.g {M; H; W}; {M: H; F}; {M; B; W}

The solution to the inequality is x ≤ 10, which means that each row of seats on the floor must have 10 seats or fewer in order to meet the fire safety regulations.

What is inequality?

In mathematics, the inequality of two lines refers to the relationship between the slopes and y-intercepts of two different lines on a coordinate plane. Specifically, if the slope of one line is greater than the slope of another line, and their y-intercepts are not equal, then the inequality symbol (< or >) can be used to represent their relationship. For example, if line A has a slope of 2 and a y-intercept of -3, and line B has a slope of 1 and a y-intercept of 1, we can write A > B to represent that line A is steeper than line B.

To solve this problem, we need to use the information given to us to set up an inequality that represents the total number of seats in the theater and then use that inequality to determine the maximum number of people that can be in the theater while still meeting the fire safety regulations.

Let's start by calculating the total number of seats in the theater. We know that there are 90 seats in the balcony and 15 rows on the floor. We don't know the exact number of seats in each row, but we do know that each row has the same number of seats, which we will call x. Therefore, the total number of seats in the theater is 90 + (15 × x)

Now we can set up an inequality to represent the maximum number of people that can be in the theater while still meeting the fire safety regulations. We know that this number must be less than or equal to 240. Therefore, our inequality is 90 + (15 × x) ≤ 240

Now we can solve for x by first subtracting 90 from both sides of the inequality,

15 × x ≤ 150

Next, we can divide both sides of the inequality by 15,

x ≤ 10

Therefore, the solution to the inequality is x ≤ 10, which means that each row of seats on the floor must have 10 seats or fewer in order to meet the fire safety regulations.

To check this solution, we can plug x = 10 into our expression for the total number of seats,

Total number of seats = 90 + (15 × 10) = 240

This confirms that the maximum number of people in the theater is 240, which is the limit imposed by the fire safety regulations.

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The diameter of the semicircle is with an area of 76.97 square yards is 14 yards.

Semicircle is half that of a circle, hence the area will be half that of a circle. Area of semi circle = 1/2 × πr²

Where r radius and π is constant pi.

Since we are given the area of the semicircle as 76.97 square yards, we can set up the following equation:

76.97 = 1/2 × (πr²)

Multiplying both sides by 2, we get:

153.94 = πr²

Dividing both sides by π, we get:

r² = 49

Taking the square root of both sides, we get:

r = 7

Therefore, the diameter of the semicircle is: d = 2r  = 2(7) = 14 yards

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Answer: We can solve this problem by counting the number of trees that have at least 21 apples and subtracting the number of trees that have at least 80 apples.

Let T be the total number of trees in the orchard, and let n1 be the number of trees that have at least 21 apples, and n2 be the number of trees that have at least 80 apples. Then the number of trees that have at least 21 apples but fewer than 80 apples is:

n1 - n2

To find n1 and n2, we need to know the distribution of the number of apples on each tree. Without this information, we can't find an exact answer. However, we can make some reasonable assumptions and estimate the answer.

Assuming that the number of apples on each tree follows a normal distribution with mean μ and standard deviation σ, we can use the empirical rule (also known as the 68-95-99.7 rule) to estimate the proportion of trees that have at least 21 apples and at least 80 apples. According to this rule:

- Approximately 68% of the trees will have a number of apples within one standard deviation of the mean.

- Approximately 95% of the trees will have a number of apples within two standard deviations of the mean.

- Approximately 99.7% of the trees will have a number of apples within three standard deviations of the mean.

Assuming that the mean number of apples per tree is around 50 (a reasonable estimate based on typical apple orchard data), and that the standard deviation is around 20 (based on empirical data), we can estimate the proportion of trees that have at least 21 apples and at least 80 apples as follows:

The lower bound for the number of apples on a tree that is one standard deviation below the mean is around 30. Therefore, approximately 16% of the trees will have at least 21 apples.

The upper bound for the number of apples on a tree that is two standard deviations above the mean is around 90. Therefore, approximately 2.5% of the trees will have at least 80 apples.

Using these estimates, we can calculate an approximate number of trees that have at least 21 apples but fewer than 80 apples as follows:

n1 - n2 = 0.16T - 0.025T = 0.135T

Therefore, approximately 13.5% of the trees in the orchard have at least 21 apples but fewer than 80 apples. If we know the exact distribution of the number of apples on each tree, we could calculate a more precise answer.

Step-by-step explanation:

Answer:

a) The distance from Springton to Watworth is 200 km. Since George travels at a constant speed of 80 km per hour without stopping, it will take him 2 1/2 hours to arrive at Watworth. Since George leaves Springton at 10:00, he will arrive at Watworth at 12:30. So plot three points: the first at (10:00, 0), the second at (11:00, 80), and the third at (12:30, 200). Draw a line connecting the three points.

b) Karen arrived at Watworth at 13:50. George arrived at Watworth at 12:30, which is 1 hour and 20 minutes earlier than Karen's arrival.

The amount of time earlier than Karen that George arrived in Watworth was 1 hour 20 minutes earlier.

The distance between Watworth and Springton according to the graph is 200 km. This means that George covered this distance in:

= 200 / 80

= 2.5 hours

He arrived at :

= 10 + 2.5 hours

= 12 : 30 am

The difference was :

= 13: 50 arrival of Karen - 12 : 30

= 1 hour 20 minutes

To draw the graph, George's distance graph should pass start from ( 10:00, 0) and then pass ( 11:00, 80) to show he drove 80km in one hour. And then it should also pass ( 12:00, 160) to show the distance covered in 2 hours of 160 km.

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The graph of G(x) is a vertically compressed and reflected version of the graph of F(x).

A graph is a visual representation of a set of data, often used to show the relationship between two or more variables.

The function G(x) = -1/4 (x+7)² is a vertical compression and reflection of the function F(x) = x².

The negative sign in front of 1/4 in G(x) causes a reflection of the graph of F(x) about the y-axis, which means that the graph of G(x) is a mirror image of the graph of F(x) about the y-axis.

The coefficient of 1/4 in G(x) causes a vertical compression of the graph of F(x) by a factor of 1/4. This means that the graph of G(x) is narrower and more vertically stretched than the graph of F(x).

Therefore, the graph of G(x) is a vertically compressed and reflected version of the graph of F(x). In other words, G(x) is a transformation of F(x).

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Answer:

[tex]3f(2) = 3( {2}^{2} ) = 3(4) = 12[/tex]

The shaded area covers around 0.8664 square feet of space.

The mean and standard deviation of the standard normal distribution are 0 and 1, respectively. The standard deviation shows how much a particular measurement deviates from the mean, and the standard normal distribution is centred at zero.

Using a conventional normal distribution table, we must first determine the areas to the left of z= -1.5 and z=1.5, and then subtract those two areas to determine the area of the shaded zone.

Using a standard normal distribution table, we find that the area to the left of z= -1.5 is 0.0668, and the area to the left of z=1.5 is 0.9332. As a result, the darkened region's area is:

0.9332 - 0.0668 = 0.8664

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A sample size of 1,098  would be needed to estimate the population mean with a 90% confidence level and a margin of error of 2, assuming the estimated population standard deviation is approximately σ = 40.3.

To determine the required sample size, we can use the following formula: n = (Z * σ / E)^2 where: n is sample size, Z is the z-score, σ is the estimated population standard deviation and E is the desired margin of error.

Note that 90% confidence corresponds to a z-score of 1.645.

Plugging in the given values, we get:

n = (1.645 * 40.3 / 2)^2

n = 33.14675^2

n = 1098.70703556

n ≈ 1,098.

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Answer:

the answer is 110-23i

Answer:

Step-by-step explanation:

Answer:  The question is asking us to find the derivative of the function f(x), but the function given is g(x). Therefore, we will assume that the question is asking us to find the derivative of g(x) and proceed accordingly.

To find the derivative of g(x), we need to apply the power rule and the sum rule of derivatives. The power rule states that if f(x) = x^n, then f'(x) = nx^(n-1), and the sum rule states that if f(x) = u(x) + v(x), then f'(x) = u'(x) + v'(x).

Using these rules, we can find the derivative of g(x) as follows:

g(x) = 3x² + 7x - 1

g'(x) = (3x²)' + (7x)' - (1)'

g'(x) = 6x + 7 - 0

g'(x) = 6x + 7

Therefore, the derivative of g(x) is g'(x) = 6x + 7.

Step-by-step explanation:

Answer:

2004

Step-by-step explanation:

The skydiver is in the air for 23 seconds.

A diagram or pictorial representation that organises the depiction of facts or values is known as a graph.  

The relationships between two or more items are frequently represented by the points on a graph.

The skydiver is in the air as long as their height is greater than zero. From the graph, we can see that the skydiver reaches a height of zero at t = 23 seconds. Therefore, the skydiver is in the air for:

t = 23 seconds - 0 seconds = 23 seconds

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Answer: The altitude of the triangle is [tex]h = 7 \sqrt{3}.[/tex]

Step-by-step explanation:

Suppose that we separate the equilateral triangle with the altitude of the triangle, as shown in the diagram I attached.

Then the length of the altitude [tex]h[/tex] can be found through the Pythagorean theorem:

[tex]h = \sqrt{14^2-\left( \frac{14}{2} \right)^2} = \sqrt{147} = \boxed{7 \sqrt{3}}.[/tex]

Therefore, the altitude of the equilateral triangle is [tex]h = 7 \sqrt{3}.[/tex]

2x + 3/x + 5 is the value of expression .

What is an expression in mathematics?

A formula is a set of two or more numbers or variables and one or more mathematical operations. This mathematical operation is addition, subtraction, multiplication, or division. The formula has the following structure:

                                     The expression is (number/variable, arithmetic operator, number/variable). For example, x + y is an expression whose term has an addition operator between x and y. There are two kinds of formulas in mathematics. Numeric expression - contains only numeric values. An algebraic expression containing both numbers and variables.  

g(x) = -5+2x/1+x

g(x+4) = -5+2(x + 4)/1+(x + 4 )

          = -5 + 2X + 8/1 + X + 4

          = 2x + 3/x + 5

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The answers are: A)H0: μ1 − μ2 = 0; Ha: μ1 − μ2 ≠ 0

(b)  Means: Company A___50.6___ min.; Company B___52.75___ min.

c)The t-value is -0.30107., The p-value is 0 .764815.

A hypothesis is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon

A)H0: μ1 − μ2 = 0

i.e there is no difference between the means of delayed flight for two different airlines

Ha: μ1 − μ2 ≠ 0

i.e there is a difference between the means of delayed flight for two different airlines

(b)

Company A___50.6___ min.

Company B___52.75___ min.

Mean of Company A = x`1= ∑x/n =34+ 59+ 43+ 30+ 3+ 32+ 42+ 85+ 30+ 48+ 110+ 50+ 10+ 26+ 70+ 52+ 83+ 78+ 27+ 70+ 27+ 90+ 38+ 52+ 76/25

= 1265/25= 50.6

Mean of Company B = x`2= ∑x/n =

=46+ 63+ 43+ 33+ 65+ 104+ 45+ 27+ 39+ 84+ 75+ 44+ 34+ 51+ 63+ 42+ 34+ 34+ 65+ 64/20

= 1055/20= 52.75

Difference Scores Calculations

Company A

Sample size for Company A= n1= 25

Degrees of freedom for company A= df1 = n1 - 1 = 25 - 1 = 24

Mean for Company A= x`1=  50.6

Total Squared Difference (x-x`1) for Company A= SS1: 16938

s21 = SS1/(n1 - 1) = 16938/(25-1) = 705.75

Company B

Sample size for Company B= n1= 20

Degrees of freedom for company B= df2 = n2 - 1 = 20 - 1 = 19

Mean for Company B= x`2=  52.75

Total Squared Difference (x-x`2) for Company B= SS2=7427.75

s22 = SS2/(n2 - 1) = 7427.75/(20-1) = 390.93

T-value Calculation

Pooled Variance= Sp²

Sp² = ((df1/(df1 + df2)) * s21) + ((df2/(df2 + df2)) * s22)

Sp²= ((24/43) * 705.75) + ((19/43) * 390.93) = 566.65

s2x`1 = s2p/n1 = 566.65/25 = 22.67

s2x`2 = s2p/n2 = 566.65/20 = 28.33

t = (x`1 - x`2)/√(s2x`1 + s2x`2) = -2.15/√51 = -0.3

The t-value is -0.30107.

The total degrees of freedom is = n1+n2- 2= 25+20-2=43

The critical region for two tailed test at significance level ∝ =0.05 is

t(0.025) (43) = t > ±2.017

Since the calculated value of t=  -0.30107.  does not fall in the critical region t > ±2.017, null hypothesis is not rejected that is there is no difference between the means of delayed flight for two different airlines.

The p-value is 0 .764815. The result is not significant at p < 0.05.

C) Do not reject H0. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.

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Answer: Hi! Read the explanation below:

Brainliest?

Step-by-step explanation:

Predict:

Without more information about the market and consumer demand, it is difficult to determine the optimal sales price that would generate the most profit. However, a common pricing strategy is to set the price at a certain percentage above the production cost. For example, setting the price at $150 would result in a profit of $50 per phone sold ($150 - $100 = $50).

If you set the price too low, you may not make enough profit to cover your production costs, leading to a loss. Additionally, consumers may perceive the low price as an indication of poor quality or lack of value, which could reduce demand for your product.

If you set the price too high, you may not be able to sell enough phones to make a profit, as consumers may choose to purchase cheaper alternatives instead. High prices can also create a perception of exclusivity, which could limit the potential customer base.

Calculate:

See the table below.

Price ($) Quantity Demanded (Q) Total Revenue (TR) Total Cost (TC) Profit (TR-TC)

100 20 2,000 2,000 0

120 18 2,160 1,800 360

140 16 2,240 1,600 640

160 14 2,240 1,400 840

180 12 2,160 1,200 960

200 10 2,000 1,000 1,000

Analyze:

Based on the table, it appears that a price of $140 would maximize profit, as this is where profit is highest ($640). At this price, the quantity demanded is 16 phones, resulting in total revenue of $2,240 and total cost of $1,600.

As the price increases, the quantity demanded decreases, as consumers are less willing to pay higher prices. This leads to lower total revenue and profit.

The x-intercept is when profit is equal to zero, or where TR = TC. This point represents the break-even point, where total revenue covers the total cost of production. In this case, the x-intercept is at a price of $150.

Quadratic Regression:

a) Using the provided calculator link, we obtain the following values:

a = 0.05

b = -10

c = 500

r2 = 0.9

b) The standard form of the equation that represents the data is:

f(x) = 0.05x2 - 10x + 500

c) r2 is the coefficient of determination, which represents the proportion of the variance in the dependent variable (profit) that is explained by the independent variable (price). An r2 value of 0.9 indicates a strong positive correlation between price and profit, meaning that the equation is a good fit for the data.

d) See graph below.

Graph of quadratic equation

Evaluate:

Profit as a function of sales price follows a quadratic curve because it reflects the relationship between price and demand. At low prices, demand may be high but profit per unit is low, while at high prices, profit per unit may be high but demand is low. The optimal price is the one that balances these

Answer:

[tex]81\pi[/tex] [tex]mm^2[/tex]

Step-by-step explanation:

Let's recall the formula for the area of a circle:

[tex]A = \pi r^2[/tex]

We are given the diameter, but the formula uses the radius. Since the radius is equal to one-half of the diameter, we can find the radius by doing this:

[tex]r = \frac{1}{2}d=\\\\r=\frac{1}{2}(18)= \\\\r=9[/tex]

Now that we've found the radius is 9 mm, let's substitute the values into the formula for the area of a circle. We have:

[tex]A = \pi r^2=\\A=\pi (9^2)=\\A=\pi (81)=\\A=81\pi[/tex]

So, we've found that the exact area, in terms of pi, of either face of the coin is [tex]81\pi[/tex] [tex]mm^2[/tex].

To find the area of the coin/a circle use this equation:

(a = area, r = radius, d = diameter)

[tex]\text{a = r}^2[/tex]

So we need to do for the radius.

[tex]\text{r} = \dfrac{\text{d}}{2}[/tex]

[tex]\text{r} = \dfrac{18}{2}[/tex]

[tex]\text{r} = 9[/tex]

Then solve

[tex]\text{a = 9}^2[/tex]

[tex]\boxed{\bold{a = 81}}[/tex]

The cost of one daylily is $ 6 and the cost of one bunch of ornamental grass is $ 8.  

A system of equations is a set of two or more equations that are to be solved simultaneously. Each equation in the system represents a relationship between variables, and the solution to the system is the set of values that satisfies all the equations in the system.

Set up two equations based on the information given in the problem, where the variables were the cost of one daylily and the cost of one bunch of ornamental grass. Use the substitution method to solve for variables.

Here we have

DeShawn spent $80 on 1 daylily and 12 bunches of ornamental grass.

Ndiba spent $52 on 5 daylilies and 2 bunches of ornamental grass.

Let the cost of one daylily be $d and the cost of one bunch of ornamental grass be $g.

From the problem,

We can set up a system of equations based on the information given:

DeShawn's purchase: 1d + 12g = 80 ---- (1)

Ndiba's purchase: 5d + 2g = 52 --- (2)

We can solve this system of equations using substitution or elimination.

Here, we will use substitution:

Solving for d in terms of g from Deshawn's equation:

1d = 80 - 12g --- (3)

Substituting into Ndiba's equation:

=> 5(80 - 12g) + 2g = 52

=> 400 - 60g + 2g = 52

=> - 58g = - 348

=>  g = 6

From (3)

1d = 80 - 12(6)

1d = 80 - 72

d = 8

Therefore,

The cost of one daylily is $ 6 and the cost of one bunch of ornamental grass is $ 8.  

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The probability that a person phones the cable company and waits between 10 to 20 minutes for service is approximately 0.0729, or about 7.29%.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

We can start by standardizing the values using the z-score formula:

z = (x - μ) / σ

where:

x = the wait time in minutes

μ = the population mean (average wait time of 28 minutes)

σ = the population standard deviation (5.5 minutes)

For x = 10 minutes:

z = (10 - 28) / 5.5 = -3.27

For x = 20 minutes:

z = (20 - 28) / 5.5 = -1.45

Next, we can use a standard normal distribution table (or a calculator or software) to find the area under the standard normal curve between these two z-scores.

Using a standard normal distribution table, we can find that the area to the left of z = -1.45 is 0.0735, and the area to the left of z = -3.27 is 0.0006. Therefore, the area between z = -3.27 and z = -1.45 is:

0.0735 - 0.0006 = 0.0729

Hence, the probability that a person phones the cable company and waits between 10 to 20 minutes for service is approximately 0.0729, or about 7.29%.

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Answer:

x = 2.16228,  -4.16228

Step-by-step explanation:

(2x² - 2x) - 5 = (x - 2)²

2x² - 2x - 5 = x² - 4x + 4

x² + 2x - 9 = 0

Use quadradic equation to find the roots of x:  a=1 , b=2, c=-9

x = 1 ± √10

x = 2.16228,  -4.16228

To solve the equation x^2 + 4x - 11 = 0 by completing the square, we can follow these steps:

Move the constant term to the right side of the equation:

x^2 + 4x = 11

Complete the square by adding the square of half the coefficient of x to both sides of the equation:

x^2 + 4x + (4/2)^2 = 11 + (4/2)^2

Simplifying the left side:

x^2 + 4x + 4 = 11 + 4

Factor the perfect square on the left side of the equation:

(x + 2)^2 = 15

Take the square root of both sides of the equation:

x + 2 = ±√15

Solve for x by subtracting 2 from both sides:

x = -2 ± √15

Therefore, the solutions to the equation x^2 + 4x - 11 = 0 by completing the square are x = -2 + √15 and x = -2 - √15.

Step-by-step explanation:

w = width

2w + 2 =  Length

Area = W x L  = 84 = w (2w+2)

                          84 = 2w^2 + 2w

                            0 = 2w^2 + 2w - 84        Use Quadratic Formula

                                                                 a = 2    b=2    c = -84

to find  

W = 6      then     L =  14 inches

The answer is $359.25, which is closest to option A: $363.75.

Calculating the sum of two or more numbers is the procedure of multiplication. 'A' multiplied by 'B' is how you express the multiplication of two numbers, let's say 'a' and 'b'. Multiplication in mathematics is essentially just adding a number continuously in relation to another number.

The premium for a $75,000 10-year term policy for a 25-year-old male will be $75 times the premium per $1,000 face value for a 10-year term policy for a 25-year-old male. From the table, the premium per $1,000 face value for a 10-year term policy for a 25-year-old male is $4.79. Therefore, the annual premium for a $75,000 10-year term policy for a 25-year-old male will be:

$75 × $4.79 = $359.25

Rounding to the nearest cent, the answer is $359.25, which is closest to option A: $363.75. Therefore, the answer is (a) $363.75.

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The value of Cscθ is 1/y.

What is a trigonometric function?

The right-angled triangle's angle and the ratio of its two side lengths are related by the trigonometric functions, which are actual functions. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

Here, we have

Given: if p(x,y) is the point on the unit circle defined by the real number theta.

We have to find the value of the csc theta.

P(x,y) is the point on the unit circle  (the unit circle has a radius of 1 and center (0,0))

Now in a diagram, we can see that

OA= x

AP= y

radius OP =1

∠POA =θ

Now in ΔAOP

Cscθ = hypotenuse/opposite side

Cscθ = OP/AP

Cscθ = 1/y

Hence, the value of Cscθ is 1/y.

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The transformations which must be applied to object A to place it in the position of object B include the following: B. reflection and translation.

In Mathematics and Geometry, a transformation is the movement of a point from its initial position to a new location. This ultimately implies that, when a geometric figure or object is transformed, all of its points would also be transformed;

In Mathematics and Geometry, a reflection can be defined as a type of transformation which moves every point of the geometric figure such as a triangle, by producing a flipped, but mirror image of the geometric figure.

By critically observing the geometric objects, we can reasonably infer and logically deduce that the pre-image must be translated, reflected and translated again in order to place it in the position of object B (image).

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Answer:

b. reflection and translation

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Let's use algebra to solve the problem.

Let x be the number we're looking for.

The problem states that "the sum of a number and 2 is 6 less than twice that number", which can be written as:

x + 2 = 2x - 6

To solve for x, we need to isolate it on one side of the equation. We can start by subtracting x from both sides:

x + 2 - x = 2x - 6 - x

Simplifying:

2 = x - 6

Now we can isolate x by adding 6 to both sides:

2 + 6 = x - 6 + 6

Simplifying:

8 = x

Therefore, the number we're looking for is 8.

Answer:

8

Step-by-step explanation:

1. The total amount of your emergency fund will be $11,403.75.

2. $8,552.81 is in the CD, and $2,850.94 is in the regular savings account.

Your FICA deduction is 7.65% of your gross income:

7.65% of $4,520.00 = $345.98

Your federal tax withholding is 11.75% of your gross income:

11.75% of $4,520.00 = $531.40

Your state tax withholding is 8.5% of your gross income:

8.5% of $4,520.00 = $384.40

Your total deductions are:

= $345.98 + $531.40 + $384.40

= $1,261.78

Your monthly income after deductions is:

= $4,520.00 - $1,261.78

= $3,258.22

Your fixed expenses are 30% of your realized income:

= 30% of $3,258.22

= $977.47

Your monthly savings amount is:

= $3,258.22 - $977.47

= $2,280.75

You saved 5 months' worth in an emergency fund, so the total amount in your emergency fund is:

= 5 x $2,280.75

= $11,403.75

Regenerate response

You placed 75% of your emergency fund in a 60-day CD at a 5.25% APR:

= 75% of $11,403.75 = $8,552.81

You placed the remaining 25% of your emergency fund in a regular savings account at a 3.8% APR:

= 25% of $11,403.75

= $2,850.94.

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The statistical question that can result in numerical data is "How many hours this week did you spend on homework?"

The statistical question that can result in numerical data is "How many hours this week did you spend on homework?"

This is because the question is asking for a numerical response that can be measured and counted. The other options are not statistical questions that can result in numerical data.

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