Answer:
Yes, No, Yes, No, No
Step-by-step explanation:
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for events A and B, P(A)= 3/14 and P(B)= 1/5. Also, P(A and B)= 3/65. Are A and B independent events?
No, A and B are not independent events
Step-by-step explanation:
Let us study the meaning independent probability
Two events are independent if the result of the second event is not affected by the result of the first eventIf A and B are independent events, the probability of both events is the product of the probabilities of the both events P (A and B) = P(A) · P(B)∵ P(A) = [tex]\frac{3}{14}[/tex]
∵ P(B) = [tex]\frac{1}{5}[/tex]
∴ P(A) . P(B) = [tex]\frac{3}{14}[/tex] × [tex]\frac{1}{5}[/tex]
∴ P(A) . P(B) = [tex]\frac{3(1)}{14(5)}[/tex]
∴ P(A) . P(B) = [tex]\frac{3}{70}[/tex]
∵ P(A and B) = [tex]\frac{3}{65}[/tex]
∵ P(A) . P(B) = [tex]\frac{3}{70}[/tex]
- The two answers are not equal
∴ P (A and B) ≠ P(A) · P(B)
- In independent events P (A and B) = P(A) · P(B)
∴ A and B are not independent events
No, A and B are not independent events
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Events A and B are not independent.
The events A and B are independent given that P(A) = 3/14, P(B) = 1/5, and P(A AND B) = 3/65. To determine if two events are independent, the product of their individual probabilities, P(A) and P(B), should equal the probability of both events occurring together, P(A and B).
Let's calculate this:
P(A) × P(B) = (3/14) × (1/5) = 3/70
Since P(A AND B) = 3/65, we compare it to the calculated product of P(A)P(B).
P(A AND B) is not equal to P(A)P(B). Therefore, events A and B are not independent because their joint probability is not the product of their individual probabilities.
make b the subject of this equation A = 1/2 x b x h
The equation is [tex]b=\frac{2A}{h}[/tex]
Step-by-step explanation:
Let us revise how to make a variable subject of an equation
Write the equation and circle the variable you want to make it subjectKeep it in one side and move all other in the other sideMake the coefficient of the subject 1∵ A = [tex]\frac{1}{2}[/tex] × b × h
∵ b is the subject
∴ Multiply the two sides by 2
∴ 2A = b × h
- Divide both sides by h
∴ [tex]\frac{2A}{h}= b[/tex]
- Switch the two sides
∴ [tex]b=\frac{2A}{h}[/tex]
The equation is [tex]b=\frac{2A}{h}[/tex]
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Which of the following is not a way to determine if a relation is a function?
A.
Use the vertical line test on a graph of the relation.
B.
Check to see if each input maps to only one output.
C.
There should be no duplicated x-coordinates in the ordered pair set.
D.
Determine if the relations’ graph forms a line.
D. Determine if the relations’ graph forms a line.
Step-by-step explanation:
A function is a relation if the input values lead to only one output value.The input values, normally x values make up the domain, where as the output values form the domain.A function is a relation where the input values are associated with a single output.The vertical test is used to determine if a curve is a function.The line graph should only hit a single point on the curve.
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Keywords; relation, a function, vertical line test, output, input, maps
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find the sum of the following gp:6,12,24,......to 10term and 1,-1/2,1/4,1/8,1/16.........to 20term
Answer:
Sₙ = 6 x (1 - 2¹⁰) / (1 - p) = 6 x 1023 = 6138
S'ₙ =2.52
Step-by-step explanation:
sum of this sequence: Sₙ = A₁ x (1 - pⁿ) / (1 - p)
Sₙ: sum of n terms
A₁: initial value 6
p: common ratio 2
n: terms 10
Sₙ = 6 x (1 - 2¹⁰) / (1 - p) = 6 x 1023 = 6138
Is there any mistake in the 2nd question - about the common ratio (-1/2)?
S'ₙ =1 + (-1/2) + 1 x (1 - (1/2)¹⁸)) / (1 - (1/2)) = 1/2 + 2 x (1 - (1/2)¹⁸)
S'ₙ = 1/2 + 2 x (1 - 1/262144) = 1/2 + 262143/130072= 0.5 +2.02 = 2.52
Which statement is true about the function f(x)= -√-x?
Answer:
Never mind, but your question makes no sense.
Step-by-step explanation:
List the rest of the question.
You worked the following hours this week: Monday 8 AM to PM, Tuesday 9 AM to 3 PM, Thursday 8:30 AM to 2:15 PM.
You get a 30-minute unpaid lunch break every work day. How many hours will you be paid for this week?
To calculate the total hours you will be paid for this week, subtract the total lunch break time from the total working hours. Therefore, the total hours you will be paid for this week is 19 hours and 45 minutes.
Explanation:To calculate the number of hours you will be paid for this week, you need to subtract the total lunch break time from the total working hours.
On Monday, you worked from 8 AM to PM, which is 10 hours.
On Tuesday, you worked from 9 AM to 3 PM, which is 6 hours.
On Thursday, you worked from 8:30 AM to 2:15 PM, which is 5 hours and 45 minutes.
Overall, your total working hours for the week are 10 + 6 + 5 hours and 45 minutes.
Each day you have a 30-minute unpaid lunch break, so for the entire week you would have 4 lunch breaks x 30 minutes = 2 hours taken for lunch breaks.
Therefore, the total hours you will be paid for this week are 10 + 6 + 5 hours and 45 minutes - 2 hours = 19 hours and 45 minutes.
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Factor completely: 2x4 − 32.
a 2(x2 − 4)(x2 + 4)
b 2(x − 2)(x + 2)(x2 + 4)
c 2(x − 2)(x + 2)(x + 2)(x + 2)
d 2(x − 2)(x + 2)(x2 − 4)
Answer:
Option b) is correct.
The completed factor of given expression is [tex]2(x-2)(x+2)(x^2+4)[/tex]
Step-by-step explanation:
Given expression is [tex]2x^4-32[/tex]
To find the completed factor for the given expression:
[tex]2x^4-32[/tex]:
Taking the common number "2" outside to the above expression we get
[tex]2x^4-32=2(x^4-16)[/tex]
Now rewritting the above expression as below
[tex]=2(x^4-2^4)[/tex] (since 16 can be written as the number 2 to the power of 4)
[tex]=2((x^2)^2-(2^2)^2)[/tex]
The above expression is of the form [tex]a^2-b^2=(a+b)(a-b)[/tex]
Here [tex]a=x^2[/tex] and [tex]b=2^2[/tex]
Therefore it becomes
[tex]=2(x^2+2^2)(x^2-2^2)[/tex]
[tex]=2(x^2+4)(x^2-2^2)[/tex]
The above expression is of the form [tex]a^2-b^2=(a+b)(a-b)[/tex]
Here [tex]a=x[/tex] and [tex]b=2[/tex]
Therefore it becomes
[tex]=2(x^2+4)(x+2)(x-2)[/tex]
[tex]=2(x+2)(x-2)(x^2+4)[/tex]
Therefore [tex]=2(x+2)(x-2)(x^2+4)[/tex]
[tex]2x^4-32=2(x-2)(x+2)(x^2+4)[/tex]
Option b) is correct.
The completed factor of given expression is [tex]2(x-2)(x+2)(x^2+4)[/tex]
Answer:
b
Step-by-step explanation:
PLEASE HELP!!!!!!! CORRECT GETS BRAINLIEST!!!!!!
Answer:
Step-by-step explanation:
If angle STU is given as 82 degrees, then arc SVU is twice the measure of its inscribed angle. That means that arc SVU is 164 degrees.
arc SVU = arc SV + arc VU. By substitution,
164 = 120 + arc VU so
arc VU = 44 degrees
Kara and Lindsey both hike in separate directions from their campsite, with Kara hiking straight to the east and Lindsey hiking straight north. At
2:00 p.m., Kara hiked twice as far to the east as Lindsey hiked to the north. At 2:30 p.m., Kara had covered another mile, while Lindsey had
covered another half of a mile. If x represents Lindsey's distance, in miles, from the campsite at 2:00p.m., what function could be used to
represent the area of the triangular region formed by the girls' locations and the campsite at 2:30 p.m.?
Answer:
A. f(x)=x^2+x+0.25
Step-by-step explanation:
If x represents Lindsey's distance at 2:00 PM, then 2x represents Kara's distance at 2:00 PM because she walked twice as far as Lindsey. Then adding on the values we got for 2:30 PM, we get that Kara walked a distance of 2x+1 and Lindsey walked a distance of x+0.5 at the time of 2:30 PM. Now, we know that they have formed a right triangle because we are given the directions they walked in; east and north. This allows us to use a formula for the area of a right triangle: 1/2(L x W). Plugging in our values, we get...
1/2(2x+1)(x+0.5)
which simplifies to...
1/2(2x^2+2x+0.5)
which further simplifies to...
x^2+x+0.25
which is our answer.
Answer:
A. f(x) = x^2 + x + 0.25
Step-by-step explanation:
the hypotenuse longest side of similar triangles ABC and DFA both lie on line k, as shown below. Demonstrate whether the slope of line k is constant(same) between C and D. Use the leg length short sides of triangles ABC and DFA in your answer
Answer:
Yes, The slope of the line k between C and D is constant
Step-by-step explanation:
Lets find the slope of the line K from the points AC and AD
Step1:
Slope of line K from AC (point C)
= [tex]\frac{AB}{BC}[/tex]
= [tex]\frac{1}{3}[/tex]
Step 2:
Slope of line k from AD (point D)
= [tex]\frac{DF}{A F}[/tex]
= [tex]\frac{2}{3}[/tex]
=[tex]\frac{1}{3}[/tex]
The slope of the line K from the points AC and AD are equal
kylie has a rectangular poster that has an area of 2/3 square meters. the width of the poster is 3/5 meter. what is the length of the poster?
Answer:
1 1/9 (10/9) meter
Step-by-step explanation:
area of rectangle = width x length
2/3 m² = 3/5 m x Length
Length = (2/3) / (3/5) = 10/9 = 1 1/9
Answer:
10/9
Step-by-step explanation:
Which of the following could be a solution to a system of linear equations including the line graphed below?
Select one:
A. (-2, 3)
B. (1,4)
OC. (3,0)
D.(-5,-4)
Correct answer:
D. (-5,-4)
Explanation:In order to solve this problem, let's plot each point. So, see the attached file below and keep in mind the following:
Point (-2, 3) is the red one.Point (1, 4) is the blue one.Point (3, 0) is the orange one.Point (-5, 4) is the yellow one.As you can see on the graph, only point (-5, -4) lies on the given line. Therefore, the conclusion is that this point could be a solution to a system of linear equations including the line graphed below.
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Mr. Babe used to work at a local furniture store.
This is what my answers were for these questions(If it is correct, just write a comment. But if it is incorrect, explain why in the answers box)
A. While he worked there, Mr. Babe earned 3% on how much he sells. If he sold $495 couch, how much commission did he make?
What I did:
495 x 3 = 1485
1485/100 = 14.85
B. On top of his commission, Mr. Babe made $15 per hour. He eventually got a raise with an increase of 5% per hour. After the raise, how much did he make per hour?
What I did:
495 x 5 = 2475
2475/100 = 24.75
A. Mr. Babe made a commission of $14.85
B. He makes $15.75 per hour after the raise.
Step-by-step explanation:
A. While he worked there, Mr. Babe earned 3% on how much he sells. If he sold $495 couch, how much commission did he make?
Worth of sold couch = $495
Commission = 3%
Amount of commission = 3% of total worth sold
Amount of commission = [tex]\frac{3}{100}*495[/tex]
Amount of commission = [tex]\frac{1485}{100}=\$14.85[/tex]
Mr. Babe made a commission of $14.85
B. On top of his commission, Mr. Babe made $15 per hour. He eventually got a raise with an increase of 5% per hour. After the raise, how much did he make per hour?
Amount earned per hour = $15
Increase = 5%
As the increment is on per hour amount, therefore,
Amount of increase = 5% of per hour amount
Amount of increase = [tex]\frac{5}{100}*15=\frac{75}{100} = \$0.75[/tex]
New amount per hour = Per hour amount + amount of increase
New amount per hour = 15+0.75 = $15.75
He makes $15.75 per hour after the raise.
Keywords: percent, addition
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ALGEBRA 24 POINTS
simplify?
Answer:
1200
Step-by-step explanation:
its just common sense that 2*2=4 and 10*4=40 so now all you have to do is 40*30 which its just common knowledge that 4*3=12 now just add the zeros 1200
Mandy has a 10.2-ounce container of mustard. She uses 130 of the mustard to put on her hot dog each time. How many ounces of mustard are left after she has eaten 6 hot dogs?
Answer:
fevervrv
Step-by-step explanation:
3v43gvr3r54v4bv
As per question, Mandy has a 10.02-ounce container of mustard. The required Amount of Mustard left after she has eaten 6 hot dogs is 8.16 ounce.
Given:
Mandy has a 10.2-ounce container of mustard.
She uses 1/30 of the mustard to put on her hot dog each time.
According to question, Mandy has a 10.2-ounce container of mustard.
Now, 1/30 of the mustard to put on her hot dog each time to 6 hot dogs, so weight of mustard used is calculated as,
[tex]\frac{1}{30}\times10.2\times 6=2.04\;\rm{ounce}[/tex]
So, Amount of Mustard left after eating 6 hot dogs is,
[tex]10.2-2.04=8.16\;\rm{ounce[/tex]
Therefore, the required amount of mustard left after eating 6 hot dogs is 8.16 ounce.
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Jennifer wants to rent a car for 5 days, and she's interested in the loss
damage waiver but not the collision damage waiver. If the daily rate is $45
and LDW is $65, what is her total rental cost?
Answer:
290
Step-by-step explanation:
What is the solution to the equation 5a^2 - 44 = 81
A. Plus minus 25
B. -5
C. Plus minus 5
D. Plus minus 125
Answer:
Step-by-step explanation:
5a^2 - 44 = 81
5a^2 = 81 + 44 {add 44 both the sides}
5a^2 = 125
a^2 = 125/5 {divide both sides by 5}
a^2 = 25
a^2 = 5*5
a = ±5
Answer:
Option c) is correct
ie, a=plus minus 5 or [tex]a=\pm 5[/tex]
Step-by-step explanation:
Given equation is [tex]5a^2-44=81[/tex]
To find the solution of the given equation we have to solve the equation
[tex]5a^2-44=81[/tex]
[tex]5a^2=81+44[/tex]
Now applying the algebraic sum to the terms on the right hand side of the equation
[tex]5a^2=125[/tex]
[tex]a^2=\frac{125}{5}[/tex]
Now applying the division rule
[tex]a^2=25[/tex]
Therefore [tex]a=\pm 5[/tex]
Therefore option c) is correct
ie, [tex]a=\pm 5[/tex].
is √ 4/9 a rational number
Answer:
yes
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
Recall that a rational number is a number that results from dividing 2 integers
I'm not sure if your question refers to (√4) / 9 or √(4/9), but either way both are rational numbers:
If (√4) / 9, Then,
(√4) / 9
= 2/9
Since both 2 and 9 are integers, then 2/9 is a rational number
If √(4 / 9), Then,
√(4 / 9)
= √4 / √9
= 2/3
Since both 2 and 3 are integers, then 2/3 is also a rational number
a bedroom measures 13.62 feet long and 11.5 feet wide. what is the most accurate measure of the area of the bedroom, in square feet?
Answer:
156.63 Square feet
Step-by-step explanation:
Final answer:
The area of a bedroom that is 13.62 feet by 11.5 feet is 156.63 square feet, found by multiplying the length by the width.
Explanation:
The most accurate measure of the area of a bedroom that measures 13.62 feet long and 11.5 feet wide is calculated by multiplying the length by the width. The formula for the area of a rectangle is:
Area = length × width
Thus, the area is:
Area = 13.62 feet × 11.5 feet = 156.63 square feet
This calculation ensures that you have the most accurate measure of the square footage necessary, for example, if you are planning to replace the carpet or perform other renovations that require an accurate measure of the room's floor space.
Two step equations
-5n+8=-7
a 45-45-90 right triangle is formed when a ____ is cut in half
A 45-45-90 right triangle is formed when a square is cut in half diagonally. This forms two such right triangles, where the sides are in a specific ratio, with the length of the hypotenuse being root 2 times the length of each leg.
Explanation:A 45-45-90 right triangle is formed when a square is cut in half. This is because when you draw a diagonal on a square, the angles it forms with the sides are all 45 degrees, and the angles at the vertices remain 90 degrees. Therefore, it forms two 45-45-90 right triangles.
In a 45-45-90 triangle, the sides are in a specific ratio. The length of the hypotenuse is root 2 times the length of each leg, which are equal in measure because it is an isosceles triangle. These properties are unique to 45-45-90 right triangles.
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What are the domain and range of the function f(x)=(√x-7)+9?
Answer:
the domain of the function f(x) is [tex]x\ge 7[/tex]
the range of the function f(x) is [tex]f(x)\ge 9[/tex]
Step-by-step explanation:
Consider the parent function [tex]y=\sqrt{x}.[/tex]
The domain og this function is [tex]x\ge 0,[/tex] the range of this function is [tex]y\ge 0.[/tex]
The function [tex]f(x)=\sqrt{x-7}+9[/tex] is translated function [tex]y=\sqrt{x}[/tex] 7 units to the right and 9 units up, so
the domain of the function f(x) is [tex]x\ge 7[/tex]
the range of the function f(x) is [tex]f(x)\ge 9[/tex]
Answer:
C
Step-by-step explanation:
Just took quiz
What is the simplified form of 100x36 ?
Answer:
36
100x
Step-by-step explanation:
Answer: I believe 1036 ur welcome :)
The midpoint of AB is (3,-5).
A = (9,4)
What are the coordinates of point B?
Give your answer in the form (x,y).
Answer:
(-3, -14)
Step-by-step explanation:
the difference between 9 and 3 is 6 so subtract 6 from 3 to get negative 3. the difference between 4 and - 5 is 9 so subtract 9 from -5
Find the unit rate. Please and thank you.
Answer:
(20-10)/(4-2)= 10/2= 5 miles/day
The unit rate in this case is the miles travelled per day.
2 days = 10 miles
1 day = 5 miles
answer: 5 miles/day
If g (x) = StartFraction x + 1 Over x minus 2 EndFraction and h(x) = 4 – x, what is the value of (g circle h) (negative 3)?
Answer:
[tex]\frac{8}{5}[/tex]
Step-by-step explanation:
Given that [tex]g(x) = \frac{x + 1}{x - 2}[/tex] and h(x) = 4 - x
Now, if y = f(x) and y = g(x) then the composite function (f∘g)(x) is given by f[g(x)].
Hence, (g∘h)(x) = [tex]g[h(x)] = \frac{(4 - x) + 1}{(4 - x) - 2} = \frac{5 - x}{2 - x}[/tex] .......... (1)
Now, from equation (1) we get,
(g∘h)(x) = [tex] \frac{5 - x}{2 - x}[/tex]
⇒ (g∘h)(- 3) = [tex]\frac{5 - ( - 3)}{2 - ( - 3)} = \frac{8}{5}[/tex] (Answer)
Answer:
The answer is 8/5
Step-by-step explanation:
Katy makes 48 cookies an hour. If she has 24 alr, how long would it take her to make 120?
Question:
Katy makes 48 cookies an hour. If she has 24 already, how long would it take her to make 120?
Answer:
It takes 2.5 hours for Katy to make 120 cookies
Step-by-step explanation:
Given:
Time taken to make 48 cookies = 1 hour
To Find:
Time taken to make 120 cookies = ?
Solution:
Time taken to make 48 cookies = i hour
So now time taken to make 1 cookie = [tex]\frac{1}{48} hour[/tex]
So time taken to make 120 cookies
= Number of cookies X time taken to make one cookie
=>[tex]120 \times \frac{1}{48}[/tex]
=>[tex] \frac{120}{48}[/tex]
=> 2.5 hours
Convert to standard form 25x^2 + 4y^2 - 50x -75 = 0
Answer:
[tex]\frac{(x-1)^{2}}{4}+\frac{y^{2}}{25}=1[/tex]
Step-by-step explanation:
we have
[tex]25x^{2}+4y^{2}-50x-75=0[/tex]
Convert to standard form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex](25x^{2}-50x)+4y^{2}=75[/tex]
Factor the leading coefficient of each expression
[tex]25(x^{2}-2x)+4y^{2}=75[/tex]
Complete the square twice. Remember to balance the equation by adding the same constants to each side.
[tex]25(x^{2}-2x+1)+4y^{2}=75+25[/tex]
[tex]25(x^{2}-2x+1)+4y^{2}=100[/tex]
Rewrite as perfect squares
[tex]25(x-1)^{2}+4y^{2}=100[/tex]
Divide both sides by the constant term to place the equation in standard form
[tex]\frac{25(x-1)^{2}}{100}+\frac{4y^{2}}{100}=\frac{100}{100}[/tex]
Simplify
[tex]\frac{(x-1)^{2}}{4}+\frac{y^{2}}{25}=1[/tex]
Paul is looking at two vacation packages while planning a trip to Cancun, Mexico. In the first vacation package, round-trip airfare costs $799, and it costs $139 per night to stay at the resort. In the second vacation package, it costs $587 per night to stay in the resort and $285 for round-trip airfare. Let x represent the number of nights spent at the resort, and let y represent the total cost of the trip. Which system of equations could be used to find how many nights Paul needs to stay at either resort so that both vacation packages have the same cost? A. B. C. D.
Answer:
y = 139x + $ 799
y = 587x + $ 285
Step-by-step explanation:
Let x represent the number of days spent at the resort and y represent the total cost.
for the first option
y = 139x + $799 since $ 139 is the amount per night at the resort, $139x must be the cost for x number of days
y = 587x + $285 similarly x number of days should equal $587x
a line with a slope of 10 passes through the point 0,2. what is the equation in slope intercept form
Answer:
y=10x+2
Step-by-step explanation:
y-y1=m(x-x1)
y-2=10(x-0)
y-2=10(x)
y-2=10x
y=10x+2