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3 years ago

I need help with this plz help

Mathematics

2 answers:

Nimfa-mama [501]3 years ago

5 0

Answer:

-2

Step-by-step explanation:

I did the problem!

Lunna [17]3 years ago

4 0

Answer:-9 this was so easy for me and you allways try your best if you don,t get it then you don,t get it

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How can i prove this property to be true for all values of n, using mathematical induction.

chubhunter [2.5K]

Proof -

So, in the first part we'll verify by taking n = 1.

$\implies \: 1 = {1}^{2} = \frac{1(1 + 1)(2 + 1)}{6}$

$\implies{ \frac{1(2)(3)}{6} }$

$\implies{ 1}$

Therefore, it is true for the first part.

In the second part we will assume that,

$\: { {1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} = \frac{k(k + 1)(2k + 1)}{6} }$

and we will prove that,

$\sf{ \: { {1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k + 1)(k + 1 + 1) \{2(k + 1) + 1\}}{6}}}$

$\: {{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k + 1)(k + 2) (2k + 3)}{6}}$

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

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

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

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

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(2k^2+7k+6) }{6}$

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

Henceforth, by using the principle of mathematical induction 1²+2² +3²+....+n² = n(n+1)(2n+1)/ 6 for all positive integers n.

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8 0

2 years ago

9^2 - (4) (2) (-6) what is the answer?

Rus_ich [418]

Answer:

129

Step-by-step explanation:

pls heart and give brainliest much appreciated

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3 years ago

about 30% of the population is left-handed. If two people are random selected what is the probability that both are left handed?

Svetradugi [14.3K]

Answer:

0.91

Step-by-step explanation:

1 - P(both left handed)

1 - 0.3² = 0.91

4 0

4 years ago

I need some serious help with standard form, Im really confused . Here's a problem ,

OLEGan [10]

I can see that the equation given above is a linear equation since y and x are the only variable and the degree is one. The standard form of a linear equation is written as:

Ax + By = C

We write the given equation into standard form as follows:

y - 2 = 2(x - 3)
y - 2 = 2x - 6
y -2x = -6 +2
y - 2x = -4
2x - y = 4

6 0

3 years ago

one batch of cookies makes 24 cookies. the recipe calls for 1 3/4 cups of flour. if Sarah needs to make 60 cookies how much flou

Svetllana [295]

Answer:

4 3/8 cups of flour needed for 60 cookies

Explanation:

You can multiply 24 by 2.5 to get 60 so you'd multiply the cups of flour by 2.5 as well. You multiply both of them by the same number because it's a ratio. You'd multiply then simplify to get the answer 4 3/8 cups of flour.

7 0

3 years ago