31 wyatt can husk at least 12 dozen ears of corn per hour and at most 18 dozen ears of corn per hour. based on this information, what is a possible amount of time, in hours, that it could take wyatt to husk 72 dozen ears of corn? 32 the posted weight - limit for a covered wooden bridge in pennsylvania is 6000 pounds. a delivery truck that is carrying x identical boxes each weighing 14 pounds will pass over the bridge. if the combined weight of the empty delivery truck and its driver is 4500 pounds, what is the maximum possible value for x that will keep the combined weight of the truck, driver, and boxes below the bridges posted weight limit? 33 number of portable media players sold worldwide each year from 2006 to 2011 according to the line graph above, the number of portable media players sold in 2008 is what fraction of the number sold in 2011? 34 a local television station sells time slots for programs in 30 - minute intervals. if the station operates 24 hours per day, every day of the week, what is the total number of 30 - minute time slots the station can sell for tuesday and wednesday? 35 a dairy farmer uses a storage silo that is in the shape of the right circular cylinder above. if the volume of the silo is 72π cubic yards, what is the diameter of the base of the cylinder, in yards? 36 h(x)=\frac{1}{(x - 5)^2+4(x - 5)+4} for what value of x is the function h above undefined? 37 jessica opened a bank account that earns 2 percent interest compounded annually. her initial deposit was $100, and she uses the expression $100(x)^t to find the value of the account after t years. what is the value of x in the expression? 38 jessicas friend tyshaun found an account that earns 2.5 percent interest compounded annually. tyshaun made an initial deposit of $100 into this account at the same time jessica made a deposit of $100 into her account. after 10 years, how much more money will tyshauns initial deposit have earned than jessicas initial deposit? (round your answer to the nearest cent and ignore the dollar sign when gridding your response.)

Question

Accepted Answer

### 31
# Explanation:
## Step1: Calculate minimum time
Wyatt husks at least 12 dozen ears of corn per hour. To husk 72 dozen ears, use the formula $t=\frac{total\ amount}{rate}$. So $t_{min}=\frac{72}{12}=6$ hours.
## Step2: Calculate maximum time
Wyatt husks at most 18 dozen ears of corn per hour. Using the same formula, $t_{max}=\frac{72}{18}=4$ hours. So a possible amount of time is between 4 and 6 hours.
# Answer:
Any value $t$ such that $4\leq t\leq6$

### 32
# Explanation:
## Step1: Set up the weight - inequality
The combined weight of the empty truck and driver is 4500 pounds, and each box weighs 14 pounds. The total weight (truck + driver+ boxes) must be less than or equal to 6000 pounds. So the inequality is $4500 + 14x\leq6000$.
## Step2: Solve the inequality for $x$
Subtract 4500 from both sides: $14x\leq6000 - 4500=1500$. Then $x\leq\frac{1500}{14}\approx107.14$. Since $x$ represents the number of boxes and must be an integer, the maximum value of $x$ is 107.
# Answer:
107

### 33
# Explanation:
## Step1: Read values from the graph
From the graph, the number of portable media - players sold in 2008 is 100 million and in 2011 is 160 million.
## Step2: Calculate the fraction
The fraction is $\frac{100}{160}=\frac{5}{8}$.
# Answer:
$\frac{5}{8}$

### 34
# Explanation:
## Step1: Calculate the number of 30 - minute intervals per day
The station operates 24 hours a day. Since each interval is 30 minutes (or 0.5 hours), the number of 30 - minute intervals per day is $\frac{24}{0.5}=48$.
## Step2: Calculate the number of intervals for Tuesday and Wednesday
There are 2 days (Tuesday and Wednesday), so the total number of 30 - minute intervals is $48	imes2 = 96$.
# Answer:
96

### 35
# Explanation:
## Step1: Recall the volume formula for a cylinder
The volume formula for a cylinder is $V=\pi r^{2}h$. Given $V = 72\pi$ and $h = 8$. Substitute these values into the formula: $72\pi=\pi r^{2}	imes8$.
## Step2: Solve for $r$
First, divide both sides of the equation by $8\pi$: $\frac{72\pi}{8\pi}=r^{2}$, so $r^{2}=9$, and $r = 3$.
## Step3: Calculate the diameter
The diameter $d = 2r$, so $d=6$.
# Answer:
6

### 36
# Explanation:
## Step1: Simplify the denominator
Let $u=x - 5$. Then the denominator is $u^{2}+4u + 4=(u + 2)^{2}=(x-5 + 2)^{2}=(x - 3)^{2}$.
## Step2: Find when the function is undefined
A rational function is undefined when the denominator is equal to 0. Set $(x - 3)^{2}=0$. Solving for $x$, we get $x = 3$.
# Answer:
3

### 37
# Explanation:
## Step1: Recall the compound - interest formula
The compound - interest formula is $A=P(1 + r)^{t}$, where $P$ is the principal amount, $r$ is the annual interest rate as a decimal, and $t$ is the number of years. Jessica's account has an interest rate of 2% or 0.02, and the formula for the value of her account after $t$ years is $A = 100(1+0.02)^{t}=100(1.02)^{t}$. So $x = 1.02$.
# Answer:
1.02

### 38
# Explanation:
## Step1: Calculate the value of Jessica's account after 10 years
Using the formula $A=P(1 + r)^{t}$ with $P = 100$, $r=0.02$, and $t = 10$, we have $A_{J}=100(1.02)^{10}\approx100	imes1.218994427=121.90$.
## Step2: Calculate the value of Tyshaun's account after 10 years
Using the formula $A=P(1 + r)^{t}$ with $P = 100$, $r = 0.025$, and $t=10$, we have $A_{T}=100(1.025)^{10}\approx100	imes1.280084544=128.01$.
## Step3: Find the difference
The difference is $A_{T}-A_{J}=128.01-121.90 = 6.11$.
# Answer:
6.11

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QUESTION IMAGE

Question

Explanation:

31

Step1: Calculate minimum time

Step2: Calculate maximum time

Step1: Set up the weight - inequality

Step2: Solve the inequality for $x$

Step1: Read values from the graph

Step2: Calculate the fraction

Answer:

32