f(x)=x^3-7x^2+25x-175 and f(7)=0

Therefore , the solution of the given problem of  equation comes out to be for 0 brothers, 78°, for 1 brother, 132°, for two brothers, 66°,for 3 brothers, 42° and for 4 brothers, 42°.

A linear recovery model is founded on the formula: y=mx+b. B is the slope, and m is the y-intercept. The phrase "Bivariate logistic formulas have two components" is frequently used, despite the fact that y and y are two separate elements. When it comes to using linear functions, there are no easy solutions. and. Y=mx+b is the expression, where m stands for slopes and b for the y-intercept.

Here,

(Frequency  Total Frequency) x 360 equals angle (0).

the aggregate of all frequencies is the total frequency.

We can see from the provided chart that:

13 individuals lack relatives.

22 individuals each have one sibling.

11 individuals have two siblings, and 7 people have three.

7 individuals have 4 brothers.

13 + 22 + 11 + 7 + 7 = 60 is the overall frequency.

Using the aforementioned method, we can now determine the angle for each category:

For 0 siblings: Angle = (13 ÷ 60) x 360 = 78°

For 1 sibling: Angle = (22 ÷ 60) x 360 = 132°

For 2 siblings: Angle = (11 ÷ 60) x 360 = 66°

For 3 siblings: Angle = (7 ÷ 60) x 360 = 42°

For 4 siblings: Angle = (7 ÷ 60) x 360 = 42°

The total of all angles ought to

All the angles should total up to 360 degrees, which we can verify by:

78° + 132° + 66° + 42° + 42° = 360°

Therefore, the angles needed to represent the number of siblings among 60 individuals on a pie chart are:

for 0 brothers, 78°

for 1 brother, 132°

For two brothers, 66°

for 3 brothers, 42°

for 4 brothers, 42°

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The given triangles are  similar by AA~, SSS~, SAS~, or not similar.

What is similar triangles in maths?

Triangles that are similar to one another in terms of shape but not necessarily size are called congruent triangles. Examples of related objects are all equilateral triangles and squares with any side length. To put it another way, if two triangles are comparable, then their corresponding angles and sides are congruent and equal in size.

7.  In triangles AEB & BDC

 AE/BD = EB/DC

We can conclude that, the corresponding sides are  in common ratio, so triangles are  similar.

Hence, The given triangles are  similar.

8. Given a figure of two triangles, ΔLKM and ΔLJN

Here,

              LK/LJ = LM/LN

             21 - 6/21 = 10/14

                 15/21 = 10/14

                 5/7 = 5/7

We can conclude that, the corresponding sides are in common ratio, so triangles are  similar.

Hence, The given triangles are  similar.

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Step-by-step explanation:

To find the vertical asymptotes of the function f(x) = (x^2+3x+6)/(x^2-4), we need to find the values of x that make the denominator equal to zero.

The denominator (x^2-4) factors into (x+2)(x-2). Therefore, the denominator is equal to zero when x = -2 or x = 2.

These values of x give us vertical asymptotes since the function becomes unbounded as x approaches these values. Therefore, the vertical asymptotes of the function are x = -2 and x = 2.

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Answer:

Let the length of the rectangle be x and the width of the rectangle be y.

Then, we can use the Pythagorean Theorem to find the value of x and y:

x2 + y2 = 62

x2 + y2 = 36

We can use trigonometry to find the value of x and y:

x = 6 sin 30°

y = 6 cos 30°

Therefore, the length of the rectangle is 6 sin 30° cm and the width of the rectangle is 6 cos 30° cm.

The dimensions of the box are 30 cm by 50 cm by 25 cm.

Area is a measure of the amount of space enclosed by a two-dimensional object, such as a shape or a surface. It is usually expressed in square units, such as square meters (m²), square inches (in²), or square centimeters (cm²), depending on the unit system used.

Let x be the side length of the squares that are cut out of each corner of the cardboard.

When the squares are cut out and the sides are folded up, the resulting box will have dimensions (80-2x) cm by (100-2x) cm by x cm.

The area of the base of the box is:

(80-2x) cm × (100-2x) cm = 8000 - 360x + 4x² cm²

We know that the area of the base is 4000 cm², so we can set this equal to the expression we just found:

8000 - 360x + 4x² cm² = 4000 cm²

Simplifying and rearranging, we get a quadratic equation:

4x² - 360x + 4000 = 0

Dividing both sides by 4, we get:

x² - 90x + 1000 = 0

This quadratic can be factored as:

(x - 40)(x - 25) = 0

Therefore, the possible values of x are x = 40 cm and x = 25 cm.

If we use x = 40 cm, then the dimensions of the box are:

Length = 80 - 2x = 0 cm (not possible)

Width = 100 - 2x = 20 cm

Height = x = 40 cm

If we use x = 25 cm, then the dimensions of the box are:

Length = 80 - 2x = 30 cm

Width = 100 - 2x = 50 cm

Height = x = 25 cm

Therefore, the dimensions of the box are 30 cm by 50 cm by 25 cm.

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The principal from difference between Simple interest and Compound interest of a certain sum of money is 50.4 at 6% p.a. for 2 years is $14,000.

Let the principal be P.

Simple interest = P x 0.06 x 2 = 0.12P

Compound interest = P(1 + 0.06)^2 - P = 1.1236P - P = 0.1236P

Given: Compound interest - Simple interest = 50.4

0.1236P - 0.12P = 50.4

0.0036P = 50.4

P = 50.4 / 0.0036

P = 14000

Therefore, the principal is $14,000.

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Answer:

Step-by-step explanation:

yes

If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio and the ratio in the given situation is 3a:2b = 6:1.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0.

A proportion is an equation that sets two ratios at the same value.

For instance, if there is 1 boy and 3 girls, you may express the ratio as 1: 3 (there are 3 girls for every boy), meaning that there are 1 in 4 boys and 3 in 4 girls.

Ratios contrast two figures by ordinarily dividing them. A/B would be your formula if you were comparing one data point (A) to another data point (B).

So, we know that:

a+b/a-b = 5/3

Now, solve as follows:

3 ( a + b) = 5 ( a - b)

3 a + 3 b = 5 a - 5 b

5 b + 3 b = 5 a - 3 a

8 b = 2 a

2 a = 8 b

a = 4 b

3 a = 3 × 4 b

3 a = 12 b

3 a: 2 b = 12 b : 2 b

Then: 3a:2b = 6:1

Therefore, if b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio and the ratio in the given situation is 3a:2b = 6:1.

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Correct question:

A+b/a-b=5/3 what are the following ratios? 3a:2b

After answering the provided question, we can conclude that Therefore, inequality the answer is (D) x > -3 and y > 1.

In mathematics, an inequality is a non-equal relationship between two expressions or values. As a result, imbalance leads to inequality. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal sign is commonly used (). Different inequalities, no matter how small or large, are used to contrast values. Many simple inequalities can be solved by modifying the two sides until only the variables remain. But a number of things contribute to inequality: Negative values are divided or added on both sides. Trade off the left and right.

domain and range of the inequality

[tex]y - 1 < \sqrt{x + 3}\\(y - 1)^2 < x + 3\\(y - 1)^2 - 3 < x\\[/tex]

Therefore, the answer is (D) x > -3 and y > 1.

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A 95% confidence interval for the average is 3898.

In statistics, the confidence interval formula is used to express the degree of uncertainty surrounding a sample estimate of a population parameter.

Formula of confidence interval:

If n ≥ 30,

Confidence Interval = m ± z(SD/√n)

where,

n = Number of terms

m = Sample average

SD = Standard Deviation

Value for the confidence interval in the z table is z.

Table of Confidence interval  and Z

CI      z

0.70 1.04

0.75 1.15

0.80 1.28

0.85 1.44

0.90  1.645

0.92 1.75

0.95 1.96

0.96 2.05

0.98 2.33

0.99 2.58

According to the question

random sample of student (n) =  99

average savings = 3800 dollars

Standard deviation =  500 dollars

95% confidence interval for the average needed

i.e , z = 1.96

Now, By using Formula of confidence interval:

Confidence Interval = m ±  z(SD/√n)

substituting the values

Confidence Interval = 3800 ± 1.96(500/√99)

                                 = 3800 ± 98.49

                                 = 3898.49

values to the nearest whole number

Confidence Interval = 3898

Hence,  A 95% confidence interval for the average is 3898 .

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The evaluation of expression 7√3 / (√10 + √3) - 2√5 / (√6 + √5) - 3√2 / (√15 + 3√2) and simplification to get the final result of 2√5 - 2√6 + 6.

To evaluate the expression is

7√3 / (√10 + √3) - 2√5 / (√6 + √5) - 3√2 / (√15 + 3√2)

we need to rationalize the denominators of each fraction. To do this, we can multiply both the numerator and denominator of each fraction by the conjugate of the denominator.

For the first fraction, we can multiply the numerator and denominator by (√10 - √3):

7√3(√10 - √3) / [(√10 + √3)(√10 - √3)]

Simplifying the denominator gives:

7√3(√10 - √3) / 10 - 3

For the second fraction, we can multiply the numerator and denominator by (√6 - √5):

-2√5(√6 - √5) / [(√6 + √5)(√6 - √5)]

Simplifying the denominator gives:

-2√5(√6 - √5) / 6 - 5

For the third fraction, we can multiply the numerator and denominator by (√15 - 3√2):

-3√2(√15 - 3√2) / [(√15 + 3√2)(√15 - 3√2)]

Simplifying the denominator gives:

-3√2(√15 - 3√2) / 15 - 9

Now, we can simplify each expression separately and then combine them:

7√3(√10 - √3) / 7 = √30 - 3

-2√5(√6 - √5) / 1 = -2√6 + 2√5

-3√2(√15 - 3√2) / 6 = -√30 + 9

Combining the expressions gives:

√30 - 3 - 2√6 + 2√5 - √30 + 9

Simplifying further gives:

2√5 - 2√6 + 6

Therefore, the value of the expression 7√3 / (√10 + √3) - 2√5 / (√6 + √5) - 3√2 / (√15 + 3√2) is 2√5 - 2√6 + 6.

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The answer is  option (A)  BC=YZ ,to show that AABC = AXYZ by ASA, we need to know that angle C is congruent to angle ∠Y, angle ∠Z is congruent to angle ∠B, and BC is congruent to ZY.

An angle is a geometric figure formed by two rays with a common endpoint, called the vertex of the angle. The two rays are called the sides of the angle, and they can be named in any order. The measure of an angle is the amount of rotation needed to bring one of the rays into alignment with the other.

To show that AABC = AXYZ by ASA, we need to show that two angles and the included side of one triangle are congruent to two angles and the included side of the other triangle. Since we are given that ZZZC and CB ZY, we know that angle ∠C is congruent to angle ∠Y, and angle ∠Z is congruent to angle ∠B. Therefore, we need to find another piece of information that shows that the included sides are congruent.

Looking at the diagram, we can see that side BC is congruent to side ZY, since they are opposite sides of a rectangle. Therefore, we have BC = ZY, which means that statement A, BC=YZ, is true.

So, to show that AABC = AXYZ by ASA, we need to know that angle ∠C is congruent to angle ∠Y, angle ∠Z is congruent to angle ∠B, and BC is congruent to ZY. Since we have all three of these conditions, we can conclude that AABC = AXYZ by ASA.

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If the standard deviation is 12,000 dollars for four electricians, then the standard deviation for the sampling distribution of the sample mean is 6000 dollars.

The standard deviation of the sampling distribution of the sample mean, is also known as the standard error of the mean,

The standard deviation is be calculated using the formula,

⇒ standard-error of mean is = σ/√n,

Where σ = population standard deviation and n = sample size,

In this case, σ = 12,000 dollars and n = 4.

Substituting these values into the standard deviation formula, we get,

⇒ "standard-error" of mean = 12000/√4 = 6,000 dollars.

Therefore, the standard deviation for the sampling distribution of the sample mean is 6,000 dollars.

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The given question is incomplete, the complete question is

Suppose that, on average, electricians earn approximately μ = 54,000 dollars per year in the United States. Assume that the distribution for electrician's yearly earnings is normally distributed and that the standard deviation is σ = 12,000 dollars. Given a sample of four electricians,

What is the standard deviation for the sampling distribution of the sample mean?

A sphere's volume may be calculated using the formula [tex]137.25[/tex] cm cube.

V = 4/3 r3, where V is the volume and r is the radius, is the formula for a sphere's volume. 1/2 of a sphere's radius makes up its radius. Therefore, you may determine the radius first, followed by the volume, to get the surface of a circle given its diameter.

The radius of a sphere is the distance between its center and its outside surface. The amount of space a satellite's surface covers is known as its surface area, and it is equal to 4r2.

The diameter of the sphere, [tex]d = 6.4[/tex] cm

Radius,[tex]r = 3.2[/tex] cm

We need to find the volume of the sphere. The formula for the volume of a sphere is given by :

[tex]V=4/3pir^{3}[/tex]

[tex]4/3pi*(3.2)^{3}[/tex]

[tex]=137.25 cm^{3}[/tex]

The radius of the bowling ball is [tex]6.4 cm/2 = 3.2 cm[/tex], and its volume is [tex]V[/tex] bowling [tex]= 4/3 pi(3.2)^{3} * 8 = 1,100.8[/tex] cubic cm.

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Therefore, the probability of Mrs. Vo winning is 1 - 91/300 - 8/21 = 11/30.

Probability refers to the likelihood or chance that a particular event or outcome will occur. It is a mathematical concept that quantifies the degree of uncertainty associated with an event or situation. Probability is typically expressed as a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that it is certain to occur.

by the question.

let's consider the first case: Mrs. Vo spins a number greater than 65 on her first spin. There are a total of 8 numbers greater than 65 on the wheel: 70, 75, 80, 85, 90, 95, 100. Since there are 21 sections on the wheel, the probability of spinning a number greater than 65 on the first spin is 8/21.

The number of possible outcomes for Mrs. Vo's spin is 21, since there are 21 equal portions on the wheel. However, we need to exclude the outcomes that would cause Mrs. Vo's sum to exceed 100, since that would result in an automatic loss. The largest possible outcome on the wheel is 100, so Mrs. Vo cannot spin a number greater than or equal to 35 on her first spin.

The number of outcomes that would give Mrs. Vo a winning sum of at least 66 is the number of outcomes greater than 65, which are 70, 75, 80, 85, 90, 95, and 100. There are 7 such outcomes.

If Mrs. Vo spins a number less than or equal to 65 on her first spin, the probability of this happening is 13/21. The probability of her second spin being between 1 and 35 is 35/100 (since there are 35 numbers between 1 and 35 on the wheel). So, the probability of her total sum being less than or equal to 65 is (13/21) * (35/100) = 91/300.

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The area of the blue paper obtained by subtracting the 6 circle areas from the rectangle is 20.64 sq. cm.

A circle is made up of all points in a single plane that are equidistant from one another. Only the bordering points make up the circle. The radius is the distance from the centre to the outside of the circle.

The diameter is the length of a line that connects the circle's ends to its middle point. The radius is half as large as the diameter.

Given data:

length l = 12 cm

width w = 8 cm

radius r = 4/2 = 2 cm.

Area of blue page = Total area of rectangle - 6*area of circle

Area of blue page = length * width - 6*π*r²

Area of blue page = 12*8 - 6*3.14*2²

Area of blue page = 20.64 sq. cm.

Thus, the area of the blue paper obtained by subtracting the 6 circle areas from the rectangle is 20.64 sq. cm.

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The volume of the sphere is approximately 33.51 cubic centimeters.

The volume of a sphere can be calculated using the formula:

V = (4/3)π[tex]r^{3}[/tex]

where r is the radius of the sphere

V is the volume of the sphere

Since the diameter of the sphere is 4 centimeters, the radius is half of that, or 2 centimeters.

Plugging this value into the formula, we get:

V = (4/3)π([tex]2^{3}[/tex])

V = (4/3)π(8)

V = (32/3)π

So the answer is (a)  32/3π[tex]cm^{3}[/tex]

the volume of the sphere is approximately 33.51 cubic centimeters.

The volume of the sphere is a measure of how much space the sphere occupies. The formula for the volume of the sphere tells us that the volume is proportional to the cube of the radius. This means that as the radius increases, the volume of the sphere increases much more rapidly. This is why a small increase in the radius can result in a much larger increase in the volume of the sphere.

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Answer:

An exponential function can be used to model this situation.

In this case, we know that each hour following the initial dose, 80% of the concentration remains in the body from the preceding hour. This means that the amount of penicillin remaining in the body is decreasing exponentially.

We can use the formula for exponential decay, which is:

A = A0 * e^(-kt)

where A is the amount of penicillin remaining in the body at time t, A0 is the initial amount of penicillin (in this case, 500 milligrams), k is the decay constant, and e is the mathematical constant approximately equal to 2.718.

The decay constant, k, can be calculated using the following formula:

k = ln(0.8)

where ln is the natural logarithm.

So the exponential function that can be used to model this situation is:

A = 500 * e^(-0.2231t)

where t is the time in hours since the initial dose was administered.

This function will give us the amount of penicillin remaining in the body at any time t, based on the initial dose and the rate of decay.

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We can conclude after answering the provided question that Therefore, diameter m GFH = 21° and m GZH = 116°.

In geometry, the diameter of a circle is any straight line segment that has an endpoint on the circle and travels through its centre. Another way to put it is the longest chord of a circle. Either concept can be used to define the diameter of a sphere. The diameter is the length of the line that runs tangent to the two points at either end of the circle. If you consider length to be the distance between two points, diameter equals length. The diameter of a circle is the distance between its two furthest points.

We know that angle EGF is a right angle (90°) because EG is a diameter.

Given that m FG = 116°, we can calculate m FGE by subtracting it from 180° (the sum of triangle angles):

m FGE = 180 degrees - m FG = 180 degrees - 116 degrees = 64 degrees

m GFH = 180° - m ZGF - m ZGFH = 180° - 90° - 69° = 21°

Finally, we can calculate m GZH by subtracting m FGE from 180° (the sum of triangle angles):

180° m GZH - 180° m FGE - 64° = 116°

Therefore, m GFH = 21° and m GZH = 116°.

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Answer:

Common difference = 2

Step-by-step explanation:

We can find the common difference by subtracting any two consecutive terms with the smaller number being subtracted from the larger:

Thus, to find the common difference, d, we can subtract -13 from -15:

d = -15 - (-13) = -15 + 13 = 2

Using the proportionality theorem we know that the length of the side AE is 28 units respectively.

The intercept theorem often referred to as Thales' theorem, the basic proportionality theorem, or the side splitter theorem is a crucial concept in introductory geometry that deals with the ratios of different line segments produced when two intersecting lines are intercepted by a pair of parallels.

A triangle's other two sides are divided in the same proportion if a line drawn parallel to either one of its sides intersects the other two sides at two different spots.

So, the given proportion is:

= 32/56

= 4/7

Then,

= AE/49

We will be using table 7:

= AE/49

= 7*4/7*7

= 28/49

Therefore, using the proportionality theorem we know that the length of the side AE is 28 units respectively.

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Answer:

16

Step-by-step explanation:

When you square a square root (√1^2) it just cancels out. :)

Answer:

5 + 10[tex]\sqrt{3}[/tex]

= 22.3205080757

Step-by-step explanation:

Answer:

≈ 13,7 inches

Step-by-step explanation:

Just use trigonometry (sin or cos) from the right triangles ∆ABC and ∆ADC

An equation of the line that passes through the points (-7, 7) and (−2, −6) in point-slope form is y - 7 = -13/5(x + 7).

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁) or [tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)[/tex]

Where:

At data point (-7, 7), a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

[tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)\\\\y - 7 = \frac{(-6- 7)}{(-2 -(-7))}(x -(-7))\\\\y - 7 = \frac{(-6- 7)}{(-2 +7)}(x +7)[/tex]

y - 7 = -13/5(x + 7)

y = -13x/5 + 7 - 91/5.

y = -13x/5 - 56/5

In this context, we can reasonably infer and logically deduce that an equation of the line that represents this line in slope-intercept form is y = -13x/5 - 56/5.

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Answer:

1/4

Step-by-step explanation:

As given the figure, 3 out of 4 rectangles are shaded,

So,

4/4-3/4=1/4

Answer:

[tex] \frac{y - y1}{m} = x - x1 \\ x1 = x - \frac{y - y1}{m} [/tex]

so,A is the correct answer...

Answer:

Step-by-step explanation:

The circumference is the perimeter of a circle, which is equal to 131.88ft.

Circumference = [tex]2\pi r^{2}[/tex]

[tex]131.88=2\pi r^{2} \\r^{2} =\frac{131.88}{2\pi } \\r=\sqrt{20.989} \\r=4.581[/tex]

This means that the diameter is:

[tex]d=2r\\d=9.163[/tex]

So our area is:

[tex]A=\pi r^{2} \\A=\pi (4.581)^{2} \\A=65.940[/tex]

Hope this helped!

The values in the columns which completes the table for the COLA salary adjustments are as follows;

[tex]\begin{tabular}{|c|c|c|c|} \cline{1-4}&Amount & Amount&New Salary\\ \cline{1-4}1& \$1,672&\$1,584&\$47,256 \\ \cline{1-4} 2 & \$1,312&\$3,116&\$45,428 \\ \cline{1-4}3&\$1,483&\$1,425&\$34,408 \\ \cline{1-4}\end{tabular}[/tex]

4. The COLA Increase and New Salaries are presented as follows;

[tex]\begin{tabular}{|c|c|c|c|c|c|} \cline{1-6} & J. Spar&T. Beggins & R. Stokes &D. Garcia& J. Stiles\\ \cline{1-6}COLA Increase & 6.5\%&6.5\%&6.3\%&7.5\%&6.3\% \\ \cline{1-6} New Salary & \$20,430&\$23,925&\$35,480.04&\$15,792.3&\$31,385.64 \\ \cline{1-6} \end{tabular}[/tex]

5. Ron Fortini's weekly salary prior to the increase was about $899.12

What is a COLA?

COLA is an acronym for Cost-Of-Living-Adjustment, which is an increase in salary or income to keep pace with the current inflation rate or trend and increased societal cost of living.

The amount C. North received based on COLA is; $44,000 × 2.80% = $1,232

The amount received as merit is; $44,000 × 3.60% = $1,584

The New Salary amount  = $1,232 + $1,584 + $44,000 = $47,256

The amount N. Vanders received as COLA is; $41,000 × 3.20% = $1,312

The amount received as merit is; $41,000 × 7.60% = $3,116

The New Salary is; $41,000 + $1,312 + $3,116 = $45,428

The amount M. Clark received as COLA is; $31,500 × 4.70% = $1,480.5

The amount M. Clark received as merit is; $31,500 × 4.50% = $1,417.5

M. Clark's New Salary is; $31,500 + $1,480.5 + $1,417.5 = $34,397

Please find above the completed columns that complete the questions 1, 2, and 3 above.

4. The COLA received based on the sliding scale for the cost-of-living adjustment are;

J. Spar; 6.5%

T. Beggins; 6.5%

R. Stokes; 6.3%

D. Garcia; 7.5%

J. Stiles; 6.3%

The New Salaries based on the total increase are;

               [tex]{}[/tex]                                      New Salary

J. Spar; $18,000 + $18,000 × 12.50%  = $20250

T. Beggins; $21,750 + $21,750 × 10.00% = $23,925

R. Stokes; $31,860 + $31,860 × 11.4% = $35,492.04

D. Garcia; $14,615 + $14,615 × 8.20% = $15,813.43

J. Stites; $27,916 + $27,916 × 12.525% = $31,412.479

Please find included the completed rows for the COLA Increase and the New Salary above

5. Let x represents Ron Fortini's prior weekly salary

Ron Fortini's weekly salary after 5.20% merit increase and 2.75% cost-of-living increase, Ron Fortini's new salary is $968.80

Therefore;

New weekly salary =  Prior weekly salary + (Prior weekly salary × (5.20% + 2.75%))

$968.80 = x + x × 0.0775 = 1.0775·x

1.0775·x = $968.80

x = $968.80/1.0775 ≈ $899.12

Therefore, Ron Fortini's weekly salary prior to the increases was $899.12

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The value of m∠Q is 148°.

What is tangent?

The straight line that "just touches" the curve at a given location is referred to as the tangent line to a plane curve in geometry. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.

Here, we have

Given: PR is ranger to circle Q at Point R. PS is tangent to circle Q at Point S.

We have to find the value of m∠Q.

We know that PR = PS

In ΔPRS

∠P + ∠R + ∠S = 180°

∴ ∠R = ∠S

∠P + ∠R + ∠R = 180°

38 + 2∠R  = 180°

2∠R  = 180° - 32°

2∠R = 148°

∠R  = 74°

∠S =  74°

∠PRQ = 90°

In ΔSRQ

∠SRQ = 90° - 74° = 16°

∠RSQ = 90° - 74° = 16°

∴ ∠SRQ + ∠RSQ + ∠RQS   = 180°

16° + 16° +∠RQS = 180°

∠RQS = 180° - 32°

∠RQS = 148°

m∠Q = 148°

Hence, the value of m∠Q is 148°.

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