Problems Involving Fundamental Counting Principle


1. Patrick wants to buy a computer system. In a computer shop, a customer can choose one of the 4 monitors, one of the 2 keyboards, one of the 4 CPU, and one of 3 printers. Determine the number of possible systems that Patrick can choose from.


2. An ice cream parlor is offering different flavors of ice cream with two kinds of containers available, cone and paper cup. The flavors of their ice cream include cheese, vanilla, mango, and chocolate. What is the total number of possible combinations if a customer can choose a container and 3 flavors of ice cream?


3. Emma has 5 blouses, 3 skirts, and 4 pairs of shoes. In how many different ways consisting of a blouse, a skirt, and a pair of shoes can Emma dress up?


4. Tess, Rina, Rose, Ronnie, Bryan, and Gab are all members of the Student Council. In how many ways can you form a committee of three students?



Problems Involving Probability of Simple Events


5. A letter is to be chosen from the letters of the word EXTRAVAGANT. What is the probability that it is a consonant?


6. An auditor of a club is to be selected from 8 Grade 7, 9 Grade 8, 12 Grade 9, and 5 Grade 10 students. What is the probability that he/she is not a Grade 8 student?


7. A spinner is divided into parts and whose colors are similar to a color wheel. What is the probability that the pointer lands on a secondary color?


8. Slips of paper are numbered 4, 5, 6, …, 34, folded into similar squares and placed in a bowl. If a paper is to be picked at random, what is the probability that the number is a prime number?

Answer:

37 and 43

Step-by-step explanation:

There are some ways to do this, but this is what I like to do. First, since there are 2 people, I divide 80 by 2, which is 40. Now I add 3 to one person and subtract 3 from one person, because the age difference is 6 years, and there are two people (if you divide them you get 3). Now you get the answer; 37 and 43.

Answer:

→ Compare the 2 grade A's

School B's is higher

→ Compare the 2 grade B's

School B's is higher

→ Now formulate a brief response

School B has more entrants in the exam and therefore has a higher proportion of students achieving top grades

Answer:

838 inches²

Step-by-step explanation:

Finding the area of the countertop including the hole

⇒ Area of countertop including hole: LB

⇒ Area of countertop including hole: (24)(48)

⇒ Area of countertop including hole: 1152 inches²

Finding the area of the hole (sink)

⇒ Area of hole: πr²

⇒ Area of hole: (π)(D/2)²

⇒ Area of hole: (π)(20/2)²

⇒ Area of hole: (π)(10)²

⇒ Area of hole: (π) x 100

⇒ Area of hole: 3.14 x 100 = 314 inches²

Finding the area excluding the hole

1152 - 314 = Area of countertop (excluding the hole)

838 inches² = Area of countertop (excluding the hole)

Answer:

Step-by-step explanation:

The perimeter of an equilateral triangle is:

P = 3a (where a any length of the triangle)

The area of an equilateral triangle is:

[tex]A = \frac{\sqrt{3} }{4} a^{2}[/tex] (where a is the side length)

Using the area formula we can rearrange it to get the formula of the length of the equilateral triangle:

[tex]a = \frac{2}{3} 3^{\frac{3}{4} } \sqrt{A}[/tex]

Then three important formulas are

[tex]\\ \rm\Rrightarrow Perimeter=3s[/tex](As sides are equal)

[tex]\\ \rm\Rrightarrow Area=\dfrac{\sqrt{3}}{4}s^2[/tex]

[tex]\\ \rm\Rrightarrow Height=\dfrac{\sqrt{3}s}{2}[/tex]

Answer:

C. 16(0.5x - 0.75y + 2) = 8x - 12y + 32

Step-by-step explanation:

Answer:

Yeah I got the answer

Step-by-step explanation:

C option is correct

We will have to take common like this

. 16(0.5x - 0.75y + 2) = 8x - 12y + 32

PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASE

if dimensions were 5 and 12, that means ratio was 5:12. if we increase wach dimension by the same amount, the ratio is the same.

so:

5x×12x=120

60x²=120

x²=120÷60

x²=2

x=√2

that means each dimension was increased by √2

so dimensions are: 5√2 and 12√2

Answer:

17 because 2 is taken from 18 and 18-2=16 but 17 and 17 is close to 16

Answer:

refer to this image here:

hope this helps :)

We will use graphical way to solve it

Graph it

Solution is

You should keep 0.97 seconds of distance between you and the vehicle ahead.

The formula for calculating distance is expressed as:

distance  = speed * time

Time = Distance/Speed

Given the following parameters

Distance = 50 feet

Speed = 35mph = 51.3ft/s

Time taken = 50/51.3
Time taken = 0.97

Hence you should keep 0.97 seconds of distance between you and the vehicle ahead.

Learn more on distance and speed here: https://brainly.com/question/11495758

Answer:

200

Step-by-step explanation:

156.7

since the number before the hundred is more than 4

it becomes 200

Answer: 12

Step-by-step explanation:

     A straight line has a measurement of 180° so these two angles added together will equal 180°.

     (10x - 20)° + (6x + 8)° = 180°

     10x° + 6x° + 8° - 20° = 180°

     16x° -12° = 180°

     16x° = 192°

     x = 12

Supplementary angles

Answer: C

Step-by-step explanation:

This is a Pythagorean triple.

Answer:

5

x

2

+

20

x

−

60

Factor

5

out of

5

x

2

+

20

x

−

60

.

Tap for more steps...

5

(

x

2

+

4

x

−

12

)

Factor.

Tap for more steps...

5

(

x

−

2

)

(

x

+

6

)

Step-by-step explanation:

ANSWER IS =5X2+20X-60

------------------------------

THIS ANSWER IS CORRECT

To calculate the area of a parallelogram

 ⇒ we must know the formula

     ⇒ Area = base * height

What are we given:

Thus:

   Area = 3ft * 4ft = 12 [tex]ft^2[/tex]

Hope that helps!

Answer:

70 fl oz

Step-by-step explanation:

Find how much is added to the punch bowl.

2 containers and each holds 6 fluid ounces.

2 x 6 = 12

Now find the total amount of liquid by adding the original amount and the amount added.

58 + 12 = 70

Answer:

Slope of the line that is parallel: 2

Slope of the line that is perpendicular: [tex]-\frac{1}{2}[/tex]

Step-by-step explanation:

For the parallel line:

Rewrite your equation to slope-intercept form: y = mx + b

y = mx + b

2x - y = 1 <== subtract 2x to both sides

-2x     -2x

-y = -2x + 1 <== divide both sides by -1

/-1      /-1

y = 2x - 1

The slope of the line that is parallel to this line is 2.

For the perpendicular line:

*Perpendicular lines have negative reciprocals*

Steps:

1. Take your original slope (2)

2. Flip it (1/2)

3. Change the sign (-1/2)

For a slope of 2, the reciprocal would be: [tex]-\frac{1}{2}[/tex]

Hope this helps!

Note that.

Slopes of parallel line are equal

Slopes of perpendicular lines are negative reciprocals

So

Compare to slope intercept form

Slope of the parallel line=2

Slope of the perpendicular line=-1/2

Answer:

2

Step-by-step explanation:

Following the substitution rules:

O becomes P and

E becomes F

because they are vowels(a,e,i,o,u) change to next letter.

C becomes A

L becomes J

G becomes E

because constants change to the letter two before the given letter.

So COLLEGE becomes APJJFEF

so it now has 2 vowels.

Translating the figure involves chaging the position of the figure

The coordinates of the new figure are (0, 7), (1 , 6), and (2, 0)

The coordinates are given as:

(−3, 2), (−4, 1), and (−1, −5)

The rule of translation 3 units right and 5 units up is:

(x + 3, y + 5)

So, we have:

(−3 + 3, 2 + 5), (−4 + 5 , 1 + 5), and (−1 + 3, −5 + 5)

Evaluate the sum

(0, 7), (1 , 6), and (2, 0)

Hence, the coordinates of the new figure are (0, 7), (1 , 6), and (2, 0)

Read more about translation at:

https://brainly.com/question/11468584

The bond's time to maturity for the Ford bond based on the present date and the maturity date is 77 years 6 months.

The time to maturity for a bond is the length of time that a bondholder would receive interest payments on the bonds held. It is the difference between the present date and the matuity date of the bond.

Time to maturity = May 15 2097 - November 16, 2020 = 77 years 6 months

To learn more about bonds, please check: https://brainly.com/question/13326746

Considering a six-sided spinner, it is found that the probability of spinning a 1 and tossing a head is of [tex]\frac{1}{12}[/tex].

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem:

Since the events are independent, the probability of spinning a 1 and tossing a head is given by:

[tex]p = \frac{1}{6} \times \frac{1}{2} = \frac{1}{12}[/tex].

More can be learned about probabilities at https://brainly.com/question/14398287

Answer:

12 years old

Step-by-step explanation:

3x+5=41

3 times a number and 5 more

'more' usually means adding

41-5 =36

36/3 =12

Answer:

Equation: 41 = 3x + 5

x = 12

Step-by-step explanation:

Hello!

Betty is 5 more than 3 times Jadyn's age. Since Jadyn's age is unknown, we'll call that unknown variable x.

Betty is 5 more than 3 times x. Betty is also 41 years old.

Equation: 41 = 3x + 5

Now we have to solve for x

Solve for x:

Jadyn is 12 years old.

Answer: y = x + 5

Step-by-step explanation:

Step-by-step explanation:

Slope= 7-7/-3-4

0/-7

0

y-7 = 0(x-4)

y-7= 0

Answer: 75$

Step-by-step explanation:

1/4 is equal to 25/100.

meaning that 1/4 is 25 out of 100.

Based on that, if we subtract 25 from 100 we get 75.

Answer:

answer 436 tubig is water halimaw is monster ang Ganda mo Sana kaso ang height mo pang kinder

Step-by-step explanation:

answer is 436 I hope it helps

Answer:

i think that the correct answer would be A or C

Step-by-step explanation:

hope this helps

sorry if the answers that i gave you is incorrect

Answer:

2nd option

Step-by-step explanation:

the nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = 64 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{32}{64}[/tex] = [tex]\frac{1}{2}[/tex] , then

[tex]a_{n}[/tex] = 64 [tex](\frac{1}{2}) ^{n-1}[/tex]

Using the percentage concept, it is found that 40% of Alberto’s income is used to pay for his rent and groceries.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

[tex]P = \frac{a}{b} \times 100\%[/tex]

In this problem:

Then, the percentage is given by:

[tex]P = \frac{1280}{3200} \times 100\% = 40\%[/tex]

More can be learned about the percentage concept at https://brainly.com/question/10491646

Answer:

x = 25

Step-by-step explanation:

The 45-45-90 triangle is a special isoceles right triangle. If you look at the help image attached, you will see that it has the following rules:

Find x

c = x√2

25√2 = x√2

25√2 ÷ √2 = x

x = 25

I hope this helps!