8) Write an absolute value equation that has 5 and 15 as its solutions?

John can type 2/3 of a manuscript in 12 hours. How much of the manuscript can John write in 1 hour?

Marina86 [1]

John can write 1/18 of the manuscript in 1 hour
Hope this helps!!

8 0

2 years ago

Susan is attending a talk at her son's school. There are 8 rows of 10chairs where 54 parents are sitting. Susan notices that eve

kozerog [31]

Answer:

The largest possible number of adjacent empty chairs in a single row is 3

Step-by-step explanation:

The parameters given are;

The number of chairs = 8 × 10 = 80 chairs

The number of parents = 54

Sitting arrangements of parents = Alone or to one other person

Therefore;

The maximum number of parents on a row = 1 + 1 + 0 + 1 + 1 + 0 + 1 + 1 + 0 + 1 = 7

Hence when the rows have the maximum number of parents occupying the seats we have for the 8 rows;

7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 = 56

But there are only 54 parents, therefore, up to the 7th row will have 7 parents while the 8th row will have only 5 parents to make the possible sitting arrangement to be as follows;

7 + 7 + 7 + 7 + 7 + 7 + 7 + 5 = 54

The sitting arrangement for the 8th row is therefore

1 + 1 + 0 + 1 + 1 + 0 + 1 + 0 + 0 + 0

Hence there will be three empty seats in the 8th row making the largest possible number of adjacent empty chairs in a single row = 3.

4 0

2 years ago

Jenny multiplies the square root of her favorite positive integer by $\sqrt{2}$. Her product is an integer. a) Name three number

Dmitry [639]

Answer:

Part a) $2,50,18$

Part b) When Jenny divides the square root of her favorite positive integer by $\sqrt{2}$ , she gets an integer

Step-by-step explanation:

Let

x-------> the favorite positive integer

Part a)

1) For $x=2$

$\sqrt{2}*\sqrt{2}=\sqrt{4}=2$ -----> the product is an integer

so

The number $x=2$ could be Jenny favorite positive integer

2) For $x=50$

$\sqrt{50}*\sqrt{2}=\sqrt{100}=10$ -----> the product is an integer

so

The number $x=50$ could be Jenny favorite positive integer

3) For $x=18$

$\sqrt{18}*\sqrt{2}=\sqrt{36}=6$ -----> the product is an integer

so

The number $x=18$ could be Jenny favorite positive integer

Part B)

1) For $x=2$

$\sqrt{2}/\sqrt{2}=\sqrt{1}=1$ -----> the result is an integer

2) For $x=50$

$\sqrt{50}/\sqrt{2}=\sqrt{25}=5$ -----> the result is an integer

3) For $x=18$

$\sqrt{18}/\sqrt{2}=\sqrt{9}=3$ -----> the result is an integer

Therefore

When Jenny divides the square root of her favorite positive integer by $\sqrt{2}$ , she gets an integer

4 0

2 years ago

List the first five terms of the sequence. a1 = 4, an+1 = 5an − 3

RUDIKE [14]

The recursive formula

$a_{n+1} = 5a_n-3$

is telling you that the next term in the sequence is five times the previous one, minus 3.

So, if we start with $a_1=4$ , we have to multiply it by 5 and subtract 3 to get the next:

$a_2 = 5a_1-3 = 5\cdot 4 - 3 = 20-3 = 17$

And similarly we can obtain all the next terms:

$a_3 = 5a_2-3 = 5\cdot 17 - 3 = 85-3 = 82$

$a_4 = 5a_3-3 = 5\cdot 82 - 3 = 410-3 = 407$

$a_5 = 5a_4-3 = 5\cdot 407 - 3 = 2035-3 = 2032$

5 0

2 years ago

Mickey built his lemonade stand out of $75,000 worth of plywood and paint. he sells a glass of lemonade for $30 and uses $1.25 o

Leviafan [203]

Break even point is where all the expense is already covered by the revenue. In this case, the expense would be the stand ($75,000) and the lemon+sugar+water ( $1.25 per glass). The revenue comes from lemonade($30/glass). Then the equation would be:

$30 * glass of lemonade= $75,000 + $1.25 * glass of lemonade
($30-$1.25) * glass of lemonade= $75,000
glass of lemonade= 2608.7

4 0

2 years ago