Analyze the diagram below and complete the instructions that follow.
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X14
Determine if the proportion is true. If it is not true, correct the error.
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If Lois is retiring from her job after 27 years, then if she waited for 4 years, her pension will be $38 higher than if she retires this year.

If Lois retires this year, the flat-amount is $52, So, her monthly pension can be calculated as follows;

⇒ Monthly pension = (52 × 27)/12,

⇒ Monthly pension = $117,

If Lois works for another 4 years, the flat amount used to calculate her monthly pension will increase to $60 for each year of service.

So, her monthly pension will be calculated as follows:

⇒ Monthly pension = (60 × 31)/12,

⇒ Monthly pension = $155,

So, The difference in monthly pension between retiring this year and retiring after working another 4 years can be calculated as follows:

⇒ Difference in monthly pension = $155 - $117,

⇒ Difference in monthly pension = $38,

Therefore, if Lois waits another 4 years before retiring, her monthly pension will be $38 higher than if she retires this year.

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Answer:

1/60

Step-by-step explanation:

For each cake, there is a 1/20 chance to find the gold ring since it is in one of the 20 slices. The probability for each cake is independent of each other, so we multiply

1/20 x 1/20 x 1/20

=1/60

Answer:d

Step-by-step explanation:

The range of the repairs to the cars is 241.

The sample variance is 11, 671.33

The sample standard deviation would be 108.03.

Range = Maximum repair cost - Minimum repair cost

= 456 - 215

= 241

Find mean :

= (422 + 456 + 401 + 215) / 4

= 373. 5

Sample variance :

= Sum of ( each repair cost - mean ) ² / (Number of cars - 1)

= ( 2, 340.25 + 6, 812.25 + 756.25 + 25, 105.25 ) / ( 4 - 1 )

= 11, 671. 33

Sample standard deviation:

= √sample variance

= √11, 671. 33

= 108. 03

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Where the information relating to the circle and its diameter are given, the equation of the circle would be: "(x  5)²  + y2 = 81" (Option B)

The above is determined by the standard form equation of a circle which is:

(x- h) ² + (y - k)² = r²

Here,

(h, k)  is the center of the circle and r   is the radius

In this case, the center is (-5 , 0) and the diameter is 18, so the radius is half the diameter, whic is 18/ 2 = 9

So making the required substitutions, the expression becomes:

(x-(-5))² + (y-(0))² = 9²

Which becomes

(x  5)²  + y2 = 81

Thus, it is correct to state that Option B is the equation of the circle.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

The center of a circle is at (-5, 0), and the diameter of the circle is 18. Which of the following is the equation of the circle?

A. (x  5)²  + y = 9

B. (x  5)²  + y2 = 81

C. (x  5)²  + y2 = 9

D. (x  5)²  + y2  81

Answer:

True

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

Every number has multiple qualities beyond its distance from zero. Some of the qualities of a number include its sign (positive or negative), its magnitude (Absolute Value), its parity (whether it is even or odd), and its relationship to other numbers (greater than, less than, or equal to). Additionally, numbers can have properties such as being prime or composite, rational or irrational, and real or complex. Therefore, a number is characterized by more than just its distance from zero.

Answer:

33

Step-by-step explanation:

To solve for the range, simply subtract the largest-value term from the smallest-value term. First, set all numbers from least to greatest:

14 , 23 , 28 , 36 , 40 , 42 , 47

The smallest term is 14.

The largest term is 47.

Subtract 47 with 14:

[tex]47 - 14 = 33[/tex]

The given range value will be 33.

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Yes, The given graph is shows a function.

And, Range = {y | y ≥ - 2}

Domain = (- ∞ , ∞)

We have to given that;

the graph is shown in image.

Now, We can check the graph is a function or not by vertical line test.

Hence, By vertical line test it's shows the function as it cut at one point for each value of y.

Thus, The given graph is shows a function.

Since, The set of all inputs of the function is called Domain of set.

Hence, We get;

Domain = (- ∞ , ∞)

And, The set of all outputs of the function is called range of set.

Hence, We get;

Range = {y | y ≥ - 2}

Thus, Yes, The given graph is shows a function.

And, Range = {y | y ≥ - 2}

Domain = (- ∞ , ∞)

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Answer: x < 5, see attached

Step-by-step explanation:

     To solve for x, we will isolate the given variable.

Given:

  [tex]\displaystyle 1 > \frac{x}{5}[/tex]

Multiply both sides of the equation by 5:

  [tex]\displaystyle5 > x[/tex]

Flip equation:

  [tex]\displaystyle x < 5[/tex]

     To graph, we will first plot a point on 5 with an open circle. Then, we will shade to the left since x is less than 5. See attached.

The solution set for the given equation is 25.

In Mathematics and Geometry, a square root function is a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.

Next, we would determine the solution set for the given equation by translating the word problem into an equation and then divide both sides of the square root function as follows;

-√x = 5

√x = -5

By taking the square of both both sides of the square root function, we have:

x = (-5)²

x = 25

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The area of a flower bed is 24 square feet and the equation to represent the equal area is 24+20x+4x²=24.

Given that, the dimensions of rectangular flower bed are length= 6 feet and  width = 4 feet.

Dimensions of large rectangle are Length = 6+2x and width = 4+2x

Now, area of large rectangle = (6+2x)×(4+2x)

= 24+8x+12x+4x²

Area of a rectangular flower bed = 6×4

= 24 square feet

Tulips and Daisy have same area to plant

So, the equation is 24+20x+4x²=24

4x²+20x=0

Therefore, the area of a flower bed is 24 square feet and the equation to represent the equal area is 24+20x+4x²=24.

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The equation that represents the number of credits the student has earned after t semesters is C(t) = 12t + 15.

Let x be the number of credits the student had before starting college, and let y be the number of credits the student takes each semester. We can use this information to write an equation that represents the number of credits the student has earned after t semesters.

After 2 semesters, the student had 39 credits, which means the student earned 2y + x credits in those two semesters. Similarly, after 5 semesters, the student had 75 credits, which means the student earned 5y + x credits in those five semesters.

Using this information, we can write the following equation:

C(t) = yt + x

where C(t) represents the number of credits the student has earned after t semesters.

We know that C(2) = 2y + x = 39 and C(5) = 5y + x = 75. We can use these two equations to solve for x and y:

2y + x = 39

5y + x = 75

Subtracting the first equation from the second equation gives:

3y = 36

Therefore, y = 12, which means the student takes 12 credits each semester. Substituting y = 12 into either of the two equations above gives x = 15, which means the student had 15 credits before starting college.

Thus, the equation that represents the number of credits the student has earned after t semesters is C(t) = 12t + 15.

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Answer:

260

Step-by-step explanation:

The z score for a normal distribution is given by the formula
[tex]z = \dfrac{X-\mu}{\sigma}[/tex]

where
X is the data point, μ is the mean and  σ is the standard deviation

Given

Mean μ = 500
Standard deviation σ = 80
z-score = -3

and plugging in these values for z-score formula we get

[tex]-3 = \dfrac{X -500}{80}[/tex]

==>
-240 = X - 500
-240 + 500 = X

260 = X

or

X = 260

Answer: 15,625,000

Step-by-step explanation: x5, 8, 40, 200, 1,000, 5,000, 25,000, 125,000, 625,000, 3,125,000, 15,625,000

The area of triangle LMN is 49.61 square units.

We have,

To find the area of triangle LMN.

Area = (1/2) x base x height

where the base and height are the sides of the triangle perpendicular to each other.

First, we need to find the length of side L.

We can use the Law of Cosines.

L² = M² + N² - 2MNcos(132°)

L² = 6² + 8.3² - 268.3cos(132°)

L² = 36 + 68.89 + 99.36

L² = 204.25

L = √204.25

L = 14.28

Now that we know the length of the base of the triangle, we can find the height by dropping a perpendicular from vertex M to side LN.

Since triangle LMN is obtuse, the perpendicular will fall outside of the triangle.

Let's call the foot of the perpendicular point P.

Since M∠M is 132°, we can find the measure of the acute angle ∠LMP:

M∠LMP = 180° - M∠M

M∠LMP = 180° - 132°

M∠LMP = 48°

We can use trigonometry to find the length of MP:

tan(48°) = h/6

h = 6 x tan(48°)

h = 6.93

The area of triangle LMN is:

Area = (1/2) x base x height

Area = (1/2) x 14.28 x 6.93

Area ≈ 49.61

Thus,

The area of triangle LMN is 49.61 square units.

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When p = 9 and w = 225, the value of m is 94.5

We know that m varies jointly as p and the square root of w, then we can write.

m = k*p*√w

Where k is a constant.

We know that m=21 when p=5 and w=36, replacing that we will get:

21 = k*5*√46

21 = k*30

21/30 = k

7/10 = k

Then the equation is:

m = (7/10)*p*√w

Then when p = 9 and w = 225 we will have:

m = (7/10)*9*√225

m = 94.5

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Based on the rate of change, the total charge will be $ 12.60 in 4 days

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

Rate of change of investment = $3.15

Value of the investment = $12.60

Using the above as a guide, we have the following:

Number of days = Value of the investment/Rate of change of investment

Substitute the known values in the above equation, so, we have the following representation

Number of days = 12.60/3.15

Evaluate

Number of days = 4

Hence, the number of days is 4

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The resultant of the two vectors or the sum of the two vector is equal to the diagonal of parallelogram.

Parallelogram law of vector addition states that if two vectors are represented in magnitude and direction by the adjacent sides of a parallelogram, the diagonal of the parallelogram drawn from the point of intersection of the vectors represents the resultant vector in magnitude and direction.

For the given vector a, and vector, the resultant of the two vector is calculated as;

-----------> a  and --------------->b = a + b

The diagram represents the addition of the two vectors, a and b;

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Taxes and transfers are used by the government to more equitably share revenue. A Medicaid participant typically receives $1500 in benefits.

We know that,

Medicare is a health insurance program for seniors, disabled individuals under 65, and dialysis patients. Medicaid is a program that provides financial aid for low-income patients' medical costs.

The federal government and the states share funding for the Medicaid program. The amount that the federal government reimburses states for program costs is known as the Federal Medical Assistance Percentage, or FMAP (FMAP).

Spending on Medicaid is mostly targeted at the elderly and those with disabilities. Despite accounting for over two-thirds of Medicaid spending, seniors and individuals with disabilities make up one in four beneficiaries, which reflects the high per-enrollee expenses for both acute and long-term care.

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The number of photos from Julia dance class = 5/7 or 40/56 photos.

We shall use mathematical operations to calculate the photos that are of Julia dance class

Five sevenths of the images are photos from dance class, meaning that 5/7 x 56 = 40 photos from dance class.

We express the answer as a fraction with a denominator of 56 like this:

Number of photos / Total number of photos = 40/56

Number of photos from dance class / Total number of photos = 5/7

Therefore, the fraction of photos that are of Julia dance class (as a fraction with a denominator of 56) = 5/7 or 40/56.

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Making x as a subject, we get equation as x=(y+2)/5.

The given equation is y=5x-2.

To make x as the subject

y+2=5x

x=(y+2)/5

Therefore, making x as a subject, we get equation as x=(y+2)/5.

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"Your question is incomplete, probably the complete question/missing part is:"

Rearrange the formula to make x the subject y=5x-2.

The x-intercept will be (5/3, 0) and the y-intercept will be (0, -5/2).

The x-intercept of an equation is the point at which the graph of the equation intersects the x-axis, which means that the y-coordinate of that point is 0. To find a x-intercept, we can set y = 0 in equation and solve for x.

Given the equation: 3x - 2y = 5

Setting y = 0, we get;

3x - 2(0) = 5

3x = 5

x = 5/3

So, the x-intercept is (5/3, 0).

The y-intercept of an equation is the point at which the graph of the equation intersects the y-axis, which means that the x-coordinate of that point is 0. To find y-intercept, we can set x = 0 in equation and solve for y.

Setting x = 0, we get;

3(0) - 2y = 5

-2y = 5

y = -5/2

So, the y-intercept is (0, -5/2).

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Krell's equity cost of capital, or expected total return, is 5.57%.

We have,

The dividend yield is the annual dividend divided by the current share price:

Dividend yield

= Annual dividend / Share price

= $0.98 / $22.08 = 0.0444 = 4.44%

The equity cost of capital is the expected total return on the stock, which includes both the dividend yield and the expected capital appreciation:

Equity cost of capital = Dividend yield + Capital Appreciation

= 4.44% + [(24.98 - 22.08) / 22.08]

= 4.44% + 0.1314

= 5.57%

Therefore,

Krell's equity cost of capital, or expected total return, is 5.57%.

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The formula for the nth term of the geometric sequence is given as follows:

[tex]a_n = 7(-3)^{n - 1}[/tex]

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

The formula for the nth term of the sequence is given as follows:

[tex]a_n = a_1q^{n-1}[/tex]

The first term of the sequence is given as follows:

[tex]a_1 = 7[/tex]

Each term is the previous term multiplied by -3, hence the common ratio is given as follows:

q = -3.

Thus the formula for the sequence is given as follows:

[tex]a_n = 7(-3)^{n - 1}[/tex]

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