How much more cheese is in one serving of Nancy’s dish than in Carlos dish?

How many ways are there to arrange 7 distinct red and 5 distinct blue balls in a row such that:?

BARSIC [14]

You can change them around up to 144 times.

5 0

3 years ago

Find the greatest common factor of 12a^3b, 16a^2b^2, and 36ab^3

scoundrel [369]

Answer:

The greatest common factor of $12 a^{3} b, 16 a^{2} b^{2}, 36 a b^{3} \text { is } 4 a b$

Solution:

To find the greatest common factor we have to find the prime factors of individual numbers and then find the number which is common to each given number.

Here the numbers are $12 a^{3} b, 16 a^{2} b^{2}, 36 a b^{3}$

Let us find out the prime factors of each number .

$\begin{array}{l}{\text { Prime factors of } 12 a^{3} b=2 \times 2 \times 3 \times a \times a \times a \times b} \\ {\text { Prime factors of } 16 a^{2} b^{2}=2 \times 2 \times 2 \times 2 \times a \times a \times a \times b \times b} \\ {\text { Prime factors of } 36 a b^{3}=2 \times 2 \times 3 \times 3 \times a \times b \times b \times b}\end{array}$

We can see that $2 \times 2 \times \mathrm{a} \times \mathrm{b}$ is common to all the given numbers $12 a^{3} b, 16 a^{2} b^{2}, 36 a b^{3}$

Therefore the greatest common factor of $12 a^{3} b, 16 a^{2} b^{2}, 36 a b^{3} \text { is } 2 \times 2 \times a \times b=4 a b$

3 0

3 years ago

Factor 16x4 - 4y2 A) (x + 4y)(x - 4y) B) 4(2x2 + y)(2x2 - y)

Alex73 [517]

Step-by-step explanation:

$16 {x}^{4} - 4 {y}^{2} \\ {4}^{2} {x}^{4} - {2}^{2} {y}^{2} \\ {4}^{2} {x}^{2} \times {x}^{2} - {2}^{2} {y}^{2} \\ (4 {x}^{2} - 2y)(4 {x}^{2} - 2y)$

6 0

3 years ago

Read 2 more answers

Find the inverse of each function. Is the inverse a function? y=(x+4)³-1

tatuchka [14]

Inverse of the give function F(x) = ( x + 4 )³ - 1 is F⁻¹(x) = [√( x + 1 ) ] - 4.

Given is a function of x, F(x) = ( x + 4 )³ - 1

These question can be solved by following 4 easy steps

Step 1 : Switch the F(x) with the variable y

This implies, F(x) = ( x + 4 )³ - 1 becomes y = ( x + 4 )³ - 1

Step 2 : Interchange the variable x and y in the above obtained equation

This implies, from the equation y = ( x + 4 )³ - 1, we get

x = ( y + 4 )³ - 1

Step 3 : Solve the new obtained equation for y

This implies, we have to simplify the equation by rearranging the terms to get the equation in terms of the variable x.

x = ( y + 4 )³ - 1

=> x + 1 = ( y + 4 )³

=> (y + 4 )³ = x + 1

=> y + 4 = √( x + 1 )

=> y = √( x + 1 ) - 4

Hence we obtain the required equation.

Step 4 : Switch the variable y with F⁻¹(x)

This implies, y = √( x + 1 ) - 4 becomes F⁻¹(x) = √( x + 1 ) - 4

Therefore, we get the inverse of the give function F(x) = ( x + 4 )³ - 1 as F⁻¹(x) = [√( x + 1 ) ] - 4.

Learn more about Inverse of a Function here:

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4 0

1 year ago

A middle schooler took all the 6th grader on a field trip to see ballet. The students filled up 570 seats, which was 95% of the

Musya8 [376]

The total number of seats in the theater is 600 seats, if the students filled up 570 seats, which was 95% of the total number of seats in the theater.

Step-by-step explanation:

The given is,

Seats filled by students are 570 seats

Which is 95% of the total number of seats in the theater

Step: 1

Let, x - Total number of seats available in theater

Percentage of seats filled, y= 95%

Seats filled by students = 570

Formula to calculate total number of seats in theater,

95% of seats $= \frac{95}{100}( x)$

570 = $0.95 (x)$

x = $\frac{570}{0.95}$

= 600

x = 600 seats

Step: 2

Check for solution,

5% of seats $= \frac{5}{100} (600)$

= (0.05 × 600)

= 30 seats

Total no. of seats = 5% of seats + 95% of seats

= 30 + 570

600 = 600

Result:

The total number of seats in the theater is 600 seats.

7 0

3 years ago