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3 years ago

Help asap pleaseee ?:)

Mathematics

1 answer:

igomit [66]3 years ago

4 0

2 and 3 are correct. 1 is false because the graph opens downward. If the a value, which is -1 in this case, is less than 0, the graph will open downward. -1 is less than 0 so the graph opens downward

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Given the following discrete uniform probability distribution, find the expected value and standard deviation of the random vari

romanna [79]

Answer:

$E(x) = 4.500$ --- Expected value

$SD(x) = 2.872$ --- Standard deviation

Step-by-step explanation:

Given

$\begin{array}{ccccccccccc}x & {0} & {1} & {2} & {3} & {4}& {5} & {6} & {7} & {8} & {9} \ \\ P(X=x) & {\frac{1}{10}} & {\frac{1}{10}} & {\frac{1}{10}} & {\frac{1}{10}} & {\frac{1}{10}}& {\frac{1}{10}} & {\frac{1}{10}} & {\frac{1}{10}} & {\frac{1}{10}} & {\frac{1}{10}} \ \end{array}$

Solving (a): Expected value

This is calculated using:

$E(x) = \sum\limits^{9}_{i=0} x_i * P(X = x_i)$

Since they all have the same probability, the formula becomes:

$E(x) = \frac{1}{10}\sum\limits^{9}_{i=0} x_i$

$E(x) = \frac{1}{10}(0+1+2+3+4+5+6+7+8+9)$

$E(x) = \frac{1}{10}*45$

$E(x) = \frac{45}{10}$

$E(x) = 4.500$

Solving (b): Standard Deviation

First, we calculate the variance using

$Var(x) = E(x^2) - (E(x))^2$

In (a), we have:

$E(x) = 4.500$

$E(x^2)$ is calculated as:

$E(x^2) = \sum\limits^{9}_{i=0} x_i^2 * P(X = x_i)$

Since they all have the same probability, the formula becomes:

$E(x^2) = \frac{1}{10}\sum\limits^{9}_{i=0} x_i^2$

So, we have:

$E(x^2) = \frac{1}{10}(0^2+1^2+2^2+3^2+4^2+5^2+6^2+7^2+8^2+9^2)$

Using a calculator

$E(x^2) = \frac{1}{10}(285)$

$E(x^2) = 28.5$

So:

$Var(x) = E(x^2) - (E(x))^2$

$Var(x) = 28.5 - 4.5^2$

$Var(x) = 28.5 - 20.25$

$Var(x) = 8.25$

The standard deviation is then calculated as:

$SD(x) = \sqrt{Var(x)}$

$SD(x) = \sqrt{8.25}$

$SD(x) = 2.872$ ---- approximated

3 0

3 years ago

Joseph has started completing the square on the equation 3x^2-7x+12=0. He has worked to the point where he has the expression x^

Dima020 [189]

Starting with 3x^2-7x+12=0, we divide all four terms by 3, resulting in the following factored form:

3(x^2-[7/3]x+4)=0.

Since 3 cannot equal 0, we can focus on the following:

x^2 - 7/4 x =-4

This completes the assignment (describe Joe's steps up to this point).

If you wish to go further:

Next, take HALF of the coefficient of x and square your result:

(-7/[4][2])^2 = 49/64

Add this to both sides of x^2 - 7/4 x =-4: x^2 - 7/4x + 49/64 =-4+49/64

Rewrite the left side as (x-7/8)^2 and the right side as 49/64 - 256/64

Simplify the right side by combining these terms: -207/64

Then x-7/8 = plus or minus (1/8)sqrt(-207)

Next, x = 7/8 plus or minus (1/8)*i*√207, or

7 plus or minus i*√207
x = ----------------------------------
8

4 0

3 years ago

A bag of snack mix weighs 12 ounces. A serving size is 3/4

Talja [164]

Answer:

16 servings and 1920 calories in 1 snack bag

Step-by-step explanation:

12 ounces divided by 3/4 = 16 servings

120 calories/servings x 16 servings = 1920 calories in 1 snack bag

8 0

3 years ago

1/3m = 12 - m solve for m p.s im bad at math lol

olga55 [171]

M = 9

(check photo, for the work.. click on the picture for all of the work:) )

6 0

4 years ago

What is 23.791 rounded to the nearest tenth?

sergejj [24]

The nearest tenth would be the first decimal place, so the answer would be 23.8

6 0

3 years ago