Answer: First Option
Step-by-step explanation:
Quadratic quadratic functions have the following form:
Where the point (h, k) is the vertex of the function.
For a quadratic function of the form the vertex of the function is at the point
In this case the function is:
Then:
The vertex is:
Note that
Therefore the vertex is the point
Finally we have that
The function in vertex form is :
Going from f(x) to f(x-1), we shift the graph 1 unit to the right. Tacking -5 at the end will shift the graph down 5 units.
<h3>Answer: Choice D</h3>
Answer:
7.57
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.
The height of sunflowers is Normally distributed with mean 50 inches and standard deviation 8 inches.
This means that
Percent of all sunflowers that are between 35 and 40 inches tall.
As a proportion, this is the pvalue of Z when X = 40 subtracted by the pvalue of Z when X = 35. So
X = 40
has a pvalue of 0.1057
X = 35
has a pvalue of 0.03
0.1057 - 0.03 = 0.0757
As percent: 0.0757*100% = 7.57%
Answer:
Claim :The proportion, p, of full-term babies born in their hospital that weigh more than 7 pounds is 36%.
n = 170
x = 56
We will use one sample proportion test
The proportion, p, of full-term babies born in their hospital that weigh more than 7 pounds is 36%.
Formula of test statistic =
=−0.8311
Now refer the p value from the z table
P-Value is .202987 (Calculated by online calculator)
Level of significance α = 0.05
Since p value < α
So we reject the null hypothesis .
Hence the claim is true
Answer:
cos(F) = 9/41
Step-by-step explanation:
The triangles are similar, so you know that ...
... cos(D) = cos(A) = 40/41.
From trig relations, you know ...
... cos(F) = sin(D)
and
... sin(D)² +cos(D)² = 1
So ...
... cos(F) = sin(D) = √(1 -cos(D)²) = √(1 -(40/41)²) = √(81/1681)
... cos(F) = 9/41
_____
The ratio for cos(A) tells you that you can consider AB=40, AC=41. Then, using the Pythagorean theorem, you can find BC = √(41² -40²) = √81 = 9.
From the definition of the cosine, you know cos(C) = BC/AC = 9/41. Because the triangles are similar, you know
... cos(F) = cos(C) = 9/41