Sophia Milestone 1 College Algebra Questions with Correct answers.
1 view 0 purchase
Course
SOPHIA MILESTONES
Institution
Ashford University
Sophia Milestone 1 College Algebra Questions with Correct answers.Score 18/21 You passed this Milestone 18 questions were answered correctly. 3 questions were answered incorrectly. 1 Simplify the following radical expression. RATIONALE To simplify this expression, we can use the Product Property of...
sophia milestone 1 college algebra questions with correct answers
Written for
Ashford University
SOPHIA MILESTONES
All documents for this subject (17)
Seller
Follow
StudyConnect
Reviews received
Content preview
8/14/2021 Sophia :: Welcome
Score 18/21
You passed this Milestone
18 questions were answered correctly.
3 questions were answered incorrectly.
1
Simplify the following radical expression.
UNIT 1 — MILESTONE 1
RATIONALE
To simplify this expression, we can use the Product Property of Radicals to separate the expression into two radicals.
The cube root of can be written as the cube root of 64 times the cube root of . Next, we can write each radical expression using a fractional exponent in
order to simplify. The index of the radical determines the denominator of the fractional exponent. The index here is 3, so each expression underneath the
radical will be raised to the power.
Now that we have changed our original expression from a radical to fractional exponents, we can evaluate and simplify the two expressions that are raised
to the power.
to the power of evaluates to 4 because 4 raised to the 3rd power is 64 ( ). To simplify , we multiply the two exponents together.
3 times equals 1 and x to the power of 1 is simply x. The expression simplifies to 4x.
RATIONALE
First, apply the Power of a Power Property of Exponents, which states that when an exponent is raised to another exponent, you can multiply the exponents.
Therefore, multiply 3 times 4 to evaluate the first part, .
3 times 4 is 12, so is equivalent to . Next, combine the two terms. The Product Property of Exponents states that if two expressions with the same base
are multiplied together, you can add the exponents. Add the exponents 12 and 5 to simplify.
12 plus 5 is 17. The expression is equivalent to .
CONCEPT
Properties of Exponents
3
There are about 208,000,000,000 different 8-letter passwords that can be formed using a 26-letter alphabet.
Express this number using scientific notation.
RATIONALE
To express this number in scientific notation, you must find two parts: a number between one and ten (it can be equal to one, but not
ten), and a power of 10. To find the first part, place the decimal after the first non-zero number, 2.
The decimal will be placed after the 2. We will also include the numbers right after the 2, which were 08. These will go immediately
after the decimal. To find the second part, you must find the exponent to which 10 will be raised. To do this, count how many times
the decimal is moved from 2.08 to obtain 208,000,000,000
If we start with the decimal right after the 2, it would take us eleven moves to the right to obtain the original number. Because we
must move the decimal point eleven times, the exponent is 11.
Combine the two parts to state the solution in scientific notation. There are about 8-letter passwords using the 26-letter
alphabet.
CONCEPT
Writing Numbers in Scientific Notation
4
The diameter of a hydrogen atom is about meters. A protein molecule has an overall length of 3000 times (or times) the diameter of a hydrogen
atom.
What is the length of the protein molecule, in meters, if it were written in scientific notation?
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller StudyConnect. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $15.49. You're not tied to anything after your purchase.
