PROBLEM 1
Peter has many socks, all the same except that they are in three different colours. He is leaving to catch an early train to go on a business trip, and he does not want to wake his wife, so he packs in the
dark. He needs eleven pairs of socks, each sock in each pair the same colour. How many socks must he take from his drawer to be sure of achieving this?

Answer: It's 4

Step-by-step explanation: 12-8 is 4, 4-3 is 1

Answer:

The two different point on a segment joining the United States Capital and the White House such that the ratio of the shorter segments created by each is 1 : 3 are [tex]\vec C_{1} =(-1,7)[/tex] and [tex]\vec C_{2} = (-7,13)[/tex].

Step-by-step explanation:

At first we need to calculate the vector distance between [tex]A(x,y) = (2, 4)[/tex] and [tex]B(x,y) =(-10,16)[/tex] by following vectorial subtraction:

[tex]\overrightarrow{AB} = \vec B - \vec A[/tex] (Eq. 1)

Where:

[tex]\overrightarrow{AB}[/tex] - Vector distance between points A and B, dimensionless.

[tex]\vec A[/tex], [tex]\vec B[/tex] - Vector distance between each point and origin, dimensionless.

If we know that [tex]A(x,y) = (2, 4)[/tex] and [tex]B(x,y) =(-10,16)[/tex], then we have the following result:

[tex]\overrightarrow {AB} = (-10,16)-(2,4)[/tex]

[tex]\overrightarrow{AB} = (-10-2,16-4)[/tex]

[tex]\overrightarrow{AB} = (-12,12)[/tex]

Besides, we can find the location of any point inside the line segment by using the following vectorial equation:

[tex]\vec C = \vec A + r\cdot \overrightarrow{AB}[/tex] (Eq. 2)

Where:

[tex]r[/tex] - Segment factor, dimensionless.

[tex]\vec C[/tex] - Location of resulting point, dimensionless.

There are two different options for the location of resulting point: [tex]r_{1} = \frac{1}{4}[/tex] and [tex]r_{2} = \frac{3}{4}[/tex]. Now we proceed to find each option:

[tex]r_{1} = \frac{1}{4}[/tex]

[tex]\vec C_{1} = (2,4) +\frac{1}{4}\cdot (-12,12)[/tex]

[tex]\vec C_{1} = (2,4)+(-3,3)[/tex]

[tex]\vec C_{1} =(-1,7)[/tex]

[tex]r_{2} = \frac{3}{4}[/tex]

[tex]\vec C_{2} = (2,4) +\frac{3}{4}\cdot (-12,12)[/tex]

[tex]\vec C_{2} = (2,4) +(-9,9)[/tex]

[tex]\vec C_{2} = (-7,13)[/tex]

The two different point on a segment joining the United States Capital and the White House such that the ratio of the shorter segments created by each is 1 : 3 are [tex]\vec C_{1} =(-1,7)[/tex] and [tex]\vec C_{2} = (-7,13)[/tex].

Answer:

did you get it ?

Step-by-step explanation:

Answer: They earned 500 bucks in total

Answer:

They want to make 200 dollars

Step-by-step explanation:

40*5=200

To find the actual discount, multiply the discount rate by the original amount 'x'. To find the sale price, subtract the actual discount from the original amount 'x' and equate this to given sale price.

Answer:

C

Step-by-step explanation:

We can fill in the negative in front of the parenthesis with a one. So you'd be multiplying -1 by your negative fraction. A negative times a negative makes a positive. So that would be the only answer that's a positive.

Answer:

There are 1,890 seats in the hall

Step-by-step explanation:

The number of seats in the first row = 20 seats

The number of rows in the hall = 35 rows

The number of additional seat per row = 2 Seat

Therefore, the sequence of seats in the hall is an arithmetic sequence with the first term, a = 25, the common difference, d = 2, and the number of terms, n = 35

The formula for finding the sum of n-terms of an arithmetic progression, Sₙ is given as follows;

Sₙ = n/2 × [2·a + (n  - 1)·d]

Plugging in the values, we get;

Sₙ = 35/2 × [2 × 25 + (35  - 1)×2] = 1890 seats

Therefore, there are 1,890 seats in the hall.

Answer:

39,160

Step-by-step explanation:

20x22=440 x89=39,160

I don't know the correct answer but I know its not 0.60 watts

Answer:

it is 3.6 watts

Step-by-step explanation:

there is no explanation but if needed proof i will try to post a picture of it

Answer:

14/17

Step-by-step explanation:

14/17 as a fraction can't be simplified. 17 is a prime number, so it can't be divided by anything except 1.

If the question you're asking is 14-17, the answer would be -3...

I hope this helped you out!! Have an awesome day C:

Step-by-step explanation:

if you are subtracting it is -3

if you are dividing it is 0.823

if you are looking for an equivalent fraction it is 28/34

Answer:

$22.50

Step-by-step explanation:

$500.00 × 0.045=22.50

Answer:

6=-4x+b

Step-by-step explanation:

You plug in the numbers but the formula that you use is y=mx+b with x being the number you don't know

Answer:

Recipe 1: 1/2tbs of lemonade mix per cup of sparkling water

Recipe 2: 2/3tbs per cup

Recipe 3: 3/5tbs per cup

Recipe 4: 1/3tbs per cup

Step-by-step explanation:

To find the amount of lemonade mix per cup of sparkling water, we just need to divide the amount of lemonade mix in each recipe by its respective amount of sparkling water as this will give us the average amount per cup.

Recipe 1: 4 tbs lemonade mix, 12c sparkling water.

4/12 = 1/3, Recipe 1 requires 1/3 tablespoon per cup of sparkling water.

Recipe 2: 4tbs Lemonade, 6c water

4/6 = 2/3, Recipe 2 requires 2/3 tablespoon per cup of sparkling water.

Recipe 3: 3 tbs lemon, 5c water

Recipe 3 requires 3/5 tablespoon per cup of sparkling water.

Recipe 4: 1 tbs, 3c water

Recipe 4 requires 1/3 tablespoon per cup of sparkling water.

Hope this helped!

Answer:the answer is 1)30

Step-by-step explanation:

Step-by-step explanation:

Molly should have multiplied three first so that it would have been

x + 6 + 3x + 12

4x + 18

Dylan did not add x to 5x

it should have been

6x - 12

Jose did not multiply 7 and -5

it should have been

x + 3 + 7x - 35

8x - 32

Answer:

The renters have to pay 1.5 months rent before moving in (first month plus security deposit) so we can write the following equation to represent the situation:

1.5

m

=

1725

where

m

is the amount of one month's rent.

Using algebra

1.5

m

1.5

=

1725

1.5

1.5

m

1.5

=

1150

m

=

1150

The monthly rent is $1,150.

Step-by-step explanation:

Answer:

the person above me is right ⬆⬆⬆

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Answer:

The investment of $40,000 is worth $94,529.80 now

Step-by-step explanation:

Compound Interest

It occurs when the interest is reinvested along with the principal, rather than paying it out. When it happens interest in the next period is then earned on the principal sum plus previously accumulated interest.

To calculate the final amount we use:

[tex]{\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]

Where:

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

The investment is for t=6 1/4 years = 6.25 years with an initial balance of P=40,000 at a rate r=14% = 0.14 compounded quarterly. Since there are 4 quarters per year, then n=4.

Applying the formula:

[tex]{\displaystyle A=40,000\left(1+{\frac {0.14}{4}}\right)^{4*6.25}}[/tex]

[tex]{\displaystyle A=40,000\left(1+0.035\right)^{25}}[/tex]

A=$94,529.80

The investment of $40,000 is worth $94,529.80 now

Answer:

Step-by-step explanation:

Answer:

5.03 L

Step-by-step explanation:

we know that 1 inch = 2.54 centimeters

 (1 inch)3 = (2.54 cm)3

1 in3 = 16.387 cm3

therefore

volume in cm^3 = (volume in in3) x (16.387 cm3/1 in3)

volume in cm3 = (307x 16.387) cm^3

volume in cm3 = 5030.809cm^3

let us convert to liters.

we know that

1 L = 1,000 cm3

volume in L = (volume in cm3) x (1 L/1,000 cm3)

volume in L = (5030.809/1,000) L

volume in L = 5.03 L

307 cubic inche engine displaces 5.03 L

Answer:

number 2......................

Answer:

Since the slope of the line x= - 5 is infinite

The line will be parallel to y axis.

And the line passes through - 2, so the equation will become x= -2

Answer:42

Step-by-step explanation: You have to multiply 7 per 6 and so the result will be 42.

Answer:

12+y

Step-by-step explanation:

12y

Step-by-step explanation:

2 multiplied by all the products in the bracket

Answer:

$54.79 is the answer

Step-by-step explanation:

Answer :

Width : 9

length: 3.6

The perimeter will be 25.2

-----------------------------------------------------------------------------------------------------------------

Show your work : Since the length and width are 3 times bigger have to multiply the old one by 3

so 1.2  times 3 = 3.6

so 3 times 3 = 9

thats the length

to find the perimeter its 2L + 2W

2(3.6) + 2(9)=25.2

Answer:

you forgot the number before times

Step-by-step explanation:

Hello there! Your correct answer would be 21 gallons.

When you convert 80 liters to gallons.. It would be 21 gallons.

In a short answer... You could use google or your notes. I prefer your notes, as that'll help you much more than google.  

✨ There is your answer, have a nice day! ✨

(Kinda figured you meant "80")

⌨ Please give me brainlest!! ⌨

Answer:

Only move the negative exponents. Product Rule: am ∙ an = am + n, this says that to multiply two exponents with the same base, you keep the base and add the powers. , this says that to divide two exponents with the same base, you keep the base and subtract the powers.

Answer:

D. 40

Step-by-step explanation:

Triangles add up to 180 degrees so...

110 + 30 + x = 180

140 + x = 180

x = 40

Yeah Ik!

You're cool too!