Sophia College Algebra 101 Final Milestone Retake Tips
And Concepts Review Questions And Answers Updated
Solutions
,
, Sophia :: Welcome
25/25
25/25 that's 100%
Retake
25 questions were answered correctly.
Milestone Tips
Remember that Milestones are open-book.
Take the Practice Milestone before taking the Milestone.
Take the Milestone at a time and in a place where you can be focused and undisturbed for the entire Milestone time limit.
Milestone Retake
You are allowed one retake per Milestone.
The questions on the retake are different from the original Milestone attempt.
MILESTONE
Only your highest score is counted.
Make sure you're ready. Review our list of Milestone Tips.
Retake Now Maybe Later
Milestone Retake
Before you begin, please make sure you're in a place where you can be focused and undisturbed for the entire Milestone time limit.
Begin Retake
Cancel
1. Milestone Retakes
Sophia allows one retake per Milestone. If you ever want to retake a Milestone, click this button.
Got it
1
Suppose , , and .
Find the value of the following expression.
13
23
11
18
, 6/30/24, 3:33 PM Sophia :: Welcome
RATIONALE
This question involves several properties of logarithms. The Quotient
expressed as subtraction of individual logarithms. Property of Logs states that division inside a logarithm can be
This means we can express as
. Next, the Product Property of Logs states that multiplication inside a
logarithm can be expressed as addition of individual logarithms.
This means we can express as . Then, the Power Property of Logs states that exponents inside a logarithm can
be expressed as outside scalar multiples of the logarithm.
This means we can express as and as . Finally, we can substitute the values we were previously
given
for , , and .
Recall that , , and
. Once these given values are substituted into the expression,
simplify each term and then
perform the addition and subtraction.
3 times 5 is 15; and -2 times -3 is 6. Finally, add these values together.
The logarithmic expression evaluates to 23.
CONCEPT
Applying Properties of Logarithms
2
Edgar opened a deposit account. In the first month, he made an initial deposit of $3200. Starting in month two, he plans to contribute an additional $175 monthly. The
account does not pay any interest.
After how many months will he have a total of $6000?
18 months
15 months
17 months
14 months
RATIONALE
The amount in Edgar's deposit account can be modeled using the formula for an arithmetic sequence. The term is the value after n
months, is the initial balance, d is the common difference (or steady monthly deposits), and n is the number of months. Use the information provided to find
each value.
The initial deposit, , is $3200. Edgar deposits $175 each month, which is the difference, d. We want to know how many months, n, it
will take for the balance to reach $6000, which is the value for . Next, substitute each value in for , d, and .
Once each known value is substituted, we can solve for n. First, distribute 175 into (n – 1).
175(n – 1) is equivalent to 175n – 175. Next, combine like terms on the right side.
3200 minus 175 is equal to 3025. Subtract this value from both sides to isolate the n term.
6000 minus 3025 equals 2975. Finally divide both sides by 175.
2975 divided by 175 is equal to 17. It will take 17 months for the balance to reach $6,000.
2/30
And Concepts Review Questions And Answers Updated
Solutions
,
, Sophia :: Welcome
25/25
25/25 that's 100%
Retake
25 questions were answered correctly.
Milestone Tips
Remember that Milestones are open-book.
Take the Practice Milestone before taking the Milestone.
Take the Milestone at a time and in a place where you can be focused and undisturbed for the entire Milestone time limit.
Milestone Retake
You are allowed one retake per Milestone.
The questions on the retake are different from the original Milestone attempt.
MILESTONE
Only your highest score is counted.
Make sure you're ready. Review our list of Milestone Tips.
Retake Now Maybe Later
Milestone Retake
Before you begin, please make sure you're in a place where you can be focused and undisturbed for the entire Milestone time limit.
Begin Retake
Cancel
1. Milestone Retakes
Sophia allows one retake per Milestone. If you ever want to retake a Milestone, click this button.
Got it
1
Suppose , , and .
Find the value of the following expression.
13
23
11
18
, 6/30/24, 3:33 PM Sophia :: Welcome
RATIONALE
This question involves several properties of logarithms. The Quotient
expressed as subtraction of individual logarithms. Property of Logs states that division inside a logarithm can be
This means we can express as
. Next, the Product Property of Logs states that multiplication inside a
logarithm can be expressed as addition of individual logarithms.
This means we can express as . Then, the Power Property of Logs states that exponents inside a logarithm can
be expressed as outside scalar multiples of the logarithm.
This means we can express as and as . Finally, we can substitute the values we were previously
given
for , , and .
Recall that , , and
. Once these given values are substituted into the expression,
simplify each term and then
perform the addition and subtraction.
3 times 5 is 15; and -2 times -3 is 6. Finally, add these values together.
The logarithmic expression evaluates to 23.
CONCEPT
Applying Properties of Logarithms
2
Edgar opened a deposit account. In the first month, he made an initial deposit of $3200. Starting in month two, he plans to contribute an additional $175 monthly. The
account does not pay any interest.
After how many months will he have a total of $6000?
18 months
15 months
17 months
14 months
RATIONALE
The amount in Edgar's deposit account can be modeled using the formula for an arithmetic sequence. The term is the value after n
months, is the initial balance, d is the common difference (or steady monthly deposits), and n is the number of months. Use the information provided to find
each value.
The initial deposit, , is $3200. Edgar deposits $175 each month, which is the difference, d. We want to know how many months, n, it
will take for the balance to reach $6000, which is the value for . Next, substitute each value in for , d, and .
Once each known value is substituted, we can solve for n. First, distribute 175 into (n – 1).
175(n – 1) is equivalent to 175n – 175. Next, combine like terms on the right side.
3200 minus 175 is equal to 3025. Subtract this value from both sides to isolate the n term.
6000 minus 3025 equals 2975. Finally divide both sides by 175.
2975 divided by 175 is equal to 17. It will take 17 months for the balance to reach $6,000.
2/30
