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3 years ago

Jk=8x+6 and kL=6x+20 Find JL

Mathematics

1 answer:

mr Goodwill [35]3 years ago

3 0

Jk=8x+6
J=(8x+6)/k

kL=6x+20
L=(6x+20)/k

JL=(8x+6)/k * (6x+20)/k
=(48x²+196x+120)/k²

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In parallelogram EFGH, the measure of angle G is (4x + 16)° and the measure of angle H is (2x − 16)°. What is the measure of ang

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m∠H = 44°

Step-by-step explanation:

Consecutive angles of a parallelogram are supplementary. So,

∠H and ∠G are supplementary

4x + 16 + 2x - 16 = 180

6x = 180

x = 30

m∠H = 2x - 16 = 2(30) - 16 = 60 - 16 = 44°

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A 95% confidence interval estimate of the mean number of hours a legal professional works on a typical workday is [7.44 hours, 10.56 hours].

Step-by-step explanation:

We are given that x is normally distributed with a known standard deviation of 12.6.

A sample of 250 legal professionals was surveyed, and the sample's mean response was 9 hours.

Firstly, the pivotal quantity for finding the 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 average mean response = 9 hours

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$\mu$ = mean number of hours a legal professional works

Here for constructing a 95% confidence interval we have used One-sample z-test statistics as we know about population standard deviation.

So, 95% confidence interval for the population mean, $\mu$ is ;

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

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

= [ $9-1.96 \times {\frac{12.6}{\sqrt{250} } }$ , $9+1.96 \times {\frac{12.6}{\sqrt{250} } }$ ]

= [7.44 hours, 10.56 hours]

Therefore, a 95% confidence interval estimate of the mean number of hours a legal professional works on a typical workday is [7.44 hours, 10.56 hours].

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