Answer:
The value of ∠A is 62° ⇒ c
The value of ∠B is 54°⇒ d
Step-by-step explanation:
<em>In a triangle, the measure of an exterior angle at a vertex of the triangle equals the sum of the measures of the two opposite interior angles to this vertex.</em>
<em />
In Δ ABC
∵ The measure of the exterior angle at the vertex C = 116°
∵ The opposite interior angles to vertex C are ∠A and ∠B
∵ m∠A = (3x - 13)°
∵ m∠B = (2x + 4)°
→ By using the rule above
∴ (3x - 13) + (2x + 4) = 116
→ Add the like terms in the left side
∵ (3x + 2x) + (-13 + 4) = 116
∴ 5x + -9 = 116
∴ 5x - 9 = 116
→ Add 9 to both sides
∵ 5x - 9 + 9 = 116 + 9
∴ 5x = 125
→ Divide both sides by 5
∴ x = 25
→ To find the measures of angle A and B substitute x in their
measures by 25
∵ m∠A = 3(25) - 13 = 75 - 13
∴ m∠A = 62°
∴ The value of ∠A is 62°
∵ m∠B = 2(25) + 4 = 50 + 4
∴ m∠B = 54°
∴ The value of ∠B is 54°
Answer:
The test statistic is Z = 1.157
Step-by-step explanation:
Given that:
The sample size n = 1200
The sample proportion of those that will vote for the Republican candidate is represented by 
The null and the alternative hypothesis can be computed as:
The formula for the one-sample Z-test for the population proportion can be expressed as:
Z = 1.157
You use the first formula. You plug in the values to get A=400(1+(0.05/1))^6. You should get approximately $536.04. I used 0.05 because you need to change the percent to a decimal, and 1 for n because it is compounded annually, meaning once a year.
