The profit region is empty and cannot be shaded in blue. Which means that the business will not be profitable for any values of x greater than [tex]150[/tex] .
What is the profitable for all values?To determine which graph corresponds to the given situation, we need to understand the relationship between cost, profit, and revenue.
The revenue (R) of a small business is given by the product of the price per unit (p) and the number of units sold (x):
[tex]R = px[/tex]
The profit (P) of a small business is the difference between its revenue and cost (C):
[tex]P = R - C = px - (3000 + 12x) = (p - 12)x - 3000[/tex]
The profit will be positive when P > 0, which means that the revenue is greater than the cost:
[tex](p - 12)x > 3000[/tex]
[tex]x > 3000/(p - 12)[/tex]
This inequality tells us that the business will be profitable for all values of x greater than [tex]3000/(p - 12).[/tex]
Graph A: This graph shows a linear revenue function (R = 20x) and a linear cost function [tex](C = 3000 + 10x).[/tex] The profit function [tex](P = R - C)[/tex] is also linear.
To find the profit region, we need to shade the area above the profit function [tex](P > 0)[/tex]. However, we cannot determine if this corresponds to the given situation without knowing the price per unit.
Graph B: This graph shows a linear revenue function [tex](R = 25x)[/tex] and a quadratic cost function [tex](C = 3000 + 15x + 0.5x^2).[/tex] The profit function [tex](P = R - C)[/tex] is also quadratic. To find the profit region, we need to shade the area above the profit function [tex](P > 0)[/tex] .
We can solve for the roots of the quadratic equation [tex]P = 25x - (3000 + 15x + 0.5x^2) = -0.5x^2 + 10x - 3000[/tex] and find the interval of x-values for which [tex]P > 0.[/tex]
This corresponds to the range of x-values for which the graph of P is above the x-axis. We can see that this region is shaded in blue, so Graph B corresponds to the given situation.
Graph C: This graph shows a linear revenue function [tex](R = 15x)[/tex] and a linear cost function [tex](C = 3000 + 20x).[/tex]The profit function [tex](P = R - C)[/tex] is also linear.
To find the profit region, we need to shade the area above the profit function [tex](P > 0)[/tex]. However, we can see that the profit function intersects the x-axis at [tex]x = 150.[/tex]
Therefore, the profit region is empty and cannot be shaded in blue. Which means that the business will not be profitable for any values of x greater than [tex]150[/tex].
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matt saves $100 one month, $50 for three months, $150 for four months, and $75 for the rest of the months of that year. how much does he save in one year?
Add.
Your answer should be an expanded polynomial in
standard form.
(−46² + 8b) + (−46³ + 56² – 8b) =
The polynomial expression (−4b² + 8b) + (−4b³ + 5b² – 8b) when evaluated is −4b³ + b²
Evaluating the polynomial expressionWe can start by combining like terms.
The first set of parentheses has two terms: -4b² and 8b. The second set of parentheses also has three terms: -4b³, 5b², and -8b.
So we can first combine the like terms in the set of parentheses:
(−4b² + 8b) + (−4b³ + 5b² – 8b) = −4b³ + b²
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help with math problems.
Answer:
yes.
Step-by-step explanation:
cause yes.
how can 32 div 4 help you solve 320 div 4
Answer:
you just add a 0 at the end of the answer of what 32 divided by 4 is, so in this case 320 divided by 4 is 80
Step-by-step explanation:
32 divided by 4 is 8.
320 divided by 4 is 80.
To get from 32 to 320 all you need is a 0 at the end, so you can just add the 0 the end of the answer. This means you're going from an 8, to an 80.
OR
Another way you can look at it is 32 multiplied by 10 to get 320. So you need to mutiple your answer by 10 to get the right answer.
32*10=320
8*10=80
Hope this helps!
What is the range of the function represented by the graph?
A.
all real numbers
B.
y ≤ 1
C.
1 ≤ y ≤ 6
D.
y ≥ 1
Let X1 and X2 denote the proportions of time, out of one working day, that employee A and B, respectively, actually spend performing their assigned tasks. The joint relative frequency behavior of X1 and X2 is modeled by the density function. ( ) ⎩ ⎨ ⎧ + ≤ ≤ ≤ ≤ = 0 ,elsewhere x x ,0 x 1;0 x 1 xf x 1 2 1 2 1 2 , a) Find P( ) X1 ≤ 0.5,X 2 ≥ 0.25 answer 21/64 b) Find P( ) X1 + X 2 ≤ 1
Answer:
a) To find the probability that X1 is less than or equal to 0.5 and X2 is greater than or equal to 0.25, we need to integrate the given density function over the region where X1 ≤ 0.5 and X2 ≥ 0.25.
P(X1 ≤ 0.5, X2 ≥ 0.25) = ∫∫(x1,x2) f(x1,x2) dxdy
where the limits of integration are:
0.25 ≤ x2 ≤ 1
0 ≤ x1 ≤ 0.5
Substituting the given density function:
P(X1 ≤ 0.5, X2 ≥ 0.25) = ∫0.25^1 ∫0^0.5 (x1 + x2) dx1 dx2
Evaluating the inner integral:
P(X1 ≤ 0.5, X2 ≥ 0.25) = ∫0.25^1 [(x1^2/2) + x1x2] |0 to 0.5 dx2
Simplifying the expression:
P(X1 ≤ 0.5, X2 ≥ 0.25) = ∫0.25^1 [(0.125 + 0.25x2)] dx2
Evaluating the upper and lower limits:
P(X1 ≤ 0.5, X2 ≥ 0.25) = [0.125x2 + 0.125x2^2] |0.25 to 1
Substituting the limits:
P(X1 ≤ 0.5, X2 ≥ 0.25) = [(0.125 + 0.125) - (0.03125 + 0.015625)]
Solving for the final answer:
P(X1 ≤ 0.5, X2 ≥ 0.25) = 21/64
Therefore, the probability that X1 is less than or equal to 0.5 and X2 is greater than or equal to 0.25 is 21/64.
b) To find the probability that X1 + X2 is less than or equal to 1, we need to integrate the given density function over the region where X1 + X2 ≤ 1.
P(X1 + X2 ≤ 1) = ∫∫(x1,x2) f(x1,x2) dxdy
where the limits of integration are:
0 ≤ x1 ≤ 1
0 ≤ x2 ≤ 1-x1
Substituting the given density function:
P(X1 + X2 ≤ 1) = ∫0^1 ∫0^(1-x1) (x1 + x2) dx2 dx1
Evaluating the inner integral:
P(X1 + X2 ≤ 1) = ∫0^1 [(x1x2 + 0.5x2^2)] |0 to (1-x1) dx1
Simplifying the expression:
P(X1 + X2 ≤ 1) = ∫0^1 [(x1 - x1^2)/2 + (1-x1)^3/6] dx1
Evaluating the integral:
P(X1 + X2 ≤ 1) = [x1^2/4 - x1^3/6 - (1-x1)^4/24] |0 to 1
Substituting the limits:
P(X1 + X2 ≤ 1) = (1/4 - 1/6 - 1/24) - (0/4 - 0/6 - 1/24)
Solving for the final answer:
P(X1 + X2 ≤ 1) = 1/8
Therefore, the probability that X1 + X2 is less than or equal to 1 is 1/8.
< Rewrite the set O by listing its elements. Make sure to use the appropriate set nota O={y|y is an integer and -4≤ y ≤-1}
What is the answer please?
Answer:
O = { -4,-3,-2,-1,0,-1 }
(5r^2+5r+1)-(-2+2r^2-5r)
Answer:
3r^2+10r+3
Step-by-step explanation:
What is the perimeter of a rectangle with a base of 9 ft and a height of 10 ft?
Answer:
P=2(l+w)=2·(9+10)=38ft
Polygon JKLMNO and polygon PQRSTU are similar. The area of polygon
JKLMNO is 27. What is the area of PQRSTU?
Check the picture below.
[tex]\cfrac{3^2}{4^2}=\cfrac{27}{A}\implies \cfrac{9}{16}=\cfrac{27}{A}\implies 9A=432\implies A=\cfrac{432}{9}\implies A=48[/tex]
The quality control manager at a computer manufacturing company believes that the mean life of a computer is 120 months, with a standard deviation of 10 months. If he is correct, what is the probability that the mean of a sample of 90 computers would be greater than 117.13 months? Round your answer to four decimal places.
The probability that the mean of a sample of 90 computers would be greater than 117.13 months, if the quality control manager is correct, is approximately 0.9955 or 99.55%.
The sampling distribution of the sample mean follows a normal distribution with a mean of 120 and a standard deviation of 10/sqrt(90) = 1.0541 months (using the formula for the standard deviation of the sample mean).
To find the probability that the mean of a sample of 90 computers would be greater than 117.13 months, we can standardize the sample mean using the formula:
z = (sample mean - population mean) / (standard deviation of sample mean) = (117.13 - 120) / 1.0541 = -2.6089
Using a standard normal distribution table or calculator, we can find that the probability of obtaining a z-score greater than -2.6089 is approximately 0.9955.
Therefore, the probability that the mean of a sample of 90 computers would be greater than 117.13 months, if the quality control manager is correct, is approximately 0.9955 or 99.55%.
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a book sold 33,600 copies in its first month of release. suppose this represents 6.7% of the number of copies sold to date. how many copies have been sold to date? answer to the nearest whole number
First, 6.7 % can be written in decimal form as 0.067 (6.7 / 100 = 0.067).
Let's use the variable x to represent the number of copies sold to date.
Then we can write and solve the following equation to represent 6.7% of the total sold to date:
0.067 • x = 33600
You can solve this equation by dividing both sides of the equation by 0.067:
0.067 • x = 33600
0.067 0.067
x = 501493
To date, 500000 copies would have been sold rounded to the nearest whole.
Find the perimeter and total area
The perimeter is 27 feet and the area is 35 square feet
From the question, we have the following parameters that can be used in our computation:
The figure
The perimeter is the sum of tthe side lengths
So, we have
Perimeter = 7.5 + 6 + (6 - 2.5) + 4 + 2.5 + 3.5
Evaluate
Perimeter = 27
The area is calculated as
Area = 6 * 3.5 + 4 * (6 - 2.5)
Evaluate
Area = 35
Hence, teh area is 35 square feet
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Solve problem in the picture!
The equation
(x² + y²)² = 4(x² - y²)
defines a lemniscate (a "figure eight" or "oo-shaped curve"). The point P= (√5/8, √3/8) is on this lemniscate. Determine an
equation for the line , which is tangent to the lemniscate at the point P. The figure below, which is drawn to scale, may help to
understand the problem (and may help you to check your answer for "reasonableness").
Bonus Question: [up to 3 points] Let Q = (2,1), and determine an equation for the line which is tangent to the lemniscate at Q.
1. The equation for the line, which is tangent to the lemniscate at the point P is y = -√3x + (5/4 + √3/8). The equation for the line which is tangent to the lemniscate at Q is y = (-5/3)x + 11/3.
What is derivative of a function?The pace at which a function is changing at a specific point is known as its derivative. It shows the angle at which the tangent line to the curve at that location slopes. A key idea in calculus, the derivative can be utilised to tackle a range of issues, such as curve analysis, rates of change, and optimisation.
The tangent line to the lemniscate at point P, is determined using the derivative of the function.
(x² + y²)² = 4(x² - y²)
Taking the derivative on both sides we have:
2(x² + y²)(2x + 2y(dy/dx)) = 8x - 8y(dy/dx)
dy/dx = (x² + y²)/(y - x)
Substituting P= (√5/8, √3/8) for the x and y we have:
dy/dx = (√5/8)² + (√3/8)²) / (√3/8 - √5/8) = -√3
Thus, the slope of the tangent line at point P is -√3.
Using the point slope form:
y - y1 = m (x - x1)
Substituting the values we have:
y - (√3/8) = -√3(x - √5/8)
y = -√3x + (5/4 + √3/8)
Hence, equation for the line, which is tangent to the lemniscate at the point P is y = -√3x + (5/4 + √3/8).
Bonus question:
The equation of tangent for the lemniscate at point Q = (2,1) is:
dy/dx = (2² + 1²)/(1 - 2) = -5/3
Using the point slope form:
y - 1 = (-5/3)(x - 2)
y = (-5/3)x + 11/3
Hence, equation for the line which is tangent to the lemniscate at Q is y = (-5/3)x + 11/3.
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A camel can drink 15 gallons of water in 10 minutes. At this rate, how much water can the camel drink in 11 minutes?
HELP
Answer: 16.5 gallons of water.
Step-by-step explanation:
If it was me. I would be setting up as a table to keep my work organized.
So first we find how much 1 minute is.
15g : 10m
15/10 : 10m/10
1.5g : 1m
Then I multiply how many minutes there are.
1.5g x 11 : 1m x 1
16.5g : 11m
And there we find the answer of 16.5 gallons.
Happy Solving
Answer:16.5
Step-by-step explanation:
HELPP!
When are the values of f(x) positive, and when are they negative?
The values of function f(x) positive, and negatives are (-infinity, infinity )
What exactly is a function?A function is a procedure or link that connects every element of one non-empty set A to at least one element of another non-empty set B. The phrases "domain" and "co-domain" are used in mathematics to define a function f between two sets, A and B. The constraint F = (a,b)| is satisfied by all values of a and b.
In the case of the question,
f (x) = x²
f (x) will be positive for all x values. As a result of the function:
x² = x × x
That is, when any number or integer is multiplied by itself, the result is positive. (For example, - - = + and + + = +)
As a result, f (x) = x2 will be positive for (,).
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a basement bedroom must have a window with an opening area of at least 5.7 square feet per the international residential code. a rectangular basement window opening is 0.75 meters wide.Among the following heights, in meters, which is the smallest that will qualify the window opening per the code.
The smallest that will qualify the window opening per the code is 0.71
What is rectangular?
A quadrilateral with four right angles is a rectangle. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides.
Here, we have
Given: a basement bedroom must have a window with an opening area of at least 5.7 square feet per the international residential code. A rectangular basement window opening 0.75 meters wide.
First, we convert square feet into square meters.
5.7 square feet = 0.53 square meters
Now,
0.53 / 0.75 = 0.71
Hence, the smallest that will qualify the window opening per the code is 0.71
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Prove that,
If I = A then I U{—A} is not satisfiable.
Our assumption that I U{—A} is satisfiable must be false. Hence, I U{—A} is not satisfiable if I = A.
What is concept of satisfiability?A set of propositional formulae, sometimes referred to as a propositional theory, can be satisfiable in terms of propositional logic by having the quality of being true or untrue according to a certain interpretation or model. If there is at least one interpretation that makes all of a set of formulae true, the set is said to be satisfiable.
Using the proof by contradiction we have:
Assume that I U{—A} is satisfiable.
Then, by definition of satisfiability, every formula in the set I U{—A} is true in M.
Since I = A, every formula in I is also in A. Therefore, every formula in I is true in M, since A is true in M.
Consider the formula —A, which is in {—A}. Since M satisfies {—A}, —A is true in M.
But this contradicts the fact that A is true in M, since —A is the negation of A.
Therefore, our assumption that I U{—A} is satisfiable must be false. Hence, I U{—A} is not satisfiable if I = A.
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Find the sum of the first 25 terms of the following arithmetic sequence. Rather that write out each term use a Fourmula
a1=5,d=3
Answer:
1025
Step-by-step explanation
The formula to find the sum of the first n terms of an arithmetic sequence is
Sn = n/2 * [2a1 + (n-1)d]
Where
a1 = the first term of the sequence
d = the common difference between consecutive terms
n = the number of terms we want to sum
Substituting the given values, we get
a1 = 5
d = 3
n = 25
S25 = 25/2 * [2(5) + (25-1)3]
= 25/2 * [10 + 72]
= 25/2 * 82
= 25 * 41
= 1025
THIS IS TWO PARTS !!
Angela worked on a straight 11%
commission. Her friend worked on a salary of $950
plus a 7%
commission. In a particular month, they both sold $23,800
worth of merchandise.
Step 1 of 2 : How much did Angela earn for this month? Follow the problem-solving process and round your answer to the nearest cent, if necessary.
The amount Angela earned this month is $2,618.
How much did Barbara earn?Percentage can be described as a fraction of an amount expressed as a number out of hundred.
Angela's earnings = percentage commission x worth of goods sold
[tex]11\% \times 23,800[/tex]
[tex]0.11 \times 23,800 = \bold{\$2618}[/tex]
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The average temperature at the South Pole is - 45" F. The average
temperature on the Equator is 92º F. How much warmer is the average
temperature on the Equator than at the South Pole?
Answer:
The average temperature on the Equator is 137°F warmer than the average temperature at the South Pole.
76°c
Step-by-step explanation:
Suppose a jar contains 12 red marbles and 12 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.
As a result, there is a 26% chance that two red marbles will be chosen at random, or around 0.26.
what is probability ?The area of mathematics known as probability is concerned with analysing the results of random events. It represents a probability or likelihood that a specific occurrence will occur. A number in 0 and 1 is used to represent probability, with 0 denoting an event's impossibility and 1 denoting its certainty. In order to produce predictions and guide decision-making, probability is employed in a variety of disciplines, such science, finance, economics, architecture, and statistics.
given
Given that there are 12 red marbles and a total of 24 marbles in the jar, the likelihood of choosing the first red marble is 12/24.
There are 11 red marbles and a total of 23 marbles in the jar after choosing the first red marble.
As a result, the likelihood of choosing a second red marble is 11/23.
We compound the probabilities to determine the likelihood of both outcomes occurring simultaneously (i.e., choosing two red marbles):
P(choosing 2 red marbles) = (12/24) x (11/23) = 0.2609, which is roughly 0.26.
As a result, there is a 26% chance that two red marbles will be chosen at random, or around 0.26.
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Find the area of this composite figure: *find the area of each figure, then add those areas together
Answer:
136 units
Step-by-step explanation:
All sides are equal in a rectangle:
Value of b : 16-8 = 8 units
h = 13-7 = 6 units.
So Area of triangle= bh/2 = 8*6/2 = 24 units
Area of rectangle = lb = 16*7 = 112 units
So Area of figure= 112+24 units = 136 units
(-3+i)^2 in simplest a + bi form
Answer:
[tex]\boxed{8-6i}[/tex]
Step-by-step explanation:
First, we developed the square binomial [tex](-3+\mathrm{i})^2[/tex].
[tex]\implies (-3+\mathrm{i})(-3+\mathrm{i})\\9-3\mathrm{i}-3\mathrm{i}+i^2\\9-6\mathrm{i}+\mathrm{i}^2[/tex]
Remember the next product:
[tex]i^2= \mathrm{i} \times \mathrm{i} = -1[/tex]
then:
[tex]9-6\mathrm{i}+ (-1)\\8-6i[/tex]
Hope it helps
[tex]\text{-B$\mathfrak{randon}$VN}[/tex]
3x-4>2
solve the inequality
Answer:
x > 2
Hope this helps!
Step-by-step explanation:
3x - 4 > 2
3x - 4 ( + 4 ) > 2 ( + 4 )
3x > 6
3x ( ÷ 3 ) > 6 ( ÷ 3 )
x > 2
Given sin x = 4/5 and cos x= 3/5.
What is the ratio for tan x?
Enter your answer in the boxes as a fraction in simplest form.
Answer:
[tex]tan(x)=\frac{4}{3}[/tex]
Step-by-step explanation:
In the unit circle,
- [tex]cos(a)=\frac{x}{r}[/tex] where [tex]a[/tex] is the degree measure, [tex]x[/tex] is the x-coordinate of the triangle, and [tex]r[/tex] is the radius of the circle
- [tex]sin(a)=\frac{y}{r}[/tex] where [tex]a[/tex] is the degree measure, [tex]y[/tex] is the y-coordinate of the triangle, and [tex]r[/tex] is the radius of the circle
Thus, since tangent is equal to sine over cosine, we can simplify our knowledge to: [tex]tan(a)=\frac{sin(a)}{cos(a)}=\frac{y}{x}[/tex]
In this problem, [tex]sin(x)=\frac{4}{5}[/tex]. We can conclude from our previous knowledge that [tex]y=4[/tex] and the radius is 5.
Similarly, [tex]cos(x)=\frac{3}{5}[/tex], which means [tex]x=3[/tex] and the radius is the same, at 5.
Since we know that [tex]x=3[/tex] and [tex]y=4[/tex], we can find the value of [tex]tan(x)[/tex] by using the formula [tex]tan(x)=\frac{y}{x}[/tex] and plug in the numbers.
Therefore, [tex]tan(x)=\frac{4}{3}[/tex].
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Valeria thinks that smoking suppresses a person's appetite so they will weigh less than those who do not smoke. She randomly collected the weights of some smokers and nonsmokers and created the graph shown.
Which statement correctly compares the distributions?
Responses
A Since the range of nonsmokers is 13 lbs more than that of smokers there is much more variability in their weights.Since the range of nonsmokers is 13 lbs more than that of smokers there is much more variability in their weights.
B On average smokers weighed 35 pounds more than nonsmokers.On average smokers weighed 35 pounds more than nonsmokers.
C Almost half of the smokers weighed more than all of the nonsmokers in the sample.Almost half of the smokers weighed more than all of the nonsmokers in the sample.
D On average, nonsmokers weighed 13 lbs less than smokers.On average, nonsmokers weighed 13 lbs less than smokers.
E Even though smokers on average weighed more than nonsmokers the variability in their weights was about the same.
The correct statement that compares the distributions is:
D On average, nonsmokers weighed 13 lbs less than smokers.
What is the variability?
Variability refers to the amount of spread or dispersion in a set of data. It is a measure of how much the data values in a sample or population differ from each other.
One commonly used measure of variability is the standard deviation, which is the square root of the variance. The variance is the average of the squared differences from the mean.
Looking at the graph, we can see that the center of the distribution of smokers is around 178 lbs, while the center of the distribution of nonsmokers is around 165 lbs. This means that, on average, nonsmokers weigh less than smokers.
Option A is incorrect because the range is not a good measure of variability, and it does not necessarily mean that there is more variability in the weights of nonsmokers.
Option B is incorrect because the graph clearly shows that nonsmokers weigh less on average than smokers.
Option C is incorrect because we cannot make any conclusion about half of the smokers weighing more than all of the nonsmokers from the graph.
Option E is incorrect because the graph shows that the variability in the weights of smokers is greater than that of nonsmokers.
Hence, The correct statement that compares the distributions is:
D On average, nonsmokers weighed 13 lbs less than smokers.
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A small ferry runs every half hour from one side of a large river to the other. The probability distribution for the random variable = money collected (in dollars) on a randomly selected ferry trip is shown here.
Money collected 0 5 10 15 20 25
Probability 0.02 0.05 0.08 0.16 0.27 0.42
Calculate the cumulative probabilities. Do not round.
(≤0) =
(≤5) =
(≤10) =
(≤15) =
(≤20) =
(≤25) =
The median of a discrete random variable is the smallest value for which the cumulative probability equals or exceeds 0.5.
What is the median of ?
The cumulative probabilities for the given probability distribution were calculated, and the median of the discrete random variable was found to be 20.
To find the median, we need to find the smallest value of the random variable for which the cumulative probability equals or exceeds 0.5.
The cumulative probabilities are:
(≤0) = 0.02
(≤5) = 0.07
(≤10) = 0.15
(≤15) = 0.31
(≤20) = 0.58
(≤25) = 1
The cumulative probability is the sum of the probabilities of all events that have an outcome less than or equal to a given value. For example, the cumulative probability for the event of collecting 5 dollars or less is the sum of the probabilities for collecting 0 dollars and 5 dollars, which is 0.02 + 0.05 = 0.07. Similarly, the cumulative probability for the event of collecting 10 dollars or less is the sum of the probabilities for collecting 0 dollars, 5 dollars, and 10 dollars, which is 0.02 + 0.05 + 0.08 = 0.15. The same process is used to calculate the cumulative probabilities for all other values. The median is the smallest value of the random variable for which the cumulative probability is greater than or equal to 0.5.
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. Mateo and Haley both collect coins. Mateo has 8 more (+) coins in his
collection than Haley. Which expression represents the total number of
coins (c) in both collections?
Answer:
Let Haley be represented as x
Now Mateo has 8 more coins than haley
Mateo = 8 + x
total number of coins is Mateo coins and Haley coins.
x + 8 + x
2x + 8
Factor 12m2 + 17m – 5.