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3 years ago

One positive number is 5 times another number . The difference between the two numbers is 80, Find the numbers.

1 answer:

4 0

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Define the numbers:
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Let x be one number.
One number = x
Other number = 5x

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Construct the equation:
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5x - x = 80

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Combine like terms:
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4x = 80

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Divide by 4 on both sides:
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x = 20

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Find the 2 numbers:
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One number = x = 20
Other number = 5x = 5(20) = 100

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Answer: The two numbers in increasing order are 20 and 100.
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The braking distance, in feet of a car a Travling at v miles per hour is given.

irakobra [83]

The braking distance is the distance the car travels before coming to a stop after the brakes are applied

a. The braking distances are as follows;

The braking distance at 25 mph, is approximately 63.7 ft.

The braking distance at 55 mph, is approximately 298.35 ft.

The braking distance at 85 mph, is approximately 708.92 ft.

b. If the car takes 450 feet to brake, it was traveling with a speed of 98.211 ft./s

Reason:

The given function for the braking distance is D = 2.6 + v²/22

a. The braking distance if the car is going 25 mph is therefore;

25 mph = 36.66339 ft./s

$D = 2.6 + \dfrac{36.66339^2}{22} = 63.7 \ ft.$

At 25 mph, the braking distance is approximately 63.7 ft.

At 55 mph, the braking distance is given as follows;

55 mph = 80.65945 ft.s

$D = 2.6 + \dfrac{80.65945^2}{22} \approx 298.35 \ ft.$

At 55 mph, the braking distance is approximately 298.35 ft.

At 85 mph, the braking distance is given as follows;

85 mph = 124.6555 ft.s

$D = 2.6 + \dfrac{124.6555^2}{22} \approx 708.92 \ ft.$

At 85 mph, the braking distance is approximately 708.92 ft.

b. The speed of the car when the braking distance is 450 feet is given as follows;

$450 = 2.6 + \dfrac{v^2}{22}$

v² = (450 - 2.6) × 22 = 9842.8

v = √(9842.2) ≈ 98.211 ft./s

The car was moving at v ≈ 98.211 ft./s

Learn more here:

brainly.com/question/18591940

8 0

2 years ago

I need help on this please help!

Licemer1 [7]

Answer:

(b)0.56

Step-by-step explanation:

(a)

P(Ben Pass) =0.8

Therefore: P(Ben fails)=1-0.8 =0.2

P(Tom Pass) =0.7

Therefore: P(Tom fails)=1-0.7 =0.3

See attached for the completed tree diagram

(b)Probability that both will pass

P(both will pass)=P(Ben pass and Tom pass)

=P(Ben pass) X P(Tom pass)

=0.8 X 0.7

=0.56

(c)The probability that only one of them will pass

Since either Tom or Ben can pass, we have:

P(only one of them will pass)

=P(Ben pass and Tom fails OR Ben Fails and Tom Pass)

=P(Ben pass and Tom fails)+P(Ben Fails and Tom Pass)

=(0.8 X 0.3) + (0.2 X 0.7)

=0.24 + 0.14

=0.38

8 0

3 years ago

The average score of all pro golfers for a particular course has a mean of 70 and a standard deviation of 3.0 (Think of these as

bija089 [108]

Answer:

0.477 is the probability that the average score of the 36 golfers was between 70 and 71.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 70

Standard Deviation, σ = 3

Sample size, n = 36

Let the average score of all pro golfers follow a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

P(score of the 36 golfers was between 70 and 71)

$\text{Standard error of sampling} = \displaystyle\frac{\sigma}{\sqrt{n}} = \frac{3}{\sqrt{36}} = \frac{1}{2}$

$P(70 \leq x \leq 71) = P(\displaystyle\frac{70 - 70}{\frac{3}{\sqrt{36}}} \leq z \leq \displaystyle\frac{71-70}{\frac{3}{\sqrt{36}}}) = P(0 \leq z \leq 2)\\\\= P(z \leq 2) - P(z \leq 0)\\= 0.977 - 0.500 = 0.477= 47.7\%$