Assume employees' weekly gross earnings are $80,000, federal income tax withholding is $22,634.50, and FICA taxes are $11,920 in total for the employee and the employer. Determine the net amount to be paid to employees.

Answer: a) Each group has 5 members as its greatest possible.

b) There are 4 groups of sixth graders and 5 groups of seventh graders.

Step-by-step explanation:

Since we have given that

Number of sixth grader = 20

Number of seventh grader = 25

We need to find the greatest possible number of members in each group will contain:

For greatest possible number we will find "Highest common factor (H. C.F) of 20 and 25 = 5

a) Each group has 5 members as its greatest possible.

b) Number of groups of sixth graders would be

[tex]\dfrac{20}{5}=4[/tex]

Number of groups of seventh graders would be

[tex]\dfrac{25}{5}=5[/tex]

Hence, there are 4 groups of sixth graders and 5 groups of seventh graders.

Answer:

A) -4 over 9

Step-by-step explanation:

We have the fraction [tex]\frac{4}{-9}[/tex] the equivalent of this fraction is [tex]\frac{-4}{9}[/tex]

[tex]\frac{4}{-9}= \frac{-4}{9} =-\frac{4}{9}[/tex]

Both fractions are the same and equivalent, the negative sign makes the whole fraction negative regardless of whether it is in the numerator or denominator.

As modeled by the function below: t=0.007x^2+0.003x. The time it will  take the computer to sort 15 objects is 1.62sec

What is Time?

Time is the ongoing progression of existence and things that happen in what seems to be an irrevocable order from the past, present, and forward into the future.

Given:

t = 0.007x^2+0.003x

x = 15

Substituting the value in the equation we get,

t = 0.007(15)^2+0.003(15)

t = 0.007(225) + 0.045

t = 1.575 + 0.045

t = 1.62sec

Hence, It will take 1.65sec to sort 15 objects

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To solve the given differential equation, variables need to be separated, followed by integration of both sides. Since the equation involves both exponential and inverse square terms, separation of variables and integration are key steps. A specific solution also requires substituting a given function of y into the found general solution to determine any integration constants.

The question involves solving a differential equation 3e^(3x)dy/dx = -9x/y^2. First, we need to recognize this as a separable differential equation, which can be solved by isolating all terms involving y on one side and all terms involving x on the other side. After separation, we integrate both sides with respect to their respective variables.

Step 1: Separate the variables. We get dy/y^2 = -3x e^(-3x) dx.

Step 2: Integrate both sides. The integration of dy/y^2 with respect to y is -1/y, and the integration of -3x e^(-3x) with respect to x requires integration by parts or a table of integrals.

Step 3: Upon integration, we would find an implicit solution involving y and x, combined with an integration constant that needs to be determined based on initial conditions or additional information. Since specific initial conditions are not provided in the initial question, we'd include a constant C in our final expression.

For a specific solution when y(x) = cos(3x), additional steps are required to substitute this y expression into our general solution and solve for the constant.

Answer:

The answer is only one piece of candy

Step-by-step explanation:

Firstly, we have to determine the total amount of pieces of candy:

There are three bags with 75 pieces in each one, so the total is:

[tex]75+75+75=225[/tex]

Then, in order to determine the amount of pieces of candy for every friend,

we have to divide the total amount by 7, where the remainder of the division is the answer.

[tex]\frac{225}{7}=32*7+1[/tex]

Remainder=1

Finally, every friend of Scott receive 32 pieces of candy evenly and Scott is left with only one piece of candy.

Final answer:

The constant of proportionality when y = 18 and x = 60 is calculated by dividing y by x, which results in a constant of 0.3.

Explanation:

To find the constant of proportionality when y = 18 and x = 60, we must assume that the relationship between y and x is directly proportional. This means that as x increases, y increases at a constant rate, and vice versa. If the relationship is directly proportional, we can write y = kx, where k is the constant of proportionality.

To calculate k, we simply divide y by x. So we have:

k = y / x
k = 18 / 60
k = 0.3

Therefore, the constant of proportionality is 0.3.

To find the standard deviation of the weights of a species of cockroach when it is known that 14% weigh more than 55 grams, you can use the Empirical Rule of a normal distribution and solve using the given mean and the equivalent standard deviation for the 14% threshold. The estimated standard deviation in this case is around 4.63 grams.

Your question is about using statistical information about a normally distributed population - in this case, the weights of a certain species of cockroach - to estimate the standard deviation of that population.

One thing we know about normally distributed data is that approximately 68% of all measurements fall within one standard deviation (either above or below) of the mean, about 95% fall within two standard deviations, and about 99.7% fall within three standard deviations. This is often referred to as the Empirical Rule or 68-95-99.7 rule.

According to the information provided, 14% of the cockroaches in the studied population weigh more than 55 grams. On a standard normal distribution, 14% represents approximately 1.08 standard deviations above the mean (you can find this value on a standard normal distribution table). Since we know that the mean weight is 50 grams, we can set up the following equation to solve for the standard deviation:

50 (mean weight) + 1.08 (standard deviation equivalents for 14%) * σ (standard deviation) = 55

Solving for σ we find that the standard deviation σ for the population of these cockroaches is approximately 4.63 grams.

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The correct answer should be +18

Option C)The sales tax will be $2.25.

Convert the sales tax rate from a percentage to a decimal,
7.5% becomes 0.075.

Multiply the decimal by the total cost of the shoes,

0.075 × 29.95
= 2.24625.

$2.25.

Therefore, the sales tax on the shoes will be $2.25,Option C

Answer:

Answer is 31,

Step-by-step explanation:

PLATO Confirmed

Answer:

Since, by the quadratic formula,

The solution of a quadratic equation [tex]ax^2+bx+c=0[/tex] is,

[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

Here, the given quadratic equation,

[tex]5-10x-3x^2=0[/tex]

[tex]-3x^2-10x+5=0[/tex]

By the above formula,

[tex]x=\frac{-(-10)\pm \sqrt{(-10)^2-4\times -3\times 5}}{2\times -3}[/tex]

[tex]=\frac{10\pm \sqrt{100+60}}{-6}[/tex]

[tex]=\frac{10\pm \sqrt{160}}{-6}[/tex]

[tex]=\frac{5\pm 2\sqrt{10}}{-3}[/tex]

[tex]\implies x=-\frac{5+2\sqrt{10}}{3}\text{ or }x=-\frac{5-2\sqrt{10}}{3}[/tex]

The solution is, the value of x is 7.

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

here, we have,

given that,

(10x-20)=(6x+8)

We simplify the equation to the form, which is simple to understand

(10x-20)=(6x+8)

Remove unnecessary parentheses

10x-20=(6x+8)

Remove unnecessary parentheses

10x-20=6x+8

We move all terms containing x to the left and all other terms to the right.

+10x-6x=+8+20

We simplify left and right side of the equation.

+4x=+28

We divide both sides of the equation by 4 to get x.

x=7

Hence, The solution is, the value of x is 7.

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"-1 modulo 25" is "1 less than a precise multiple of 25". 
So what are the exact or precise multiples of 25 in the appropriate interval? 
It is -75, -50, -25, 0, 25, 50, 75, and 100. 
Now just subtract 1 from each of them.

So the answers are -76, -51, -26, -1, 24, 49, 74, and 99.

Answer:

(0, 139) and (139/35, 0)

Step-by-step explanation:

To graph a line, two points are needed. Taking x = 0 and replacing this value in the equation, we get:

y+1=−35(0−4)

y = 140 - 1

y = 139

Then, the point (0, 139) is on the line.

Taking y = 0 and replacing this value in the equation, we get:

0+1=−35(x−4)

1/(-35) = x -4

1/(-35) + 4 = x

139/35 = x

3.971 = x

Then, the point (139/35, 0) is on the line.