Diameter of a circle is 20m. Take π = ²²/₇ and find a) Radius b) Circumference c) Area of the circle.

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

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ziro4ka [17]

Y=v(initial)*t+1/2at^2
since the velocity is zero at the maximum height then we get
y=1/2at^2
a is just acceleration due to gravity so a=g which is 9.8 m/s^2.
so y=1/2gt^2.

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3 years ago

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Ronch [10]

Answer:

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Step-by-step explanation:

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3 years ago

The following expression represents the profit made by John as he mows lawns: P = 20L

Nat2105 [25]

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8 0

3 years ago

ΔABC and ΔXYZ are similar triangles. The lengths of two sides of each triangle are shown. Find the lengths of the third side of

Norma-Jean [14]

Answer:

b=9

x=5.5

Step-by-step explanation:

find the common ration

AB is 6, and XY is 3 (they are the corresponding sides)

ratio is 2 to 1 (6/3=2/1)

AC corresponds with YZ

XY is 4.5 so b is 4.5*2=9

ZY corresponds with CB

CB is 11, since XYZ is the smaller divide by 2 instead of multiplying by 2

4 0

2 years ago

Diameter of a circle is 20m. Take π = ²²/₇ and find a) Radius b) Circumference c) Area of the circle.​

Diameter of a circle is 20m. Take π = ²²/₇ and find a) Radius b) Circumference c) Area of the circle.