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enot [183]
3 years ago
10

Suppose we want a 90% confidence interval for the average amount spent on entertainment (movies, concerts, dates, etc.) by fresh

man in their first semester at a large university. The interval is to have a maximum bound on the error (or simply margin of error) of $2, and the amount spent has a normal distribution with a known standard deviation $30. The number of observations required is at least
Mathematics
1 answer:
katovenus [111]3 years ago
6 0

Answer:

609

Step-by-step explanation:

Standard deviation = \sigma = $30

Margin of error = E = $2

Confidence level = 90%

Since the distribution is said to be normal, we will use z scores to solve this problem.

The z score for 90% confidence level = z = 1.645

Sample size= n = ?

The formula to calculate the margin of error is:

E=z\frac{\sigma}{\sqrt{n}}\\\\\sqrt{n}=z\frac{\sigma}{E}\\\\n=(\frac{z\sigma}{E} )^{2}

Using the values in above equation, we get:

n=(\frac{1.645 \times 30}{2} )^{2}\\\\ n = 608.9

This means, the minimum number of observations required is 609

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18 POINTS--SHOW WORK
Oksi-84 [34.3K]

Answer:

14 in 19

Step-by-step explanation:

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13+6

7 0
3 years ago
Solve the following quadratic equations using factoring.<br><br> b. x2 + 3x = 70
Katarina [22]

We can easily silve it by splitting the middle term or by using the discriminate method *

<h3>* <u>splitting</u></h3>

x 2 +3x -70

x2 + 10x - 7x -70

x(x + 10) -7(x +10)

(x / 7) ( x + 10)

x = 7 or -10

6 0
3 years ago
Suppose the radius of the sphere is increasing at a constant rate of 0.3 centimeters per second. At the moment when the radius i
elixir [45]
<h2>At the moment when the radius is 24 centimeters, the volume is increasing at a rate of 2171.47 cm³/min.</h2>

Step-by-step explanation:

We have equation for volume of a sphere

             V=\frac{4}{3}\pi r^3

where r is the radius

Differentiating with respect to time,

            \frac{dV}{dt}=\frac{d}{dt}\left (\frac{4}{3}\pi r^3 \right )\\\\\frac{dV}{dt}=\frac{4}{3}\pi \times 3r^2\times \frac{dr}{dt}\\\\\frac{dV}{dt}=4\pi r^2\times \frac{dr}{dt}

Given that

           Radius, r = 24 cm

           \frac{dr}{dt}=0.3cm/s

Substituting

           \frac{dV}{dt}=4\pi r^2\times \frac{dr}{dt}\\\\\frac{dV}{dt}=4\pi \times 24^2\times 0.3\\\\\frac{dV}{dt}=2171.47cm^3/min

At the moment when the radius is 24 centimeters, the volume is increasing at a rate of 2171.47 cm³/min.

4 0
3 years ago
Can someone please help me with this. please &amp; thank you !
Kryger [21]
From the first picture, the triangle can be redrawn. It is an isosceles triangle.
The base angles of an isosceles triangle are angle. Hence, angle A = angle C = 56°.

Note that: angle À + angle B + angle C = 180° (sum of angles in a triangle)
56 + B + 56 = 180°
B + 112° = 180°
B = 180° - 112°
B = 68°

4 0
4 years ago
Read 2 more answers
The length and width of a book cover are 22.2 centimeters and 12 centimeters respectively. The actual length (and width) can be
expeople1 [14]

Part (a)

The length is supposed to be 22.2 cm, but it could be 0.3 cm less

So 22.2 - 0.3 = 21.9 cm is the smallest value for the length. This is the lower bound of the length.

The upper bound is 22.2 + 0.3 = 22.5 cm as it is the largest the length can get.

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

Use this for the width as well

The width is supposed to be 12 cm, but it could be as small as 12-0.3 = 11.7 cm and as large as 12+0.3 = 12.3 cm

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

<h3>Answers:</h3>
  • smallest length = 21.9 cm
  • largest length = 22.5 cm
  • smallest width = 11.7 cm
  • largest width = 12.3 cm

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

Part (b)

Use the smallest length and width to get the smallest possible area

smallest area = (smallest width)*(smallest length) = 11.7*21.9 = 256.23

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

Repeat the same idea but for the largest length and width to get the largest possible area

largest area = (largest width)*(largest length) = 12.3*22.5 = 276.75

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

<h3>Answers:</h3>
  • smallest area = 256.23 square cm
  • largest area = 276.75 square cm
7 0
3 years ago
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