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2 years ago

The dairy goats on a farm give 2 gallons of milk each day. How much milk do they give in 5 days?

Mathematics

1 answer:

Dovator [93]2 years ago

4 0

Answer:

$\huge\boxed{\sf 10\ gallons\ of\ milk}$

Step-by-step explanation:

=> 2 gallons of milk each day.

<u>This means</u>

1 day = 2 gallon of milk

Multiply both sides by 5

5 (1 day) = 5 (2 gallons of milk)

<h3>5 days = 10 gallons of milk</h3>

$\rule[225]{225}{2}$

Hope this helped!

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Use induction to prove: For every integer n > 1, the number n5 - n is a multiple of 5.

nignag [31]

Answer:

we need to prove : for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

1) check divisibility for n=1, $f(1)=(1)^{5}-1=0$ (divisible)

2) Assume that $f(k)$ is divisible by 5, $f(k)=(k)^{5}-k$

3) Induction,

$f(k+1)=(k+1)^{5}-(k+1)$

$=(k^{5}+5k^{4}+10k^{3}+10k^{2}+5k+1)-k-1$

$=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k$

Now, $f(k+1)-f(k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-(k^{5}-k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-k^{5}+k$

$f(k+1)-f(k)=5k^{4}+10k^{3}+10k^{2}+5k$

Take out the common factor,

$f(k+1)-f(k)=5(k^{4}+2k^{3}+2k^{2}+k)$ (divisible by 5)

add both the sides by f(k)

$f(k+1)=f(k)+5(k^{4}+2k^{3}+2k^{2}+k)$

We have proved that difference between $f(k+1)$ and $f(k)$ is divisible by 5.

so, our assumption in step 2 is correct.

Since $f(k)$ is divisible by 5, then $f(k+1)$ must be divisible by 5 since we are taking the sum of 2 terms that are divisible by 5.

Therefore, for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

3 0

2 years ago

PLS HELP SHOW ALL YOUR WORKING OUT AND THE CORRECT ANSWER WILL RECIEVE BRAINLIEST

EastWind [94]

So the length is 4*28=112mm
The width would be calculated like this:

you draw an equilateral triangle in the middle with sides or 2r(56mm). The based on pythagorean theorem u know that
h=rad(56^2-28^2)=48.497
28+28+h=104.497

The area would be S=l*w which is 11703.7113mm

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2 years ago

Which expressions are equivalent to the given sort 40 (there is more than one and the one selected is correct)

Basile [38]

Answer:

$40 {}^{ \frac{1}{2} }$

Step-by-step explanation:

The last one is also the answer

Using the rational exponet rule,

$\sqrt[n]{ {x}^{m} } = x {}^{ \frac{m}{n} }$

Using this number,

$\sqrt{40}$

40 is the base so it will stay same. Remember this is a square root sign so our nth root is 2 so our denominator if the rational exponet is 2.

$40 {}^{1} = 40$

so our numerator is 1 so

$40 {}^{ \frac{1}{2} }$

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3 years ago

A train travels a total of 38 km at a constant speed of 90 km/h.

Zarrin [17]

Answer:

25 minutes and 33 seconds

Step-by-step explanation:

please brainiest

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2 years ago

A ten-foot-long board is cut into three pieces. The second piece is half as long as the first. The third piece is 4 feet longer

VladimirAG [237]

Let's say the second piece is x ft long
The first piece is 2x ft long
The third piece is x+4 ft long
All of the pieces should add up to 10ft
x+2x+x+4=10
4x= 6
x=1.5ft
The first piece is 2x ft long=3 ft long

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2 years ago