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2 years ago

A committee must be formed with 4 teachers and 5 students. If there are 11 teachers

Mathematics

1 answer:

Ivenika [448]2 years ago

7 0

Answer:

11C4 × 11C5

$\binom{11}{4} \times \binom{11}{5} = \frac{11 \times 10 \times 9 \times 8}{4 \times 3 \times 2 \times 1} \times \frac{11 \times 10 \times 9 \times 8 \times 7}{5 \times 4 \times 3 \times 2 \times 1} = 330 \times 462 = 152460$

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What is the slope of the line that passes through the points (-2,3) and (-1,8)

yaroslaw [1]

Answer:

Slope m = 5

Step-by-step explanation: sorry if Im wrong but If i am then it is just 5:)

5 0

2 years ago

A business has two loans totaling $50,000. One loan has a rate of 8% and the other has a rate of 12%. This year, the business ex

Debora [2.8K]

Answer:

the 8% loan has a principal of $37500

the 12% loan has a principal of $12500

Step-by-step explanation:

Let's start by writing the general equation for the interest hwre I is the interest, P is the principal (in our case would be loan amounts), "r" is the interest rate in decimal form (in our case one would be 0.12, and the other one 0.08), and t is the time in years (in our case 1 year).

$I=P*r*t$

Then we write the interest equation coming from each loan at the end of this year (we call I1 the interest coming from the 12% loan and I2 the interest coming from the 8% one). Since we don't know the loan amounts (in fact those are what we need to find) we will name one "x" and the other "y":

$I=P*r*t\\I1=x * 0.12*1\\I2=y*0.08*1$

Next, we add these last two equations term by term, and replace the addition of both interests by $4500 as given in the information:

$I1=x * 0.12*1\\I2=y*0.08*1\\I1+I2 = 0.12x+0.08y\\4500=0.12x+0.08y$

This is our first equation in the variables x and y which are our unknowns.

Now we generate the second equation on x and y by writing in agebraic terms the other piece of information we have: "the total of the two loans is $50000. That is the addition of the principals x and y should equal $50000:

$x+y=50000$

We solve for y in this last equation and replace its form in terms of x in the equation of the interest, and solve for the unknown x:

$y=50000-x\\4500 = 0.12x +0.08 y\\4500=0.12x+0.08(50000-x)\\4500=0.12x+4000-0.08x\\4500=0.12x-0.08x+4000\\4500=0.04x+4000\\4500-4000=0.04x\\500=0.04x\\x=\frac{500}{0.04} =12500$

Therefore the amount of the loan at 12% is $12500

Now to find the amount of the second loan "y" we use the equation for the totals of the loans:

$x+y=50000\\12500+y=50000\\y=50000-12500=37500$

Therefore, the loan at 8% is $37500

5 0

3 years ago

Which two operations are needed to write the expression that represents "five less than the quotient of a numb

melomori [17]

Division and subtraction because the quotient is the result of a division and 'less than is a subtraction.

3 0

3 years ago

Read 2 more answers

What is an equation of the line that passes through the point (-2 1) and is parallel to the line whose equation is 4x-2y=8 ?

monitta

4x-2y=8 ==> y=2x-4 (to better show you what I mean)

2 lines are parallel if they have the same slope (m the coefficient of x).

So y=mx + b // y =2x-4 means m=2 & y=mx + b, becomes y=2x + b.
Moreover they are telling us that this function passes by (-2,1), where -2 represents x & 1, represents y. To calculate b , replace x & y by their values:
y=2x+b ==> 1 = 2(- 2) + b==> 1 = -4 + b ==> b= 5. Finally the equation is
y=-2x+5

4 0

3 years ago

What is the surface area of a right come with a radius of 20 and a height of 15?

Allisa [31]

The first step in finding the surface area of a cone is to measure the radius of the circle part of the cone. The next step is to find the area of the circle, or base. The area of a circle is 3.14 times the radius squared (πr2). Now, you will need to find the area of the cone itself. In order to do this, you must measure the side (slant height) of the cone. Make sure you use the same form of measurement as the radius.

You can now use the measurement of the side to find the area of the cone. The formula for the area of a cone is 3.14 times the radius times the side (πrl).

So the surface area of the cone equals the area of the circle plus the area of the cone and the final formula is given by:

SA = πr2 + πrl

5 0

3 years ago