Answer:
107 inches
Step-by-step explanation:
28+45+x=180
x=180-28+45
x=180-73
x=107
7,14,21,28,35,42,49,56,63,70,77,84,91,98,105,112,119,126
18,36,54,72,90,108,126
So the first person to get both of them is the 126th person
i) The given function is

The domain is all real values except the ones that will make the denominator zero.



The domain is all real values except, x=2.5.
ii) To find the vertical asymptote, we equate the denominator to zero and solve for x.



iii) If we equate the numerator to zero, we get;


This implies that;

iv) To find the y-intercept, we put x=0 into the given function to get;
.
.
.
v)
The degrees of both numerator and the denominator are the same.
The ratio of the coefficient of the degree of the numerator to that of the denominator will give us the asymptote.
The horizontal asymptote is
.
vi) The function has no common factors that are at least linear.
The function has no holes in it.
vii) This rational function has no oblique asymptotes because it is a proper rational function.
Answer:
2.0%
Step-by-step explanation:
The probability of two events happening in the sequence is calculated by multiplying the probability of each event happening separately by one another. Since there are a total of 7 letters in this word then the probability of choosing one letter correctly is
. Since the first letter is replaced before choosing the second letter the probability remains the same. Therefore, the sequence would be the following...
= 0.020164 or 2.0%
This is an independent scenario because it does not depend on any external factors and under these circumstances the percentage will remain the same.
Answer:
a) z* = -1.97
b) z* = -2.33
c) z* = -1.65
d) z* = 2.04
e) z* = 2.33
f) z* = -1.25.
Step-by-step explanation:
Z-score:
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.
a. P(z < z*) = 0.0244
We have to look at the ztable, and find z which has a pvalue of 0.0244. So it is z* = -1.97
b. P(z < z*) = 0.0098
We have to look at the ztable, and find z which has a pvalue of 0.0098. So it is z* = -2.33
c. P(z < z*) = 0.0496
We have to look at the ztable, and find z which has a pvalue of 0.0496. So it is z* = -1.65
d. P(z > z*) = 0.0204
We have to look at the ztable, and find z which has a pvalue of 1 - 0.0204 = 0.9796. So z* = 2.04
e. P(z > z*) = 0.0098
We have to look at the ztable, and find z which has a pvalue of 1 - 0.0098 = 0.9902. So z* = 2.33
(f) P(z > z* or z < -z*) = 0.201
This is z which has a pvalue of 0.201/2 = 0.1055. So it is z* = -1.25.