Question

Evaluate the expression:

(10 −1 )^2/227

Answer 1

simplify 81/227

Answer 2

Evaluate the expression:
(10 −1 )^2/27

Answer 3

Evaluate the following to determine the value of 𝑛:

(8^3)^n = 8^12

Answer 4

Inessa ran 3 laps in 10 minutes. How long would it take her to run 5 laps at this pace?

Answer 5

what is the constant rate of proportionality in
X: 0,1,2,3,4,
Y: 0,4,8,12,16

Answer 6

To evaluate the expression, we can follow the order of operations: parentheses first, then exponents, then division.

(10 - 1) ^ 2 / 227

(9) ^ 2 / 227

81 / 227

So, the evaluated value of the expression is 81/227.

Answer 7

To simplify 81/227, we can check if there are any common factors that can be divided out from both the numerator and the denominator. However, in this case, 81 and 227 do not have any common factors other than 1. Therefore, 81/227 is already in its simplified form.

Answer 8

To evaluate the expression, we follow the order of operations: parentheses first, then exponents, then division.

(10 - 1)^2 / 27
(9)^2 / 27
81 / 27
3

So, the evaluated value of the expression is 3.

Answer 9

To determine the value of 𝑛, we can set up an equation given that the base is the same on both sides:

(8^3)^n = 8^12

Now we can simplify the left side of the equation:

8^(3n) = 8^12

Since the bases are the same, the exponents must be equal:

3n = 12

To isolate 𝑛, we divide both sides of the equation by 3:

3n/3 = 12/3

n = 4

So, the value of 𝑛 is 4.

Answer 10

To find out how long it would take Inessa to run 5 laps at the same pace, we can set up a proportion using the ratio of the number of laps to the time it takes.

The ratio of the number of laps to the time is constant, so we can create the following proportion:

3 laps / 10 minutes = 5 laps / x minutes

Now, let's solve for x by cross-multiplying and then dividing:

3 * x = 10 * 5

3x = 50

x = 50 / 3

x ≈ 16.67

Therefore, it would take Inessa approximately 16.67 minutes to run 5 laps at the same pace.

Answer 11

To find the constant rate of proportionality, we can choose any two corresponding values of X and Y, and then calculate the ratio between the two. Let's choose X = 2 and Y = 8.

The ratio is: Y / X = 8 / 2 = 4.

Therefore, the constant rate of proportionality is 4.