Question

ratios & proportions
mr. cox filled up his car with gas yesterday. he paid $24 for 6 gallons of gas.
determine the cost per gallon of gas.
cost ($) 24
gas (gallons) 6
the number system
determine the quotient 1440÷40
expressions and equations
simplify the following expression 2³÷2+(5 - 1)
determine the area of the composite figure.
statistics & probability
determine the median of the following: 5, 10, 2, 3, 7, 2, 12, 9

Explanation:

Step1: Calculate cost per - gallon

To find the cost per gallon, divide the total cost by the number of gallons. The formula is $\text{Cost per gallon}=\frac{\text{Total cost}}{\text{Number of gallons}}$. Given total cost = 24 dollars and number of gallons = 6. So, $\frac{24}{6}=4$.

Step2: Calculate the quotient

For $1440\div40$, we can simplify by dividing both numbers by 10 first, getting $144\div4$. And $144\div4 = 36$.

Step3: Simplify the expression

First, calculate the exponent: $2^{3}=2\times2\times2 = 8$. Then the expression $2^{3}\div2+(5 - 1)$ becomes $8\div2+4$. Next, $8\div2 = 4$, and $4 + 4=8$.

Step4: Calculate the area of the composite - figure

We can split the composite figure into two rectangles. One rectangle has dimensions $2\times5$ and the other has dimensions $4\times(9 - 5)=4\times4$. The area of the first rectangle is $A_1=2\times5 = 10$ square feet, and the area of the second rectangle is $A_2=4\times4=16$ square feet. The total area $A=A_1 + A_2=10 + 16=26$ square feet.

Step5: Find the median

First, arrange the data set $2,2,3,5,7,9,10,12$ in ascending order. Since there are $n = 8$ (an even number of data points), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th values. $\frac{n}{2}=4$ and $\frac{n}{2}+1 = 5$. The 4th value is 5 and the 5th value is 7. The median is $\frac{5 + 7}{2}=6$.

Answer:

Cost per gallon of gas: 4 dollars
Quotient of $1440\div40$: 36
Simplified expression value: 8
Area of the composite figure: 26 square feet
Median of the data - set: 6