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Sergio039 [100]
1 year ago
10

Condense the expression into a

Mathematics
1 answer:
liberstina [14]1 year ago
7 0

2(\log 18-\log 3)+\dfrac 12 \log \dfrac{1}{16}=2 \log \dfrac{18}{3}+\log \sqrt{\dfrac{1}{16}}\\=2 \log 6+\log \dfrac{1}{4}=\log 6^2+\log \dfrac{1}{4}=\log 36+\log \dfrac{1}{4}\\=\log \dfrac{36}{4}=\log 9

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The National Center for Education Statistics surveyed a random sample of 4400 college graduates about the lengths of time requir
Paha777 [63]

Answer:

95​% confidence interval for the mean time required to earn a bachelor’s degree by all college students is [5.10 years , 5.20 years].

Step-by-step explanation:

We are given that the National Center for Education Statistics surveyed a random sample of 4400 college graduates about the lengths of time required to earn their bachelor’s degrees. The mean was 5.15 years and the standard deviation was 1.68 years respectively.

Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;

                              P.Q. =  \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \bar X = sample mean time = 5.15 years

            \sigma = sample standard deviation = 1.68 years

            n = sample of college graduates = 4400

            \mu = population mean time

<em>Here for constructing 95% confidence interval we have used One-sample z test statistics although we are given sample standard deviation because the sample size is very large so at large sample values t distribution also follows normal.</em>

<u>So, 95% confidence interval for the population mean, </u>\mu<u> is ;</u>

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5%

                                               level of significance are -1.96 & 1.96}  

P(-1.96 < \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < 1.96) = 0.95

P( -1.96 \times {\frac{\sigma}{\sqrt{n} } } < {\bar X-\mu} < 1.96 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.95

P( \bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } } < \mu < \bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.95

<u>95% confidence interval for</u> \mu = [ \bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } } , \bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } } ]

                                              = [ 5.15-1.96 \times {\frac{1.68}{\sqrt{4400} } } , 5.15+1.96 \times {\frac{1.68}{\sqrt{4400} } } ]

                                             = [5.10 , 5.20]

Therefore, 95​% confidence interval for the mean time required to earn a bachelor’s degree by all college students is [5.10 years , 5.20 years].

8 0
3 years ago
A soccer league has 200 players. Of those players 50% are boys. How many boys are in the soccer league
Lelechka [254]
What's 200 minus 50 that's your answer simple
7 0
3 years ago
What is the value of f(2) for f(x)=2x5−8x4+3x3−4x2+9x−1?(1 point)
Yanka [14]

Answer:

-39

Step-by-step explanation:

just took the quick check

4 0
3 years ago
U0ukj787y8fr7hjhy7 which one
Sedbober [7]

If ABC and DEF are complementary, then the value of x will be,

90 - ABC = x

90 - 53 = x

x = 37°

5 0
2 years ago
Read 2 more answers
Find the following rates. Round your answer to the nearest hundredth. a. ? % of 75 = 5 b. ? % of 28 = 140 c. ? % of 100 = 40 d.
Nimfa-mama [501]
A.15 b.500 c.40 d.7.5 yeah, not to confident but I think it's correct.
5 0
3 years ago
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