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2 years ago

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David drives from his home to the airport to catch a flight. He drives 35 miles in the first hour, but realizes that he will be

1 hour late if he continues at this speed. He increases his speed by 15 miles per hour for the rest of the way to the airport and arrives 30 minutes early. How many miles is the airport from his home

1 answer:

sweet-ann [11.9K]2 years ago

7 0

The distance between David's home and the airport is 210 miles.

<h3>Distance traveled after 1 hour</h3>

let the distance traveled after first 1 hour = y

distance/speed = time

after 1 hour his speed = (35 + 15) = 50 mph

total time after 1 hour and 30 mins = 1.5 hr

y/50 + 1.5 = y/35

multiply through by350

7y + 525 = 10y

3y = 525

y = 525/3

y = 175 miles

In the first 1 hour, at 35 mph, distance covered = 35 miles

Distance from his home to airport = 175 miles + 35 miles = 210 miles

Thus, the distance between David's home and the airport is 210 miles.

Learn more about distance here: brainly.com/question/2854969

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Suppose you purchase a bundle of 18 bare-root broccoli plants. The sales clerk tells you that on average you can expect 8% of th

neonofarm [45]

Answer:

There is a 57.18% probability that you will lose at most 1 of the broccoli plants.

Step-by-step explanation:

For each plant, there are only two possible outcomes. Either they die, or they do not. This means that we can solve this problem using the binomial probability distribution.

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 combinatios 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.

In this problem, we have that

There are 18 plants, so $n = 18$ .

8% of the plants die before producing any broccoli. So $p = 0.08$ .

Use the binomial formula to find the probability that you will lose at most 1 of the broccoli plants.

This is

$P = P(X = 0) + P(X = 1)$

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

$P(X = 0) = C_{18,0}.(0.08)^{0}.(0.92)^{18} = 0.2229$

$P(X = 1) = C_{18,1}.(0.08)^{1}.(0.92)^{17} = 0.3489$

$P = P(X = 0) + P(X = 1) = 0.2229 + 0.3489 = 0.5718$

There is a 57.18% probability that you will lose at most 1 of the broccoli plants.

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3 years ago

What is 5 x 7 - 12 + 56 - 9 ?

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Answer: 70

Step-by-step explanation:

5 multiplied by 7 is 35.

35 - 12 is 23.

23 + 56 is 79.

79 - 9 is 70.

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3 years ago

Jessica Reads a story about a turtle that swam 16 feet in 24 seconds. She assumes that the time that it takes the turtle to swim

Zigmanuir [339]

Answer:

Time (secs) => distance (ft)

1 => ⅔

15 => 10

24 => 16

45 => 30

Step-by-step explanation:

Equation to represent this proportional relationship is $d = tk$ , where,

t = time

d = distance

k = constant of proportionality

To complete the table, let's find k given that the turtles swarm 16 ft (d) in 24 secs (t).

Substitute d = 16, t = 24 into the equation.

$d = tk$

$16 = 24k$

$\frac{16}{24} = k$ (division property of equality)

$\frac{2}{3} = k$

Let's complete the table by substituting the value of k and the other given value of t or d, as the case may be:

For 1 sec, let's find distance (d):

$d = tk$

$d = 1*\frac{2}{3}$

d = ⅔ ft

For 10 ft, let's find the time (t) taken:

$d = tk$

$10 = t*\frac{2}{3}$

Multiply both sides by 3

$10*3 = t*\frac{2}{3}*3$

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Divide both sides by 2

$\frac{30}{2} = \frac{t*2}{2}$

$15 = t$

t = 15 secs

For 45 secs, let's find distance (d):

$d = tk$

$d = 45*\frac{2}{3} = 15*2$

d = 30 ft

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Answer:

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Step-by-step explanation:

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