If X and Y vary directly, as x decreases, what happens to the value of y?

Simplify: ? (10x = 105 - (12x – 247)

Greeley [361]

Answer:

x = 16

Step-by-step explanation:

10x = 105 - (12x - 247) //Distribute - sign

10x = 105 - 12x + 247 // Add 12x & combine like terms

10x + 12x = 352

22x = 352 //Divide 22

x = 352/22

x = 16

7 0

3 years ago

What is the value of S in the equation 1/3s+14=26

Law Incorporation [45]

First, isolate 1/3s:
1/3s=12
Second, multiply both sides by 3 to get a singular value of s (just s):
s=36

4 0

3 years ago

How many solutions does the equation 5x+17=4(3x−1) have?

Stella [2.4K]

<u>Answer:</u>

one solution = 3

<u>Step-by-step explanation:</u>

Let's solve your equation step-by-step.

5x+17=4(3x−1)

Step 1: Simplify both sides of the equation.

5x+17=4(3x−1)

5x+17=(4)(3x)+(4)(−1)(Distribute)

5x+17=12x+−4

5x+17=12x−4

Step 2: Subtract 12x from both sides.

5x+17−12x=12x−4−12x

−7x+17=−4

Step 3: Subtract 17 from both sides.

−7x+17−17=−4−17

−7x=−21

Step 4: Divide both sides by -7

-7x/-7 = -21/-7 = 3

4 0

3 years ago

At Munder Difflin Paper Company, the manager Mitchell Short randomly places golden sheets of paper inside of 30% of their paper

Korvikt [17]

Answer:

90.67% probability that John finds less than 7 golden sheets of paper

Step-by-step explanation:

For each container, there are only two possible outcomes. Either it contains a golden sheet of paper, or it does not. The probability of a container containing a golden sheet of paper is independent of other containers. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

At Munder Difflin Paper Company, the manager Mitchell Short randomly places golden sheets of paper inside of 30% of their paper containers.

This means that $p = 0.3$

14 of these containers of paper.

This means that $n = 14$

What is the probability that John finds less than 7 golden sheets of paper?

$P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{14,0}.(0.3)^{0}.(0.7)^{14} = 0.0068$

$P(X = 1) = C_{14,1}.(0.3)^{1}.(0.7)^{13} = 0.0407$

$P(X = 2) = C_{14,2}.(0.3)^{2}.(0.7)^{12} = 0.1134$

$P(X = 3) = C_{14,3}.(0.3)^{3}.(0.7)^{11} = 0.1943$

$P(X = 4) = C_{14,4}.(0.3)^{4}.(0.7)^{10} = 0.2290$

$P(X = 5) = C_{14,5}.(0.3)^{5}.(0.7)^{9} = 0.1963$

$P(X = 6) = C_{14,6}.(0.3)^{6}.(0.7)^{8} = 0.1262$

$P(X < 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) = 0.0068 + 0.0407 + 0.1134 + 0.1943 + 0.2290 + 0.1963 + 0.1262 = 0.9067$