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3 years ago

Please answer it now in two minutes

Mathematics

1 answer:

scZoUnD [109]3 years ago

6 0

Answer: 8 yd

Step-by-step explanation:

The dotted triangle is a right triangle, the distance on the top of the triangle is the same distance as WZ

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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

Steve paid 10% tax on a purchase of $40. Select the dollar amount of the tax and the total dollar amount Steve paid on the numbe

Shalnov [3]

10% of 40 =
10% × 40 =
.10 × 40 = 4.00

Tax is $4
Amount Paid is 40 + 4 = $44

6 0

3 years ago

The angle θ 1 is located in Quadrant IV, and cos ⁡ ( θ 1 ) = 9/ 19 , theta, start subscript, 1, end subscript, right parenthesis

Firdavs [7]

Answer:

$sin\theta_1 = - \frac{2\sqrt{70}}{19}$

Step-by-step explanation:

We are given that $\theta_1$ is in <em>fourth</em> quadrant.

$cos\theta_1$ is always positive in 4th quadrant and

$sin\theta_1$ is always negative in 4th quadrant.

Also, we know the following identity about $sin\theta$ and $cos\theta$ :

$sin^2\theta + cos^2\theta = 1$

Using \theta_1 in place of \theta:

$sin^2\theta_1 + cos^2\theta_1 = 1$

We are given that $cos\theta_1 = \frac{9}{19}$

$\Rightarrow sin^2\theta_1 + \dfrac{9^2}{19^2} = 1\\\Rightarrow sin^2\theta_1 = 1 - \dfrac{81}{361}\\\Rightarrow sin^2\theta_1 = \dfrac{361-81}{361}\\\Rightarrow sin^2\theta_1 = \dfrac{280}{361}\\\Rightarrow sin\theta_1 = \sqrt{\dfrac{280}{361}}\\\Rightarrow sin\theta_1 = +\dfrac{2\sqrt{70}}{19}, -\dfrac{2\sqrt{70}}{19}$

$\theta_1$ is in <em>4th quadrant </em>so $sin\theta_1$ is negative.

So, value of $sin\theta_1 = - \frac{2\sqrt{70}}{19}$

6 0

3 years ago

You have $60 and your sister has $120. you are saving $7 per week and your sister is saving $5 per week. how long will it take b

hodyreva [135]

Well if you have 60 and she has 120 i will set it out as a sequence week by week
60,67,74,81,88,95,102,109,116,123,130,137,144,151,158,165,172,179,186,193,200,207,214,221,228,235,242,249,256,263,270
120,125,130,135,140,145,150,155,160,165,170,175,180,185,190,195,200,205,210,215,220,225,230,235,240, 245,250,255,260,265,270
it would take 31 weeks and the total is 270

4 0

3 years ago

Read 2 more answers

Watch help video

aleksley [76]

Answer:

1.55 feet.

Step-by-step explanation:

From the question given above, the following data were obtained:

Angle R = 24°

Hypothenus = RS = 3.8 feet

Opposite = ST = x

The value of x can be obtained by using the sine ratio. This is illustrated below:

Sine R = Opposite / Hypothenus

Sine 24 = x / 3.8

Cross multiply

x = 3.8 × Sine 24

x = 3.8 × 0.4067

x = 1.55 feet

Thus, the Lenght ST is 1.55 feet.

3 0

3 years ago