Answer:
238
Step-by-step explanation:
Important note: ∠FAH is an inscribed angle and arc mFGH is it's intercepted arc
opposite angles in a quadrilateral formed inside of a circle area supplementary
Supplementary meaning that they add up to equal 180
So 13x + 15 + 8x - 3 = 180
We now solve for x
step 1 combine like terms
13x + 8x = 21x
15 - 3 = 12
12 + 21x = 180
step 2 subtract 12 from each side
12 - 12 cancels out
180 - 12 = 168
21x = 168
step 3 divide each side by 21
21x / 21 = x
168 / 21 = 8
we're left with x = 8
Now we substitute 8 for x in 13x + 15
13 ( 8 ) + 15
13 * 8 = 104
104 + 15 = 119
So ∠FAH = 119
Recall that an included angle is equal to half the measure of its intercepted arc.
so arc mFGH = 2 (119)
2 * 119 = 238
Therefore your answer is A
Andrew drove at 78 km/h
Brian drove at 83 km/h
234/83 = 2.819 hours, or 169 minutes.
180-169=11
Answer:
Using a 95% confidence level, the lower end point of a two-tailed interval that would be used to predict the range of values that this 17th sampled unit would be in with respect to seconds soaking a component part in solution is of 29.137 seconds.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 16 - 1 = 15
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 15 degrees of freedom(y-axis) and a confidence level of . So we have T = 2.1315
The margin of error is:
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 33.4 - 4.263 = 29.137 seconds.
Using a 95% confidence level, the lower end point of a two-tailed interval that would be used to predict the range of values that this 17th sampled unit would be in with respect to seconds soaking a component part in solution is of 29.137 seconds.
3 - 2a > 7
We need to solve for a
First, let's subtract 3 on both sides to have the variables on a side and the numbers on another side:
3 - 2a > 7
3 - 2a - 3 > 7 - 3
- 2a > 4
Let's divide both sides by -2 to have a on side and its value on the other side:
-2a > 4
(-2a)/(-2) > (4/-2)
a < -2 (In a case of an inequality, we change the sign when we divide by a negative number to its opposite).
So 3 - 2a > 7 when a < -2 (answer c)
Hope this helps! :D
The main formula is:
Distance traveled = (average)Speed*Time.
i) when Ted Climbs up:
let D be the distance, T the time it takes Ted to climb, S_u=3mph is the speed as Ted climbs up.
then: D=3T
ii) when Ted goes down:
D is the distance, T-40 the time it takes Ted go down, S_d=5mph is the speed as Ted climbs up.
then: D=5(T-40)
equalizing the equations in i and ii:
(D=) 3T=5(T-40)
3T=5T-200
200=2T
T=100 (minutes)
the total length of the hike is T+T-40=100+100-40=160 (minutes)
Answer: 160 minutes