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3 years ago

Answer with explanation I will and rate on the feedback. Will mark brainliest too

Mathematics

1 answer:

yarga [219]3 years ago

6 0

Answer: 6.6

Step-by-step explanation:

We have two triangles. Find the hypothenuse of the first triangle to make it easier to solve the second triangle.

First triangle:

a = 6

b = 8

c = ?

Use pythagorean's theorem

$c^2=a^2+b^2\\c=\sqrt{a^2+b^2}$

$c=\sqrt{(6)^2+(8)^2}\\ c=\sqrt{36+64}\\ c=\sqrt{100}\\ c=10$

This hypothenuse is valid for both triangles. Having said this, we already have 2 sides of the second triangle; c and a. We need to find b.

$c^2=a^2+b^2\\b^2=c^2-a^2\\b=\sqrt{c^2-a^2}$

$b=\sqrt{(12)^2-(10)^2}\\ b=\sqrt{144-100}\\ b=\sqrt{44}\\ b=6.6$

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The mean SAT score in mathematics, M, is 600. The standard deviation of these scores is 48. A special preparation course claims

kupik [55]

Answer:

Step-by-step explanation:

The mean SAT score is $\mu=600$ , we are going to call it \mu since it's the "true" mean

The standard deviation (we are going to call it $\sigma$ ) is

$\sigma=48$

Next they draw a random sample of n=70 students, and they got a mean score (denoted by $\bar x$ ) of $\bar x=613$

The test then boils down to the question if the score of 613 obtained by the students in the sample is statistically bigger that the "true" mean of 600.

- So the Null Hypothesis $H_0:\bar x \geq \mu$

- The alternative would be then the opposite $H_0:\bar x < \mu$

The test statistic for this type of test takes the form

$t=\frac{| \mu -\bar x |} {\sigma/\sqrt{n}}$

and this test statistic follows a normal distribution. This last part is quite important because it will tell us where to look for the critical value. The problem ask for a 0.05 significance level. Looking at the normal distribution table, the critical value that leaves .05% in the upper tail is 1.645.

With this we can then replace the values in the test statistic and compare it to the critical value of 1.645.

$t=\frac{| \mu -\bar x |} {\sigma/\sqrt{n}}\\\\= \frac{| 600-613 |}{48/\sqrt(70}}\\\\= \frac{| 13 |}{48/8.367}\\\\= \frac{| 13 |}{5.737}\\\\=2.266\\$

<h3>since 2.266>1.645 we can reject the null hypothesis.</h3>