Answer:
The next time both will leave the bus station at the same time is 7:15 a.m.
Step-by-step explanation:
Since 15 and 75 are multiples to each other.
So, L.C.M. of 15 and 75 is 75.
So, after 75 minutes both buses will leave the station at the same time.
Also since buses begin their routes at 6 a.m.
So, next time they will meet at
6 hours 0 minutes + 75 minutes = 7 hours 15 minutes = 7:15 a.m.
Let f(x)=y
f^-1(x)=x
y=1/(x+5) - 1
y+1=1/(x+5)
(x+5)=1/(y+1)
x=1/(y+1)-5
f^-1(x)=1/(x+1) -5
denominator cannot equals to zero
x+1≠0
x≠-1
answer
B
z = -2.83
<u>Explanation:</u>
Given:
Mean, μ = 68
Standard deviation, σ = 6
Data point, x = 51
Z score, z = ?
We know:

Substituting the value we get:

A negative z score says that the data point is below average.
Answer:
The z-score of a male bird of this species with a weight of 29.37 grams is 1.7.
Step-by-step explanation:
We are given that the weights of adult male birds of a certain species are normally distributed with a mean of 27.5 grams and a standard deviation of 1.1 grams.
<u><em>Let X = weights of adult male birds of a certain species</em></u>
So, X ~ Normal(
)
The z score probability distribution for normal distribution is given by;
Z =
~ N(0,1)
where,
= population mean weight = 27.5 grams
= standard deviation = 1.1 grams
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.
SO, the z-score of a male bird of this species with a weight of 29.37 grams is given by;
<u>Z score</u> =
=
= <u>1.7</u>