A bag contains 4 red marbles, 3 white marbles, and 7 blue marbles. You pick a marble without looking. What is the probability of drawing a white marble.
Answers
Answer:
3/14
Step-by-step explanation:
You add all the marbles to get your total/denominator then take the white marbles and that is the numorator.
Related Questions
The probability that Sara wins a raffle is given by the expression n/n+3
Write down an expression, in the form of a combined single fraction, for the probability that Sara does not win.
Answers
Answer:
3/(n + 3)
Step-by-step explanation:
The given probability that Sara wins a raffle draw, P = n/(n + 3)
Given that the sum of all probabilities is 1, we get
The probability that Sara does not win, Q = 1 - P
Therefore;
Q = 1 - n/(n + 3) = (n + 3) - n/((n + 3) = 3/(n + 3)
The probability that Sara does not win, Q = 3/(n + 3)
Show if (Ω, ℬ([0,1]),P) is a Probability space.
if
A = (a,b)
P(A) = b-a
Ω = [0,1]
Answers
The triplet (Ω, ℬ([0,1]), P) is a probability space if certain conditions for the same are met.
To determine if (Ω, ℬ([0,1]), P) is a probability space, we need to check if the conditions for a probability space are satisfied:
Sample Space Ω: The sample space Ω is given as [0,1], which is a valid set.
Sigma-Algebra ℬ([0,1]): The sigma-algebra ℬ([0,1]) should contain the sample space Ω and satisfy certain properties. In this case, ℬ([0,1]) is the Borel sigma-algebra on the interval [0,1], which is the smallest sigma-algebra containing all the open intervals in [0,1]. It is a valid sigma-algebra.
Probability Measure P: The probability measure P assigns probabilities to subsets of Ω. In this case, P(A) is defined as b - a for the interval (a, b). It satisfies the properties of a probability measure, such as being non-negative and assigning a probability of 1 to the entire sample space.
Therefore, based on the given information, (Ω, ℬ([0,1]), P) can be considered a probability space as it satisfies the conditions of having a valid sample space, sigma-algebra, and probability measure.
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Find the sum of the geometric series
1+1.2 + 1.22 +1.23 + ... +1.274
Answers
Answer:
5.924 I may be wrong though sorry
Step-by-step explanation:
I hope I could help you! (:
Ok so I messed up big time I’m so sorry I don’t understand
Let X and Y be two random variables with joint probability density function: f(x,y)={ 3y
0
If 0
otherwise
1. Justify that f is a density probability function 2. Find the conditional density function of X given Y=y 3. Find the marginal density function of X and Y 4. Calculate E(X∣Y=y) when 0
Answers
The function f is a density probability function because it satisfies all the properties of a probability density function. The conditional density function of X given Y=y is 3y/y^2, and the marginal density function of X is 3/2. The expected value of X given Y=y is y/2.
A probability density function (pdf) is a function that assigns a probability to each possible value of a random variable. A pdf must satisfy the following properties:
It must be non-negative for all possible values of the random variable.
The integral of the pdf over the entire range of the random variable must be equal to 1.
The function f(x,y) satisfies both of these properties. First, it is non-negative for all possible values of x and y. Second, the integral of f(x,y) over the entire range of x and y is equal to 1: ∫∫f(x,y)dxdy = ∫∫3y0dxdy = ∫013ydy = 3
Therefore, f(x,y) is a density probability function.
The conditional density function of X given Y=y is the probability density function of X given that Y is equal to y. It can be found by conditioning f(x,y) on Y=y: f(x|y) = P(X=x|Y=y) = ∫f(x,y)dy
In this case, f(x|y) is equal to 3y/y^2.
The marginal density function of X is the probability density function of X without considering the value of Y. It can be found by integrating f(x,y) over the entire range of y: f(x) = P(X=x) = ∫f(x,y)dy
In this case, f(x) is equal to 3/2.
The expected value of X given Y=y is the mean of X when Y is equal to y. It can be found by integrating x*f(x|y) over the entire range of x:
E(X|Y=y) = ∫xf(x|y)dx = ∫01xy3y/y^2dx = y/2
Therefore, the expected value of X given Y=y is y/2.
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2(c-5) - 3
What is the answer?
Answers
Step-by-step explanation:
2 · c - 5 · 2 - 3 = 2c - 10 - 3
2c - 10 - 3 = 2c - 7
PLEASE HELP ME IM BEGGING YOU
Answers
Answer:
A: 2x-1
Step-by-step explanation:
Graph it. if you plug in the x and y of (1,1)
1= 2(1)-1
1=2-1
correct
Answer: A
Step-by-step explanation:
Since we are given the slope, all we have to do is use the given point to find the y-intercept.
y=2x+b [plug in (1,1)]
1=2(1)+b [multiply]
1=2+b [subtract both sides by 2]
b=-1
Now, we know the equation is y=2x-1.
A generation company owns three generating units that have the following cost functions: Unit 1: 5000+215P 1 +0.5P 1 2 [c/h] Unit 2: 5000+270P 2 +1.0P 2 2 [C/h] Unit 3:9000+160P 3 +0.7P 3 2 [C/h] The output Power of each unit is limited as follows: For unit 1: min=50MW,max=130MW For unit 2:min=39MW,max=128MW For unit 3:min=40MW,max=149MW a) How should these units be dispatched if the company wants to supply a load of 200MW at minimum cost? step-by-step calculation is required. b) How would the dispatch change if the company had the opportunity to buy some of this energy on the spot market at the price of 300 d/MWh and 220c/MWh, respectively? note: for both scenarios, please include clear calculation and workout.
Answers
a) The combination of units that results in the minimum cost to supply a load of 200MW is Combination 1, with Unit 1 generating 130MW, Unit 2 generating 39MW, and Unit 3 generating 31MW. b) the optimal dispatch remains the same as before, which is Combination 1: Unit 1 generating 130MW
a) To determine how the units should be dispatched to supply a load of 200MW at minimum cost, we need to compare the costs of operating each unit within their respective output limits.
Unit 1 cost calculation:
At minimum output (50MW):
Cost = 5000 + 215P + 0.5P^2
= 5000 + 215(50) + 0.5(50^2)
= 5000 + 10750 + 0.5(2500)
= 5000 + 10750 + 1250
= 17000 + 1250
= 18250 [C]
At maximum output (130MW):
Cost = 5000 + 215P + 0.5P^2
= 5000 + 215(130) + 0.5(130^2)
= 5000 + 27950 + 0.5(16900)
= 5000 + 27950 + 8450
= 32950 + 8450
= 41400 [C]
Unit 2 cost calculation:
At minimum output (39MW):
Cost = 5000 + 270P + 1.0P^2
= 5000 + 270(39) + 1.0(39^2)
= 5000 + 10530 + 1.0(1521)
= 5000 + 10530 + 1521
= 16051 [C]
At maximum output (128MW):
Cost = 5000 + 270P + 1.0P^2
= 5000 + 270(128) + 1.0(128^2)
= 5000 + 34560 + 1.0(16384)
= 5000 + 34560 + 16384
= 55944 [C]
Unit 3 cost calculation:
At minimum output (40MW):
Cost = 9000 + 160P + 0.7P^2
= 9000 + 160(40) + 0.7(40^2)
= 9000 + 6400 + 0.7(1600)
= 9000 + 6400 + 1120
= 16520 [C]
At maximum output (149MW):
Cost = 9000 + 160P + 0.7P^2
= 9000 + 160(149) + 0.7(149^2)
= 9000 + 23840 + 0.7(22201)
= 9000 + 23840 + 15540.7
= 48380.7 [C]
To supply a load of 200MW at minimum cost, we need to determine the combination of units that results in the lowest total cost.
To find the optimal dispatch, we'll compare the costs of different combinations:
Combination 1: Unit 1 = 130MW, Unit 2 = 39MW, Unit 3 = 31MW
Total cost = Cost(Unit 1) + Cost(Unit 2) + Cost(Unit 3)
= 41400 + 16051 + 16520
= 73971 [C]
Combination 2: Unit 1 = 130MW, Unit 2 = 39MW, Unit 3 = 40MW
Total cost = Cost(Unit 1) + Cost(Unit
2) + Cost(Unit 3)
= 41400 + 16051 + 16520
= 73971 [C]
Combination 3: Unit 1 = 130MW, Unit 2 = 39MW, Unit 3 = 41MW
Total cost = Cost(Unit 1) + Cost(Unit 2) + Cost(Unit 3)
= 41400 + 16051 + 18307.7
= 75758.7 [C]
Based on these calculations, the combination of units that results in the minimum cost to supply a load of 200MW is Combination 1, with Unit 1 generating 130MW, Unit 2 generating 39MW, and Unit 3 generating 31MW.
b) If the company has the opportunity to buy energy on the spot market at the price of 300 d/MWh and 220 c/MWh, respectively.
To determine the new dispatch, we compare the costs of operating the units with the market prices:
Unit 1 cost with spot market price: 300 d/MWh
Cost = 5000 + 215P + 0.5P^2
= 5000 + 215(300) + 0.5(300^2)
= 5000 + 64500 + 0.5(90000)
= 5000 + 64500 + 45000
= 114500 [C]
Unit 2 cost with spot market price: 220 c/MWh
Cost = 5000 + 270P + 1.0P^2
= 5000 + 270(220) + 1.0(220^2)
= 5000 + 59400 + 1.0(48400)
= 5000 + 59400 + 48400
= 112800 [C]
Unit 3 cost with spot market price: 220 c/MWh
Cost = 9000 + 160P + 0.7P^2
= 9000 + 160(220) + 0.7(220^2)
= 9000 + 35200 + 0.7(48400)
= 9000 + 35200 + 33880
= 78080 [C]
To determine the new optimal dispatch, we compare the costs considering the spot market prices:
Combination 1: Unit 1 = 130MW, Unit 2 = 39MW, Unit 3 = 31MW
Total cost = Cost(Unit 1) + Cost(Unit 2) + Cost(Unit 3)
= 114500 + 112800 + 78080
= 305380 [C]
Combination 2: Unit 1 = 130MW, Unit 2 = 39MW, Unit 3 = 40MW
Total cost = Cost(Unit 1) + Cost(Unit 2) + Cost(Unit 3)
= 114500 + 112800 + 78080
= 305380 [C]
Combination 3: Unit 1 = 130MW, Unit 2 = 39MW, Unit 3 = 41MW
Total cost = Cost(Unit 1) + Cost(Unit 2) + Cost(Unit 3)
= 114500 + 112800 + 79912
= 307212 [C]
Based on these calculations, even with the spot market prices, the optimal dispatch remains the same as before, which is Combination 1: Unit 1 generating 130MW.
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PLZZZZZZ HURRRRYYYYY Why did Allan Bakke file a lawsuit? His medical test application was incorrectly scored. He was an advocate of affirmative action. His test scores were lower than minority students. He felt he was denied admission to school based on race.
Answers
Answer: The answer is D
Allan Bakke filed a lawsuit because he felt he was denied admission to school based on race.
What is a Lawsuit?This is defined as a case in a court of law which concerns a dispute between two people or organizations.
Allan Bakke was a White and his score was higher than some minority applicants and was denied admission which made him sue the school, University of California. The case led to desegregation in all public schools thereby making option D the most appropriate choice.
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Work out, giving your answer in its simplest form:
4/7 / 2 1/3
Answers
Answer:
4
Step-by-step explanation:
4/7 × 21÷3
4/7×7
=4
this is the answer ....thank you
a party has a ratio of men to women as 8:13.Two more men join, 5 women leave. The new ratio then becomes 7:10..find the original number of people in the party both men and women?
Answers
Answer:
revenge time
Step-by-step explanation:
Adrian bought a car worth $12000 on 36 easy installments of $375. Answer the following questions. (1) How much total amount did Adrian pay in 36 months? Answer: Total payment A = $ (2) Identify the letters used in the simple interest formula I = Prt. I= $ P= $ and t years. (3) Find the rate of interest in percentage. Answer: r %. ASK YOUR TEACHER
Answers
3) since we don't have the information about the interest paid (I), we cannot determine the rate of interest at this time.
(1) To find the total amount Adrian paid in 36 months, we can multiply the monthly installment by the number of installments:
Total payment A = Monthly installment * Number of installments
= $375 * 36
= $13,500
Therefore, Adrian paid a total of $13,500 over the course of 36 months.
(2) In the simple interest formula I = Prt, the letters used represent the following variables:
I: Interest (the amount of interest paid)
P: Principal (the initial amount, or in this case, the car worth)
r: Rate of interest (expressed as a decimal)
t: Time (in years)
(3) To find the rate of interest in percentage, we need more information. The simple interest formula can be rearranged to solve for the rate of interest:
r = (I / Pt) * 100
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Can someone please help me
p.s. round to the nearest tenths
Answers
Answer:
Apothem:
radius is the same length as the base/length of each side of the hexagon.
r = 8
use pythagorean theorem to calculate the apothem
\(4^2+a^2=8^2\\\\16+a^2=64\\\\a^2=48\\\\a= 6.928\)
≈ 6.9
Area
\(A = \frac{3\sqrt{3} }{2} *a^2\\\\=\frac{3\sqrt{3} }{2}(6.928)^2\\\\=124.7\)
Find the coordinate of the midpoint of a segment with the endpoints (5,11) and (3,1)
Answers
Answer:
(1,5)
Step-by-step explanation:
You can use the midpoint formula: \(\frac{ChangeInX}{2} ,\frac{ChangeInY}{2}\)
So, the Change In X is: 5 - 3= 2
And the Change in Y is: 11 - 1 = 10
Once you divide both of the changes by 2, you get
X: 1
Y: 5
So the midpoint is: (1,5)
is the statement true or false: in a left skewed distribution, the median tends to be higher than the mean. group of answer choices true false
Answers
True . In this distribution, the mean salary is lower than the median salary because the few employees who earn a very high salary pull the mean towards the left.
In a left-skewed distribution, the tail of the distribution is longer on the left-hand side, which means that there are more values on the left side of the distribution that are lower than the mean. This pulls the mean towards the left, making it lower than the median. Therefore, the median tends to be higher than the mean in a left-skewed distribution.
When we talk about the shape of a distribution, we refer to the way in which the values are spread out across the range of the variable. A left-skewed distribution is one in which the tail of the distribution is longer on the left-hand side, which means that there are more values on the left side of the distribution that are lower than the mean. The mean is the sum of all values divided by the number of values, while the median is the middle value of the distribution. In a left-skewed distribution, the mean is pulled towards the left, making it lower than the median. This happens because the more extreme values on the left side of the distribution have a larger impact on the mean than they do on the median.
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Behold. Longest explanation for 1 + 1 I have done.
First you take the first number that you have, which is 1(one). and then you take the second number that is shown, which is also 1(one). Then you check the symbol in which what the problem is asking you to do, which is +(plus). Then, finally you can see what the problem is asking. The equation translates to: 1 + 1 (one plus one.) Plus is the symbol in which what a problem is asking you to add add two or more numbers together, so you will add 1 and 1 together. To see how to do so is you can count to get the sum. We know that the number that comes first when counting is 1, so you can begin by counting up by 1's, until you get the sum. The number that comes after 1 is 2, which so happens to be 1 number after 1, so which is what the question is asking, so therefore, 1 + 1 is equal to 2. (The sum of 1 and 1 is 2.)
No haters better delete this. This took time!
Answers
Answer:1. Let a = 1 and b = 1 .
2. Now this means that a = b .
3. If we multiply both sides by a we get a^{2} = ab .
4. If we then subtract b^{2} from both sides we would have a^{2} - b^{2} = ab - b^{2} .
5. We can then factorise both sides to get (a + b)(a - b) = b(a - b) .
6. Dividing both sides by (a - b) would give us a + b = b .
7. Substituting back the values of a = 1 and b = 1 would give us that 1 + 1 = 1 .
8. So this "proves" that 1 + 1 = 1 not 2 .
Except that in step 6, when we are dividing by a - b , we are in fact dividing by zero. This is a violation of the rules of mathematics :/ soo... Um lol...
Step-by-step explanation: this is what happens when you dont do math correct
Write a declaration for a variable rate_of_pay that can hold values like 11.50 or 12.75.
Answers
Float rate_of_pay a declaration for a variable rate_of_pay that can hold values like 11.50 or 12.75.
What is float rate_of_pay?
In contrast to fixed (or unchangeable) interest rates, floating interest rates change on a regular basis. Companies that offer credit cards and mortgages frequently use floating rates. Floating rates follow the market, a benchmark interest rate, an index, or both.Is a fixed or floating rate preferable?
In a rising rate environment, banks offer fixed rate loans at a higher rate than variable rate loans in order to profit more from the latter when rates rise. Fixed rate loans may have interest rates that are 300–350 basis points higher than floating rate loans.float rate_of_pay
rate_of_pay = 11.50, 12.75;
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Which equation matches the table? (I have a screenshot)
If I get this wrong I will lose my 57 streak :(
Answers
Answer:
b-2a
Step-by-step explanation:
this is beacuse when u find the slope u look in the chart and divide the numbers and will give u the sum of 2
8/4
8/12
12/16
Answer:
b=a+4
Step-by-step explanation:
Its a 58 streak now :)
What is the difference between an atom and an ion?
A. The number of electrons
B. The atomic mass
C. The number of neutrons
Answers
Atoms are neutral particles. Because they have an equal number of protons and electrons.
Ions are electrically charged particles that can be created by either taking electrons away from neutral atoms to form positive ions or adding electrons to neutral atoms to produce negative ions.
The quantity of protons remains constant during the formation of an ion.
In a neutral atom, there are exactly as many electrons as protons. The total number of protons and neutrons in the atom's nucleus is equal to the mass number (M) of the atom. The difference between the atomic number and the mass number of the atom (M) is equal to the number of neutrons.
The amount of an element's atomic mass expressed in units of atomic mass. It is roughly equivalent to the mass number—the sum of the protons and neutrons in an atom—or to the average number that takes into account the relative abundances of various isotopes.
The difference between the atomic number and the mass number of the atom (M) is equal to the amount of neutrons (Z).
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.
Factor to write an equivalent expression
36a - 16
Answers
Answer:
4(9a-4)
Step-by-step explanation:
36a - 16
We can factor 4 from each expression.
4*9a - 4*4
4(9a-4)
Maurice buys a dozen of donuts on sale for $7.99 before tax.
The sales tax is 4%.
What is the total price Maurice pays for the dozen donuts?
Answers
Answer:
$8.30
Step-by-step explanation:
7.99 + 4% = 8.30
peter has 4 more 50 dollar bills than 10 dollar bills in his wallet if the total amount of his money is 380 dollars how many ten dollar bills does peter have
Answers
Answer:
3
Step-by-step explanation:
7*50=350
7-4=3
3*10=30
350+30=380
find a value of c so that p(z ≥ c) = 0.55.
Answers
To find a value of c such that P(z ≥ c) = 0.55, we need to use a standard normal distribution table or calculator.From the standard normal distribution table, we find that the z-score corresponding to a right-tailed area of 0.55 is approximately 0.126.
Therefore, we have:
P(z ≥ c) = 0.55
P(z ≤ c) = 1 - P(z ≥ c) = 1 - 0.55 = 0.45
Using the standard normal distribution table, we find that the z-score corresponding to a left-tailed area of 0.45 is approximately -0.126.
So, c = -0.126.
Therefore, the value of c that satisfies P(z ≥ c) = 0.55 is approximately -0.126.
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Joshua has 30 trading cards. He adds 20 cards to his collection each week.
Mackenzie has 45 trading cards and adds 20 cards to her collection each week.
How many cards will each person have after 6 weeks?
Answers
Answer:
Joshua will have 150 cards.
Mackenzie will have 165 cards.
Mackenzie - 165 cards
7. Ifa = 3an * db = - 2 . find the values of: (a + b)ab
Answers
The Values of (a+b)ab are undefined.
Given that, a = 3an and db = -2We need to find the values of (a+b)
Now, we have a = 3an... equation (1)Also, we have db = -2... equation (2)From equation (1), we get: n = 1/3... equation (3)Putting equation (3) in equation (1), we get: a = a/3a = 3... equation (4)Now, putting equation (4) in equation (1), we get: a = 3an... 3 = 3(1/3)n = 1
From equation (2), we have: db = -2=> d = -2/b... equation (5)Multiplying equation (1) and equation (2), we get: a*db = 3an * -2=> ab = -6n... equation (6)Putting values of n and a in equation (6), we get: ab = -6*1=> ab = -6... equation (7)Now, we need to find the value of (a+b).For this, we add equations (1) and (5),
we get a + d = 3an - 2/b=> a + (-2/b) = 3a(1) - 2/b=> a - 3a + 2/b = -2/b=> -2a + 2/b = -2/b=> -2a = 0=> a = 0From equation (1), we have a = 3an=> 0 = 3(1/3)n=> n = 0
Therefore, from equation (5), we have:d = -2/b=> 0 = -2/b=> b = ∞Now, we know that (a+b)ab = (0+∞)(0*∞) = undefined
Therefore, the values of (a+b)ab are undefined.
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Systems requests do not deal with factors involved in improving service.
a. true
b. false
Answers
Each histogram represents a set of data with a median of 29.5. Which set of data most likely has a mean that is closest to 29.5?
A graph shows the horizontal axis numbered 9 to 48. The vertical axis is numbered 1 to 5. The graph shows an upward trend from 1 to 33 then a downward trend from 33 to 45.
A graph shows the horizontal axis numbered 15 to 48. The vertical axis is numbered 1 to 5. The graph shows an upward trend from 1 to 30 then a downward trend from 30 to 45.
A graph shows the horizontal axis numbered 12 to 56. The vertical axis is numbered 2 to 8. The graph shows an upward trend from 1 to 32 then a downward trend from 32 to 56.
A graph shows the horizontal axis numbered 15 to 54. The vertical axis is numbered 1 to 5. The graph shows an upward trend from 1 to 24, a downward trend from 24 to 27, an upward trend from 27 to 30, a downward trend from 30 to 39, an upward trend from 39 to 45, a downward trend from 45 to 48, then an upward trend from 48 to 51.
Answers
To determine which set of data most likely has a mean closest to 29.5, we need to analyze the shape and position of the histograms in relation to the value 29.5.
Looking at the histograms described:
The first histogram ranges from 9 to 48, and the upward trend starts from 1 and ends at 33, followed by a downward trend. This histogram suggests that there may be values lower than 29.5, which would bring the mean below 29.5.
The second histogram ranges from 15 to 48, with an upward trend from 1 to 30 and then a downward trend. Similar to the first histogram, it suggests the possibility of values lower than 29.5, indicating a mean below 29.5.
The third histogram ranges from 12 to 56, and the upward trend starts from 1 and ends at 32, followed by a downward trend. This histogram covers a wider range but still suggests the possibility of values below 29.5, indicating a mean below 29.5.
The fourth histogram ranges from 15 to 54 and exhibits multiple trends. While it has fluctuations, it covers a wider range and includes both upward and downward trends. This histogram suggests the possibility of values above and below 29.5, potentially resulting in a mean closer to 29.5.
Based on the descriptions, the fourth histogram, with its more varied trends and wider range, is most likely to have a mean closest to 29.5.
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The rectangle below has an area of x^2-6x-7 sq meters and a width of x-7 meters.
What expression represents the length of the rectangle?
Length=______ meters
Answers
Answer:
Length = ( x - 1 ) ( m)
Step-by-step explanation:
Area of rectangle is:
A(r) = l*w ( in m² ) where l is the length in m and w is the width in m
If we have: A(r) = x² - 6*x - 7 (m²), as an area of a rectangle, then we can factoring the equation, and get the rectangle dimensions, then:
x² - 6*x - 7 = ( x - 1 ) * ( x - 7 ) = area of the rectangle in m²
As problem statement establishes that ( x - 7 ) ( m) is the width, then
( x - 1 ) ( m) is the length
Nina is selling three types of energy bars at a market stall. She bought 60 Enerbars at 40p per bar and 200 Grainbars at 60p per bar from her normal supplier. She was also given 40 Amazebars as a promotion from a new supplier. Nina sells the bars for £2.40 and manages to sell all the Enerbars and Grainbars but only some Amazebars. She makes a profit of £542.40. How many Amazebars did she sell?
Answers
Answer:
Nina sold 24 Amazebars Plz Mark Brainliest
Step-by-step explanation:
Cost:
80 x 0.40 = 32
180x 0.30 = 54
40 x 0 = 0
Total = 86
Income
80 x 2.25 = 180
180 x 2.25 = 405
X x 2.25 = 2.25x
Total = 585 + 2.25x
How many did she sell:
553 = 585 - 86 + 2.25x
553 = 499 + 2.25x
553 - 499 = 2.25x
54 = 2.25x
54/2.25 = x
24 = x
make a simple linear regression model using education level as independent variable. if the education level is 14 years, the estimated annual income is
Answers
The estimated annual income can be calculated using the equation above. If the data point is used to calculate the slope and y-intercept of the regression line, then the annual income can be estimated using the equation y = m(14) + b.
If the education level is 14 years,
To create a simple linear regression model using education level as the independent variable, you will need to input data for education level and annual income.
This data can be used to estimate the annual income for any given education level. The equation for this linear regression model is y = mx + b, where y represents the annual income, m is the slope of the line, x is the education level, and b is the y-intercept.
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The students in a class guessed the age
of their teacher, Mrs Forster, and
recorded their guesses in this
stem-and-leaf diagram. Mrs Forster is 48
years old.
What fraction of the class overestimated
Mrs Forster's age?
Give your answer in its simplest form.
2
3
4
5
Students' guesses
9
1 2 3 4 6 6 79
0 3 4 5 7789
012
Key
29 represents 29 years
Answers
The fraction of the class that overestimated Mrs. Forster's age, given the stem and leaf plot, is 1 / 5
How to find the proportion ?To find the proportion of the class that overestimated Mrs. Forster's age, count the number of ages that are over the age of 48:
49, 50, 51, 52
From the stem and leaf plot, we see that the number of students in the class were 20 students.
The fraction which overestimated Mrs. Forster's age would therefore be :
= Number of students with age predictions over 48 / Number of total students
= 4 / 20
= 1 / 5
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