The starting line up for a basketball team is to consist of two forwards and three guards. Two brothers are on the team. Matthew is a forward and Tony a guard. There are four forwards and six guards from which to choose the line up. If the starting players are chosen at random, what is the probability that the two brothers will end up in the starting line up

Answers

Answer 1

Answer:

0.25 = 25% probability that the two brothers will end up in the starting line up

Step-by-step explanation:

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

The order in which the players are chosen is not important, which means that the combinations formula is used to solve this question.

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]

Desired outcomes:

Matthew plus another forward from a set of 3.

Tony plus another two guards from a set of 5.

So

[tex]D = C_{3,1}C_{5,2} = \frac{3!}{1!2!} \times \frac{5!}{2!3!} = 3*10 = 30[/tex]

Total outcomes:

Two forwards from a set of 4.

Three guards from a set of 6.

So

[tex]T = C_{4,2}C_{6,3} = \frac{4!}{2!2!} \times \frac{6!}{3!3!} = 6*20 = 120[/tex]

What is the probability that the two brothers will end up in the starting line up?

[tex]p = \frac{D}{T} = \frac{30}{120} = 0.25[/tex]

0.25 = 25% probability that the two brothers will end up in the starting line up


Related Questions

The polynomial p(x) = x3 – 7x - 6 has a known factor of (x + 1).
Rewrite p(x) as a product of linear factors.
p(x)

Answers

Hi there!

[tex]\large\boxed{(x -3)(x + 2)(x + 1)}[/tex]

We can use long division to find the other roots of p(x).

We know that x + 1 is a factor, so:

Set up:

Find how many times that the first term in the divisor goes into the first of the dividend. Subtract from like terms.

         x² - x - 6

x + 1 | x³ + 0x² - 7x - 6

         x³ + x²

         0 - x²     - 7x

            - x²      - x

             0        - 6x - 6

                        -6x - 6

                          0     0

Therefore, x² - x - 6 is another factor. We can factor this further:

Find two numbers that add up to -1 and multiply into -6. We get:

-3, 2

(x - 3)(x + 2)

The entire polynomial factored is:

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

A pizza parlor has a choice of 10 toppings for its pizzas. From these 10 toppings, how many different 7-topping pizzas are possible?

Answers

Answer:

120

Step-by-step explanation:

There are 10 possible toppings to choose from, you choose 7.

Using combinatorics, it's 10!/(7! 3!), or 120.

The formula is (total amount to choose from )! divided by (amount you choose)!(amount you don't choose)!

Or search up combination formula

A combination is an arrangement of a set of numbers from a total set where the order of the set is not relevant.

The formula for combination.

= [tex]^nC_r[/tex]

= n! / r! (n -r)!

The number of possible 7-toppings for the pizza is 120.

What is a combination?

A combination is an arrangement of a set of numbers from a total set where the order of the set is not relevant.

We have,

The total number of toppings = 10.

n = 10

The number of required toppings = 7.

r = 7

The formula for combination.

= [tex]^nC_r[/tex]

= n! / r! (n -r)!

The possible number of possible 7-toppings pizzas.

= [tex]^{10}C_7[/tex]

= (10 x 9 x 8) / (3 x 2)

= 120

Thus,

n = 10 and r = 7

[tex]^{10}C_7[/tex] = 120

The number of possible 7-toppings for the pizza is 120.

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The function f(x) = −x2 + 18x − 72 models the daily profit, in dollars, a gym makes for selling memberships, where x is the number of memberships sold, and f(x) is the amount of profit.

Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points)

Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (5 points)

(10 points)

Answers

Answer:

Step-by-step explanation:

The way to do this so as to streamline both the vertex and finding the zeros is to complete the square. That method will provide us with the vertex, and then we can continue on to factor from that form to find the zeros. Completing the square requires us to set the quadratic equal to 0 then move over the constant, giving us

[tex]-x^2+18x=72[/tex] The leading coefficient HAS to be a positive 1; ours is negative 1 so we factor out the negative to get:

[tex]-(x^2-18x)=72[/tex] Now we're ready to complete the square.

Take half the linear term, square it, and add it to both sides. Our linear term is 18 (from -18x; don't worry about the negative because squaring it makes it positive anyway). Half of 18 is 9, and 9 squared is 81.

BUT on the left we have that -1 sitting out front that refuses to be ignored. What we actually added on to the left side, inside the parenthesis, is -1(81) which is -81.   -81 is what we add to the right since that turns out to be what we added to the left:

[tex]-(x^2-18x+81)=72-81[/tex] and we clean that up.

The reason we complete the square is because when we simplify the left side, we end up with a perfect square binomial found from taking the square root of x-squared, the first sign we come to, then the square root of 81:

[tex]-(x-9)^2=-9[/tex].  Move the constant back over to get

[tex]-(x-9)^2+9=y[/tex] telling us that the vertex is (9, 9). In the context of the problem that means that the gym sells on average 9 memberships a day and the profit it makes on average per day is $9.

To factor, we will go back one step to

[tex]-(x-9)^2=-9[/tex] and begin by dividing both sides by -1 to get

[tex](x-9)^2=9[/tex] and undo the squaring by taking the square root of both sides to get

x - 9 = ±3 so

x = 9 + 3 and

x = 9 - 3 so

x = 6 and 12

Those are the zeros. This means that if they sell either 6 or 12 memberships they have a 0 profit. That may sound strange, but in business it does often work like that...selling too many of something makes your company lose money (this is often due to the cost required by you to produce or manufacture the product).

6 times the sum of 5 and K​

Answers

Answer:

6(5+k)

Step-by-step explanation:

The sum of 5  and k

5+k

6 times the sum

6(5+k)

Picking a card and spinning a spinner are independent events.

True
False

Answers

Answer:

True

Step-by-step explanation:

Both happened in different times and are seprate events

Independent simple random samples are selected to test the difference between the means of two populations whose standard deviations are not known. We are unwilling to assume that the population variances are equal. The sample sizes are n1 = 25 and n2 = 35. The correct distribution to use is the:
1) t distribution with 59 degrees of freedom.
2) t distribution with 58 degrees of freedom.
3) t distribution with 61 degrees of freedom.
4) t distribution with 60 degrees of freedom.

Answers

Answer:

2) t distribution with 58 degrees of freedom.

Step-by-step explanation:

Population standard deviations not known:

This means that the t-distribution is used to solve this question.

The sample sizes are n1 = 25 and n2 = 35.

The number of degrees of freedom is the sum of the sample sizes subtracted by the number of samples, in this case 2. So

25 + 35 - 2 = 58 df.

Thus the correct answer is given by option 2.

N is one of the numbers below. N is such that when multiplied by 0.75 gives 1. Which number is equal to
N?
A) 1 1/2
B 1 1/3
C) 5/3
D) 3/2

Answers

Answer:

it should be letter c 5/3 I could be wrong but I hope this help

2. The cost of 5 pen is Rs 1200, find the cost of 1 pen.​

Answers

Step-by-step explanation:

cost of 5 pen is Rs 1200,

cost of 1 pen is 1200/5 = Rs 240

Answer:

Rs 240

Step-by-step explanation:

1200÷5=240

If 2/3 of the girls in class have brown eyes and 1/4 of the girls have blue eyes what fraction of the girls in class have neither blue or brown

Answers

1/12, make the denominators the same by making the 12 that makes 8/12 and 3/12 together it’s 11/12 which means 1/12 I not blue or brown

Annie is opening a savings account which earns 5.2% interest compounded continuously how much will she need to deposit in the account so she has $2300 after seven years

Answers

Hi

let's call X the initial deposit.

the interest rate is 5.2 %

so each year X increase by 1.052.

so we have : X *1.052^7 =2300

X = 2300/1.052^7

X = 1612,94

please note that the deposit was rounded to the next cent. as the result would be 1612,937...

Answer:

1686.22

Step-by-step explanation:

1686.22

 2300=P(1+(0.052x7))  

2300=P1.364  

P=2300/1.364  

=1686.217...  

=1686.22..

=1686 for the nearest dollar

Multiplying and bmbFREE BRAINLIST AND POINTS!! Fast! RIGHT ANSWERS ONLY! Scam and wrong answers will be reported and dealed with.
1. 6x(-4)=
3. (-11) x 5=
4. (-12) x (-7)=
5. (-2) x (-10)
6. 4 x (-15)=

Answers

Answer:

Step-by-step explanation:

-24

-55

84

20

-60

What is the slope of the points (-2,7) and (2,-5)?
4
-3
-12
3

Answers

Answer:

-3

Step-by-step explanation:

Slope is equal to (-5-7)/(2-(-2)=-12/4=-3

Select the correct answer.
As part of a class project, a university student surveyed the students in the cafeteria lunch line to look for a relationship between eye color and hair color among students. The table below contains the results of the survey.

Answers

Answer: Choice B)  0.27

=========================================================

Explanation:

There are a lot of data values here, and it's possible to easily get lost in them. However, we're asked only about students with blond hair. So we only focus on the first row. Ignore everything else.

We see that there are 78 of these students total. Of this total, 21 have green eyes.

Therefore, the relative frequency of blonds with green eyes is 21/78 = 0.2692 which rounds to 0.27; so that's why the answer is choice B.

Make mathematical expressions then, simplify ,50 is divided by 2 times one more than the difference of F and 3.​

Answers

Answer:

F = 27

Step-by-step explanation:

50/2 = (F - 3) + 1

25 = F - 2

F = 27

Find the missing length indicated

Answers

Answer:

60

Step-by-step explanation:

Use similar triangles or the ratios from the right triangle altitude theorem.

x/36 = (64 + 36)/x

x² = 3600

x = 60

PLEASE HELP WITH BOTH OF THESE ASAP!

Answers

Answer:

Hello,

Step-by-step explanation:

[tex]\overline{x}=3262\\\sigma=1100\\\\P(x\geq 1000)=P(x\leq 3262+(3262-1000))=P(x\leq 5524)\\\\z=\dfrac{x-\overline{x}}{\sigma} =\dfrac{5524-3262}{1100} =2.05\overline{63}\\\\\\P(z\leq 2.05)=0.9789\\\\P(z\leq 2.06)=0.9803\\\\\\\boxed{0.9789\leq P\leq 0.9803}\\\\\\[/tex]

[tex]P(x\leq 4000)=P(z\leq \dfrac{4000-3262}{1100} )=P(z\leq 0.67\overline{09})\\\\P(z\leq 0.67)=0.7486\\P(z\leq 0.68)=0.7517\\\\0.7486\leq P\leq 0.7517\\[/tex]

find the LCM of 220,440,660 by common division method​

Answers

Answer: LCM = 1320

Step-by-step explanation:

2 | 220, 440, 660

2 | 110, 220, 330

2 | 55, 110, 165

3 | 55, 55,165

5 | 55, 55 , 55

11 | 11, 11, 11

| 1, 1, 1

= 2 × 2 × 2 × 3 × 5 × 11

= 1320

Therefore the LCM is 1320

Must click thanks and mark brainliest

properties of exponents. the answer is 1/2^3 i need help with the work

Answers

(2^-1)^2/2×2^0

2^(-1×2)/2^1

2^-2/2^1

2^(-2-1)

2^(-3)

(1/2)^3

Properties used (m^n)^a = m^na

(m)^-n = (1/m)^n

m^0 = 1

m^n/m^a = m^(n-a)

Must click thanks and mark brainliest

by solving a pair of linear equation X + Y is equal to 20 and x-y=10 the value of 'x' and 'y' are​

Answers

Answer:

x=15, y=5

Step-by-step explanation:

x+y=20

x-y=10

Adding both equations;

(x+x) + (y-y) = 20+10

2x = 30

x = 30/2 = 15

Substitute x=15 into x+y=20

y= 20-x = 20-15= 5

Canada has a population of 33 million while Russia has 144 million inhabitants. Indonesia population is 50% greater then that of Russia while it is only 72% of the population of the United States. How many million people must be added to the United States so that the population of that country becomes 10 times of Canada?

Answers

Answer: 30 million people must be added.

Step-by-step explanation: 50% of 144 million is 72 million. You add these to find Indonesia’s population. 144 million + 72 million= 216 million. If 216 million is only 72% of the US population, then divide 216 million by 72 to find 1%. 216 million/72=3 million. Multiply this by 100 to find the US population. 3 million times 100= 300 million. Now, multiply Canada’s population by 10. 33 million times 10= 330 million. Finally, subtract 300 million from 330 million to find the amount needed to make the US population 10 times that of Canada’s. 330 million-300 million=30 million. So , you need 30 million people in order to make the US population 10 times that of Canada’s.

A garden table and a bench cost $717 combined. The garden table costs $67 more than the bench. What is the cost of the bench?

Answers

Subtract the difference form the total:

717 - 67 = 650

Divide the remaining amount by 2:

650/2 = 375

The bench cost$375

look at the image below

Answers

that's what I got, you can confirm if it's correct or not... I'm not sure

have a nice dayʘ‿ʘ

In a standardized normal distribution the mean is ____ while the standard deviation is ____.
A. 0; 1
B. 1; 0
C. 0; 0
D. 1; 1

Answers

Answer:

A. 0; 1

Step-by-step explanation:

Required

Mean and standard deviation of a standardized normal distribution

A standardized normal distribution is represented as:

[tex](\mu,\sigma) = (0,1)[/tex]

This implies that:

[tex]\mu = 0[/tex] -- mean

[tex]\sigma = 1[/tex] --- standard deviation

Hence, (a) is true

The table below shows the number of pets kept by the students in a class.
-----------------------------------------------------------
No. of pets | No. of students
-----------------------------------------------------------
0 | 9
1 | k
2 | 2
3 | 1
4 | 2
-----------------------------------------------------------
If the median number of pets is 1, what is the smallest value of k ?

Answers

Answer:

The answer for this question is 5

Cheyenne's bi-weekly gross pay is $529.81. She sees that $18.54 was deducted for Medicare tax. What percent of Cheyenne's gross pay has been withheld for Medicare tax? Round to the nearest tenth. (2 points)
0.35%
2.2%
3.5%

Answers

18.54/529.81= 0.0349
0.0349*100=3.49%= 3.5%

Answer:

I got 3.5%

Step-by-step explanation:

Hope this helps

Determine whether (a) x = -1 or (b) x = 2 is a solution to this equation

Answers

Answer:

x = 2 is the solution to x + 1.5 = 3.5

Step-by-step explanation:

x + 1.5 = 3.5

   -1.5      -1.5

--------------------

x = 2

what is 2x2x2x3x3 please give me answer

Answers

Answer:

The answer is 72.

I am right .

Vas happenin!
Hope your day is good

2 time 2 is 4
4 times 2 is 8
8 times 2 is 16
16 times 3 is 48
48 times 3 is 144
144 is your answer
Hope this helps *smiles*

By Using 0,2,4,5,6 Write The Smallest Number And the Greatest Number​

Answers

Answer:

smallest is 0 and greatest is 6

simple

Answer:

0 and 6

Step-by-step explanation:

Because 0 is means nothing.And the highest number is 6


Match each polynomial on the left with its two factors on the right.

Answers

Answer:

Hello

Step-by-step explanation:

[tex]Formula: \\\\\boxed{\Large a^3\pm b^3=(a \pm b)(a^2 \mp ab+b^2)}\\\\8x^3+1=(2x)^3+1^3=(2x+1)(4x^2-2x+1)\\\\8x^3-1=(2x)^3-1^3=(2x-1)(4x^2+2x+1)\\[/tex]

The factors of the expression 8x³ + 1 and 8x³ - 1³ will be (2x + 1) & (4x² – 2x + 1) and (2x – 1) & (4x² + 2x + 1), respectively.

What is a polynomial?

A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.

The expression is given below.

8x³ + 1 and 8x³ - 1³

(2x)³ + 1³ and (2x)³ - 1³

We know that the formula is given as,

a³ + b³ = (a + b) (a² – ab + b²)

a³ – b³ = (a – b) (a² + ab + b²)

Then the expression is written as,

(2x)³ + 1³ = (2x + 1) [(2x)² – 2x + 1²]

(2x)³ + 1³ = (2x + 1) (4x² – 2x + 1)

(2x)³ – 1³ = (2x – 1) [(2x)² + 2x + 1²]

(2x)³ – 1³ = (2x – 1) (4x² + 2x + 1)

The factors of the expression 8x³ + 1 and 8x³ - 1³ will be (2x + 1) & (4x² – 2x + 1) and (2x – 1) & (4x² + 2x + 1), respectively.

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Find y when x = 22, if y varies directly as x,
and y = 42 when x = 5.

Answers

Answer:

184.8

Step-by-step explanation:

y =kx

k=y/x

k=42/5=8.4

y=8.4*22

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