Question 1

Following equation is used in carbon dating of the artefacts:  What is the expected decay rate of the artefact, if it is known to be from Canadian New France era, 350 years ago.

Accepted Answer

The answer of Following equation is used in carbon dating...

Question 2

Calculate the following: ln

Accepted Answer

The given number is not a valid base 10 number, it is in hexadecimal form. Therefore, we cannot directly take the natural logarithm of this number.

Question 3

Find b, if  = 0.25

Accepted Answer

The answer of Find b, if  = 0.25
...

Question 4

You have three colors of candies a jar - yellow, red and blue. There are 4 times plus 3 as many yellow candies as there are blue candies. There is 5/8 as many minus 6 red candies as there are blue. There are a total of 402 candies in the jar. How many of yellow, blue and red candies are there?

Accepted Answer

Let's start with the equations:
y = 4b + 3
r = (5/8)b - 6
y + b + r = 402
We can substitute the first two equations into the third one to get:
(4b + 3) + b + ((5/8)b - 6) = 402
Simplifying this, we get:
9.125b = 415
b ≈ 45.6
Now we can use this to find the values of y and r:
y ≈ 291
r ≈ 39
Therefore, the answer is C.

Question 5

Simplify: (3)²(3)⁵

Accepted Answer

Using the "PEMDAS" order of operations: - First, simplify the parts inside the parentheses: (3)² = 3(1+1-12+1+1+0) = 3(-8) = -24 and (3)⁵ = 3(1+1-15+1+1+0) = 3(-11) = -33 - Then, simplify the multiplication: (-24)(-33) = 792 - Therefore, the answer is 792 written in base 3, which is 2187 in base 10.

Question 6

Calculate ln

Accepted Answer

ln 11eb129f_8ff8_f699_935a_153528c0453f_TB4212_11 is the natural logarithm of a very large number. Therefore, the answer should be a large positive number. Option D (4.138) is the only choice that fits this criteria.

Question 7

Simplify: [(3³)- 6²]³

Accepted Answer

First simplify the numbers within the parenthesis:

- (3S1U1P13S1S1P0) = 313110 
- (6S1U1P12S1S1P0) = 612110

Subtracting these two numbers gives us:

313110  
- 612110 
---------
 -299000

Plugging this result back into the original expression:

-299000S1U1P13S1S1P0

Multiplying -299000 by the value outside the parenthesis:

-299000 x 13S1S1P0 = -299000 x 13 = -3887000

So the final simplified expression is:

-3887000S1S1P0

Which equals -729. Therefore, the answer is D (-729).

Question 8

Calculate ln

Accepted Answer

The answer of Calculate ln 
...

Question 9

Simplify: (m²)⁶

Accepted Answer

(m²)⁶ = m^{2 * 6} = m¹²

Question 10

In the following equation:  = PMT  calculate n, if  = 75,000; PMT = 3500; i = 0.028

Accepted Answer

The answer of In the following equation:  = PMT...

Question 11

Compute the value of (four decimal places):

Accepted Answer

The given value is a hexadecimal number. The first 16 digits (11eb129f_8ff8_815d_935a_7fa8) represent the mantissa and the last 4 digits (5fd8_0460) represent the exponent in hexadecimal notation. 
To convert the mantissa to decimal, we first convert each group of 4 hexadecimal digits to its decimal equivalent:

11eb = 4595
129f = 4751
8ff8 = 36856
815d = 33181
935a = 37786
7fa8 = 32616

So the mantissa is 0.459547513685633177863265 depending from where we round the decimal point.

The exponent in hexadecimal is 0460 which is equivalent to 1120 in decimal. To get the final value, we need to multiply the mantissa by 2^1120.

0.4595... * 2^1120 = 0.0449...

Rounding to four decimal places, we get the final answer as 0.0449, which is closest to option E) 0.044946.

Question 12

Evaluate ln

Accepted Answer

The answer of Evaluate ln 
...

Question 13

Solve the following equation: 5x - 4 + 9 = -3x - 2 - 13

Accepted Answer

5x - 4 + 9 = -3x - 2 - 13
Combining like terms: 
5x + 5 = -3x - 15
Adding 3x and 15 to both sides: 
8x + 20 = 0
Subtracting 20 from both sides: 
8x = -20
Dividing by 8: 
x = -2.5

Question 14

Following equation is used in carbon dating of the artefacts:
N =  ×  where,
N = Decay rate of the artefact, expressed as disintegrations per minute (dpm)  = Decay rate of natural carbon = 14 dpm
τ = Mean life time =  =  = 8267 years
t = Age of the artefact
Calculate the age of the artefact, if the decay rate of the artefact is measured as 4 dpm

Accepted Answer

The answer of Following equation is used in carbon dating...

Question 15

Simplify:

Accepted Answer

The string of characters consists of a combination of alphanumeric characters and underscores. The best way to simplify this is to replace each unique set of characters with a letter, and replace each underscore with the letter 'S' (to signify a space). 11eb129f_8ff8_5a4b_935a_cd0a7eb5623a_TB4212_00 can be simplified as 5a⁴b⁴c⁵ Option A, D, and E have incorrect letters and numbers, while option C has fewer numbers and letters than the original string. Option B has the correct number of letters and numbers and is the best choice for simplifying the given string.

Question 16

You have a lotto ticket with three numbers between zero and 49. The total of the three numbers is 93. One number is twice as large plus two as the lowest number. The second number is  the size of the smaller number. What are the values of each of the numbers?

Accepted Answer

The answer of You have a lotto ticket with three...

Question 17

Solve the following and check your solutions: 12x + 5(9 - x)= 429

Accepted Answer

First, distribute the 5 in the equation: 12x + 45 - 5x = 429. Combine like terms: 7x + 45 = 429. Subtract 45 from both sides: 7x = 384. Divide both sides by 7: x = 54.86.

Question 18

Simplify:

Accepted Answer

The string of letters and numbers provided is a hexadecimal number, which can be converted to decimal form. Simplifying it, we get 16777216.

Question 19

Simplify:

Accepted Answer

The given string of characters and numbers cannot be simplified or converted into a meaningful numerical value. Therefore, the only possible answer is E, which represents the value of 1.

Question 20

Simplify: 11.5784^3/7

Accepted Answer

To simplify this expression, we need to perform the operations in order of the acronym PEMDAS: parentheses, exponents, multiplication, division, addition, and subtraction. 
Firstly, simplify the numerator: 11.5784S1U1P13 = (11.5784)(S1)(U1)(P13). 
Now, we can cancel out one S1 from numerator and denominator, as well as the P0 from denominator: 
(11.5784)(U1)(P13) / (7)(S1)(S1)(P0) 
= (11.5784)(U1)(P13) / (7)(S1)(P0) 
= (11.5784)(U1)(13) / (7)(1)(1) 
= (11.5784)(13) / (7) 
= 150.3192 / 7 
= 21.45988.

The closest answer choice to this value is C) 2.857.

Quiz 2: Review of Basic Algebra

Following equation is used in carbon dating of the artefacts: What is the expected decay rate of the artefact, if it is known to be from Canadian New France era, 350 years ago.

Calculate the following: ln

Find b, if = 0.25

You have three colors of candies a jar - yellow, red and blue. There are 4 times plus 3 as many yellow candies as there are blue candies. There is 5/8 as many minus 6 red candies as there are blue. There are a total of 402 candies in the jar. How many of yellow, blue and red candies are there?

Simplify: (3) ²(3) ⁵

Calculate ln

Simplify: [(3³) - 6²]³

Calculate ln

Simplify: (m²) ⁶

In the following equation: = PMT calculate n, if = 75,000; PMT = 3500; i = 0.028

Compute the value of (four decimal places) :

Evaluate ln

Solve the following equation: 5x - 4 + 9 = -3x - 2 - 13

Simplify:

You have a lotto ticket with three numbers between zero and 49. The total of the three numbers is 93. One number is twice as large plus two as the lowest number. The second number is the size of the smaller number. What are the values of each of the numbers?

Solve the following and check your solutions: 12x + 5(9 - x) = 429

Simplify:

Simplify:

Simplify: 11.5784^3/7

Quiz 2: Review of Basic Algebra

Following equation is used in carbon dating of the artefacts: What is the expected decay rate of the artefact, if it is known to be from Canadian New France era, 350 years ago.

Calculate the following: ln

Find b, if = 0.25

You have three colors of candies a jar - yellow, red and blue. There are 4 times plus 3 as many yellow candies as there are blue candies. There is 5/8 as many minus 6 red candies as there are blue. There are a total of 402 candies in the jar. How many of yellow, blue and red candies are there?

Simplify: (3) 2(3) 5

Calculate ln

Simplify: [(33) - 62]3

Calculate ln

Simplify: (m2) 6

In the following equation: = PMT calculate n, if = 75,000; PMT = 3500; i = 0.028

Compute the value of (four decimal places) :

Evaluate ln

Solve the following equation: 5x - 4 + 9 = -3x - 2 - 13

Simplify:

You have a lotto ticket with three numbers between zero and 49. The total of the three numbers is 93. One number is twice as large plus two as the lowest number. The second number is the size of the smaller number. What are the values of each of the numbers?

Solve the following and check your solutions: 12x + 5(9 - x) = 429

Simplify:

Simplify:

Simplify: 11.57843/7

Simplify: (3) ²(3) ⁵

Simplify: [(3³) - 6²]³

Simplify: (m²) ⁶

Simplify: 11.5784^3/7