What is the area of the shaded region? 37 ft 29 ft 21 ft 16 ft

Determine whether 81 − 49n4 is a difference of two squares. If so, factor it. If not, explain why.

Mumz [18]

We have

$81-49n^4=9^2-(7n^2)^2$

so this is indeed a difference of squares. Factorizing would give

$81-49n^4=(9-7n^2)(9+7n^2)$

making the answer D.

We can further factor the first term here and write

$9-7n^2=3^2-(\sqrt 7\,n)^2=(3-\sqrt7\,n)(3+\sqrt7\,n)$

but that's clearly out of the scope of this question.

7 0

3 years ago

How to write 79031 expanded form

Jet001 [13]

Seventy-nine-thousand-and-thirty-one

I hope that's right I'm not too sure lol

6 0

3 years ago

Read 2 more answers

Calculate the expected value, the variance, and the standard deviation of the given random variable X. (Round all answers to two

Tom [10]

Answer:

E (X) = 1.8

Var (X) = 0.36

σ = 0.6

Step-by-step explanation:

Solution:-

- Denote the random variable X : is the number of red marbles that Suzan has in her hand after she selects three marbles.

- Total sample space (bag) have the following quantity of colored marbles:

Bag : { 3 Red , 2 Green }

- Suzan selects three marbles from the bag. The Event (X) defines the number of red marbles out of 3.

- The total number of outcomes / selections for randomly selecting 3 balls from the bag:

All outcomes = 5 C 3 = 10

- The probability distribution of the random variable X, we will use combinations to determine the required probabilities:

X = 1 red marble:

P ( X = 1 ) : Suzan chooses 1 Red marble from the available 3 red marble and 2 green marbles.

P ( X = 1 ) = [ 3C1*2C2 ] / all outcomes = (3*1) / 10 = 0.3

X = 2 red marble:

P ( X = 2 ) : Suzan chooses 2 Red marble from the available 3 red marble and 1 green marbles.

P ( X = 2 ) = [ 3C2*2C1 ] / all outcomes = (3*2) / 10 = 0.6

X = 3 red marble:

P ( X = 3 ) : Suzan chooses 3 Red marble from the available 3 red marble.

P ( X = 3 ) = [ 3C3] / all outcomes = (1) / 10 = 0.1

- The probability distribution is as follows:

X : 1 2 3

P (X): 0.3 0.6 0.1

- The expected value E(X) for the given random variable X is:

E ( X ) = ∑Xi*P(Xi)

= 1*0.3 + 2*0.6 + 3*0.1

=1.8

- The variance Var(X) for the given random variable X is:

Var ( X ) = ∑Xi^2*P(Xi) - [ E(X) ] ^2

= 1^2*0.3 + 2^2*0.6 + 3^2*0.1 - 1.8^2

= 0.36

- The standard deviation for the given random variable X is:

σ = √Var(X)

σ = √0.36

σ = 0.6

5 0

4 years ago

From a box containing 10 cards numbered 1 to 10, four cards are drawn together. The probability that their sum is even is 21 21

ankoles [38]

Answer:

Step-by-step explanation:

We know that between 1 to 10 there are 5 even and 5 odd numbers.

We could get 4 even cards , 4 odd cards or 2 odd and 2 even cards

Let´s check all this combinations

Case 1: When all 4 numbers are even:

We are going to take 4 of the 5 even numbers in the box so we have

$5C4=5$

Case 2: When all 4 numbers are odd:

We are going to take 4 of the 5 odd numbers in the box, so we have

$5C4=5$

Case 3: When 2 are even and 2 are odd:

We are giong to take 2 from 5 even and odd cards in the box so we have

$5C2 * 5C2$

Remember that we obtain the probability from

$\frac{Number-of-favourable-Outcome}{Total-number-of-outcomes}$

So we have the number of favourable outcomes but we need the Total cases for drawing four cards, so we have that:

We are taking 4 of the 10 cards:

$10C_4=210$

Hence we have that the probability that their sum is even

$\frac{5+5+100}{210}=\frac{11}{21}$

8 0

3 years ago

The table displays the amount of time, in minutes, Jordan rode his bike for five days. How many total hours did Jordan ride his

Zinaida [17]

Answer:98.9276

Step-by-step explanation:

The table displays the amount of time, in minutes, Jordan rode his bike for five days. How many total hours did Jordan ride his bike in the five days? DayTime (minutes)11 4545 22 109109 33 5151 44 121121 55 3838 Jordan rode his bike total hours in the five days.

8 0

2 years ago