Answer:
We are 95% confident that the percent of executives who prefer trucks is between 19.43% and 33.06%
Step-by-step explanation:
We are given that in a group of randomly selected adults, 160 identified themselves as executives.
n = 160
Also we are given that 42 of executives preferred trucks.
So the proportion of executives who prefer trucks is given by
p = 42/160
p = 0.2625
We are asked to find the 95% confidence interval for the percent of executives who prefer trucks.
We can use normal distribution for this problem if the following conditions are satisfied.
n×p ≥ 10
160×0.2625 ≥ 10
42 ≥ 10 (satisfied)
n×(1 - p) ≥ 10
160×(1 - 0.2625) ≥ 10
118 ≥ 10 (satisfied)
The required confidence interval is given by
Where p is the proportion of executives who prefer trucks, n is the number of executives and z is the z-score corresponding to the confidence level of 95%.
Form the z-table, the z-score corresponding to the confidence level of 95% is 1.96
Therefore, we are 95% confident that the percent of executives who prefer trucks is between 19.43% and 33.06%
Answer:
8(15-m)
Step-by-step explanation:
By looking at the options, we can understand that the right one is 8(15-m), since we need to multiply the time by the number of question.
Also, we can check that result by arranging an equations usint the total time.
55 = 3m - 8(15-m)
55 = 3m - 120 + 8m
55 = 11m - 120
55 + 120 = 11m
175 = 11m
m = 175/11 = 15.91
55 = 3*15.91 - 8(15-15.91) = 47.73 - 120 + 127.28 = 55.01 ≈ 55
Answer: B) Dilate by scale factor of 2
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Explanation:
Your teacher isn't saying this directly, but I'm assuming s/he wants you to find a similar figure that isn't congruent to the original. Informally, your teacher seems to want you to find a figure that is the same shape but not the same size as the original.
If so, then any dilation will shrink or enlarge the image depending on the scale factor. So the new image will not be the same as the old one. In this case, a dilation with scale factor 2 means the new figure is twice as large (each side is twice as long). But the old image is similar to the new image. The angles keep their values and therefore we get the same shape. This is why choice B is the answer. Again this is assuming what I mentioned in the first paragraph.
Choices A, C, and D are all known as rigid transformations and they preserve the same size of the figure. Applying any of those operations will lead to the same figure (just rotated, reflected or shifted somehow). In other words, applying operations A,C, or D will have us get two congruent triangles. If two triangles are congruent, then they are automatically similar, but not vice versa. This is why we can rule out A,C, and D.
Answer:
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Step-by-step explanation:
g(x) = x² - 2x - 6
h(x) = 2x² - 5x + 2
To find (h-g) (-2) we must first find h - g(x)
To find h - g(x) subtract g(x) from h(x)
We have
<h3>
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</h3>
To find (h-g) (-2) substitute the value of x that's - 2 into (h - g)(x) that's replace every x in (h - g)(x) by - 2
That's
<h3>
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We have the final answer as
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Hope this helps you
