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3 years ago

9

At a benefit concert, fourteen bands have volunteered to perform but there is only enough time for six of the bands to play. How

many lineups are possible?

2 answers:

Setler [38]3 years ago

6 0

We are given with a total of fourteen bands which we can choose from and choose six of them to play. we use comnbination instead of permutation because order of choosing in this case, is not important. The formula is 14C6 equal to 3003 ways

Maurinko [17]3 years ago

4 0

Answer:

3003

Step-by-step explanation:

Total no. of bands volunteered to perform = 14

There is only enough time for 6 of the bands to play.

So, to find How many lineups are possible we will use combination:

$^nC_r = \frac{n!}{r!(n-r)!}$

n = 14

r = 6

So, no. of lineups are possible = $^{14}C_6$

= $\frac{14!}{6!(14-6)!}$

= $\frac{14!}{6!(8)!}$

= $\frac{14\times 13 \times 12\times 11\times 10\times 9}{6 \times 5\times 4\times 3\times 2 \times 1}$

= $3003$

Hence 3003 lineups are possible .

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A cosmetic company makes three bottles of scented lotion using the recipe shown. Each bottle holds a different amount of lotion.

seropon [69]

Answer:

Part 1) Bottle 1 (vanilla=1,almond=3,pineapple=4)

Part 2) Bottle 2 (vanilla=2,almond=6,pineapple=8)

Part 3) Bottle 3 (vanilla=1 1/2,almond=4 1/2,pineapple=6)

Step-by-step explanation:

Let

x ----> the amount of vanilla sent

y ----> amount of almond sent

z ----> the amount of pineapple sent

we know that

$x:y:z=\frac{1}{8}:\frac{3}{8}:\frac{1}{2}$

so

$\frac{x}{y}=\frac{1}{8}:\frac{3}{8}$

$\frac{x}{y}=\frac{1}{3}$

$x=\frac{y}{3}$ -----> equation A

$\frac{x}{z}=\frac{1}{8}:\frac{1}{2}$

$\frac{x}{z}=\frac{1}{4}$

$x=\frac{1}{4}z$ -----> equation B

$\frac{y}{z}=\frac{3}{8}:\frac{1}{2}$

$\frac{y}{z}=\frac{3}{4}$

$y=\frac{3}{4}z$ -----> equation C

Part 1) Bottle 1

vanilla=?

almond=?

pineapple=4

we have

$z=4$

<em>Find the value of x</em>

substitute the value of z in equation B

$x=\frac{1}{4}(4)$

$x=1$

<em>Find the value of y</em>

substitute the value of z in equation C

$y=\frac{3}{4}(4)$

$y=3$

therefore

<em>Bottle 1</em>

vanilla=1

almond=3

pineapple=4

Part 2) Bottle 2

vanilla=?

almond=6

pineapple=?

we have

$y=6$

<em>Find the value of x</em>

substitute the value of y in equation A

$x=\frac{6}{3}=2$

<em>Find the value of z</em>

substitute the value of x in equation B

$2=\frac{1}{4}z$

solve for z

$z=8$

therefore

<em>Bottle 2</em>

vanilla=2

almond=6

pineapple=8

Part 3) Bottle 3

vanilla=1 1/2

almond=?

pineapple=?

we have

$x=1\frac{1}{2}$

convert to an improper fraction

$x=1\frac{1}{2}=\frac{1*2+1}{2}=\frac{3}{2}$

<em>Find the value of y</em>

substitute the value of x in equation A

$\frac{3}{2}=\frac{y}{3}$

$y=\frac{9}{2}$

convert to mixed number

$y=\frac{9}{2}=\frac{8}{2}+\frac{1}{2}=4\frac{1}{2}$

<em>Find the value of z</em>

substitute the value of x in equation B

$\frac{3}{2}=\frac{1}{4}z$

$z=6$

therefore

<em>Bottle 3</em>

vanilla=1 1/2

almond=4 1/2

pineapple=6

5 0

3 years ago

Read 2 more answers

-8=-(x+4). Please help I don't know the answer or steps to solve this equation.

Ne4ueva [31]

Answer:

x = 4

Step-by-step explanation:

First u need to distribute the -1 to (x + 4), creating the equation, -8 = -x - 4. Then add the -4 to both sides, and you get, -4 = -x. Then divide by -1 to both sides, and x = 4.

6 0

3 years ago

Read 2 more answers

Evaluate 10.2x + 9.4y when x=2 and y=3

vekshin1

10.2 x 2 = 20.40
9.4 x 3 = 28.20
Total= 48.60

5 0

3 years ago

Lenny and Lisa have obtained a 30-year, fixed rate mortgage for $675,250 with a 7.25% interest rate. They purchased 3 points and

Vikentia [17]

Answer:

119 months

Step-by-step explanation:

In this question, we are asked to calculate the amount of time it would take for a break-even point on a mortgage, if there is a factoring in the cost of points.

We proceed to answer the;

Mathematically,

The Break Even Point = Amount Paid for purchasing Discount Points divided by Monthly savings in the interest payments

We lost out the important values given in the question as follows:

Amount of Mortgage - $675,250

Tenure - 30 Years

The Rate of interest without points = 7.25%

The number of points = 3 points

The rate of interest with the 3 points = 6.875%

The amount to be paid for purchasing the discount point is now calculated below;

Since 1 discount point = 1% of mortgage value;

Therefore, 3 discount points = 3% of mortgage value

The amount paid is thus = 3% of $675,250 = $20,257.5

To calculate Monthly payment without points, we use the mathematical formula;

M = P[r(1+r)^n/((1+r)^n)-1)]

Where M

Is monthly payment, r is the interest rate, n is the number of months.

According to the question M = 675,250, r = 7.25% = 7.25/100 = 0.0725 , n= 30 * 12 months = 360 months

M = 675,250[0.0725(0.0725+1)^30/(1+0.0725)^360)-1) = $4606.40

To get the monthly payment with points, we simply use the formula again but this time interest rates will be 6.875% = 0.06875 I.e r = 0.06875

Inputting the terms in the formula will yield a value of $4435.91. This means monthly payment with discount will be $4435.91

Savings in monthly payments after purchasing the discount points = $4,606.40 - $4,435.91 = $170.48

Break Even = Purchase cost of Discount Points / Monthly savings

= $20,257.5 / $170.48

= 119 Months

Hence, the number of months it will take Lisa and Lenny to break-even point on their mortgage will be 119 months

6 0

3 years ago

Ill give Brainliest. please explain your answers. im so confused on these questions :((

Katen [24]

Answer:

I'll answer the first one. Neither vehicles are crossing the speed limit since both are under 40mph.

Step-by-step explanation:

6 miles every 10 minutes = 36 miles every hour.

15 miles every 25 minutes = 36 miles every hour.

Speed limit = 40 mph

Neither vehicles are crossing the speed limit since both are under 40mph.

Hope this helped! :))

8 0

2 years ago