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3 years ago

a baseball team played 35 games and won 4/7 of them. How many games were won? How many games were lost?

Mathematics

1 answer:

nikklg [1K]3 years ago

6 0

Won: 4/7 x 35 = 20
lost: 3/7 x 35 = 15

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What is the coefficient of x2y3 in the expansion of (2x + y)5?

Zigmanuir [339]

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.

5 0

2 years ago

Equivalent fractions for 2 1/5 and 1 5/6

Verizon [17]

2 1/5: 11/5, 22/10, 33/15, 44/20 etc.
1 5/6: 11/6, 22/12, 33/18, 44/24, etc.

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3 years ago

The length of a garden can be expressed as 2X +6 feet and the width is X +7 feet what is the perimeter of the garden what is the

Virty [35]

Answer:

6x + 26 feet

Step-by-step explanation:

Assuming the garden is a rectangular shape, we have four sides, where two sides are 2x + 6 feet and two sides are x + 7 feet. To find the perimeter, we add up the lengths of all four sides.

2x + 6 + 2x + 6 + x + 7 + x + 7

2(2x + 6) + 2(x + 7)

6x + 26

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3 years ago

PLSS help <br><br><br> the answer either has to be -3 , 1/2, 2, 3, 0 , 1 , -2 , 5 , undefined

77julia77 [94]

Answer:

-3

Step-by-step explanation:

4-7/1-0

1-4/2-1

-2-1/3-2

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2 years ago

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Answer:

Mean absolute deviation. The mean absolute deviation of a dataset is the average distance between each data point and the mean. It gives us an idea about the variability in a dataset

Step-by-step explanation:

Hope this helps

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2 years ago

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