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3 years ago

5

Find the measure Of K

1 answer:

Mariana [72]3 years ago

7 0

Answer:

K = 10

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp/ hyp

sin K = 11 / 61

Taking the inverse sin of each side

sin ^-1 ( sin K) = sin ^-1 (11/61)

K =10.38885782

K = 10

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Two independent samples of sizes 20 and 30 are randomly selected from two normally distributed populations. Assume that the popu

aleksley [76]

Answer:

b. Student-t with 48 degrees of freedom

Step-by-step explanation:

For this case we need to use a Two Sample t Test: equal variances.

Assumptions

When running a two-sample equal-variance t-test, the basic assumptions are "that the distributions of the two populations are normal, and that the variances of the two distributions are the same".

Let $\bar x$ and $\bar y$ be the sample means of two sets of data of size $n_x$ and $n_y$ respectively. We assume that the distribution's of x and y are:

$x \sim N(\mu_x ,\sigma_x =\sigma)$

$y \sim N(\mu_y ,\sigma_y=\sigma)$

Both are normally distributed but without the variance equal for both populations.

The system of hypothesis can be:

Null hypothesis: $\mu_x =\mu_y$

Alternative hypothesis: $\mu_x \neq \mu_y$

We can define the following random variable:

$t=\frac{(\bar x -\bar y)-(\mu_x -\mu_y)}{s\sqrt{\frac{1}{n_x}+\frac{1}{n_y}}}$

The random variable t is distributed $t \sim t_{n_x +n_y -2}$ , with the degrees of freedom $df=n_x +n_y -2= 20+30-2=48$

And the pooled variance can be founded with the following formula:

$s^2=\frac{(n_x -1)s_x^2 +(n_y-1)s_y^2}{n_x +n_y -2}$

So on this case the best answer would be :

b. Student-t with 48 degrees of freedom

5 0

3 years ago

In 2000, the world population 6.08 billion and was increasing at a rate of 1.5% each year.

serg [7]

Answer:

7.8 billion

Step-by-step explanation:

<u>Given:</u>

Initial population = 6.08 billion
Increase rate = 1.5% or 0.015 times per year

Time passed = 2017 - 2000 = 17 years

<u>Population in 2017:</u>

P = 6.08*(1 + 0.015)^17 = 7.8 billion

5 0

3 years ago

540 divided by 3 in area model

lubasha [3.4K]

Answer:

180

Step-by-step explanation:

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3 years ago

Think about a standard deck of 52 playing cards. Which of the following events is mutually exclusive?

Shtirlitz [24]

Answer:

1.) Drawing a king or a queen.

Step-by-step explanation:

1.) Drawing a king or a queen.

You cannot get a king and a queen at the same time= mutually exclusive

2.) Drawing a club or a black card.

King of clubs is both a club and a black card

3.) Drawing a king or a heart.

king of hearts is both a heart and a king

4.) Drawing a face card or a heart

queen of hearts is a heart and a face card

7 0

4 years ago

A survey of a group of seventh-graders and a group of teachers at a local middle school asked how many siblings they each have.

adelina 88 [10]

Answer:

there both different the only same number is four

Step-by-step explanation:

7 0

3 years ago