Answer:
B
Step-by-step explanation:
Hey there!
Line passes through (4, -1) & is parallel to 2x -3y=9
Let's start off by identifying what our slope is. In the slope-intercept form y=mx+b, we know that "m" is our slope.
The given equation needs to be converted into slope-intercept form and we can do this by getting y onto its own side of the equal sign.
Start off by subtracting 2x from both sides.
-3y = -2x + 9
Then, divide both sides by -3.
y = (-2x + 9)/-3
Simplify.
y = 2/3x - 3
"M" is simply a place mat so if we look at our given line, the "m" value is 2/3. Therefore, our slope is 2/3.
We should also note that we're looking for a line that's parallel to the given one. This means that our new line has the same slope as our given line. Therefore, our new line has a slope of 2/3.
Now, we use point-slope form ( y-y₁=m(x-x₁) ) to complete our task of finding a line that passes through (4, -1). Our new slope is 2/3 & it passes through (4, -1).
y-y₁=m(x-x₁)
Let's start by plugging in 2/3 for m (our new slope), 4 for x1 and -1 for y1.
y - (-1) = 2/3(x - 4)
Simplify.
y + 1 = 2/3 + 8/3
Simplify by subtracting 1 from both sides.
y = 2/3x + 8/3 - 1
Simplify.
y = 2/3x + 5/3
~Hope I helped!~
Add the two numbers 3004000000+2749000000 and divide by 2
which equals 2876500000 or 2.8765x10^9
Ok so we'll go ahead and solve for y first - we just need to get it alone on one side of the equal sign
Step 1: subtract 2x from each side
2x - 7y - 2x = 19 - 2x
This cancels out the 2x on the left, giving us
-7y = 19 - 2x
Step 2: divide both sides by -7
=
+ 
This gives us
y = -19/7 + 2x/7
That should be your answer for the first question. Now solving the next parts are easy. All you need to do is plug in x.
When x = -3
y = -19/7 + 2x/7
y = -19/7 + 2(-3)/7
y = -19/7 - 6/7
y = -25/7
When x = 0
y = -19/7 + 2x/7
y = -19/7 + 2(0)/7
y = -19/7
When x = 3
y = -19/7 + 2x/7
y = -19/7 + 2(3)/7
y = -19/7 + 6/7
y = -13/7
Hope that helps! Feel free to ask if I can help with anything else :)
Answer:
The score that cuts off the bottom 2.5% is 48.93.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:

What is the score that cuts off the bottom 2.5%
This is X when Z has a pvalue of 0.025, so X when Z = -1.96.




The score that cuts off the bottom 2.5% is 48.93.