Answer:
24
Step-by-step explanation:
Here's how we construct the LCD:
Factor the denominators 6 and 8: 6 = 2*3 and 8 = 2*2*2
The LCD involves 2*2*2 as well as 3:
LCD: 2*2*2*3 = 24. Note that 24 is divisible by both 6 and 8. There is no smaller LCD that is divisible by 6 and 8 both.
Answer:
10. Supplementary
11. Congruent
12. Congruent.
13 . congruent
14 supplement
15 supplementary
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Answer:
b = 159 m
a = 103 m
angle B is 57 degrees
Step-by-step explanation:
Let’s start with getting the measure of angle B
Mathematically, since we have a right triangle , we have to subtract the given angle from 90 to get the other acute angle
So we have the measure of B as;
90-33 = 57 degrees
To get the value of a, we use the appropriate trigonometric ratio
a faces the angle 33, that makes it an opposite to that angle
190 faces the right angle and that makes it the hypotenuse
Mathematically , the relationship between the two is that trigonometrically, they are related by the sine which is the ratio of the opposite to the hypotenuse
so, we have it that;
sine 33 = a/190
a = 190 * sine 33
a = 103 m
to get b, it is adjacent to the given angle
So with the hypotenuse, the ratio between it and the hypotenuse is the cosine
so;
cos 33 = b/190
b = 190 * cos 33
b = 159 m
Answer:
Step-by-step explanation:
Hello!
The variable of interest is:
X: number of daily text messages a high school girl sends.
This variable has a population standard deviation of 20 text messages.
A sample of 50 high school girls is taken.
The is no information about the variable distribution, but since the sample is large enough, n ≥ 30, you can apply the Central Limit Theorem and approximate the distribution of the sample mean to normal:
X[bar]≈N(μ;δ²/n)
This way you can use an approximation of the standard normal to calculate the asked probabilities of the sample mean of daily text messages of high school girls:
Z=(X[bar]-μ)/(δ/√n)≈ N(0;1)
a.
P(X[bar]<95) = P(Z<(95-100)/(20/√50))= P(Z<-1.77)= 0.03836
b.
P(95≤X[bar]≤105)= P(X[bar]≤105)-P(X[bar]≤95)
P(Z≤(105-100)/(20/√50))-P(Z≤(95-100)/(20/√50))= P(Z≤1.77)-P(Z≤-1.77)= 0.96164-0.03836= 0.92328
I hope you have a SUPER day!
Answer:
the approximate range of change is 150 for 3
the approximate range of change is 1600 for 4
between 1970 and 1975
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