Answer:
A.0.4477
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 problem, we have that:
What is the probability that a randomly selected exam will require between 14 and 19 minutes to grade?
This probability is the pvalue of Z when X = 19 subtracted by the pvalue of Z when X = 14. So
X = 19
has a pvalue of 0.7389.
X = 14
has a pvalue of 0.2912
0.7389 - 0.2912 = 0.4477
So the correct answer is:
A.0.4477
Answer:
- sin(X) = 6/7.5
- XY = 4.5
- cos(X) = 4.5/7.5
- tan(X) = 6/4.5
Step-by-step explanation:
It is convenient to use the Pythagorean theorem to find XY to start with. That theorem tells you ...
XZ² = YZ² + XY²
Solving for XY, you find ...
XY² = XZ² - YZ²
XY = √(XZ² - YZ²) = √(7.5² -6²) = √(56.25 -36) = √20.25
XY = 4.5
The mnemonic SOH CAH TOA is very helpful here. It reminds you that ...
Sin = Opposite/Hypotenuse
sin(X) = 6/7.5
Cos = Adjacent/Hypotenuse
cos(X) = 4.5/7.5
Tan = Opposite/Adjacent
tan(X) = 6/4.5
_____
<em>Comment on the triangle and ratios</em>
The side lengths of this triangle are in the ratios ...
XY : YZ : XZ = 3 : 4 : 5
If you recognize that the given sides are in the ratio 4 : 5, this tells you that you have a "3-4-5" right triangle with a scale factor of 1.5. At least, you can find XY = 1.5·3 = 4.5 with no further trouble.
The trig ratios could be reduced to sin(X) = 4/5; cos(X) = 3/5; tan(X) = 4/3, but the wording "don't simplify" suggests you want the numbers shown on the diagram, not their reduced ratios.
Answer:
I think this question is incomplete or maybe incorrect but if it's OK then the answer would be 7x + 5y.
Step-by-step explanation:
the answer remains the same because the question has no like terms so no further calculations can be made.
Step-by-step explanation:
x²y = k, where k is a real constant.
When x = 3.5, y = 8.
=> (3.5)²(8) = k, k = 98.
When y = 8/9,
we have x²(8/9) = (98).
=> x² = 110.25
=> x = 10.5 or x = -10.5.
Since we want the negative value,
the answer is x = -10.5.
