4 students from a class of 15 are going to be chosen to be on the dance committee. Findthe number of different 4-person committees that can be made.

Answers

Answer 1

Answer:

[tex]C(15,4)=1365\text{ different committees}[/tex]

Step-by-step explanation:

This situation can be approached using the formula for combinations:

[tex]\begin{gathered} C(n,r)=\frac{n!}{r!(n-r)!} \\ \text{where,} \\ n=\text{ number of possible items that can be }selected \\ r=\text{ number of items that were selected} \end{gathered}[/tex]

Therefore, solve for n=15 and r=4.

[tex]\begin{gathered} C(15,4)=\frac{15!}{4!(15-4)!} \\ C(15,4)=1365\text{ different committees} \end{gathered}[/tex]


Related Questions

What is 13.496 rounded to the nearest tenth?A.13B.13.4C.13.5D.14

Answers

[tex]C)13.5[/tex]

1) When we need to round up or down to the nearest tenth, it's necessary to consider the hundredth's place.

2) Note this number:

We can see that 13.496 is greater than 13.45 so it is closer to 14 than 13, then we can round it off to the nearest greater number than 4.

3) Thus, we can round it off to:

[tex]13.5[/tex]

can you explain this to me what you are supposed to do this

Answers

Solution

If we see the two tirangles given BAC and A'B'C' we can conclude that we have the following congruent angles

< CAB = < C'A'B'

< BCA = < B'C'A'

< ABC = < A'B'C'

Write a relation consisting of five ordered pairs that satisfies the following conditions. The relation is a function. Switching the x- and y-coordinates of each ordered pair results in a relation that is not a function.

Answers

Answer:

Step-by-step explanation:

If each value of x only has one corresponding value of y, it is a function. You can test this just by eye or by graphing and doing the vertical line test by rolling a pencil or other straight object across to make sure only one point is on the line at a time

A random number generator is used to select an integer from 1 to 100 ​(inclusively). What is the probability of selecting the integer 730​?

Answers

If a random number generator is used to select an integer from 1 to 100, then the probability of selecting the integer 730 is zero.

Here a random number generator is used to select an integer from 1 to 100.

Therefore the range of the outcome = 1 to 100

Here we have to find the probability of selecting the integer 730

The probability = Number of favorable outcomes / Total number of outcomes.

Here a random number generator is used to select an integer from 1 to 100, but the given number is 730  which is out of range. Therefore the probability is zero

Hence, if a random number generator is used to select an integer from 1 to 100, then the probability of selecting the integer 730 is zero.

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Solving a Debra, Ravi, and Ahmad sent a total of 76 text messages during the weekend. Ahmad sent 2 times as many messages as Ravi. Debra sent 8 more messages than Ravi. How many messages did they each send?

Answers

Let the number of messages sent by Ravi be x.

Ahmad sent 2 times as many messages as Ravi. Therefore, Ahmad sent 2x messages.

Debra sent 8 more messages than Ravi. Therefore, Debra sent (x + 8) messages.

The sum of all the messages is 76:

[tex]x+2x+x+8=76[/tex]

Solving for x, we have:

[tex]\begin{gathered} 4x+8=76 \\ 4x=76-8 \\ 4x=68 \\ x=\frac{68}{4} \\ x=17 \end{gathered}[/tex]

The number of messages Ahmad sent will be:

[tex]2(17)=34[/tex]

The number of messages Debra sent will be:

[tex]17+8=25[/tex]

ANSWER

[tex]\begin{gathered} Debra\to25\text{ }messages \\ Ravi\to17\text{ }messages \\ Ahmad\to34\text{ }messages \end{gathered}[/tex]

Given that events A and B are independent with P(A) = 0.08 and P(B) = 0.25,determine the value of P(A and B), rounding to the nearest thousandth, ifnecessary.

Answers

To find: P(AandB)

P(AandB)=P(A)*P(B)

P(AandB)=0.08*0.25

P(AandB)=0.02

Thus the required answer is 0.02

Ms. Morgan is the cafeteria manager. She keeps track of how many students select each type of drink. Today during breakfast, 32 children picked milk while 44 children picked juice. What is the ratio of the numbe of children who picked juice to those who picked milk?

Answers

Answer:

ratio of those who picked juice to milk

it refers to division

Match each step with the correct expression to factor s2 + 78 + 6 by using the decomposition method.

Answers

We have the following:

[tex]s^2+7s+6[/tex]

solving:

[tex]\begin{gathered} \text{step 1} \\ s^2+s+6s+6 \\ \text{step 2} \\ s\mleft(s+1\mright)+6\mleft(s+1\mright) \\ \text{step 3} \\ (s+1)(s+6) \end{gathered}[/tex]

You invent a game that is played on a perfect 12 foot by 12 foot square. What is the longest distance between any two points on the square? A. 12 feetB. 15 feetC. 17 feetD. None of the aboveI will really appreciate the help on this problem.

Answers

The given figure is a square that measures 12 foot by 12 foot. please see illustration below;

The square in the sketch above shows the longest distance between two opposite diagonals, and that is the hypotenuse, labelled as a.

In the triangle ADC, using Pythagoras' theorem;

[tex]\begin{gathered} AD^2+DC^2=AC^2 \\ 12^2+12^2=a^2 \\ 144+144=a^2 \\ 288=a^2 \\ \sqrt[]{288}=a \\ a=16.97 \end{gathered}[/tex]

The longest distance which is a (that is AC) is approximately 17 ft as shown above (16.97 ft).

At a local school, 164 students play soccer and 112 students play baseball. What is the ratio of soccer players to baseball players?41:2828:4113:2828:13

Answers

Given

The number of students who play soccer is 164.

The number of students who play baseball is 112

Explanation

To find the ratio of soccer player to baseball players .

Divide the number of soccer player by the number of baseball player.

[tex]\frac{164}{112}=\frac{41}{28}[/tex]

Answer

Hence the ratio of soccer players to baseball players is

[tex]41:28[/tex]

plant A produced 3 times as many panels as plant b. two percent of the panels from plant A and 5% of the panels from plant b were defective. how many panels did plant b produce if the two plants together produced 990 defective panels

Answers

let x the number of panels that Plant A produced

y the number of panels that Plant B produced

then, we have

x = 3y

0.02x + 0.05y = 990

and solve the system:

[tex]\begin{gathered} 0.02(3y)+0.05y=990 \\ 0.06y+0.05y=990 \\ 0.11y=990 \\ \frac{0.11y}{0.11}=\frac{990}{0.11} \\ y=9000 \end{gathered}[/tex]

answer: plant b produced 9000 panels

how do i solve the equation?

Answers

Answer: 7x=63 and 12x+9= 117

Step-by-step explanation:

add those two equations and set it to 180 degree

7x+12x+9=180

19x=171

x= 9

7x = 7 (9) = 63

12x+9 = 12 (9)+9 = 117

y = (x+3)^3 find the zeros of each function

Answers

Given,

[tex]y=(x+3)^3[/tex]

We have,

[tex]y=0[/tex]

when,

[tex]\begin{gathered} x+3=0 \\ \Rightarrow x=-3 \end{gathered}[/tex]

The zeros of the function are x=-3,-3,-3

help me pleaseeeeeeeee

Answers

The values of given functions f(-2), f(0) and f(7) when f(x) = 1-6x are 13, 1 and -41 respectively.

According to the question,

We have the following function:

f(x) = 1-6x

Now, we can find the values of each function by putting the numbers in place of x.

Now, in order to find the value of f(-2), we will put -2 in place of x in the given function.

f(-2) = 1-6*(-2)

f(-2) = 1+12

f(-2) = 13

Now, in order to find the value of f(0), we will put 0 in place of x in the given function.

f(0) = 1-6(0)

f(0) = 1-0

(We know that when a number is multiplied with 0 then the result is always 0.)

f(0) = 1

Now, in order to find the value of f(7), we will put 7 in place of x in the given function.

f(7) = 1-6*7

f(7) = 1-42

f(7) = -41

Hence, the values of f(-2), f(0) and f(7) are 13, 1 and -41 respectively.

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Find the tangent of the angle whose measure is pi/2....pi divided by 2.

Answers

We have the following:

[tex]\begin{gathered} \tan \theta=x \\ \tan \frac{\pi}{2}=x \end{gathered}[/tex]

the value of pi / 2 is not defined

Area of a sector A sector with a radius of \maroonD{8\,\text{cm}}8cmstart color #ca337c, 8, start text, c, m, end text, end color #ca337c has an area of \goldE{56\pi\,\text{cm}^2}56πcm

Answers

To find the angle of the sector, follow the steps below.

Step 01: Find the total area of the circle.

The area (A) of a circle with radius r is:

[tex]A=\pi r^2[/tex]

Knowing that r = 8 cm, then the area is:

[tex]\begin{gathered} A=8^2\pi \\ A=64\pi\text{ cm}^2 \end{gathered}[/tex]

Step 02: Find the central angle.

To find the angle, use proportions.

Knowing that:

When angle = 2π, A = 64π,

Then when angle is x, A = 56π

[tex]\begin{gathered} \frac{x}{2\pi}=\frac{56\pi}{64\pi} \\ \\ \text{ Multiplying both sides by 2}\pi: \\ \frac{x}{2\pi}*2\pi=\frac{56\pi}{64\pi}*2\pi \\ x=\frac{56*2}{64}\pi \\ x=\frac{112}{64}\pi \\ \\ \text{ Dividing both the numerator and the denominator by 16:} \\ x=\frac{\frac{112}{16}}{\frac{64}{16}}\pi \\ x=\frac{7\pi}{4} \end{gathered}[/tex]

Answer: The central angle measure is:

[tex]\frac{7\pi}{4}[/tex]

Express y in terms of x. Then find the value of y when x= -1-3 (x + 2) = 5yY in terms of x:Y=

Answers

LEt's express y in term of x:

[tex]\begin{gathered} -3(x+2)=5y \\ y=\frac{-3(x+2)}{5} \end{gathered}[/tex]

Therefore:

[tex]y=-\frac{3}{5}x-\frac{6}{5}[/tex]

Now, if x=-1, then we have:

[tex]\begin{gathered} y=-\frac{3}{5}(-1)-\frac{6}{5} \\ =\frac{3}{5}-\frac{6}{5} \\ =-\frac{1}{5} \end{gathered}[/tex]

Therefore, if x=-1 then y=-1/5

hector recorded the amount of rainfall in the desert each month over a period of two years. the list shows the number of inches fell for each month for year 1 and year 2 year 1: 2,2,0,0,0,1,2,2,3,2,2,2year 2:1,1,0,0,0,0,2,2,2,1,2,1 whats the difference in rain fall between the mean of the rain fall in two years hurry its a test

Answers

ANSWER

The difference is 0.5

EXPLANATION

We have to find the mean of the rain fall for each year. To do this we have to add all the data and then divide by the total number of data.

Year 1: number of data = 12:

[tex]\bar{x_1}=\frac{2+2+0+0+0+1+2+2+3+2+2+2}{12}=\frac{18}{12}=\frac{3}{2}=1.5[/tex]

Year 2: number of data = 12:

[tex]\bar{x_2}=\frac{1+1+0+0+0+0+2+2+2+1+2+1}{12}=\frac{12}{12}=1[/tex]

The difference is:

[tex]\bar{x}_1-\bar{x}_2=1.5-1=0.5[/tex]

I wonder what I’m doing wrong ?

P^2-10p+16=1+6p


Answer is (15,1)
But I can’t seem to figure it out.

Answers

Steps to Solve:

1. Collect like terms

2.  Factor quadratic

3. solve for p

Factoring a Quadratic where a = 1

1. find two numbers that are the product of ac and the sum of b

2. set up the two linear terms with the variable associated with a

2. insert the values found in step 1 into parentheses

1. collect like terms

[tex]p^2-10p-6p+15-1=0[/tex]

[tex]p^2-16p+15 = 0[/tex]

2. Factor quadratic

ac = 15 and b =-16, two numbers that multply to ac and are the sum of b are -15 and 1

[tex](p-15)(p-1)=0[/tex]

2 solutions can be found

[tex]p-15=0[/tex]              OR        [tex]p-1=0[/tex]

[tex]p= 15[/tex]                                   [tex]p=1[/tex]

have $100 to spend on Halloween candy. A pack of M&Ms cost $3.50. 15 Twix bars cost $7.00. 9 Hershey Bars cost $3.00. If I need 15 M&M packs, 17 Twix bars and 9 Hershey bars how much will it cost? How much money will I have left?

Answers

Answer:

Assuming this is rounding to the nearest cent, $36.51

Step-by-step explanation:

    1 ) Find the cost of each individual candy.

M&Ms are given at $3.50 per pack.

To find the cost of one Twix bar, divide $7.00 by 15. This makes Twix equal $0.47 per bar.

You don't need to find the individual price of the Hershey's bars because 9 bars cost $3.00 and you need 9 bars in the equation.

    2 ) Now that you have the prices you need, multiply.

For M&Ms 15 x $3.50 = $52.50

For Twix 17 x $0.47 = $7.99

For Hershey's, it is given that 9 bars are $3.00

    3 ) Add all of these up to get the total spent on candy.

$52.50 + $7.99 + $3.00 = $63.49

    4 ) Subtract this from the budget to get the total amount left over.

$100 - $63.49 = $36.51

List the angle measures of △VWX in order from smallest to largest. Assume that t is a positive number.

Answers

Explanation

To begin with, we will first have to obtain the length of side VX

[tex]VX^2=WX^2+VW^2-2\times WX\times VWcosw[/tex]

In our case

[tex]\begin{gathered} WX=28t \\ VW=95t \\ w=94^0 \end{gathered}[/tex]

Thus

[tex]\begin{gathered} VX^2=(28t)^2+(95t)^2-2\times(28t\times95t)cos94 \\ \\ VX^2=784+9025+371.104 \\ VX^2=100180.10 \\ \\ VX=100.90t \end{gathered}[/tex]

Next, we will determine the angles at V and X

using sine rule

[tex]\begin{gathered} \frac{sin94}{100.9t}=\frac{sinV}{28t} \\ \\ sinV=\frac{28t\times sin94}{100.9t} \\ \\ sinV=0.27683 \\ \\ V=16.07^0 \\ \end{gathered}[/tex]

Then, we will get the measure at X

[tex]180^0-16.07^0-94=69.93^0[/tex]

Therefore, the order from smallest to largest angles will be

m

OR

m

The half-life of a radioactive kind of iodine is 21 hours. How much will be left after 42 hours,if you start with 19,296 grams of it?In grams

Answers

The half-life of a radioactive material is the time that it takes to reduce to half

In this case, the half-life is 21 hs, and since 42hs is twice the half-life, the material will reduce to half after 21 hours and then to half again.

one half of one half is:

[tex]\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{4}[/tex]

Then we multiply by the initial amount:

[tex]19,296\cdot\frac{1}{4}=4824gr[/tex]

The amount left after 42 hours is 4824 grams.

* The functions f(x) and g(x) are both linear. f(2) = 4 and f(3) = -1, while g(2) = 6 and g(-3) = 7. Are these lines parallel, perpendicular, or neither? Show your work algebraically.

Answers

Solution

f(2) = 4 and f(3) = -1

g(2) = 6 and g(-3) = 7

From the info given we can see this :

x = 2 f(2) = 4 , g(2)= 6

x= 3 f(3)= -1 , g(3)= 7

And we can calculate the slope with the following formula:

[tex]m=\frac{-1-4}{3-2}=-5[/tex][tex]m=\frac{7-6}{3-2}=1[/tex]

And for this case we can conclude that the lines are neither

Since m1 is different from m2

And m1*m2 is not -1

2. Graph the image of Parallelogram WXYZ under a translation 4 units to the left and 6 units up

Answers

Translation 4 units to the left transforms the point (x, y) into (x-4, y). Applying this rule to the parallelogram WXYZ, we get:

W(0, -2) → (0-4, -2) →W'(-4, -2)

X(2, -2) → (2-4, -2) → X'(-2, -2)

Y(2, -5) → (2-4, -5) → Y'(-2, -5)

Z(0, -5) → (0-4, -5) → Z'(-4, -5)

Translation 6 units up transforms the point (x, y) into (x, y+6). Applying this rule to the parallelogram W'X'Y'Z', we get:

W'(-4, -2) → (-4, -2+6) → W''(-4, 4)

X'(-2, -2) → (-2, -2+6) → X''(-2, 4)

Y'(-2, -5) → (-2, -5+6) → Y''(-2, 1)

Z'(-4, -5) → (-4, -5+6) → Z''(-4, 1)

Where the parallelogram W''X''Y''Z'' is the image of Parallelogram WXYZ translated 4 units to the left and 6 units up, as can be seen in the next graph:

use the generic rectangle 3x-8)² and -7x⁴(3x-2) what's the product and sum?

Answers

In this case the answer is very simple .

Step 01:

Data:

eq1. (3x - 8)²

eq2. -7x⁴(3x-2)

Step 02:

Sum.

eq.1 + eq.2

(3x - 8)² + (-7x⁴(3x-2))

(9x² - 2*3x*8 - 64) + (-21x⁴ - 14x⁴)

9x² -

Solve by using a proportion. Round answers to the nearest hundredth if necessary. 1. You jog 3.6 miles in 30 minutes. At that rate, how long will it take you to jog 4.8 miles? 2. You earn $33 in 8 hours. At that rate, how much would you earn in 5 hours?

Answers

EXPLANATION

Let's see the facts:

rate ---> 3.6 miles / 30 minutes

The unit rate is:

Unit rate = 0.12 miles/minute

Now, dividing the needed 4.8 miles by the unit rate will give us our desired number:

Time= 4.8 miles/ 0.12miles/minute = 40 minutes

The answer is 40 minutes.

Jack scored 80 out of 85 points on a recent test. What is his score as a percent, rounded to the nearest whole percent?

Answers

jack scored = 80

total point = 85

so the percentage is,

[tex]=\frac{80}{85}\times100[/tex][tex]\begin{gathered} =\frac{8000}{85} \\ =94.11\text{ \%} \end{gathered}[/tex]

thus, the nearest whole percentage is 94 %

heyy could you help me out with this problem I'm stuck

Answers

Since congruent angles are equal

Therefore the two figures are similar

we have

9 / 9 = 2x / x + 4

introduce cross multiplication

9 (2x) = 9(x + 4)

18x = 9*x + 9*4

18x = 9x + 36

collect the like terms

18x - 9x = 36

9x = 36

divide boths sides by 9

9x / 9 = 36/9

x = 4

The first missing variable is 2x

2 x 4

= 8

The second is x + 4

we have 4 + 4

= 8

m

Ashley‘s Internet service is terribly unreliable in fact on any given day there’s a 60% chance that her Internet‘s connection will be lost at some point that day what is the probability that her Internet service is not broken for seven days in a row inner a fraction or round your answer to four decimal places if necessary.

Answers

Let the event that her internet will be broken be A

The event that her internet will not be broken be B

Therefore:

[tex]\begin{gathered} P(A)=60\%=0.60 \\ P(B)=1-0.60=0.4 \end{gathered}[/tex]

Thus, the probability that her internet is not broken for 7 days in a row:

[tex]P(B\text{ for 7 days\rparen=P\lparen B\rparen}\times\text{P\lparen B\rparen}\times\text{P\lparen B\rparen}\times\text{P\lparen B\rparen}\times\text{P\lparen B\rparen}\times\text{P\lparen B\rparen}\times\text{P\lparen B\rparen}[/tex]

Substitute the value:

[tex]P(B\text{ for 7 days\rparen=0.4}\times\text{0.4}\times\text{0.4}\times\text{0.4}\times\text{0.4}\times\text{0.4}\times\text{0.4=0.001634}[/tex]

Round to four decimal places is 0.0016

Answer: 0.0016

To produce a textbook, suppose the publisher spent $110,000 for typesetting and $7.50 per book for printingand binding. The total cost to produce and print n books can be written asC = 110,000+ 7.51a. Suppose the number of books printed in the first printing is 10,000. What is the total cost?The total cost is $b. If the average cost is the total cost divided by the number of books printed, find the average cost of producing10,000 textbooks.The average cost of producing 10,000 textbooks is $c. Find the cost to produce one more textbook when you have already produced 10,000 textbooks.If you have already produced 10,000 textbooks, it'll cost you $ to produce one more.

Answers

The given equation is

[tex]C=110000+7.5n[/tex]

a)

The number of books=10000

Substitute n=10000 in the given equation, we get

[tex]C=110000+7.5\times10000[/tex][tex]C=185000[/tex]

The total cost is $185,000.

b)

[tex]\text{Average cost =}\frac{185000}{10000}=18.5[/tex]

The average cost of producing 10,000 textbooks is $18.5.

c)

If we need to produce one more after producing 10000 books.

substitute n=10001 in the given equation, we get

[tex]C=110000+7.5(10001)=185007.5[/tex]

[tex]\text{One book cost after printed 10000 book=cost of 10000 books-cost of 10001 books}[/tex]

[tex]\text{One book cost after printed 10000 book=1}85000-185007.5=7.5[/tex]

If you have already produced 10,000 textbooks, it'll cost you $7.5 to produce one more.

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The Turks, Avars, and Arabs are all able to make significant encroachments over the course of this period. The same can be said for China where the Wei dynasty collapsed in 534 and decades of infighting ensued, which was reduced somewhat by the Sui dynasty (589618) but only properly brought under control with the establishment of the Tang dynasty by Emperor Gaozu (61826). The Persian Empire suffered the most, since its capital, Seleucia-Ctesiphon, was dangerously close to the steppe lands, and the deserts and mountains within its realm favored regional autonomy and limited centralization.Ignominious [shameful] defeat at the hands of Emperor Heraclius and an ensuing civil war fatally weakened the regimes ability to respond when the Arabs overran their lands. The capitals of the Byzantine and Chinese empires, on the other hand, were far from the steppe and extremely well defended, and the empires themselves, organized around large bodies of water (the Mediterranean Sea and the Yellow and Yangtze Rivers, respectively), were reasonably well integrated. This meant that though they also suffered many defeats at the hands of steppe raiders, they were able to weather the storm. The Avars and Turks clearly had ambitions to penetrate further into the lands of Byzantium and Persia, but they were coming from the difficult northern and eastern sides of the two empires, where they faced substantial man-made and natural obstacles, whereas the Arabs were directly adjacent to the soft southern underbellies of these empires, and so it was they who ultimately triumphed in this seventh-century great game.From Robert Hoyland's In God's Path: The Arab ConquestFrom this excerpt, what argument can be made about imperial expansion and conflict?Choose 1 answer:Choose 1 answer:(Choice A)AEmpires grow weak when they overextend themselves militarily, opening themselves up to invasion from outside forces or infighting(Choice B)BBecause of their strategy of raiding, steppe peoples do not have stable enough economies to run an empire(Choice C)CThe best borders for an empire are natural borders: mountains, rivers, and oceans(Choice D)DRegional autonomy always leads to greater imperial stability Which of these equations is perpendicular to the midpoint of the line segment that contains the point (-4,4) and (2,-2)? 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