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marusya05 [52]
3 years ago
9

Fifty-eight boys were asked if they play football and/or baseball. Thirty-one of them said they do not play baseball. Sixteen of

them said they play football. Twenty of them said they do not play baseball or football.
Enter your answers in the boxes to complete the two-way table based on the given data.

Mathematics
1 answer:
Arte-miy333 [17]3 years ago
4 0
The two-way table is attached.

We start out placing 31 in the Total column beside the Don't Play Baseball row.  We then place 16 in the Total row under the Play Football column.  20 goes in the Don't Play Baseball row under the Don't Play Football column.

Since there are 31 people that do not play baseball, and 20 of them don't play football, this leaves us with 31-20=11 that do not play baseball and play football.

There are 58 people total, so this goes in the Total row under the Total column.

There are 58 people, and 31 of them do not play baseball; this leaves us 58-31=27 total that play baseball.

16 total people play football, and 11 of them don't play baseball.  This leaves us 16-11=5 people that play football and play baseball.

There are 58 people, and 16 of them play football; this leaves us 58-16=42 total that don't play football.

42 people don't play football, and 20 of them don't play baseball; this leaves us 42-20=22 people that don't play football and play baseball.

5 people play baseball and play football, and 22 people play baseball and don't play football; this gives us 5+22=27 people total that play baseball.

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EastWind [94]

Answer:

6x - 13y

Step-by-step explanation:

5(2x - 2y) - (4x + 3y)

10x - 10y - 4x - 3y

10x - 4x - 10y - 3y

6x - 13y

7 0
2 years ago
Expand the following using the Binomial Theorem and Pascal’s triangle. (x + 2)6 (x − 4)4 (2x + 3)5 (2x − 3y)4 In the expansion o
ivolga24 [154]
\bf (2x+3)^5\implies 
\begin{array}{llll}
term&coefficient&value\\
-----&-----&-----\\
1&&(2x)^5(+3)^0\\
2&+5&(2x)^4(+3)^1\\
3&+10&(2x)^3(+3)^2\\
4&+10&(2x)^2(+3)^3\\
5&+5&(2x)^1(+3)^4\\
6&+1&(2x)^0(+3)^5
\end{array}

as you can see, the terms exponents, for the first term, starts at highest, 5 in this case, then every element it goes down by 1, till it gets to 0

for the second term, starts at 0, and every element it goes up by 1, till it gets to the highest

now, to get the coefficient, they way I get it, is "the product of the current coefficient and the exponent of the first term, divided by the exponent of the second term plus 1"

notice the first coefficient is always 1

so...how did we get 10 for the 3rd element?  well, 5*4/2
how did we get 10 for the fourth element?  well, 10*2/4


\bf (2x-3y)^4\implies 
\begin{array}{llll}
term&coefficient&value\\
-----&-----&-----\\
1&&(2x)^4(-3y)^0\\
2&+4&(2x)^3(-3y)^1\\
3&+6&(2x)^2(-3y)^2\\
4&+4&(2x)^1(-3y)^3\\
5&+1&(2x)^0(-3y)^4
\end{array}


\bf (3a+4b)^8\implies 
\begin{array}{llll}
term&coefficient&value\\
-----&-----&-----\\
1&&(3a)^8(+4b)^0\\
2&+8&(3a)^7(+4b)^1\\
3&+28&(3a)^6(+4b)^2\\
4&+56&(3a)^5(+4b)^3\\
5&+70&(3a)^4(+4b)^4\\
6&+56&(3a)^3(+4b)^5\\
7&+28&(3a)^2(+4b)^6\\
8&+8&(3a)^1(+4b)^7\\
9&+1&(3a)^0(+4b)^8
\end{array}

and from there, you can simplify the elements of the expansion by combining the coefficients

like for example, the 7th element of (3a+4b)⁸ will then be 1032192a²b⁶
7 0
3 years ago
Read 2 more answers
Find the value of x in the following diagram,<br> 3x + 10<br> Here, B and D are points of tangency.
SVEN [57.7K]

<u>Given</u>:

The given circle with center at C. The lines AB and AD are tangents to the circle C.

The length of AB is (3x + 10)

The length of AD is (7x - 6)

We need to determine the value of x.

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Since, we know the property of tangent that, "if two tangents from the same exterior point are tangent to a circle, then they are congruent".

We shall determine the value of x using the above property.

Thus, we have;

AB = AD

Substituting the values, we get;

3x+10=7x-6

Subtracting both sides of the equation by 7x, we get;

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Subtracting both sides of the equation by 10, we get;

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Dividing both sides of the equation by -4, we get;

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Thus, the value of x is 4.

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Answer:

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Step-by-step explanation:

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Triangle 1 = 1/2 x 2 x 5 = 5 units ^2

Triangle 2 = 1/2 x 2 x 2 = 2 units ^2

Triangle 3 = 1/2 x 3.5 x 9 = 15.75 units ^2

Square = 2 x 2 = 4 units squared.

Now add all these up 15.75 + 2 + 5 + 4 = 26.75 units squared.

Hope this helps

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