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CaHeK987 [17]
2 years ago
6

375 is 112% of what number?

Mathematics
2 answers:
Lera25 [3.4K]2 years ago
5 0

Answer:

420

Step-by-step explanation:

maybe I don't know sorry

miv72 [106K]2 years ago
5 0

Answer:

answer is 420

step by step explanation

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If the sum of the even integers between 1 and k, inclusive, is equal to 2k, what is the value of k?
Alisiya [41]
If k is odd, then

\displaystyle\sum_{n=1}^{\lfloor k/2\rfloor}2n=2\dfrac{\left\lfloor\frac k2\right\rfloor\left(\left\lfloor\frac k2\right\rfloor+1\right)}2=\left\lfloor\dfrac k2\right\rfloor^2+\left\lfloor\dfrac k2\right\rfloor

while if k is even, then the sum would be

\displaystyle\sum_{n=1}^{k/2}2n=2\dfrac{\frac k2\left(\frac k2+1\right)}2=\dfrac{k^2+2k}4

The latter case is easier to solve:

\dfrac{k^2+2k}4=2k\implies k^2-6k=k(k-6)=0

which means k=6.

In the odd case, instead of considering the above equation we can consider the partial sums. If k is odd, then the sum of the even integers between 1 and k would be

S=2+4+6+\cdots+(k-5)+(k-3)+(k-1)

Now consider the partial sum up to the second-to-last term,

S^*=2+4+6+\cdots+(k-5)+(k-3)

Subtracting this from the previous partial sum, we have

S-S^*=k-1

We're given that the sums must add to 2k, which means

S=2k
S^*=2(k-2)

But taking the differences now yields

S-S^*=2k-2(k-2)=4

and there is only one k for which k-1=4; namely, k=5. However, the sum of the even integers between 1 and 5 is 2+4=6, whereas 2k=10\neq6. So there are no solutions to this over the odd integers.
5 0
3 years ago
What is the volume of this sphere?
Inga [223]

Answer:

V=2143.57\ mm^3

Step-by-step explanation:

Given that,

The radius of the sphere, r = 8 mm

We need to find the volume of the sphere. The formula for the volume of a sphere is given by :

V=\dfrac{4}{3}\pi r^3

Put all the values,

V=\dfrac{4}{3}\times 3.14\times 8^3\\\\=2143.57\ mm^3

So, the volume of the sphere is equal to 2143.57\ mm^3.

6 0
2 years ago
Help need done fast pls.
Arada [10]
The total degrees of a triangle is 180.
So
37+63=100
And well
180-100=80
U=80
5 0
2 years ago
Read 2 more answers
A bathtub contains 12 gallons of water. With these 12 gallons, the bathtub is only 30% full. How many gallons of water can the b
Pachacha [2.7K]

Answer:

40 gallons

Step-by-step explanation:

Let the number of gallons that would completely fill the bathtub be represented by N.

Since 12 gallons of water gives 30% of the number of gallons to fill the bathtub, then;

30% of N = 12

\frac{30}{100} x N = 12

30N = 12 x 100

30N = 1200

divide both sides by 30,

N = \frac{1200}{30}

   = 40

The number of gallons that would completely fill the bathtub is 40 gallons.

6 0
2 years ago
Can you guys help on simplifying 3 (-4)
Volgvan

Answer:

sure

Step-by-step explanation:

8 0
3 years ago
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