MATHEMATICS
HIGH SCHOOL

Answer: Total price = Original price + (original price * sales tax decimal)

Total price = 10000 + (10000 * 0.075)

= 10000 + 750

Your price on the car is 10,750

Total price = 10000 + (10000 * 0.075)

= 10000 + 750

Your price on the car is 10,750

MIDDLE SCHOOL

What is the solution set of x2 – 10 = 30x?

Steps:

So for this, I will be completing the square to solve for x. Firstly, add 10 and subtract 30x on both sides of the equation:

Next, we want to make the left side of the equation a perfect square. To find the constant of this soon-to-be perfect square, divide the x coefficient by 2 and square the quotient. Once you get that result, add it to both sides of the equation:

Now, factor the left side:

Next, square root both sides:

Now, add 15 to both sides of the equation:

This is the exact solution. To find the approximate solution, solve the left side twice -- once with the plus sign, once with the minus sign:

Answer:In short:

- Exact Solution:
- Approximate Solution (Rounded to the hundredths):

HIGH SCHOOL

You have 52 cards and you choose 2 what is probability of drawing 2 cards of the same suite

In a pack of 52 cards, there are 26 black cards (13 spade and 13 club), and 26 red cards (13 heart and 13 diamond).

Now, the probability of selecting 1st card from 52 cards: 1;

Remaining cards of same colors = 25;

And, Total remaining cards = 51;

So, the probability of selecting 2nd card of same color = (1 x 25) / 51

= 25/51

An Alternate Method:

The probability of getting two red cards is 26/52 x 25/51

= 1/2 x 25/51

= 25/102.

Since the number of black cards is the same as the number of reds, the probability of selecting two black cards is also 25/102.

So, the probability of selecting two cards of the same color (either both red or both black) is 25/102 + 25/102 = 25/51.

By using PnC:

Total ways = 52C2

Selecting both Red cards = 26C2

Selecting both Black cards = 26C2

Thus, Probability = (2 x 26C2)/52C2

= 25/51

∴ The probability of drawing 2 cards of the same suite is 25/51

Regards

#Exotic Explorer

Now, the probability of selecting 1st card from 52 cards: 1;

Remaining cards of same colors = 25;

And, Total remaining cards = 51;

So, the probability of selecting 2nd card of same color = (1 x 25) / 51

= 25/51

An Alternate Method:

The probability of getting two red cards is 26/52 x 25/51

= 1/2 x 25/51

= 25/102.

Since the number of black cards is the same as the number of reds, the probability of selecting two black cards is also 25/102.

So, the probability of selecting two cards of the same color (either both red or both black) is 25/102 + 25/102 = 25/51.

By using PnC:

Total ways = 52C2

Selecting both Red cards = 26C2

Selecting both Black cards = 26C2

Thus, Probability = (2 x 26C2)/52C2

= 25/51

∴ The probability of drawing 2 cards of the same suite is 25/51

Regards

#Exotic Explorer

HIGH SCHOOL

Which of the following equations could be the result of using the comparison method to solve the system shown? x + 2y = 6

x - 4y = 8

2y - 6 = 4y + 8

6 - 2y = -4y + 8

6 - 2y = 4y + 8

Answer:

The result that is obtained on comparing the system of equations in order to get the solution to the system of equations is:

6 -2y =4y + 8

Step-by-step explanation:

We are given a system of equations in term of variable x and y as follows:

x + 2y = 6 --------(1)

x - 4y = 8-------------(2)

- From equation (1) we have the value of x in terms of y as:

x=6-2y

- From equation (2) we have the value of x in terms of y as:

x=8+2y

Hence, on equation the above two values of 'x' we obtain:

6 - 2y = 4y + 8

6-2y=4y+8

since you show x through y

since you show x through y

COLLEGE

television network is about to telecast a new television show. Before a show is launched, the network airs a pilot episode and receives a report assessing favorable or unfavorable viewer response. In the past, 60% of the network's shows have received a favorable response from viewers, and 40% have received an unfavorable response. If 50% of the network’s shows have received a favorable response and have been successful, and 30% of the network’s shows have received an unfavorable response and have been successful, what is the probability that this new show will be successful if it receives a favorable response?

Answer:

The probability that this new show will be successful if it receives a favorable response is 0.833

Step-by-step explanation:

We are going to solve this problem using conditional probability. From the question lets state some of the conditions.

Let X be the event that the TV show is successful, so the probability that the TV show is successful is P(X) = 0.5

Let X' be the event that the TV show is unsuccessful, so the probability that the TV show is unsuccessful is P(X') = 0.5

Let Y be the event that there was a favorable response, so the probability that the show had a favorable response P(Y) = 0.6

Let Y' be the event that there was an unfavorable response, so the probability that the show had an unfavorable response P(Y') = 0.4

If 50% of the network’s shows have received a favorable response and have been successful then,

P(X∩Y) = 0.5

and 30% of the network’s shows have received an unfavorable response and have been successful then,

P(X∩Y') = 0.3

The probability that this new show will be successful if it receives a favorable response will be

P(X/Y) = =

P(X/Y) = 0.833

We have:

P(Favorable) = 0.6 and from this we have P(Successful) = 0.5 and P(unsuccesful) = 0.5

P(Unfavorable) = 0.4 and from this, we have P(Successful) = 0.3 and P(Unsuccesful) = 0.7

P(Successful) = (0.6×0.5) + (0.4×0.3) = 0.3 + 0.12 = 0.42

The question is a conditional probability: what is the probability of a program being successful GIVEN a program is favourable.

P(Successful | Favourable) = P(Successful∩Favourable) / P(Favourable)

P(S | F) = 0.42/0.6 = 0.7

P(Favorable) = 0.6 and from this we have P(Successful) = 0.5 and P(unsuccesful) = 0.5

P(Unfavorable) = 0.4 and from this, we have P(Successful) = 0.3 and P(Unsuccesful) = 0.7

P(Successful) = (0.6×0.5) + (0.4×0.3) = 0.3 + 0.12 = 0.42

The question is a conditional probability: what is the probability of a program being successful GIVEN a program is favourable.

P(Successful | Favourable) = P(Successful∩Favourable) / P(Favourable)

P(S | F) = 0.42/0.6 = 0.7