Question

m3 td lesson 18

1. the chemical element helium remains a liquid when it is below $-452^{\circ}f$.

remember
for problems 25-27, evaluate each expression by substituting the given value for $x$.

1. $4x + \frac{1}{3}$ when $x = \frac{3}{4}$
2. $6x - \frac{3}{4}$ when $x = \frac{5}{2}$
3. $6x - 4\frac{1}{3}$ when $x = 3\frac{1}{3}$
4. so far this week, sara has run 3.5 miles. her goal is to run a total of 8.75 miles. if sara runs 1.75 miles per day, how many more days must she run to reach her goal? write and solve an equation. check your solution.
5. ____________ are measures of center that summarize a typical data point in a data set.

a. mean and median
b. median and interquartile range
c. mean and mean absolute deviation
d. mean absolute deviation and interquartile range

Explanation:

Problem 25

Step1: Substitute $x=\frac{3}{4}$

$4\times\frac{3}{4} + \frac{1}{3}$

Step2: Calculate product first

$3 + \frac{1}{3}$

Step3: Sum the terms

$\frac{9}{3}+\frac{1}{3}=\frac{10}{3}$

Problem 26

Step1: Substitute $x=\frac{5}{2}$

$6\times\frac{5}{2} - \frac{3}{4}$

Step2: Calculate product first

$15 - \frac{3}{4}$

Step3: Subtract the terms

$\frac{60}{4}-\frac{3}{4}=\frac{57}{4}$

Problem 27

Step1: Convert mixed numbers to fractions

$x=3\frac{1}{3}=\frac{10}{3}$, $4\frac{1}{3}=\frac{13}{3}$

Step2: Substitute $x=\frac{10}{3}$

$6\times\frac{10}{3} - \frac{13}{3}$

Step3: Calculate product first

$20 - \frac{13}{3}$

Step4: Subtract the terms

$\frac{60}{3}-\frac{13}{3}=\frac{47}{3}$

Problem 28

Step1: Define variable & set up equation

Let $d$ = days needed. Equation: $3.5 + 1.75d = 8.75$

Step2: Isolate the variable term

$1.75d = 8.75 - 3.5$
$1.75d = 5.25$

Step3: Solve for $d$

$d=\frac{5.25}{1.75}=3$

Step4: Check solution

$3.5 + 1.75\times3=3.5+5.25=8.75$, which matches the goal.

Problem 29

Step1: Identify measures of center

Measures of center summarize typical data points; mean/median are center measures, while interquartile range/mean absolute deviation are spread measures.

Answer:

1. $\frac{10}{3}$
2. $\frac{57}{4}$
3. $\frac{47}{3}$
4. 3 days
5. A. Mean and median