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2 years ago

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Tom is 45 and pays $2042 on his mortgage each month while his total take home pay is $5950 per month. The national average for t

hose aged 35-64 on housing costs is 35% of income compute the percent of toms income spent on housing. Is this more or less than the national average

2 answers:

S_A_V [24]2 years ago

5 0

Answer:

Tom pays 34.32% which is less than 35%.

Step-by-step explanation:

Tom's total take home pay per month is = $5950

The national average for those aged 35-64 on housing costs is 35% of income.

Given is that tom is 45 years and pays $2042 on his mortgage each month.

So, he pays $\frac{2042}{5950} \times100=34.32$ % of his monthly income.

This is slightly lower than the national average of 35%.

aniked [119]2 years ago

4 0

More

First, you divide 2042/5950 which is about 0.4036, then you move the decimal 2 spaces to the right which is about 40.4, which means that 40% of Tom's income is his mortgage, higher than the average

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Tarun has 4 more than the twice the number of tshirts Deepak has.Mahesh has 2 more than thrice the number of T-shirts that Tarun

Dafna11 [192]

Answer:

Deepak: 4 t-shirts,

Tarun: 12 t-shirts,

Mahesh: 14 t-shirts.

Step-by-step explanation:

Let x represent number of t-shirts that Deepak has.

Please consider the complete question.

Tarun has 4 t-shirt more than twice the number of T-shirts Deepak has. Mahesh has 2 more than thrice the number of T-shirts Deepak has. If the ratio of the t-shirt that Tarun and Mahesh have is 6 : 7, find out the number of the t-shirt each of them has.

Since Tarun has 4 t-shirt more than twice the number of T-shirts Deepak has, so the number of t-shirts that Tarun has would be $2x+4$ .

We are also told that Mahesh has 2 more than thrice the number of T-shirts Deepak has. So the number of t-shirts that Mahesh has would be $3x+2$ .

Since the ratio of the t-shirt that Tarun and Mahesh have is 6 : 7, so we can represent this information in an equation as:

$\frac{2x+4}{3x+2}=\frac{6}{7}$

Cross multiply:

$6(3x+2)=7(2x+4)$

$18x+12=14x+28$

$18x-14x+12-12=14x-14x+28-12$

$4x=16$

$x=\frac{16}{4}=4$

Therefore, Deepak has 4 t-shirts.

The number of t-shirts that Tarun has would be $2x+4\Rightarrow 2(4)+4=4+4=12$

Therefore, Tarun has 12 t-shirts.

The number of t-shirts that Mahesh has would be $3x+2\Rightarrow 3(4)+2=12+2=14$

Therefore, Mahesh has 14 t-shirts.

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2 years ago

A piece of paper is to display ~128~ 128 space, 128, space square inches of text. If there are to be one-inch margins on both si

Grace [21]

Answer:

The dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches

Step-by-step explanation:

We have that:

$Area = 128$

Let the dimension of the paper be x and y;

Such that:

$Length = x$

$Width = y$

So:

$Area = x * y$

Substitute 128 for Area

$128 = x * y$

Make x the subject

$x = \frac{128}{y}$

When 1 inch margin is at top and bottom

The length becomes:

$Length = x + 1 + 1$

$Length = x + 2$

When 2 inch margin is at both sides

The width becomes:

$Width = y + 2 + 2$

$Width = y + 4$

The New Area (A) is then calculated as:

$A = (x + 2) * (y + 4)$

Substitute $\frac{128}{y}$ for x

$A = (\frac{128}{y} + 2) * (y + 4)$

Open Brackets

$A = 128 + \frac{512}{y} + 2y + 8$

Collect Like Terms

$A = \frac{512}{y} + 2y + 8+128$

$A = \frac{512}{y} + 2y + 136$

$A= 512y^{-1} + 2y + 136$

To calculate the smallest possible value of y, we have to apply calculus.

Different A with respect to y

$A' = -512y^{-2} + 2$

Set

$A' = 0$

This gives:

$0 = -512y^{-2} + 2$

Collect Like Terms

$512y^{-2} = 2$

Multiply through by $y^2$

$y^2 * 512y^{-2} = 2 * y^2$

$512 = 2y^2$

Divide through by 2

$256=y^2$

Take square roots of both sides

$\sqrt{256=y^2$

$16=y$

$y = 16$

Recall that:

$x = \frac{128}{y}$

$x = \frac{128}{16}$

$x = 8$

Recall that the new dimensions are:

$Length = x + 2$

$Width = y + 4$

So:

$Length = 8 + 2$

$Length = 10$

$Width = 16 + 4$

$Width = 20$

To double-check;

Differentiate A'

$A' = -512y^{-2} + 2$

$A" = -2 * -512y^{-3}$

$A" = 1024y^{-3}$

$A" = \frac{1024}{y^3}$

The above value is:

$A" = \frac{1024}{y^3} > 0$

This means that the calculated values are at minimum.

<em>Hence, the dimensions of the smallest piece that can be used are: 10 by 20 and the area is 200 square inches</em>

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1 year ago

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hichkok12 [17]

Answer:

DF=3.75

Step-by-step explanation:

24/6=15/x

cross multiply to get 24x=90

x=3.75

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melamori03 [73]

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