Answer:
See below in bold.
Step-by-step explanation:
For the fair coin Prob(head) = 1/2 and Prob(Tail) = 1/2.
For the biased coin it is Prob(head) = 2/3 and Prob(Tail) = 1/3.
a) Prob(2 heads) = 1/2 * 2/3 = 1/3.
b) Prob(2 tails) = 1/2 * 1/3 = 1/6.
c) Prob(1 head ) = Prob(H T or T H) = 1/2 * 1/3 + 1/2 * 2/3) = 1/6+1/3 = 1/2.
d) Prob (at least one head) = prob (HH or TH or HT) = 1/3 + 1/2 =<em> </em>5/6.
The formula for arithmetic sequence is given by:
an=a+(n-1)d
where:
an=nth term
a=first term
n=number of terms
thus our first term will be:
a1=8
a2=8+(2-1)(-6)=2
a3=8+(3-1)(-6)=-4
a4=8+(4-1)(-6)=-10
a5=8+(5-1)(-6)=-16
a5=-16
thus the sequence will be:
8,2,-4,-10,-16...
At 13% significance level, there isn't enough evidence to prove the administrators to claim that the mean score for the state's eighth graders on this exam is more than 280.
<h3>How to state hypothesis conclusion?</h3>
We are given;
Sample size; n = 78
population standard deviation σ = 37
Sample Mean; x' = 280
Population mean; μ = 287
The school administrator declares that mean score is more (bigger than) 280. Thus, the hypotheses is stated as;
Null hypothesis; H₀: μ > 280
Alternative hypothesis; Hₐ: μ < 280
This is a one tail test with significance level of α = 0.13
From online tables, the critical value at α = 0.13 is z(c) = -1.13
b) Formula for the test statistic is;
z = (x- μ)/(σ/√n)
z = ((280 - 287) *√78 )/37
z = -1.67
c) From online p-value from z-score calculator, we have;
P[ z > 280 ] = 0.048
d) The value for z = -1.67 is smaller than the critical value mentioned in problem statement z(c) = - 1.13 , the z(s) is in the rejection zone. Therefore we reject H₀
e) We conclude that at 13% significance level, there isn't enough evidence to prove the administrators to claim that the mean score for the state's eighth graders on this exam is more than 280.
Read more about Hypothesis Conclusion at; brainly.com/question/15980493
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AD is perpendicular to BC so slope Ad = -1/slope of BC
Slope of BC = (2 - (-1)) / (- 6- 3) = 3 / -9 = -1/3
So slope of AD = -1 / (-1/3) = -3/-1 = 3 Answer
We are given the following equation:
Subtract both sides by 17
Take the positive/negative square root of both sides
This should be your answer. Let me know if you have any questions, thanks!