Answer:
Yes, result is significant ; PVALUE < α
Step-by-step explanation:
Given :
x = 536
n = sample size = 1012
Phat = x / n = 536 / 1012 = 0.5296 = 0.53
H0 : P0 = 0.5
H1 : P0 > 0.5
Test statistic :
(Phat - P0) ÷ sqrt[(P0(1 - P0)) / n]
1-P0 = 1 - 0.5 = 0.5
(0.53 - 0.5) ÷ sqrt[(0.5*0.5)/1012]
0.03 ÷ 0.0157173
= 1.9087
Pvalue :
Using the Pvalue from test statistic :
Pvalue = 0.02815
To test if result is significant :
α = 0.05
0.02815 < 0.05
Pvalue < α ; Hence, result is significant at α=0.05; Hence, we reject H0.
Recall that for all t,
cos²(t) + sin²(t) = 1
Now,
x = 5 cos(t) - 7 ⇒ (x + 7)/5 = cos(t)
y = 5 sin(t) + 9 ⇒ (y - 9)/5 = sin(t)
so that substituting into the identity above, we get
((x + 7)/5)² + ((y - 9)/5)² = 1
which we can rewrite as
(x + 7)²/25 + (y - 9)²/25 = 1
(x + 7)² + (y - 9)² = 25
and this is the equation of a circle centered at (-7, 9) with radius 5.
<span>204
First, lookup a standard normal table and see what the z-score is for 0.025 (one half of 100% - 95%) to allow for equal sized tails. You should find that the z-score is 1.96. That means that 95% of the time, the value should be within 1.96 standard deviations of the mean. Now let's calculate the standard deviation.
800 is 800 - 1200 = -400 to the left of the mean of 1200.
1600 is 1600 - 1200 = 400 to the right of the mean of 1200.
So we are an equal distance of 400 on both sides of the mean. And we know from the z-score of 1.96, that we're 1.96 standard deviations from the mean. So a little division will give us the standard deviation. Which is:
400 / 1.96 = 204.0816327
So the standard deviation of the light bulbs is 204</span>
Answer:
1280
Step-by-step explanation:
I think it is 1280 because 20*16*8/2=1280. I am not 100% sure.
