Answer: -7.5
Step-by-step explanation:
area = 1/2bh.
area = 1/2(x+6)(5)
area = x/2 + 15
area = x/2 = -15
area = x = -7.5
area = -7.5
You can use the definition:

Then if

we have

Then the derivative is

I'm guessing the second part of the question asks you to find the tangent line to <em>f(x)</em> at the point <em>a</em> = 0. The slope of the tangent line to this point is

and when <em>a</em> = 0, we have <em>f(a)</em> = <em>f</em> (0) = -2, so the graph of <em>f(x)</em> passes through the point (0, -2).
Use the point-slope formula to get the equation of the tangent line:
<em>y</em> - (-2) = 3 (<em>x</em> - 0)
<em>y</em> + 2 = 3<em>x</em>
<em>y</em> = 3<em>x</em> - 2
<u>Answer:</u>
The correct answer option is C. 13.6 units.
<u>Step-by-step explanation:</u>
Line segment AB was dilated to create the line segment A'B' using the dilation rule
.
We are to find the value of
which is the distance between the twp points A and A'.
For this, we will divide the distance of A'Q by the dilation factor and then subtract the given length.

x =
= 13.6 units
4 [ 5 (12 + 3) - 2 ] - 7
4 [ 5 (15) - 2 ] - 7
4 [ 75 - 2 ] - 7
4 [ 73 ] - 7
292 - 7
285
Answer:
0.1069 = 10.69%
Step-by-step explanation:
Problems of normally distributed samples are solved using 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:

Between 57 and 69
This is the pvalue of Z when X = 69 subtracted by the pvalue of Z when X = 57. So
X = 69



has a pvalue of 0.9918
X = 57



has a pvalue of 0.8849
0.9918 - 0.8849 = 0.1069 = 10.69%