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Alex Ar [27]
3 years ago
5

Ten kids line up for recess. There are five boys and five girls. How many ways are there for the 10 kids to line up so that all

the boys are ahead of all the girls?
Mathematics
1 answer:
Nana76 [90]3 years ago
3 0

Answer:

14400

Step-by-step explanation:

We have 2 groups of 5 elements each

there is a condition all boys will be ahead always, therefore  in the group of boys there are

5!  =  5*4*3*2*1  =  120 differents form

And the girls at the same time can change theirs places according to

5! =  120

Then total ways for the line up in the conditions of the statement of the problem are

T = 120*120  

14400

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Choose the equation below that represents the line that passes through the point (7, -2) and has a slope of -3
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Answer:

B

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

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Here m = - 3 and (a, b) = (7, - 2 ), thus

y - (- 2) = - 3(x - 7) , that is

y + 2 = - 3(x - 7) → B

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a)

f(4)=\dfrac{4^3}{4}+6=4^2+6=16+6=22

b)

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c)

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Patrick has just finished building a pen for his new dog. The pen is 3 feet wider than it is long. He also built a doghouse to p
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General Idea:

(i) Assign variable for the unknown that we need to find

(ii) Sketch a diagram to help us visualize the problem

(iii) Write the mathematical equation representing the description given.

(iv) Solve the equation by substitution method. Solving means finding the values of the variables which will make both the equation TRUE

Applying the concept:

Given: x represents the length of the pen and y represents the area of the doghouse

<u>Statement 1: </u>"The pen is 3 feet wider than it is long"

Length \; of\; the \; pen = x\\ Width \; of\; the\; pen=x+3

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<u>Statement 2: "He also built a doghouse to put in the pen which has a perimeter that is equal to the area of its base"</u>

Area \; of\; the\; Dog \; house=y\\ Perimeter \; of\; Dog\; house=y

------

<u>Statement 3: "After putting the doghouse in the pen, he calculates that the dog will have 178 square feet of space to run around inside the pen."</u>

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------

<u>Statement 4: "The perimeter of the pen is 3 times greater than the perimeter of the doghouse."</u>

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The systems of equations that can be used to determine the length and width of the pen and the area of the doghouse is given in Option B.

178=x^2+3x-y\\ \\ -6=4x-3y

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Step-by-step explanation:

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