Convert 51.7% to a fraction in simplest form and a decimal.

Answers

Answer 1

Answer: 0.517 as a decimal 517/10 as a fraction

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A random survey of teachers found that 224 of 395 elementary school teachers, and 126 of 266 high school teachers, were very satisfied with their work. Find a 95% confidence interval for the difference (elementary minus high school) in proportions of teachers who are very satisfied with their work.

Answers

Answer: 95% confidence interval would be (0.013,0.167).

Step-by-step explanation:

Since we have given that

survey of teachers found that 224 of 395 elementary school teachers,

So, n₁ = 395

x₁ = 224

So, $p_1=(224)/(395)=0.567$

n₂ = 266

x₂ = 126

So, $p_2=(x_2)/(n_2)=(126)/(266)=0.473$

At 95% confidence level, z = 1.96

So, interval would be

$(p_1-p_2)\pm z\sqrt{((p_1(1-p_1))/(n_1)+(p_2(1-p_2))/(n_2)}}\n\n=(0.567-0.473)\pm 1.96\sqrt{(0.567* 0.433)/(395)+(0.527* 0.473)/(266)}}\n\n=0.09\pm 1.96* 0.0394\n\n=0.09\pm 0.077\n\n=(0.09-0.077,0.09+0.077)\n\n=(0.013,0.167)$

Hence, 95% confidence interval would be (0.013,0.167).

(3x^5-8x^4-10x^2+4x) divided by (2x^3)

Answers

Answer: 3x^4-8x^3-10x+4x/2x^2

Step-by-step explanation: JUST SOLVE IT

Find all solutions of the equation algebraically. Check your solutions. (Enter your answers as a comma-separated list x^4-7x^2-144=0

Answers

Answer:

The solutions are: $x=4,\:x=-4,\:x=3i,\:x=-3i$

Step-by-step explanation:

Consider the provided equation.

$x^4-7x^2-144=0$

Substitute $u=x^2\mathrm{\:and\:}u^2=x^4$

$u^2-7u-144=0$

$u^2-16u+9u-144=0$

$(u-16)(u+9)=0$

$u=16,\:u=-9$

Substitute back $\:u=x^2$ and solve for x.

$x^2=16\nx=√(16)\n \quad x=4,\:x=-4$

$x^2=-9\nx=√(-9)\n \quad x=3i,\:x=-3i$

Hence, the solutions are: $x=4,\:x=-4,\:x=3i,\:x=-3i$

Check:

Substitute x=4 in provided equation.

$4^4-7(4)^2-144=0$

$256-112-144=0$

$0=0$

Which is true.

Substitute x=-4 in provided equation.

$(-4)^4-7(-4)^2-144=0$

$256-112-144=0$

$0=0$

Which is true.

Substitute x=3i in provided equation.

$(3i)^4-7(3i)^2-144=0$

$81+63-144=0$

$0=0$

Which is true.

Substitute x=-3i in provided equation.

$(-3i)^4-7(-3i)^2-144=0$

$81+63-144=0$

$0=0$

Which is true.

John ordered five large size pizzas for a party. Five kids each ate 1/10 slice, and twelve adults each at 3/10 slices.a) Find the total number of slices consumed.
41/10
b) Find the leftover pizza if any.

Answers

Answer:

a) 4 1/10 slices eaten

b) cannot be solved because we don't know how many slices in each pizza

Step-by-step explanation:

5*1/10=5/10

12*3/10=36/10

36/10+5/10=41/10

41/10=4 1/10 slices

40% as fraction and decimal

Answers

Answer:

40% as a decimal is 0.4

40% as a fraction is 2/5

Step-by-step explanation:

Let's go over each of these step by step.

First, let's see 40% as a fraction.

Since 40% is out of 100%, we can rewrite that as 40/100.

If you want to simplify it, let's do the following.

40/100

Divide both sides by 20, and you'll end up with:

2/5.

Now, let's do 40% as a decimal.

This is pretty simple.

40% is 40/100 as said before, and to find it as a decimal,

let's divide 40 and 100.

40 divided by 20 = 0.4

Therefore, we can conclude the following:

40% as a fraction is 40/100, or 2/5.

40% as a decimal is 0.4

Hope this helped! :)

8 POINTS WILL BE GIVEN!!

Answers

24° because it says x=24° have a nice day :)

Answer:

x=39 degrees

Step-by-step explanation:

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Which of the following values cannot be probabilities? 0.04, 5 divided by 3, 1, 0, 3 divided by 5, StartRoot 2 EndRoot, negative 0.59, 1.49 Select all the values that cannot be probabilities. A. 1.49 B. 1 C. three fifths D. StartRoot 2 EndRoot E. five thirds F. 0 G. negative 0.59 H. 0.04

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I have no idea what I am doing. Here is one of my problems, A gas station sells 1500 gallons of gasoline per hour if it charges $ 2.10 per gallon but only 1300 gallons per hour if it charges $ 2.95 per gallon. Assuming a linear model(a) How many gallons would be sold per hour of the price is $ 2.70 per gallon?(b) What must the gasoline price be in order to sell 800 gallons per hour?(c) Compute the revenue taken at the four prices mentioned in this problem -- $ 2.10, $ 2.70, $ 2.95 and your answer to part (b). Which price gives the most revenue?