Bakery rolls are being prepared to go to grocery stores. Divide 72 rolls into 2 groups so the ratio is 3 to 5.

Carol bought a coloring book. It is 11 inches long and 8 inches wide. What is the diagonal length of the book?

Leokris [45]

Answer:

13.6 inches

Step-by-step explanation:

We can use Pythagorean theorem: $c=\sqrt{a^{2} +b^{2} }$

Let c be the diagonal length, a for length, and b for width.

Substitute the values.

$c=\sqrt{11^{2}+8^{2} }$

c=13.6 inches

7 0

3 years ago

The values of x and y are proportional. Determine the constant of proportionality(k)

Studentka2010 [4]

<h3>The constant of proportionality is k = 5</h3>

For direct proportion equations, you divide the y value over its corresponding x value to get the value of k.

For example, the point (x,y) = (2,10) is on the diagonal line. So k = y/x = 10/2 = 5.

Another example: the point (x,y) = (6, 30) is also on the same diagonal line, so k = y/x = 30/6 = 5 is the same result as before.

You can use any point on the diagonal line as long as it is not (0,0). This is because division by zero is not allowed.

side note: the direct proportion equation y = k*x becomes y = 5*x which is the graph of that diagonal line. The slope is m = 5, the y intercept is b = 0. All direct proportion graphs go through the origin as shown in the diagram.

3 0

4 years ago

2. How many solutions does the below system of equations have?

bearhunter [10]

Y=5x-4

3y=15x-8
3(5x-4)=15x-8
15x-12=15x-8
??

Therefore, there is no solution.

8 0

3 years ago

Read 2 more answers

The following parts refer to the letters: LAMEFIREALARM. Recall that "word" means distinguishable letter arrangements. (a) How m

larisa86 [58]

Answer:

Step-by-step explanation:

The word "LAMEFIREALARM" word consists of

2L , 2M, 2E , 2R , 3A , F and I

no of words with the above letters such that M's are not together

=Total No of words- M's are together

Total no of words $=\frac{13!}{4\times 2!\times 3!}=64,864,800$

When M's are together . considering 2 M's as one

therefore there are $\frac{12!}{3\times 2!\times 3!}=9,979,200$

No of ways $=\frac{13!}{4\times 2!\times 3!}-\frac{12!}{3\times 2!\times 3!}=54,885,600$

(b)No of ways such that M's are separated by at least 2 letters

at least 2 letter means 2 letter, 3 letter ......11 letters

So we have to subtract no of ways where there are 1 letter in between M's from total no of ways where 2 M's are not next to each other

No of ways in which there is 1 letter between 2 M's

This can be done by considering 11 cases

In first case Place first M in Starting Position and 2 M on third place

Second case place First M in 2 nd Position and second M on 4 th place

Similarly For 11th case

Place first M in 11th place and second M on 13th place

Total ways

$=\frac{11\times 11!}{3!\times 2!\times 2!\times 2!}$

So , the total number of arrangements of the letters of the word LAMEFIREALARM where the two M's are separated by atleast two letters is

$=\frac{13!}{4\times 2!\times 3!}-\frac{12!}{3\times 2!\times 3!}-\frac{11\times 11!}{3!\times 2!\times 2!\times 2!}$

$=45738000$

7 0

3 years ago

Which number line shows the solution to the inequality?<br> y-2 <-5

spin [16.1K]

I think it would be A.

4 0

3 years ago