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kipiarov [429]
3 years ago
15

Precious treated 3 of her friends and herself to ice cream sundaes. The bill for the sundaes $16 . Each sundae cost the same amo

unt. How much was each sundae
Mathematics
1 answer:
mariarad [96]3 years ago
4 0
Each sundae was 4 dollars. It was 3 of her friends and herself which make 4 people.
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An Equation is shown.<br><br> 8/10 + ___ = 93/100<br><br> What is the missing fraction?
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The missing fraction is 13/100
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3 years ago
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Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false:
kondaur [170]
\text{Proof by induction:}
\text{Test that the statement holds or n = 1}

LHS = (3 - 2)^{2} = 1
RHS = \frac{6 - 4}{2} = \frac{2}{2} = 1 = LHS
\text{Thus, the statement holds for the base case.}

\text{Assume the statement holds for some arbitrary term, n= k}
1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2} = \frac{k(6k^{2} - 3k - 1)}{2}

\text{Prove it is true for n = k + 1}
RTP: 1^{2} + 4^{2} + 7^{2} + ... + [3(k + 1) - 2]^{2} = \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2} = \frac{(k + 1)[6k^{2} + 9k + 2]}{2}

LHS = \underbrace{1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2}}_{\frac{k(6k^{2} - 3k - 1)}{2}} + [3(k + 1) - 2]^{2}
= \frac{k(6k^{2} - 3k - 1)}{2} + [3(k + 1) - 2]^{2}
= \frac{k(6k^{2} - 3k - 1) + 2[3(k + 1) - 2]^{2}}{2}
= \frac{k(6k^{2} - 3k - 1) + 2(3k + 1)^{2}}{2}
= \frac{k(6k^{2} - 3k - 1) + 18k^{2} + 12k + 2}{2}
= \frac{k(6k^{2} - 3k - 1 + 18k + 12) + 2}{2}
= \frac{k(6k^{2} + 15k + 11) + 2}{}
= \frac{(k + 1)[6k^{2} + 9k + 2]}{2}
= \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2}
= RHS

Since it is true for n = 1, n = k, and n = k + 1, by the principles of mathematical induction, it is true for all positive values of n.
3 0
3 years ago
Operations with complex numbers <br>I+6i
IRISSAK [1]
So the answer is |6i|.
8 0
3 years ago
I really need help on this problem. I don’t get it
Sveta_85 [38]
The domain is {-9,-4,3,9}
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8 0
3 years ago
Robert has 60 feet of fence to make a dog pen. He will use the house for one side of the pen, as shown above. What dimensions wi
irinina [24]

The formula for an area of a regular parallelogram is:

A = l * w

Where,

l = length

w = width

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l + 2 w = 60

<span>or simplifying to make an explicit expression for one  variable, say l:</span>

l = 60 – 2 w

<span>Substituting to the 1st equation:</span>

A = (60 – 2 w) * w

A = 60 w – 2 w^2

<span>The maxima are obtained by getting the 1st derivative then equating dA/dw = 0:</span>

dA/dw = 60 – 4 w

60 – 4 w = 0

4 w = 60

w = 15

Since l = 60 - 2w

l = 60 – 30

l = 30

<span>Therefore the dimension that will make the largest pen is 15 ft by 30 ft.</span>

<span>ANSWER: C</span>

7 0
3 years ago
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