A paycheck is issued for $329.40. The paystub reflects an amount earned of $400.00, Medicare tax of $5.80, Social Security tax of $24.80, and a federal tax of $40.00. What is the net income for the paycheck? Group of answer choices

Answer:

0.6247

Step-by-step explanation:

The formula for calculating a Z-score is Z = (X - μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

From the question,

μ = 51, σ = 10. We are to find P(36 ≤ X ≤ 56)

Step 1

Find the Probability of X ≤ 36

μ = 51, σ = 10

Z = (X - μ)/σ

Z = 36 - 51/ 10

Z = -15/10

Z = -1.5

We find the Probability of Z = -1.5 from Z-Table

P(X <36) = P(X = 36) = P(Z = -1.5)

= 0.066807

Step 2

Find the Probability of X ≤ 56

μ = 51, σ = 10

Z = (X - μ)/σ

Z = 56 - 51/ 10

Z = 5/10

Z = 0.5

We find the Probability of Z = 0.5 from Z-Table:

P(X < 56) = P(X = 56) = P(Z = 0.5)= 0.69146

Step 3

Find P(36 ≤ X ≤ 56)

P(36 ≤ X ≤ 56) = P(X ≤ 56) - P(X ≤ 36)

= P( Z = 0.5) - P(Z = -1.5)

= 0.69146 - 0.066807

= 0.624653

Approximately to 4 decimal places , P(36 ≤ X ≤ 56) = 0.6247

Answer:

12x+27

Step-by-step explanation:

The solution is A = 12x + 27

The value of the equation is A = 12x + 27

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is given by

A = 3 ( 4x + 9 )

Now , on simplifying the equation , we get

By using the distributive property in the equation

Multiplying by 3 on both the values in the brackets , we get

A = 3 ( 4x ) + 3 ( 9 )

On further simplification of the equation ,

The value of A = 12x + 27

Therefore , the value of A is 12x + 27

Hence , the value of the equation is A = 12x + 27

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Answer:

y=3x

2y=x

Step-by-step explanation:

N/A

big brain award pls

Answer:

y = -1/3x + 6[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

First, change the original equation to slope intercept form:

y + 4 = 3x

y = 3x - 4

Now, find the slope of the perpendicular line. It will be the opposite reciprocal:

The opposite reciprocal of 3 is -1/3.

Next, plug this into the slope intercept equation along with the given point, so we can solve for b:

y = mx + b

6 = -1/3(2) + b

6 = -2/3 + b

6.67 = b

So, the equation will be y = -1/3x + 6[tex]\frac{2}{3}[/tex]

Answer:

$1.50

Step-by-step explanation:

1.50 x 3 = 4.50

Answer:

1.50$ per pound

Step-by-step explanation:

Step 1: State what is known

They tell us that 3 pounds cost 4.50$

Step 2: Find how much 1 pound cost

We divide 4.50$ by 3 to find out how much 1 pound costs

4.5/3 = 1.5

Therefore 1 pound of sour candies cost 1.50$

Answer:

82/3

Step-by-step explanation:

Hi! I'm back!

16+8r-48=5r+50

8r-32=5r+50

3r=82

r=82/3

Answer:

R = 82/3

Step-by-step explanation:

16 + 8(R - 6) = 5R + 50.

16 + 8 × R - 8 × 6 = 5R + 50

16 + 8R - 48 = 5R + 50

8R - 5R = 50 + 48 - 16

3R = 82

R = 82/3

R = 82/3

Thus, the value of R is 82/3

Answer:

900

Step-by-step explanation:

Answer:

No.

Step-by-step explanation:

A regular pentagonal tiling on the Euclidean plane is impossible because the internal angle of a regular pentagon, 108°, is not a divisor of 360°.

Answer:

The arcs are drawn to find a point on the bisecting ray. If the arcs are the same width, it makes sure that they are equidistant from the points on the rays of the angle. This causes the point to be on the bisecting ray.

Step-by-step explanation:

Bisection of an angle implies dividing the angle into two equal parts. The ray that divides the angle is called a bisector.

The hunter should use the same radius or width to draw the two arcs, using points P and Q as the center interchangeably, so that they would intersect at an equidistant point to P and Q. The point of intersection lies on the bisecting ray of the angle.

Answer:

Step-by-step explanation:

Answer:

The answer is not complete. But you can use a spreadsheet to construct a simulation model to estimate the average profit per unit of a set of data.

Step-by-step explanation:

To calculate the Expected value of profit, we use:

Selling price - Expected value of different costs

Selling price is Total Cost * Probability

Confidence Interval

A Confidence Interval is a range of values that someone can be sure the true value lies in.

To calculate the confidence interval, we use the formula x ± z * S/√n

Where S is the standard deviation

n is the number of observations

x is the mean

z is the chosen z value

Answer:

C. $824.74, $175.26

Step-by-step explanation:

1) Amount Credited

The formula to calculate the amount credited =

Amount paid ÷ ( 100% - Discount)

Discount is given in the question as 3/10

Where 3 = Discount rate

Amount paid = $800

Amount credited = 800/( 100% - 3%)

= 800/ 97%

= 800/ 0.97

= $824.74

b) Outstanding balance = Invoice - Amount credited

Invoice = $1000

Amount credited = $824.74

Outstanding balance = $1000 - $824.74

= $175.26

Answer:

Step-by-step explanation:

The complete question tells us  that;

A dataset from a government survey contains variables for 87 adults age from 18 to 85. The variables include iron level ( µ g/dL), cholesterol level (mg/dL), and systolic blood pressure (mmHg). The researchers built a multiple regression to predict the mean iron level based on 2 variables, cholesterol level and systolic blood pressure.A partial regression ANOVA table is provided. Complete the ANOVA table aning. Use a significance level of a 0.05. Regression ANOVA Table Source df SSMSF Statistic p-value regression104535226.5 error 84 53813 640.6 Give the degrees of freedom as a whole number, the value of F to at least two decimals, the the p-value to at least three decimals. Then form the conclusion based on your results.

NOTE: the attached minilab worksheet calculates this problem.

below is the attached image.

Answer:

Step-by-step explanation:

Cardinality of a set is defined as number of element in a set. It is represented as n(X) where X is any set.

a) Given the set A =(x l x € N and 20.< x<27). According to the set, the set contains the values of natural numbers between 20 and 27. The values are 21, 22, 23, 24, 25 and 26

A = (21, 22, 23, 24, 25, 26)

According to the set A, it can be seen that there are 6 elements in the set, this means n(A) = 6.

b) Given B=(x | xeN and x+1=x)

Since natural numbers starts from 1, the first element in the set is 2 i.e 1+1

The elements of the set B = (2, 3, 4, 4...)

The number of whole number in the set is therefore infinite.

c) For the set C={x l xe N and (x- 1)(x - 9) = 0)

We need to get the root of the equation  (x- 1)(x - 9) = 0

x-1 = 0 and x-9 = 0

x = 1 and x = 9

Hence the element C = (1,9)

The number of whole number in the set is n(C) = 2

d)  D={xlx E N, H X 5 100, and x is divisible by both 5 and 8)

Given the value of x between 5 and 100, the values of x divisible by 5 = (10, 15, 20, 25, 30, 35, 40, 45, 50 , 55, 60 , 65, 70, 75, 80 85, 90, 95)

values of x divisible by 8 = (16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96)

The total number of elements in both set = 29 i.e n(D) = 29

Answer: 4

Step-by-step explanation:

  (x+3)/(x-5)=(19-3x)/(x-5)

          x+3=19-3x

             4x=16

               x=4    

Answer:

4 + x/3

4 + 1/3x

Step-by-step explanation:

Step 1: Convert "four" to number

4

Step 2: Covert "more than" to number

4 +

Step 3: Convert "one-third" to number

4 + 1/3

Step 4: Add variable x (multiplication)

4 + 1/3x

to find the mid point,

m=-2+1/2,-5+3/2

=-1/2,-1

minus 90 degree means that it will go anti clock-wise direction. So, this shape will touch on under the y-axis

Answer: To find the area of a circle you use pi x rsquared. So just 3.14x7^2= 153.86

Step-by-step explanation:

Answer:

147

Step-by-step explanation:

f(3)=83

f(5)=377

377-83=294

5-3=2

294/2=147

To find the average rate of change, we divide the change in the output value by the change in the input value.

Answer:

6ab+3a^2b

Step-by-step explanation:

13ab+4a^2b-9ab+2ab-a^2b

13ab-9ab+2ab+4a^2b-a^2b

4ab+2ab+4a^2b-a^2b

6ab+3a^2b

Hope this helps ;) ❤❤❤

Answer:

6ab+3a^2b

Step-by-step explanation:

13ab + 4a^2b - 9ab + 2ab - a^2b

13ab - 9ab + 2ab + 4a^2b - a^2b

4ab + 2ab + 4a^2b - a^2b

6ab + 3a^2b

Answer:

A. -4

Step-by-step explanation:

F(-1) means we must plug the number "-1" in for each x.

F(x) = x^2 + 3x - 2

F(-1) = (-1)^2 + 3(-1) - 2

= 1 - 3 - 2

= -4

Answer:

6x^3-5x^2

Step-by-step explanation:

(4x^3+x^2)+2(x^3-3x^2)

4x^3+x^2+2x^3-6x^2

4x^3+2x^3+x^2-6x^2

6x^3+x^2-6x^2

6x^3-5x^2

The simplest form of the given expression [tex](4x^{3} +x^{2} )+2 (x^{3} -3x^{2} )[/tex] is,

[tex]6x^{3} - 5x^{2}[/tex].

Here, given expression is,

[tex](4x^{3} +x^{2} )+2 (x^{3} -3x^{2} )[/tex]

What is simplest form of equation?

The simplest form is the smallest possible equivalent fraction of the number.

Now,

Simplest form of expression,

[tex](4x^{3} +x^{2} )+2 (x^{3} -3x^{2} )\\4x^{3} +x^{2} +2 x^{3} -6x^{2} \\6x^{3} - 5x^{2}[/tex]

Hence, The simplest form of the given expression [tex](4x^{3} +x^{2} )+2 (x^{3} -3x^{2} )[/tex] is, [tex]6x^{3} - 5x^{2}[/tex].

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Answer:

The second number line represent the location of 3N values.

Step-by-step explanation:

The first number line represent the inequality N > 3.

Now, the new number is 3N.

Consider the second number line values:

3N = {12, 15, 18, 21, ....}

The second number line represent the location of 3N values.

Answer:

d

Step-by-step explanation:

Answer:

The null hypothesis is  rejected

Therefore there is sufficient evidence to conclude that the professors teaching method favored the male

Step-by-step explanation:

From the question we are told that

   The sample size for each population is  [tex]n_1 = n_2 = n = 10[/tex]

   The  first sample  mean is  [tex]\= x_1 = 82[/tex]

    The  second sample  mean is  [tex]\= x_2 = 74[/tex]

    The  first standard deviation is [tex]\sigma _1 = 4[/tex]  

    The second standard deviation is  [tex]\sigma_2 = 8.0[/tex]

     The  level of significance is  [tex]\alpha = 0.05[/tex]

The  null hypothesis is  [tex]H_o : \mu_1 = \mu_2[/tex]

The  alternative  hypothesis is  [tex]H_a : \mu_1 \ne \mu_2[/tex]

Generally the standard error is mathematically represented as

           [tex]SE = \sqrt{ \frac{ \sigma_1^2}{n_1} + \frac{ \sigma_2^2}{n_2} }[/tex]

=>        [tex]SE = \sqrt{ \frac{ 4^2}{10} + \frac{ 8^2}{10} }[/tex]

=>        [tex]SE = 2.83[/tex]

Generally the test statistics is mathematically represented as

          [tex]t = \frac{\= x_1 - \= x_2 }{SE}[/tex]

=>        [tex]t = \frac{82 - 74}{2.83}[/tex]

=>        t =  2.83

Generally the p-value  mathematically represented as

        [tex]p-value = 2 P(Z > 2.83)[/tex]

From the z table  

           [tex]P(Z > 2.83) = 0.0023274[/tex]

So

    [tex]p-value = 2 * 0.0023274[/tex]

   [tex]p-value = 0.0047[/tex]

Since  

      [tex]p-value < \alpha[/tex]

Hence the null hypothesis is  rejected

Therefore there is sufficient evidence to conclude that the professors teaching method favored the male

Answer:

A. [0, 65]

Step-by-step explanation:

Given that

Distance that Marcus drives every day = 32 miles.

The table having average speed as input and time taken as output is shown below in the table format:

[tex]\begin{center}\begin{tabular}{ c c}Speed(mph) & Time(minutes) \\ 60 & 32 \\ 45 & 43 \\ 55 & 35 \\ 50 & 38 \\ 62 & 31 \\\end{tabular}\end{center}[/tex]

To find:

The domain that includes all possible average speeds using interval notation = ?

Solution:

First of all, let us understand what is a domain of a function.

Domain of a function is set of valid input values that can be provided to the function so that it has a valid output.

If a function is written as:

[tex]y=f(x)[/tex] then values of [tex]x[/tex] are the input given to the function.

In the given question statement, we are given that maximum Average speed attained by Marcus is 65 miles per hour.

That means domain has a maximum value of 65.

Let us learn something about interval notation.

( or ) means the value is not inclusive.

[ or ] means the value is inclusive.

Here 65 will be inclusive.

On the left side of comma, lower value is written and on the right side of comma, larger value is written.

So, domain for the current situation will be:

[0, 65]

0 is taken as the minimum value of domain here, because average speed value can not be negative.

This interval will contain all the possible values of input (average speed) as shown in the above table of values.

Answer:

35/36

Step-by-step explanation:

Sample space = S

n(S) = 36

Event of obtaining sum greater than 2, = A

Event of obtaining sum less than 2, B =( 1, 1)

n(B) = 1  

Probability of obtaining sum less than 2, P(B) = n(B)/n(S) = 1/36

n(A) = 36 - 1 = 35

∴ Probability of obtaining sum greater than 2, P(A) = n(A)/n(S) = 35/36

Answer:

Rectangle is a 2dimensional shape so, let me explain using it

The diagonal of a rectangle divides the rectangle into two triangles that are congruent and they are the same size and shape.

Another example is parallelogram

The diagonal of a parallelogram also divides the figure into two triangles that are congruent.

Step-by-step explanation:

Answer:

Step-by-step explanation:

  In mathematics it has to do with movement of digits/factors without affecting the overall outcome of an operation

in addition of numbers, commutative explains that

A+B= B+A  which ever way it must give the same outcome

example say A= 2

and B= 3 then

2+3= 3+2

5= 5

In multiplication

A*B= B*A as we can see

2*3= 3*2

6=6

Both figures in the equal signs are same