find the sq root of 0.00033124​

a. Martina's career average salary is $37577.5.

b. Martina's annual pension benefit is $21193.71.

c.  Martina's annual retirement salary will be approximately 40.76% of her final annual salary.

d. Martina's monthly pension benefit is $1766.14.

a. To find Martina's career average salary, we need to calculate the total salary earned over the last 24 years and divide it by 24.

Total salary = 28,800 + 29,300 + 30,250 + 31,000 + 35,500 + 42,000 + 45,000 + 50,000 + 28,800 + 29,900 + 30,350 + 35,000 + 35,700 + 43,000 + 48,000 + 52,000 + 29,210 + 29,900 + 30,450 + 35,000 + 38,000 + 43,900 + 48,800 + 52,000

Total salary = 901860

Career average salary = Total salary/24 = 901860/24

Career average salary = 37577.5

Martina's career average salary is $37577.5.

b. Martina's annual pension benefit is calculated by multiplying 2.35% of the career average salary by the number of years employed. Martina has been employed for 24 years.

Annual pension benefit = 2.35% x Career average salary x Years employed

Annual pension benefit = 2.35% x 37577.5 x 24

Annual pension benefit = $21193.71

Martina's annual pension benefit is $21193.71.

c. To find the percentage of Martina's final annual salary that her annual retirement salary will be, we need to divide the annual pension benefit by her final annual salary and then multiply by 100.

Percentage of final annual salary = (Annual pension benefit/Final annual salary) x 100

Percentage of final annual salary = (21193.71/52,000) x 100

Percentage of final annual salary = 40.76%

Martina's annual retirement salary will be approximately 40.76% of her final annual salary.

d. To find Martina's monthly pension benefit, we need to divide the annual pension benefit by 12.

Monthly pension benefit = Annual pension benefit/12

Monthly pension benefit = 21193.71/12

Monthly pension benefit = $1766.14 (rounded to the nearest penny)

Martina's monthly pension benefit is $1766.14.

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Answer:

B. x > 0

Step-by-step explanation:

Domain is all x-values that can be plugged in to get an output of y. When we graph out equation, we should see that we have an asymptote when we approach negative infinity and that we approach infinity when we approach positive infinity (looking at x-values). Therefore, we have to have x > 0 as our answer.

Answer:

X > 0

Step-by-step explanation:

Answer:

2\3 cups will be needed..good luck

Answer:

40%

Step-by-step explanation:

Answer:

Step-by-step explanation:

½(x-2) = 8 + 5x

Multiply both sides by 2

2⋅½(x-2) = 2(8 + 5x)

1(x-2) = 2(8 + 5x)

Apply the distributive rule

x - 2 = 16 + 10x

Subtract x from both sides

-2 = 16 + 9x

Subtract 16 from both sides

-18 = 9x

Divide both sides by the coefficient of x

-18 ÷ 9 = 9x ÷ 9

-2 = x

By using the linear equation y=3x we draw the graph for proportional relationship.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

A proportional relationship graph between two variables is a relationship where the ratio between the two variables is always the same

the graph of any proportional relationship is characterized by a straight line with data points passing through the origin (0, 0).

By the definition of proportional relationship of graph, we can reduce relationship between the values on the x-coordinate and y-coordinate of the given graph

As they are  proportional and represented by euation

y = 3x

Where, x represent the time and y represent the number of sit-ups.

Hence by using the linear equation y=3x we draw the graph for proportional relationship.

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The value u > -16 that makes the inequality 5u > -80 is true.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

We have the inequality,

5u > -80

To find the solution set of the inequality;

Divide by 5 to both sides,

5u/5 > -80/5

u > -16.

That means, the inequality is true for u > -16.

Therefore, the inequality is true for u > -16.

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Answer:

bhai sorry bhai Ham Hindi Wale Hain English Nahin samajhte to please Ham bhi a question mat dena Humko is question ka answer Nahin patahai

The amount of money Calvin and Sasha have, is an illustration of equivalent expressions.

Calvin has exactly 13 quarters

From the question, we have:

\(\mathbf{Calvin = 0.25Q}\)

\(\mathbf{Sasha = 0.05N + 0.01P + 0.10D}\)

Calvin has the same number of quarters as Sasha has dimes.

So, we have:

\(\mathbf{Q = D}\)

Sasha has $1.95 in coins that are not dimes.

So, we have

\(\mathbf{0.05N +0.01P = 1.95}\)

They have the same amount of money i.e.

\(\mathbf{Calvin = Sasha}\)

This gives

\(\mathbf{0.25Q = 0.05N + 0.01P + 0.10D }\)

Substitute \(\mathbf{0.05N +0.01P = 1.95}\)

\(\mathbf{0.25Q = 1.95 + 0.10D }\)

Substitute \(\mathbf{Q = D}\)

\(\mathbf{0.25Q = 1.95 + 0.10Q }\)

Collect like terms

\(\mathbf{0.25Q -0.10Q= 1.95 }\\\)

\(\mathbf{0.15Q= 1.95 }\)

Divide both sides by 0.15

\(\mathbf{Q= 13 }\)

Hence, Calvin has exactly 13 quarters

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Answer:

Set your calculator to degree mode.

\( \tan( \alpha ) = \frac{23}{35} \)

\( \alpha = {tan}^{ - 1} \frac{23}{35} = 33.31\)

The angle of elevation of the sun is about 33°.

Answer  k=16

A recipe says to use 3 cups of flour to make 48 cookies.

the number of cookies made, y, to the number of cups of flour used,x .

Than

y = kx

Where k is the constant of proportionality.

48 = 3k

k = 16

Therefore the constant of proportionality is 16.

Yes , (x+4) is a factor of f(x)=5x⁴ +16x³ -15x² +8x+16 because , the conditions of the factor theorem are satisfied .

In order to determine whether (x+4) is a factor of the polynomial f(x) = 5x⁴ + 16x³ - 15x² + 8x + 16, we use the factor theorem, which states that if a polynomial f(x) has a factor (x - r), then f(r) = 0.

In this case, we use r = -4,

Since , (x+4) is of the form (x-r) with r = -4.

So, if (x+4) is a factor of f(x), then f(-4) should be equal to 0.

Evaluating f(-4),

We get ,

⇒ f(-4) = 5(-4)⁴ + 16(-4)³ - 15(-4)² + 8(-4) + 16

⇒ 5(256) - 16(64) - 15(16) - 32 + 16

⇒ 1280 - 1024 - 240 - 16

⇒ 0

Since, f(-4) is equal to 0, we can conclude that (x+4) is a factor of f(x).

Therefore, (x+4) is a factor of the polynomial f(x) = 5x⁴ + 16x³ - 15x² + 8x + 16.

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The given question is incomplete , the complete question is

Is (x+4) a factor of f(x)=5x⁴ +16x³ -15x² +8x+16?

When only three sides are provided without any information regarding the angle, such as a = 5 m and b = 9 m, c = 6m we can either create no triangle or create an unique triangle. Hence, either 0 or 1 Triangle.

For example :

How many different triangles may be formed with side lengths of 5m,9m and 6 m ?

Create a triangle with the following measurements: 5 meters, 9 meters , and 6meters, by protractor-adjusted to the given length of sides. You have constructed a triangle.

We can only create one triangle here, as no choice can be made in the given length of side as they are prefixed.

This implies that you cannot chose the side length independently. So, only one triangle which is unique will be formed. Hence, 0 or 1 triangle is formed

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Answer:

Step-by-step explanation:

We are given a ratio for this problem so we will use the formula for when we are given a ratio (as opposed to the formula for when you are given that the point you're looking for is a fraction of the way from one point to another, like 1/3 of the way from point A to point B. That's a different formula).

The formulas are for the x and y coordinates of the point in question:

\(x=\frac{bx_1+ax_2}{a+b}\)   and   \(y=\frac{by_1+ay_2}{a+b}\) where

a = 3 (from the ratio),

b = 1 (from the ratio),

x1 = -4, y1 = 0 (from point J)

x2 = 0, y2 = 4 (from point K). Filling in for x first:

\(x=\frac{1(-4)+3(0)}{3+1}\) gives us

\(x=\frac{-4}{4}=-1\) and now for y:

\(y=\frac{1(0)+3(4)}{3+1}\) gives us

\(y=\frac{12}{4}=3\)

Therefore, the coordinates that partition that segment into the ratio of 3:1 are (-1, 3)

Step-by-step explanation:

Say that x = 1, since x can be any real number.

From part a -> x +2 = 3

and -> 10-x =9

then multiply the two results to get y -> 3x9 = 27

Now look at y=20+8x-x and plug in the same value for x where x = 1

you get -> y = 20 + 8(1) -(1) which simplifies out to 27. Therefore the equation is proven since they equal the same value.

Answer:

z+18

Plz give brainliest

Step-by-step explanation:

Answer:

z+18

Step-by-step explanation:

4z+9-3z+9

z+9+9

z+18

Remember that the sine of an angle in a right triangle is equal to the quotient between the side opposite to the angle and the hypotenuse of the triangle.

Since the sine of the given angle θ is equal to 3/5, we can represent θ as part of a right triangle whose hypotenuse has a measure of 5 and the side opposite to θ has a measure of 3:

The length of the side adjacent to θ must be equal to 4 in order to satisfy the Pythagorean Theorem:

On the other hand, the cosine of an angle is defined as the quotient between the side adjacent to the angle and the hypotenuse of the triangle. Then, the cosine of θ must be equal to 4/5:

The rest of the trigonometric relations are defined in terms of the sine and the cosine as follows:

Since sinθ=3/5 and cosθ=4/5, then:

First, determine the number of miles covered per day:

Her car already has 45,300 miles on it.

(a)The total number of miles, f(x), Stefanie's car will have been driven after x more days will be:

(b) Stephanie works 4 days a week.

After 3 weeks, the number of days worked = 4 x 3 = 12 days

Therefore, when x=12:

The area of square will be;

⇒ 16/81 cm²

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The width of square = 4/9 centimeters

Now,

We know that;

The area of square = Side × Side

Here, The width of square = 4/9 centimeters

Hence, The area of square with side 4/9 cm is,

⇒ The area of square = Side × Side

⇒ The area of square = 4/9 × 4/9

⇒ The area of square = 16/81 cm²

Thus, We get;

⇒ The area of square = 16/81 cm

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Answer:

It is very important to use credit wisely for a few reasons.

1) You have to be very careful and conscientious about your credit because one missed payment and your credit score will fall.

2) You need to make sure you keep your credit up because if you ever have plans to buy a house or a new car or a piece of land, you'll more than likely need credit to do so and if you haven't been wise about it, your credit won't be good enough for any of those things.

These reasons, among others, are why you need to be very wise about and pay attention to your credit. Without good credit, you won't get very far in life.

The equivalent expression of the given expression (10^5 / 54x^8)^1/3 would be equal to 5^(1/3) / 3x.

A fraction represents a part of a number or any number of equal parts.

The expression is given as

\((10x^5 / 54x^8)^{1/3}\\\\(5 / 27x^3)^{1/3}\\\\5^{1/3}/ (27x^3)^{1/3}\\\\5^{1/3} / 3x\)

This is the simplest form of expression.

Thus, the equivalent expression is 5^(1/3) / 3x.

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Answer:

D

i did the test

Answer:

5

Step-by-step explanation:

As for estimation, you may round 39.76 to the whole number, resulting in 40.

7.94 to 8

40 / 8 = 5

5 is your answer for the result of estimation

Step-by-step explanation:

there are 13 out of 52 diamond cards.

and there are 26 out of 52 black cards.

so, for the first card to be diamond the probability is

13/52 = 1/4 = 0.25

but now, he does not put the card back.

he pulls the second card out of 51 possible cards.

the desired cases are still 26.

so, the probability to pull a black card as the second card under the restriction that the first card was a diamond is

26/51 = 0.509803922...

the probability for that combined event is then

1/4 × 26/51 = 26/204 = 13/102 = 0.12745098...

so, c. is the right answer.

The statement "The mean decreases as the degrees of freedom increase" is not true about chi-square distributions.

In fact, the mean of a chi-square distribution is equal to its degrees of freedom. It does not decrease as the degrees of freedom increase.

The mean remains constant regardless of the degrees of freedom. This is an important characteristic of chi-square distributions.

Regarding the other statements:

In summary, the statement that is not true about chi-square distributions is that the mean decreases as the degrees of freedom increase.

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The maximum period of time they could reserve the meeting space is 9 hours.

Mathematical expressions with the symbols > and are known as inequality. Finding a range, or ranges within ranges, of values that an unknown x can have while still satisfying the inequality is referred to as "solving" an inequality. In this lesson, inequalities are resolved using graphs and algebra.

An algebraic inequality expression is a mathematical statement that uses the it as a sign to connect an expression to a value, a variable, or another expression. One type of variable inequalities can have solutions that can be graphed either in a coordinate plane or on a number line.

Inequality expression is 31 + 5.9*t < 84.10.

To understand it, collect all constant on the right side:

5.9*t < 84.10 - 31 = 53.10,

Hence, t < 53.10 % 5.9 = 9 hours.

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Correct Question:

To rent a certain meeting room, a college charges a reservation fee of $31 and an additional fee of $5.90 per hour. The chemistry club wants to spend less than $84.10 on renting the meeting room. What are the possible amounts of time for which they could rent the meeting room? Use t for the number of hours the meeting room is rented, and solve your inequality for t.

The width of the rectangle is approximately 9.66 meters.

The formula for the area of a rectangle is:

Area = length * width

Let's assume the width of the rectangle as x meters.

According to the problem, the length of the rectangle is 4 meters longer than its width.

So,

the length of the rectangle would be (x+4) meters.

Substituting the given values, we get:

117 = (x+4) * x

\(117 = x^2 + 4x\)

Rearranging the terms, we get a quadratic equation in standard form:

\(x^2 + 4x - 117 = 0\)

To solve for x, we can use the quadratic formula:

x = [-b ± (\(\sqrt{ b^2 - 4ac\))] / 2a

Where a = 1, b = 4, and c = -117.

Substituting the values, we get:

x = [-4 ± \(\sqrt{4^2 - 4(1)(-117)\))] / 2(1)

x = [-4 ± √472)] / 2

x = (-4 ± 2√118)) / 2

x = -2 ± √118

The width of the rectangle cannot be negative. Therefore, we take the positive root:

x = -2 + √118

x ≈ 9.66 meters (rounded to two decimal places)

Therefore, the width of the rectangle is approximately 9.66 meters.

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Answer:

\(\frac{1}{27}\)

Step-by-step explanation:

The value of y from the given figure is 6√3

From the given figure, according to the theorem;

H² = 6² - 3²

H² = 36 - 9

H²  = 27

H = 3√3

Determine the value of y using the same theorem;

y² = 9² + ( 3√3)²

y² = 81. + 27

y = √108

y = 6√3

Hence the value of y from the given figure is 6√3

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Answer:

7

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Recall that absolute value is the positive of a real number so

|-5| = 5

This added to 2 gives 7

The given conditions are as follows:

Riley and her friends went to the Color Splat paint-tag course last weekend.

The course charges $40 for an hour of group tag plus a rental fee for each paint marker.

Riley's group played for one hour, rented 6 paint markers, and paid a total of $94.

We have to find which equation can be used to find the rental fee, x, for each paint marker.

Let the rental fee for each paint marker be x.

Riley and her friends played for one hour at the cost of $40.

The cost of 6 paint markers is 6x dollars.

The total cost of the game and rentals is $94.

Thus, the equation can be formed as:

40 + 6x = 94

Now, we can solve for x by simplifying the given equation:

Subtracting 40 from both sides:

6x = 54

Dividing both sides by 6:

x = 9

Therefore, the rental fee for each paint marker is $9.

So, the equation we used to find the rental fee, x, for each paint marker is

40 + 6x = 94.

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Average waiting time for FCFS: 8.75

Average waiting time for SJF: 4.75

To solve this scheduling problem using FCFS (First-Come, First-Served) and SJF (Shortest Job First) algorithms, let's go step by step:

Schedule order for FCFS:

The FCFS algorithm schedules processes based on their arrival time. So, the schedule order for FCFS is as follows:

Pl -> P2 -> P3 -> P4

Average waiting time for FCFS:

To compute the average waiting time for FCFS, we need to calculate the waiting time for each process and then take the average.

Process | Arrival Time | Running Time | Waiting Time

Pl | 0 | 3 | 0

P2 | 3 | 10 | 3

P3 | 4 | 6 | 13

P4 | 5 | 1 | 19

Average waiting time = (0 + 3 + 13 + 19) / 4 = 8.75

Therefore, the average waiting time for FCFS is 8.75.

Schedule order for SJF:

The SJF algorithm schedules processes based on their running time. The process with the shortest running time gets executed first. If multiple processes have the same running time, the process with the earliest arrival time is selected first. The schedule order for SJF is as follows:

Pl -> P4 -> P3 -> P2

Average waiting time for SJF:

To compute the average waiting time for SJF, we need to calculate the waiting time for each process and then take the average.

Process | Arrival Time | Running Time | Waiting Time

Pl | 0 | 3 | 0

P4 | 5 | 1 | 3

P3 | 4 | 6 | 6

P2 | 3 | 10 | 10

Average waiting time = (0 + 3 + 6 + 10) / 4 = 4.75

Therefore, the average waiting time for SJF is 4.75.

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