Which lines can you conclude are parallel given that ? Justify your conclusion with a theorem.

A newsgroup is interested in constructing a 90% confidence interval for the proportion of all Americans who are in favor of a ne

Leto [7]

Answer:

The 90% confidence interval for the proportion of all Americans who are in favor of a new Green initiative is (0.6247, 0.6923).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

Of the 533 randomly selected Americans surveyed, 351 were in favor of the initiative.

This means that $n = 533, \pi = \frac{351}{533} = 0.6585$

90% confidence level

So $\alpha = 0.1$ , z is the value of Z that has a p-value of $1 - \frac{0.1}{2} = 0.95$ , so $Z = 1.645$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6585 - 1.645\sqrt{\frac{0.6585*0.3415}{533}} = 0.6247$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6585 + 1.645\sqrt{\frac{0.6585*0.3415}{533}} = 0.6923$

The 90% confidence interval for the proportion of all Americans who are in favor of a new Green initiative is (0.6247, 0.6923).

6 0

2 years ago

How many liters of a 10% antifreeze solution and a 40% antifreeze solution must be mixed to make 15 liters of a 25% solution? Ro

butalik [34]

Answer:

7.5 liters of a 10% antifreeze solution AND

7.5 liters of a 40% antifreeze solution

Step-by-step explanation:

According to the question,we were asked to find out how many liters of 10% anti freeze solution and 40% anti freeze each to make a 15 liters 25% mixture

Let’s call

the amount of liters needed of our 10% solution “x”. So, how

many liters do we need of the 40% solution? Well, there are 15

liters in total, x liters have been spoken for, so what remains

of our allotted 10 liters then, is 15-x.

Now let's solve for "x"

10% of x + 40% of (15 - x) = 25% of 15 liters

0.1x + 0.4(15 - x) = 0.25(15)

0.1x + 6 - 0.4x = 3.75

Collect the like terms and we have

0.3x = 2.25

x = 2.25 × 3

X = 7.5(Liters for the 10% anti freeze solution)

The 40% solution= 15 - 7.5 = 7.5 liters

Since "X" was used to fill for the unknown amount of 10% anti freeze solution,we have 7.5 liters of the 10% solution and another 7.5 liters for the 40% solution to end up with 15 liters of the desired 25% solution.

8 0

2 years ago

Wen takes a job with a starting salary of $100,000 for the first year. she earns a 3% increase each year. what does s5 represent

steposvetlana [31]

$S_{n} = \frac{ a_{1}(1- r^{n}) }{1-r}$ $a_{1} = 100000, r=1.03, n=5$
$S_{5} = \frac{100000(1- 1.03^{5}) }{1-1.03} = \frac{100000(-.159)}{-.03} =530,000$

So after 5 years she is making $530,000.

Hope that helps

8 0

3 years ago

Read 2 more answers

Complete the pattern. 3, 9, 27, 81, _, _,<br><br><br>Thank you!

fiasKO [112]

Answer:

243 then 729

Step-by-step explanation:

each number is being multipled by 3.

3 0

2 years ago

Helpppp ill mark u as brainlist

ollegr [7]

Answer:

a and c

Step-by-step explanation:

5 0

2 years ago