If the knowledge that an event "a" has occurred implies that another event "b" cannot occur, then the events "a" and "b" are said to be disjoint events.
As per the question statement, the knowledge that an event "a" has occurred implies that another event "b" cannot occur.
We are required to determine the characteristic name for the above mentioned events.
Now as per the Probability Theory in Mathematics, two events are said to be "mutually exclusive" or "disjoint" if they cannot occur at the same time or simultaneously.And here, if event "a" occurs, even "b" does not, implying the fact that, events "a" and "b" cannot occur simultaneously. Hence, as per the above definition of disjoint events, the events "a" and "b" are be disjoint.
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Find an angle in each quadrant with a common reference angle with 41°, from 0°≤θ<360°
The angles in each of the four quadrants with a common reference to the acute angle 41° are as follows;
For 2nd quadrant; 139°.For 3rd quadrant; 221°.For 4th quadrant; 319°.Which angles in each quadrant have a common reference angle with 41°?It follows from the task content that the angles which have a common reference to the angle 41° in each quadrant he determined.
On this note, the angles can be determined from custom formulas for reference angles in each quadrant as follows;
For 2nd quadrant; θ = (180 - θ) = (180 - 41) = 139°.For 3rd quadrant; θ = (180 + θ) = (180 + 41) = 221°.For 4th quadrant; θ = (360 - θ) = (360 - 41) = 319°.Ultimately, the angles in each quadrant with a common reference alongside 41° are; 139°, 221° and 319°.
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The length of a rectangular billboard is 9 meters more than the width. If the perimeter is 42 meters find the dimensions.
Given, the perimeter of the rectangular billboard, P=42 m.
The length of the rectangular billboard is 9 m more than the width.
Let l be the length and w be the width of the rectangular billboard.
Then, the length can be expressed as,
[tex]l=9+w[/tex]The perimeter of a rectangle can be expressed as,
[tex]P=2(l+w)[/tex]Now, put l=9+w and P=42 m in the above equation to find w.
[tex]\begin{gathered} 42=2(9+w+w) \\ \frac{42}{2}=9+2w \\ 21=9+2w \\ 21-9=2w \\ 12=2w \\ \frac{12}{2}=w \\ 6m=w \end{gathered}[/tex]Hence, the length is,
[tex]\begin{gathered} l=9+w \\ l=9+6 \\ l=15\text{ m} \end{gathered}[/tex]Therefore, the length of the rectangular billboard is 15 m and the width of the rectangular billboard is 6 m.
Not sure what to do here.
The trigonometric ratios of the right triangle are as follows:
sin E = 12 / 13cos E = 5 / 13tan E = 12 / 5sin F = 5 / 13cos F = 12 / 13tan F = 5 / 12How to find the angles of right triangle?A right triangle is a triangle that has one of its angles as 90 degrees.
The side and angles of a right triangle can be solved using trigonometric ratios.
The ratios of the sides of a right triangle are called trigonometric ratios.
A right angle triangle has the opposite side, adjacent side and hypotenuse side depending on the angles location.
Using ratios,
sin ∅ = opposite / hypotenuse
cos ∅ = adjacent / hypotenuse
tan ∅ = opposite / adjacent
Therefore,
sin E = 12 / 13cos E = 5 / 13tan E = 12 / 5sin F = 5 / 13cos F = 12 / 13tan F = 5 / 12learn more on right triangle here: https://brainly.com/question/15284655
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a random sample of size is selected from a population with . a. what is the expected value of (to decimals)? b. what is the standard error of (to decimals)? c. show the sampling distribution of . (to decimals) (to decimals) d. what does the sampling distribution of show? - select your answer -
a. The expected value is 0.40
b. The standard error is 0.0024
Given that:
Sample size, n=100
Population proportion, p=0.40
a) The expected value of the sample proportion is defined as:
E(^p)=p
now,
E(^p)=0.40
b) The standard error of the sample proportion is defined as:
SE(^p) = √p(1-p)/n
SE(^p) = √0.40(1-0.40)/100
SE(^p) = 0.0024
c) The sampling distribution of the sample proportion is normally distributed with the expected value of the sample proportion of 0.40.
Therefore,
E(^p) = 0.40
d) The central limit theorem states that the sample statistic (sample proportion) tends to the population parameter (population proportion) as the sample size tends to infinity (OR n→∞).
^P~N(p, p(-p)/n) as n→∞
Hence we get the required answers.
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how many packages of diapers can you buy with 40$ if one packages cost 8$. this is a one step equation
In order to determine how many packages of diapers you can buy, it is only necessary to divide the total money you have, between the price of each package.
You have:
available money = 40$
package cost = 8$
Then, you calculate the quotient between available money and package cost:
[tex]\frac{40}{8}=5[/tex]Hence, you can buy 5 packages of diapers with 40$
The number of bacteria in a culture triples every 3 hours. If there were 2 bacteria present at noon one day, how many were there at noon the next day assuming that all bacteria survived?
use lagrange multipliers to prove that the rectangle with maximum area that has a given perimeter p is a square. let the sides of the rectangle be x and y and let f and g represent the area (a) and perimeter (p), respectively. find the following.
we get x=y =0 which gives 0 perimeter or x=y this implies rectangle must be a square
1. Method of Langrage Multipliers:
To find the extremum values of f(x,y) subject to constraint g(x,y) = k
find all values of x,y and λ, such that :
Δλ(f,x) = λΔg(x,y)
And g(x,y) = k
2. let the two side of the rectangle be x and y
therefore
f(x,y) = xy And g(x,y)= 2(x+y)=p
fₓ=λgₓ => y=2λ ----------------- 1
fy = λgy => x = 2λ----------------2
using equation and 1 and 2
λ=0, but this is not possible because tis implies x = y = 0, which gives 0 perimeter
or
x=y
Hence the rectangle must be a square
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What is x/3 + 6 - 2x = -6?
Answer: 7.5
Step-by-step explanation: 2 x 7.5 = 15
3 + 6 - 15
9 -15
-6
Mr. Charles drinks 8 glasses of water each day. Each glass contains 240ml. How many
millimeters of water does he drink in a week?
Answer:
13440ml a week
Step-by-step explanation:
8x240=1920
1920x7=13440
13440is the amount of mls a week
Answer:
13440ml
Step-by-step explanation:
8 x 240 = 1920ml (per day)
(8 x 240) x 7 = 13440ml (7 days = 1 week)
EASY! SHAPES! (points, brainliest, stars)
How many units the function y = |x| - 3 is translated from the parent function?3 units upwards from the origin3 units downwards from the origin3 units left from the origin3 units right from the origin
From the expression we can see that it is translated 3 units downwards from the origin.
LaTanya buys 6 yards of blue fabric and 9 yards of green fabric. The blue fabric costs $2 more per yard than the green fabric. She pays a total of $57. What would be the combined cost of 1 yard of blue fabric and yard of green fabric?
The price of 1 yard of blue fabric and 1 yard of green fabric is obtained by solving the system of linear equations and it is $8
Let
x = price of blue fabric per yard
y = price of green fabric per yard
"The blue fabric costs $2 more per yard than the green fabric" means:
x = y + 2 (Equation 1)
" LaTanya buys 6 yards of blue fabric and 9 yards of green fabric and pays $57" means:
6x + 9y = 57 (Equation 2)
Substitute equation 1 into equation 2:
6x + 9y = 57
6 (y + 2) + 9y = 57
6y + 12 + 9y = 57
15 y = 45
y = 3
Substitute y = 3 into equation 1
x = 3 + 2 = 5
Hence, the price of blue fabric is $5 per yard while the green fabric is $3 per yard.
The price of 1 yard of blue fabric and 1 yard of green fabric = x + y = 3 + 5 = $8
Complete question:
LaTanya buys 6 yards of blue fabric and 9 yards of green fabric. The blue fabric costs $2 more per yard than the green fabric. She pays a total of $57. What would be the combined cost of 1 yard of blue fabric and 1 yard of green fabric?
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Noah wants to sign up for a streaming service. Company A charges a one-time fee of $10 and a costs $6 per month. Company B charges a one-time fee of $20 and costs $3 per month. If x represents the number of months using the service and y represents the total cost of the service, which system of equations represent this situation?
Albert invested money into the stock market, and the table represents his earnings. What type of function could be used to model his bank account as a function of time? Justify your answer.
Week Balance ($)
1 428
2 620
3 812
4 1,004
This is an exponential function because there is a common difference in the balance between the weeks.
This is an exponential function because there is a common ratio in the balance between the weeks.
This is a linear function because there is a common difference in the balance between the weeks.
This is a linear function because there is a common ratio in the balance between the weeks.
The correct option regarding whether this is an exponential or linear function is given as follows:
This is a linear function because there is a common difference in the balance between the weeks.
When a situation is modeled by an exponential function, and when the situation is modeled by a linear function?The function will be linear or exponential depending if there is a common difference or a common ratio between the terms, as follows:
If there is a common difference between the terms, that is, if the difference between consecutive terms is the same, a linear function models the situation.If there is a common ratio between the terms, that is, if the quotient between consecutive terms is the same, an exponential function models the situation.From the given table, the differences are given as follows:
1004 - 812 = 192.812 - 620 = 192.620 - 428 = 192.The differences are the same, hence it is a linear function and the correct option is:
This is a linear function because there is a common difference in the balance between the weeks.
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Answer:
The correct answer is (C) This is a linear function because there is a common difference in the balance between the weeks.
Step-by-step explanation:
The person up top is correct
Each student read 41 pages in December How many total pages did the students read by the end of December? and there are
27 students!
data:
september: chapter 1, 35 pages.
october: chapter 2, 38 pages
november: chapter 3, 35 pages
december: 41 pages.
total 4023 pages the 27 students read by the end of December
Step-by-step explanation:
35 + 38+35+41 = 149
27 students
149 × 27
4023 pages 27 students reads in this given four month
If a polynomial f(x) has a remainder of 8 when divided by x-4, what is f(4)?
f(4) =
Answer: [tex]f(4)=8[/tex]
Step-by-step explanation:
The Remainder Theorem states, "If a polynomial [tex]p(x)[/tex] is divided by the binomial [tex]x-a[/tex], the remainder obtained is [tex]p(a)[/tex]."
In this case, we are given the polynomial [tex]f(x)[/tex], and the polynomial [tex]f(x)[/tex] is divided by the binomial [tex]x-4[/tex]. If you were to plug in [tex]4[/tex] for [tex]x[/tex] in [tex]f(x)[/tex], you would get [tex]f(4)=8[/tex] as a result of the binomial theorem.
PLEASEEEEEEEE HELPpppppppp
As per the distance concept, the speed of the buses are 79 km/h and 69km/h if the two buses leave a station at the same time and travel in opposite directions.
Distance
Distance refers the physical length or an approximation based on other physics or common usage considerations.
Given,
Two buses leave a station at the same time and travel in opposite directions. One bus travels 10 slower than the other. If the two buses are 276 miles apart after 2 hours,
Here we need to find the rate of each bus.
Let us consider the speed of the first bus is x km/h.
Then the speed of the other bus = (x - 10) km/h
We know the formula of distance is,
Distance = time × speed
When we combined speed then we get,
=> x + x - 10 = (2x - 10) km/h
=> 2(2x - 10) =276
When we expand the equation, then we get,
4x - 40 = 276
4x = 316
After calculating,
x = 79 km/h
The speed of first bus x = 79 km/h
Speed of the second bus = x - 10 = 79 - 10 = 69 km/h
Therefore, the speed of the buses are 79 km/h and 69/km/h if the two buses leave a station at the same time and travel in opposite directions.
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Rachel got a prepaid debit card with $30 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 21
cents per yard. If after that purchase there was $20.97 left on the card, how many yards of ribbon did Rachel buy?
43 yards because she spent 9.03 cents on ribbon 9.03 divided by 0.21=43
11. Find the area of the shaded region. Each square is 1 cm wide.
Answer:[tex]26cm^{2}[/tex]
Step-by-step explanation: To do this you have to dissect the shapes into singular shapes.
First, you do the parallelogram at the bottom. 4×2
Then the middle rectangle. 3×4
Then the triangle at the top. 4×3÷2
Area= [tex]26m^{2}[/tex]
A large gym with hundreds of members offers yoga classes. Members are free to take these
classes at no charge, but not all members are interested, and some never take advantage of the
yoga classes. Non-members can also take these classes, but they must pay a fee for each class.
A manager at the gym is curious about overall satisfaction with these yoga classes, so they
survey a large random sample of anyone who has taken a yoga class at the gym in the past year.
They find that 78% of those surveyed are "very satisfied" with the yoga classes.
For which population is 78% a legitimate estimate of the percent of people that are "very
satisfied" with the yoga classes?
Choose 1 answer:
only those surveyed
All members who have taken a yoga class at the gym in the past year, but not non-
members
All non-members who have taken a yoga class at the gym in the past year, but not
members
anyone who has taken a yoga class at the gym in the past year but not before that
anyone who has ever taken a yoga class at the gym
The population for which 78% is a legitimate estimate of the percent of people that are 'very satisfied" with the yoga classes is C. anyone who has taken a yoga class at the gym in the past year but not before that.
What is an estimate?An estimate is a rough calculation that may not be based on real figures or it may be based on rounded-off or appropriated facts and figures.
Estimates enable the decision-maker to make a quick guess or decision that cannot wait for all the facts to be collected.
Thus, the population of interest for the estimate includes members and non-members who have participated.
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Answer:
D
Step-by-step explanation:
State whether the Law of Detachment, the Law of Syllogism, or the Law of the
Contrapositive was used to draw the conclusion from the given statements. If it's an
invalid conclusion, write invalid.
If you go fishing, then you will need to bring your fishing rod.
If you go fishing, then you will need to bring bait.
Therefore, if you bring your fishing rod, then you will need to bring bait.
Law of Detachment
Law of Syllogism
Law of Contrapositive
Invalid Conclusion
The statement can be described as an Invalid Conclusion.
What is an invalid conclusion?An invalid conclusion arises from a series of statements where the premises are true but the conclusion is not true. The premises in the statements above are all true.
For instance, it is true that if you go fishing you will need a rod. It is also true that if you go fishing you will need bait. But there is no laid down rule that if you bring your fishing rod, you will also need to bring a bait. So, this is an invalid conclusion.
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Solve the following problem using substitution or elimination method.
Two rental car companies are running specials this month. At Johnson’s Rentals, customers will pay $50 to rent a mid-sized car for the first day, plus $2 for each additional day (x). At Martinez Rent-a-Car, the price for a mid-sized car is $30 for the first day and $4 for each additional day (x). How many additional days (x) would it cost the same to rent from either company? What is that cost?
Let x represent the number of additional days you will rent a car and y represent the total cost of renting the car. Write a system to represent the situation, and solve to answer the question.
a) 10 additional days are required for both to cost the same.
b) The cost is 70$.
At Johan's Rental:
Rent= (50+2x)$
At Martinez Rent:
Rent= (30+4x)$
For both the cost same
By using Elimination method,
50+2x = 30+4x
50-30 = 4x-2x
20 = 2x
x = 10
10 additional days are required for both to cost the same.
Cost = 50+2x
= 50+2*10
=50+20
=70.
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64 pens cost £5.76.
How much would 80 of these pens cost?
Answer: £7.20
Step-by-step explanation: £5.76/64 = £0.09 So one pen is £0.09. If you need 80, then £0.09 x 80 = £7.20
Ratio and rates pls help me
Answer:
Step-by-step explanation:
5 parts blue
yellow: 3 parts
WE SHOULD HAVE DONE EQUAL COLOURS FOR A GOOD RESULT?
What is the slope of the line on the graph
Answer:
Slope = (6/1) or 6
Step-by-step explanation:
(0, -1), (1, 5)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 5 - (-1) 5 + 1 6
m = ------------- = ------------- = ---------- = -------
x₂ - x₁ 1 - 0 1 1
y - y₁ = m(x - x₁)
y - (-1) = 6(x - 0)
y + 1 = 6x - 0
-1 -1
-----------------------
y = 6x - 1
I hope this helps!
12. Write the equation of a line that is perpendicular to y = -x - 6 that goes through
the point (3,-8).
Answer:
y = x - 11
Step-by-step explanation:
Help I neee help asap
Based on the information given, below statements are true
A. Feldman & Sons have a greater hourly rate.
B. The graph of the function for Strong Arm Movers has a greater y-intercept than the graph of the function for Feldman & Sons.
Feldman and Sons have a higher hourly rate or slope (35 compared to 25), but Strong Arm. Movers have a higher y-intercept (50 compared to 30). Feldman and Sons charge more than Strong Arms for both 3-hour and 2.5-hour transfers.
Explain about movers and packers ?Movers is an organization that helps people pack and move their belongings from one place to another. They take full responsibility for the items we have asked them to move and they also offer refunds if anything is broken or lost. That's what packers and movers mean. Movers and packers pack goods. Material load. Movement of goods and unloading of goods.
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the height, h meters, of a certain species of fir tree can be estimated from the formula h=35d2/3, where d meters is the diameter at the base. What is the approximate height of a fir tree with a base diameter of 3.2m
The approximate value of the height f the tree when the base diameter is 3.2 meters is 119.47 meters
How to approximate the height of the fir tree?From the question, the equation of the function of height is given as
h = 35d²/3
Also from the question, we have the base diameter of the fir tree to be
d = 3.2m
Next, we substitute 3.2 for d in the equation of the function of height given as
h = 35d²/3
So, we have the following equation:
h = 35 x 3.2²/3
Evaluate the exponent
So, we have
h = 35 x 10.24/3
Evaluate the product
So, we have the following equation:
h = 358.4/3
Evaluate the quotient
This gives
h = 119.47
Hence, the height is 119.47 meters
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A food truck sells Mongolian ginger bowls for $14 per bowl. At a festival, 132 bowls are sold. About how much money does the food truck collect?
The table below shows the average price of a Miami Marlins baseball ticket between 2006 and 2021.
The equation y=1.67x−3338.5 models this relationship, where x is the year and y is the average ticket price.
Use the model to predict the ticket price for a Miami Marlins baseball ticket in 2030.
$=
By evaluating the equation in x = 2030, we can estimate the price to be $51.60.
How to use the model?We know that the equation:
y = 1.67*x - 3338.5
Models the relationship between the year, x, and the average ticket price of a Miami Marlins baseball ticket.
We know that this relationship works for the years 2006 to 2021, but can be used to estimate the price for years after and before that.
if we use x = 2030, we will get:
y = 1.67*2030 - 3338.5 = 51.6
This will be the price, in dollars, of a game in the year 2030.
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