In order to find this answer we have to manipulate the equation algebraically so that we end up with a statement that x = something. We can manipulate the problem however we need to as long as we do the same thing to both sides of the equation (this keeps the equation true).
-8x/5 + 1/6 = -5x/3
first lets get the x's on one side of the equals sign by adding 8x/5 to each side.
1/6 = -5x/3 + 8x/5
Ok, now let's add the x's together (we need common denominators)
1/6 = -25x/15 + 24x/15
1/6 = -x/15
Now lets get x by itself by multiplying each side by 15
1/6 * 15 = -x
15/6 = -x
3/2 = -x
Multiply each side by -1 to make the x positive.
-3/2 = x
Answer: For the sum of 130
First: $90
Second: $40
Step-by-step explanation:
We write equations for each part of this situation.
<u>The Total Charge</u>
Together they charged 1550. This means 1550 is made up of the first mechanics rate for 15 hours and the second's rate for 5 hours. Lets call the first's rate a, so he charges 15a. The second's let's call b. He charges 5b. We add them together 15a+5b=1550.
<u>The Sum of the Rates</u>
Since the first's rate is a and the second is b, we can write a+b=130 since their sum is 130.
We solve for a and b by substituting one equation into another. Solve for the variable. Then substitute the value into the equation to find the other variable.
For a+b=130, rearrange to b=130-a and substitute into 15a+5b=1550.
15a + 5 (130-a)=1550
15a+650-5a=1550
10a+650-650=1550-650
10a=900
a=$90 was charged by the first mechanic.
We substitute to find the second mechanic's rate.
90+b=130
90-90+b=130-90
b= $40 was charged by the second mechanic
Answer:
(a) 2.22
(b) 1.3986
(c) 1.183
Step-by-step explanation:
Let <em>X</em> denote the number of women who consider themselves fans of professional baseball.
The proportion of women who consider themselves fans of professional baseball is, <em>p</em> = 0.37.
A random sample of <em>n</em> = 6 women are selected and each was asked if she considers herself a fan of professional baseball.
Each woman's reply is independent of the others.
The random variable <em>X</em> thus follows a binomial distribution with parameters <em>n</em> = 6 and <em>p</em> = 0.37.
(a)
Compute the mean of the binomial distribution as follows:
(b)
Compute the variance of the binomial distribution as follows:
(c)
Compute the standard deviation of the binomial distribution as follows:
