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s2008m [1.1K]
2 years ago
9

the area of a rectangle is 54x^9y^8 square yards if the length of the rectangle is 6x^3y^4 yards what expression represents the

width of the rectangle in yards
Mathematics
2 answers:
user100 [1]2 years ago
8 0

We are given rectangle

Area=54x^9y^8

so, we have

A=54x^9y^8

length=6x^3y^4

so, we have

L=6x^3y^4

Let's assume

width of the rectangle in yards as W

we know that

A=L*W

now, we can plug values

54x^9y^8=(6x^3y^4)*W

now, we can solve for W

W=\frac{54x^9y^8}{6x^3y^4}

W=9x^6y^4

so, width of rectangle is 9x^6y^4............Answer


valentinak56 [21]2 years ago
6 0
I think your answer will be 48x^6y^4
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Helen gathered 37 mushrooms in three hours. How many mushrooms did she gather every hour, if she gathered 7 more mushrooms in th
mihalych1998 [28]

Answer:

On the first hour she gathered 8 mushroons, on the second 15 mushroons and on the third she gathered 14 mushroons.

Step-by-step explanation:

Helen gathred a total of 37 mushroons in three hours. On the first hour she gathered "x" mushroons, on the second hour she gathered "x + 7" mushroons and on the third hour she gathered "x + 6". Therefore the sum of mushrrons she gathered on each hour should be equal to the total she gathered as shown below:

37 = x + (x+ 7) + (x + 6)

37 = 3*x + 13

3*x + 13 = 37

3*x = 37 - 13

3*x = 24

x = 24 / 3

x = 8

On the first hour she gathered 8 mushroons, on the second 15 mushroons and on the third she gathered 14 mushroons.

8 0
1 year ago
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 <u>$48,645</u>.

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.

<u><em>Social security tax = 6.2% of $70,000.</em></u>

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

<u><em>Medicare tax = 1.45% of $70,000.</em></u>

=\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
A class with n kids lines up for recess. The order in which the kids line up is random with eachordering being equally likely. T
Elis [28]

Answer:

A) P(Betty is first in line and mary is last) = P(B₁) + P(Mₙ) - (P(B₁) × P(Mₙ/B₁))

B) The method used is Relative frequency approach.

Step-by-step explanation:

From the question, we are told a sample of n kids line up for recess.

Now, the order in which they line up is random with each ordering being equally likely. Thus, this means that the probability of each kid to take a position is n(total of kids/positions).

Since we are being asked about 3 kids from the class, let's assign a letter to each kid:

J: John

B: Betty

M: Mary

A) Now, we want to find the probability that Betty is first in line or Mary is last in line.

In this case, the events are not mutually exclusive, since it's possible that "Betty is first but Mary is not last" or "Mary is last but Betty is not first" or "Betty is the first in line and Mary is last". Thus, there is an intersection between them and the probability is symbolized as;

P(B₁ ∪ Mₙ) = P(B₁) + P (Mₙ) - P(B₁ ∩ Mₙ) = P(B₁) + P(Mₙ) - (P(B₁) × P(Mₙ/B₁))

Where;

The suffix 1 refers to the first position while the suffix n refers to the last position.

Also, P(B₁ ∩ Mₙ) = P(B₁) × P(Mₙ/B₁)

This is because the events "Betty" and "Mary" are not independent since every time a kid takes his place the probability of the next one is affected.

B) The method used is Relative frequency approach.

In this method, the probabilities are usually assigned on the basis of experimentation or historical data.

For example, If A is an event we are considering, and we assume that we have performed the same experiment n times so that n is the number of times A could have occurred.

Also, let n_A be the number of times that A did occur.

Now, the relative frequency would be written as (n_A)/n.

Thus, in this method, we will define P(A) as:

P(A) = lim:n→∞[(n_A)/n]

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Answer:

¼ chance

Step-by-step explanation:

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1 year ago
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Anastaziya [24]

Answer:

I'm sorry all I know is part a is 40

Step-by-step explanation:

hope this helps you answer all of the other parts.

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3 0
1 year ago
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