Use the order of operations to simplify one ninths time three cubed minus nine times one sixth plus two thirds

"A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 20 child bikes and 6 adult bikes in the week. No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100 Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100 Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100"

Answer:

Correct answer for this question is first option because it satisfies the first inequality but not the second one.

Step by Step Explanation:

$NO,\\4c+6a\leq 120\\ and\\4c+4a\leq 100$

First Inequality:

4(20)+6(6)≤120

80+36≤120

116≤120 ⇒ TRUE

Second Inequality:

4(20)+4(6)≤100

80+24≤100

104≤100 ⇒ FALSE

5 0

3 years ago

Last year, the hiking club had 25 members. This year, there’s 37. What is the percent increase?

borishaifa [10]

Answer:

The hiking club's member count increased by 48%.

Step-by-step explanation:

We are given two data values: 25 members and 37 members. We need to determine how many members the club gained first. We can set up an equation where we solve for an unknown, or x, in this case.

$25 + x = 37\\\\x = 12$

The club increased by 12 members, so now we can divide this value by the initial amount of members and multiply the decimal we receive by 100 to express it in percentage form.

$\frac{12}{25} =0.48\\\\0.48 \times 100 = 48\%$