The table shows the speeds of several runners on a track team. What is the speed, in feet per minute, of the fastest runner?

Help please ASAP thank you

jonny [76]

<u>Question 1</u>

If we let $FE=x$ , then $DE=x-5$ .

Also, as $\overline{DF}$ bisects $\overline{BC}$ , this means $BE=EC=6$ .

Thus, by the intersecting chords theorem,

$6(6)=x(x-5)\\\\36=x^2 - 5x\\\\x^2 - 5x-36=0\\\\(x-9)(x+4)=0\\\\x=-4, 9$

However, as distance must be positive, we only consider the positive case, meaning FE=9

<u>Question 2</u>

If we let CE=x, then because AB bisects CD, CE=ED=x.

We also know that since FB=17, the radius of the circle is 17. So, this means that the diameter is 34, and as AE=2, thus means EB=32.

By the intersecting chords theorem,

$2(32)=x^2\\\\64=x^2\\\\x=-8, 8$

However, as distance must be positive, we only consider the positive case, meaning CE=8

4 0

2 years ago

Suppose you by a 1.25 pound package of ham at $5.20 per pound

marishachu [46]

I suppose I can do that and end up spending 6.50$?

1.25 x 5.20 = 6.50 final amount due.

6 0

3 years ago

Can someone please help me please

harina [27]

Answer:

If two angles are congruent, then they have the same measure.

Step-by-step explanation:

8 0

3 years ago

Many utility companies promote energy conservation by offering discount rates to consumers who keep their energy usage below cer

aleksley [76]

Answer:

a. 0.1681 = 16.81% probability that all five qualify for the favorable rate.

b. 0.5283 = 52.83% probability that at least four qualify for the favorable rates

Step-by-step explanation:

For each Puerto Rico resident, there are only two possible outcomes. Either they qualify for discounted rates, or they do not. The probability of a person in the sample qualifying for discounted rates is independent of any other person in the sample. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

70% of the island residents of Puerto Rico have reduced their electricity usage sufficiently to qualify for discounted rates.

This means that $p = 0.7$

Five residential subscribers are randomly selected from San Juan, Puerto Rico

This means that $n = 5$

a. All five qualify for the favorable rate

This is P(X = 5). So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 5) = C_{5,5}.(0.7)^{5}.(0.3)^{0} = 0.1681$

0.1681 = 16.81% probability that all five qualify for the favorable rate.

b. At least four qualify for the favorable rates

This is

$P(X \geq 4) = P(X = 4) + P(X = 5)$

So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 4) = C_{5,4}.(0.7)^{4}.(0.3)^{1} = 0.3602$

$P(X = 5) = C_{5,5}.(0.7)^{5}.(0.3)^{0} = 0.1681$

$P(X \geq 4) = P(X = 4) + P(X = 5) = 0.3602 + 0.1681 = 0.5283$

0.5283 = 52.83% probability that at least four qualify for the favorable rates

5 0

3 years ago

One plane can travel 30 miles per hour faster than another. one of them goes 185 miles in the same time it takes the other to go

ycow [4]

Plane #1 speed: x mph
Plane #2 speed: (x+30) mph

time = time becomes

170 mi 185 mi
---------- = --------------
x x+30

Solving for x, the speed of the slower plane, we get

170x + 5100 = 185 x
5100
Then 15x = 5100, and x = ---------- (mi/hr) = 340 mph
15

The slower plane flies at 340 mph, and the faster one at 370 mph.

6 0

3 years ago