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Snowcat [4.5K]
3 years ago
5

Joe is making a ramp.Find the length of the ramp if the height is 7meters and the base is 24 meters

Mathematics
1 answer:
Musya8 [376]3 years ago
8 0

Answer:

the length of the ramp is 25 meters

Step-by-step explanation:

Joe is making a ramp. Ramp forms a right angle triangle with the base

So we use Pythagorean theorem to find the length of the ramp

AC^2(hypotenuse) = AB^2 + BC^2

Length of ramp is the hypotenuse = \sqrt{height^2 + base^2}

=\sqrt{7^2 +24^2}

= \sqrt{49 + 576^2}

= \sqrt{625}

= 25

so the length of the ramp is 25 meters

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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
What is the probability of randomly drawing an odd number between 24 and 33?
Studentka2010 [4]
Write out the numbers between 24 and 33:  {24, 25, 26, 27, 28, 29, 30, 31, 32, 33}

How many numbers have we here?  10.

How many of these numbers are odd?  {25, 27, 29, 31, 33}

Strictly speaking, "between 24 and 33" does not include {24, 33}.

Thus, the odd numbers between 24 and 33 are {25, 27, 29, 31}

The chances of drawing an odd number between 24 and 33 are then 4 / 10.

If, however, we omit the endpoints 24 and 33, then there are 8 numbers between 24 and 33:  {25, 27, 29, 31}

and the odds of choosing an odd number from these eight numbers is 4/8, or 1/2, or 0.50.
6 0
3 years ago
Log6 8 + log6 27 as single logarithm
Vsevolod [243]
Log[8/(36*3)] Log[2/27] Hope I really help you !
6 0
2 years ago
What is the side length of the square if A=81 m squared
Nesterboy [21]

Answer:

The side length is 9m

Step-by-step explanation:

A = 81 m^2

Since the figure is a square, we know the area of a square is A = s^2 where s is the side length

81 m^2 = s^2

Take the square root of each side

sqrt(81 m^2 ) = sqrt( s^2)

9 m = s

The side length is 9m

8 0
3 years ago
Geometry Angles question 3, Thanks if you help
Andre45 [30]

Answer:

54

Step-by-step explanation:

64 + 62 = 126

180 - 126 = 54

5 0
3 years ago
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