MATHEMATICS HIGH SCHOOL

How many different 12 member juries can be chosen from a pool of 25 people?

Answers

Answer 1

Answer:

Answer: 5200300

Step-by-step explanation:

Given: Total number of people = 25

The number of member juries can be chosen from a pool of 25 people= 12

To calculate combinations, we use the formula as :-

$^nC_r = (n!)/(r!(n-r)!)$ , where n represents the total number of items, and r represents the number of things being chosen at a time.

Now, the number of different 12 member juries can be chosen from a pool of 25 people is given by :_

$^(25)C_(12) = (25!)/(12!(25-12)!)\n\n=(25!)/(12!13!)=5200300$

Hence, the number of different 12 member juries can be chosen from a pool of 25 people is 5200300.

Answer 2

Answer: A formula for the number of possible combinations or r objects from a set of n objects is
$nCr = (n!)/(r!(n-r)!)$
where n is 25 and r is 12. The number of ways is 5,200,300.

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HELP ME PLZ DUE SOON WILL GIVE BRAINLESTWhat is the slope of the line that passes through the points (2, 1)(2,1) and (17, -17) ?(17,−17)? Write your answer in simplest form.
Write the explicit formula for the sequence. -1, 4, -16, 64,...
Marisa wants to buy a DVD player that costs$150. She already saved $80 and plans to save an additional $10 each week. Write an equation that represents this.

10x -2y = 10 in slope intercept form

Answers

slope-intercept form: y = mx + b
the point is to get y alone on one side of the equation:

10x - 2y = 10
-10x -10x
-2y = -10x + 10
-2y/-2 = -10x/-2 + 10/-2
y = 5x - 5

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!What is the sum of the first 7 terms of the series − 3 + 6 − 12 + 24 −... ?

Answers

Answer: -129

Step-by-step explanation:

Given the sequence {-3, 6, -12, 24, ... }, we can see that the first term (a) is -3 and the ratio (r) is $(6)/(-3) = -2$ .

Input those values into the Sum formula:

$S_n=(a(1-r^n))/(1-r)\n\nS_7=(-3(1-(-2)^7))/(1-(-2))\n\n.\quad=(-3(1-(-128)))/(1+2)\n\n.\quad=(-3(1+128))/(3)\n\n.\quad=(-3(129))/(3)\n\n.\quad=-129$

Find the diameter of the circle that has a circumference equal to its area.2
4
8
10

Answers

Circumference may have the same numerical magnitude as area, but they will never be "equal". Circumference is a length or distance, and area is an area.
So they can never have the same units, and quantities can't be equal without
the same units.

You might say that   π D (circumference) = π (D/2)² (area) .

Then D = (D/2)²

   D = D² / 4

   1 = D / 4

   D = 4 .

But this is no more than a parlor trick. In order to do it, you need to
ignore units completely, and that's unacceptable in math.

The formula for circumference of a circle:
$C=2 \pi r$

The formula for area of a circle:
$A=\pi r^2$
r - radius

The circumference is equal to the area.
$C=A \n2 \pi r=\pi r^2 \ \ \ |/ \pi r, \ r>0 \n2=r \nr=2$

The diameter is two times the radius.
$d=2r=2 * 2=4 \n \n\boxed{d=4}$

What is a situation in which you might locate points on a coordinate grid?

Answers

A situation could be when you have a y=axsquared+bx+c equation. You'd find the X, or vertex, by doing x=-b divided by 2•a. Then you'd plug in x and find y. Now you have a point you can plot. To find another, you can find the y-intercept by plughing in 0 for x and finding another y.

The width,w, of a rectangular garden is X -2 the area of the garden is X^3-2X-4 what is an expression for the length of the garden? A. X^2-2x-2
B. X^2+2x-2
C. X^2-2x+2
D. X^2+2x+2

Answers

Answer:

D. $x^2+2x+2$

Step-by-step explanation:

We know that,

The area of a rectangle is,

A = l × b,

Where, l is the length of the rectangle,

w is the width of the rectangle,

Given,

$A = x^3-2x-4$

$w=(x-2)$

By substituting values,

$x^3-2x-4=(x-2)l$

$\implies l = (x^3-2x-4)/(x-2)=x^2+2x+2$ ( By long division shown below )

Hence, the length of the rectangular garden is $x^2+2x+2$

Option D is correct.

$A=lw \Rightarrow l=(A)/(w)$
A - area, l - length, w - width

$w=x-2 \nA=x^3-2x-4 \n \nl=(x^3-2x-4)/(x-2)=(x^3-2x^2+2x^2-4x+2x-4)/(x-2)=(x^2(x-2)+2x(x-2)+2(x-2))/(x-2)= \n=((x^2+2x+2)(x-2))/(x-2)=x^2+2x+2$

The answer is D. x²+2x+2.

John is going to start saving $20 every month to buy a new IPod. His parents gave him $10 for his birthday to open his savings account. The equation y = 20x + 10 represents John’s savings account balance x months after be began saving.a) How many months will it take John to save enough money for the $300 IPod? Explain.

b) If John saved $40 per month instead of $20, how would you expect the slope of the graph to change? Explain.

Answers

a) The number of months for the saving of $300 will be 14¹/₂.

b) The slope of the saving of $40 will be y = 40 x + 10

What is an equation of the line?

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that John is going to start saving $20 every month to buy a new iPod. His parents gave him $10 for his birthday to open his savings account. The equation y = 20x + 10 represents John’s savings account balance x months after he began saving.

Part (a),

The number of the months will be calculated as,

y = 20x + 10

300 = ( 20 x + 10 )

290 = 20x

x = 14¹/₂ months

Part(b),

The slope will be 40 for the saving of $40.

To know more about an equation of the line follow

brainly.com/question/18831322

#SPJ2

Answer A: It would take fifteen months, or one year and three months, to get three hundred dollars.

Answer B: It would take seven and a half months to get three hundred dollars at this rate. It would also change the slope by making it go down more.

Step-by-step explanation:

Three hundred divided by twenty equals fifteen, which represents the amount of months.

If you do the same thing with the other ratio, but change twenty to forty, you get seven and a half.

Have a nice day!

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