Simplify the given expression. Write your answer with positive exponents.

A school district is considering a change that would involve switching the daily start times for its elementary and

aleksklad [387]

Using the Central Limit Theorem, it is found that each random sample must have at least 10 parents supporting the change and 10 opposing.

<h3>What does the Central Limit Theorem state?</h3>

It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1 - p)}{n}}$ , as long as $np \geq 10$ and $n(1 - p) \geq 10$ .

For the test hpyothesis, two conditions are needed:

Random samples.

The sampling distribution must be approximately normal.

Hence each random sample must have at least 10 parents supporting the change and 10 opposing.

More can be learned about the Central Limit Theorem at brainly.com/question/24663213

4 0

3 years ago

PLEASE HELP! Is the following trinomial factorable why or why not h=-4(4t^(2)-9t+2)

sineoko [7]

Answer:

h = -4(t - 2)(4t - 1)

Step-by-step explanation:

Given trinomial

h= -4(4t² - 9t + 2)

Let's try to factor 4t² - 9t + 2

First find it's zeros:

t = (9 ± √9² - 4*4*2)/(2*4)
t = (9 ± √81 - 32)/8
t = (9 ± 7)/8
t = 2 and t = 1/4

So yes, it is factorable:

4t² - 9t + 2 = 4(t - 2)(t - 1/4)
or
4t² - 9t + 2 = (t - 2)(4t - 1)

The given trinomial factored:

h = -4(t - 2)(4t - 1)

7 0

3 years ago

Read 2 more answers

Mark spins a spinner 25 times. He spins a BLUE 12 times. How many times would he expect to get the color BLUE if he did 100 spin

lina2011 [118]

D. 48.
100 / 25 = 4
4 x 12 = 48 ! (:

8 0

3 years ago

A skier has decided that on each trip down a slope, she will do 2 more jumps than before. On her first trip she did 6 jumps. Der

elixir [45]

The correct answers are:

$\Sigma_{n=4}^{12} 6+2(n-1) \\ \\=180$

Explanation:

Since she is adding two more jumps every time she goes down hill, this is an arithmetic sequence. The general form of an arithmetic sequence is

$a_n=a_1+d(n-1), \\ \text{where } a_n \text{represents the nth term, } a_1 \text{represents the first term, and n represents the term number}$

Since we want the number of jumps on her 4th through 12th trips, we will set n in the summation from 4 to 12. n=4 goes at the bottom of Σ and 12 goes at the top, to represent the values we are interested in.

Beside this, we write our general form. The first term is 6 and d, the common difference, is 2. This gives us 6+2(n-1) beside the summation:

$\Sigma_{n=4}^{12} 6+2(n-1)$

To evaluate this, we substitute the values 4, 5, 6, 7, 8, 9, 10, 11 and 12 in for n, adding all of the values together:

6+2(4-1)+6+2(5-1)+6+2(6-1)+6+2(7-1)+6+2(8-1)+6+2(9-1)+6+2(10-1)+6+2(11-1)+6+2(12-1)

=6+6+6+8+6+10+6+12+6+14+6+16+6+18+6+20+6+22

=180

8 0

3 years ago

Read 2 more answers

A student drew a circle and two secant segment. He concluded that if PQ ~= PS, Then QR ~= ST. Do you agree with the student’s co

9966 [12]

Answer:

Yes

Step-by-step explanation:

You can get there a couple of ways. One makes use of the secant rules that tell you ...

PQ × PR = PS × PT

Substituting for PR and PT, you have ...

PQ × (PQ + QR) = PS × (PS + ST)

PQ² + PQ×QR = PS² + PS×ST

Substituting PQ for PS everywhere, we have ...

PQ² + PQ×QR = PQ² + PQ×ST

Dividing by PQ gives ...

PQ + QR = PQ + ST

and subtracting PQ leads us to the conclusion ...

QR = ST

_____

Another way to look at it is to draw the chord QS. Then ΔQPS is an isosceles triangle, and the perpendicular bisector of QS bisects ∠P and also goes through the circle center. Then the figure is symmetrical about that diameter secant, making QR ≅ ST.

6 0

3 years ago