Answers
Answer:
Option A.
Step-by-step explanation:
Let A represents have soup and B represents having salad for lunch.
If two events are not dependent on each other, then they are known as independent events.
Probability of having soup is not dependent on Probability of having salad.
[tex]P(A\cap B)=P(A)P(B)[/tex]
Using the formula of conditional probability, we get
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}\Rightarrow \frac{P(A)P(B)}{P(B)}=P(A)[/tex]
[tex]P(B|A)=\frac{P(A\cap B)}{P(A)}\Rightarrow \frac{P(A)P(B)}{P(A)}=P(B)[/tex]
Having soup or salad for the lunch are two independent event because [tex]P(A|B)=P(A)[/tex] and [tex]P(B|A)=P(B)[/tex].
Therefore, the correct option is A.
The correct answer is:
c) Having soup and salad are not independent events because P(A|B) ≠ P(A) and P(B|A) ≠ P(B).
Given that two events A and B, A represent having soup and B represent having salad for lunch.
We need to determine if the events are independent.
To determine if having soup (A) and salad (B) for lunch are independent events, we need to compare the conditional probabilities with the individual probabilities.
The events A and B are independent if and only if:
P(A|B) = P(A) and P(B|A) = P(B)
where P(A|B) is the probability of having soup given that salad is already chosen, P(A) is the probability of having soup in general, P(B|A) is the probability of having salad given that soup is already chosen, and P(B) is the probability of having salad in general.
Now, let's evaluate each statement:
a) Having soup and salad for lunch are independent events because P(A|B) = P(A) and P(B|A) = P(B).
This statement suggests that both conditional probabilities are equal to the individual probabilities, which would mean the events are independent. However, this contradicts the definition of independent events, where both conditional probabilities should be equal for independence.
b) Having soup and salad for lunch are not independent events because P(A|B) = P(A) and P(B|A) = P(B).
This statement is also incorrect because it states that the conditional probabilities are equal to the individual probabilities, which would indicate independence, but that is not the case.
c) Having soup and salad are not independent events because P(A|B) ≠ P(A) and P(B|A) ≠ P(B).
This statement correctly states that both conditional probabilities are not equal to the individual probabilities, indicating that the events are not independent. This is the correct answer.
d) Having soup and salad for lunch are independent events because P(A|B) ≠ P(A) and P(B|A) ≠ P(B).
This statement is incorrect because it suggests that the events are independent based on the fact that the conditional probabilities are not equal to the individual probabilities. However, this reasoning is flawed, and the correct interpretation for independence is when the conditional probabilities are equal to the individual probabilities.
Therefore, the correct answer is:
c) Having soup and salad are not independent events because P(A|B) ≠ P(A) and P(B|A) ≠ P(B).
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Related Questions
What is the coefficient of the term of degree 5 in the polynomial below?
3x +5 - +4x3 - 9x
Answers
ANSWER
D. 4
EXPLANATION
The given polynomial is
[tex]3 {x}^{6} + 5 - {x}^{2} + 4 {x}^{5}- 9x[/tex]
The term in degree 5 in this polynomial is
[tex]4 {x}^{5} [/tex]
The coefficient of this term is the constant that is multiplying the variable raised to exponent 5.
This number is 4.
Therefore the coefficient of term in degree 5 is 4
The correct answer is D.
A ball is dropped from the top of a building that is 1,000 feet high. Its height, in feet, as a function of the time, x, in seconds, after the ball was dropped, is given by the following equation, ƒ(x) = 1,000 - 16x 2. Which set of numbers is appropriate as the domain for this function?
Answers
Real numbers from 0 to sqrt(1000/16) = 0 to 2.5sqrt(10).
Before 0, it hadn't been dropped. After 2.5sqrt(10), it has hit the ground and stopped falling.Positive Real Numbers. This includes fractions of seconds, the other two don't.
The appropriate domain for the function describing the height of a ball dropped from a 1,000 feet high building as a function of time is 0 <= x <= 25 seconds, indicating the ball's descent time until it hits the ground.
The student has asked about the appropriate domain for a function describing a ball dropped from a height of 1,000 feet, given by the equation f(x) = 1,000 - 16x². To find the domain, we need to understand when the ball hits the ground, marking the end of its free fall and the function's practical use.
The height (f(x)) becomes 0 when the ball reaches the ground. Setting the equation to zero gives us 0 = 1,000 - 16x². Solving for x, we find x = 25 seconds. This means the ball will hit the ground after 25 seconds, indicating the end of its descent and the maximum value of x in the domain. Therefore, the appropriate domain for this function, representing the time from when the ball was dropped until it hits the ground, is 0 ≤ x ≤ 25 seconds.
Find the difference. Express your answer in simplest form. 7r/s - 4r/s
Answers
[tex]7 \frac{r}{s} \: - 4 \frac{r}{s} \\ taking \: common \: factor \: ( \frac{r}{s} ) \\ = \frac{r}{s} (7 - 4) \\ =3 \frac{r}{s} [/tex]
Hope it helps...
Regards;
Leukonov/Olegion.
Gold has a density of 19.32 grams per cubic centimeters and is worth $40.26 per gram. The figure shows the dimensions of a particular bar of gold. What is this bar of gold worth?
Answers
Do 19.32 x 40.26 which should equal $777.82
Solve the following equation for x
Answers
Answer:
C
Step-by-step explanation:
Using the laws of logarithms
• log x + log y ⇔ log(xy)
• log x = log y ⇒ x = y
Given
logx + log(x - 3) = log 3x
log x(x - 3) = log 3x, hence
x(x - 3) = 3x
x² - 3x = 3x ( subtract 3x from both sides )
x² - 6x = 0 ← factor out x from each term
x(x - 6) = 0
Equate each factor to zero and solve for x
x = 0
x - 6 = 0 ⇒ x = 6
Solutions are x = 0, x = 6 → C
Answer: OPTION A
Step-by-step explanation:
You need to remember the logarithms properties:
[tex]log(a)+log(b)=log(ab)\\\\log(a)-log(b)=log(\frac{a}{b})\\\\log(a)^b=b*log(a)[/tex]
Rewrite the equation:
[tex]log(x(x-3))=log(3)+log(x)[/tex]
Like this logarithm has base 10, you can make this procedure:
[tex]log(x(x-3))-log(x)=log(3)[/tex]
[tex]log\frac{(x(x-3))}{(x)}=log(3)[/tex]
[tex]log(x-3)=log(3)[/tex]
[tex]10^{log((x-3))}=10^{log(3)}[/tex]
Then:
[tex](x-3)=3[/tex]
Now you need to solve for the variable "x":
[tex]x=3+3\\x=6[/tex]
An engineer is designing a roller coaster. The tallest peak is 310 feet high.
The roller coaster travels 155 horizontal feet as it descends the hill.
What is the slope of the hill?
Answers
The answer is:
The slope of the hill is equal to 2.
Why?To solve the problem, we need to remember that the slope of a line, is the rate of increase or decrease of the line.
From the statement we know that the tallest peak of the roller coaster is 310 feet (y), while the roller coaster travels 155 horizontal feet (x), so, calculating we have:
[tex]Slope=\frac{height}{base}=\frac{y}{x}[/tex]
Then, substituting the given information and calculating, we have:
[tex]Slope=\frac{310ft}{155ft}=2[/tex]
We have that the slope of the hill is equal to 2.
Have a nice day!
Answer:
The slope of the hill is equal to 2
Step-by-step explanation:
Savvas realize benchmark test
The bar graph shown here provides the numbers of scoops of different ice cream flavors that were sold during school lunch today.
How many more scoops of strawberry were sold than vanilla?
A) 2
B) 3
C) 4
D) 5
Answers
The number of more scoops of strawberry were sold than vanilla is 4. Therefore, option C is the correct answer.
What is bar graph?A bar graph is a graph that shows complete data with rectangular bars and the heights of bars are proportional to the values that they represent. The bars in the graph can be shown vertically or horizontally. Bar graphs are also known as bar charts and it is a pictorial representation of grouped data.
From the given graph, number of scoops of strawberry sold is 10 and the number of scoops of Vanilla sold is 6.
Difference = 10-6
= 4
Therefore, option C is the correct answer.
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What is the value of x?
x=15
x=30
x=37.5
x=52.5
Answers
Answer:
x = 15Step-by-step explanation:
[tex]\text{If}\ \angle1\ \text{and}\ \angle2\ \text{are complementary, then}\ \angle1+\angle2=90^o.\\\\\text{We have:}\\\\\angle1=x^o\\\angle2=(3x+30)^o\\\\\text{Substitute:}\\\\x+(3x+30)=90\\\\(x+3x)+30=90\qquad\text{subtract 30 from both sides}\\\\4x=60\qquad\text{divide both sides by 4}\\\\x=15[/tex]
The value of x is 52.5.
Explanation:The value of x can be determined by examining the given equations:
x = 15x = 30x = 37.5x = 52.5Since x is a variable, it can take on different values. In this case, the value of x is 52.5 because that is the only value that satisfies the given equations.Learn more about Value of x here:https://brainly.com/question/26914436
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Need Help Please!!!!!!!!!!:>
Answers
divide by 2 for each of the numbers
32/2=16
16/2=8
8/2= 4
Answer is 4
ANSWER
The next term in the given geometric sequence is 4.
EXPLANATION
We want to find the next term in the geometric sequence
32,16,8,
We can observe that there is a common ratio of
[tex] \frac{16}{32} = \frac{1}{2} [/tex]
This implies that, we obtain the subsequent terms by multiplying the previous terms by ½.
To obtain the next term after 8, we multiply 8 by half to get.
[tex] 8 \times \frac{1}{2} = 4[/tex]
Therefore the next term is 4.
What is the missing measure on the small rectangle?
Answers
Answer:
4 inches
Step-by-step explanation:
If you divide 18 by 6, the answer is three, so it is scaled down 3x.
So, you have to divide 12 by 3, and the answer is 4.
Answer: 4 Inches
Step-by-step explanation: The rectangle on the left shows that the length is 18 inches and the height is 12 inches. Now, to find the height on the right, First we must realize what changed has been made from the left to the right. We know that our length has decreased to 6 inches from 18. 18 can be divided by 3 and that will give us the quotient of 6. Now, we must divide our height on our original rectangle by 3 as well. Once we divide, our new height of our rectangle also known as X will be 4 Inches Long.
Have A Great Day!
In a standard deck of cards there are four suits: spades, clubs, hearts, and diamonds. Each suit has one each of 13 cards: ace, king, queen, jack, 2, 3, 4, 5, 6, 7, 8, 9, and 10.
If event A is choosing a king, event B is choosing a heart, and event C is choosing a jack, which Venn diagram could represent this description?
Answers
Answer:
The answer would be graph A.
Step-by-step explanation:
Since the cards all belong to four suites, the king can be a heart as well as the jack, but they cannot be the same card. So the choice is graph A.
A Venn diagram displaying events A, B, and C, with overlaps representing the king of hearts (A intersect B) and the jack of hearts (B intersect C), correctly describes the description given.
The Venn diagram that represents the description given should consist of three overlapping circles, one for each event: choosing a king (event A), choosing a heart (event B), and choosing a jack (event C).
Since there is one king and one jack in the hearts suit, the events are not mutually exclusive and the intersections between the circles will represent these possibilities.
There will be an overlap between events A and B, which represents the king of hearts, and an overlap between events B and C, which represents the jack of hearts. However, there will not be an overlap between events A and C since a card cannot be a king and a jack simultaneously.
A rectangle has perimeter of 20, if the length and width are halved. What is the new perimeter ?
Answers
Answer:
10
Step-by-step explanation:
The perimeter will also be halved: (1/2)(20) = 10.
Example: a rectangle of length 14 ft and width 8 ft has perimeter P = 2(14 ft) + 2(8 ft), or 28 ft + 16 ft = 44 ft.
If we halve the length and width, we get 7 ft and 4 ft, and the P is
2(7 ft) + 2(4 ft) = 14 ft + 8 ft = 22 ft, which is half of the original perimeter 44.
Nine less than the quotient of two and a number xxx.
Answers
the expression to represent "Nine less than the quotient of two and a number ( x )" is:[tex]\[ \frac{2}{x} - 9 \][/tex]
To represent "Nine less than the quotient of two and a number ( x )", we first need to find the quotient of two and ( x ), and then subtract nine from it.
Let's break it down:
1. Quotient of two and a number ( x ):
This is represented as [tex]\( \frac{2}{x} \).[/tex]
2. Nine less than the quotient:
Subtracting nine from the quotient gives [tex]\( \frac{2}{x} - 9 \).[/tex]
So, the expression to represent "Nine less than the quotient of two and a number ( x )" is:
[tex]\[ \frac{2}{x} - 9 \][/tex]
complete question given below:
Write an expression to represent: Nine less than the quotient of two and a number xxx.
Use completing the square to solve for x in the equation x^2-10x+25=35.
Answers
It actually has 2 answers
x =(10+√140)/2=5+√ 35 = 10.916
or:
x =(10-√140)/2=5-√ 35 = -0.916
ANSWER
[tex]x =5 \pm \sqrt{35} [/tex]
EXPLANATION
The given quadratic equation is:
[tex] {x}^{2} - 10x + 25 = 35[/tex]
Group the constants on the RHS,
[tex] {x}^{2} - 10x= 35 - 25[/tex]
[tex] {x}^{2} - 10x= 10[/tex]
Add the square of half the coefficient of x to both sides of the equation,
[tex]{x}^{2} - 10x + ( - {5)}^{2} = 10 + ( - {5)}^{2} [/tex]
[tex]{x}^{2} - 10x + 25= 10 + 25[/tex]
We factor the perfect square to get:
[tex]{(x - 5)}^{2} =35[/tex]
[tex]x - 5 = \pm \sqrt{35} [/tex]
[tex]x =5 \pm \sqrt{35} [/tex]
The question is a picture.
Answers
Answer:
904.32 cm³Step-by-step explanation:
The formula of a volume of a cylinder:
[tex]V=\pi r^2H[/tex]
r - radius
H - height
We have r = 6cm and H = 8cm. Substitute:
[tex]V=\pi(6^2)(8)=\pi(36)(8)=288\pi\ cm^3[/tex]
[tex]\pi\approx3.14\to V\approx(288)(3.14)=904.32\ cm^3[/tex]
Answer:
904.32 cm³
Step-by-step explanation:
The volume (V) of a cylinder is calculated using the formula
V = πr²h ( r is the radius of the base and h the height )
here r = 6 and h = 8, so
V = 3.14 × 6² × 8
= 3.14 × 36 × 8 ≈ 904.32 cm³
What’s the radius of a circle with an area of 123 square feet
Answers
Answer:
6.25716517287
Step-by-step explanation:
Area of circle = π × r²
→ 123 = π × r²
⇒ Divide both sides by π
→ 39.1521160006 = r²
⇒ Square root both sides
→ 6.25716517287 = r
which expression is 444 times as large as the expression 34 -15
A
4 x 34 - 15
B
4 x (34 - 15)
C
(4 x 34) - 15
Answers
Final answer:
The expression that is 444 times as large as the expression 34 - 15 is (4 x 34) - 15.
Explanation:
To find the expression that is 444 times as large as the expression 34 - 15, we need to multiply the expression by 444. The correct expression is option C, which is (4 x 34) - 15. Let's break it down:
First, we perform the multiplication: 4 x 34 = 136.
Then, we subtract 15 from the result: 136 - 15 = 121.
Therefore, the expression (4 x 34) - 15 is 444 times as large as the expression 34 - 15.
Hank's pickup can travel 68 miles on 4 gallons of gas. How many gallons will Hank's pickup need to travel 51 miles?
Answers
Answer:
3
Step-by-step explanation:
68/4 to get how many miles per gallon
17
51/17 to see how many gallons of gas
3 gallons of gas
Based on the information given, Hank's pickup has a fuel efficiency of 17 miles per gallon. Therefore, it will require approximately 3 gallons of gas to travel 51 miles.
Explanation:To determine how many gallons of gas Hank's pickup will need to travel 51 miles, we first establish the rate of gas consumption for the vehicle. As per the given data, Hank's pickup can travel 68 miles on 4 gallons. This gives us a rate of 68 miles/4 gallons = 17 miles per gallon.
Now, to find out how many gallons are required to travel 51 miles, we divide 51 miles by the rate of 17 miles per gallon. So, the calculation is as follows:
51 miles ÷ 17 miles/gallon = 3 gallons.
Therefore, Hank's pickup will require approximately 3 gallons to travel 51 miles.
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Determine whether the function is linear or quadratic. Identify the quadratic, linear, and constant terms.
y = (x - 1)(4x + 2) - 4x2
Answers
Answer:
Quadratic. But what is 4x2?
Step-by-step explanation:
Which of the following points lies on the graph of f(x) = -x 2?
(-4, 2)
(-2, -4)
(-2, 4)
(4, -2)
Answers
Answer:
(-2, -4)
Step-by-step explanation:
we have
[tex]f(x)=-x^{2}[/tex]
we know that
If a ordered pair lies on the graph, then the ordered pair must satisfy the equation of f(x)
Verify each ordered pair
case A) (-4, 2)
Substitute the value ox x and the value of y in the equation and then compare the results
[tex]2=-(-4)^{2}[/tex]
[tex]2=-16[/tex] ------> is not true
therefore
The point not lies on the graph
case B) (-2, -4)
Substitute the value ox x and the value of y in the equation and then compare the results
[tex]-4=-(-2)^{2}[/tex]
[tex]-4=-4[/tex] ------> is true
therefore
The point lies on the graph
case C) (-2, 4)
Substitute the value ox x and the value of y in the equation and then compare the results
[tex]4=-(-2)^{2}[/tex]
[tex]4=-4[/tex] ------> is not true
therefore
The point not lies on the graph
case D) (4, -2)
Substitute the value ox x and the value of y in the equation and then compare the results
[tex]-2=-(4)^{2}[/tex]
[tex]-2=-16[/tex] ------> is not true
therefore
The point not lies on the graph
A movie was shown 6 times every day from November 24 through December 19. How
many times was the movie shown in all?
(Note: The month of November has 30 days.)
Select your answer.
О 138
0 144
О156
О162
Answers
How?
During that time period there were 23 days so 23 multiplied by the amount of times played per day (6)
You get the answer 138
Answer:
162
Step-by-step explanation:
Ax-bx-y=z
which of the following represents the formula that could be used to find x?
Answers
Answer:
see explanation
Step-by-step explanation:
Given
Ax - bx - y = z ( add y to both sides )
Ax - bx = z + y ← factor out x from both terms on the left side
x(A - b) = z + y ← divide both sides by (A - b)
x = [tex]\frac{z+y}{A-b}[/tex]
if x represents a number, write an expression to represent a number which is 5 less than 3 times x
Answers
Answer:
the correct answer is x = 3x - 5
addison walked 6 miles in 4 hours what was her walking rate in hours per mile
Answers
Answer:
2/3 hour per mile.
Step-by-step explanation:
Hours per mile
= hours taken / miles walked
= 4/6 = 2/3 hour per mile.
Answer:
she walked 1.5 miles for every hour
Step-by-step explanation:
Divide the miles by the hours: 6/4 =1.5
To make sure this is correct multiply 1.5 times 4(the hours) and you will get 6(the miles she walked
Hope this helped:3
what is k equal to if 7.6/2 =9.5/k
Answers
Answer:
k=2.5
Step-by-step explanation:
7.6/2 = 3.8
9.5/3.8 = 2.5
Answer:
Step-by-step explanation:
7.6/2 =9.5/k
7.6k=2×9.5
k = (2×9.5)/7.6
k = 19/7.6
k= 2.5
vrify : 7.6/2 = 3.8 and 9.5/2.5 = 3.8 .....true
In March, volunteers for a charity walkathon in Toronto raised $89,351. Volunteers in Montreal raised $102,459. Volunteers in Edmonton raised $78,505.
a. Round each amount to the nearest thousand dollars.
b. Add the rounded amounts to estimate the total amount of money raised.
c. Use the estimate to choose the exact total from among the following.
(1) $250,615 (2) $350,615 (3) $270,315 (4) $170,015
Answers
In your question, we are trying to find the total amount of money raised when the money is rounded to the nearest thousands.
Answer: (3) 270,315In order to solve the problem, we would need to round the money raised to the thousands place.
The thousands place would be the number before the comma. (_),000.
Lets round for Part A:
89,351. The thousands place would be 9 in this case, when you look at the number to the right of it (3), it's not big enough to make 9 bigger, so we would keep the thousands place the same. It would end up as 89,000.
102,459. The thousands place would be 2, the number to the right of it is not big enough to be rounded up, so we would keep it the same. It would end up as 102,000.
78,505. The thousands place would be 8. The number to the right of it is a big enough number to let the number 8 be rounded, therefore we would round the 8 up to 9. It would end up as 79,000.
Part B
Our current values would be 89,000, 102,000, and 79,000.
Now, for part B, we would add the rounded values to get an estimate of the money saved:
[tex]89,000+102,000+79,000 =270,000[/tex]
You should get 270,000. Remember, that's just an estimate number.
Part C:
The answer choice that's close to that number is answer choice (3), $270,315.
Your FINAL answer should be (3) $270,315.
how do i find the altitude of a right triangle when given two sides but not the hypotenuse?
Answers
You can use the Pythagorean Theorem to find the hypotenuse. Then you should be able to find the altitude.
Given:
A = V3
B = 2V3
C= 25
D= V16
Which expressions result in a rational number? Select all that apply.
Answers
Answer:
The ones that give a rational number answer are:
C+D
A*B
C*D
A*A
Step-by-step explanation:
A+B does not give a rational number answer; √3+2√3 = 3√3
C+D is a rational number; √25=5 and √16=4; 5+4=9.
A+D is not a rational number; √3+√16 = √3+4
A*B is a rational number; √3*2√3 = 2√9 = 2*3 = 6
B*D is not a rational number; 2√3*√16 = 2√3*4 = 8√3
C*D is a rational number; √25*√16 = 5*4 = 20
A*A is a rational number; √3*√3 = √9 = 3
What is the constant term of −3x4−7x+2
-
3
x
4
-
7
x
+
2
?
Answers
Answer:
The constant term is 2
Step-by-step explanation:
The given polynomial is [tex]-3x^4-7x+2[/tex].
To find the constant term, we must make sure the polynomial is in standard form.
The constant term is the term that is independent of x.
Considering [tex]-3x^4-7x+2[/tex], the term that is independent of x is the last term which is 2.
Therefore the constant term is [tex]2[/tex].
Choose the correct symbol to form a true statement. 11/18 ____5/9
Answers
For this case we have the following numbers:
[tex]\frac {11} {18} = 0.611111111111\\\frac {5} {9} = 0,555555555556[/tex]
Note that [tex]\frac {11} {18}[/tex]is greater than[tex]\frac {5} {9},[/tex] so the inequality sign must be placed with the opening towards [tex]\frac {11} {18}[/tex].
Answer:
[tex]\frac {11} {18}> \frac {5} {9}[/tex]