a) 10 men are selected at random, the probability their average height is above 72 inches is 0.0122.
b) Exactly one man is selected at random, the probability his average height is above 72 inches is 0.0122.
c) The 80th percentile for the average height of 10 men is 0.0097%.
d) The probability the average height of 10 men is between 70 and 71 inches is 0.13607.
Mean = 69.7 inches
Standard Deviation = 2.8 inches
a) Using normal distribution,
P(Y > 72) = P(Y - mean > 72 - mean)
P(Y > 72) = P((Y - mean ÷ SD) > (72 - mean ÷ SD))
P(Y > 72) = P(Z > (72 - mean ÷ SD))
P(Y > 72) = P(Z > (72 - 69.7 ÷ 2.8))
P(Y > 72) = P(Z > 2.25)
P(Y > 72) = 1 - P(Z ≤ 2.25)
P(Y > 72) = 0.0122
b) P(man's height is above 72 inches) = 0.0122
c) (80 × 0.0122) ÷ 100
= 0.0097%
d) P( 70 > Y > 71) = P(70 - mean > Y - mean > 71 - mean)
P( 70 > Y > 71) = P((70 - mean ÷ SD) > (Y - mean ÷ SD) > (71 - mean ÷ SD))
P( 70 > Y > 71) = P((70 - mean ÷ SD) > Z > (71 - mean ÷ SD))
P( 70 > Y > 71) = P((70 - 69.7 ÷ 2.8) > Z > (71 - 69.7 ÷ 2.8))
P( 70 > Y > 71) = P(0.107 > Z > 0.464)
P( 70 > Y > 71) = 0.13607
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given that tank=8 and sinx is negative determine sin(2x) cos(2x) and tan(2x)
Answer:
sin2x = 16/65
cos2x = -63/65
tan2x = -16/63
Explanation:
the tangent of an angle is equal to the opposite side over the adjacent side. So, if the tan(x) = 8, we can represent this as the following diagram:
Therefore, we can calculate the value of the hypotenuse as:
[tex]\text{Hypotenuse = }\sqrt[]{8^2+1^2}=\sqrt[]{64+1}=\sqrt[]{65}[/tex]With the hypotenuse, we can calculate sin(x) and cos(x) as follows:
[tex]\begin{gathered} \sin x=\frac{Opposite}{hypotenuse}=-\frac{8}{\sqrt[]{65}} \\ \cos x=\frac{\text{Adjacent}}{\text{hypotenuse}}=-\frac{1}{\sqrt[]{65}} \end{gathered}[/tex]We type the negative sign because the question says that sin(x) is negative.
Now, we will use the following trigonometric identities to find sin(2x), cos(2x) and tan(2x)
[tex]\begin{gathered} \sin 2x=2\sin x\cos x \\ \cos 2x=1-2\sin ^2x \\ \tan 2x=\frac{2\tan x}{1-\tan ^2x} \end{gathered}[/tex]Therefore, replacing the values, we get:
[tex]\sin 2x=2(\frac{-8}{\sqrt[]{65}})(\frac{-1}{\sqrt[]{65}})=\frac{16}{65}[/tex][tex]\cos 2x=1-2(\frac{-8}{\sqrt[]{65}})^2=1-2(\frac{64}{65})=-\frac{63}{65}[/tex][tex]\tan 2x=\frac{2(8)}{1-8^2}=-\frac{16}{63}[/tex]So, the answers are:
sin2x = 16/65
cos2x = -63/65
tan2x = -16/63
A 6-foot- tall electric pole casts a shadow that is 24 feet long. What is the ratio
of the pole's height to its shadow?
The ratio of the pole's height to its shadow is 1:4.
What is a ratio?An ordered pair of numbers a and b, written as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could write the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls).A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.So, the ratio of height:shadow:
The height of the pole is 6 feet.The shadow the pool creates is 24 feet.The ratio will be:
6:246/241/41:4
Therefore, the ratio of the pole's height to its shadow is 1:4.
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HELP ASAP PLSSSPLSPSLSPLSSSSSS
Graph g(x) = |x + 3|.
Answer:
Hope this helps!!
Hi can someone help me with this?Writing the algebraic equation for the phrase below.. 1. The sum of X and 96 equals half of X .
Given:
1. The sum of X and 96 equals half of X.
To determine the algebraic equation, we note that the sum of x and 96 would be:
x+96
Next, half of x must be like this:
x/2
Then, the phrase equals means we set x+96 equals to x/2.
Therefore, the answer is:
[tex]x+96=\frac{x}{2}[/tex]Just need the answer A, B , C or D
Answer:
A. 2.25 feet.
Explanation:
We know the following equation:
[tex]v=\sqrt[]{2gh}[/tex]Where v is the speed, g is the gravity and h is the height. So, replacing v by 12 feet per second and g by 32 feet per second square, we get:
[tex]12=\sqrt[]{2(32)h}[/tex]So, solving for h, we get:
[tex]\begin{gathered} 12=\sqrt[]{64h} \\ 12^2=(\sqrt[]{64h})^2 \\ 144=64h \\ \frac{144}{64}=\frac{64h}{64} \\ 2.25=h \end{gathered}[/tex]Therefore, the answer is A. 2.25 feet.
Write the equation in the form of f(x) for the following problems. You have solutions of: x=-4 and 3 and a point at (0,-60).
Equation in the form of f(x) for the solutions of x=-4 and x=3 and a point (0,-60) is equal to f(x) = 5(x+4)(x-3) .
As given in the question,
For the function f(x):
Standard form of the equation with solution x =a and x=b is:
f(x) = k(x-a)(x-b)
Solutions for the given function f(x) is x =-4 and x=3 and a point (0,-60)
is given by:
f(x) = k(x-(-4))(x-3)
= k(x+4)(x-3)
Point at (0,-60) we get,
-60 = k ( 0+4)(0 -3)
⇒-60 = -12k
⇒ k =5
Required equation is :
f(x) = 5(x+4)(x-3)
Therefore, equation in the form of f(x) for the solutions of x=-4 and x=3 and a point (0,-60) is equal to f(x) = 5(x+4)(x-3) .
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A volume of the cone is 1/3 the volume of a cylinder. The volume of the sphere is what fraction of the volume of the cylinder?
The volume of the sphere is 4/3 times the volume of the cylinder.
What is a cone?It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.
We have,
The volume of the cone is 1/3 the volume of a cylinder.
The volume of a cone is given as:
V = (1/3)πr²h ____(1)
The volume of a cylinder is given as:
V = πr²h _____(2)
From (1) and (2) we get,
(1/3)πr²h = 1/3 πr²h
The volume of a sphere:
V = 4/3 πr³
Since the height of the sphere and the radius is the same we can have
V = 4/3πr²h
So,
Volume of sphere = 4/3 x πr²h
The volume of the sphere = 4/3 x the Volume of the cylinder.
Thus,
The volume of the sphere is 4/3 times the volume of the cylinder.
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gary gets an average of 15 text messages during his 8 hour work day. in order to find the probability that gary will get exactly 3 text messages in a 2 hour portion of his work day using the poisson distribution, what is the time interval of interest?
The probability that Gary will get exactly 3 text messages in a 2-hour portion of his work day using the Poisson distribution, what is the time interval of interest: 2 hours
Gary will get calls according to Poisson distribution with an average # of calls per hour = 15.
Let x be the Poisson random Variable Such that X ~Poisson (15).
We need to find P(x≤3) in 2 hours.
Thus, the time interval of interest is 2 hours.
What is probability ?
Probability is the likelihood of an event occurring. It can range from an impossible event to a probability to an absolute certainty. In mathematics, probability is on a scale of 0-1. Zero means the event is impossible, like rolling seven dice with only the numbers 1-6. One is an event that will happen, that's for sure. An example of a specific event is tomorrow is Friday if today is Thursday. It will definitely happen. The median is 0.5 or half and these events are equally likely. A good example of half probability is tossing a coin. It gets straight heads or tails.
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Tyee has $720 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax. He buys a new bicycle for $401.83. He buys 4 bicycle reflectors for $12.85 each and a pair of bike gloves for $23.83. He plans to spend some or all of the money he has left to buy new biking outfits for $40.49 each. Use the drop-down menu below to write an inequality representing oo, the number of outfits he can buy while staying within his budget.
The inequality that represents the number of outfits he can buy while staying within his budget is M ≤ 6.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal =
Greater than and equal=
We have,
Total amount to spend = $720
Cost of bicycle = $401.83
Cost of bicycle reflector = $12.85 ( 4 reflector bought )
Cost of bike cloves = $23.83
Cost of biking outfits = $40.49
The number of possible biking outfits:
401.83 + 4 x 12.85 + 23.83 + M40.49 ≤ 720
401.83 + 51.4 + 23.83 + M40.49 ≤ 720
477.06 + M40.49 ≤ 720
M40.49 ≤ 720 - 477.06
M40.49 ≤ 242.94
M ≤ 242.94 / 40.49
M ≤ 6
M = Number of possible outfits
Thus,
The inequality that represents the number of outfits he can buy while staying within his budget is M ≤ 6.
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Which property is demonstrated below?
a(b+c)=(a.b)+(a.c)
O Inverse property
O Distributive property
O Communitive property
O Identity property
( and 15 points for this and will make brainliest to best answer) Please be fast!
Which property is demonstrated below?
a(b + c) = (a*b) + (a*c)
O Inverse property
O Distributive property
O Communitive property
O Identity property
Help This is due at the end of class
The coordinates of the vertices of the image of the square are S'(x, y) = (- 1, - 4), T'(x, y) = (- 1, 1), U'(x, y) = (4, 1) and V'(x, y) = (4, - 4).
How to translate a geometric locus set on a Cartesian plane
In this problem we need to make use of a translation on a geometric locus on a Cartesian plane, which is generated by four points representing the vertices of the square. The translation is a kind of rigid transformation, whose formula is shown below:
P'(x, y) = P(x, y) + t(x, y)
Where:
P(x, y) - Original pointt(x, y) - Translation vector.P'(x, y) - Resulting pointIf we know that S(x, y) = (- 6, - 5), T(x, y) = (- 6, 0), U(x, y) = (- 1, 0) and V(x, y) = (- 1, - 5) and t(x, y) = (5, 1), then the locations of the vertices of the triangle are:
S'(x, y) = (- 6, - 5) + (5, 1)
S'(x, y) = (- 1, - 4)
T'(x, y) = (- 6, 0) + (5, 1)
T'(x, y) = (- 1, 1)
U'(x, y) = (- 1, 0) + (5, 1)
U'(x, y) = (4, 1)
V'(x, y) = (- 1, - 5) + (5, 1)
V'(x, y) = (4, - 4)
The location of the image of the square is shown below.
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The ages of students at a university are normally distributed with a mean of 21. What percentage of the student body is at least 21 years old?.
Percentage of the student body exists at least 21 years old exists 50%.
What is meant by normal distribution?A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.
As one moves away from the center, values start to taper off and the majority of values are concentrated in this area. In a normal distribution, the mean, mode, and median are identical measures of central tendency.
When given a normal or Symmetric distribution, the mean of the distribution exists at the center with 0.5 or 50% of the distribution to either side (right and left) of the distribution.
Therefore, if the mean = 21 ; then the percentage of student body with at least 21 years is the percentage to the left of the distribution, which exists 50%.
P(x ≤ 21) = 0.5 = 50%
Therefore, 50 percentage of the student body exists at least 21 years old
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Find (3.0x10^15) over (5.0x10^6)(2.4x10^3), expressed in scientific notation.
The result of 3.0×[tex]10^{15}[/tex] over 5.0×[tex]10^6[/tex] in scientific notation is 6×[tex]10^8[/tex]
The first number = 3.0×[tex]10^{15}[/tex]
The second number = 5.0×[tex]10^6[/tex]
3.0×[tex]10^{15}[/tex] over 5.0×[tex]10^6[/tex] means we have to divide the first number by the second number
The scientific notation is the a method of representing the a very large number or a very small number in a simple way. The general from of the scientific notation is when a number from 1 to 10 is multiplied by the power of 10.
Here we have to divide 3.0×[tex]10^{15}[/tex] by 5.0×[tex]10^6[/tex]
3.0×[tex]10^{15}[/tex] ÷ 5.0×[tex]10^6[/tex] = (3/5) × [tex]10^{15-6}[/tex]
= 0.6×[tex]10^9[/tex]
= 6×[tex]10^8[/tex]
Hence, the result of 3.0×[tex]10^{15}[/tex] over 5.0×[tex]10^6[/tex] in scientific notation is 6×[tex]10^8[/tex]
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One of the rows in the table has an error and does not have the same ratio as the other rows. Which explains how to correct the error in the table?
Conversion Chart
Feet
Centimeters
Row 1
3
91.44
Row 2
6
172.88
Row 3
7
213.36
Row 4
9
274.32
Row 1 should show 3 feet is equivalent to 92.44 centimeters.
Row 2 should show 6 feet is equivalent to 182.88 centimeters.
Row 3 should show 7 feet is equivalent to 223.36 centimeters.
Row 4 should show 9 feet is equivalent to 284.32 centimeters.
The correct option regarding the error in the proportional relationship is given as follows:
Row 2 should show 6 feet is equivalent to 182.88 centimeters.
Direct proportional relationshipA direct proportional relationship is a function in which the output variable y is calculated by the multiplication of the input variable x and the constant of proportionality k, as follows:
y = kx.
In the context of this problem, the input and the output are given as follows:
Input: Length in feet.Output: Length in centimeters.The constant is calculated dividing the output by the input of each of the lengths, hence:
Row 1: k = 91.44/3 = 30.48.Row 2: k = 172.88/6 = 28.81.Row 3: k = 213.36/7 = 30.48.Row 4: k = 274.32/9 = 30.48.Due to the different ratio, the mistake is in Row 2, and the correct value should be of:
6 x 30.48 =182.88 centimeters.
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the area of a rectangular garden in square is xsquare -5x-300 If x=45 what is the width and the height of the garden 12a.widthheight 12b.please pot it step by step show all your work thank you
If a rectangle has an area of A and sides b and h, then:
[tex]A=b\cdot h[/tex]Solving for the base:
[tex]b=\frac{A}{h}[/tex]Basically, the sides b and h could have any value provided that b*h=A.
Nevertheless, this problem seems to want from us to factorize the expression:
[tex]x^2-5x-300[/tex]So that each side is a binomial.
Part a)
To factorize that expression, find two numbers so that if they are added up, the sum is equal to -5, and if they are multiplied, the product is equal to -300.
Since the product is negative, one number must be negative. Since the sum is negative, the biggest number should be the negative one.
Consider the factors of 300:
[tex]300=2\cdot2\cdot3\cdot5\cdot5[/tex]Using those factors, we can find pairs of numbers that give 300 as a result from multiplying.
After a bit of trial and error, notice that 15*20=300. If we choose 20 as the negative number, then 15*(-20)=-300 and 15+(-20)=-5. Therefore:
[tex]x^2-5x-300=(x+15)(x-20)[/tex]So, we can choose the width and the height to be those factors. Since (x+15) is greater then (x-20), then:
[tex]\begin{gathered} \text{Width}=x+15 \\ \text{Height}=x-20 \end{gathered}[/tex]Part b)
If x=45, then:
[tex]\begin{gathered} \text{Width}=60feet \\ \text{Height}=25feet \end{gathered}[/tex]Find the midpoint of the segment below and enter its coordinates as anordered pair. If necessary, express coordinates as fractions, using the slashmark (/) for the fraction bar.
Each midpoint's coordinate is given by the mean of the respective coordinates of the two endpoints of the segment. Then, if we say M is the midpoint of that segment, we have:
Mx = (-4 + 4)/2 = 0/2 = 0
My = [6 + (-2)]/2 = (6 - 2)/2 = 4/2 = 2
Therefore, writing those coordinates as an ordered pair, we have:
M = (0, 2)
What is the slope of -2,1 and 2,1
Is should be 50% slope
Answer:
m=0
Step-by-step explanation:
(-2,1) (2,1)
x1=-2,x2=2,y1=1,y2=1
Gradient/slope
m=y2-y1/x2-x1
m=1 - 1/2-(-2)
m=0/2+2
m=0/4
m=0
The coordinates of quadrilateral ABCD are A (-6,2) B (-5,3) C (7,3) D (0,4). What are the coordinates of the image if the quadrilateral is translated 4 units down and 3 units right
If the coordinates of quadrilateral ABCD are A (-6,2) B (-5,3) C (7,3) D (0,4) and it is translated 4 units down and 3 units right, then the coordinates of the image is A'(-3,-2), B'(-2,-1), C'(10,-1) and D'(3,0)
The coordinates of the quadrilateral ABCD is
A (-6,2) , B(-5,3), C(7,3) and D(0,4)
The quadrilateral is translated 4 units down and 3 units right
After translation
A(x, y)⇒ A(x + a, y +b)
The value of a and b will be positive if the shift is right and up.
The value of a and b will be negative if the shift is left and down.
Therefore
a = 3, b = -4
The coordinates of A' =(-6+3,2-4)=(-3,-2)
The coordinates of B' =(-5+3,3-4)=(-2,-1)
The coordinates of C' =(7+3,3-4)=(10,-1)
The coordinates of D' =(0+3,4-4)=(3,0)
Hence, If the coordinates of quadrilateral ABCD are A (-6,2) B (-5,3) C (7,3) D (0,4) and it is translated 4 units down and 3 units right, then the coordinates of the image is A'(-3, -2), B'(-2, -1), C'(10, -1) and D'(3, 0)
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determine the equation of line from the graph
Answer:
y=2x+0
Step-by-step explanation:
This is slope intercept form. The slope is 2 you can tell by the two points on the graph at (0,0) and (1,2). The points move up 2 and over 1. That makes the slope 2/1 but since the bottom half is just a one it can be simplified to 2.
And the +0 just means that its y intercept is 0,0
however it is not required to put +0 at the end
Answer:y=2x+0
Step-by-step explanation:
Gwen says that the sum of -1 3/4 and 2 1/2 is the same as the difference between 2 1/2 and 1 3/4 is Gwen correct explain why or why not
The sum of -1 and 3/4 and 2 and 1/2 is the same as the difference between 2 and 1/2 and 1 and 3/4.
First we will convert the mixed fractions into improper fractions.
-1 and 3/4 = -7/4
2 and 1/2 = 5/2
Sum of -1 and 3/4 and 2 and 1/2 = -7/4 + 5/2 = -7/4 + 10/4 = 3/4
Difference between 2 and 1/2 and 1 and 3/4 = 5/2 - 7/4 = 10/4 - 7/4 = 3/4
As both the values equal to 3/4 , we can say that the sum of -1 and 3/4 and 2 and 1/2 is the same as the difference between 2 and 1/2 and 1 and 3/4.
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Evelyn sells beauty supplies. She gets 5% commission for selling beauty products. How much commission will she receive if she sells 1,648 worth of beauty products?
Given:
Evelyn sells beauty supplies. She gets 5% commission for selling beauty products.
Required:
To find the commission she receive if she sells $1,648 worth of beauty products.
Explanation:
The commission she receive if she sells $1,648 worth of beauty products is
[tex]\begin{gathered} =\frac{5}{100}\times1648 \\ \\ =82.4 \end{gathered}[/tex]Final Answer:
$82.4
Please help me find the quadratic inequality for this
y ≥ x2 - 4x + 1
Answer:
x/> -y/2 + 1/2
20) g(a) = a² - 2
h(a) = -3a
Find g(a) + h(a)
The value of g(a) + h(a) is a²-3a-2 or (a-2)(a-1) using addition of functions.
What is the Function?Given a collection of inputs X (domain) and a set of potential outputs Y (codomain), a function is more technically defined as a set of ordered pairings (x,y) where x belongs to X and y belongs to Y, with the caveat that there can only be one ordered pair with the same value of x. The function notation f:XY can be used to express that f is a function from X to Y
Adding two functions-
g(a) = a²- 2
h(a) = -3a
Let h(a) be g(a) + h(a)
So h(a) = a² - 2 - 3a.
We can factorize the function into (a-2)(a-1).
So we get h(a) = (a-2)(a-1).
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The cost of mailing a package is proportional to the weight of the package. The proportional relationship can be represented with the equation c = 0.4w, where c represents the total cost and w represents weight in ounces. A graph for the equation is shown.
graph with x axis labeled weight in ounces and y axis labeled cost in dollars, with a line from 0 comma 0 going through 2 comma 0.8
Which of the following statements is true about the graph shown?
The graph is incorrect and the line should go through the point (0.4, 1).
The equation c = 0.4w is correctly represented by the graph.
The x-axis and y-axis are labeled incorrectly.
The graph does not show a proportional relationship.
Among the given statements The equation c = 0.4w is correctly represented by the graph is correct.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
A proportional relationship graph between two variables is a relationship where the ratio between the two variables is always the same.
By given the equation c = 0.4w, where c represents the total cost and w represents weight in ounces.
Given that graph with x axis labeled weight in ounces and y axis labeled cost
Let us construct a table
Weight(x) 1 2
Cost (Y) 0.4 0.8
As given graph with x axis labeled weight in ounces and y axis labeled cost in dollars, with a line from 0 comma 0 going through 2 comma 0.8
The equation c = 0.4w is correctly represented by the graph.
Hence among the given statements The equation c = 0.4w is correctly represented by the graph is correct.
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In Mr. Patterson’s class, the average score among students who studied for an exam was 78. The average among students who did not study was 54. The overall class average was 70. What portion of the class did not study? Express your answer as a common fraction.
What’s the answer plsss
Answer:
option a is the right answer .
Step-by-step explanation:
Cos theta = B/h = 8/21
theta = 67.6 °
Step-by-step explanation:
imagine the triangle being flipped upwards around DE, so that F is on top instead of on the bottom.
then you see clearly that
DF (21) is the radius of the trigonometric circle,
DE is cos(angle D)×radius,
EF (8) is sin(angle D)×radius.
so,
8 = sin(angle D)×21
sin(angle D) = 8/21 = 0.380952381...
angle D = 22.39268781...° ≈ 22.4°
and so, something is wrong with your problem definition.
the answer options seem to aim for angle F, for which EF (8) is the cosine × radius.
but for angle D EF is clearly the sine × radius.
and for answer option b (20.9°) EF would have to be about 7.5 units long (with the radius DF still being 21). that is all too much off.
your teacher made a mistake. send him/ her my regards.
3/4 of a number is 30. What is the number? )) What is the number?
To find the number we can create the following equation and solve for x:
[tex]\frac{3}{4}\cdot x=30[/tex]Let x be the missing number, use inverse operations to solve the equation:
[tex]\begin{gathered} x=30\cdot\frac{4}{3} \\ x=\frac{120}{3} \\ x=40 \end{gathered}[/tex]The number is 40.
Rewrite the following equation as a function of x.
1+ 3y - 29 = 0
O A. f(x)
f(x) = 9,2808 2
OB. f(x) = -9,280 +
O c. f(x) = -9,280 + 20
O D. f(x) = 9,280
1
20x
a jar contains 22 red marbles number 1 to 22 and 52 blue marbles number 1 to 50 to a marble is drawn at random from the drawer find the probability of the given event around solution to three decimal places
We are given a jar that contains 22 red marble( 1 to 20) and 52 blue marbles (1 to 52). We can proceed to find the solution for each part of the question.
PART 1
Let the probability that the marble is red be P(r).
Therefore,
[tex]P(r)=\frac{Number\text{ of red balls}}{\text{Total number of balls}}[/tex]This gives,
[tex]\begin{gathered} P(r)=\frac{22}{22+52}=\frac{22}{74} \\ \therefore P(r)=\frac{11}{37}=0.297 \end{gathered}[/tex]Therefore, the probability that the marble is red is:
ANSWER= 0.297
PART 2:
Let the probability of picking odd-numbered balls be P(o)
Therefore,
[tex]P\mleft(o\mright)=\frac{Number\text{ of odd balls}}{\text{Total number of balls}}[/tex]We already know that the total number of balls is 72 for the previous question. Therefore, the total number of oddballs will be the sum of odd red balls and odd blue balls. This consists of 11 odd red balls and 26 odd blue balls.
Therefore,
[tex]\begin{gathered} P(o)=\frac{26+11}{74}=\frac{37}{74} \\ \therefore P(o)=0.5 \end{gathered}[/tex]The probability of picking odd-numbered balls is
ANSWER = 0.5
PART 3:
Let the probability of picking a red or odd-numbered ball be P(r U o)
[tex]P(r\cup o)=P(r)+p(o)-p(r\cap o)[/tex]Since we already have the values of P(r) and P(o), therefore we only need to find p(r n o).
p(r n o) is the probability of the ball being red and odd. The number of the red and oddball is 11.
Therefore,
[tex]\begin{gathered} P(r\cap o)=\frac{nu\text{mber of red and odd balls}}{\text{Total number of balls}} \\ =\frac{11}{74} \\ =0.149 \end{gathered}[/tex]This implies that,
[tex]\begin{gathered} P(r\cup o)=P(r)+p(o)-p(r\cap o) \\ P(r\cup o)=0.297+0.5-0.149 \\ \therefore P(r\cup o)=0.648 \end{gathered}[/tex]Hence, the probability of picking a red or odd-numbered ball is
ANSWER = 0.648
PART 4:
Let the probability of picking a blue or even-numbered ball be P(b U e)
Therefore,
[tex]P(b\cup e)=p(b)+p(e)-p(b\cap e)[/tex]From the above formula, we would need to figure out all the parts. p(b) represents the probability of blue marble. This gives,
[tex]\begin{gathered} p(b)=\frac{Number\text{ of blue balls}}{\text{Total number of balls}} \\ \therefore p(b)=\frac{52}{74}=0.703 \end{gathered}[/tex]p(e) represents the probability of even balls. The total number of even balls will be the sum of the even red balls and even blue balls.
[tex]\begin{gathered} p(e)=\frac{26+11}{74}=\frac{37}{74} \\ \therefore p(e)=0.5 \end{gathered}[/tex]p(b n e) represents the probability of blue and even balls. We have 26 blue and even balls
[tex]\begin{gathered} p(b\cap e)=\frac{Number\text{ of blue and even balls}}{\text{Total number of balls}} \\ P(b\cap e)=\frac{26}{74}=0.351 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} P(b\cup e)=p(b)+p(e)-p(b\cap e) \\ P(b\cup e)=0.703+0.5-0.351 \\ \therefore P(b\cup e)=0.852 \end{gathered}[/tex]Therefore, the probability of picking a blue or an even ball is:
ANSWER = 0.852
Select the correct answer.
Which of the following represents a function?
A. The first graph
B. The second graph
C. {(0,1), (3,2), (-8,3), (-7,2), (3,4)}
D.
x -5 -1 9 8 -1
y 1 7 23 17 1
The relation that represents a function is given as follows:
B. The second graph.
When does a relation represents a function?A relation represents a function if each value of the input is mapped to only one value of the output, that is, one input cannot be mapped to multiple outputs.
For a point in the standard format (x,y), we have that:
x is the input.y is the output.The meaning is that the input given by the x-coordinate is mapped to the output given by the y-coordinate.In a graph, the equivalent to this is that there can be no vertically aligned points.
Then, for the options in this problem, we have that:
a does not represent a function, as the input -1 is mapped to two outputs, meaning that there are vertically aligned points.b represents a function, as each input value(-4, 9, 13 and -7) is mapped to only one output.c does not represent a function, as the input 3 is mapped to two outputs.d does not represent a function, as the input -1 is mapped to two outputs.More can be learned about relations and functions at https://brainly.com/question/12463448
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