The sample space (S) has four regions (1, 2, 3 and 4) and two events A and B. The sample space has 15 equally likely outcomes, of which 5 are in A and 6 are not in A or in B. If events A and B are independent, how many outcomes are in region 2?
A) 2
B) 6
C) 7
D) 8
Answers
Answer:
Option A. 2
Step-by-step explanation:
From the question given, we were told that the total outcome in event A is 5.
Now if region 2 is 6, 7 or 8, as given in the other options, it therefore means that the total out in event A will be more than 5. So region 2 must be 2 in order to satisfy the event A.
Further more, considering the diagram, event B is bigger than event A. With this idea we can give the summary in diagram as follow:
Region 1 => 3 outcomes
Region 2 => 2 outcomes
Region 3 => 4 outcomes
Region 4 => 6 outcomes
Total => 15 outcomes
Now we can see that the total outcome correspond to the total outcome of 15 given in the question.
Therefore, region 2 has 2 outcome
Given the information, we can determine that B has 4 outcomes, but the number of outcomes specifically in region 2 cannot be found without additional information.
Explanation:Let's break down the given information one piece at a time. The sample space (S) consists of 15 equally likely outcomes. Out of these, we know that 5 outcomes are in region A, and 6 outcomes neither belong to event A nor to event B.
Since events A and B are independent, they do not share outcomes. Now, we can calculate the number of outcomes in event B by subtracting the outcomes not belonging in A or B and belonging in A from the total outcomes. Hence, there are 15 - 5 - 6 = 4 outcomes in event B.
However, the question requires us to find outcomes in the second region (2). Since the regions were not specified concerning events A and B, we cannot identify the precise number of outcomes in region 2. Therefore, we cannot accurately answer the question with the given information.
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Related Questions
Add the polynomials:
6a - 4b+cand 4a + 4b+c
Answers
Step-by-step explanation:
6a - 4b + c + 4a + 4b + c
Solving like terms
10a + 2c
Because - 4b + 4b = 0
A flat screen television cost 1306.62 A monthly fee of $5.50 is added if it is paid in Installments Marisa Will pay for the television over 18 months how much will she pay each month
Answers
$1306.62 divided by 18 = $72.59
$72.59+5.50=$78.09
If y = 3x squared + 4 find the value of y when x = 2
Answers
Answer:
The value of y is 16.
Step-by-step explanation:
You have to substitute x = 2 into the equation :
[tex]y = {3x}^{2} + 4[/tex]
Let x = 2,
[tex]y = 3( {2)}^{2} + 4[/tex]
[tex]y = 3(4) + 4[/tex]
[tex]y = 12 + 4[/tex]
[tex]y = 16[/tex]
Answer:
y = 16
Step-by-step explanation:
Let's solve your equation together
3x^2 + 4
We have been given that x = 2
So first we must replace x by 2.
y = 3(2)^2 + 4
Now we solve the equation
2^2 = 4
y = 3(4) + 4
3 * 4 = 12
y = 12 + 4
12 + 4 = 16
y = 16
Hope this helps :)
Two standard 6 sided dice are rolled. One is purple and one is green. What is the probability that sum of the two dice on a roll is 7 given that the purple die for that roll landed on 6?
P(Sum of the dice is 7 | Purple Die Landed on 6)
Answers
The probability that the sum of two dice is 7 given that the purple die landed on 6 is 1/6, as only one outcome from the green die (rolling a 1) will achieve this sum.
Explanation:The question is about calculating the conditional probability of rolling a sum of 7 on two dice, given that the purple die has already landed on 6. Since we know the outcome of the purple die, we only need to determine the probability that the green die will land on a 1 to make the sum 7 (6 from the purple die and 1 from the green die).
There are 6 possible outcomes when rolling a six-sided die. Since only one of these outcomes (rolling a 1) will result in the sum of 7 when the purple die is a 6, the conditional probability is 1/6.
what is the sum of -6 and 9
Answers
Answer:
the answer is 3
Step-by-step explanation:
please help me out on this!
Answers
All to blue 11:4
Find the zeros: 5w=35
Answers
Answer:
w=7
Step-by-step explanation:
Answer:
I want brainliest
Step-by-step explanation:
5w=35
w=7
for which value of x would this model make the least sense to use?
Answers
Answer: A. -2.75
Step-by-step explanation: I took the test on edge
can you give me an explanation on why one of them doesn’t belong, it will mean a lot to me if you do!
Answers
Answer:
the top righ andt doesn't belong to each other because the first antenna is at the left. equal means it needs to have a connection or its have to be absolutely the same. in this case the equal picture is not the same
So the 1st box doesn’t belong.
let f(x) = 4x - 5 ; g(x) = 6x - 3
find 2f(x) + 3g(x)
select the correct response:
1. 8x - 13
2. 10x + 1
3. 26x - 19
4. -24x -21
Answers
Answer:
the answer is 3: 26x-19
Step-by-step explanation:
f(x)=4x-5 g(x)=6x-3
2f(x)+3g(x)
=2*(4x-5)+3*(6x-3)
=8x-10+18x-9
26x-19
.help.me.im.really.lazy.
Answers
Answer:
[tex]1 \frac{1}{6} [/tex]
Step-by-step explanation:
[tex]7 \div 6 \\ = 1.167 = 1 \frac{1}{6} [/tex]
What is 2.85 to the nearest hundredth I ready
Answers
Answer: 2.85
Rounded to the nearest 0.01
2.85 rounded to the nearest hundredth is 2.85
Answer:
2.9
Step-by-step explanation:
Find the limit of the sequence of partial sums whose general term is [tex]a_n=\frac{100^n}{n!}[/tex]
10
1
DNE
0
I am torn between the limit not existing and it being = 0.
Thank you so much.
Answers
Answer:
0
Step-by-step explanation:
If ∑aₙ converges, then lim(n→∞)aₙ = 0.
Using ratio test, we can determine if the series converges:
If lim(n→∞) |aₙ₊₁ / aₙ| < 1, then ∑aₙ converges.
If lim(n→∞) |aₙ₊₁ / aₙ| > 1, then ∑aₙ diverges.
lim(n→∞) |(100ⁿ⁺¹ / (n+1)!) / (100ⁿ / n!)|
lim(n→∞) |(100ⁿ⁺¹ / (n+1)!) × (n! / 100ⁿ)|
lim(n→∞) |(100 / (n+1)|
0 < 1
The series converges. Therefore, lim(n→∞)aₙ = 0.
Kevin is making a picture frame. He has a piece of trim that is 3 feet long.
How many 14−inch-long pieces can Kevin cut from the trim?
How much of a foot will he have left over?
Kevin can cut 14−inch-long pieces with of a foot left over.
Answers
Kevin can cut approximately 2 pieces of 14-inch-long trim from his 3-foot-long trim, with about 0.66667 feet left over.
To find out how many 14-inch-long pieces Kevin can cut from a 3-foot-long trim, we need to convert everything to the same unit. Since Kevin's trim is given in feet, we need to convert inches to feet to make the comparison easier.
[tex]1 foot = 12 inches[/tex]
So, 14 inches is equal to:
[tex]\[14 \text{ inches} \times \frac{1 \text{ foot}}{12 \text{ inches}} = \frac{14}{12} \text{ feet}\][/tex]
[tex]\[= 1.16667 \text{ feet}\][/tex]
Now, we can find out how many 14-inch-long pieces Kevin can cut from the 3-foot-long trim:
[tex]\[ \text{Number of pieces} = \frac{\text{Length of trim}}{\text{Length of each piece}} \][/tex]
[tex]\[ \text{Number of pieces} = \frac{3 \text{ feet}}{1.16667 \text{ feet}} \][/tex]
[tex]\[ \text{Number of pieces} \approx 2.571 \][/tex]
Now, let's find out how much of a foot will be left over:
[tex]\[ \text{Leftover} = \text{Length of trim} - (\text{Number of pieces} \times \text{Length of each piece}) \][/tex]
[tex]\[ \text{Leftover} = 3 \text{ feet} - (2 \times 1.16667 \text{ feet}) \][/tex]
[tex]\[ \text{Leftover} = 3 \text{ feet} - 2.33333 \text{ feet} \][/tex]
[tex]\[ \text{Leftover} \approx 0.66667 \text{ feet} \][/tex]
Complete correct question:
Kevin is making a picture frame. He has a piece of trim that is 3 feet long.
How many 14-inch-long pieces can Kevin cut from the trim?
How much of a foot will he have left over?
Kevin can cut ______ 14-inch-long pieces with ______ of a foot left over.
What are the solutions to the quadratic equation 3(x - 4)2 = 75?
O x= -9 and x = 1
x= -5 and x = 5
O x = -4 and x = 4
Ox= -1 and x = 9
OOO
Answers
Answer:
x = -1 and x = 9
Step-by-step explanation:
3(x-4)^2 = 75
(x-4)^2 = 75/3 = 25
(x-4)=[tex]\sqrt25[/tex]
(x-4)= 5 or (x-4)=-5
x=9 or x= -1
Final answer:
To solve the quadratic equation 3(x - 4)^2 = 75, we isolate the squared term, take the square root of both sides, and solve for x, which gives us the solutions x = -1 and x = 9.
Explanation:
The equation given is 3(x - 4)2 = 75. To solve for x, follow these steps:
Divide both sides of the equation by 3 to isolate the squared term: (x - 4)2 = 25.Take the square root of both sides of the equation to remove the exponent: x - 4 = ±5.Add 4 to both sides of the equation to solve for x: x = 4 ± 5.So, the solutions to the equation are x = -1 and x = 9.
¿Cuál es el area de un círculo con un diámetro de 5 pulgadas a la décima más cercana ?
Answers
Answer:
19.6 o 2.5π
Step-by-step explanation:
la fórmula para el área del círculo es A = πr ^ 2
Find the mean for this data set: 19, 12, 9, 6, 12, 8, 18, 12, 14, 10
Answers
Answer:
12
Step-by-step explanation:
To find the mean, we add up all the numbers and divide by the number of numbers
(19+ 12+9+ 6+ 12+ 8+ 18+ 12+ 14+ 10)/10
120/10
12
Answer:
the mean to this problem is 12
Step-by-step explanation:
19+2+9+6+12+8+18+12+14+10= 120
120/10=
12
WILL GIVE BRAINIEST
What is the Magnitude of A?
a) 4
b) −4
c) 3
d) −3
Graph:
Answers
Answer:
c) 3
Step-by-step explanation:
The magnitude of a vector is its length, ignoring its direction.
Vector a goes from 0 to -3, so its length is 3.
Answer:
c) 3
Step-by-step explanation:
Vector A: < -3, 0 >
Magnitude:
sqrt[(-3)² + 0²]
sqrt(9)
3
Solve the equation 1 4 (16 + 12x) = 28 by first using the distributive property. The equivalent equation is found by distributing the One-fourth to get . The first step is . The second step is . The answer is .
Answers
Answer:
The equivalent equation is found by distributing the 1/4 to get 4 + 3x = 28
The first step is subtract 4 to both sides.
The second step is divide both sides by 3.
The answer is x = 8.
Step-by-step explanation:
Answer:
Divide by 1/4
Subtract
Divide
8
Step-by-step explanation:
Joel needs 785 tickets to get the prize he wants at the arcade. He already has 284 tickets and can earn 35 tickets each time he plays an arcade game. How many games will he have to play in order to have enough tickets to win the prize he wants?
Answers
Answer:14
Step-by-step explanation:
Final answer:
Joel must play at least 15 games to earn the remaining 501 tickets he needs for the prize at the arcade, after subtracting the 284 tickets he already has from the total 785 required.
Explanation:
Joel needs to accumulate a certain number of tickets to win a prize at the arcade. We can approach this problem by calculating the total number of tickets he still needs and then dividing that number by the amount of tickets he can earn per game.
Step-by-Step Calculation:
First, find out how many tickets Joel is short of the prize by subtracting the tickets he already has from the total number of tickets needed: 785 - 284.Second, calculate how many games he needs to play by taking the remaining number of tickets and dividing it by the number of tickets he earns per game, which is 35.Let's execute these steps:
Joel needs 785 tickets and has 284 tickets. So, the number of tickets he still needs is 785 - 284 = 501 tickets.To find out how many games he needs to play, we divide the tickets he needs by tickets per game: 501 / 35. This gives us approximately 14.31, which means Joel needs to play at least 15 games to earn enough tickets, since he cannot play a fraction of a game.a bullet fired from a gun traveled 3,600 m south in 6.0 seconds. What was its velocity in (a) m/sec and (b) km/hour?
Answers
Step-by-step explanation:
Velocity = Displacement/Time
a) Velocity in m/s = 3600m/6s
= 600m/s
b) (Converting m into km)
1000m = 1km
3600m = ?
3600/1000 = 3.6km
(Converting secs to hours)
1mins = 60secs
60mins = ?
60 * 60 = 3600 secs
This means there are 3600 secs in 1 hour
3600secs = 1hour
6.0 secs = ?
6.0/3600 = 0.00167 hours (approximately)
Velocity in km/h = 3.6km/0.00167h
= 2155.69km/h (approximately)
In summary...
a) 600m/s
b) 2155.69km/h
The bullet's velocity is 600 meters per second (m/s) and also 2,160 kilometers per hour (km/h), calculated by dividing the distance traveled by the time taken and converting the units accordingly.
To find out the bullet's velocity in meters per second (m/s), you'll need to use the formula for velocity which is distance traveled divided by the time taken. Here, the bullet traveled 3,600 meters in 6.0 seconds.
Velocity in m/s = Distance / Time
Velocity in m/s = [tex]\frac{3600}{6}[/tex]
Velocity in m/s = 600 m/s
For velocity in kilometers per hour (km/h), first convert meters to kilometers by dividing by 1,000 and then convert seconds to hours by dividing by 3,600 (the number of seconds in an hour).
Velocity in km/h =[tex]\frac{ (Velocity in m/s x 3,600) }{1000}[/tex]
Velocity in km/h = [tex]\frac{(600 m/s x 3,600) }{1000}[/tex]
Velocity in km/h = 2,160,000 / 1,000
Velocity in km/h = 2,160 km/h
Therefore, the bullet's velocity is 600 m/s and 2,160 km/h.
Rachel invites thirty guests to her party, and she wants to provide party gifts for her guests. She represents the relationship between guests (x) and the number of party gifts (y) using different representations. If the patterns in the table and graph continue, which item would she need the most of for 30 people? granola bars toy cars miniature figurines
Answers
Answer:it’s granola bars
Step-by-step explanation:
Rachel would need the most toy cars for 30 people.
Explanation:If the patterns in the table and graph continue, Rachel would need the most toy cars for 30 people.
From the table, we can see that for every 10 guests, the number of party gifts is increasing by 5. So, for 30 guests, the number of party gifts would be 25.
From the graph, we can see that the number of guests is increasing linearly with a slope of 0.5. If the pattern continues, for 30 guests, the number of party gifts would be 25.
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The Smiths spend 10% of their budget on entertainment. Their total budget this year is $2,000 more than last year, and this year they plan to spend $2,450 on entertainment. What was their total budget last year?
Answers
Answer:
$22500
Step-by-step explanation:
First, we have to find the total budget for this year.
They spend 10% on entertainment and $2450 will be spent on entertainment this year.
Let the total budget this year be x. Therefore:
[tex]\frac{10}{100} * x = 2450[/tex]
Simplifying:
[tex]10x = 2450 * 100 \\\\10x = 245000\\\\x = 245000 / 10[/tex]
=> x = $24500
Their total budget of this year is $24500.
Since they will spend $2000 more this year than last year, we have to deduct $2000 from this year's budget to find last year's.
This means that their budget last year was:
$24500 - $2000 = $22500
Their budget last year was $22500.
California has a land area of 163,676 mi2 and a population of 39.51 million people. Find the population density of California to the nearest tenth
answer choices
241.4 people per mi2
4142.6 people per mi2
24.1 people per mi2
0.004 people per mi2
Answers
Answer:
(A)241.4 people per mi²
Step-by-step explanation:
California's Population=39.51 million=39,510,000
California's Land Area=163,676 mi²
Population Density=Population ÷Area
=39,510,000÷163,676
=241.39
≈241.4 people per mi² (correct to the nearest tenth)
how many meters longer is 3 meters than 3 yards
Answers
Answer:
0.2568 mStep-by-step explanation:
How many meters longer is 3 meters than 3 yards?
Yard to meter
1 yard = 0.9144 mThe difference:
3 meters - 3 yards = 3*( 1 - 0.9144) m =0.2568 mAnswer:
0.279
Step-by-step explanation:
3 meters = 3.279 yards
~Subtract to find the difference
3.279 - 3 = 0.279
As you can see, 3 meters if larger than 3 yards.
Best of Luck!
help Evaluate: -18 + 4(6 ÷ 2)^2
Answers
Answer:
18
Step-by-step explanation:
6 divided by 2 is 3, 3 to the power of 2 is 9, 9 times 4 is 36, 36 plus -18 is 18.
Answer:
18
Step-by-step explanation:
-18 + 4(6 ÷ 2)^2
PEMDAS says parentheses first
-18 + 4(3)^2
Then exponents
-18 + 4*9
Then multiply and divide
-18 +36
Then add and subtract
18
Given CS = 3, SB = 6, CR = 4, and RA = x. What must the value of x be in order to prove SR II BA? Justify your answer.
UPLOAT
Answers
Answer:
4, because CR and RA are the same length
Answer:
Just cross muiltiply
Step-by-step explanation:
3 4
- - = 8 (POP Theorem)
6 x
Converse of Theorem 5-6: If a line divides two sides of a triangle proportionally, it is parallel to the third side.
You're welcome Ody$$eyware
An item is regularly priced at $85. Juan bought it on sale for 55% off the regular price. How much did Juan pay?
Answers
Consider the expression 7x2 + 9 + 3x. Tell whether each statement is
True or False.
a. The expression has three terms.
b. The coefficient of x is 3.
c. The expression can be simplified to 10x2 + 9.
d. The constant term is 9.
Answers
Answer:
A is false
b is true
c is false
d is false
Step-by-step explanation:
Final answer:
In this response, the terms of the given algebraic expression are identified, coefficients are determined, and simplification possibilities are explored.
Explanation:
a. True: The expression 7x2 + 9 + 3x has three terms.
b. True: The coefficient of x is 3.
c. False: The expression cannot be simplified to 10x2 + 9. It remains as 7x2 + 9 + 3x.
d. True: The constant term in the expression is 9.
what is the area of a room that is 3 3/4 yards long and 3 1/3 yards wide
Answers
Answer:
12 1/2 yd^2
Step-by-step explanation:
The area is length times width
A = 3 3/4 * 3 1/3
Change to improper fractions
A = 15/4 * 10/3
Rewriting
A = 15/3 * 10/4
= 5 * 5/2
= 25/2
Changing back to a mixed number
= 12 1/2
Answer:
12½ yards²
Step-by-step explanation:
Area = length × width
Area = 3¾ × 3⅓
= 15/4 × 10/3
= 25/2
= 12½ yards²