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: x = 37.8
Step-by-step explanation: We start with triangle ABC with two sides given as 15 and 18. We shall make angle C the reference angle and thereby calculate the third side, line BC.
Since we have the opposite side as 15, and the adjacent side (which lies between the reference angle and the right angle) as 18, we can use the tangent of the angle C
Tan C = Opp/Adj
Tan C = 15/18
Tan C = 0.8333
From our table of values/use of the calculator
Tan C = 39.8
Angle C in triangle ACB = Angle C in triangle ECD (Opposite angles are equal).
That takes us to triangle ECD, since the reference angle is known (39.8) and the opposite side is also given (31.5), we can now calculate the adjacent which is side x.
Tan C = Opp/Adj
Tan 39.8 = 31.5/x
when you cross multiply, x moves to the left hand side, while Tan 39.8 moves to the right hand side
x = 31.5/Tan 39.8
x = 31.5/0.8333
<u>x = 37.8</u>
The answer is Tuesday there will be 15 teachers for 179 students and 12 times 15 is 180
Gcf first
21y(y+5)
solutions are 0,-5
PEMDAS
multiply 2x2=4 and simplify the equation by looking for like terms to combine.
4+16x+y+34=0
4 and 34 are like terms so add them.
the simplified expression is 16x+y+38
