Answer:
x = 14
< A = 58 degrees
< B = 52 degrees
< C = 70 degrees
Step-by-step explanation:
Recall that the addition of the three internal angles of a triangle must render 180 degrees, then we can write:
<A + <B + <C = 180
and now replace with the algebraic expressions given for each angle:
2(x + 15) + 3 x + 10 + 5 x = 180
eliminate parenthesis
2 x + 30 + 3 x + 10 + 5 x = 180
combine like terms
10 x + 40 = 180
subtract 40 from both sides
10 x = 140
divide both sides y 10 to isolate x
x = 14
Now that we know x, we can calculate each of the angles using the fiven expressions:
< A = 2 (x + 15) = 2 (14 + 15) = 2 * 29 = 58 degrees
< B = 3 x + 10 = 3 * 14 + 10 = 52 degrees
< C = 5 x = 5 * 14 = 70 degrees
Answer:
37
Step-by-step explanation:
Margin of error = critical value × standard error
For 98% confidence, CV = 2.326 (from t table).
Standard error is σ / √n, where σ is the population standard deviation, and n is the sample size.
Plugging in:
5 = 2.326 × 13 / √n
n = 36.6
Rounding up, n = 37.
Answer: Rachel's prediction is faster than the actual unit rate, and Theadore's prediction is slower.
Answer:
<em>Part A: 45</em>
<em>Part B: 22</em>
Step-by-step explanation: