What does 4m^2 +5m if m=-2 equal?
1 answer:
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Answer:
a) P(Z > 1.09) = 0.1379
b) P(Z < -0.22) = 0.4129.
c) P(Z < -1.96) = 0.025, P(Z > -1.96) = 0.025
d) Z = 1.4
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
a. P(Z > 1.09)
This is 1 subtracted by the pvalue of Z = 1.09.
Z = 1.09 has a pvalue of 0.8621
1 - 0.8621 = 0.1379, so
P(Z > 1.09) = 0.1379
b. P(Z < -0.22)
This is the pvalue of Z = -0.22.
Z = -0.22 has a pvalue of 0.4129. So
P(Z < -0.22) = 0.4129.
c) P(Z < -1.96) or P(Z > -1.96)
Z = -1.96 has a pvalue of 0.025. So
1 - 0.025 = 0.975
P(Z < -1.96) = 0.025
P(Z > -1.96) = 0.025
d. What is the value of Z if only 8.08% of all possible Z-values are larger?
Z with a pvalue of 100 - 8.08 = 91.92 = 0.9192, so Z = 1.4
From the description we can infer that we have the expression: 
.
Now, to write our expression as a as a root, we are going to apply the law of exponents:
first
Next, we are going to apply the law about fractional exponents:![x^{ \frac{m}{n}}= \sqrt[n]{x^m}](https://tex.z-dn.net/?f=x%5E%7B%20%5Cfrac%7Bm%7D%7Bn%7D%7D%3D%20%5Csqrt%5Bn%5D%7Bx%5Em%7D%20%20)
![\frac{1}{41^{ \frac{2}{5} }}= \frac{1}{ \sqrt[5]{41^2} }](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B41%5E%7B%20%5Cfrac%7B2%7D%7B5%7D%20%7D%7D%3D%20%5Cfrac%7B1%7D%7B%20%5Csqrt%5B5%5D%7B41%5E2%7D%20%7D%20)
We can conclude that the value of B is 2.
Now, to write our expression as a as a root, we are going to apply the law of exponents:
Next, we are going to apply the law about fractional exponents:
We can conclude that the value of B is 2.
Answer:
The angle is 55°
Step-by-step explanation:
To find the angle at which a bid is looking up on top of a tree that is 10feet tall if the bird is on the ground 7 feet away from the tree, we will follow the steps below:
we will use trigonometric ratio to find the angle
SOH CAH TOA
sinФ = opposite / hypotenuse
cosФ = adjacent / hypotenuse
tanФ = opposite /adjacent
from the diagram below, opposite = 10 feet and adjacent = 7 feet
the best trig.ratio to use is tan
tanФ = opposite /adjacent
tanФ = 10 /7
tan Ф =1.42857
to get the value of Ф, we will take the tan⁻¹ of both-side
tan⁻¹ tan Ф = tan⁻¹ 1.42857
Ф= tan⁻¹ 1.42857
Ф≈55°
Therefore, the angle is 55°
