Question 1

Using the graph below determine  .

Accepted Answer

The answer of Using the graph below determine  ....

Question 2

Use the table of values to solve the system.

Accepted Answer

The table of values shows that the x-values of both equations are the same, which means they can be combined into one equation. From the table, we can see that when x = 2, y = 3 for the first equation and y = 1 for the second equation. Therefore, the solution to the system is (2, 3) since it satisfies both equations. Option C is the only choice that correctly lists (2, 3) as a solution to the system.

Question 3

Two functions and are given by the tables below. Determine .

Accepted Answer

The answer of Two functions and are given by the...

Question 4

Use the table of values to solve the system.

Accepted Answer

The answer of Use the table of values to solve...

Question 5

Find the inverse of  .

Accepted Answer

The answer of Find the inverse of  .
...

Question 6

If  and  determine  .

Accepted Answer

The answer of If  and  determine  .
...

Question 7

Use the table of values to solve the system.

Accepted Answer

Since there are only two variables in the system, we can use the table of values to substitute into the equations and find the values of the variables. From the table, when $x=1$, $y=3$ in the first equation, and when $x=1$, $y=2$ in the second equation. Therefore, the solution to the system is $(1,3)$. This corresponds to Choice A.

Question 8

The half-life of Radon-222 is 3.8 days. A 32-gram sample of Radon-222 is monitored for one day. How long will it take for the sample to be 24% of the initial amount? (rounded to the nearest hundredths)?

Accepted Answer

To find how long it will take for a 32-gram sample of Radon-222 to be 24% of its initial amount, we first determine what 24% of 32 grams is: 24% of 32 grams = 0.24 * 32 = 7.68 grams. The question essentially asks how long it takes for the sample to decay to 7.68 grams. The half-life formula is used to calculate the time it takes for a substance to decay to a certain amount: $t = \frac{\ln(\frac{N_0}{N})}{k}$, where $t$ is the time, $N_0$ is the initial quantity, $N$ is the final quantity, $k$ is the decay constant, and $\ln$ is the natural logarithm. The decay constant $k$ can be found from the half-life formula $t_{1/2} = \frac{\ln(2)}{k}$. Given the half-life of Radon-222 is 3.8 days, we can calculate $k$ and then use it to find $t$. However, for this question, a simpler approach can be used based on understanding the nature of half-lives. Since the question asks for a rounded answer and involves understanding the concept rather than detailed calculation, knowing that each half-life reduces the amount by half, we can estimate how many half-lives it takes to reach approximately 24% (which is close to 25%, or $1/4$). This approach simplifies the calculation, leading to the conclusion that it takes approximately 7.8 days to reach 24% of the initial amount, without needing to perform detailed logarithmic calculations.

Question 9

Two functions and are given by the tables below. Determine .

Accepted Answer

The answer of Two functions and are given by the...

Question 10

You are choosing between two jobs. Job one pays $10 per hour for 32 hours per week. Job 2 pays $8 per hour plus a commission of 10% of your sales again based on 32 hours per week. At what amount of sales is your weekly pay the same at the two jobs? Let s be your amount of sales and let p be amount of pay. Use the table of values to solve the system.

Accepted Answer

To find when the two jobs pay the same, we need to set the equations equal to each other and solve for s.

For job 1, the pay equation is:
p = 10(32) = 320

For job 2, the pay equation is:
p = 8(32) + 0.1s

Set the two equations equal to each other:
320 = 8(32) + 0.1s

Simplify and solve for s:
320 = 256 + 0.1s
64 = 0.1s
s = 640

Therefore, at $640 in sales, the pay for job 2 will be the same as job 1. None of the other choices equal this value, so the answer is C.

Question 11

Use the table of values to solve the system.

Accepted Answer

The answer of Use the table of values to solve...

Question 12

The mass of bacteria in a Petri dish is 56 micrograms. After 3 hours the bacteria's mass as increased to 164 micrograms. How long will it take for the population to quadruple?

Accepted Answer

The mass of bacteria doubles every 3 hours. So, it will take 3.9 hours for the population to quadruple.

Question 13

Find the inverse of  .

Accepted Answer

The answer of Find the inverse of  .
...

Question 14

The mass of bacteria in a Petri dish is 30 micrograms. After 3 hours the bacteria s mass as increased to 141 micrograms. Which one of the following exponential functions model the bacteria s growth where  is measured in hours.

Accepted Answer

The answer of The mass of bacteria in a Petri...

Question 15

A car dealer advertises a 35% discount on all cars available in the current inventory. In addition the car dealer offers a $1800 rebate on the purchase of a new care. The dealer decides to apply the rebate first and then award the 35% discount afterwards. Let  represent the sticker price of the new car. Which one of the following functions model the final price of the car once the rebate and discount have been awarded?

Accepted Answer

The answer of A car dealer advertises a 35% discount...

Question 16

Use the table of values to solve the system.

Accepted Answer

The answer of Use the table of values to solve...

Question 17

If  and  determine  . Round to the nearest tenth.

Accepted Answer

The answer of If  and  determine  ....

Question 18

The graphs of two functions  and  are given below. Using the graphs determine  .

Accepted Answer

From the graph of 11ec19db_84bd_dc2e_9dbe_1f1a87a44870_TBX8673_11, we can see that the y-intercept of the function is approximately 3.2. This means that the function has the form 11ec19db_84bd_dc2e_9dbe_1f1a87a44870_TBX8673_11 = ax + 3.2 for some constant a.

From the graph of 11ec19db_84bd_dc2f_9dbe_c5e4f7093dba_TBX8673_11, we can see that the function passes through the point (4, 0). This means that when x = 4, 11ec19db_84bd_dc2f_9dbe_c5e4f7093dba_TBX8673_11 = 0.

Substituting x = 4 into the equation 11ec19db_84bd_dc2e_9dbe_1f1a87a44870_TBX8673_11 = ax + 3.2, we get:
11ec19db_84bd_dc2f_9dbe_c5e4f7093dba_TBX8673_11 = a(4) + 3.2 = 0
Simplifying, we get:
a = -0.8

Therefore, the equation of the line represented by the graph of 11ec19db_84bd_dc2e_9dbe_1f1a87a44870_TBX8673_11 is:
11ec19db_84bd_dc2e_9dbe_1f1a87a44870_TBX8673_11 = -0.8x + 3.2

To find the value of 11ec19db_84bd_dc30_9dbe_e1db58dd905a_TBX8673_00, we need to find the x-value where the two functions intersect. From the graph, we can see that this occurs at x = 6.

Substituting x = 6 into the equation 11ec19db_84bd_dc2e_9dbe_1f1a87a44870_TBX8673_11 = -0.8x + 3.2, we get:
11ec19db_84bd_dc2e_9dbe_1f1a87a44870_TBX8673_11 = -0.8(6) + 3.2 = -1.6

Therefore, 11ec19db_84bd_dc30_9dbe_e1db58dd905a_TBX8673_00 = -1.6.

Question 19

Find the inverse of  .

Accepted Answer

To find the inverse of this hexadecimal number, we need to apply XOR operation with the key TBX8673_11, which is 10 characters long. Therefore, we need to break the given number into blocks of 10 characters each and apply XOR operation with the key.

11ec19db_84be_2a54_9dbe_d3cff81f6041_TBX8673_11
= 11ec19db_84be_2a54_9dbe_d3cff81f60 XOR 41TBX8673_11

Now, we convert 41TBX8673_11 into hexadecimal format, which is equivalent to:

34 31 54 42 58 38 36 37 33 5F 31 31

We can now apply XOR operation between the two blocks:

11ec19db_84be_2a54_9dbe_d3cff81f60 XOR 34315442583637335F3131
= 22dd04e3_cf06_6b06_0cab_ea0c090e5542

Therefore, the inverted hexadecimal number is:

22dd04e3_cf06_6b06_0cab_ea0c090e5542_TBX8673_11

which is equivalent to choice D: 11ec19db_84be_5168_9dbe_f9f5c255b1e4_TBX8673_11.

Question 20

Jennifer invests $5100 in a saving certificate with an interest rate of 4.25% per year compounded monthly. How long will it take for her investment to grow to $13000? Round to the nearest tenth.

Accepted Answer

The formula for compound interest is $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years. Here, $A = 13000$, $P = 5100$, $r = 0.0425$, and $n = 12$. We solve for $t$. Rearranging the formula to solve for $t$, we get $t = \frac{\log(A/P)}{n \cdot \log(1 + r/n)}$. Plugging in the values, we find that $t$ is approximately 22.1 years.

Quiz 4: Systems of Linear Equations

Using the graph below determine .

Use the table of values to solve the system.

Two functions and are given by the tables below. Determine .

Use the table of values to solve the system.

Find the inverse of .

If and determine .

Use the table of values to solve the system.

The half-life of Radon-222 is 3.8 days. A 32-gram sample of Radon-222 is monitored for one day. How long will it take for the sample to be 24% of the initial amount? (rounded to the nearest hundredths) ?

Two functions and are given by the tables below. Determine .

Use the table of values to solve the system.

The mass of bacteria in a Petri dish is 56 micrograms. After 3 hours the bacteria's mass as increased to 164 micrograms. How long will it take for the population to quadruple?

Find the inverse of .

The mass of bacteria in a Petri dish is 30 micrograms. After 3 hours the bacteria s mass as increased to 141 micrograms. Which one of the following exponential functions model the bacteria s growth where is measured in hours.

Use the table of values to solve the system.

If and determine . Round to the nearest tenth.

The graphs of two functions and are given below. Using the graphs determine .

Find the inverse of .

Jennifer invests $5100 in a saving certificate with an interest rate of 4.25% per year compounded monthly. How long will it take for her investment to grow to $13000? Round to the nearest tenth.