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>
Answer:
2/3
Step-by-step explanation:
Let's define z = x-y, so solving for z will tell us exactly what we want to know. Then we can substitute for x: x = z+y, and our equations become ...
7(z+y)+3y = 8 ⇒ 7z +10y = 8
6(z+y)-3y = 5 ⇒ 6z +3y = 5
We can eliminate the y-variable by subtracting 3 times the first equation from 10 times the second:
10(6z +3y) -3(7z +10y) = 10(5) -3(8)
60z +30y -21z -30y = 50 -24 . . . . eliminate parentheses
39z = 26 . . . . collect terms
z = 26/39 = 2/3 . . . . . divide by the coefficient of z and reduce
The value of x - y is 2/3.
_____
The attached graph shows (x, y) = (1, 1/3), so x - y = 1 - 1/3 = 2/3.
Answer:
657
Step-by-step explanation:
312 + 138 + 207
= 450 + 207
= 657
∠P = 6x + 6
∠Q = 2x + 11
∠R = 2x + 3
∠P + ∠Q + ∠R = 180
(6x + 6) + (2x + 11) + (2x + 3) = 180
10x + 20 = 180
10x = 160
x = 16
∠Q = 2x + 11 = 2(16) + 11 = 32 + 11 = 43
Answer: 43°
Given:
Number of miles covered = 
Length of each lap = 
of a mile.
To find:
The number of laps.
Solution:
We know that,
Therefore, Grayson ran 3 laps.
