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IceJOKER [234]
2 years ago
8

During a school event, there were 8 times as many pupils as teachers and there were three times as many boys as girls. There wer

e 70 fewer teachers than boys. How many people were there at the school event?
Mathematics
1 answer:
Lilit [14]2 years ago
3 0
We know that pupils are students

Students = S
boys = B
Teachers = T

So....

S = 8T
Boys = 3G
T = B - 70

Since there is 8x students than teachers, I did Boys = 6x and girls = 2x

I'm going to use this next: S = 8T

8x = 8(B -70)

8x = 8(6x - 70)

8x = 4x - 560

x = 14

We know there is 8x students, so there are 112 students and we know that there is 1/8 of teachers, so there are 14 teachers.

Answer = 126.
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Citrus2011 [14]
First I'd expand the brackets so that you can re-simplify the values, so:
(2x + 3)(3x + 4)
6x^2 + 9x + 8x + 12
6x^2 + 17x + 12
The answer A. 2x(3x + 4) + 3(3x + 4) can be simplified the same way, with 6x^2 + 8x + 9x + 12, and so the answer is A. I hope this helps!
3 0
3 years ago
Read 2 more answers
Please help ASAP!!! Thank you so much!!! Just want confirm my answer it is y=150x-50. A concession stand at a football game took
jekas [21]

Answer: You have the correct answer. It is y = 150x-50

Nice work on getting the correct answer. For anyone curious, the explanation is below.

=============================================

x = number of hours the stand is open

y = amount earned

(1,100) is from the fact the stand is open 1 hour and earns $100

(3,400) is due to the stand earning $400 after 3 hours.

Slope Formula

m = (y2 - y1)/(x2 - x1)

m = (400-100)/(3-1)

m = 300/2

m = 150 is the slope, and it is the amount earned per hour. It is the rate of change.

Use m = 150 and (x,y) = (1,100) to find the value of b as shown below

y = mx+b

100 = 150(1) + b

100 = 150 + b

100-150 = b

-50 = b

b = -50 is the y intercept and it is the starting amount they earn. The negative earning indicates that they spent $50 to set up the stand, which is the cost of buying the food, equipment, etc.

So we have m = 150 as the slope and b =  -50 as the y intercept.

Therefore, y = mx+b turns into y = 150x-50.

-------

As a check, plugging in x = 1 should lead to y = 100

y = 150x-50

y = 150(1)-50

y = 150-50

y = 100 and indeed it does

The same should be the case with (3,400). Plug in x = 3 and we should get y = 400

y = 150x-50

y = 150(3)-50

y = 450-50

y = 400, we have confirmed the answer by showing that the line y = 150x-50 goes through the two points (1,100) and (3,400).

3 0
3 years ago
Many people use scanners to read documents and store them into pdf file. To help determine which brand of scanner to buy, a stud
konstantin123 [22]

The data is missing in the question. The data is provided below :

Document : 1     2      3      4      5     6      7      8

Brand A       17  29    18    14    21   25    22    29

Brand B       21  38    15    19    22   30    31   37

Solution :

State of the hypothesis of the null hypothesis and alternate hypothesis.

Null hypothesis : $h_A = h_B$

Alternate hypothesis : $h_A > h_B$

These hypothesis is a one tailed test. The null hypothesis will get rejected when the mean difference between the sample means is very small.

Significance level = 0.05

Therefore the standard error is :  $SE = \sqrt{(\frac{s^2_1}{n_1})+(\frac{s^2_2}{n_2})}$

                                                         = 3.602

And the degree of freedom, DF = 14

$t=\frac{(x_1-x_2)-d}{SE}$

 = -1.319

Here, $s_1$ = standard deviation of the sample 1

        $s_2$ = standard deviation of the sample 2

         $n_1$ = size of the sample 1

        $n_2$ = size of the sample 2

         $x_1$ = mean of the sample 1

        $x_2$ = mean of the sample 2      

          d = the hypothesis difference between the population mean

The observed difference in a sample means t static of -1.32. From t distribution calculator to determine P($t \leq -1.32$) = 0.1042  

Since the P value of 0.1042 is greater than significance level o 0.05, we therefore cannot reject the null hypothesis.

But from the test, we have no sufficient evidence that supports that Brand A is better than Brand B.      

8 0
3 years ago
I don't really understand the question so can someone help me answer the question please?​
Ksivusya [100]

Answer:

1/ 3

Step-by-step explanation:

If each of the cards is turned over, the probability of picking up a card of one type P(E) becomes equal to:

=> P(E) = number of cards of the required type/ total number of cards

● Total number of spades( ♤ ) = 3

{the queen, one ace and the nine are all spades}

● Total number of cards = 6

Probability of drawing a spade= 3/ 6

= 1/ 2

● Total number of "7" = 1

● Total number of cards = 6

Probability of drawing a 7

= 1/ 6

Now, what's asked is the difference in the probabilities of drawing a spade and a seven.

= 1/ 2 - 1/ 6

= 3/ 6 - 1/ 6

= 2/ 6

= 1/ 3

Hence, 1/ 3 of a greater chance of drawing a spade over a 7.

5 0
2 years ago
Simplify<br> 21^6y^5/14x^2y^9
nevsk [136]

1 2 2 5 2 3 0 3 ^1 4 ^2/2

6 0
2 years ago
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