There are 7 people taking part in a raffle. Ann, Hans, Jim, Kira, Omar, Ravi, and Soo. Suppose that prize winners are randomly selected from the 7 people. Compute the probability of each of the following events. Event A: Ann is the first prize winner, Jim is second, Soo is third, and Kira is fourth. Event B: The first four prize winners are Soo, Ann, Ravi, and Hans, regardless of order. Write your answers as fractions in simplest form.
P(A) =
P (B) =
The probability of event A is 0.0012 and the probability of event B is 0.0288
How to find the probabilities?There are 7 people and 4 prices.
A) The probability that Ann wins the first prize is 1/7, assuming that all 7 people have the same probability of winnig.
Then Jim is second, now the probability is 1/6 (because we don't count Ann anymore).
Soo wins the third one, with a probability 1/5.
Kira wins the last one, with a probability of 1/4.
The joint probability is the product of all the individual ones:
P(A) = 1/7*1/6*1/5*1/4 = 0.0012
B) Now we just want that Soo, Ann, Ravi, and Hans win, but the order does not matter.
So we have the same probability than above, but now we need to include the permutations of the 4 elements, so we add a factor 4!.
P(B) = 4!*0.0012 = 4*3*2*1*0.0012 = 0.0288
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A state's recidivism rate is 22%. This means about 22% of released prisoners end up back in prison (within three years). Suppose two randomly selected prisoners who have been released are studied. What is the probability that both of them go back to prison?
The probability that both of them go back to prison is 4.48%.
What is probability?Probability is a measure of the likelihood of an event occurring. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it.The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.
The state recidivism rate is given by 22%.
So, the probability that both of the prisoners will go back to prison will be:
= 22% × 22%= 0.22 × 0.22= 4.84%Hence, the probability that both of them go back to prison is 4.48%.
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4. Find the volume of the cylinder. Leave youranswer in terms of π.
ANSWER
637.5π mm³
EXPLANATION
The volume of a cylinder is the product of its base area and its height. In this problem, the radius of the base of the cylinder is 5 mm, and its height is 25.5 mm. The volume is,
[tex]V=B\cdot h=(\pi\cdot r^2)\cdot h=\pi\cdot5^2mm^2\cdot25.5mm=\pi\cdot25\cdot25.5mm^3=637.5\pi\text{ }mm^3[/tex]Hence, the volume is 637.5π mm³.
Consider the following information: Cash = $6,000 Beginning Balance = $200,000 Capital added = $15,000 Revenues = $10,000 Expenses = $5,000 Net Income = $56,000 Owner’s Withdrawals = $60,000 What is the ending balance on the Statement of Changes in Owner's Equity for this data?
The ending balance Statement of Changes in Owner's Equity for this data is given by: $222,000.
How to calculate the ending balance?The ending balance is given by the difference between all the amounts that were on the account, and were added, by all amounts that were removed from the account.
The amounts that were added to the balance are given as follows:
Cash = $6,000.Beginning Balance = $200,000.Capital added = $15,000Revenues = $10,000Net Income = $56,000The amounts that were removed from the balance are given as follows:
Expenses = $5,000.Owner’s Withdrawals = $60,000Hence the ending balance is calculated as follows:
6,000 + 200,000 + 15,000 + 10,000 + 56,000 - 5,000 - 60,000 = $222,000.
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Runners at a cross-country meet run 3 miles north and then 5 miles west from the starting line. Determine the shortest straight path they must run to get back to the starting line.
square root of 8 miles
4 miles
square root of 34 miles
8 miles
The shortest straight path they must run back to the starting line is the square root of 34 miles.
What is the shortest straight path?The distance run by the runners forms a right triangle. A right triangle is a polygon that has three sides. The length, base and the hypotenuse. The hypotenuse is the longest side of the right triangle.
The miles run north is the length, the miles run west is the base and the shortest straight path to the starting line is the hypotenuse.
In order to determine the hypotenuse, the Pythagoras theorem would be used.
The Pythagoras theorem: a² + b² = c²
where a = length
b = base
c = hypotenuse
3² + 5²
= 9 + 25
= 34
c = √34
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Write 9⁴ as a power of 3.
Answer:
3^8
Step-by-step explanation:
9^4 = 9*9*9*9
9 = 3*3
9^4 = (3*3)*(3*3)*(3*3)*(3*3)
9^4 = 3*3*3*3*3*3*3*3 = 3^8
or, more simply
9 = 3^2
9^4 = (3^2)^4
we use (x^y)^z = x^(y*z)
(3^2)^4 = 3^(2*4) = 3^8
Please solve this question!! Please help me
In order to simplify the expression, start by solving the subtraction of fractions in the form
[tex]\frac{a}{b}-\frac{c}{d}=\frac{ad-bc}{bd}[/tex]then,
[tex]undefined[/tex]The table represents a quadratic function. Write an equation of the function in standard form.
-9-7-5-3
0 8 8
X
y
y=0
Previous
1 2
0
30
4
32
5
6
7
10
Next
Answer:
Step-by-step explanation:
What are the solutions of equation (x-2)^2=-3x+6Select all that apply(The choices are in the image)
SNSWER
. x = 2
F. x = -1
EXPLANATION
e can rewrite this equation as a quadratic frunction equal to zero.
First apply the binomial squared on the left side:
[tex](x-2)^2=x^2-4x+4[/tex]This is to write it in standard form. Now we have the equation:
[tex]x^2-4x+4=-3x+6[/tex]We can add 3x on both sides of the equation:
[tex]\begin{gathered} x^2-4x+3x+4=-3x+3x+6 \\ x^2-x+4=6 \end{gathered}[/tex]And subtract 6 from both sides:
[tex]\begin{gathered} x^2-x+4-6=6-6 \\ x^2-x-2=0 \end{gathered}[/tex]Now we can use the quadratic formula to solve this for x:
[tex]\begin{gathered} ax^2+bx+c=0 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]In our equation a = 1, b = -1 and c = -2:
[tex]\begin{gathered} x=\frac{1\pm\sqrt[]{1^2+4\cdot2\cdot1}}{2\cdot1} \\ x=\frac{1\pm\sqrt[]{1+8}}{2} \\ x=\frac{1\pm\sqrt[]{9}}{2} \\ x=\frac{1\pm3}{2} \\ x_1=\frac{1+3}{2}=\frac{4}{2}=2_{} \\ x_2=\frac{1-3}{2}=\frac{-2}{2}=-1 \end{gathered}[/tex]Therefore the solutions to the given equation are x = 2 and x = -1
2x-3>7 i kinda need help can i get the answer
Answer:
x>5
Step-by-step explanation:
2x>10
x>5
What's the answer to this equation? Please include steps
6(915 - x) = 100 + x
Answer:
x = 770
Step-by-step explanation:
You want the solution to the equation 6(915 - x) = 100 + x.
SolutionIt often works well to simplify the equation first. Here, that means eliminating parentheses using the distributive property:
6(915) -6(x) = 100 +x
5490 -6x = 100 +x . . . . . . . . carry out the multiplication
5490 -6x +6x = 100 +x +6x . . . . . add 6x to both sides
5490 = 100 +7x . . . . . . . . . . collect terms
5490 -100 = 100 +7x -100 . . . . . . subtract 100 from both sides
5390 = 7x . . . . . . . . . . . . . . collect terms
5390/7 = (7x)/7 . . . . . . . . . . . . . . . . divide both sides by 7
770 = x . . . . . . . . . . . . . . . . carry out the division
The solution to the equation is x = 770.
__
Check
6(915 -770) = 100 +770 . . . . use the value of x in the equation
6(145) = 870 . . . . true
__
Additional comment
After eliminating parentheses, this is a 3-step linear equation, so is solved in the usual way. First, the variable terms are collected on one side of the equal sign. Then the constant terms are collected on the other side of the equal sign. Finally, the equation is divided by the coefficient of the variable.
Can you solve this please.
what is 3.3 in fraction
Answer: 33/10
Step-by-step explanation:
=3.3 X 10/10
= 33/10
Answer done. 33/10 #
Peter has 480 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?
A rectangle that maximizes the enclosed area has a length of _____ yards and a width of _____
1. Length of rectangular area = 120 yards
Width of rectangular area = 120 yards
2. Maximum area = 14,400 square yards.
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Total fencing Peter has = 480 yards
Now,
We can say that the total fencing he has in terms of length L and width W of the rectangle will be;
⇒ L + L + W + W = 480
⇒ 2(L+W) =480
Divide both sides by 2 to get
⇒ L+W = 240
Subtract W from both sides so we get L in terms of W;
⇒ L= 240 - W
Since, The area of a rectangle is Length times width.
So, Area = (L × W)
⇒ Area = (240-W) W
⇒ Area = 240W - W²
Now, By comparing the equation with an quadratic equation
ax² + bx + c , we get;
⇒ a = -1 and b = 240
Since, Area is maximum when;
W = -b/2a
W = - 240/-2
W = 120
So, for W = 120 yards area is maximum.
Hence, Length of yards = 240 - 120 = 120 yards.
(b) Maximum area of the rectangle can be found by substitute this
W = 120 in the Area equation;
So, the maximum area ,
A = 240 (120) - 120²
A = 28800 - 14400
A = 14400
Hence, Maximum area = 14,400 square yards.
Thus,
1. Length of rectangular area = 120 yards
Width of rectangular area = 120 yards
2. Maximum area = 14,400 square yards.
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Based on the diagram below, which statement is
true?
1. a || b
2. a || c
3. b || c
4. d || e
Based on given diagram we can conclude that d || e.
As per the diagram given there are some lines and angles which are defined and some of them are to be find so that we can conclude answer from the given options.
The attached image shows the Angles which are solved for the solution of the question as follows;
For line 'a' makes an angle of 110° with line 'd' and as total angle made by a line is always 180° Therefor another angle made by line 'a' with line 'd' will be 180° - 110° = 70° a shown in the attached figure.
For line 'c' makes an angle of 115° with line 'd' and as total angle made by a line is always 180° Therefor another angle made by line 'c' with line 'd' will be 180° - 115° = 65° a shown in the attached figure.
For line 'b' makes an angle of 60° with line 'd' and as total angle made by a line is always 180° Therefor another angle made by line 'b' with line 'd' will be 180° - 60° = 120° a shown in the attached figure.
By Comparing All the angles we can conclude that line a ∦ b, a ∦ c, b ∦ c.
∴ Line 'd' is parallel to line 'e'. => d || e.
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A statement is made about correlation. State whether the correlation is positive or negative and whether the correlation is most likely due to coincidence, a common underlying cause, or a direct cause.
As Thomas's income rose over the last 20 years so has his stress level.
Select one:
A.
Positive correlation; direct cause
B.
Negative correlation; common underlying cause
C.
Positive correlation; common underlying cause
D.
Positive correlation; coincidence
Based on the statement about Thomas's income rising along with his stress income, the correlation and cause is C. Positive correlation; common underlying cause.
What is a positive correlation?Positive correlation between two variables means that they move in the same direction. When one of the variables increases, the other variable increases as well. When one variable decreases, the other variable decreases too.
The income level of Thomas is increasing at the same time the stress is increasing so this is a positive correlation.
A higher Income level might lead to more work and responsibilities which is most likely the common underlying cause for the positive correlation.
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Classify the relationship between each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles. 5 7 8 1 point 21 and 28 choose your answer... 1 point 22 and 24 choose your answer... 1 point 23 and 26 choose your answer... 1 point 26 and 27 choose your answer... + 56 3/4 78
∠1 and ∠8 are alternate exterior angle.
∠2 and ∠4 are corresponding angle.
∠3 and ∠6 are alternate interior angle.
∠6 and ∠7 are consecutive interior angle.
What is alternate exterior angle ?When a transversal intersects two or more lines, alternate exterior angles are produced. These angles are created on the various transversal sides' outer sides.Any two parallel lines that cross a transversal produce a few pairs of angles with the transversal. In the area inside the parallel lines, interior angles are generated, whilst alternate external angles are created in the area outside the parallel lines.
what is corresponding angle ?Corresponding angles are those that are created when two parallel lines are intersected by another line, whether it be a transversal or a matching corner (i.e. the transversal). Angle p and angle w, for instance, are the matching angles in the illustration below.
What is alternate interior angle ?The pair of angles created on the inner side of the parallel lines and on the opposite sides of the transversal when two parallel lines are intersected by a transversal are referred to as alternate internal angles. All of these angles are equal. There is another way to look at this. The alternative interior angles can establish the parallelism or non-parallelism of the given lines. The supplied lines that are crossed by a transversal are said to be parallel if these angles are equal.
What is consecutive interior angle ?The pair of interior angles that are not contiguous to one another and are on the same side of the transversal are referred to as consecutive interior angles. Things that follow one another are referred described as being "consecutive." On a transversal's internal side, adjacent interior angles are found next to one another.
∠1 and ∠8 are alternate exterior angle.
∠2 and ∠4 are corresponding angle.
∠3 and ∠6 are alternate interior angle.
∠6 and ∠7 are consecutive interior angle.
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The side length of a cube is x^-2 inches. What is the volume of the cube?
If the side length of the cube is x⁻² inches then the volume of the cube will be x⁻⁶ .
The volume of the cube with side length "a" can be calculated using the formula
Volume = a³ ,
For Example : if the side length of the cube is 2m , then the volume of the cube will be
Volume = 2³ = 8m³ .
In the question ,
it is given that ,
the side length of the cube is x⁻² inches ,
So, substituting the value of side length in the Volume formula , we get
volume = (x⁻²)³
= x⁻⁶ ....(as (xᵃ)ᵇ = (x)ᵃˣᵇ = xᵃᵇ )
Therefore , If the side length of the cube is x⁻² inches then the volume of the cube will be x⁻⁶ inches³ .
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Please help I’ll mark you as brainliest if correct!!
Answer:
A. 366-249=125
B. 13386-9608=4788
An agency charges $100 per person for a trip to a concert if 50 people travel in a group. But for each person above the 50, the amount charged for each traveler will be reduced by $3. If x represents the number of people above the 50, write the agency's revenue R as a function of x. (Assume that x is greater than zero.)
R(x) =
The equation of the function of the agency revenus in terms of x is R(x) = (50 + x) * (100 - 3x)
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to determine the agency's revenue R as a function of x?From the question, the given parameters are given as
Number of people = 50
Amount charged per person = $100
The above means that the total charges is
Total = Number of person * Amount charged per person
Rewrite as
Revenue = Number of person * Amount charged per person
From the question, we have
The charges for each traveller reduces by $3 for each additional person
Let the number of added person be x
So, we have
Revenue = (Number of person + x) * (Amount charged per person - 3x)
Substitute the known values in the above equation
So, we have
R(x) = (50 + x) * (100 - 3x)
Hence, the agency's revenue R as a function of x is R(x) = (50 + x) * (100 - 3x)
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In 6 and 7, use the diagram. The art room at a school is made up of three sections: a pottery section, a painting section, and a sculpture section. 6. Artwork will be on display for an art show in all sections of the art room except the sculpture section. How much space is available for the art show? 7. What is the area of the painting section? Please im confused
Space available for the art show is 2/3 or 66.6%.
What is fraction?A number that represents a rational number is called a common fraction. Additionally, that same quantity can be expressed as a decimal, a percent, or a negative exponent.
The art room is divided into a total of three divisions, as can be seen from the information given. There is 2/3 of the total amount of space available for the art section because the artwork will only be presented on 2 of the 3 available parts. With 33.3% of the art room currently filled and unavailable, only 66.6% of the space is available for the art to be displayed on.
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Write an equation in point-slope form of the line that passes through the given points, then write the equation in slope-intercept form.
(-3,5), (9,1)
What is the point-slope form of the equation of the line?
(Simplify your answer. Use integers or fractions for any numbers in the equation.)
The x and y coordinates of the line are utilized to compute the steepness of the line using the slope formula.We are aware that one of a line's most crucial qualities is its slope because it aids in determining the pace of change.
What is the point-slope form of the equation of the line?
A line's steepness can be determined by looking at its slope.Slope is calculated mathematically as "rise over run" (change in y divided by change in x).
Using the formula
m=y2y1/2x1,
which is the change of y over the change of x, determine the slope of the line between (3,5) and (9,1).
Slope is equal to the change in y over the change in x
, or rise over run.
m=change in y /change in x
The change in x is equal to the difference in x-coordinates (also called run), and the change in y
is equal to the difference in y-coordinates (also called rise).
m=y2−y1/x2−x1
To determine the slope, enter the values of x and y into the equation.
m=1−(5)/9−(−3)
m=-4/12
m=12/4
m=3
To replace x1 and y1 in the point-slope form yy1=m(xx1), which is derived from the slope equation
m=y2y1/x2x1,
use the slope 3 and the specified point (3,5).
y−(5)=3(x+3)
Keep the equation in point-slope form and make it simpler.
y−5=3(x+3)
Do the y math.
To continue, tap...
y=x+8
List the equation in all its variations.
Form of a slope-intercept:
y=x+8
Forming a point-slope: y=5=1(x+3)
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The set of irrational numbers is the of the set of rational numbers Q in the real numbers R
Select one:
A. complement
B. ratio
C. union
D. Intersection
The set of irrational numbers is the union of the set of rational numbers Q in the real numbers R. Therefore, the correct answer option is C. union.
What is an irrational number?An irrational number is a type of number which comprises non-terminating or non-repeating decimals such as the square root of 11.
What is a rational number?A rational number simply refers to a type of number which comprises fractions, integers, terminating or repeating decimals such as 4.
In Mathematics, the union of the set of all irrational numbers (Q') and the set of all rational numbers (Q) are generally referred to as a set of real numbers (R).
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Complete Question:
The set of irrational numbers is the ______ of the set of rational numbers Q in the real numbers R
Select one:
A. complement
B. ratio
C. union
D. Intersection
Write a function g in terms of f so that the statement is true. The graph of g is a vertical translation 4 units up of the graph of f
g=?
The function g in terms of f so that the statement is true is g(x) = 4f(x)
The point (x, y) on the graph of f (x) is changed to the point (x, ky) on the graph of g (x), where k 1. This is known as a vertical stretch. If k is equal to 1, the graph remains the same; otherwise, it shrinks vertically.
There is a 4-inch vertical stretch in our query. As a result, the points on the new graph would be (x.y/4) rather than f(x)=y.
g(x) = 4f as a result of transformation (x)
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The statement is true g(x) = 4 +f(x).
The point (x, y) on the graph of f (x) is changed to the point (x, k y) on the graph of g (x), where k=1. This is known as a vertical stretch. If k is equal to 1, the graph remains the same otherwise, it shrinks vertically.
There is a 4-inch vertical stretch in our query. As a result, the points on the new graph would be (x. y/4) rather than f(x)=y.
g(x) = 4 +f(x) as a result of transformation of x.
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Solve for X using the information below
The value of x is 10 .
In the question ;
from the given figure , we can see that MS=SL and KR=RL which means
that R and S are the mid points of sides ML and KL respectively .
The Mid Point Theorem states that
If the line segment adjoining the mid points of any of the sides of the triangle then the line segment is said to be parallel to the third side and is half of the length of the third side .
which means RS parallel to KM and KM/2=RS ( ... by mid point theorem)
Substituting the values of RS=2x-10 and KM=2x, we get
2x/2=2x-10
2x = 2(2x-10)
2x = 4x -20
4x-2x=20
2x=20
x=10
Therefore , the value of x is 10 .
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A retail variety store that advertises extensively by mail circulars expects a sale with 20% probability. Suppose 30 prospects are randomly selected from a city-wide mailing.
c. What is the probability that at least 12 sales will result from mailing to the 30 prospects?
Using the normal approximation to the binomial distribution, there is a 0.0060 = 0.60% probability that at least 12 sales will result from mailing to the 30 prospects.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean given by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is above(in case the score is positive) or below(in case the score is negative) the mean. From the z-score table, the p-value associated with the z-score is found, which represents the percentile of the measure X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].The parameters for the binomial distribution in the context of this problem are given as follows:
n = 30, p = 0.2.
Hence the mean and the standard deviation for the approximation are given as follows:
[tex]\mu = np = 30 \times 0.2 = 6[/tex].[tex]\sigma = \sqrt{np(1 - p)} = \sqrt{30 \times 0.2 \times 0.8} = 2.19[/tex]Using continuity correction, the probability that at least 12 sales will result from mailing to the 30 prospects is P(X > 11.5), which is one subtracted by the p-value of Z when X = 11.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (11.5 - 6)/2.19
Z = 2.51
Z = 2.51 has a p-value of 0.9940.
1 - 0.9940 = 0.0060.
Hence the probability is of 0.0060 = 0.60%.
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I will give brainliest, like and rating if u solve this right
6) TRUE OR FALSE?
Answer: True
Step-by-step explanation:
5. Are these two claims equivalent, in conflict, or not comparable because they're talking about
different things?9 a. "75 percent of the federal health care law's taxes would be paid by those
earning less than $120,000 a year" b. "76 percent of those who would pay the penalty [health
care law's taxes] for not having insurance in 2016 would earn under $120,000"
well, one uses 75% and that other uses 76%, so hmmmm those values aren't equal however the statements are talking about the same type of group.
let's reword them
a)
75% of the HCLT will be paid by folks making < 120K
b)
HCLT is paid in 76% by folks making < 120k
a) we know that 75% of the HCLT is paid by those folks
b) we only know that many folks pay for the HCLT, but 76% of it is paid by folks making < 120k, namely 76% of the HCLT is paid by them.
pretty much the same group is referred on both statements.
help meeeeeeeeeeeeeeeeeeeeeeeeee
Answer and Explanation:
1B: {x | -7 ≤ x ≤ 8}
2A: [-4, 3]
2B: {y | -4 ≤ y ≤ 3}
The range of a function is its set of y-values.
Set builder notation (roster method) is a way to define the values within a set.
The length of a rectangle is 5 less than twice it’s width. If the perimeter of the rectangle is 56 inches, find it’s dimensions.
L = 2w - 5
Plug this in for perimeter equation:
2l + 2w = 56
4w - 10 + 2w = 56
6w = 66
W=11
now find length
L = 22 - 5
L = 17