4. Dr. Olson's receptionist will receive a 5% raise in June. How much will be withheld each two weeks for Social Security after the raise?
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The probability of success at the second mall is 3/4 which mall should be chosen in order to maximize the expected profit $135,000.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

First mall:

Profit if successful = $300,000

Loss if otherwise = $100,000

Probability of success = 1/2

Second mall:

Profit if successful = $200,000

Loss if otherwise = $60,000

Probability of success = 3/4

If probability of profit 'P(profit)' = 3/4

Then,

Probability of loss P(loss) = 1 - P(profit)

P(loss) = 1 - 3/4 = 1/4

Expected profit:

= [P(profit) x profit] + [P(loss) x loss])

= (0.75 x $200,000) + (0.25 x (-$60,000))

= 150,000 - 15000

= $135,000

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The vertices of triangle J'K'L' after a reflection of the triangle JKL over the x-axis is given as follows:

The original vertices of the figure are given as follows:

J(-5,5), K(5,7) and L(2,3).

For a reflection over the x-axis, the reflection rule is defined as follows:

(x,y) -> (x,-y).

Meaning that the x-coordinate remains constant while the y-coordinate has the sign exchanged.

Then the vertices of the reflected figure are given as follows:

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Answer: 5.49 × 10-4

Step-by-step explanation:

When you move the decimal over move it over to the right by 4 units.

When you move right it is (-) negative. So you get 5.49 x 10-4.

The range of the side of the square is 24 to 31. The interval notation is (24,31).

What is interval notation?

An interval on a number line can be represented using interval notation. It is a method of representing subsets of the real number line, in other words.

Given that, the perimeter of a square must be greater than 96 inches but less than 124 inches.

Inequality form is

96 < P < 124

Where P is the perimeter.

The perimeter of a square is P = 4s, where s is the length of the side.

Putting P = 4s in 96 < P < 124

96 < 4s < 124

Divide by 4:

24 < s < 31

The interval notation is (24,31).

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Solution is in the attachment!!

Answer:If the radius of the cone is equal to one half the height, we can write the radius as r = h/2. Substituting this expression into the formula for the volume of a cone, we get:

V = 1/3 * (h/2)^2 * h = 1/3 * h^3 / 4

So, the volume of a cone in terms of the height, if the radius is equal to one half the height, is V = 1/3 * h^3 / 4.

Step-by-step explanation:

If the radius of the cone is equal to one half the height, we can write the radius as r = h/2. Substituting this expression into the formula for the volume of a cone, we get:

V = 1/3 * (h/2)^2 * h = 1/3 * h^3 / 4

So, the volume of a cone in terms of the height, if the radius is equal to one half the height, is V = 1/3 * h^3 / 4.

Answer:-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0  1  2  3  4  5  6  7  8  9 10

-5 -4 -3 -2 -1 0  1  2  3  4  5  6  7  8  9 10

Step-by-step explanation:

Answer:

x = 3  rounded to the nearest whole number (actually 2.735)

Step-by-step explanation:

The triangle formed by the sides of length 7x, 12x and 32 form a right triangle with the side of length 32 as they hypotenuse

By the Pythagorean theorem

c² = a² + b² where c = hypotenuse, a and b being the other two sides

Plugging in values we get

38² = (7x)² + (12x)²

1,444 = 49x² + 144x² = 193x²

Switching sides:

193x² = 1444

x² = 1444/193 = 7.48

x = √7.48= 2.735 = 3  rounded to the nearest whole number

The solution is Option A.

The sum of the infinite geometric progression is S = -( 9/5 )

A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.

The nth term of a GP is aₙ = arⁿ⁻¹

The general form of a GP is a, ar, ar2, ar3 and so on

Sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )

Given data ,

Let the sum of the geometric progression be represented as S

Now , the equation will be

∑ n = 1 to ∝ ( -3 ( 3/8 )ⁿ )   be equation (1)

The sum of the infinite GP is S = a / ( 1 - r ) , where r is the common ratio

Substituting the values in the equation , we get

when n = 1

a₁ = -3 ( 3/8 )

a₁ = -9/8

when n = 2

a₂ = -3 ( 3/8 )²

a₂ = -27/64

So , the common ratio r = a₂ / a₁

The common ratio r = 3/8

Substituting the values in the equation , we get

The sum of the infinite GP is S = a / ( 1 - r )

The sum of the infinite GP is S = ( -9/8 ) / ( 1 - 3/8 )

The sum of the infinite GP is S = ( -9/8 ) / ( 5/8 )

The sum of the infinite GP is S = - ( 9/5 )

Hence , the sum of GP is - ( 9/5 )

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The sum of 5 of the interior angles of a regular octagon is 675°.

Angles inside a polygon are referred to as interior angles. A triangle, for instance, has three internal angles. Interior angles are sometimes defined as "angles confined in the interior area of two parallel lines when they are crossed by a transversal."

A regular octagon has equal interior angles.

And one interior angle is equal to 135°.

The sum of 5 of the interior angles of a regular octagon,

= 135 x 5

= 675°

Therefore, the sum is 675°.

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The salary of each of specialist, manager and director are $62,000, $75,000 and $90,000.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Linear equations may include one or more variables.

Let x, y and z be the salary of specialist, manager and director respectively.

From the given information, we have three linear equations.

5x + 2y + z = 550,000

6x + 3y + 2z = 777,000

8x + 0y + 2z = 676,000

From the third equation,

2z = 676,000 - 8x

z = 338,000 - 4x

Substituting the value of z in the first equation,

5x + 2y + 338,000 - 4x = 550,000

x + 2y = 212,000

2y = 212,000 - x

y = 106,000 - (1/2) x

Substituting z = 338,000 - 4x and y = 106,000 - (1/2) x in the second equation 6x + 3y + 2z = 777,000,

6x + 3(106,000 - (1/2) x) + 2(338,000 - 4x) = 777,000

6x + 318,000 - (3/2)x + 676,000 - 8x = 777,000

(6x - 3/2 x - 8x) + (318,000 + 676,000) = 777,000

-(7/2) x = -217,000

x = 62,000

y = 106,000 - (1/2) x = 75,000

z = 338,000 - 4x = 90,000

Hence the salary of each specialist is $62,000, each manager is  $75,000 and each director is $90,000.

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Answer:

1. The unit price for a doll is three dollars. The unit price for a purse is six dollars.

2. One doll costs three. One purse costs six.

3. Polly spends $24 on the 2 dolls and 3 purses.

Step-by-step explanation:

Doing some calculations, 1 doll costs three dollars and 1 purse costs six dollars.

5 x 3 + 6 = 21

7 x 3 + 1  = 27

If Polly buys 2 dolls and 3 purses, that means she spends six dollars on the dolls and eighteen dollars on the purses.

(2 x 3) + (3 x 6) = $24

Polly spends $24 on 2 dolls and 3 purses.

The absolute inequality 3/4 * |(1/3)x + 2| < 6 has a solution of (d) x > -30 and x < 18

To solve the inequality, we'll start by isolating the absolute value expression on one side of the inequality.

3/4 * |(1/3)x + 2| < 6

We'll first distribute the 3/4 across the absolute value:

|(1/3)x + 2| < 8

To simplify this, we'll split the inequality into two cases:

(1/3)x + 2 < 8

(1/3)x + 2 > -8

First, let's consider the case where (1/3)x + 2 < 8

(1/3)x < 6

x < 18

Now let's consider the case where (1/3)x + 2 > -8

(1/3)x > -10

x > -30

So, the solution set is x > -30 and x < 18

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Complete question

Solve the inequality three-fourths times the absolute value of the quantity one third times x plus 2 end quantity is less than 6. x > −8 and x < −4 x > −30 and x < 2 x < −30 and x < 18 x > −30 and x < 18

The situation can be described by the equation x - 3 = 13 = x = 13 + 3 = x = 16.

A mathematical phrase with two equal sides and an equal sign is called an equation. An example of an equation is 4 + 6 = 10. 4 + 6 can be seen on the equal sign's left side, and 10 can be seen on the equal sign's right side. A relationship between two terms on either side of an equal sign is represented by a simple equation. The four mathematical operations of addition, subtraction, multiplication, and division are also used in simple equations, either singly or in combination.

no of egg is decreased e= x - 3

equation to represent the situation

x - 3 = 13

x = 13 + 3

x = 16

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The circle graph for the given table is as mentioned.

In graph theory, a circle graph is the intersection graph of a chord diagram. That is, it is an undirected graph whose vertices can be associated with a finite system of chords of a circle such that two vertices are adjacent if and only if the corresponding chords cross each other.

Given is a data as shown in the table.

The circle graph for the given table is attached with the answer.

Therefore, the circle graph for the given table is as mentioned.

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Answer:

2483 in 8yrs means you multiply the two first

2483

× 8

_____

19864

so 8% of 19864

you have to divide the number by the percentage

o. 8÷ 19864= 2483

Answer: 588π = 1846.32

Step-by-step explanation:

Volume of cylinder = πr²h

Volume = (7)²*12*π = 588π = 1846.32

Worker B has the higher variance and standard deviation than Worker A.

Standard deviation in statistics, typically denoted by σ, is a measure of variation or dispersion (refers to a distribution's extent of stretching or squeezing) between values in a set of data. The lower the standard deviation, the closer the data points tend to be to the mean (or expected value), μ.

Given,

The number of parts produced per hour by the workers are as follows:

Worker A: 5, 4, 4, 6, 7, 5, 6, 3

Worker B: 4, 8, 1, 9, 2, 9, 4, 3

Average μ = 5

Variance = σ² = Σ(xi - μ)²/N

Variance for first worker

= [(5 - 5)² + (4 - 5)² + (4 - 5)² + (6 - 5)² + (7 - 5)² + (5 - 5)² + (6 - 5)² + (3 - 5)²]/8

= [0² + -1² + -1² + 1² + 2² + 0² + 1² + -2²]/8

= [1 + 1 + 1 + 4 + 1 + 4]/8

= 12/8

= 1.5

Standard deviation σ = √1.5

 = 1.2247448713916

Variance for second worker

= [(4 - 5)² + (8 - 5)² + (1 - 5)² + (9 - 5)² + (2 - 5)² + (9 - 5)² + (4 - 5)² + (3 - 5)²]/8

= [-1² + 3² + -4² + 4² + -3² + 4² + -1² + -2²]/8

= [1 + 9 + 16 + 16 + 9 + 16 + 1 + 4]/8

= 72/8

= 9

Standard deviation σ = √9

= 3

Hence, Variance and Standard deviation of worker B are higher than worker A.

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The measure of the largest exterior angle is 96°.

Heptagon is a two-dimensional shape with seven angles, seven vertices, and seven edges. This seven-sided polygon “heptagon” is made up of two words ‘Hepta’ and ‘Gonia’, which means seven angles. Another name given to it is septagon or 7-gon.

In heptagon, the sum of the interior angles is equal to 900 degrees. The sum of exterior angles of a heptagon is 360 degrees.

Here, x°+2x°+3x°+4x°+5x°+7x°+8x°=360°

30x°=360°

x°=12°

So, 8x°= 96°

Therefore, the measure of the largest exterior angle is 96°.

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Counting of numbers by 5's end with 0, 5, 0, 5, 0, .....

Counting in mathematics is defined as the process of finding the number of objects in a set which is finite.

Counting numbers are the natural numbers.

The question is how to count by 5's.

In order to count by 5's, we have to add 5 to each of the preceding number  to get the next number.

So the pattern will be,

5, 10, 15, 20, 25, 30, 35, ........

So the numbers end either in 0 or 5.

Hence the pattern of counting by 5's are the numbers which ends in either 0 or 5.

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The acceleration of the object when the force on the object changes to 16 N is 4 m/s²

The second law of motion by Newton says that the force is equal to the change in momentum per change in the time. For a constant mass, force equals the mass times acceleration, i.e. F = m x a.

Given here: A force acting on an object.

We know, The formula for force states that the force is equal to mass that is multiplied by the acceleration.

Thus we have the equation as F=m.a

Now in case 1 we have  

20=m×5

m=4 kg

Again in case 2 we have

16 = 4×a

a=4 ms⁻²

Hence, The acceleration of the object when the force on the object changes to 16 N is 4 m/s²

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The area of the triangle in terms of 'x' will be (x² + 13x + 28) / 2.

Assume 'h' is the height of the triangle and 'b' be the base of the triangle. Then the area of the triangle is given as,

A = (1/2) × h·b

The area of the triangle is given as,

A = 1/2 [(x + 4)(x + 7)]

Simplify the equation, then we have

A = [(x + 4)(x + 7)] / 2

A = (x² + 7x + 4x + 28) / 2

A = (x² + 13x + 28) / 2

The area of the triangle in terms of 'x' will be (x² + 13x + 28) / 2.

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The value of x are:

2) x = 18.87

3) x = 26.68

5) x = 35.52

6) x = 13.75

9) x = 3.69

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

2)

Tan 48 = x / 17

1.11 = x / 17

x = 17 x 1.11

x = 18.87

3)

Sin 67 = x / 29

0.92 = x / 29

x = 0.92 x 29

x = 26.68

5)

Cos 16 = x / 37

0.96 = x / 37

x = 0.96 x 37

x = 35.52

6)

Tan 58 = 22/x

1.6 = 22 / x

x = 22/1.6

x = 13.75

9)

Sin 24 = x / 9

0.41 = x / 9

x = 0.41 x 9

x = 3.69

Thus,

The value of x is given above.

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a) The measure of angle 3 is given as follows: m < 3 = 3x + 105.

b) The value of x is given as follows: x = 10.

c) It is not possible for a triangle to have side lengths 5, 8 and 14, as the sum of the lengths of the two smaller sides would be less than the length of the larger side.

The measure of angle 1 is given as follows:

m<1 = 3x + 15.

As the sum of the measures of the internal angles of a triangle is of 180º, and there is a right triangle, we have that angles 1 and 2 are complementary, hence:

m < 1 + m < 2 = 90

3x + 15 + m < 2 = 90

m < 2 = 75 - 3x.

An angle is always supplementary with it's exterior angle, hence the measure of angle 3 is obtained as follows:

m < 2 + m < 3 = 180

75 - 3x + m < 3 = 180

m < 3 = 180 - 75 + 3x

m < 3 = 3x + 105.

For an isosceles right triangle, the two non-right angles measure 45º, hence the value of x is obtained as follows:

3x + 15 = 45

3x = 30

x = 30/3

x = 10.

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3 pounds of grapes she buy grapes in the market.

A division is a process of splitting a specific amount into equal parts.

Given that each pound of grapes cost 0.85.

Clarissa buys grapes and pays a total of 2.55.

We have to find the number of pounds of grapes does she buy.

To find this we have to divide 2.55 by 0.85.

Two point five five by zero point eight five.

2.55/0.85

3 pounds of grapes.

Hence, 3 pounds of grapes she buy grapes in the market.

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The solution graph is given in the attached image.

The solution is x = 2 and y = 70.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

Robert and Tony love to read.

Robert reads 30 pages the first day and 20 pages each day after that.

Tony reads 40 pages the first day and 15 pages each day after that.

We have a system of equations,

y = 20x + 30

y = 15x + 40

Subtracting the equations, we get,

5x = 10

x = 2

And y = 70.

And the graph is given in the attached image.

Therefore, the solution is x = 2 and y = 70.

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Answer:

The possible formula for the linear function h(x) is h(x) = -7x + 190. This can be determined by using the information from numerade.com, which states that the formula for a linear function is y = mx + b. Applying this formula to the given values of h(-30) = 90 and h(20) = -160 gives a formula of h(x) = -7x + 190.

Step-by-step explanation:

Answe

Step-by-step explanation:

answer is 9