Answer:
You can find the mean, by adding all the terms in each data set and dividing by the number of terms. For example, if there were four data points, you would add them all up and divide by four.
hope this helps!
The graph of the absolute value parent function, f(x) = Ixl, is stretched
horizontally by a factor of 5 to create the graph of g(x). What function is g(x)?
Answer: [tex]g(x)=\left|\frac{x}{5} \right|[/tex]
Step-by-step explanation:
See atached image.
Suppose that you and a friend are playing cards and decide to make a bet. If you draw two face cards, where a face card is a Jack, a Queen, or a King, in succession from a standard deck of 52 cards replacing the first card, you win $50. Otherwise, you pay your friend $20. What is the expected value of your bet? Round your answer to the nearest cent, if necessary.
The expected value of your bet will be the negative $16.27 that mean loses.
What is the binomial distribution?Binomial distributions consist of n independent Bernoulli trials.
The expected value will be
E(X) = np
Suppose that you and a friend are playing cards and decide to make a bet.
If you draw two face cards, where a face card is a Jack, a Queen, or a King, in succession from a standard deck of 52 cards replacing the first card, you win $50.
Otherwise, you pay your friend $20.
Then the probability of winning will be
p = (12 / 52)(12 / 52)
p = 9 / 169
Then the probability of loosing will be
q = 1 – p
q = 1 – 9/169
q = 160 / 169
Then the expected value will be
E(x) = (9/169) x 50 + (160/169) x (-20)
E(x) = -$16.27
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Solve using the Quadratic Formula. 122+6−5=0
Step-by-step explanation:
You can't use quadratic formula in this
A cubic yard of topsoil is to be spread evenly in the garden at Prove It! Math Academy. Thegarden measures 10 feet by 8 feet. How many inches deep will the topsoil be?
The topsoil will be 4.05 inches deep
Calculating depthFrom the question, we are to determine how many inches deep the topsoil will be
From the given information,
The volume of the topsoil = 1 cubic yard
Convert to cubic feet
1 cubic yard = 27 cubic feet
∴ The volume of the topsoil = 27 cubic feet
Then,
The depth of the topsoil will be = 27/(8 ×10)
Depth of topsoil = 27/80
Depth of topsoil = 0.3375 foot
Now, convert to inches
1 foot = 12 inches
∴ 0.3375 foot = 0.3375×12 inches
= 4.05 inches
Hence, the topsoil will be 4.05 inches deep
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HELP ASAP!!!!!!
Ken and Betty each write a proof of the statement: if m
The statement third "Betty wrote an indirect proof using contradiction' and statement fourth "Ken wrote direct proof using deductive evidence" are correct.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called a "Angle."
We have Ken's statements are shown in the table:
Angle AOC = Angle BOD (given)
Angle AOB + Angle BOC = Angle BOC + Angle COD (angle addition postulate)
Angle AOB = ANgle COD (subtraction property of equality)
Ken wrote direct proof using deductive evidence.
As we can in betty's proof:
Betty wrote an indirect proof using contradiction.
Thus, the statement third "Betty wrote an indirect proof using contradiction' and statement fourth "Ken wrote direct proof using deductive evidence" are correct.
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G.SRT.1 In the coordinate plane, quadrilateral ABCD has vertices A (1, 1), * 1 point B (5,1), C (5,9), and D (1, 9). Quadrilateral FGHJ is shown in the coordinate plane below. What are the scale factor and the center of dilation that map quadrilateral BCD onto quadrilateral FGHJ?
Based on the vertices of quadrilateral ABCD and Quadrilateral FGHJ, A. The scale factor is 1/2, and the center of dilation is point A.
What is the scale factor?First, note the vertices of Quadrilateral FGHJ:
F(1,1) G(3 ,1) J (1 , 5) H(3 , 5)
Find the lengths of the sides of both quadrilaterals:
FG = (3, 1) - (1, 1) AB = (5,1) - (1, 1)
= (2,0) = (4, 0)
FH = (3, 5) - (1, 1) AC = (5,9) - (1, 1)
= (2,4) = (4, 8)
AB is twice the size of FG.
AC is twice the size of FH
This shows that quadrilateral FGHJ is 1/2 the size of quadrilateral ABCD.
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The height of a projectile launched upward at a speed of 25 meters/second from a height of 70 meters is given by the function h(t)=-5sup(t,2)+25t+70. How long will it take the projectile to hit the ground?
6.5 s take the projectile to hit the ground.
What is projectile?A projectile is any object thrown into space upon which the only acting force is gravity.
Given:
speed = 25 m/s
h(t) = -5t² + 25t + 70
height = 70 m
Time to reach maximum height
( u sin90)/2g
= 25/2*9.8
= 1.275s
Max height = u²Sin²[tex]\theta[/tex]/g
=25*25/9.8
=63.775
So, total height=63.775 + 70 = 133.775 m
Now, time to fall back to the ground
h = ut+(1/2)gt²
t² = (h- ut)2/g
u=0
H= 133.775 m
(133.775*2)/9.8= t²
t² = 27.3010
t= 5.225 s
Total time taken to hit ground
= 5.225 + 1.275
= 6.5 s
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Word Problem
(D) Joshua is going shopping for (E) paintings and (F) spoons. The cost of (E) painting is (B) 10$ and the cost of each (F) spoon is (A) 8$.
If (D) Joshua can spend at most (C) 100$, how many (F) spoons can be purchased?
3. Write an inequality of the form Ax + B ≤ C to represent the word problem using your answers for A, B, and C. Solve the inequality and show your work.
4. Graph the solution to your inequality on a number line or describe, in words, how to graph the inequality on a number line.
The number of spoons that can be purchased is 11, whereas the equation is given as 8x + 10 ≤ 100
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The cost of each spoon is $8, hence A = 8. The cost of painting is 10, hence B = 10. Joshua can spend at most 100$, C = 100
8x + 10 ≤ 100
x ≤ 11.25
The number of spoons that can be purchased is 11, whereas the equation is given as 8x + 10 ≤ 100
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Answer:
92 spoons can be purchased.
Step-by-step explanation:
10x + 8 ≤ 100
10x + 8 ≤ 100
8 - 8 10x 100 - 8
10x ≤ 92
x = 1/5
10 x 1/5 = 92.
<---------------------------------------------------------------------------------------------------------->
<----------------------------------------------------0---------------------------- 92
9-22 Throughput costing (continuation of 9-21). The variable maufacturing costs per unit of Nascar Motors are as follows:
April May
Direct cost per unit $6,700 $6,700
Direct manufacturing labor cost per unit $1,500 $1,500
Manufacturing overhead cost per unit $1,800 $1,800
1. Prepare income statements for Nascar Motors in April and May 2017 under throughput costing.
2. Contrast the results in requirement 1 with those in requirement 1 of Exercise 9-21.
3. Give one motivation for Nascar Motors to adopt throughput costing.
The Income Statement for Nascar Motors in April and May 2017 under Throughput Costing is given as attached.
What is a throughput costing?This refers a costing technique, also known as super-variable costing, which solely takes direct materials into account when calculating product costs.
The other expenses are all classed as period costs and are all deducted from income in the time period in which they are spent.
What is the Contrast between the results in requirement 1 with those in requirement 1 of Exercise 9-21?It is to be noted that Throughput costing has the lowest operating income in April while having the greatest operating income in May.
More so than either absorption or variable costing, throughput costing emphasizes sales as the source of operational income. See the attached.
What is one motivation for Nascar Motors to adopt throughput costing?It is to be noted that production that doesn't result in a commensurate sale in the same time period is penalized under throughput costing.
When compared to variable costing, costs that are variable with regard to production but are not direct materials are expensed in the period of incurrence.
In contrast to variable costing or absorption costing, throughput costing offers less of motivation to create inventory.
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QUESTION IS DOWN BELOW WORTH 30 POINTS
Answer:
40 yds^3
Step-by-step explanation:
Please help!!! If the first 4 terms of a geometric sequence are...
Answer:
c.) aₙ = 5 × 4ⁿ⁻¹
Explanation:
Geometric sequence: aₙ = a(r)ⁿ⁻¹
where 'a' resembles first term of a sequence, 'r' is the common difference.
Here sequence: 5, 20, 80, 320,...
First term (a) = 5
Common difference (d) = second term ÷ first term = 20 ÷ 5 = 4
Hence putting into equation: aₙ = 5(4)ⁿ⁻¹
Identify the key features of the following graph. If the Domain is all real numbers, type in "All Real" into the Domain box.
The key features of the graph are:
Vertex (-2, -1)Axis of symmetry x = -2y-intercept (0, 3)MinimumDomain, -∞ < x < ∞Range y > = -1How to determine the key features?The graph has a minimum value at (-2, -1)
This represents the vertex
The x coordinate of the vertex is the axis of symmetry.
So, we have
x = -2
The graph crosses the y-axis at (0, 3)
This represents the y-intercept
The graph opens up.
This means that the vertex is minimum.
The domain is the set of all real number, because the graph extends in both directions on the x-axis without end
While the range is y >= -1, because it has a minimum at this point
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On a unit circle, the terminal point of 0 is (1, 0). What is tan ?
By using the definitions of unit circle and trigonometric functions, we find that the tangent of the terminal point of the angle is equal to 0.
How to find determine a trigonometric function associated with an unit circle
In trigonometry, an unit circle is a circle with a radius of 1 and used to determine the values of trigonometric functions. There are two fundamental trigonometric functions: (i) sine, (ii) cosine, and the tangent is a derivate trigonometric function, which is defined below:
tan θ = y/x (1)
If we know that x = 1 and y = 0, then the tangent of the terminal point of angle is:
tan θ = 0/1
tan θ = 0
By using the definitions of unit circle and trigonometric functions, we find that the tangent of the terminal point of the angle is equal to 0.
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Answer:
tan= 0
Step-by-step explanation:
^^^correct :)
Evaluate: 216 1/2 Question 2 options: A) 9 B) 1 C) 6 D) -3
Find the outliers in the given data set below. 69, 16, 79, 80, 82
Answer:
16
Step-by-step explanation:
The outlier in the given dataset is "16".
Given is a data set 69, 16, 79, 80, 82, we need to determine the outliners of the set,
To identify outliers in a dataset, we generally use a statistical method such as the z-score or the IQR (interquartile range).
Since, the provided dataset is small with only five values, we can manually identify the outliers by observing the data.
An outlier is a value that significantly deviates from the rest of the dataset.
Let's examine the given dataset:
69, 16, 79, 80, 82
To identify outliers, we can consider any data points that are notably different from the others.
In this case, it seems that the value "16" is considerably lower than the other values.
Let's label it as a potential outlier.
Therefore, the outlier in the given dataset is "16".
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Can somebody walk me through this?
2 y + 14 = 6 ( 4 y + 1 )
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{y = 4/11}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{2y + 14 = 6(4y + 1)}[/tex]
Find: [tex]\textsf{Solve for y}[/tex]
Solution: In order to solve for y we need to distribute the ride side of the expression, simplify, subtract 14 from both sides, subtract 24y from both sides, and divide both sides by -22.
Distribute and simplify
[tex]\textsf{2y + 14 = (6 * 4y) + (6 * 1)}[/tex][tex]\textsf{2y + 14 = 24y + 6}[/tex]Subtract 14 from both sides
[tex]\textsf{2y + 14 - 14 = 24y + 6 - 14}[/tex][tex]\textsf{2y = 24y + 6 - 14}[/tex][tex]\textsf{2y = 24y - 8}[/tex]Subtract 24y from both sides
[tex]\textsf{2y - 24y = 24y - 24y - 8}[/tex][tex]\textsf{2y - 24y = -8}[/tex][tex]\textsf{-22y = -8}[/tex]Divide both sides by -22
[tex]\textsf{-22y/-22 = -8/-22}[/tex][tex]\textsf{y = -8/-22}[/tex][tex]\textsf{y = 8/22}[/tex][tex]\textsf{y = 4/11}[/tex]Therefore, the expression simplifies down to y = 4/11.
+
Select the correct answer.
The parent function f(x)=√ is transformed to g(x)=2x-3). Which is the graph of g(x)?
The graph is in the attached image.
Draw the graphs of the lines below on the same grid to find the coordinates of the point of intersection.
y=3x−3 y=7−2x
The coordinates of the point of intersection of y=3x−3 and y=7−2x is (2, 3)
Graphing linear equationsFrom the question, we are to graph the given equations.
The graph of the equations is attached below.
In the graph, we can observe that the coordinates of the point of intersection of the is (2, 3)
Hence, the coordinates of the point of intersection of y=3x−3 and y=7−2x is (2, 3)
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find the indefinite integral.
Using substitution, the result of the indefinite integral is:
[tex]3\ln{(1 + x^{\frac{1}{3}})} + C[/tex]
What is the integral?The integral is:
[tex]\int \frac{1}{x^{\frac{2}{3}}(1 + x^{\frac{1}{3}})} dx[/tex]
The substitution is:
[tex]u = 1 + x^{\frac{1}{3}}[/tex]
Then the derivative is:
[tex]du = \frac{1}{3}x^{-\frac{2}{3}} dx[/tex]
ttex]dx = 3dux^{-\frac{2}{3}}[/tex]
Hence the integral is:
[tex]\int \frac{1}{x^{\frac{2}{3}}(1 + x^{\frac{1}{3}})} dx[/tex]
[tex]\int \frac{1}{x^{\frac{2}{3}}u} \times 3dux^{-\frac{2}{3}}[/tex]
[tex]\int \frac{3du}{u}[/tex]
[tex]3\ln{u} + C[/tex]
Returning to x:
[tex]3\ln{(1 + x^{\frac{1}{3}})} + C[/tex]
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A basket of oranges has 10 fruits, of which 4 are bad. Three balls are drawn at random.a)Calculate the probability of getting 3 bad balls.b)Calculate the probability of getting 1 bad fruit.c)Calculate the probability of getting at least one bad fruit.d)Calculate the probability of getting the most 2 bad fruits
Using the hypergeometric distribution, the probabilities are given as follows:
a) 0.0333 = 3.33%.
b) 0.5 = 50%.
c) 0.8333 = 83.33%.
d) 0.9667 = 96.67%.
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.The values of the parameters are:
N = 10, n = 3, k = 4.
Item a:
The probability is P(X = 3), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 3) = h(3,10,3,4) = \frac{C_{4,3}C_{6,0}}{C_{10,3}} = 0.0333[/tex]
Item b:
The probability is P(X = 1), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 1) = h(1,10,3,4) = \frac{C_{4,1}C_{6,2}}{C_{10,3}} = 0.5[/tex]
Item c:
The probability is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,10,3,4) = \frac{C_{4,0}C_{6,3}}{C_{10,3}} = 0.1667[/tex]
Then:
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.1667 = 0.8333[/tex]
Item d:
The probability is:
[tex]P(X \leq 2) = 1 - P(X = 3)[/tex].
Considering item a:
[tex]P(X \leq 2) = 1 - P(X = 3) = 1 - 0.0333 = 0.9667[/tex]
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Let [tex]O[/tex] be the random variable for the number of bad oranges picked out. Then
[tex]P(O=o) = \dfrac{\dbinom6{3-o} \dbinom4o}{\dbinom{10}3}[/tex]
if [tex]o\in\{0,1,2,3\}[/tex] and zero otherwise, where
[tex]\dbinom nk = \dfrac{n!}{k!(n-k)!}[/tex]
is the so-called binomial coefficient.
(a) Of the 6 good oranges, you pick 0. Of the 3 bad oranges, you pick 3. Of the 10 total oranges, you pick 3. So the probability of picking out all bad oranges is
[tex]P(O=3) = \dfrac{\dbinom60 \dbinom43}{\dbinom{10}3} = \boxed{\dfrac1{30}}[/tex]
(b) By similar reasoning, the probability of drawing exactly 1 bad orange is
[tex]P(O=1) = \dfrac{\dbinom62 \dbinom41}{\dbinom{10}3} = \boxed{\dfrac12}[/tex]
(c) "At least 1 bad orange" means you pick out 1, 2, or 3 bad oranges. These events are mutually exclusive, and we already know the probabilities of picking out exactly 1 or all 3 bad oranges. The remaining probability of drawing 2 bad oranges is
[tex]P(O=2) = \dfrac{\dbinom61 \dbinom42}{\dbinom{10}3} = \dfrac3{10}[/tex]
so the overall probability of drawing at least 1 bad orange is
[tex]P(O\ge1) = P(O=1)+P(O=2)+P(O=3) =\dfrac1{30} + \dfrac3{10} + \dfrac12 = \boxed{\dfrac56}[/tex]
(d) I assume you mean "at most 2 bad oranges," meaning you pick out 0, 1, or 2 bad oranges. Again, these events are mutually exclusive, and the probability of picking out no bad oranges is
[tex]P(O=0) = \dfrac{\dbinom63 \dbinom40}{\dbinom{10}3} = \dfrac16[/tex]
hence the probability of drawings at most 2 bad oranges is
[tex]P(O\le2) = P(O=0) + P(O=1) + P(O=2) = \dfrac16 + \dfrac12 + \dfrac3{10} = \boxed{\dfrac{29}{30}}[/tex]
Select all the correct answers.
For which values is this expression undefined?
x-1/(x^2-2x-3) + 5/(2x^2+2x)
The answer choice which represents values for which the expression is undefined is; x = -1.
What value of x renders the expression undefined?It follows from the task content that the expression in discuss is made up of 2 rational expressions and hence, the value of x which makes the expression undefined is -1 because, upon substitution, we have; (1/0) + (5/0); which yields undefined.
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Answer:
x= 3. x= 0, x= -1
Step-by-step explanation:
Correct on edmentum
a) The difference between the circumference and the diameter of a circle is 90cmFind the radius of the circle
Answer:
r=21.01 cm
Step-by-step explanation:
2r = diameter
Circumference of a circle = pi 2r
difference = 90
pi2r - 2r =90
2r (pi-1) =90
90/(2(pi-1) = r = 21.01 cm
Sanjeet paid $32.85 for 1 file and 3 identical pens. Leon paid $83.50 for 2 files and 8 identical pens. Find the cost of one such pen
The cost of the file is $6.15 and the cost of the pen is $8.9
Solving word problems with systems of linear equations.The interpretation of the given word problem leads to a system of linear equations.
From the given information:
Let the file be denoted with f and the pen be denoted with pf + 3p = 32.85 --- (1)
2f + 8p = 83.5 --- (2)
From equation (1)
f = - 3p+32.85
Replace the value of f in the above equation into equation (2)
2(-3p + 32.85) + 8p = 83.5
2p + 65.7 = 83.5
2p = 83.5 -65.7
2p = 17.8
p = 17.8/2
p = 8.9
Replacing the value of p = 8.9 into f = - 3p+32.85
f = -3(8.9)+32.85
f = 6.15
Therefore, we can conclude that the cost of the file is $6.15 and the cost of the pen is $8.9.
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What is x/7 >= -6? Please Answer!
Step-by-step explanation:
x/7 ≥ -6
we rewrite it as :
x/7 = -6
by cross multiplication
x = -42
In order words:
x ≥ -42
Hope this helps
Good luck ✅
LCM of 4x²-100 and 4x + 20
LCM of 4x²-100 and 4x + 20 is 4(x+5)(x-5)
What is Least Common Multiple?
Least Common Multiple is defined as the smallest number that is a multiple of two or more numbers.
We have to factorise 4x²-100 which is of the form A²-B²,
= (2x)² -(10)²
= (2x+10)(2x-10)
= 2×2(x+5)(x-5)
= 4(x+5)(x-5).
We have to factorise 4x + 20
= 4(x+5)
LCM of 4x²-100 and 4x + 20 = 4(x+5)(x-5).
Hence, LCM of 4x²-100 and 4x + 20 is 4(x+5)(x-5)
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What would be your weight on the Moon if your weight on Earth is 80 lbs?
6 times 80 lbs
one-sixth of 80. Four Times 80 lbs one-fourth of 80 lbs
A rectangle has a perimeter of 92cm and its length is 1cm more than twice its width.
Using the definition of perimeter write an equation for P in terms of L and W
Using the relationship given in the problem statement, write an equation for L in terms of W.
Answer: Width = 15cm
L = 31cm
Step-by-step explanation:
P = 92 cm
L = 1 + 2W
P = 2L + 2W
P = 2(1+2W) + 2W
P = 2+4W+2W
P = 2 + 6W
92cm = 2 + 6W
subtract 2 on both sides to cancel the 2 on the right side.
90cm = 6W
W = 90/6
Width = 15cm
L = 1+2W
L = 1 + 30cm
L = 31 cm
Verification:
P = 2L+2W
P = 2(31)+2(15)
P = 62+30
P = 92cm
Hope I Helped!
Answer:
P = 2(L + W) = 2L + 2W (first part)
L = 2W + 1 (second part)
Step-by-step explanation:
L = length of rectangle
W = width of rectangle
P = perimeter of rectangle = 2 * (L + W)
So P = 2(L + W) = 2L + 2W (1)
It is also given that length is 2 * width + 1
So we get the equation
L = 2W + 1 for L in terms of W (2)
This question does not ask you to compute L and W but if you wanted to do that use the following steps
Substitute for L from equation 2 to equation 1 giving
P = 2(2W+1) + 2W = 4W + 2 + 2W = 6W + 2
We know P = 92
So 6W + 2 = 92
Subtracting 2 from both sides we get 6W = 90
Dividing both sides by 6 gives us W = 15
and L = 2 * 15 + 1 = 31
We can check this by finding the perimeter from L and W
perimeter = 2(L+W) = 2(31 + 15) = 2 (46) = 92 which matches the data in the question
prime factorization of 220
Answer:
The Prime Factorization of 220 is 22 × 51 × 111.
Step-by-step explanation:
Factors of 220 are integers that can be divided evenly into 220. It has total 12 factors of which 220 is the biggest factor and the prime factors of 220 are 2, 5, 11. There for, the Prime Factorization of 220 is 22 × 51 × 111.
Which expression correctly represents “twice the sum of four and a number”?
Answer:
2 (4+x)
Step-by-step explanation:
4 + x is the sum of four and a number 'x' now multiply by 2
2 ( 4+ x)
From the sample space S= (1, 2, 3, 4..., 15} a single number is to be selected at random. Given the following events, find the indicated probability. A: The selected number is even. B: The selected number is a multiple of 4. C: The selected number is a prime number. P(A and C) P(A and C) = (Simplify your answer. Type an integer or a fraction.)
Probability the selected number is even is 7/15
Probability the selected number is a multiple of 4 is 1/5
Probability the selected number is prime = 2/5
What is probability?Probability is the likelihood of an event happening or an event not happening.
When it is certain an event would happen the probability is 1.
Probability can be independent or mutually exclusive.
Analysis:
Required outcome
A = {2, 4, 6, 8, 10, 12, 14} (even numbers)
Total entry = 7
Total Sample = 15
P(even numbers) = 7/15
B (multiples of 4) = {4, 8, 12}
Total entry = 3
P(B) = 3/15 = 1/5
C(prime numbers) = {2, 3, 5, 7, 11, 13}
Total entry = 6
P(C) = 6/15
P(A and C) = 0.
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