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marishachu [46]
2 years ago
7

A professor at a university wants to estimate the average number of hours of sleep the students get during exam week. The profes

sor wants to find a sample mean that is within 4.266 hours of the true average for all college students at the university with 99% conconfidence. If the professor knows the standard deviation of the sleep times for all college students is 2.539, what sample size will need to be taken
Mathematics
1 answer:
balandron [24]2 years ago
6 0

Answer:

The sample size is n = 2

Step-by-step explanation:

From the question we are told that

   The margin of error is  E =4.266

    The standard deviation is  \sigma = 2.539

From the question we are told the confidence level is  99% , hence the level of significance is    

      \alpha = (100 - 99 ) \%

=>   \alpha = 0.01

Generally from the normal distribution table the critical value  of  \frac{\alpha }{2} is  

   Z_{\frac{\alpha }{2} } =  2.58

Generally the sample size is mathematically represented as  

   n = [\frac{Z_{\frac{\alpha }{2} } *  \sigma }{E} ] ^2

=>  n = [\frac{2.58  *  2.539  }{4.266} ] ^2

=>  n = 2

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What is the measure of m<1 will ensure that the rail is parallel to the bottom of the staircase?
cricket20 [7]

You can observe that angle 1 and angle with 47° are inside a parallelogram.

Consider that the sum of the internal angles of a parallelogram is 360°.

Moreover, consider that the angle at the top right of the parallogram is congruent with the angle of 47°, then, such an angle is if 47°.

Consider that angle down right side is congruent with angle 1, then, they have the same measure.

You can write the previous situation in the following equation:

47 + 47 + ∠1 + ∠1 = 360 simplify like terms

94 + 2∠1 = 360 subtract both sides by 94

2∠1 = 360 - 94

2∠1 = 266 divide by 2 both sides

∠1 = 266/2

∠1 = 133

Hence, the measure of angle 1 is m∠1 = 133°

6 0
11 months ago
I need help with this question asap
Nataly_w [17]

Answer:

The correct answer would be the bottom equation.

Step-by-step explanation:

y=7.25x

y=7.25(3)

y=21.75

y=7.25(4)

y=29.00

y=7.25(5)

y=36.25

7 0
3 years ago
For which value of x is the equation 4x + 24 = 8x + 2x true?
Paha777 [63]

Answer:

x=4

Step-by-step explanation:

4x+24=8x+2x

4x+24=10x

-4x     -4x

24=6x

/6   /6

x=4

3 0
3 years ago
The system of equations below represents p, the number of photo files, and v, the number of video files Helena uploaded to an on
ss7ja [257]
P + v = 650....p = 650 - v
4p + 9v = 2925

4(650 - v) + 9v = 2925
2600 - 4v + 9v = 2925
-4v + 9v = 2925 - 2600
5v = 325
v = 325/5
v = 65.....video files

p + v = 650
p + 65 = 650
p = 650 - 65
p = 585....photo files

answer : Helena uploaded 9 times as many photo files as video files
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5 0
3 years ago
Read 2 more answers
Sheila, janice, and katen, working together at the same rate, can complete a job in 3 1/3 days. Working at the same rate, how mu
pychu [463]

Answer:

Janice and Karen could do in 1 day:

  • <u>20% of the job</u>.

Step-by-step explanation:

To identify how much of the job could janice and caren do in 1 day, first, we must find how much of the job make just 1 person at the same rate:

If three persons make a job in 3 1/3 days, 1 person make the job in x:

  • 3 persons ⇒ 3 1/3 days or 10/3 days
  • 1 person ⇒ x

Then:

  • x=\frac{1 person*\frac{10}{3}days }{3 persons} (we cancel the unit "persons")
  • x=\frac{\frac{10}{3}days }{3}
  • x = 10 days

Just a person would need 10 days to complete a job, now, we're gonna divide this value in 2 to obtain the time that need two persons to complete a job:

  • Time to complete a job between 2 persons = \frac{10}{2}days
  • Time to complete a job between 2 persons = 5 days

How two persons need 5 days to complete a job (in this case, the two persons are Janice and Karen), we can make a simple rule of three to obtain the percentage made in 1 day:

  • 5 days ⇒ 100% of a job
  • 1 day ⇒ x

Then:

  • x=\frac{1*100}{5} (you can use the % if you want, the result is the same)
  • x=\frac{100}{5}
  • x=20

As you can see, <u><em>Janice and Karen just in a day could do 20% of the job</em></u>.

3 0
2 years ago
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