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Aleksandr [31]
3 years ago
9

Assume every 10-digit natural number is a possible telephone number except those that begin with 0, 1 or 2. What fraction of tel

ephone numbers begins with 8 and ends with 8?
Mathematics
1 answer:
lana [24]3 years ago
5 0

Answer: 1/70

Step-by-step explanation:

This is a question that can also be interpreted as what is the probability of having the first number of a phone number to be 8 and the last number of the phone number to also be 8. This answer gives the fraction of the phone numbers that starts with 8 and end with 8.

Since three numbers (0,1,2) cannot start a phone number and we are left to pick from 7 numbers,

then the probability of figure "8" starting phone number = 1/7

Since all 10 numbers can possibly end a phone number,

then the probability of having figure "8" as the last digit of a phone number = 1/10

Hence probability of having "8" as the first and last digit of a phone number = fraction of total telephone numbers that begin with digit 8 and end with digit 8 = 1/7 × 1/10 = 1/70.

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Step-by-step explanation:

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Oliver and Lenny started hiking a hill simultaneously from the bottom to the top. Oliver hiked at a speed of 5 km/h during the f
Papessa [141]

Answer:

<u>Oliver and Lenny reached the top of the hill at the same time</u>

<u>The proportion of time Oliver spent hiking to that of Lenny is 1:1</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Oliver's speed = 5 km/h during the first half, then decreased his speed to 4 km/h during the second half.

Lenny's speed = 4 km/h during the first half, then increased his speed to 5 km/h in the second half.

2. Who reached the top of the hill first? What is the proportion of time he spent hiking to that of his friend?

Let's assume the distance from the bottom to the top of the hill is 10 kilometers for calculating the time it will take Oliver and Lenny to reach the top of the hill:

Speed = Distance/Time

Time = Distance/Speed

Oliver = Time of hiking first 5 km + Time of hiking second 5 km

Lenny = Time of hiking first 5 km + Time of hiking second 5 km

Oliver = 5/5 + 5/4

Oliver = 1 + 5/4 = 2 1/4 hours

Lenny = 5/4 + 5/5

Lenny = 5/4 + 1 = 2 1/4 hours

<u>Oliver and Lenny reached the top of the hill at the same time</u>

<u>The proportion of time Oliver spent hiking to that of Lenny is 1:1</u>

3 0
3 years ago
A ball of mass 0.4 kg flies through the air at low speed, so that air resistance is negligible. What is the net force acting on
arsen [322]

Answer:

-3.92 N

Step-by-step explanation:

We are given that

Mass of ball=0.4 kg

Acceleration due to gravity=-9.8m/s^2

Because the ball flies against to gravity

We have to find the net force acting on the ball while it is in motion.

We know that when there is no air resistance then the net  force acts on the ball is equal to weight of ball.

Net force,F =mg

Substitute the values then we get

F=0.4(-9.8)

F=-3.92N

Hence, the net force acting on the ball while it is on motion=-3.92 N

6 0
3 years ago
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