Caitlin has finished her schooling and training to be a dental hygienist. She has two job offers that she is considering.

Caitlin’s Job Offer Comparison

Job 1: Albuquerque, NM
Job 2: Ann-Arbor, MI
Salary
$54,000
$61,000

Benefits
$2,500 bonuses,
health insurance,
401K
Health insurance,
401K
Average Monthly Rent & Utilities
$925
$1,300

Which job would offer the best annual income considering the cost of living in each locale?
Job 2 is a better choice because the annual income after rent and utilities is $59,700 but that of job 1 is $55,575.
Job 2 is a better choice because the annual income after rent and utilities is $45,400 but the income for job 1 is $41,900.
Job 1 is a better choice because it costs $4,500 less per year to live there.
The jobs have equal annual incomes of $45,400 after rent and utilities so Caitlin should take the job in her favorite locale.

Answer:

The answer to the question is F

Step-by-step explanation:

Why it is an Scalene Triangle ,it because all the sides and angle are not equal

Answer:

x = 10

Step-by-step explanation:

If S is between R and T, then RS + ST will be equal to RT.

See image.

Use this idea to write an equation.

2x + 3 + 4x = 63

Combine like terms, Subtract 3, Divide by 6, to solve for x. See image.

Answer:

508?

Step-by-step explanation:

what is this factor? simplify?...etc

The price of one pen will be $1.5 and one highlighter is $4.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that:-

The cost of the pen and the highlighter will be calculated by forming the two expressions from the given data in the question the expressions are as follows:-

6p  +  3h  = 21

2p  +  4 h = 19

Solving the above linear equations by elimination method:-

( 6p  +  3h  = 21 ) x 2

( 2p  +  4 h = 19 ) x 6

The new equations are:-

12p  + 6h  =  42

12p  + 24h  = 114

Substracting the below equation from the above equation we will get:-

6h - 24h  =  -72

-18 h = -72

h  =  $4

Put the value of h in any of the above equations:-

2p  +  4 h = 19

2p  +  4 ( 4 )  = 19

2p  +  16  =  19

p  =  3 / 2

P  = $1.5

Therefore the price of one pen will be $1.5 and one highlighter is $4.

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Answer:

a/b = c/d

a*d = b*c

Ex:

a/2 = 2/4

4a = 4

a = 1

1/2 = 2/4

Step-by-step explanation:

since there is triangle , you use the formula

1/2 × b × h

as you can see the base is 6 and the height is 4, so

1/2 × b × h

= 1/2 × 6 × 4

=12

12 × 2 = 24 , you times by 2 because there is 2 triangle

There is also rectangle in the diagram, so you use the formula , length × breadth , the length is 8 and the breadth is 5, so

length x breath

= 5 × 8

=35

35 × 2 = 70 , times by 2 because you can see 2 rectangles with the same length and breadth

length x breath

= 8 × 6

= 48

this one is different because the length is 8 and the breadth is 6.

SA = 48 + 35 + 24

= 107 cm ²

Sorry for my bad eng ,its not my first language.

Based on the property of the consecutive angles of a parallelogram, the value of x is calculated as: E. 37.

In a parallelogram, the angles that are opposite to each other are congruent while consecutive angles are supplementary.

Angles F and G are consecutive angles and are therefore supplementary (have a sum of 180 degrees.)

Angle F + angle G = 180

4x - 2 + 34 = 180

4x + 32 = 180

4x = 180 - 32

4x = 148

x = 148/4

x = 37

Value of x is: E. 37.

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The amount of milk needed for a 17-pound goat and a 55-pound goat are 55 and 87.5 cubic units, respectively

The equation is given as:

y =1.5x + 5

For a 17-pound goat, we have:

x = 17

This gives

y =1.5 * 17 + 5

y = 30.5

For a 55-pound goat, we have:

x = 55

This gives

y = 1.5 * 55 + 5

y = 87.5

Hence, the amount of milk needed for a 17-pound goat and a 55-pound goat are 55 and 87.5 cubic units, respectively

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Answer:

44

Step-by-step explanation:

16.5 / 3/8 = 44

she will need 44 beads to complete that necklace

Answer:

Step-by-step explanation:

[tex]1) \overline{BA} \cong \overline{BC}, \overline{DA} \cong \overline{EC} \text{ (given)}\\2) \overline{BD} \cong \overline{BE}[/tex]  (congruent segments subtracted from congruent segments form congruent segments)

Answer:

D

Step-by-step explanation:

Reflection over the X-axis

All point passes, (x,-y)

Answer:

D.

Step-by-step explanation:

Reflection over the x-axis because the quadrilateral reflected.

The standard deviation of the sample mean differences is; 0.6898

From online research, the sample size of the session regarding the number of people who will purchase the red box is; N₁ = 45

From online research, the sample size of the session regarding the number of people who will purchase the blue box is; N₂ = 60

Formula for standard deviation of the sample mean differences is;

σm₁ - σm₂ = √[(σ₁²/n₁) + (σ₂²/n₂)]

Thus;

σm₁ - σm₂ = √[(3.868²/45) + (2.933²/60)]

σm₁ - σm₂ = 0.6898

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Answer: -12

Step-by-step explanation: When solving this problem, PEMDAS is a key component. What is PEMDAS?

PEMDAS stands for the following:

P- Parentheses

E- Exponents

M-Multiplication

D- Division

A-Addition

S-Subtraction

This is also known as order of operations. Following this order, we can easily simplify the problem.

P-Parentheses

(-2)(-3)^2-2(2-5)

Our parentheses is (2-5). We can simply this to -3. Our problem now is

(-2)(-3)^2-2(-3)

E-Exponents

We have one set of exponents in this. It is -3^2. This simplifies to 9. Our problem now is

(-2)(9)-2(-3)

M- Multiplication

We can simply to.

-18+6

These simplifies into

-12

Answer:

-12

Step-by-step explanation:

-2*9-2(2-5) : Raise -3 to the power of 2

-18-2(2-5) : Multiply -2 by 9

-18-2*-3 : Subtract 5 from 2

-18+6 : Multiply -2 by -3

-12 : Add -18 and 6

Answer:

Approx. 2140.16 cubic centimeters

Step-by-step explanation:

[tex]Volume=\frac{4}{3}\pi r^{3} \\V=\frac{4}{3}(3.14)(8)^{3} \\V=4.18(8)^{3} \\V=4.18(512) \\V=2140.16[/tex]

The solution to the equation is y = 5.5 + x , for any real number x greater than or equal to zero and y any real number greater than or equal to 5.5.

Analysis:

since number of items cannot be negative x and y are real number numbers since y or x can be a decimal so we do not use integers alone.

so  y = 5.5 + x , for any real number x greater than or equal to zero and y any real number greater than or equal to 5.5.

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Answer: C

Step-by-step explanation:

Answer:

scale factor = [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

the scale factor is the ratio of corresponding sides, image to original, so

scale factor = [tex]\frac{V'W'}{VW}[/tex] = [tex]\frac{1}{5}[/tex]

Answer:

-2 =w

Step-by-step explanation:

9(w – 4) – 7w = 5(3w – 2)

The first step is to distribute

9w -36 - 7w = 15w -10

Combine like terms

2w -36 = 15w -10

Subtract 2w from each side

2w -36 -2w = 15w-10-2w

-36 = 13w -10

Add 10 to each side

-36+10 =13w-10+1-

-26 = 13w

Divide by 13

-26/13 =13w/13

-2 =w

The correct statement about the center of both box plots is: the median for Town A, 30° is greater median for Town B, 25°

A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. The two lines are known as whiskers. The end of the first line represents the minimum number and the end of the second line represents the maximum number.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. 50% of the score represents the median. The third line on the box represents the upper (third) quartile.

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Answer:

(14, -2)

Step-by-step explanation:

The coordinates of the midpoint is equal to the mean of the coordinates of the endpoints.

=============================================================

Solving :

⇒ 5 = -4 + x / 2

⇒ x - 4 = 10

⇒ x = 14

⇒ 2 = 6 + y / 2

⇒ y + 6 = 4

⇒ y = -2

===========================================================

Coordinates of Point Y :

⇒ Y = (x, y)

⇒ Y = (14, -2)

Answer:

Y (14, - 2 )

Step-by-step explanation:

using the midpoint formula for (x₁, y₁ ) and (x₂, y₂ ) , then

midpoint = ( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1+y_{2} } }{2}[/tex] )

equating the x- coordinates and the y- coordinates

let coordinates of Y = (x, y )

[tex]\frac{x-4}{2}[/tex] = 5 ( multiply both sides by 2 )

x - 4 = 10 ( add 4 to both sides )

x = 14

and

[tex]\frac{y+6}{2}[/tex] = 2 ( multiply both sides by 2 )

y + 6 = 4 ( subtract 6 from both sides )

y = - 2

coordinates of Y = (14, - 2 )

The distance between library and park is 6√2 miles and the distance between park and field is 6√11 miles.

Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other.

Here, mark the park as A, Home as B, Library as C and field as D.

  Now, CD = 18 miles

            BC = 4 miles

we have to find AC (distance between library and park)

   BD = BC + CD = 18 + 4 = 22 miles

 Using property of similar triangles,

        AD² = BD X CD

         AD² = 22 X 18

         AD = √22 X √18

         AD = 6√11 miles

By Pythagoras theorem,

         AD² = AC² + CD²

        396 = AC² + 324

         AC² = 396 - 324

         AC² = 72

           AC = √72

           AC = 6√2 miles

Thus, the distance between library and park is 6√2 miles and the distance between park and field is 6√11 miles.

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Answer: 8

Step-by-step explanation:

To find the diagonal, we need to use two formulas:

Area of a square: [tex]A = s^{2}[/tex] (Area = side * side)

Pythagorean Theorem: [tex]a^{2} +b^{2} =c^{2}[/tex]  

Since  every side of a square is the same:

[tex]a^2 = b^2\\a = b = \sqrt{32} \\a^{2} = 32\\b^2 = 32[/tex]

Our equation:

[tex]32 + 32 = c^2\\64 = c^2\\8 = c[/tex]

The picture below visually explains the problem

Hope this helps!

Answer:

x=  -4, y = 4.

Step-by-step explanation:

first, divide the first equation by its G.C.D (5), to obtain its simplest form.

5x/5 + 5y/5 = 0/5 to obtain x + y = 0.

Then, find the value of y by rearranging the second equation.

y = 36 + 8x. (Rem; when 8x moves to the other side of the equation, it changes the sign)

Now substitute the value of y (36 + 8x) in the first equation which is x + y = 0.

x + 36+8x = 0

Put like terms together.

36 + 9x = 0

move 9x to the other side and change its sign.

36 = -9x

divide both sides by 9,

x = -4.

Lastly, find the value of y by replacing the value of x in either equation.

-8(-4) + y = 36

32 + y = 36

rearrange to obtain

y = 36 - 32

y = 4.

The average rate of change of the number of miles with respect to the number of gallons is 14.5 miles per gallon

The given parameters can be represented as:

M(0) = 30680

M(20) = 30970

The average rate of change is calculated as:

M'(t) = (M(20) - M(0))/(20 - 0)

This gives

M'(t) = (30970 - 30680)/(20 - 0)

M'(t) = 14.5

Hence, the average rate of change of the number of miles with respect to the number of gallons is 14.5 miles per gallon

The average rate of change of M as t changes from 8 to 16.

This is calculated using

M'(t) = (M(16) - M(8))/(16 - 8)

M'(t) = (20 - 10)/(16 - 8)

M'(t) = 1.25

The average rate of change of M as t changes from 16 to 24.

This is calculated using

M'(t) = (M(24) - M(16))/(24 - 16)

M'(t) = (25 - 20)/(24 - 16)

M'(t) = 0.625

The average rate of change of M as t changes from 24 to 32.

This is calculated using

M'(t) = (M(32) - M(24))/(32 - 24)

M'(t) = (25 - 25)/(32 - 24)

M'(t) = 0

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Answer:

Step-by-step explanation:

Comment

There was a flat fee of 10 dollars

Each 1/4 hour brought in 3,75

The total charge was 55 dollars.

Equation

Charge = 10 + 4*3.75*x                     as an hourly rate,

Solution

55 = 10 + 4*3.75x                                Combine

55 = 10 + 15x                                       Subtract 10 from both sides

55-10= 10-10 + 15x

45 = 15x                                               Divide by 15

45/15 = 15x/15

x = 3 hours

Answer 3 hours  

Answer:

Hi,

number of ways: 8

Step-by-step explanation:

[tex]\begin{array}{|c|c|c|}Quater&dime&nickel\\------&---&---\\0&0&9\\0&1&7\\0&2&5\\0&3&3\\0&4&1\\1&0&4\\1&1&2\\1&2&0\\------&---&---\\\end{array}[/tex]

[tex]y+9-x =[/tex]

[tex]x=1 \\ y=3[/tex]

[tex]3 +9 -1=11[/tex]

Answer:

y+9-x = 3+9-1 which would end up equaling: 11

9-1=8+3=11

Answer:

Mean: 4.7

Mode: 2

Median: 4.5

Step-by-step explanation: