Question 1

Find the integer value of  without using a calculator.
A) 27
B) 216
C) 54
D) 18

Accepted Answer

To find the integer value of 11eaa948_cded_bb6a_84bc_fb59fc3ae3a8_TB2342_11 without using a calculator, we need to convert the hexadecimal number to decimal.

First, we can split the number into two parts: 11eaa948_cded_bb6a_84bc_fb59fc3ae3a8 and TB2342_11.

The first part is a 31-digit hexadecimal number, which can be converted to decimal by multiplying each digit by its corresponding power of 16 and adding them all together:

1*16^30 + 1*16^29 + 14*16^28 + 10*16^27 + 10*16^26 + 9*16^25 + 4*16^24 + 8*16^23 + 12*16^22 + 13*16^21 + 14*16^20 + 11*16^19 + 6*16^18 + 10*16^17 + 8*16^16 + 4*16^15 + 11*16^14 + 12*16^13 + 8*16^12 + 4*16^11 + 11*16^10 + 12*16^9 + 5*16^8 + 9*16^7 + 15*16^6 + 12*16^5 + 3*16^4 + 10*16^3 + 14*16^2 + 3*16^1 + 8*16^0

Simplifying this expression, we get:

21970406912751833485093065127714835304

The second part, TB2342_11, does not represent a number in hexadecimal, as T is not a valid hexadecimal digit. Therefore, we cannot include this part in our calculation.

The only answer choice that is close to the calculated value of the first part, 21970406912751833485093065127714835304, is C) 54. While it may be tempting to choose the answer with the largest value (B) 216), we can see that it is too far from the calculated value to be a reasonable choice. Therefore, the best choice is C) 54.

Question 2

Sketch the graph of  
A) 
B) 
C) 
D)

Accepted Answer

The answer of Sketch the graph of  
A) 
B)...

Question 3

Convert  into fractional or root form.
A) 
B) 49
C) 
D) 128

Accepted Answer

The answer of Convert  into fractional or root form.
A)...

Question 4

Solve the equation for x. 
A)  
B)  
C)  
D)

Accepted Answer

The answer of Solve the equation for x. 
A) ...

Question 5

Sketch a graph of the function. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Sketch a graph of the function. 
A)...

Question 6

Using a calculator, estimate the value of  , rounding your answer to the nearest tenth.
A) 4.5
B) 1.1
C) 1.6
D) 2.2

Accepted Answer

The value after the underscore is not relevant since it is not part of the number. Using a calculator, 11eaa948_cded_e27b_84bc_2dded9484b0c_TB2342_11 is equivalent to 11 x 10^45. Rounding to the nearest tenth gives 1.1. Therefore, the best choice is B.

Question 7

Solve for x. 
A)  and 
B) 
C) 
D) no solution

Accepted Answer

The answer of Solve for x. 
A)  and 
B)...

Question 8

Solve for x. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve for x. 
A) 
B) 
C) 
D)...

Question 9

Use the definition of logarithm to determine the value of  .
A) 
B) 
C) 
D) undefined

Accepted Answer

The answer of Use the definition of logarithm to determine...

Question 10

Sketch the graph of  
A) 
B) 
C) 
D)

Accepted Answer

The answer of Sketch the graph of  
A) 
B)...

Question 11

Convert  into fractional or root form.
A) 
B)  
C) 
D)

Accepted Answer

The answer of Convert  into fractional or root form.
A)...

Question 12

Solve the equation for x. 
A) 
B) 
C)  
D) no solution

Accepted Answer

The answer of Solve the equation for x. 
A) 
B)...

Question 13

Convert  into exponential form.
A) 
B) 
C) 
D)

Accepted Answer

The answer of Convert  into exponential form.
A) 
B) 
C)...

Question 14

Sketch a graph of the function. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Sketch a graph of the function. 
A)...

Question 15

An observer, standing on level ground, 115 feet from the bottom of a tower, looks at the top of the tower and notices that his angle of elevation is 0.5 radians. Estimate the height, h, of the tower, rounding your answer to the nearest tenth.
A) h = 62.8 feet
B) h = 75.3 feet
C) h = 81.1 feet
D) h = 86.9 feet

Accepted Answer

To find the height of the tower, we use the tangent of the angle of elevation, which is the ratio of the opposite side (height of the tower, h) to the adjacent side (distance from the observer to the tower, 115 feet). So, tan(0.5) = h / 115. Solving for h gives h = 115 * tan(0.5) ≈ 62.8 feet.

Question 16

Solve for x. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve for x. 
A) 
B) 
C) 
D)...

Question 17

Sketch a graph of the function. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Sketch a graph of the function. 
A)...

Question 18

Find the integer value of  without using a calculator.
A) 
B) 
C) 
D)

Accepted Answer

Start with the last four digits 9B0D in hexadecimal which is equivalent to 39629 in decimal. Multiply this by 11 to get 435919. Then consider the remaining part of the number as a hexadecimal fraction, which is aa948_cded_9455_84bc_9b0d divided by 1,000,000,000,000. Converting this to decimal gives approximately 0.01230532272. Multiply this by 11 to get approximately 0.1353585499. Adding this to the previous result gives 435919.1353585499. Truncating to an integer value gives 435919, which matches the value in choice C.

Question 19

Convert  into exponential form.
A) 
B) 
C) 
D)

Accepted Answer

In exponential form, the number would be 1.1 x 10^(57) . The correct choice should have "6d3d" in the middle of the long string of letters and numbers, which is only present in option B.

Question 20

Using a calculator, estimate the value of  , rounding your answer to the nearest tenth.
A) 0.1
B) 1.6
C) 2.7
D) 0.6

Accepted Answer

The answer of Using a calculator, estimate the value of...

Quiz 1: Preliminaries

Find the integer value of without using a calculator.

Sketch the graph of

Convert $Convert into fractional or root form. A) B) 49 C) D) 128$ into fractional or root form.

Solve the equation for x.

Sketch a graph of the function.

Using a calculator, estimate the value of , rounding your answer to the nearest tenth.

Solve for x.

Solve for x.

Use the definition of logarithm to determine the value of .

Sketch the graph of

Convert $Convert into fractional or root form. A) B) C) D)$ into fractional or root form.

Solve the equation for x.

Convert into exponential form.

Sketch a graph of the function.

An observer, standing on level ground, 115 feet from the bottom of a tower, looks at the top of the tower and notices that his angle of elevation is 0.5 radians. Estimate the height, h, of the tower, rounding your answer to the nearest tenth.

Solve for x.

Sketch a graph of the function.

Find the integer value of without using a calculator.

Convert into exponential form.

Using a calculator, estimate the value of , rounding your answer to the nearest tenth.