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2 years ago

The length of a rectangle is six times its width. if the perimeter of the rectangle is 140 in , find its area.

1 answer:

4 0

L = 6W ---- the lenght is 6 times its width
P = 2(L + W) = 140
A =?

P = 2(L+W)
P = 2L + 2W
we know that L = 6W so we plug it into the equation
P = 2(6W) + 2W= 140
12W + 2W = 140
14W = 140
W = 140/14
W = 10

Lets plug 10 into the equation L = 6W
L = 6(10)
L = 60

AREA = LW
= 60 * 10
= 600

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Susan, a recent college graduate, makes a base salary of $70,000 per year. Susan has federal income tax withholding of $12,000,

Damm [24]

Answer:

Susan's take-home pay $48,645.

Step-by-step explanation:

Given:

Susan, a recent college graduate, makes a base salary of $70,000 per year. Susan has federal income tax withholding of $12,000, and state tax withholding of $4,000. Employers are required to withhold a 6.2% Social Security tax and a 1.45% Medicare tax.

Now, to find Susan's take-home pay.

Basic salary = $70,000.

Now, her tax withholdings:

Federal income tax = $12,000.

State tax = $4,000.

Social security tax = 6.2% of $70,000.

$=\frac{6.2}{100} \times 70,000\\\\=0.062\times 70,000\\\\=\$4340.$

Medicare tax = 1.45% of $70,000.

$=\frac{1.45}{100} \times 70000\\\\=0.0145\times 70000\\\\=\$1015.$

Now, to get the take-home pay of Susan's we subtract all the tax holdings of federal, state, social and medicare from the basic salary:

$70,000-(12,000+4,000+4340+1015)$

$=70,000-(21,355)$

$=70,000-21,355$

$=\$48,645.$

Therefore, Susan's take-home pay $48,645.

7 0

1 year ago

The equation y = 1.55x + 110,419 approximates the total cost, in dollars, of raising a child in the united states from birth to

Andru [333]

Answer:

The correct option is A). $112295.05

Step-by-step explanation:

The equation for approximating the total cost is given to be :

y = 1.55x + 110419 , where x is the annual household's income and y is the total cost in dollars of raising a child in the united states from birth to 17 years

We need to calculate the total cost of raising a child in the united states from birth to 17 years if the annual household's income is given to be $1211

So, for this we will use the given equation and substitute x = 1211 and find the value of y which will be our total cost

⇒ Total cost , y = 1.55 × 1211 + 110419

⇒ y = 1877.05 + 110419

⇒ y = 112296.05 ≈ 112295.05

Hence, The approximate total cost of raising a child from birth to 17 years in a household with a weekly income of $1211 = $112295.05

Therefore, The correct option is A). $112295.05

8 0

1 year ago

Karen finished watching a movie at 1:00 PM. The movie lasted 1 hour 38 minutes. at what time Karen started watching the movie. -

Andrew [12]

The correct answer would be 11:32am. i hope this helps!

6 0

2 years ago

Read 2 more answers

The baker pays $0.80 per pound for sugar and $1.25 per pound for butter. Write an expression that shows how much the baker will

alekssr [168]

X is sugar
y is butter
z is total money

$0.80x + $1.25y = z

the total money spent if the Baker bought 6 pounds of butter and 20 pounds of sugar would be $23.50.

5 0

2 years ago

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From past experience, a company has found that in carton of transistors: 92% contain no defective transistors 3% contain one def

jasenka [17]

Answer:

$E(X) = 0*0.92 + 1*0.03 +2*0.03 +3*0.02 = 0.1500$

In order to find the variance we need to find first the second moment given by:

$E(X^2) = \sum_{i=1}^n X^2_i P(X_i)$

And replacing we got:

$E(X^2) = 0^2*0.92 + 1^2*0.03 +2^2*0.03 +3^2*0.02 = 0.3300$

The variance is calculated with this formula:

$Var(X) = E(X^2) -[E(X)]^2 = 0.33 -(0.15)^2 = 0.3075$

And the standard deviation is just the square root of the variance and we got:

$Sd(X) = \sqrt{0.3075}= 0.5545$

Step-by-step explanation:

Previous concepts

The expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete.

The variance of a random variable X represent the spread of the possible values of the variable. The variance of X is written as Var(X).

Solution to the problem

LEt X the random variable who represent the number of defective transistors. For this case we have the following probability distribution for X

X 0 1 2 3

P(X) 0.92 0.03 0.03 0.02

We can calculate the expected value with the following formula:

$E(X) = \sum_{i=1}^n X_i P(X_i)$

And replacing we got:

$E(X) = 0*0.92 + 1*0.03 +2*0.03 +3*0.02 = 0.1500$

In order to find the variance we need to find first the second moment given by:

$E(X^2) = \sum_{i=1}^n X^2_i P(X_i)$

And replacing we got:

$E(X^2) = 0^2*0.92 + 1^2*0.03 +2^2*0.03 +3^2*0.02 = 0.3300$

The variance is calculated with this formula:

$Var(X) = E(X^2) -[E(X)]^2 = 0.33 -(0.15)^2 = 0.3075$

And the standard deviation is just the square root of the variance and we got:

$Sd(X) = \sqrt{0.3075}= 0.5545$

8 0

2 years ago