Y = -16x2 + 32x + 3.

15. For each of the following, write the probability as the intersection of two events. Then, indicate whether the two events ar

LuckyWell [14K]

Answer:

Step-by-step explanation:

a. The probability of selecting a 6 from the first draw and a 7 on the second draw when two balls are selected without replacement from a container with 10 balls numbered 1 to 10

Not independent because without replacement

Prob for both = $\frac{1}{10} \frac{1}{9} \\=\frac{1}{90}$

b. The probability of selecting a 6 on the first draw and a 7 on the second draw when two balls are selected with replacement from a container with 10 balls numbered 1 to 10

Here independent because with replacement makes probability independent.

Prob for both = P(A) *P(B) = $\frac{1}{10} *\frac{1}{10} \\=\frac{1}{100}$ d

c. The probability that two people selected at random in a shopping mall on a very busy Saturday both have a birthday in the month of June. Assume that all 365 birthdays are equally

likely, and ignore the possibility of a February 29 leap-year birthday.

Here independent because one person birthday will not affect the other person birthday

Prob for both = $(\frac{30}{365})^2\\ =\frac{25}{5329}$

d. The probability that two socks selected at random from a drawer containing 10 black socks and 6 white socks will both be black

Prob for I sock black = 10/16 and II sock black if first sock is black = 9/15

Hence not independent

Prob for both = $\frac{10C2}{16C2} \\=\frac{3}{8}$

5 0

4 years ago

Three pipes A, B and C take 24, 36 and 32 hours to fill a pool, respectively. How long would it take the three pipes to fill the

Murrr4er [49]

Answer:

12 hours

Step-by-step explanation:

Time taken by pipe A = 24 hours

Time taken by pipe B = 36 hours

Time taken by pipe C = 32 hours

To find:

How long would it take the three pipes to fill the pool if pipe B is turned on 3 hours after pipe A and pipe C is turned on 1 hour after pipe B?

Solution:

First of all, let us assume the total capacity of the pool.

Let us take LCM of 24, 36 and 32.

LCM of 24, 36 and 32 = 288

Let the total capacity of the pool = 288 units

Total units filled by pipe A in one hour = $\frac{288}{24} = 12\ units$

Total units filled by pipe B in one hour = $\frac{288}{36} = 8\ units$

Total units filled by pipe C in one hour = $\frac{288}{32} = 9\ units$

Now, for the first 3 hours, only pipe A operates, so units filled in first three hours = $12\times 3 =36\ units$

For the next one hour, A and B both operate together, so units filled in the next 1 hour = 12 + 8 = 20 units

Total number of units filled in 4 hours = 36 + 20 = 56 units

Units to be filled to completely fill the pool = 288 - 56 = 232 units

Now, after the 4th hours, all the pipes operate together.

So, number of units filled in each hour = 12 + 8 + 9 = 29 units

Time taken to fill 232 units = $\frac{232}{29} = 8\ hours$

Total time taken = 4 + 8 = 12 hours

8 0

3 years ago

I NEED THIS ANSWER ASAP!!!!

Naddik [55]

Solution:

We know the following rules:

Rule: If an exponent is negative, it will be in the fraction 1/nˣ.
Rule: If an exponent is positive, it will be in whole number form and will multiply itself m times.
Rule: if a number's exponent is 0, then the number is 1.

Now, let's solve each problem.

Question-7

4³ = 4 x 4 x 4 = 64
4² = 4 x 4 = 16
4¹ = 4
4⁰ = 1

Question-8

(-2)³ = (-2) x (-2) x -(2) = -8
(-2)² = (-2) x (-2) = 4
(-2)¹ = -2
(-2)⁰ = 1

Hoped this helped!

4 0

2 years ago

Read 2 more answers

If someone type an average of 63 words per minute. how many word can they type in 135 minutes?

Rasek [7]

8505. You would do 63 times 135 to get 8505

7 0

4 years ago

Read 2 more answers

Question is in the picture

padilas [110]

Answer:

3.2

Step-by-step explanation:

Add up the first group then add up the second group then divide the group Y by group X

round to the nearest integer. The rule for rounding is simple: look at the digits in the tenth’s place (the first digit to the right of the decimal point).

Hope This Helps bud ^^

6 0

4 years ago

Read 2 more answers