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3 years ago

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A group of students calculated their average score at a spelling bee. They realized that if one of them scored 9 more points, th

eir average score would be 81 points. If one of them scored 3 points less, their average score would be 78 points. How many students were in the group?

1 answer:

alukav5142 [94]3 years ago

8 0

Answer: There are 4 students in the group.

Step-by-step explanation:

Let the number of students in the group be n

If one of them scored 9 more points , their average score would be 81 points.

So, our equation (1) will be

$\frac{\sum x+9}{n}=81\\\\\sum x+9=81n$

Similarly,

If one of them scored 3 points less, their average score would be 78 points.

So, our equation (2) will be

$\frac{\sum x-3}{n}=78\\\\\sum x-3=78n$

So, from equation (1) and (2) we get:

$81n-9=\sum x=78n+3\\\\81n-9=78n+3\\\\81n-78n=3+9\\\\3n=12\\\\n=\frac{12}{3}\\\\n=4$

Hence, there are 4 students in the group.

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Divide, and enter the exact quotient.<br> 22,500 ÷ 500 =

Solnce55 [7]

Answer:

45

Step-by-step explanation: 45 x 500 = 22,500 meaning 22,500 ÷ 500 = 45

8 0

3 years ago

Refrigerators in a random sample of 60 refrigerators, the mean repair cost was $150.00 and the standard deviation was $15.50. Co

worty [1.4K]

Answer:

The 99% confidence interval is given by ($144.677;$155.323)

We are confidenct at 99% that the true mean for the reapir cost of refrigerators is between 144.677 and 155.323.

Step-by-step explanation:

1) Notation and definitions

n=60 represent the sample size

$\bar X= 150$ represent the sample mean

$s=15.5$ represent the sample standard deviation

m represent the margin of error

Confidence =99% or 0.99

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

2) Calculate the critical value tc

In order to find the critical value is important to mention that we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . The degrees of freedom are given by:

$df=n-1=60-1=59$

We can find the critical values in excel using the following formulas:

"=T.INV(0.005,59)" for $t_{\alpha/2}=-2.66$

"=T.INV(1-0.005,59)" for $t_{1-\alpha/2}=2.66$

The critical value $tc=\pm 2.66$

3) Calculate the margin of error (m)

The margin of error for the sample mean is given by this formula:

$m=t_c \frac{s}{\sqrt{n}}$

$m=2.66 \frac{15.5}{\sqrt{60}}=5.323$

4) Calculate the confidence interval

The interval for the mean is given by this formula:

$\bar X \pm t_{c} \frac{s}{\sqrt{n}}$

And calculating the limits we got:

$150 - 2.66 \frac{15.5}{\sqrt{60}}=144.677$

$150 + 2.66 \frac{15.5}{\sqrt{60}}=155.323$

The 99% confidence interval is given by ($144.677;$155.323)

We are confidenct at 99% that the true mean for the reapir cost of refrigerators is between 144.677 and 155.323.

7 0

3 years ago

How to find x using trigonometry

I am Lyosha [343]

Soh Cah Toa

Sine of the angle = opposite side over the hypotenuse

sin(42°) = 6.5/h
rearrange, solve for h
h = 6.5/sin(42°)
h = 9.7 cm

For the other triangle, the angle is unknown. I'd split it into two right triangles; down angle x since it is an isosceles it will be bisected into two equivalent triangles.

The hypotenuse we just found is now split in half. 9.7/2 = 4.9 base of the new smaller right triangle.

The new hypotenuse of the smaller triangle is 7.4 cm

Then you have..

sin(x/2) = 4.9/7.4
sin(x/2) = 0.67
use inverse sine function
arcSin(0.67) = x/2
41 = x/2
82° = x

There are many ways to solve this problem. This is just what I thought of first using trig.

3 0

3 years ago

Need help asap …………………………………..

nirvana33 [79]

Answer:

<em>7 </em> $\frac{5}{6}$

Step-by-step explanation:

- 2 $\frac{1}{3}$ - ( - 10 $\frac{1}{6}$ ) =

- 2 $\frac{1}{3}$ + 10 $\frac{1}{6}$ =

( - 2 + 10 ) + ( - $\frac{1}{3}$ + $\frac{1}{6}$ ) =

8 + $\frac{-2+1}{6}$ =

8 + ( - $\frac{1}{6}$ ) =

8 - $\frac{1}{6}$ = 7 + 1 - $\frac{1}{6}$ = 7 + $\frac{6-1}{6}$ = <em>7 </em> $\frac{5}{6}$

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2 years ago

Which of the following statements must be true about the diagram

Dovator [93]

Answer:

D ) x+y=w

Step-by-step explanation:

An exterior angle of a triangle is equal to the sum of the two opposite interior angles.

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3 years ago