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omeli [17]
3 years ago
10

The equation of the line that goes through the point ( 3 , 4 ) and is parallel to the line 3 x + 4 y = 2 can be written in the f

orm y = m x + b
Mathematics
1 answer:
Oksanka [162]3 years ago
7 0

Answer:

y = -3/4x + 7/4

Step-by-step explanation:

For it to be parallel it needs the same slope. We can find this by putting the equation 3x + 4y = 2 into y = mx + b form and using the m.

3x+4y=2 can be written as y= -3/4x + 1/2

so the m for our new equation is -3/4

now to find b we just plug in the given point

y = -3/4x + b

4 = -3/4(3) + b

b = 4 + (-9/4)

b = 7/4 or b = 1.75

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3 years ago
Each year, all final year students take a mathematics exam. It is hypothesised that the population mean score for this test is 1
Yuri [45]

Answer:

90% confidence interval for the population mean test score is [95.40 , 106.59]

Step-by-step explanation:

We are given that the population mean score for mathematics test is 115. It is known that the population standard deviation of test scores is 17.

Also, a random sample of 25 students take the exam. The mean score for this group is 101.

The, pivotal quantity for 90% confidence interval for the population mean test score is given by;

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

where, X bar = sample mean = 101

              \sigma = population standard deviation

              n = sample size = 25

So, 90% confidence interval for the population mean test score, \mu is ;

P(-1.6449 < N(0,1) < 1.6449) = 0.90

P(-1.6449 < \frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } } < 1.6449) = 0.90

P(-1.6449 * \frac{\sigma}{\sqrt{n} } < {Xbar-\mu} < 1.6449 * \frac{\sigma}{\sqrt{n} } ) = 0.90

P(X bar - 1.6449 * \frac{\sigma}{\sqrt{n} } < \mu < X bar + 1.6449 * \frac{\sigma}{\sqrt{n} } ) = 0.90

90% confidence interval for \mu = [ X bar - 1.6449 * \frac{\sigma}{\sqrt{n} } , X bar + 1.6449 * \frac{\sigma}{\sqrt{n} } ]

                                                  = [ 101 - 1.6449 * \frac{17}{\sqrt{25} } , 10 + 1.6449 * \frac{17}{\sqrt{25} } ]

                                                  = [95.40 , 106.59]

Therefore, 90% confidence interval for the population mean test score is [95.40 , 106.59] .

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3 years ago
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