I would solve the first equation for x and then sub that value into x in the second equation. That's the easiest way. x - 2y = 3 solved for x is x = 2y+3. Now sub that in for x in the second equation: 5(2y+3)+3y=2 and 10y + 15 + 3y = 2. 13y = -13, and y = -1. Now sub that y value into either equation to solve for x: x = 2(-1) + 3 gives us an x value of x = 1. Therefore, your solution to this system is (1, -1), first choice above.
To find X, we can divide 5 into 40.
40 divided by 5 is 8.
Now we can do 5 x 8. That is 40.
X=40
OR we can do it another way.
40 divided by 5 is 8.
Cross out 5 divided by 5.
Now we have 8. Still.
X is 8
Let red marbles = X.
The probability is 1 out of 5, written as 1/5
1/5 in terms of red marbles is equal to the number of red marbles divided by 5x, where 5x is the total number of marbles.
1/5 = x/5x
Now you have 5x total marbles, x red and 4x blue.
Add 5 more red and the new probability is:
(x+5)/(5x+5) = 1/3
Simplify:
3x+15 = 5x+5
Now solve for x:
Subtract 3x from both sides:
15 = 2x +5
Subtract 5 from each side:
2x = 10
Divide both sides by 2:
x = 10/2
X = 5
There were originally 5 red marbles.
You start with a 1/4 chance of picking a diamond.
you remove it from the deck you now have a 12/51 chance of picking a diamond
1/17 is your answer!
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Answer:
The 99% confidence interval for the mean commute time of all commuters in Washington D.C. area is (22.35, 33.59).
Step-by-step explanation:
The (1 - <em>α</em>) % confidence interval for population mean (<em>μ</em>) is:

Here the population standard deviation (σ) is not provided. So the confidence interval would be computed using the <em>t</em>-distribution.
The (1 - <em>α</em>) % confidence interval for population mean (<em>μ</em>) using the <em>t</em>-distribution is:

Given:

*Use the <em>t</em>-table for the critical value.
Compute the 99% confidence interval as follows:

Thus, the 99% confidence interval for the mean commute time of all commuters in Washington D.C. area is (22.35, 33.59).