Answer:
∠6=78° ∠7=102° ∠14=78°
Step-by-step explanation:
Angles 6 and 7 are supplementary angles so ∠a+∠b=180°
in this case it would be 102°+x=180° and you subtract 102° from 180° getting 78°
∠7 is the vertical angles postulate stating that any angles vertical to each other are eaqual
First you would find the area of the triangle which would be 84×92 then divide that answer by 2.
Then you will find the area of the circle using the given radius 20.5.
Lets work it out.
84×92=7728
7728÷2=3864 ft²
3864 ft² is the area of the backyard including the pool.
A=pi(20.5)²
A=1320.25 ft²
1320.25 ft² is the area of the pool.
Now we have to subtract to get the area of the backyard without the pool.
3864-1320.25=2543.75 ft²
2543.75 ft² is your answer.
Hope This Helps and God Bless!
Answer:

Step-by-step explanation:
Given:
Fifth term of a geometric sequence = 
Common ratio (r) = ¼
Required:
Formula for the nth term of the geometric sequence
Solution:
Step 1: find the first term of the sequence
Formula for nth term of a geometric sequence =
, where:
a = first term
r = common ratio = ¼
Thus, we are given the 5th term to be ¹/16, so n here = 5.
Input all these values into the formula to find a, the first term.




Cross multiply

Divide both sides by 16



Step 2: input the value of a and r to find the nth term formula of the sequence
nth term = 
nth term = 

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:
Step-by-step explanation:
-1/2 + (3/4 x 4/9)
-1/2 + (3/9)
= - 1/2 + (1/3)
= - 1/6