Given:
Number of girls = 20
Number of boys = 30
The president must be a girl and the vice president a boy
To find:
Number of ways to choose a president, vice president, and secretary.
Solution:
The president must be a girl and the vice president a boy. So, out of three students 1 is girl and 1 is boy. Third student can be a girl or a boy.
Total number of ways = Selecting 2 boys and 1 girl + Selecting 1 boy and 2 girls
[tex]=^{30}C_2\times ^{20}C_1+^{30}C_1\times ^{20}C_2[/tex]
[tex]=\dfrac{30!}{2!(30-2)!}\times \dfrac{20!}{1!(20-1)!}+\dfrac{30!}{1!(30-1)!}\times \dfrac{20!}{2!(20-2)!}[/tex]
[tex]=\dfrac{30\times 29\times 28!}{2\times 1\times 28!}\times \dfrac{20\times 19!}{19!}+\dfrac{30\times 29!}{29!}\times \dfrac{20\times 19\times 18!}{2\times 1\times 18!}[/tex]
[tex]=\dfrac{30\times 29}{2}\times 20+20\times \dfrac{20\times 19}{2}[/tex]
[tex]=8700+3800[/tex]
[tex]=12500[/tex]
Therefore, the required number of ways is 12500.
Write an expression so that when you divide ¼ by a number the quotient will be greater than 1/4.
40/ 1/4
40 x 4 = 160
160 is greater than 1/4
Any number that is greater than 0.25 can be your answer
Hope this helps :)
6. On his fishing trip Justin takes the boat 12 km south. The fish aren't biting so he goes 4 km
west. What distance did he cover? What was his displacement?
Step-by-step explanation:
I trust that the answer is 3 because if he went 12km and bitting fish 4m which 4x3 is 12 so 3 is the answer !
Ben has a collection of Nickels and dimes has a total of $5.35 how maybe nickels and dimes does he need
Answer:
5.35$ worth
Step-by-step explanation:
You are canning 40 cups of applesauce. You have 20 glass jars, each of which will hold 134 cups of applesauce. Choose the correct explanation(s) that explain why you do not have enough jars.
You do not have enough jars because 20 jars will only hold 35 cups of applesauce.
You do not have enough jars because you have enough applesauce left to completely fill 2 more jars, and almost fill a third jar.
You do not have enough jars because you need a total of 40×134=70 jars.
You do not have enough jars because the 20 jars would need to hold 2 cups each, but each holds 14-cup less than that.
Answer:
B
Step-by-step explanation:
took the test
Morgan is going to a carnival that has games and rides. Each game costs $2.50 and each ride costs $4.25. How much would Morgan have to pay if she wanted to play 5 games and go on 2 rides? How much would Morgan have to pay if she wanted to play xx games and go on yy rides?
Answer:
5 games and 2 rides: 21
x games and y rides: 2.50x+4.25y
Step-by-step explanation:
You are shopping for a new computer monitor. It is regularly priced at $200 but it is now on sale for 25% off. After the sale discount is applied, you can also use your 20% off coupon. What is the final price?
a. 110
b. 120
c. 130
d. 140
Answer:
b=120
Step-by-step explanation:
Using proportions, it is found that the final price of the new computer monitor is given by:
b. 120
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
It is regularly priced at $200 but it is now on sale for 25% off, hence 75% of $200 is paid, so:
P1 = 0.75 x 200 = 150.
You can also use your 20% off coupon, hence the final price is of 80% of $150, then:
FP = 0.8 x 150 = $120.
Which means that option B is correct.
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a gym charges a sign-up fee of $40 and then a monthly rate of $20 per month. How long before you spend $300 on this gym membership? which equation would help you solve (let x be the # of months)
Answer:
Where cgym is the cost after m months. To find when the cost is equal, equate the right side of both equations and solve for m :.
Answer:
13 months because 13 x 20 is 260 plus the sign-up fee is 300$ all together
Step-by-step explanation:
11
3
÷ 2
3
i need you to plz help
Answer:
[tex]\frac{99}{2}[/tex]
Step-by-step explanation:
11 × 3 = 33
33÷2 = [tex]\frac{33}{2}[/tex]
[tex]\frac{33}{2}[/tex] × 3 = [tex]\frac{99}{2}[/tex]
There are 36 carpenters in a crew. On a certain day, 18 were present. What percent of the crew was present?
Answer:
On this day, 1/2, or 50%, of the crew was present.
Step-by-step explanation:
Simplify: 18/36 = 1/2
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Find the measure of angle b.
Answer:
23 degrees
Step-by-step explanation:
157+b=180
3. Which accidental is used in measure 15? How does this accidental alter the original note?
Explain the different types of rain
Answer:
Convectional rainfall. - Convectional rainfall occurs when the energy of the sun heats the surface of the Earth, causing water to evaporate to form water vapour. When the land heats up, it warms the air above it. This causes the air to expand and rise. As the air rises, it cools and condenses. ... If this process continues, rainfall will occur.
Orographic or relief rainfall. - Orographic or relief rainfall is caused when masses of air are forced up the side of elevated land formations, such as large mountains, often referred to as an upslope effect. The lift of the air up the side of the mountain results in adiabatic cooling, and ultimately condensation and precipitation.
Cyclonic or frontal rainfall. - Frontal or Cyclonic Rain is caused by cyclonic activity and it occurs along the fronts of the cyclone. It is formed when two masses of air of different temperature, humidity and density meets. For example meeting of moisture laden warm tropical wind with a polar air mass. A layer separating them is called the front.
Step-by-step explanation:
Hope this helps!
What is the range of the function y=e4x?
Oy < 0
Oy>
O y<4
Oy>4
9514 1404 393
Answer:
y > 0
Step-by-step explanation:
The range of the function ...
y = e^(4x)
is the same as the range of any exponential function:
y > 0
The function can take on any positive value, but will never be 0 or negative. It has a horizontal asymptote of y=0.
The range of the given function is y > 0.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Given function is,
y = e⁴ˣ
This is an exponential function.
The range of any exponential function is all the real numbers which are greater than 0.
So here also, the range is all the real numbers which are greater than 0.
So range is y > 0.
Hence the correct option is B.
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A parallelogram is a rectangle if and only
if its diagonals are congruent.
Answer:
A parallelogram is a rectangle if and only if its diagonals are congruent. A rectangle is a parallelogram with four right angles. A rhombus is a parallelogram with four congruent sides. If a parallelogram has two consecutive sides congruent, it is a rhombus.
Step-by-step explanation:
Jon measured the length of the 6th grade hall and found it was 7,000cm. Amy suggested that meters would be more appropriate unit, and recorded the length of the hall as_____m.
Answer:
210
Step-by-step explanation:
I NEEEDDDD HELP PLZZZZZZZZZZZZZZZZZZZZZZZZZ
The shorter diagonal of a rhombus measures 18cm. The side of the rhombus measures 41cm. Find the length of the longer diagonal.
Answer:
80 cm
Step-by-step explanation:
The diagonals divide the rhombus into four congruent triangles. The height of each triangle is 18/2 = 9, and the hypotenuse is 41. Using Pythagorean theorem, the width of each triangle is:
c² = a² + b²
41² = 9² + x²
x = 40
Therefore, the longer diagonal is 2×40 = 80.
find the value of 'x' in the given figure
Answer:
x=10
Step-by-step explanation:
The value of x is 10
rate me and thank me!!!
Answer:
x=4
Step-by-step explanation:
.................
Enter a numerical expression for the word expression.
the quotient of 40 and 8
Answer:
The answer is 40 divide by 8
if you want it solved then the answer is 5
Step-by-step explanation:
when the word quotient is being used in a question like this problem then you know it is going to be talking about division.
Answer: 5
Step-by-step explanation: Quotient means to divide. 40 \ 8 = 5
the domain of the sine function is:
the domain of a sine function is from negative to positive infinity. The domain is written as (-∞,∞) in interval notion. It it the same thing as the domain is all real numbers.
hope this helped <3
Answer:
the domain of the function y=sin(x) ) is all real numbers (sine is defined for any angle measure), the range is −1≤y≤1 .
Step-by-step explanation:
6,726 ÷ 85
with the remainder
Answer:
79.13
Step-by-step explanation:
one school purchased 18 gallons of blue paint to decorate several of its classrooms. if each classroom needs 1 4/5 gallons of paint, then how many classrooms will get painted.
Answer:
18 gallons of paint could paint 10 classrooms.
Step-by-step explanation:
Given that the school bought 18 gallons of paint, and that each classroom requires 1 4/5 of paint to be painted, to determine how many classrooms can be painted with that amount of paint, the following calculation must be performed:
4/5 = 0.8
1 + 0.8 = 1.8
18 / 1.8 = 10
Therefore, 18 gallons of paint could paint 10 classrooms.
Which expression shows the amount of tax on a T-shirt that costs x dollars, if tax is 7%?
A
0.07x
B
0.07
C
7x
D
7
Answer: A or B
Step-by-step explanation:
Rita had $20. Then she saved $5.85 each week for 8 weeks, How much money does she have now? Use the bar diagram to solve the problem. Show your work*
Answer:
$66.80
Step-by-step explanation:
multiply 5.85 by 8 and then add the product to 20 to get the total
After the eight weeks, Rita has $66.8 now.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given, Rita had $20.
Then she saved $5.85 each week for 8 weeks
That means,
she saved the amount,
= amount saved in one week multiplied by 8
She saved the amount
= $5.85 x 8
$5.85 × 8 means $5.85 is added eight times.
Rita saved the amount
= $5.85 x 8
= $46.8
To find the total amount;
$20 + $46.8 = $66.8
And bar diagram is in the attached image.
Therefore, she has $66.8.
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Find the area of a compound shape
Can you please explain
Answer:
Bruh the answer is there so uh yea
Step-by-step explanation:bruh sorry for being a little rude.
1. In a supermarket, each orange costs $3, and each apple costs $2. If you want to spend
exactly $45, write an equation in standard form modeling this situation. Let o represent
the number of oranges you buy, and a represent the number of apples you buy.
Answer:
3o + 2a = $45 ( you can buy 9 oranges and 9 apples)
Step-by-step explanation:
First I divided 45 by 3 and I got 15 so now I know that 15 is the highest amount of oranges I can buy without going over $45. I also know that 15 cannot be an answer because I also have to buy apples.
Then I divided 45 by 2 and 22 was the highest whole number.
Now I would play trial and error BUT i know that the number for oranges have to be less that 15 and the number for apples has to be less than 22.
3 times 9 equals 27 (oranges)
45 - 27 = 18
2 times 9 equals 18 (apples)
3o+2a =$45 is the equation in standard form modeling this situation.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that in a supermarket, each orange costs $3, and each apple costs $2.
Let o represents the number of oranges you buy
and a represent the number of apples you buy.
If you want to spend exactly $45
We have to find the equation to model this situation
3o+2a =$45
Hence, 3o+2a =$45 is the equation in standard form modeling this situation.
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Solve the equation. 10p -5= - 6+2p
Answer:
STEPS : 10p -5= - 6+2pArrange similar algebra given there ... which is 'p' here , Now ;
10p -5= - 6+2p
or, 10p -2p = -6+5
( NOTE : Moving to opposite side , + becomes - and - becomes + )
10p -2p = -6+5
8p = - 1
p = - 1 / 8
Answer:
[tex]\frac{-1}{8}[/tex]
Step-by-step explanation:
You balance the equation by getting rid of the variable on one side and then you get rid of the constant on the other then solve from there
10-5=-6+2p
10p-5-2p=-6+2p-2p
8p-5+5-6+5
8p=-1
[tex]\frac{8p}{8}=\frac{-1}{8}[/tex]
p=[tex]\frac{-1}{8}[/tex]
To solve the equation we put -1/8 in the p spot:
10x-1/8-5=-6+2x-1/8
-1.25-5=-6+-0.25
-6.25=-6.25
The equation = -6.25
Simplify the following: (b^4)^6 (b to the fourth all to the sixth power)
Answer please ;)ANSWER PLEASE!!!!!!!!
Answer:
y intersect is -4 and x intersect is between 6 and 7...
Step-by-step explanation:
Select the correct answer
A company is interested in learning if employees are satisfied with their jobs. To find out the company hires an independent market research
company to conduct a survey. Every survey filled out by an employee is anonymous. Which of the following statements is correct?
A This method of sampling is biased.
B This method of sampling is unbiased.
C This method of sampling is neither biased nor unbiased. D This method of sampling can be considered both biased and unbiased.
The statement (B) is correct because it is anonymous, it does not focus on a specific ethnicity, gender, or other factor.
What is a survey?A survey is a means of gathering information from a sample of people using pertinent questions with the goal of understanding populations as a whole.
We have:
A company is interested in learning if employees are satisfied with their jobs.
Every survey that an employee fills out is completely anonymous.
The statement (B) this method of sampling is unbiased because it is anonymous, it does not focus on a specific ethnicity, gender, or other factor.
Thus, the statement (B) is correct because it is anonymous, it does not focus on a specific ethnicity, gender, or other factor.
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Helllp and show all the work n o troll answer plz and if you don’t feel like doing the work plz don’t answer plz
Answer:
same way here too lol ok so nvm about the points but can i pls just have brainliest