What number must you add to complete the square? x2 + 4x = 15 A. 16 B. 4 C. 2 D. 8

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

Three-fourths of the employees at a bookstore came to a staff meeting. Less than 24 employees were at the meeting. The inequalit

Len [333]

Answer:

The correct option is 4.

Step-by-step explanation:

It is given that the three-fourths of the employees at a bookstore came to a staff meeting. Less than 24 employees were at the meeting.

Let the total number employees be e.

Three fourth of the total employees is $\frac{3}{4}e$ , the total number of employees at the meeting were less than 24.

$\frac{3}{4}e$

Multiply 4 both sides.

$\frac{3}{4}e\times 4$

$3e$

Divide both sides by 3.

$e$

Therefore the value of e is less than 32.

In a number line as we approach towards left the the value of integers decreases.

Since the value of e is less than 32, therefore the solution graph is from negative infinity to 32.

Since 32 is not included in the solution set, therefore there is an open circle on 32.

Option 4 is correct.

3 0

3 years ago

Read 2 more answers

37. Two years ago, Bob flew 6 x 105 miles in an airplane. This was 15 times as many

gogolik [260]

Answer:

A. 4·10⁴

Step-by-step explanation:

The problem statement tells you ...

6×10⁵ miles = 15 × (last year's mileage)

Dividing by 15 gives ...

(60×10⁴ miles)/15 = (last year's mileage) = 4×10⁴ miles

_____

<em>Further explanation</em>

An exponent is an indication of repeated multiplication.

10⁵ = 10·10·10·10·10 = 100,000

We can use the associative property of multiplication to rewrite the number of miles:

6×10⁵ = 6·(10·10·10·10·10) = 600,000 = (6·10)·(10·10·10·10) = 60×10⁴

3 0

4 years ago

Please help ASAP it’s due in 4 minutes

maxonik [38]

Answer:

a) well we know the hypotenuse and we know that all sides are 90 degrees, and that its an even square, so if we split it into a triangle , we know that the other 2 angles are 45 degrees total, with this we can calculate the other 2 sides, which round to 10 inches.

b) if we know the sides of the first side, knowing the fact that its a square we know that all sides are even, therefore, all sides are 10 inches, the formula the finding the perimeter is basic:

P=L(2) + W(2)

L being length, W being width and P being perimeter

so we add up all 4 sides, here is the equation:

10 + 10 + 10 + 10 = 10 x 4 = 40

With this, we know that the perimeter is 40 inches total

c) knowing how long the sides are, we can figure out the area through another basic formula:

A=L X W

With A meaning Area

since its a square, we know all the sides are even, so the width and length are both 10...

10 X 10 = 100

Step-by-step explanation:

I Hope I Helped!

3 0

3 years ago

A patio 2 pairs of two parallel sides and 2 pairs of sides that are the same length there are 4 square corners what shape is the

Tems11 [23]

Answer:

The patio is a rectangle

Step-by-step explanation:

Since it is given that we have 2 pairs of two parallel sides, which implies 4 sides, this thus shows that the shape is a quadrilateral since, only quadrilaterals have 4 sides. Also, 2 pairs of sides are the same length, and are parallel, it shows that the shape is likely a rectangle.

Finally, there are 4 square corners on the shape which implies 4 right angles. This confirms that our shape is a rectangle since only a rectangle has 2 pairs of two parallel sides and 2 pairs of sides that are the same length there are 4 square corners.

So, the patio is a rectangle.

3 0

3 years ago