An employee is paid a salary of \$73,840 per year, plus benefits and overtime (time and a half) on hours worked over 40 per week, working as a civil servant. What is the regular time hourly rate of pay for this employee, and what is her total income in a month where she works 40 hours, 44 hours, 43.5 hours, and 40 hours, weekly, in the month?
A.$37.00/hr and \$6,336.25 in total income
B. $35.50/hr and \$6,079.38 in total income
C.$37.50/hr and \$6,421.88 in total income
D.$36.00/hr and \$6,165.00 in total income

Answer:

(a) 63 cups

(b) 16 cups

Step-by-step explanation:

Given that the volume of the sink = (2000/3)×π in³

(a) For the cup that has diameter = 4 in. and height, h = 8 in.

The radius, r = Diameter/2 = 4/2 = 2 in.

The of a cone = 1/3×Base area × Height = 1/3 × π×r² ×h = 1/3×π×2²×8 = (32/3)×π in.³

The number of cups to scoop = (Volume of the sink)/(Volume of the cup)

The number of cups to scoop = ((2000/3)×π)/((32/3)×π ) = 125/2=62.5 cups

Rounding to the next whole number gives 62.5 cups ≈  63 cups

(b) For the cup that has diameter = 8 in. and height, h = 8 in.

The radius, r = Diameter/2 = 8/2 = 4 in.

The of a cone = 1/3×Base area × Height = 1/3 × π×r² ×h = 1/3×π×4²×8 = (128/3)×π in.³

The number of cups to scoop = (Volume of the sink)/(Volume of the cup)

The number of cups to scoop = ((2000/3)×π)/((128/3)×π ) = 125/8=15.625 cups

Rounding to the next whole number gives 15.625 cups ≈  16 cups.

Answer:

990 ways to choose 6 starters out of 14 with exactly two of the three triplets.

Step-by-step explanation:

Ways to choose 2 of the triplets

= C(3,2) = 3! / (2!1!) = 3

Ways to choose the remaining 4 starters out of 11 players left

= C(11,4) = 11! / (4!7!) = 330

Total number of ways to choose 6 starters

= 3*330 = 990

Answer:

b=9.96≅10

Step-by-step explanation:

b^2=a^2+c^2−(2ac)cos(64)

b=√6²+11²-2(6*11)cos64

b=9.96≅10

Answer:

[tex]\boxed{x=1}[/tex]

Step-by-step explanation:

[tex]mean=\frac{sum \: of \: terms}{number \: of \: terms}[/tex]

[tex]2=\frac{2+4+1+1+x+3+2}{7}[/tex]

[tex]2=\frac{13+x}{7}[/tex]

[tex]14=13+x[/tex]

[tex]x=1[/tex]

Answer:

71s

Step-by-step explanation:

The question we have at hand is 7s² + ___ + 13s + 6² = (7s + 6)². We can expand the perfect equation " (7s + 6)² " in order to find our solution. A perfect square consists of 3 terms, and hence the term in the blanks must add to 13s to form another term.

Applying the perfect square formula : ( a + b )² = a² + 2ab + b², let's expand the expression,

(7s + 6)² = ( 7s )² + 2( 7s )( 6 ) + ( 6 )² =  7s² + 84s + 6²

84s - 13s = 71s, which fills in the blank provided.

Answer:

[tex]y\geq 0\\y\geq \frac{3}{2}x-3\\ y\leq -x+3[/tex]

Step-by-step explanation:

The region R is surrounded by 4 lines, the first one is y=x+1, the second one is y=0 or the axis x, and the third and fourth one need to be calcualted.

To find the equation of a line through the points (x1,y1) and (x2, y2) we can use the following equation:

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

Then, our third line is going to be the line that passes through the points (2,0) and (4,3), so the equation is:

[tex]y=\frac{3-0}{4-2}(x-2)\\y=\frac{3}{2}x-3[/tex]

Our fourth line is the line that passes through the points (3,0) and (0,3), so the equation is:

[tex]y=\frac{3-0}{0-3}(x-3)\\y=-x+3[/tex]

Then we can say that the other three inequalities are:

[tex]y\geq 0\\y\geq \frac{3}{2}x-3\\ y\leq -x+3[/tex]

Answer:

30x² cubic units

Step-by-step explanation:

The volume of an Oblique prism = Base Area × Height

This oblique prism has trapezoidal bases.

Area of a Trapezoid = 1/2 × h × ( b1+b2)

where h = height

b1 and b2 = bases of the Trapezoid.

From the question,

h = 20

b1 = x

b2 = 2x

Area of the Trapezoid =

1/2 × x ×( x + 2x)

1/2 × x × (3x)

3x²/2 square units.

Remember, the volume of an Oblique prism = Base Area × Height

Height of the prism = The distance between the 2 trapezoid bases = 20 units.

Base Area = 3x²/2 square units × 20 units

= 30x² cubic units

Answer:

d

Step-by-step explanation:

Answer:

the answer is A=2

Step-by-step explanation:

a real solution is a solution that uses real numbers. This equation has 2 real solutions.

Answer:

A. 2 real solutions

Step-by-step explanation:

One graph is a parabola and 1 graph is a straight line and they intersect twice.

volume=l1*l2*l3

=8*15*20=2400cm^3

Volume = length x breadth x height = 20 x 15 x 8 = 2400 sq cm

Answer:

RS and plane RSU

Step-by-step explanation:

I think not to sure

Answer:

[tex]=3/4[/tex]

Step-by-step explanation:

[tex]\frac{4\sqrt{18}}{16\sqrt{2}}[/tex]

First, simplify the fraction:

[tex]=\frac{\sqrt{18}}{4\sqrt2}[/tex]

Now, simplify the radical in the numerator (the radical in the denominator cannot be simplified:

[tex]\sqrt{18}=\sqrt{9\cdot2}=\sqrt{9}\cdot\sqrt{2}=3\sqrt{2}[/tex]

Substitute:

[tex]=\frac{3\sqrt{2}}{4\sqrt{2}}[/tex]

The radicals cancel:

[tex]=3/4[/tex]

Answer:

15

Step-by-step explanation:

Opposite sides in a parallelogram are equal.

2x - 5 = x + 10

Subtract x and add 5 on both sides.

2x - x = 10 + 5

Combine like terms.

x = 15

Answer:

[tex]\boxed{\red {x= 15}}[/tex]

Step-by-step explanation:

We know that opposite sides in a parallelogram are equal.

So, in this sum value of the sides in a parallelogram

[tex]x + 10 \: \: \: and \: \: \: 2x - 5[/tex]

So now let's create an equation

[tex]x + 10 = 2x - 5[/tex]

Now let's solve for x

[tex]x + 10 = 2x - 5 \\ 10 + 5 = 2x - x \\ 15 = x[/tex]

Answer:

Step-by-step explanation:

7x=210

x=210/7=30 pages per day

Answer:

Emily read 30 pages per day.

Step-by-step explanation:

1. Divde 210 by 7

Number Sentance: 210÷7= 30

Reasoning:

Since Emily reads the same amount of pages each day we have too, divde 210 by 7.

Answer:

The last one, The Hypotenuse Leg Theorem, or HL Theorem,

Step-by-step explanation:

Answer:

HL theorem

Step-by-step explanation:

If any 2 right angled triangles have same length of hypotenuse then both are congruent by HL theorem

Answer:

Step-by-step explanation:

The factorization of x² - 5x + 6 can be determined thinking critically about two numbers, that if we multiply those two numbers together it will result into a value of +6 and if we add those numbers together , we will have -5

The numbers are -3 and -2 ; if we multiply -3 and -2 , we have = 6

If we add -3 + (-2) ; we have,

-3-2 = -5

Now the factorization of

x² - 5x + 6 = 0 is as follows.

x² - 3x - 2x + 6

By factorization,

x(x - 3) - 2 (x - 3) = 0

(x - 2) or  (x-3) = 0

Now, using An algebra tile configuration. The diagrammatic expression showing how an algebraic tile configuration should looks like can be found in the attached image below.

Hint:

Let represent ,

1   =   x² tile

-5 = - x tiles

6  =  1 tiles

Answer:

The answer is the first tile choice.

Step-by-step explanation:

Answer:

[tex]Side\ B = 6.0[/tex]

[tex]\alpha = 56.3[/tex]

[tex]\theta = 93.7[/tex]

Step-by-step explanation:

Given

Let the three sides be represented with A, B, C

Let the angles be represented with [tex]\alpha, \beta, \theta[/tex]

[See Attachment for Triangle]

[tex]A = 10cm[/tex]

[tex]C = 12cm[/tex]

[tex]\beta = 30[/tex]

What the question is to calculate the third length (Side B) and the other 2 angles ([tex]\alpha\ and\ \theta[/tex])

Solving for Side B;

When two angles of a triangle are known, the third side is calculated as thus;

[tex]B^2 = A^2 + C^2 - 2ABCos\beta[/tex]

Substitute: [tex]A = 10[/tex],  [tex]C =12[/tex]; [tex]\beta = 30[/tex]

[tex]B^2 = 10^2 + 12^2 - 2 * 10 * 12 *Cos30[/tex]

[tex]B^2 = 100 + 144 - 240*0.86602540378[/tex]

[tex]B^2 = 100 + 144 - 207.846096907[/tex]

[tex]B^2 = 36.153903093[/tex]

Take Square root of both sides

[tex]\sqrt{B^2} = \sqrt{36.153903093}[/tex]

[tex]B = \sqrt{36.153903093}[/tex]

[tex]B = 6.0128115797[/tex]

[tex]B = 6.0[/tex] (Approximated)

Calculating Angle [tex]\alpha[/tex]

[tex]A^2 = B^2 + C^2 - 2BCCos\alpha[/tex]

Substitute: [tex]A = 10[/tex],  [tex]C =12[/tex]; [tex]B = 6[/tex]

[tex]10^2 = 6^2 + 12^2 - 2 * 6 * 12 *Cos\alpha[/tex]

[tex]100 = 36 + 144 - 144 *Cos\alpha[/tex]

[tex]100 = 36 + 144 - 144 *Cos\alpha[/tex]

[tex]100 = 180 - 144 *Cos\alpha[/tex]

Subtract 180 from both sides

[tex]100 - 180 = 180 - 180 - 144 *Cos\alpha[/tex]

[tex]-80 = - 144 *Cos\alpha[/tex]

Divide both sides by -144

[tex]\frac{-80}{-144} = \frac{- 144 *Cos\alpha}{-144}[/tex]

[tex]\frac{-80}{-144} = Cos\alpha[/tex]

[tex]0.5555556 = Cos\alpha[/tex]

Take arccos of both sides

[tex]Cos^{-1}(0.5555556) = Cos^{-1}(Cos\alpha)[/tex]

[tex]Cos^{-1}(0.5555556) = \alpha[/tex]

[tex]56.25098078 = \alpha[/tex]

[tex]\alpha = 56.3[/tex] (Approximated)

Calculating [tex]\theta[/tex]

Sum of angles in a triangle = 180

Hence;

[tex]\alpha + \beta + \theta = 180[/tex]

[tex]30 + 56.3 + \theta = 180[/tex]

[tex]86.3 + \theta = 180[/tex]

Make [tex]\theta[/tex] the subject of formula

[tex]\theta = 180 - 86.3[/tex]

[tex]\theta = 93.7[/tex]

Answer:

A. 770,000,000

Step-by-step explanation:

7.7x10^8 First step is to simplify

7.7x100,000,000 Then, multiply

770,000,000

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Answer:

6^5  * 9^5

Step-by-step explanation:

( 6*9) ^5

We know that ( ab) ^c = a^ c* b^c

6^5  * 9^5

Answer:

A 95% confidence interval for the population average debt load of graduating students with a bachelor's degree is [$17,022.05, $20,577.94].

Step-by-step explanation:

We are given that a random sample of 28 students had an average debt load of $18,800. It is believed that the population standard deviation for student debt load is $4800. The α is set to 0.05.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                             P.Q.  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\bar X[/tex] = sample average debt load = $18,800

            [tex]\sigma[/tex] = population standard deviation = $4,800

            n = sample of students = 28

            [tex]\mu[/tex] = population average debt load

Here for constructing a 95% confidence interval we have used a One-sample z-test statistics because we know about population standard deviation.

So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 5% level of

                                                      significance are -1.96 & 1.96}  

P(-1.96 < [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < 1.96) = 0.95

P( [tex]-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95

P( [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95

95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] , [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ]

                        = [ [tex]\$18,800-1.96 \times {\frac{\$4,800}{\sqrt{28} } }[/tex] , [tex]\$18,800+1.96 \times {\frac{\$4,800}{\sqrt{28} } }[/tex] ]

                        = [$17,022.05, $20,577.94]

Therefore, a 95% confidence interval for the population average debt load of graduating students with a bachelor's degree is [$17,022.05, $20,577.94].

Answer:

The expected number of floors the elevator stops at, not counting the ground floor is =

n*(1-(1-1/n)^m)

Step-by-step explanation:

Here, we want to know the expected number of floors the elevator stops at.

let X1,X2,X3,..Xn are indicator variable for which value =1 if at least one person stops on that floor otherwise value is 0

P(at least one person stops at floor Xj)=1-P(none of m people stops at floor j)

=1-(1-1/n)^m

here total number of floors on elevetor Stops X=X1+X2+X3+...+Xn

hence expected number of floors on elevetor Stops

E(X)=E(X1)+E(X2)+E(X3)...+E(Xn)

=(1-(1-1/n)^m )+(1-(1-1/n)^m )+(1-(1-1/n)^m )+(1-(1-1/n)^m )+..... n times

=n*(1-(1-1/n)^m)

You have to shade 4 boxes of the figure.

Fractions are used to represent smaller pieces of a whole.

Given is a box with 8 parts of it,

1/2 of 8 = 8*1/2 = 4

Hence, You have to shade 4 boxes of the figure.

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Answer:

It has two solutions.

Step-by-step explanation:

Let as consider the given options are  

It has no solution.

It has one solution.

It has two solutions.

It has infinitely many solutions.

The given equation is

[tex]\dfrac{3}{4z}=\dfrac{1}{4z-3}+5[/tex]

Multiply both sides by 4z(4z-3).

[tex]3(4z-3)=4z+5(4z(4z-3))[/tex]

[tex]12x-9=4z+80z^2-60z[/tex]

[tex]0=-12x+9+80z^2-56z[/tex]

[tex]0=80z^2-68z+9[/tex]

It is a quadratic equation.

Therefore, it has two solutions.

Answer:

It has 1 solution

Step-by-step explanation:

I did the test I put the guys above me in and got it wrong

Answer:

a

Step-by-step explanation:

5 - 2x >= 1 × 7

5 - 2x >= 7

-2x >= 7 - 5

-2x >= 2

x <= -1 sign changes when divided by negative number

Answer:

b. y - 8 = -2/3(x + 3)

Step-by-step explanation:

Well point-slope form takes one point in this case (-3,8) and puts it into the equation.

So this is point slope form,

[tex]y -y_{1} = m(x - x_{1} )[/tex]

The 2 negatives in the -y and -x means you have to change the number to a negative to a positive to a negative.

We plug in (-3,8) to the equation.

y - 8 = m(x + 3)

Well we change the -3 to a 3 because of the negative.

So with the given slope -2/3 we plug that in for m.

y - 8 = -2/3(x + 3)

Thus,

answer choice b is correct.

Hope this helps :)

Answer:

The third graph

Step-by-step explanation:

Answer:

The probability that a man in this age category does NOT die of cancer during the course of the​ year is 0.997.

Step-by-step explanation:

Suppose the probability of an event occurring is [tex]P_{i}[/tex].

The probability of the given event not taking place is known as the complement of that event.

The probability of the complement of the given event will be,

[tex]1 - P_{i}[/tex]

In this case an events X is defined as a man, aged 55​ - 59, will die of cancer during the course of the year.

The probability of the random variable X is:

[tex]P (X) = \frac{300}{100000}=0.003[/tex]

Then the event of a man in this age category not dying of cancer during the course of the​ year will be complement of event X, denoted by X'.

The probability of the complement of event X will be:

[tex]P(X')=1-P(X)[/tex]

          [tex]=1-0.003\\=0.997[/tex]

Thus, the probability that a man in this age category does NOT die of cancer during the course of the​ year is 0.997.

Answer:

x= 118 y= 26 and z=36

Step-by-step explanation:

The sum of the measures of the angles of a triangle is 180

can be written as x+y+z=180

The sum of the measures of the second and third angles is four times the measure of the first angle.  

It can be written by:  x+y=4z

The third angle is 10 more than the second

It can be written as z=y+10

By solving the equations systems the above values can be determined.

x + y + z = 180

Substituting,

4z + z = 180

5z = 180

z = 180 / 5 = 36

z = y + 10

36 - 10 = y

y = 26

x + y + z = 180

x + 26 + 36 = 180

x = 180 - 62

x = 118

Answer:

x + y = 500

215x + 615y = 187,500

Step-by-step explanation:

The first equation can show the amount of land.  The farmer has 500 acres to plant corn, x, and cotton, y.

x + y = 500

The second equation can show the cost.  The farmer has $187,500 to invest when corn costs $215 per acre and cotton costs $615 per acre.

215x + 615y = 187,500

The system of equations is

x + y = 500

215x + 615y = 187,500

The correct system of represents this scenario will be,

⇒ x + y = 500

⇒ 215x + 615y = 187,500

Where,' x' is plant acres of corn and 'y' is acres of cotton.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A farmer has 500 acres to plant acres of corn, x, and acres of cotton, y.

And, Corn costs $215 per acre to produce, and cotton costs $615 per acre to produce. He has $187,500 to invest this season.

Now,

Let us take  'x' is plant acres of corn and 'y' is acres of cotton.

Since, A farmer has 500 acres to plant acres of corn, x, and acres of cotton, y.

So, we can formulate;

⇒ x + y = 500

And, He has $187,500 to invest this season for corn costs $215 per acre to produce, and cotton costs $615 per acre to produce.

So, We can formulate;

⇒ 215x + 615y = 187,500

Thus, The correct system of represents this scenario will be,

⇒ x + y = 500

⇒ 215x + 615y = 187,500

Where,' x' is plant acres of corn and 'y' is acres of cotton.

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Answer:

its harddd

Step-by-step explanation:

rightttttttt