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Maslowich
3 years ago
6

Solve. Dante's mom made 2 liters of cocoa. Dante and his 7 friends each drank a serving of cocoa. If each serving is 235 millili

ters, how much cocoa is left?
Mathematics
1 answer:
blsea [12.9K]3 years ago
5 0

Answer:

120 millimeters or 0.12 liters

Step-by-step explanation:

To solve this question :

  1. we have to convert liters to millimeters
  2. multiply the serving of coca by the number of people that consumed the coca
  3. subtract the answer gotten from the step above from 2 litters

1 liter = 1000 millimeter

2 liters = 2 x 1000 = 2000mm

8 people drank cocoa = 8 x 235 = 1880mm

Amount of cocoa left over = 2000 - 1880 = 120mm or 0.12 liters

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Option C:

The coefficient of x^{2} y^{3} is 40.

Solution:

Given expression:

(2 x+y)^{5}

Using binomial theorem:

(a+b)^{n}=\sum_{i=0}^{n}\left(\begin{array}{l}n \\i\end{array}\right) a^{(n-i)} b^{i}

Here a=2 x, b=y

Substitute in the binomial formula, we get

(2x+y)^5=\sum_{i=0}^{5}\left(\begin{array}{l}5 \\i\end{array}\right)(2 x)^{(5-i)} y^{i}

Now to expand the summation, substitute i = 0, 1, 2, 3, 4 and 5.

$=\frac{5 !}{0 !(5-0) !}(2 x)^{5} y^{0}+\frac{5 !}{1 !(5-1) !}(2 x)^{4} y^{1}+\frac{5 !}{2 !(5-2) !}(2 x)^{3} y^{2}+\frac{5 !}{3 !(5-3) !}(2 x)^{2} y^{3}

                                                            $+\frac{5 !}{4 !(5-4) !}(2 x)^{1} y^{4}+\frac{5 !}{5 !(5-5) !}(2 x)^{0} y^{5}

Let us solve the term one by one.

$\frac{5 !}{0 !(5-0) !}(2 x)^{5} y^{0}=32 x^{5}

$\frac{5 !}{1 !(5-1) !}(2 x)^{4} y^{1} = 80 x^{4} y

$\frac{5 !}{2 !(5-2) !}(2 x)^{3} y^{2}= 80 x^{3} y^{2}

$\frac{5 !}{3 !(5-3) !}(2 x)^{2} y^{3}= 40 x^{2} y^{3}

$\frac{5 !}{4 !(5-4) !}(2 x)^{1} y^{4}= 10 x y^{4}

$\frac{5 !}{5 !(5-5) !}(2 x)^{0} y^{5}=y^{5}

Substitute these into the above expansion.

(2x+y)^5=32 x^{5}+80 x^{4} y+80 x^{3} y^{2}+40 x^{2} y^{3}+10 x y^{4}+y^{5}

The coefficient of x^{2} y^{3} is 40.

Option C is the correct answer.

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Answer:

Th correct option is D. 13

Therefore the value of x is 13.

Step-by-step explanation:

Given:

measure of an intercepted arc = 86°

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Angle Inscribed in arc = (3x+4)°

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The inscribed angle theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle.

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Therefore the value of x is 13.

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