The loading ramp for a truck makes a 30° angle to the ground. The back of the truck is 4' above the ground.

A class has an equal number of boys and girls. The boys all got 78% on a test and the girls all got 84%. What are the mean and s

Sergio039 [100]

Answer:

Mean is 81%

standard deviation is approximately 4.2%

Step-by-step explanation:

Since the number of boys equals the number of girls, but it is not given, we name it "N". and proceed to calculate the mean as:

Mean = (0.78 * N + 0.84 * N) /(2 N)

using that the total number of students must be N boys + N girls = 2 N

Then the Mean becomes: N *(0.78 + 0.84) /(2 N) = (0.78 + 0.84) / 2 = 1.62 / 2 = 0.81

So the mean is 81%

Now, standard deviation will be calculated by first adding the squares of the deviations: (X-0.81)^2 for the N boys and for the N girls, and then finding the square root of this and finally dividing by the square root of N. That is:

$N\,(0.78-0.81)^2\,+\,N\,(0.84-0.81)^2= N \left \{ (-0.03)^2+(0/03)^2\right \}=N\,*0.0018$

Now finding the square root of this value, and finally dividing it by the square root of N:

$\sigma=\frac{\sqrt{N\,*\,0.0018} }{\sqrt{N} } =\sqrt{0.0018} \approx 0.042426$

which in percent form is: approximately 4.2%

7 0

3 years ago

The difference of the square of a number and three times the sum of the number and 7 is more than the product of that number and

Pachacha [2.7K]

Answer:

x2 - 3(x + 7) > 15x

x2 - 3x - 21 > 15x

6 0

3 years ago

Solve the simultaneous equation, 2p - 3q = 4 3p + 2q = 9

Kobotan [32]

Answer:

p = $\frac{35}{13}$ and q = $\frac{6}{13}$

Step-by-step explanation:

Given equations:

2p - 3q = 4 -----------(i)

3p + 2q = 9 ------------(ii)

Let's solve this equation simultaneously using the elimination method

(a) Multiply equation (i) by 3 and equation (ii) by 2 as follows;

[2p - 3q = 4] x 3

[3p + 2q = 9] x 2

6p - 9q = 12 -------------(iii)

6p + 4q = 18 -------------(iv)

(b) Next, subtract equation (iv) from equation (iii) as follows;

[6p - 9q = 12]

- [6p + 4q = 18]

-13q = -6 -----------------(v)

(c) Next, make q subject of the formula in equation (v)

q = $\frac{6}{13}$

(d) Now substitute the value of q = $\frac{6}{13}$ into equation (i) as follows;

2p - 3( $\frac{6}{13}$ ) = 4

(e) Now, solve for p in d above

Multiply through by 13;

26p - 18 = 52

Collect like terms

26p = 52 + 18

26p = 70

Divide both sides by 2

13p = 35

p = $\frac{35}{13}$

Therefore, p = $\frac{35}{13}$ and q = $\frac{6}{13}$

8 0

3 years ago

What is the sum of (–2.1x + 3.7) and (5 + 4.9x)?

vesna_86 [32]

It's easier to work with problems such as –2.1x + 3.7 -5 + 4.9x when we rearrange the like terms vertically:

–2.1x + 3.7 -5 + 4.9x

becomes

–2.1x + 3.7

+4.9x -5

------------------

2.8x - 1.3 (answer)

4 0

3 years ago

PLEASE HELP MATH!! (BRAINLIEST + MORE) questions in picture!

klasskru [66]

Answer:

A) 2x*2 +6x -3x - 9= 2x*2 +3x -9

B) 2yx*2 +2yx +2y +3x*2 +3x +3

C) 36x*2 y +48yx +3xy*2 + 4y*2

D) 2x*3 - 4x*2 y + 3x -6y

7 0

2 years ago