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NNADVOKAT [17]
3 years ago
15

The average speed of one airplane is 200 mph faster than that of an automobile. If the automobile starts at 3 a.m. and the airpl

ane starts from the same place at 11 a.m., they will have traveled the same number of miles by 1:00 p.m. If r represents the rate of the automobile, how many miles does the plane travel? 200r 2(200 + r) 10r
Mathematics
1 answer:
jok3333 [9.3K]3 years ago
7 0

Distance = 500 miles

Distance of automobile = 10r

r = 50

Distance = 10 x 50 = 500 miles

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Samuel can do 120 jumping jacks in two minutes.
ki77a [65]

Answers:

What is the ratio?         120:2

What is the unit rate?   60:1

What is the rate?          60 jumping jacks per minute

===================================================

Further Explanation:

To find the ratio of jumping jacks to minutes, you just write the two values 120 and 2 separated by a colon. That's how we get 120:2 as our first answer.

--------

Once we have 120:2, we divide both parts by 2 to get 60:1

120/2 = 60

2/2 = 1

The reason why we do this is so that the "2 minutes" turns into "1 minute". A unit ratio has the time value in unit increments so we can see how many jumping jacks Samuel can do. Writing "60:1" means "60 jumping jacks in 1 minute"

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Saying "60 jumping jacks in 1 minute" is the same as saying "60 jumping jacks per minute", which is similar to a car's speed of something like 60 miles per hour. The unit "X per Y" is the template for speed, where X is the number of items you get done and Y is the unit of time. In this case, X = 60 jumping jacks and Y = 1 minute.

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3 years ago
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I NEED HELP IN MATH!!! It’s due tonight and I’ve tried to do it and it don’t fully understand please help if u can!!!
Katyanochek1 [597]

Answer:

1. 42

2. 77

3. 87.75

4. 117

5. 119

6. 89.25

7. 39

8. 58.5

9. 218.75

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3 years ago
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Because of the relatively high interest rates, most consumers attempt to pay off their credit card bills promptly. However, this
Anastasy [175]

Answer:

Step-by-step explanation:

Let X be average interest paid monthly by a bank's Visa cardholders

Given that X is N(28, 8)

In the following to find out probability we convert X to z score and use std normal distribution table

Z = \frac{x-28}{8}

Probability being less than 1 is here equal to the proportion also.

A) P(X>32) = P(Z>0.5)=0.5-0.1915=0.3085

B) P(X>40) = P(Z>1)=0.5-0.3413=0.1687

C) P(X<19) = P(Z<-1.125)=0.5-0.0438=0.4562

D) We have to find 19th percentile here

Z =-0.88

X=28-0.88(8)\\=20.96

5 0
3 years ago
What is 88.2 rounded to the nearest whole number?​
HACTEHA [7]

Answer:

88

Step-by-step explanation:

if the decimal is below 5 then round down

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3 years ago
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A blind man wanders under a door into an empty room. After running into the walls repeatedly for a while, it stops to think and
Nostrana [21]

From the side where the man is located in the 10' by 12' rectangular room, we have;

A) 0.046

B) The average time to escape in first attempt is approximately 605.02 seconds

<h3>Which concept can be used to find the odds and time of escape?</h3>

A) From The given diagram, we have;

Width of the door = 10 - 6 - 2 = 2

Therefore, the door is 2 feet wide

Distance, d1, from the man to the side of the door closer to him is given by Pythagorean theorem as follows;

  • d1 = √(6² + 7²) = √(85)

From the furthest side of the door to the man, we have;

  • d2 = √(7² + 8²) = √(113)

According to the law of cosines, we have;

2² = 85+113 - 2×√(85)×√(113) cos(A)

Where angle <em>A </em>is the angle formed by the lines from the man to the closer and farther sides of the door.

2×√(85)×√(113) cos(A) = 85+113 - 2²

A = arccos((85+113 - 2²)/(2×√(85)×√(113)))

A = arccos (194/(2×√(9605)) ≈ 8.213°

The angle of the possible directions in which the man can turn is 180°.

Therefore;

The probability, <em>P(</em><em>E)</em>, of escaping in the first move is therefore;

  • P(E) = 8.213°/180° ≈ 0.046

B) Given that the man escapes in the first move, the shortest and longest distances the man moves are;

d1 = √(85) and d2 = √(113)

Speed of the man, <em>v </em>= 0.5 cm/sec

Therefore by unit conversion function of a graphing calculator;

  • v = (25/1524) ft./sec

The times taken are;

t1 = √(85)/(25/1524) ≈ 562.023

t2 = √(113)/(25/1524) ≈ 648.014.

Average time, <em>t </em>= (t1 + t2)/2

Which gives;

t = (562.023 + 648.014)/2 ≈ 605.02

The average time it takes the man to escape in first move is <em>t </em><em>≈</em> 605.02 seconds.

Learn more about Pythagorean theorem and probability here:

brainly.com/question/27180985

brainly.com/question/654982

brainly.com/question/24756209

#SPJ1

3 0
1 year ago
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