What two integers does the square root of 429 lie?

On a test, leo is asked to completely factor the polynomial 3x3 – 3x 5x2 – 5. he uses double grouping to get (x2 – 1)(3x 5). has

Agata [3.3K]

No, Leo's answer is not a product of prime polynomials because x2 – 1 can be factored. This is a difference of squares. He should continue factoring to get

(x – 1)(x + 1)(3x + 5).

8 0

2 years ago

Read 2 more answers

Jordan wants to play a basketball game at a carnival. The game costs the player $5 dollar sign, 5 to play, and the player gets t

Alinara [238K]

Answer:

The expected value of Jordan gains is -1 dollar.

Step-by-step explanation:

Consider the following random variables. X := #of shots that Jordan makes. Then, we can can define the random variable Y of the earnings of Jordan in a game as follows

Y = 5 if X=2 (since he gets 10, but invested 5), Y=0 if X=1(since he gets the 5 back) and Y=-5 if X=0(since he doesn't get the money back). Then, in this case, we can define the probability as follows.

P(Y=5) = P(X=2), P(Y=0) = P(X=1), P(Y=-5)= P(X=0).

By definition, the expected value of Y is given by

$E[Y] = 5\cdot P(Y=5)+0\cdot P(Y=0)-5 P(Y=-5)$ . By the previous analysis, we have that

$E[Y] = 5\cdot P(X=2)-5P(X=0)$

We only need to calculate the probabilities for X. In this case, we can consider each shot independt from each other. Then, we can consider X to be distributed as a binomial random variable with n=2 trials and p=0.4 of success (since he has a 40% chance of winning).

Then, by definition

$P(X=k) = \binom{n}{k}p^k(1-p)^{n-k} = \binom{2}{k}0.4^{k}0.6^{2-k}$

where $\binom{n}{k}=\frac{n!}{k!(n-k)!}$

Then,

$P(X=0) = \frac{2!}{0!2!}0.4^{0}0.6^{2} = 0.36$

$P(X=2)=\frac{2!}{0!2!}0.4^{2}0.6^{0} = 0.16$

Then,

$E[Y] = 5\cdot 0.16-5\cdot 0.36 = -1$

8 0

1 year ago

As part of Kayla's exercise program,she either runs 6miles/day or rides her bike 10 miles/day.Her new goal is to cover a minimum

poizon [28]

6(15) + 10b > = 200
90 + 10b > = 200
10b > = 200 - 90
10b > = 110
b > = 110/10
b > = 11

so she can do 15 days of running plus 11 days of biking....which totals 26 days

8 0

2 years ago

Turner middle school has 110 buys. Fifty-six percent of the students are girls. How many students go to this school? Please help

aleksandr82 [10.1K]

Find the percentage of boys:
100 - 56 = 44
Boys = 44%

110 = 44%

110 is 44% of what number?
This number will be the total number of students.

To calculate it further, divide 110 by 0.44.

4 0

1 year ago

Megan went clothes shopping and bought 2 pairs of flare jeans, 2 camisoles, and 4 t-shirts for $90.00. at the same store, paige

liq [111]

If you let j, c, t represent the prices of jeans, camisoles, and t-shirts, respectively, the three purchases can be described by ...
2j +2c +4t = 90.00
1j +0c +3t = 42.50
1j +3c +2t = 62.00

It is convenient to let a calculator solve these equations. It can tell you the row-reduced matrix equations are ...
[[1 0 0 24.5]
[0 1 0 8.5 ]
[0 0 1 6 ]]
which means
flare jeans cost $24.50
camisoles cost $8.50
T-shirts cost $6.00

6 0

1 year ago