All categories

2 years ago

Samuel was riding in the back seat of the station wagon on the way home after a long and tiring day at the

Mathematics

1 answer:

ki77a [65]2 years ago

7 0

Answer: One fourth of the entire trip.

Step-by-step explanation:

The initial distance is D.

" He fell asleep halfway home."

Then he fells asleep when the distance between his actual position and his house was half of D, or:

D/2.

"He didn't wake up until he still had half as far to go as he had already

gone while asleep."

So he wakes up when his actual position is a fourth of the initial distance:

(D/2)/2 = D/4.

Then if the entire trip has a distance D, and he was sleeping between:

D/2 - D/4 = 2D/4 - D/4 = D/4.

in a trip of a distance D, he was asleep a distance of D/4.

Then, returning to the question:

How much of the entire trip home was Samuel asleep?

This is equal to the quotient between the distance that he travels asleep and the total distance:

r = (D/4)/D = 1/4.

Then he was asleep in 1/4 of the entire trip.

You might be interested in

Jack,sally, and joe all work in a bookstore.jack sold 126 books.joe 1/2 as many books as jack,and sally sold 1/3 as many books a

Darina [25.2K]

Sally sold 2302323 books!

7 0

2 years ago

At the beginning of the summer Matt swim 12 laps. At the end of the summer he could swim 15 laps. What is the percent increase i

aleksandr82 [10.1K]

Percent change = (new number - old number)/(old number) * 100
A positive percent change is a percent increase.
A negative percent change is a percent decrease.

In this problem, we have:
The new number is 15 laps.
The old number is 12 laps.

percent change = (15 - 12)/(12) * 100

percent change = 3/12 * 100

percent change = 25

Since the percent change is positive, +25, it is a percent increase.

Answer: The percent increase is 25%

8 0

2 years ago

The data set shown below represents the number of times some families went out for dinner the previous week.

dimulka [17.4K]

Answer:

The answer would be the 2nd, 3rd, and 5th option on ed

Step-by-step explanation:

8 0

1 year ago

Read 2 more answers

The organizers of a talent show have budgeted $1800 to buy souvenir clothing to sell at the event. They can buy shirts for $10 e

ki77a [65]

Let s represent number of shirts and h represent number of hats.

We have been given that the organizers of a talent show have budgeted $1800 to buy souvenir clothing to sell at the event. They can buy shirts for $10 each and hats for $8 each.

The cost of s shirts would be $10s$ and cost of h hats would be $8h$ . The cost of s shirts and h hats should be less than or equal to 1800. We can represent this information in an inequality as:

$10s+8h\leq 1800$

We are also told that organizers plan to buy at least 5 times as many shirts as hats. This means that number of shirts should be greater than or equal to 5 times hats. We can represent this information in an inequality as:

$s\geq 5h$

Therefore, the second inequality should be $s\geq 5h$ and option C is the correct choice.

6 0

2 years ago

What is the following product? (StartRoot 12 EndRoot + StartRoot 6 EndRoot) (StartRoot 6 EndRoot minus StartRoot 10 EndRoot)

Crank

Answer:

The product results in: $6\,\sqrt{2} -2\,\sqrt{30} +6-2\,\sqrt{15}$ , which agrees with answer A of the given choices.

Step-by-step explanation:

We need to apply distributive property for the product of two expressions each consisting of two terms, and also use the properties of products of radicals of the same root:

$(\sqrt{12} +\sqrt{6} )(\sqrt{6} -\sqrt{10} )=\\=\sqrt{12*6} -\sqrt{12*10} +\sqrt{6*6} -\sqrt{6*10} =\\=\sqrt{72} -\sqrt{120} +\sqrt{36} -\sqrt{60}$

and now, we extract as many factors we can from the roots to reduce them:

$\sqrt{72} -\sqrt{120} +\sqrt{36} -\sqrt{60} =\\=6\,\sqrt{2} -2\,\sqrt{30} +6-2\,\sqrt{15}$

5 0

2 years ago

Read 2 more answers