1.
Which of the following is a rational number? (4 points)
square root 15 square root 16, square root 21, square root 22
square root 15
square root 16
square root 21
square root 22
2.
If (44)x = 432, what is the value of x? (4 points)
4
7
8
28
3.
There are (108)2 ⋅ 100 candies in a store. What is the total number of candies in the store? (4 points)
1
1010
1016
1017
4.
Which expression is equivalent to 34 ⋅ 3−9? (4 points)
1 over 3 to the 13th power
1 over 3 to the 5th power
35
313
5.
Which expression is equivalent to rm ÷ rn? (4 points)
rm − n
rm + n
rm ⋅ n
rm ÷ n
6.
Part A: Find a rational number that is between 5.2 and 5.5. Explain why it is rational. (2 points)
Part B: Find an irrational number that is between 5.2 and 5.5. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth. (3 points)
7.
Annabelle and Navene are multiplying (4275)(4372).
Annabelle's Work Navene's Work
(4275)(4372) = 42 + 375 + 2 = 4577 (4275)(4372) = 42⋅375⋅2 = 46710
Is either of them correct? Explain your reasoning. (5 points)
Theres no typos? And its a test-
I mightve accidentally put the questions too close but im not very good at math and dont have anyone to help me-
someone please help? :,D
1. To determine which of the following numbers is rational, we need to understand what a rational number is. A rational number is any number that can be expressed as a fraction, where the numerator and denominator are both integers.
Looking at the options:
- square root 15: This is an irrational number because the square root of 15 cannot be expressed as a fraction.
- square root 16: This is a rational number because the square root of 16 is 4, which can be expressed as the fraction 4/1.
- square root 21: This is an irrational number because the square root of 21 cannot be expressed as a fraction.
- square root 22: This is an irrational number because the square root of 22 cannot be expressed as a fraction.
So, the rational number in the given options is square root 16.
2. To find the value of x in the equation (44)x = 432, we need to solve for x.
To approach this problem, we can use logarithms. Taking the logarithm of both sides of the equation, we have:
log((44)x) = log(432)
Using the logarithm properties, we can bring down the exponent x:
x * log(44) = log(432)
Now, we can solve for x by dividing both sides by log(44):
x = log(432) / log(44)
Using a calculator, we can find that log(432) ≈ 2.635 and log(44) ≈ 1.643. Dividing the two values, we get:
x ≈ 2.635 / 1.643 ≈ 1.604
So, the value of x is approximately 1.604.
3. To find the total number of candies in a store, we need to evaluate the expression (108)2 ⋅ 100.
First, we can simplify (108)2 by squaring 108:
(108)2 = 108 * 108
Using a calculator, we find that 108 * 108 = 11,664.
Next, we multiply the result by 100:
11,664 * 100 = 1,166,400
So, the total number of candies in the store is 1,166,400.
4. To find the expression equivalent to 34 ⋅ 3^(-9), we need to simplify the exponent.
Remember that when a number is raised to a negative exponent, it can be written as the reciprocal of that number raised to the positive exponent.
So, 3^(-9) = 1 / 3^9.
Now, we can substitute this back into the original expression:
34 ⋅ 3^(-9) = 34 ⋅ (1 / 3^9) = (3^4) ⋅ (1 / 3^9) = 3^(4-9) = 3^(-5)
Therefore, the expression equivalent to 34 ⋅ 3^(-9) is 3^(-5), which can also be written as 1 / 3^5.
5. The expression equivalent to rm ÷ rn is rm - n.
When dividing two numbers with the same base, you can subtract the exponents.
So, rm ÷ rn = rm - n.
6. Part A: To find a rational number between 5.2 and 5.5, we can choose any number that can be expressed as a fraction. For example, we can choose 5.25. This can be expressed as the fraction 21/4, where both the numerator and denominator are integers.
Part B: To find an irrational number between 5.2 and 5.5, we can choose the square root of 5.3. This is an irrational number because the square root of 5.3 cannot be expressed as a fraction. The decimal approximation of the square root of 5.3 to the nearest hundredth is approximately 2.30.
7. According to the given work:
- Annabelle's work shows that she added the numbers incorrectly. The sum of (42 + 375 + 2) is 419, not 4577. Therefore, Annabelle's work is incorrect.
- Navene's work shows that he multiplied the numbers correctly. The product of (42⋅375⋅2) is 31500, not 46710. Therefore, Navene's work is also incorrect.
Neither Annabelle nor Navene's work is correct because they made mistakes in their calculations. The correct product of (4275)(4372) is 18,722,700.
sure looks like a homework dump to me.
No ideas on any of them?
of course, the typos don't help, either ...