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2 years ago

6

Suppose you want to estimate the proportion of traditional college students on your campus who own their own car. From research

on other college campuses, you believe the proportion will be near 20%. What sample size is needed if you wish to be 99% confident that your estimate is within 0.02 of the true proportion?

1 answer:

Lapatulllka [165]2 years ago

5 0

Answer:

2,655 students

Step-by-step explanation:

The z-score for a 99% confidence interval is z = 2.576

The standard error for a proportion p is:

$SE = z*\sqrt{\frac{p*(1-p)}{n} }$

For a proportion of p =0.20, in order to ensure a standard error of 0.02, the sample size 'n' must be:

$0.02 = 2.576*\sqrt{\frac{0.2*(1-0.2)}{n}}\\n=2,654.31$

Rounding up to the next whole student, the sample size needed is 2,655 students.

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Please solve this<br> (Rational numbers 8th grade)

pochemuha

Question # 1

Answer:

$\frac{-2}{3}\times \frac{3}{5}+\frac{5}{2}\times \frac{3}{5}\times \frac{1}{6}=-\frac{3}{20}$

Step-by-step explanation:

Given the expression

$\frac{-2}{3}\times \frac{3}{5}+\frac{5}{2}\times \frac{3}{5}\times \frac{1}{6}$

$=-\frac{2}{5}+\frac{5}{2}\times \frac{3}{5}\times \frac{1}{6}$ ∵ $\frac{-2}{3}\times \frac{3}{5}=-\frac{2}{5}$

$=-\frac{2}{5}+\frac{1}{4}$ ∵ $\frac{5}{2}\times \frac{3}{5}\times \frac{1}{6}=\frac{1}{4}$

$\mathrm{Least\:Common\:Multiplier\:of\:}5,\:4:\quad 20$

$=-\frac{8}{20}+\frac{5}{20}$

$\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}$

$=\frac{-8+5}{20}$

$\mathrm{Add/Subtract\:the\:numbers:}\:-8+5=-3$

$=\frac{-3}{20}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}$

$=-\frac{3}{20}$

Therefore,

$\frac{-2}{3}\times \frac{3}{5}+\frac{5}{2}\times \frac{3}{5}\times \frac{1}{6}=-\frac{3}{20}$

Question # 2

Answer:

$\frac{2}{5}\times \frac{-3}{7}-\frac{1}{6}\times \frac{3}{2}\times \frac{1}{14}\times \frac{2}{5}=-\frac{5}{28}$

Step-by-step explanation:

Given

$\frac{2}{5}\times \frac{-3}{7}-\frac{1}{6}\times \frac{3}{2}\times \frac{1}{14}\times \frac{2}{5}$

$=-\frac{6}{35}-\frac{1}{6}\times \frac{3}{2}\times \frac{2}{5}\times \frac{1}{14}$ ∵ $\frac{2}{5}\times \frac{-3}{7}=-\frac{6}{35}$

$=-\frac{6}{35}-\frac{1}{140}$ ∵ $\frac{1}{6}\times \frac{3}{2}\times \frac{1}{14}\times \frac{2}{5}=\frac{1}{140}$

$\mathrm{Least\:Common\:Multiplier\:of\:}35,\:140:\quad 140$

$=-\frac{24}{140}-\frac{1}{140}$

$\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}$

$=\frac{-24-1}{140}$

$\mathrm{Subtract\:the\:numbers:}\:-24-1=-25$

$=\frac{-25}{140}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}$

$=-\frac{25}{140}$

$\mathrm{Cancel\:the\:common\:factor:}\:5$

$=-\frac{5}{28}$

Therefore,

$\frac{2}{5}\times \frac{-3}{7}-\frac{1}{6}\times \frac{3}{2}\times \frac{1}{14}\times \frac{2}{5}=-\frac{5}{28}$

4 0

3 years ago

Darnell ran 550 yards in 3 minutes. At this rate, how many yards can he run in 6 minutes?

Elan Coil [88]

Answer:

Darnell can run 1100 yards in 6 minutes

Step-by-step explanation:

There are 2 ways you can solve this

Method 1: You would have to divide 550 by 3 which you would get about 183, (the exact answer is very long so I recommend using a calculator). Then you multiply that by 6 to get 1100.

Method 2: This one would probably be easier. Since 3 x 2 is 6 then you can multiply 550 x 2 to get 1100.

I hope this helps!

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2 years ago

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I have a hard time with fractions and I need help. <br><br> 6 2/3 × 5/6=

laila [671]

When you multiply fractions you want to make them a mixed number then multiply the two top numbers together and then the bottom two together. Basically 6 2/3 would become 20/3 x 5/6... then multiply 5 and 20 together and 3 and 6 together to get 100/18... simplify from there.

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2 years ago

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D) Vivek is 30 years younger than his father. After 10 years their ages will be in the ratio 1:2. Find their present ages.

tangare [24]

Answer:

I think Vivek is 20 and his father is 50

Because 30 + 30 equals 60 as he has to be half his age he'll be 30 but that's in 10 years time. you just subtract 30 and 60 by 10 and you'll get 20 and 50

6 0

2 years ago

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A living room will be painted with white trim. The ratio of the blue surface area between the walls is 1:10. Of 2 gallons of blu

bija089 [108]

Answer:

20 gallons

Step-by-step explanation:

The living room is made up of white trim and blue surface area between the walls. Since the ratio of the blue surface area between the walls to the white trim is given by 1 : 10.

Also 2 gallons of blue paints are used for the walls, let x represent the number of white paint used in gallons. Hence:

number of white paint in gallons = [1 / (1 + 10)] * total number of paints = 1 / 11 * total number of paints

2 = 1/11 * total number of paints used

total number of paints = 22 gallons

number of white paint (x) = [10 / (1 + 10)] * total number of paints = 1 / 11 * total number of paints

x = 10/11 * 22

x = 20 gallons

Therefore 20 gallons of white paint was used

7 0

2 years ago