7. A car dealership has 8 red, 9 silver, and 5 black cars on the lot. Seven cars are randomly chosen to be displayed(in no particular order) in front of the dealership. Find the probability that (a) all are silver (b) 5 are red and 2 are black (c) 4 are red and the rest are silver

Answer:

a) 0.0002 = 0.02% probability that all are silver.

b) 0.0033 = 0.33% probability that 5 are red and 2 are black

c) 0.0345 = 3.45% probability that 4 are red and the rest are silver

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question, the order in which the cars were selected is not important, so we use the combinations formula.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

(a) all are silver

Desired outcomes:

7 silver cars, from a set of 9. So

[tex]D = C_{9,7} = \frac{9!}{7!(9-7)!} = 36[/tex]

Total outcomes:

7 cars from a set of 8 + 9 + 5 = 22. So

[tex]T = C_{22,7} = \frac{22!}{7!(22-7)!} = 170544[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{36}{170544} = 0.0002[/tex]

0.0002 = 0.02% probability that all are silver.

(b) 5 are red and 2 are black

Desired outcomes:

5 red, from a set of 8

2 black, from a set of 5

[tex]D = C_{8,5}*C_{5,2} = \frac{8!}{5!(8-5)!}*\frac{5!}{2!(5-2)!} = 56*10 = 560[/tex]

Total outcomes:

7 cars from a set of 8 + 9 + 5 = 22. So

[tex]T = C_{22,7} = \frac{22!}{7!(22-7)!} = 170544[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{560}{170544} = 0.0033[/tex]

0.0033 = 0.33% probability that 5 are red and 2 are black

c) 4 are red and the rest are silver

Desired outcomes:

4 red, from a set of 8

3 silver, from a set of 9

[tex]D = C_{8,4}*C_{9,3} = \frac{8!}{4!(8-4)!}*\frac{9!}{3!(9-3)!} = 70*84 = 5880[/tex]

Total outcomes:

7 cars from a set of 8 + 9 + 5 = 22. So

[tex]T = C_{22,7} = \frac{22!}{7!(22-7)!} = 170544[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{5880}{170544} = 0.0345[/tex]

0.0345 = 3.45% probability that 4 are red and the rest are silver

If the fifth term in a geometric sequence is 1∕27 and the common ratio is 1∕3, find the explicit formula of the sequence.
Question 14 options:

A)

an = (1∕3)n – 1 for n ≥ 1

B)

an = (3) ⋅ (3)n – 1 for n ≥ 1

C)

an = (3) ⋅ (1∕3)n – 1 for n ≥ 1

D)

an = (1∕27) ⋅ (1∕3)n – 1 for n ≥ 1

Can someone please solve number 6 for me it’s urgent

On a math test a student, Jake, has to identify all the coefficients and constants of
the expression 8y +n + 9. Jake says that 8 is a coefficient and 9 is a constant. Identify all the
coefficients and constants of the expression. What error might Jake have made?

I can’t figure this out for the life of me.

Find the length of the third side. If necessary, round to the nearest tenth.
10
11

Srry but I need help with this

Factor the following problem: 81x^4 - 49x^4 =​

Exercise 4.3. Determine the exact probability of drawing a 10 from a shuffled pinochle deck. (In a pinochle deck, there are 48 cards. There are six values: 9, 10, Jack, Queen, King, Ace. There are two copies of each value in each of the standard four suits: hearts, diamonds, clubs, spades.)

2(3x + 2) = 2x - 1+x.

what is the prime factorization for 900​

Find the sum of 4x2 + 3x + 2 and 7x2 + 7x + 3.​

Please help for instant brainliest.

IT'S FOR MIDDLE SCHOOOLLL PLZZZ HELPPPP
Tyler’s brother works in a shoe store. Tyler’s brother earns a commission. He makes 2.5% of the amount he sells. Last week, he sold $900 worth of shoes. How much was his commission?

Which statement is true about the points shown on the number line.

The next day the gas tank in dad’s car holds 24 gallons. The gas tank in mom’s truck holds 50% less than that. How much gas does the truck’s tank hold?

Find values for a and b so that 2(3x+5)+ax=5(4x−b) is an identity equation.

Last month you spent 40$ on clothing. This month you spend 160% of what you spent last month. Set up a percent equation to model this situation. How much did you spend this month.
Choose correct answer below

A. 160%=percent•40
B. part=160%•40
C. 40=160%•whole

What is an equation of the line that passes through the points (-7, 3)
and (-4, 3)?

If f(x) = 2x^3 – 5x^2 + 5, then what is the remainder when f(x) is divided by
x + 2?

A large piece of iron has a density of 7.87 g/ml what is the density of a piece of iron that is two times heavier

A box contains 84 chocolates, of which
63 are dark chocolates. The rest are milk
chocolates. What is the ratio of milk
chocolates to the total number of chocolates
in the box?

The area of a circle is 25.12 square yards. If the dimensions of the circle are tripled, what will be the area of the new figure?

1. 226.08 yd 2
2. 8.37 yd 2
3. 75.36 yd 2
4. 150.72 yd 2

1
A line has a slope of -1/2and a y-intercept of -2.

Pls help this is really important

there are 38 students involved in planning the homecoming parade. of these students 15 are boys and 23 are girls. if two members are selected to lead the parade what is the probability that both are girls ​

Derek used 12 pencils during school week. He now has 86 pencils How many pencils did he have at the beginning of the school week

Please help!!!!!! AAA

Frozen Taste ice cream factory wants to analyze if the customers like its new flavor, peanut butter chocolate chip. The probability that a customer likes the new flavor is .83. If a customer is asked to taste the flavor twice within 4 hours, then what is the probability that a customer likes this flavor the first time and the second time

A 40-foot ladder is used to reach the top of a 24-foot wall. If the ladder extends 10 feet past the top of the wall, find the
measure of the angle that the ladder forms with the horizontal ground. Answer to the nearest degree

How is this
11% as a decimal??