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s2008m [1.1K]
2 years ago
15

A group of friends were working on a student film. They spent all their budget on costumes and equipment. They spent $396 on cos

tumes, and 45% of the total budget on equipment. What was the total budget for their student film?
Mathematics
1 answer:
PtichkaEL [24]2 years ago
6 0

Answer:

The total budget for their student film was $720.

Step-by-step explanation:

From the information given, you know that they spent all their budget on costumes and equipment and that they spent 45% of the total budget on equipment. From this, you could inferred that in order to find the percentage they spent on costumes you have to subtract 45% from 100% that would indicate the total amount spent:

100%-45%=55%

According to this, you know that they spent 55% of the total budget on costumes and the statement says that the amount was $396. With this information, you can use a rule of three to find the amount that represents 100%:

396 →  55%

 x    ← 100%

x=(396*100)/55=720

The answer is that the total budget for their student film was $720.

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You roll a number cube 20 times. Which scenario is least likely?
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Answer:

you won't roll the same number 5 times

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2 years ago
The following data were collected from 12 rain gauges in a park. Build a 95% CI for the mean rainfall at the park.
dybincka [34]

Answer:

Critical values:t_{\alpha/2}=-2.201 t_{1-\alpha/2}=2.201

95% confidence interval would be given by (3.646;4.472)

Step-by-step explanation:

1) Previous concepts

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".

The data is:

4.65 3.89 2.73 4.35 3.80 4.86 4.33 4.37 4.76 4.05 3.05 3.87

2) Compute the sample mean and sample standard deviation.

In order to calculate the mean and the sample deviation we need to have on mind the following formulas:  

\bar X= \sum_{i=1}^n \frac{x_i}{n}

s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}

=AVERAGE(4.65,3.89,2.73, 4.35, 3.8, 4.86, 4.33, 4.37, 4.76, 4.05, 3.05, 3.87)

On this case the average is \bar X= 4.059

=STDEV.S(4.65,3.89,2.73, 4.35, 3.8, 4.86, 4.33, 4.37, 4.76, 4.05, 3.05, 3.87)

The sample standard deviation obtained was s=0.6503

3) Find the critical value t* Use the formula for a CI to find upper and lower endpoints

In order to find the critical value we need to take in count that our sample size n =12 <30 and on this case 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 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. The degrees of freedom are given by:

df=n-1=12-1=11

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

"=T.INV(0.025,11)" for t_{\alpha/2}=-2.201

"=T.INV(1-0.025,11)" for t_{1-\alpha/2}=2.201

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}  

And we can use Excel to calculate the limits for the interval

Lower interval : "=4.059 -2.201*(0.6503/SQRT(12))" =3.646

Upper interval :  "=4.059 +2.201*(0.6503/SQRT(12))" =4.472

So the 95% confidence interval would be given by (3.646;4.472)

8 0
3 years ago
The diameter of a wheel of a car is 0.75 m. if the car travels at an average speed of 14 m/s, find the
raketka [301]

Step-by-step explanation:

Circumference of wheel = πd = 0.75πm.

How far the car travels per minute

= 60s * (14m/s) = 840m.

Hence number of revolutions per minute

= 840m / 0.75πm

= 356.507....

= 357. (nearest whole number)

6 0
3 years ago
Which step is the same in the construction of parallel lines and the construction of a perpendicular line through a point on the
madam [21]

Answer:

D.Place the compass on a point on the original line.

Complete Question:

A.Create only one arc that intersects the original line.

B.Create two arcs that intersect the original line.

C.Place the compass on a point off the original line.

D.Place the compass on a point on the original line.

Step-by-step explanation:

* Lets revise the steps of constructing parallel lines and a perpendicular line through a point on the line

<em># Contracting parallel lines</em>

- Given: Line AB and point P not on AB

1. Draw a slant line through point P and intersects AB at point C, this line is the transversal of the parallel lines

2.<u> Place the pin of the compass at point C</u> and draw an arc intersects AB at D and CP at E

3. Without changing the distance of the compass put the pin of the compass on point P and draw an arc intersects CP at point Q

4. Use the compass to measure the distance from D to E and place the pin of the compass at point Q and draw an arc intersects the arc from P to CP at point U

5. Join P and U by a line this line is parallel to AB

<em># Constructing a perpendicular line through a point on the line</em>

- Given line AB and point P lies on it

1. <u>Place your compass pin at P </u>and draw an arc of any size below AB that crosses the line twice at points C and D

2. Stretch the compass to a larger distance

3.<u> </u>Place the compass pin on point C<u> </u>and draw a small arc above the line

4. Without changing the distance of the compass place the compass pin on point D and draw another arc intersects the arc from C at point E

5. Using a straightedge, join P and E where PE is perpendicular to AB

*<em> Lets find the same steps in the constructions</em>

∵ In first construction we put the pin of the compass at point C which  lies in the original line AB

∵ In second construction we put the pin of the compass at point P which lies in the original line AB

∴ The common step is:  <em><u>"Place the compass on a point on the original line"</u></em>

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