Rewrite without absolute value for the given condition: y=|x−3|+|x+2|−|x−5|, if 3 < x

The average heights of x number of girls and 15 boys is 123. if the average heights of boys is 125 and that of girls is 120.find

mamaluj [8]

Answer:

$x = 10$ . In other words, there number of girls is $10$ .

Step-by-step explanation:

The average of a number of measurements is equal to the sum of these measurements over the number of measurements.

$\displaystyle \text{Average} = \frac{\text{Sum of measurements}}{\text{Number of measurements}}$ .

Rewrite to obtain:

$\begin{aligned}& \text{Sum of measurements}= (\text{Number of measurements}) \times (\text{Average}) \end{aligned}$ .

For this question:

$\begin{aligned}& \text{Sum of heights of boys} \\ &= (\text{Number of boys}) \times (\text{Average height of boys}) \\ &= 15 \times 125 = 1875\end{aligned}$ .

$\begin{aligned}& \text{Sum of heights of girls} \\ &= (\text{Number of girls}) \times (\text{Average height of girls}) \\ &= x \times 120 = 120\, x\end{aligned}$ .

Therefore:

$\begin{aligned}& \text{Sum of boys and girls} \\ &= \text{Sum of heights of boys} + \text{Sum of heights of girls}\\ &= 1875 + 120\, x\end{aligned}$ .

On the other hand, there are $(15 + x)$ boys and girls in total. Using the formula for average:

$\begin{aligned}& \text{Average height of boys and girls} \\ &= \frac{\text{Sum of heights of boys and girls}}{\text{Number of boys and girls}} \\ &= \frac{1875 + 120\, x}{15 + x}\end{aligned}$ .

From the question, this average should be equal to $123$ . In other words:

$\displaystyle \frac{1875 + 120\, x}{15 + x} = 123$ .

Solve this equation for $x$ to obtain:

$1875 + 120\, x= 123\, (15 + x)$ .

$(123 - 120)\, x = 1875 - 123 \times 15$ .

$x = 10$ .

In other words, the number of girls here is $10$ .

5 0

3 years ago

Albania is an Eastern European country that uses a currency called the Albanian Lek (ALL). Right now, $1 (1 USD) exchanges for 1

rosijanka [135]

Answer:

$9398.50

Step-by-step explanation:

Given

$\$1 = 106.40\ ALL$

Required

Equivalent of 1,000,000 ALL

We have:

$\$1 = 106.40\ ALL$

and

$\$x = 1000000\ ALL$

Cross Multiply

$x * 106.40 = 1 * 1000000$

$106.40x = 1000000$

Solve for x

$x = 1000000/106.4$

<em></em> $x = \$9398.50$ <em> -- Approximated</em>

4 0

4 years ago

4-1/4 with no decimal point

suter [353]

Answer:

4-25

Step-by-step explanation:

7 0

3 years ago

Please help I'm lost.

vova2212 [387]

Part 1: Answer:

(x+1)(x+1)(x-6) = x^3 - 4x^2 - 11x - 6

Step-by-step explanation:

To make r a root, include (x-r) as a factor. (-1+1)(-1+1)(-1-6) is zero even though (-1-6) isn't.

(6+1)(6+1)(6-6) is zero.

Part 2 Answer:

Standard form: y = -x^4 + 12

Degree 4

left end goes down, right end goes down.

Step by step: apply the definitions of standard form, polynomial degree, and "end behavior". In other words, read the textbook.

Part 3: Answer: x = 3, x = 8

Step by step:

x^2-11x = -24

x^2-11x+24 = 0

(x-3)(x-8) = 0

x = 3 or x = 8

Part 4a Answer:

quotient 2x^2 + x - 3

remainder 1

Step by step:

2x^2 + x - 3

___________________

x-4 ) 2x^3 - 7x^2 - 7x + 13

2x^3 - 8x^2

__________

0 + x^2 - 7x + 13

x^2 - 4x

____________

0 - 3x + 13

- 3x + 12

______

1

Part 4b answer:

quotient 2x^2 - 6x + 2

remainder -20

Step by step: you have to know exactly what you are doing. Refer to textbook or Wikipedia.

dividend 2x^3 +14x^2 - 58x

divisor x+10

leading coefficient of divisor must be 1

write coefficients of dividend at top

write coefficients of dividend at left

| 2 14 -58 0

-10 | -20 60 -20

___________

| 2 -6 2 -20

Coefficients of quotient are 2 -6 2

Remainder is -20

quotient = 2x^2 - 6x + 2

7 0

3 years ago

Mrs. Levi's class raised $217.35 in one-time donations for the library's new book collection. The class also had 4 people pledge

nexus9112 [7]

Answer: $817.35

Step-by-step explanation:

150x4 = 600

600+217.35 = 817.35

7 0

4 years ago

Rewrite without absolute value for the given condition: y=|x−3|+|x+2|−|x−5|, if 3 < x < 5