PLEASE HELP!!! 20 POINTS! I WILL MARK BRAINLIEST ALSO IF CORRECT!!

1) A traditional die is a cube with each of its six sides representing the numbers from 1 to 6. Mr. Dicey customized a die by re

liraira [26]

Answer:

1) $\frac{2}{5}$

2) 49.225

3) $\frac{7}{2}$

Step-by-step explanation:

1) To find the expected value of the dice we can use the following equation:

$E(x)=x_{1}*P(x_{1})+x_{2}*P(x_{2})+...+x_{n}*P(x_{n})$

So in our problem the values x will be: 1/1, 1/2, 1/3, 1/4, 1/5 and 1/6 and the probavility for all values is 1/6 so the expected values will be: $E(x)=(\frac{1}{1} *\frac{1}{6}) +(\frac{1}{2} *\frac{1}{6}) +(\frac{1}{3} *\frac{1}{6})+(\frac{1}{4} *\frac{1}{6})+(\frac{1}{5} *\frac{1}{6})+(\frac{1}{6} *\frac{1}{6})$

$E(x)=0.167+0.083+0.056+0.042+0.033+0.028=0.409\approx \frac{2}{5}$

2) To find the variance of the expected values we can use the equation:

$Var(x)=\frac{\sum_{i=1}^{n}(x_{i}-\overline{x})^{2} }{n}$

So for our problem will be:

$Var(x)=\frac{(3-10.5)^2+(4-10.5)^2+(17-10.5)^2+(18-10.5)^2}{4}$

$Var(x)=\frac{56.25+42.25+42.25+56.25}{4}$ $Var(x)=\frac{196.9}{4}=49.225$

3) To find the expected value of the dice we can use the following equation:

$E(x)=x_{1}*P(x_{1})+x_{2}*P(x_{2})+...+x_{n}*P(x_{n})$

So in our problem the values x will be: 1, 2, 3, 4, 5 and 6 and the probavility for all values is 1/6 so the expected values will be: $E(x)=(1*\frac{1}{6}) +(2 *\frac{1}{6}) +(3 *\frac{1}{6})+(4 *\frac{1}{6})+(5 *\frac{1}{6})+(6 *\frac{1}{6})$

$E(x)=0.17+0.33+0.5+0.67+0.83+1=3.5\approx \frac{7}{2}$

7 0

3 years ago

Tennis balls are sealed in a pressurized container to maintain the rebound percentage

Darina [25.2K]

Answer:

Rounding the results to the next hundredth, we have:

Bounce 1: 2 * 0.55 = 1.10 meters

Bounce 2: 1.10 * 0.55 = 0.61 meters

Bounce 3: 0.61 * 0.55 = 0.34 meters

Bounce 4: 0.34 * 0.55 = 0.19 meters

Bounce 5: 0.19 * 0.55 = 0.10 meters

Bounce 6: 0.10 * 0.55 = 0.06 meters

Bounce 7: 0.06 * 0.55 = 0.03 meters

Step-by-step explanation:

Rebound percentage = 55% = 0.55

Bounce 1: 2 * 0.55 = 1.10 meters

Bounce 2: 1.10 * 0.55 = 0.605 meters

Bounce 3: 0.605 * 0.55 = 0.33275 meters

Bounce 4: 0.33275 * 0.55 = 0.1830125 meters

Bounce 5: 0.1830125 * 0.55 = 0.10065688 meters

Bounce 6: 0.10065688 * 0.55 = 0.05536128 meters

Bounce 7: 0.05536128 * 0.55 = 0.0304487 meters

Rounding the results to the next hundredth, we have:

Bounce 1: 2 * 0.55 = 1.10 meters

Bounce 2: 1.10 * 0.55 = 0.61 meters

Bounce 3: 0.61 * 0.55 = 0.34 meters

Bounce 4: 0.34 * 0.55 = 0.19 meters

Bounce 5: 0.19 * 0.55 = 0.10 meters

Bounce 6: 0.10 * 0.55 = 0.06 meters

Bounce 7: 0.06 * 0.55 = 0.03 meters

3 0

4 years ago

How do you do this question?

Colt1911 [192]

Step-by-step explanation:

A Maclaurin series is a Taylor series that's centered at 0.

f(x) = ∑ₙ₌₀°° f⁽ⁿ⁾(0) / n! xⁿ

If we substitute f⁽ⁿ⁾(0) = (n + 1)!:

f(x) = ∑ₙ₌₀°° (n + 1)! / n! xⁿ

f(x) = ∑ₙ₌₀°° (n + 1) xⁿ

Use ratio test to find the radius of convergence.

lim(n→∞)│aₙ₊₁ / aₙ│< 1

lim(n→∞)│[(n + 2) xⁿ⁺¹] / [(n + 1) xⁿ]│< 1

lim(n→∞)│(n + 2) x / (n + 1)│< 1

│x│< 1

R = 1

4 0

3 years ago

I need help answering questions like this can someone help

Leviafan [203]

Answer:

300 in.³

Step-by-step explanation:

We find the volume of 1 prism and multiply it by 2.

V = BH

where V = volume of prism, B = area of the base of the prism, H = height of the prism

V = ½bh × H

V = ½(5 in.)(6 in.) × 10 in.

V = 150 in.³

That is the volume of one triangular prism. Now we multiply it by 2.

volume = 2 × 150 in.³ = 300 in.³

4 0

3 years ago

The current temperature is 8 degrees fahrenheit. By how many degrees does the temperature need to change to reach 7 degrees fahr

trapecia [35]

Answer:

-8-7= 15

so the answer is 15

Step-by-step explanation:

6 0

3 years ago