Henry made 200 tarts. He sold 5 of them and gave 4 of the remainder to

Please help me

madreJ [45]

Answer:

1) The total displacement vector is ((16 + √2)/2, -(6+11·√2)/2)

2) The number of miles they'd have to walk is approximately 13.856 miles

Step-by-step explanation:

1) The distance, direction, and location of the path of the walk the person takes, are listed as follows;

Start location, (0, 0)

6 miles East walk to location, (6, 0)

6 miles Southeast to location, (6 + 3·√2, -3·√2)

3 miles South to location, (6 + 3·√2, -3·√2 - 3)

5 miles Southwest to location, (6 + 3·√2 - 2.5·√2, -3·√2 - 3 - 2.5·√2)

2 miles East to location, (6 + 3·√2 - 2.5·√2 + 2, -3·√2 - 3 - 2.5·√2)

(6 + 3·√2 - 2.5·√2 + 2, -3·√2 - 3 - 2.5·√2) = ((16 + √2)/2, -(6+11·√2)/2)

Therefore the destination coordinates is ((16 + √2)/2, -(6+11·√2)/2)

The total displacement vector, $\underset{d}{\rightarrow}$ = ((16 + √2)/2, -(6+11·√2)/2)

d = (16 + √2)/2)·i - (6+11·√2)/2)·j

2) If the person walked straight home, the number of miles they'd have to walk, $\left | \underset{d}{\rightarrow} \right |$ , is given as follows;

$\left | \underset{d}{\rightarrow} \right | = \sqrt{\left(\dfrac{16 +\sqrt{2} }{2} \right)^2 + \left(-\dfrac{6 + 11 \cdot \sqrt{2} }{2} \right)^2 } = \sqrt{134 + 41 \cdot \sqrt{2} }$

Therefore;

If the person walked straight home, the number of miles they'd have to walk $\left | \underset{d}{\rightarrow} \right | \approx 13.856 \ miles$

3 0

3 years ago

Randy bought 30 marbles. 40% of them are blue. How many blue marbles are there

sveticcg [70]

Answer:

12 are blue, I hope it helps!

7 0

3 years ago

Read 2 more answers

Handles-n-Things is a small enterprise company buying new carpet for their office room. The room is 15 ft. wide and 24 ft. long.

Helen [10]

Hey there!

To find the area, we multiply the length by the width! The carpet will cover the area of the room.

24×15=360

But, the carpeting is sold in square yards, not feet. There are three feet in a yard, which means that one yard is 1/3 feet. Since we have 360 square feet, we will divide it by three to get yards.

360/3=120

Therefore, the office would need 120 square yards of carpeting.

Have a wonderful day!

4 0

4 years ago

A mother is twice as old as her daughter 5 years from now she will be thrice as old as her daughter how old is the mother five y

Ilya [14]

Answer:

Let's define the variables:

M = mother's age

D = daughter's age.

"a mother is twice as old as her daughter"

This can be written as:

M = 2*D

"5 years from now she will be thrice as old as her daughter"

(M + 5) = 3*D

We want to know how old is the mother five years from now.

First, our equations are:

M = 2*D

(M + 5) = 3*D

First, we need to isolate one of the variables in one of the equations, because for the solution we want the mother's age, we should isolate the daughter's age.

Let's isolate D in the first equation:

M/2 = D

Now we can replace this in the other equation:

Now we can replace this on the other equation:

(M + 5) = 3*(M/2)

M + 5 - (3/2)*M = 0

-(1/2)*M + 5 = 0

5 = (1/2)*M

2*5 = M = 10

So the mother is 10 years old (this hasn't a lot of sense, maybe there is a wrong number on the question)

and 5 years from now, the mother will be:

10 + 5 = 15 years old.

8 0

3 years ago

A sample of single persons receiving social security payments revealed these monthly benefits: $826, $699, $1,087, $880, $839, a

Tanya [424]

The median is the number in the middle of a sorted list.

So we need to arrange the given numbers, $699, $826, $839, $880, $965, $1,087.

Since the givenhas 6 numbers, finding the median will be the average of the two numbers in the middle. $839 + $880 = 1719 then divide this by 2 = 859.5

So there are 3 numbers that are below the median and these are $699, $826, and $839.

8 0

3 years ago