Answer:
2 boys and 3 girls were selected for the finals.
There are 3 prizes, A, B, and C (assigned in order, I suppose) assigned randomly to the five contestants.
We want to find the probability that a boy wins the prize B.
So here we have two cases:
A girl wins the first prize, A, and a boy the prize B.
The probability that a girl wins the prize A is equal to the quotient between the number of girls and the total number of contestants, this is:
p = 3/5
Next, the probability that a boy wins the prize B, is equal to the quotient between the number of boys and the total number of contestants (that now is 4, because a girl already won prize A).
q = 2/4
The joint probability is:
P = p*q = (3/5)*(2/4) = 6/20 = 3/10
Now we have the other case, where a boy wins the prize A and the other boy wins prize B.
The probability that a boy wins prize A is equal to the quotient between the number of boys and the total number of contestants, this is:
p = 2/5
The probability that the other boy wins prize B is equal to the quotient between the remaining number of boys (1) and the total number of contestants (now 4), this is:
q = 1/4
The joint probability is:
P' = p*q = (2/5)*(1/4) = 2/20 = 1/10
The total probability is the sum of the probabilities for the two cases, this is:
Probability = 1/10 + 3/10 = 4/10
(note that because the prize C is assigned after prize B, its existence does not affect the probability for the previous event, as expected)
The function f(x)=300x/x^2+200 represents the monthly sales in hundreds of cds x months after the cd was released. Each statement interpretes a key feature of the function based on the table. Which statement is an interpretation of the end behavior
The area of the base of a cylinder is 42 square inches and its height is 11 inches. A cone has the same area
for its base and the same height. What is the volume of the cone?
Find the value of LM and LN if M is between L and N.
LM = 7x + 4, MN = 20, LN = 10x
Answer:
LM = 20
LN = 160/7
Step-by-step explanation:
If M is between L and N, then LM = MN
Given
LM = 7x + 4, MN = 20, LN = 10x
7x+4 = 20
7x = 20 - 4
7x = 16
x = 16/7
LM = 16/7(7) + 4
LM = 16 + 4
LM = 20
LN = 10x
LN = 10(16/7)
LN = 160/7
What is the solution of sqareroot 1-3x = X+3?
Answer:
x=-8 or x=-1 (first option)
Step-by-step explanation:
[tex]\sqrt{1-3x}=x+3\\1-3x=(x+3)^{2} \\[/tex]
now expand the bracket on the right
[tex]1-3x=x^{2} +6x+9\\simplify:\\1-9=x^2+6x+3x\\-8=x^2+9x\\[/tex]
now make it a quadratic equation:
[tex]x^2+9x+8=0\\factorise:\\(x+1)(x+8)\\so:\\x+1=0 \\x=-1\\\\and \\x+8=0\\x=-8[/tex]
using the image,find angle x and y
Answer:
x =55 degrees
y = 35 degrees
Step-by-step explanation:
We know that the distance from the center of the circle to the circumference is the radius
that means the triangle starting out from O is isosceles since two of the sides are radii and thus the angle of those sides are the same
Let us call one of the angles z
we know that the sum of the angles in a triangle is 180 degrees
That simply means;
80 + 2z = 180
2z = 180-80
2z = 100
z = 100/2
z = 50 degrees
So the angles at each upper end of the cyclic quadrilateral are;
x + 50 and y + 50
we know that the angles that face each other in a cyclic quadrilateral are supplementary
Thus;
95 + y+ 50 = 180
y= 180-95-50
y= 180-145
y = 35 degrees
Now, for x, the angle supplementary to the angle that faces x+ 50 equals x + 50
Thus;
x + 50 = 105
x= 105-50
x = 55 degrees
Please help!!! Answer ASAP and show work!!!
Answer:
B and C. can you select more than one?
can someone help me plz
Answer:
it would probably be around 1.8 or either 1.7
HELP ME NOW OR NO DINO NUUGETS
Answer:
what do you want me to help you with cuz there's nothing attached??
Step-by-step explanation:
Solve a / a-1 - a+5/a =0. Enter your solution as an improper fraction or as a decimal rounded to the nearest hundredth
Answer: [tex]1\dfrac{1}{4}[/tex]
Step-by-step explanation:
Given
The equation in terms of a is
[tex]\Rightarrow \dfrac{a}{a-1}-\dfrac{a+5}{a}=0\\\\\Rightarrow \dfrac{a}{a-1}=\dfrac{a+5}{a}\\\\\Rightarrow a^2=(a-1)(a+5)\\\\\Rightarrow a^2=a^2+4a-5\\\\ \Rightarrow 4a=5\\\\\Rightarrow a=\dfrac{5}{4}\ \text{or}\ 1\dfrac{1}{4}[/tex]
Brette got a new phone! The length of her old rectangular phone screen was 44 centimeters. Her new rectangular phone screen is twice as long as the old screen. How much larger is the area of the new screen than the area of the old screen?
Answer:
2 times larger
Step-by-step explanation:
Area of a rectangle = length x width
assume width = 10
older area = 44 x 10 = 440
new area
length = 44 x 2 = 88
88 x 10 = 880
change in area = 880 / 440 = 2
If you complete 5 worksheets every day, how long will it take you to complete 101 worksheets?
Answer:
21 days
Step-by-step explanation:
101/5=20.2
thus u need 21 days to finish 101 worksheets
PLEASE HELPPP MEEEEEEE
Answer:
A= -42
B= 3
Step-by-step explanation:
Which of the following is equivalent to 5sqrt 13^3
Answer: D) 13^(3/5)
Step-by-step explanation: This is assuming that the question is asking the √13^3. With the five as the y root.
No files just type in please and thank you
Tables--> 2
Each table--> (4*2) 8 boxes
Each box--> (8*6) 48 crayons
On each table--> 48/2
= 24 crayons on each table.
mark me brainliestttt :)))
a person normally cost 1195 is on sale for 15% off if you only have a $10 bill do you have enough to purchase the book
Answer:
no
Step-by-step explanation:
First determine the discount
11.95 * 15%
11.95 *.15
1.79
Subtract the discount
11.95-1.79
10.16
You do not have enough money with a 10 dollar bill
PLEASE HELP ASAP PLLSSS!!!!
Patrick wants to buy a new computer. He already has $275 saved and plans to save $125 each month. The price of the computer is currently $1,850, but Patrick expects the price to drop by $100 each month. Patrick wants to determine the number of months he will need to save.
a) If x represents the number of months, then write an equation to represent A, the total amount Patrick saves.
b)If x represents the number of months, then write an equation to represent C, the cost of the computer.
c)Use your equations from part “a” and part “b” to determine how many months he will need to save before he can buy the computer. Show your work or explain how you got your answer.
Answer:
7 monthsStep-by-step explanation:
a)
A(x) = 275 + 125xb)
C(x) = 1850 - 100xc)
275 + 125x = 1850 - 100x125x + 100x = 1850 - 275225x = 1575x = 1575 / 225x = 7The answer is 7 months
What is the area of a rectangle with a length of x + 5
and a width of 4?
Answer:
[tex]area = (length \times width) \\ = (x + 5) \times 4 \\ = (4x + 20) \: square \: units[/tex]
4 oranges at Juicy Deals grocery store cost $6. For the price of $15 you can buy 10 oranges. True or false: The relationship
between the number of oranges and their price is proportional.
Answer:
the answer is true.
4/6
10/15
please help!! i’ll give you brainliest
Answer:
4
Step-by-step explanation:
Answer:
m = 5
Step-by-step explanation:
to one side length of 4 to 2, we divided by 2 so why not divide 10 by 2
10 ÷ 2 = 5
Please give me brainliest!
Which expression is equivalent to the given expression? -2x +8x -9 +4x +7x2 +2 A. B. C. D.
Answer:
The answer is "[tex]7x^2 +10x -7[/tex]"
Step-by-step explanation:
Let the given value is:
[tex]\to \bold{-2x +8x -9 +4x +7x^2 +2}\\\\[/tex]
Solving the given value:
[tex]\to7x^2 -2x +8x +4x-9 +2\\\\\to7x^2 +10x -7\\\\\to7x^2 +10x -7\\\\[/tex]
In a square PQRS, PQ = 2x +3 cm and QR = 3x – 5 cm, then the value of x is
Answer:
x = 8 cm
Step-by-step explanation:
Given that,
In a square PQRS, PQ = 2x +3 cm and QR = 3x – 5 cm.
We need to find the value of x.
In a square, all the sides are equal. So,
PQ = QR
2x +3 = 3x – 5
3+5 = 3x - 2x
x = 8
So, the value of x is equal to 8 cm.
Solve 7x+6<3(x - 2).
Answer:
x<−3
Step-by-step explanation:
hope this works
I can't figure out the answer
Answer:
39
Step-by-step explanation:
y=arctan(0.8)=38.65=39
Write the quadratic equation in standard form:
-7x+4=x^2
Answer:
x² + 7x - 4 = 0
Step-by-step explanation:
A quadratic equation in standard form is
ax² + bx + c = 0 ( a ≠ 0 )
Given
- 7x + 4 = x² ( subtract - 7x + 4 from both sides )
0 = x² + 7x - 4 , that is
x² + 7x - 4 = 0 ← in standard form
A= pi2 and find the area of a circle with radius 5 cm. Use pi = 3.14
Answer:
78.5398163397
Step-by-step explanation:
5x5= 25xpi=78.5398163397
y = 4 x − 1
y = − x + 4
Answer:
x=1 , y=3
Step-by-step explanation:
y = 4 x − 1
4(y = − x + 4)
y = 4 x − 1
4y= - 4 x +16
5y= 15
y=3
3=4x-1
+1 +1
4=4x
/4 /4
x=1
A boat travel 45 miles in three hours at this rate how many miles with a boat travel in half an hour
Answer:
7 1/2 miles per half hour
Step-by-step explanation:
First let's find how many miles you travel per hour. To find that, you divide 45 by 3. This gives you 15 miles per hour. Now we need to find how many miles in half an hour. To do this we are going to convert into minutes. We need to find out how many miles per minute. There are 60 minutes in 1 hour, so we will divide 15 by 60. That gives 0.25, or 1/4 mile per minute. So now that we know how many miles per minute, we can find out how many for half an hour. Half an hour is 30 minutes, so we are going to multiply 1/4 by 30. You will get 15/2. We need to make that a mixed number, and that gives us 7 1/2 miles per 30 minutes, or 7 1/2 miles per half hour.
I hope this helped :)
(edit: I just realized I did this the hard way. Sorry. The easier way would be to just divide 15 by 2 since it would take two halves of 15 to make the amount of miles per hour.)
Mark started walking to school at half past 9. christy arrived at school 15 minutes later .What time did she get to school
Answer:
Mark arrived at school at 9:45 A.M. or either 9:45 P.M.
Answer:
Christy got to school at 9:45am
Step-by-step explanation:
The rules of a game allow a team to score either 2 points or 5 points, depending on the nature of the scoring play. If the final score between two teams was 34 to 29, and there were 18 scoring plays altogether, how many 5-point plays were there?
Answer:
9
Step-by-step explanation:
Given that :
Total Number of scorings (both Teams) = 18
Let :
x = number of 5 point score ; y = number of 2 point score
Total points scored = 34 + 29 = 63
x + y = 18 - - - (1)
5x + 2y = 63 - - (2)
From (1)
y = 18 - x
In (2) ; we have ;
5x + 2(18 - x) = 63
5x + 36 - 2x = 63
3x + 36 = 63
3x = 63 - 36
3x = 27
x = 9
9 5-point plays
Answer:
9
Step-by-step explanation:
Your company is considering offering 600 employees the opportunity to transfer to its new headquarters in Ottawa and, as personnel manager, you decide that it would be fairest if the transfer offers are decided by means of a lottery. Assuming that your company currently employs 200 managers, 300 factory workers, and 900 miscellaneous staff, find the following probabilities, leaving the answers as formulas.
(a) All the managers will be offered the opportunity.
C(___,___)
C(___,___)
(b) You will be offered the opportunity.
C(___,___)
C(___,___)
Answer:
Probability of 100 managers being selected= 100C100*1100C800/1200C900
Probability of selecting just one manager = 1C100*1199C899/1200C900
Explanation:
Given 100 managers, 200 factory workers, 900 miscellaneous workers, and workers bring transferred 900
To find probability of 100 managers leaving given that probability = number of favorable outcomes/total number of outcomes
We use combination since order doesn't matter:
Combination formula= n!/r!(n-r)! Where n= total number of outcomes and r is number of outcome at one time and ! is factorial
Probability of 100 managers using nCr formula for each item = 100C100*1100C800/1200C900
Probability of 1 manager also applying nCr formula as above =1C100*1199C899/1200C900
The probability is the ratio of the favorable event to the total number of events. The probabilities are as follows;
a. P = ¹⁰⁰C₁₀₀ × ¹¹⁰⁰C₈₀₀ / ¹²⁰⁰C₉₀₀
b. P = ¹⁰⁰C₁ × ¹¹⁹⁹C₈₉₉ / ¹²⁰⁰C₉₀₀
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen.
Your company is considering offering 600 employees the opportunity to transfer to its new headquarters in Ottawa and, as personnel manager, you decide that it would be fairest if the transfer offers are decided by means of a lottery.
Assuming that your company currently employs 100 managers, 300 factory workers, and 900 miscellaneous staff.
We can use combination since order does not matter;
a) The probability of all the managers will be offered the opportunity will be
[tex]P = \dfrac{^{100}C_{100} * ^{1100}C_{800}}{^{1200}C_{900}}\\[/tex]
b) The probability of you will be offered the opportunity will be
[tex]P = \dfrac{^{100}C_{1} * ^{1199}C_{899}}{^{1200}C_{900}}\\[/tex]
More about the probability link is given below.
https://brainly.com/question/795909
