Please answer these! Tyvm :)

if the eggs in a basket are removed 2 at a time, 1 egg will remain. if the eggs are removed 3 at a time, 2 eggs will remain. if

Yanka [14]

The least number of eggs that could be in the basket is 119.

Multiple of the number:

The multiple is the numbers you get when you multiply a certain number by an integer.

Given,

If the eggs in a basket are removed 2 at a time, 1 egg will remain.

If the eggs are removed 3 at a time, 2 eggs will remain.

If the eggs are removed 4, 5, or 6 at a time, then 3, 4, and 5 eggs will remain, respectfully.

But if they are taken out 7 at a time, no eggs will be left over.

Here we need to find the least number of eggs in the basket.

Let the number of eggs in the basket be N.

We know that,

if the eggs in a basket are removed 2 at a time, one eggs will remain.

So N is 1 less than a multiple of 2, so

=> N=2A-1

If they are removed 3 at a time, 2 eggs remain.

So N is 2 more, and therefore 1 less than, a multiple of 3, so

=> N=3B-1

If the eggs are removed 4...at a time, then 3...eggs remain,

So N is 3 more, and therefore 1 less than, a multiple of 4, so

=> N=4C-1

Similarly,

For 5,

=> N = 5D - 1

For 6,

=> N = 6E - 1

So, if they are taken out 7 at a time, no eggs will be left over.

So,

N => 7F

Where A,B,C,D,E, and F are any positive integer.

Therefore,

N = 2A-1 = 3B-1 = 4C-1 = 5D-1 = 6E-1 = 7F

Add 1 to all those:

N+1 = 2A = 3B = 4C = 5D = 6E = 7F+1

Through this,

N + 1 = 7F + 1

has to be a common multiple of 2,3,4,5,6.

So, the LCM of 2,3,4,5,6 is 60.

So N+1 is a multiple of 60 which means N is 1 less than a multiple of 60.

So we find the least multiple of 60 that is 1 more than a multiple

of 60.

The multiples are, 60, 59, ....but 59 is not a multiple of 7.

The next multiple of 60 is 120.

1 less than 120 is 119, and sure enough, 119 is a multiple of 7.

So,

=> 119 = 17*7.

Therefore, the least number of eggs that could be in the basket is 119.

To know more about Multiple here

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4 0

1 year ago

Karen has a $140,000 home financed with a 30-year loan at 5%. If she wished to pay one extra monthly payment each year, how many

evablogger [386]

Answer:

Karen take 330 months to pay off her mortgage.

Step-by-step explanation:

Given : Karen has a $140,000 home financed with a 30-year loan at 5%. If she wished to pay one extra monthly payment each year.

To find : How many months will it take her to pay off her mortgage?

Solution : First we find the monthly payment

Formula of monthly payment

Monthly payment, $M=\frac{\text{Amount}}{\text{Discount factor}}$

Discount factor $D=\frac{1-(1+i)^{-n}}{i}$

Where, Amount = $140,000

Rate r= 5%=0.05 compounded quarterly

$i=\frac{0.05}{12}=0.00416$

Time = 30 years

$n=30\times12=360$

Now, put all the values we get,

$D=\frac{1-(1+i)^{-n}}{i}$

$D=\frac{1-(1+0.00416)^{-360}}{0.00416}$

$D=\frac{1-(1.00416)^{-360}}{0.00416}$

$D=\frac{1-0.2243}{0.00416}$

$D=\frac{0.7757}{0.00416}$

$D=186.46$

Monthly payment, $M=\frac{\text{Amount}}{\text{Discount factor}}$

$M=\frac{140000}{186.46}$

$M=750.8$

Approximately,monthly payment is $751

Extra payment for each year is = 751 × 30 = $22530

She wished to pay one extra monthly payment each year

i.e, Yearly payment is 751 × 12 = $9012

Years she paid extra payment is $\frac{22530}{9012}=2.48$

Total years is 30 years , Extra year is 2.5 years

Time she take off to pay her mortgage is 30-2.5 = 27.5 years

1 year = 12 months

27.5 years = 27.5 × 12 = 330 months

Therefore, Karen take 330 months to pay off her mortgage.

7 0

2 years ago

Read 2 more answers

What is the midpoint of a segment in the complex plane with endpoints at 6 – 2i and –4 + 6i?

Ghella [55]

The middle of 6-2i and -4+6i is 1+2i :)

5 0

3 years ago

Read 2 more answers

Jack asked 100 students to choose their favorite subject from among world cultures, math, and art. He found that 22 students cho

german

Answer:

52%

Step-by-step explanation:

while using percentages, you calculate out of 100

1/100

out of the 100, 48 students chose between world cultures or math.

48/100

the remaining 52 students chose art.

52/100

52% of students chose art.

i hope this helped!

:)

6 0

2 years ago

I NEED HELP ITS EASY NO FAKE ANSWERS AND WILL GIVE BRAINLIEST THANKS LOVES

Mashcka [7]

Answer:

Step-by-step explanation:

Quartile 1 = 5.5

Quartile 2 = 8

Quartile 3 = 10

Plz mark brainliest

6 0

2 years ago

Read 2 more answers