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3 years ago

How many ways are there to put 6 balls in 3 boxes if the balls are distinguishable but the boxes are not?

Mathematics

1 answer:

FromTheMoon [43]3 years ago

5 0

This is essentially asking how many different ways to partition 6 into 3 segments.

I am assuming "no ball in a box" is not allowed.

6 can be partitioned as

(4,1,1), (3,2,1), and (2,2,2)

So, calculate each partition, we get

(6 choose 4) + (6 choose 3)*(3 choose 2) + (6 choose 2) * (4 choose 2)

= 15 + 20*3 + 15*6

=165

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The area of a mirror is 225 Square inches, it's width is

Zepler [3.9K]

NO. The mirror will not fit in a space that is 15 inches by 16 inches

Solution:

Given that area of mirror is 225 square inches

$width = 13\frac{3}{4} \text{ inches }$

Converting the above mixed fraction we get,

$width = 13\frac{3}{4} = \frac{13 \times 4 + 3}{4} = \frac{55}{4} \text{ inches }$

Let us find the length of mirror

The area of mirror is given as:

area of mirror = length x width

Substituting the given values,

$225 = length \times \frac{55}{4}\\\\length = 225 \times \frac{4}{55}\\\\length = 225 \times 0.0727\\\\length = 16.36$

Thus length of mirror is 16.36 inches

Will the mirror fit in a space that is 15 inches by 16 inches?

NO. The mirror will not fit in a space that is 15 inches by 16 inches

Because length of mirror is 16.36 inches whereas the given space is 15 inches long

16.36 > 15 so the length of mirror will not fit inside the space

Also width of mirror is $\frac{55}{4} = 13.75$ inches which is less than the given space whose width is 16 inches

13.75 < 16 so the width of mirror will not fit inside the space

7 0

3 years ago

Identify the factors of x2 − 4x − 21. (x − 7)(x 3) (x 7)(x − 3) (x 21)(x − 1) (x − 21)(x 1)

Tanzania [10]

The factors of the quadratic expression x² - 4x - 21 is (x - 7)(x + 3), making the first option the right choice.

A quadratic expression is of the form ax² + bx + c, which can be factorized using the mid-term factorization method, where b is shown as the sum or difference of two such numbers, whose product is equal to the product of a and c.

In the question, we are asked to factorize the quadratic expression, x² - 4x - 21.

In the given expression, a = 1, b = -4, and c = -21.

Thus, ac = -21.

The numbers having a product 21 are:

1*21 = 21,

3*7 = 21.

Since, 3 - 7 = -4 (That is b), we break b into 3 and -7.

Thus, the expression can now be shown as:

x² - 4x - 21

= x² + (3 - 7)x - 21

= x² + 3x - 7x - 21

= x(x + 3) - 7(x + 3) {By taking common}

= (x - 7)(x + 3) {By taking common}.

Thus, the factors of the quadratic expression x² - 4x - 21 is (x - 7)(x + 3), making the first option the right choice.

Learn more about factorizing a quadratic expression at

brainly.com/question/52959

#SPJ1

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1 year ago

Question 13

PtichkaEL [24]

Answer:

B. 30x

D. x(45-15)

Step-by-step explanation:

The distributive property lets you factor out the common factor of x. The sum of coefficients can be simplified to a single coefficient.

45x -15x = x(45 -15) = 30x

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2 years ago

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MaRussiya [10]

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3 years ago

Simplify g^1/2 * g^1/2 using the radical form.

guapka [62]

Answer:

√g *√g = g

Step-by-step explanation:

recall that any number or variable to the power of 1/2 can also be written as that variable or number under the radical.

So, we then have

√g * √g

Recall that when we multiply radicals, we multiply what is under our radicals together and then combine them under a new radical

√g * √g = √(g * g)

This gives us √(g²)

recall that the square root of a number or variable squared will merely result in the number or variable by itself (as these are reciprocate equations)

√(g²) = g

8 0

3 years ago