Answer:
Step-by-step explanation:
1) ∠1 + ∠2 = 180 {linear pair}
105 +∠2 = 180
∠2 = 180 - 105
∠2 = 75°
Reason: Linear pair
2) ∠3 = ∠1 {Vertically opposite angles are congruent}
∠3 = 105
Reason: Vertically opposite angles are congruent
Answer:
x₁ > x₂
Step-by-step explanation:
Both actions imply a parable trajectories, since both are projectile shot cases.
Let´s call x₁ maximum distance in the first case
The maximum height is just in the middle of the curve, therefore x₁ the maximum horizontal distance is equal to 60 feet.
In the second case, the parable curve is modeled by:
y = x₂*( 0.08 - 0.002x₂) or y = 0.08*x₂ - 0.002*x₂²
A second degree equation, solving for x₂ and dismissing the value x₂ = 0
we get:
y = 0 ⇒ x₂*( 0.08 - 0.002x₂) = 0 x₂ = 0
And 0,08 - 0.002*x₂ = 0
- 0.002*x₂ = - 0.08
x₂ = 0.08/0.002
x₂ = 40 f
Then x₁ > x₂
Answer:
- There is no significant evidence that p1 is different than p2 at 0.01 significance level.
- 99% confidence interval for p1-p2 is -0.171 ±0.237 that is (−0.408, 0.066)
Step-by-step explanation:
Let p1 be the proportion of the common attribute in population1
And p2 be the proportion of the same common attribute in population2
: p1-p2=0
: p1-p2≠0
Test statistic can be found using the equation:
where
- p1 is the sample proportion of the common attribute in population1 (
)
- p2 is the sample proportion of the common attribute in population2 (
)
- p is the pool proportion of p1 and p2 (
)
- n1 is the sample size of the people from population1 (30)
- n2 is the sample size of the people from population2 (1900)
Then
≈ 2.03
p-value of the test statistic is 0.042>0.01, therefore we fail to reject the null hypothesis. There is no significant evidence that p1 is different than p2.
99% confidence interval estimate for p1-p2 can be calculated using the equation
p1-p2±
where
- z is the z-statistic for the 99% confidence (2.58)
Thus 99% confidence interval is
0.533-0.704±
≈ -0.171 ±0.237 that is (−0.408, 0.066)
Answer:
Step-by-step explanation:
4 cups of J for every 7 cups of soda 4:7
21 cups of soda will take 12 cups of J
If you take the 7 and multiply by 3 you get the 21.
So you will need to multiply the 4 by the 3 to get the 12. You need to keep everything in proportion.
4:7 same as 12:21
The answer is x=-15 and y=25