Answer:
3000 m
Step-by-step explanation:
Using Pythagoras theorem

Similarly

Length of the Tunnel = |AB|+|BC|
=1999.9+999.7
=2999.6
=3000 m
Answer:
-4
Step-by-step explanation:
3(2x+8) = 0
Distribute
6x + 24 = 0
24 = -6x + 0
24/-6 = -4
Answer:
95% confidence interval for the mean number of months is between a lower limit of 6.67 months and an upper limit of 25.73 months.
Step-by-step explanation:
Confidence interval is given as mean +/- margin of error (E)
Data: 5, 15, 12, 22, 27
mean = (5+15+12+22+27)/5 = 81/5 = 16.2 months
sd = sqrt[((5-16.2)^2 + (15-16.2)^2 + (12-16.2)^2 + (22-16.2)^2 + (27-16.2)^2) ÷ 5] = sqrt(58.96) = 7.68 months
n = 5
degree of freedom = n-1 = 5-1 = 4
confidence level (C) = 95% = 0.95
significance level = 1 - C = 1 - 0.95 = 0.05 = 5%
critical value (t) corresponding to 4 degrees of freedom and 5% significance level is 2.776
E = t×sd/√n = 2.776×7.68/√5 = 9.53 months
Lower limit of mean = mean - E = 16.2 - 9.53 = 6.67 months
Upper limit of mean = mean + E = 16.2 + 9.53 = 25.73 months
95% confidence interval is (6.67, 25.73)
Answer:
∠?=40°
Step-by-step explanation:
Remember that in a line AND a triangle there are <u>180 degree</u>s.
You correctly found the third angle in the left triangle to be 69°, Now plug it into the equation for a line, including 71°:
<u>69°+71°+x=180°</u>
1) Combine the degrees:
140°+x=180°
2) Subtract 140° from both sides:
x=40°
We have now found the bottom left angle for the triangle on the right to be 40°
To find the angle labeled "?" You must plug in all of the known angles of the triangle to be equal to 180°:
40°+100°+x=180°
1) Combine the degrees:
140°+x=180°
2) Subtract 140 from both sides:
∠?=40°