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3 years ago

If 15% of 4x is 20 less than x, what is the value of x?

Mathematics

1 answer:

Bess [88]3 years ago

4 0

The sentence "15% of 4x is 20 less than x"

translates to 0.15 • (4x) = x – 20

Solving that…

0.15(4x) = x - 20 multiplipy 0.15•4

0.6x = x - 20 subtract x from both sides

-0.4x = - 20 divide both sides by -0.4

x = 50

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Your school’s baseball team sells 1250 raffle tickets at $4 each. The grand prize is a $3000 boat. The second prize is a $450 gr

densk [106]

Answer:

The expected value of the winnings for a single-ticket purchase is -$1.0016.

Step-by-step explanation:

The total number of tickets sold is, N = 1250.

Cost of one ticket is, $4.

Let X = amount of prize.

The prize distribution is as follows:

1 Grand price = $3000

1 Second prize = $450

10 Third prize = $25

The expected value X can be computed using the formula:

$E(X)=\sum x.P(X)$

Compute the probability distribution of X as follows:

Prize Amount (X) P (X) x · P (X)

1 Grand prize $3000 $\frac{1}{1250}=0.0008$ $\$3000\times 0.0008=2.4$

1 Second prize $450 $\frac{1}{1249}=0.0008$ $\$450\times 0.0008=0.36$

10 Third prize $25 $\frac{10}{1248}=0.008$ $\$25\times 0.008=0.2$

No prize -$4 $1-\sum P(Win)\\=0.9904$ $-\$4\times 0.9904=-3.9616$

TOTAL 1.0000 -1.0016

Thus, the expected value of the winnings for a single-ticket purchase is -$1.0016.

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3 years ago

A university is building a new student center that is two- thirds the distance from the arts center to the residential complex.

Natasha2012 [34]

Answer:

$C = (\frac{21}{5},\frac{33}{5})$

Step-by-step explanation:

Given

Points: (1, 9) and (9, 3)

Ratio = 2/3

Required

Determine the coordinate of the center

Represent the ratio as ratio

$Ratio = 2:3$

The new coordinate can be calculated using

$C = (\frac{mx_2 + nx_1}{n + m},\frac{my_2 + ny_1}{n + m})$

Where

$(x_1,y_1) = (1, 9)$

$(x_2, y_2) = (9, 3)$

$m:n = 2:3$

Substitute these values in the equation above

$C = (\frac{2 * 9 + 3 * 1}{3 + 2},\frac{2 * 3 + 3 * 9}{2 + 3})$

$C = (\frac{18 + 3}{5},\frac{6 + 27}{5})$

$C = (\frac{21}{5},\frac{33}{5})$

Hence;

The coordinates of the new center is $C = (\frac{21}{5},\frac{33}{5})$

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3 years ago

Product A is a 12-ounce bottle of generic mouthwash that sells for $1.15. Product B is a 24-ounce bottle of mouthwash that costs

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3 years ago

-x+ 3 = — 3х + 23 What is it?

nekit [7.7K]

Answer:

x=10

Step-by-step explanation:

$-x+ 3 = - 3x + 23\\2x+3=23 \\2x=20\\x=10$

1. Subtract -3x from both sides of equation

2. Subtract 3 from both sides of equation

3. Divide both sides by 2

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