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Savatey [412]
3 years ago
10

Billy has 1 gallon of paint. He is going to pour it into a paint tray that measures 10 inches wide, 14 inches long, and 4 cm dee

p.
(1 gallon = 231 inches cubed , 1 inch = 2.54 cm)

Which of the following scenarios will happen?
Mathematics
1 answer:
Free_Kalibri [48]3 years ago
5 0

Answer:

The paint will not fill the tray by 10.53 in3.

Step-by-step explanation:

Length = 14 inches

Width = 10 inches

Depth = 4 cm = 1.57 inches

Volume = length x width x depth

Volume = 14 x 10 x 1.57

= 220.47 inches cube

Volume of Gallon = 231 inches cube

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Step-by-step explanation:

X^2 + 3x + 5 = -3x

x^2 + 6x + 5 = 0

(x + 5)(x + 1) = 0

x = -1,-5

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Solve the following by using mathematical Induction. For >/ 1
cluponka [151]

Answer:

See explanation

Step-by-step explanation:

Prove that

1^2+2^2+3^3+...+n^2=\dfrac{1}{6}n(n+1)(2n+1)

1. When n=1, we have

  • in left part 1^2=1;
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2. Assume that for all k following equality is true

1^2+2^2+3^3+...+k^2=\dfrac{1}{6}k(k+1)(2k+1)

3. Prove that for k+1 the following equality is true too.

1^2+2^2+3^3+...+(k+1)^2=\dfrac{1}{6}(k+1)((k+1)+1)(2(k+1)+1)

Consider left part:

1^2+2^2+3^2+...+(k+1)^2=\\ \\=(1^2+2^2+3^3+...+k^2)+(k+1)^2=\\ \\=\dfrac{1}{6}k(k+1)(2k+1)+(k+1)^2=\\ \\=(k+1)\left(\dfrac{1}{6}k(2k+1)+k+1\right)=\\ \\=(k+1)\dfrac{2k^2+k+6k+6}{6}=\\ \\=(k+1)\dfrac{2k^2+7k+6}{6}=\\ \\=(k+1)\dfrac{2k^2+4k+3k+6}{6}=\\ \\=(k+1)\dfrac{2k(k+2)+3(k+2)}{6}=\\ \\=(k+1)\dfrac{(k+2)(2k+3)}{6}

Consider right part:

\dfrac{1}{6}(k+1)((k+1)+1)(2(k+1)+1)=\\ \\\dfrac{1}{6}(k+1)(k+2)(2k+3)

We get the same left and right parts, so the equality is true for k+1.

By mathematical induction, this equality is true for all n.

3 0
3 years ago
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Answer:

52

Step-by-step explanation:

Let the number of shots Mason made be x.

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x-29 = 23

x = 23 + 29

x = 52

Thus, Mason made 52 shots.

3 0
3 years ago
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