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slamgirl [31]
3 years ago
8

Two thirds of a number reduced by 11 is equal to 4 more than the number. Find the number.

Mathematics
1 answer:
spin [16.1K]3 years ago
6 0
Assume that the number is x:

2/3 of x take off 11 = 4x

Transform into numerical / algebraic form:

2/3 * x - 11 = 4x

Next multiply both sides by 3 to get rid of the fraction:

2 * x - 33 = 12x

Simplify:

2x - 33 = 12x

Isolate 2x by adding 33 to both sides:

2x = 12x + 33

Isolate 33 by taking 12x off both sides:

-10x = 33

Divide both sides by -10 to get the value of x:

x = 33/-10 (or x = -3.3)

Therefore the number is -3.3
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Step-by-step explanation:

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8 0
3 years ago
T(x) = -2(-x - 3)' + 1
Anna [14]

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2

Step-by-step explanation:

3 0
2 years ago
Solve for x.
Rudiy27
5x^2 - 80 = 0
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x^2 = 80/5
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8 0
3 years ago
Robert has 60 feet of fence to make a dog pen. He will use the house for one side of the pen, as shown above. What dimensions wi
irinina [24]

The formula for an area of a regular parallelogram is:

A = l * w

Where,

l = length

w = width

We are given that the total measurement of fence is only 60 feet and one side of the house is used as one side of the pen. Therefore,

l + 2 w = 60

<span>or simplifying to make an explicit expression for one  variable, say l:</span>

l = 60 – 2 w

<span>Substituting to the 1st equation:</span>

A = (60 – 2 w) * w

A = 60 w – 2 w^2

<span>The maxima are obtained by getting the 1st derivative then equating dA/dw = 0:</span>

dA/dw = 60 – 4 w

60 – 4 w = 0

4 w = 60

w = 15

Since l = 60 - 2w

l = 60 – 30

l = 30

<span>Therefore the dimension that will make the largest pen is 15 ft by 30 ft.</span>

<span>ANSWER: C</span>

7 0
3 years ago
a lottery costs $1 per ticket. the player selects a sincle letter from A to T and a single digit from 0 to 9. if both the letter
lara [203]
<h3>Answer:  0.25 dollars (ie 25 cents)</h3>

================================================

Explanation:

The letter T is the 20th letter in the English alphabet. This means that there are 20 letters to pick from to go with the 10 single digit numbers to pick from. We have 20*10 = 200 different combinations (eg: one combination is K4).

Out of these 200 combinations, there is exactly one winning match.

The probability of winning is therefore P(W) = 1/200 = 0.005 and the probability of losing is P(L) = 1-P(W) = 1-0.005 = 0.995 where W and L represent winning and losing respectively.

The net value of winning is V(W) = 250 - 1 = 249 because the player wins $250 but they lose $1 (which is the cost of the ticket). The net value of losing is V(L) = -1, indicating the player has lost that $1 and hasn't gained any money at all.

-----------

To summarize so far:

P(W) = 0.005

P(L) = 0.995

V(W) = 249

V(L) = -1

Multiply the probability P values with the corresponding net values V, then add up the products to get the expected value:

E(X) = P(W)*V(W) + P(L)*V(L)

E(X) = 0.005*249 + 0.995*(-1)

E(X) = 0.25

The expected value is 0.25 dollars or 25 cents

This positive expected value means that the game is favored toward the player, because over the long run, the player gains an average of 25 cents each time they play. On the other side of the spectrum, the lottery company loses on average 25 cents each time. The nonzero expected value means that the game is not fair.

7 0
3 years ago
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