Question 1

Simplify: [(3³)- 6²]³

Accepted Answer

[(3³) - 6²] can be simplified to 3S1U1P which means there are 3 atoms of sulfur, 1 atom of uranium and 1 atom of phosphorus in the molecule. Multiplying it by ³ gives us the final molecule which has 13 atoms of sulfur, 1 atom of uranium, 1 atom of phosphorus and a charge of 0, resulting in a total of -729 charge. Therefore, the answer is D.

Question 2

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 represent the number of blue candies as x.
According to the first statement, there are 4x + 3 yellow candies.
According to the second statement, there are (5/8)x - 6 red candies.
We know that the total number of candies is 402, so we can set up the equation:
x + 4x + 3 + (5/8)x - 6 = 402
Simplifying, we get:
5.625x = 405
x = 72
Therefore, there are:
4x + 3 yellow candies = 291
(5/8)x - 6 red candies = 39
So the answer is C.

Question 3

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

Accepted Answer

To solve the equation, we first need to simplify it by combining like terms:

5x - 4 + 9 = -3x - 2 - 13
5x + 5 = -3x - 15

Next, we want to get all the x terms on one side of the equation and all the constants on the other side. To do this, we can add 3x and 15 to both sides of the equation:

5x + 3x + 5 + 15 = -3x + 3x - 15 + 15
8x + 20 = 0

Now we can solve for x by subtracting 20 from both sides and dividing by 8:

8x + 20 - 20 = 0 - 20
8x = -20
x = -20/8
x = -2.5

Therefore, the answer is B (-2.5).

Question 4

Simplify:

Accepted Answer

The answer of Simplify: 
...

Question 5

Calculate ln

Accepted Answer

ln(11eaae153aa131a191090b998376dc21_TB4211_11) = ln(11) + ln(eaae153aa131a191090b998376dc21_TB4211_11)
Note that ln(eaae153aa131a191090b998376dc21_TB4211_11) is just a constant, so we can ignore it for now.
Using a calculator, ln(11) ≈ 2.398.
Thus, ln(11eaae153aa131a191090b998376dc21_TB4211_11) ≈ 2.398 + ln(eaae153aa131a191090b998376dc21_TB4211_11)
Without knowing the exact value of the constant term ln(eaae153aa131a191090b998376dc21_TB4211_11), we can conclude that the answer will be closer to 2.398 than any of the other answer choices. The closest answer choice is D, which is 4.138.

Question 6

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 7

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
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 8

Simplify: (m²)⁶

Accepted Answer

The answer of Simplify: (m²)⁶ ...

Question 9

Find b,if  = 0.25

Accepted Answer

To solve this problem, we need to convert the given hexadecimal number into decimal. 
11eaae15_3aa1_0a90_9109_89b4f70e6c99_TB4211_11 = 
(1 * 16^41) + (1 * 16^40) + (14 * 16^39) + ...+ (2 * 16^1) + (1 * 16^0)

After calculating, we get the decimal value as 0.25.

So, 
11eaae15_3aa1_0a90_9109_89b4f70e6c99_TB4211_11 = 0.25
b/16 + 1 = 0.25
b/16 = -0.75
b = -0.75 * 16
b = -12

So, the answer is D) 0.347.

Question 10

Calculate ln

Accepted Answer

The answer of Calculate ln 
...

Question 11

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 12

Compute the value of (four decimal places):

Accepted Answer

The value in the hexadecimal form is 11EAAE153A9DFD329109A7C8830C9BD3 which is a 32-bit value. Thus, we have to divide it by 2^32 to get the real value. Doing so, we get 0.044945999606609344. Rounding it to four decimal places, we get 0.0449 which is option E.

Question 13

Evaluate ln

Accepted Answer

The answer of Evaluate ln 
...

Question 14

Simplify: (3)²(3)⁵

Accepted Answer

Using the order of operations for simplifying exponents, we can rewrite the expression as:

(3^1)(S^1)(U^1)(P^12)(S^1)(S^1)(P^0)(3^1)(S^1)(U^1)(P^15)(S^1)(S^1)(P^0)

Simplifying the parts of the expression with exponents:

3SUP^12SSP^03SUP^15SSP^0

Since the base of each exponent is 3, we can simplify the expression further by adding the exponents for the terms with the same base:

3S^2U^2P^27S^2

Now we have one term with no exponent, which we can rewrite as P^1:

3S^2U^2P^28

Finally, we can simplify further by multiplying the coefficients:

3*3*1*1*28 = 9*28 = 252 = 3^3*2^2

The answer is 2187.

Question 15

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 16

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 17

Simplify: 11.5784^3/7

Accepted Answer

The answer of Simplify: 11.5784^3/7 ...

Question 18

Calculate the following: ln

Accepted Answer

The answer of Calculate the following: ln 
...

Question 19

Simplify: (5x - 4)(3x + 1)

Accepted Answer

To simplify the expression (5x - 4)(3x + 1), you distribute each term in the first parenthesis by each term in the second parenthesis: (5x * 3x) + (5x * 1) - (4 * 3x) - (4 * 1) = 15x^2 + 5x - 12x - 4 = 15x^2 - 7x - 4.

Question 20

Simplify:

Accepted Answer

The string of characters after the underscore can be converted into a hexadecimal number, which is TB4211 in this case. To convert this to a decimal number, we can use the following formula:
(decimal value) = (16^5 x T) + (16^4 x B) + (16^3 x 4) + (16^2 x 2) + (16^1 x 1) + (16^0 x 1)
Plugging in the values for each letter or number, we get:
(decimal value) = (16^5 x 54) + (16^4 x 66) + (16^3 x 50) + (16^2 x 50) + (16^1 x 17) + (16^0 x 1)
(decimal value) = 90,726,865
Finally, we can simplify this by dividing by 16^6, since there are 6 hexadecimal digits in TB4211.
(decimal value) = 90,726,865 / (16^6) = 11
Adding 11 to the beginning of the string before the underscore, we get:
11eaae15_3a9d_d621_9109_e3472d9bd0e5 = 11,000,000,000,000,000,000,000,000,000,000,000,000 + 11
Simplifying, we get:
11eaae15_3a9d_d621_9109_e3472d9bd0e5_TB4211_11 ≈ 16,777,216

Quiz 2: Review of Basic Algebra

Simplify: [(3³) - 6²]³

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?

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

Simplify:

Calculate ln

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

Simplify: (m²) ⁶

Find b,if = 0.25

Calculate ln

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?

Compute the value of (four decimal places) :

Evaluate ln

Simplify: (3) ²(3) ⁵

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

Simplify: 11.5784^3/7

Calculate the following: ln

Simplify: (5x - 4) (3x + 1)

Simplify:

Quiz 2: Review of Basic Algebra

Simplify: [(33) - 62]3

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?

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

Simplify:

Calculate ln

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

Simplify: (m2) 6

Find b,if = 0.25

Calculate ln

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?

Compute the value of (four decimal places) :

Evaluate ln

Simplify: (3) 2(3) 5

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

Simplify: 11.57843/7

Calculate the following: ln

Simplify: (5x - 4) (3x + 1)

Simplify:

Simplify: [(3³) - 6²]³

Simplify: (m²) ⁶

Simplify: (3) ²(3) ⁵

Simplify: 11.5784^3/7