The inverse of a function is another function that "undoes" the original function. In other words, the composition of a function and its inverse results in the identity function.
To find the inverse of a function, you can follow these steps:
Replace the function with "y"
Switch the x and y variables
Solve for y (or in this case x)
So in this case, we can find the inverse of 8x^5+7 by replacing y with 8x^5+7, switching the x and y variables, and solving for x:
y = 8x^5+7
x = 8y^5+7
This is not an invertible function because it's not a one-to-one function, it's not a function of x.
Answer:
Hey there! The inverse of 8x^5+7 doesn't exist because it's not a function. Think about it like this, a function is like a machine that takes an input and gives you a unique output. But in this case, the machine isn't working correctly and it doesn't give you a unique output for a given input. So, in simple terms, it doesn't have an inverse.
________________________________________________________
How do you determine if an equation has an inverse?To determine if an equation has an inverse, we need to check if it is a one-to-one function. A one-to-one function is a function in which every unique input corresponds to a unique output. If an equation is one-to-one function, then it has an inverse. If it's not one-to-one function, then it doesn't have an inverse.
How do you find the inverse of a linear equation?To find the inverse of a linear equation, we can follow these steps:
1. Switch the x and y variables
2. Solve for y (or x)
3. Replace y (or x) with f^-1 (x) (or f^-1 (y))
For example, if we have the equation y = 2x+1, we can follow these steps:
1. x = 2y+1
2. x-1 = 2y
3. f^-1(x) = (x-1)/2
So, the inverse of the equation y = 2x+1 is f^-1(x) = (x-1)/2
A soda company would like to replace the label on a can of soda with a radius of 2 and three fourths cm. If the label touches end to end with no overlap, what is the length of the label? Use 22 over 7 for π.
121 over 7 cm
121 over 14 cm
121 over 28 cm
121 over 56 cm
The length of the perimeter will be 121/7 cm.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that a soda company would like to replace the label on a can of soda with a radius of 2 and three fourths cm. The label touches end to end with no overlap.
Perimeter of a circle is the length of the boundary of the circle. It is given by : P = 2πrThe length of the label will be its perimeter. We can write -
P = 2πr
P = 2 x 22/7 x 11/4
P = 2 x 22/7 x 11/4
P = 22/7 x 11/2
P = 11 x 11/7
P = 121/7
Therefore, the length of the perimeter will be 121/7 cm.
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find the volume v of the described solid s. the base of s is the triangular region with vertices (0, 0), (5, 0), and (0, 5). cross-sections perpendicular to the x-axis are squares.
Using the disk method, it can be concluded that the volume of the solid is 125π /3 cubic units.
Disk Method is a method used to determine the volume of a solid formed by revolving the region about the x-axis and the interval [a, b]. The volume of the solid is the integral of the area of the base times dx.
V = π ∫ Ax dx
From the question, we know that the base of the figure is a triangular region and the coordinates are (0,0), (5,0), and (0,5).
The square is perpendicular to the x-axis. Thus, we can find the side of the square, that is the straight line passing through (5,0) and (0,5) which meet the y = mx + b equation.
First, we determine the slope of the line (m).
m = (y₂ - y₁) / (x₂ - x₁)
= ( 5 - 0 ) / ( 0 - 5 )
= 5 / -5
= -1
To find b, we input the value of m into the equation for point (5,0):
y = mx + b
0 = -1*5 + b
0 = -5 + b
b = 5
So we got the side of the square:
y = mx + b
y = -x + 5
y = 5 - x
Thus the area of the square is:
A = side²
= (5 - x)²
= 25 + x² - 10x
The volume of the solid can be calculated as follows:
V = π ∫ Ax dx
= π ∫₀² (25 + x² - 10x) dx
= π (25x + 1/3x³ - 5x² |₀⁵)
= π (25*5 + 1/3*5³ - 5*5² - 0)
= π (125 + 125/3 - 125 - 0)
= 125π /3 cubic units
Thus, the volume of the solid is 125π /3 cubic units
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how do you solve -2x=8
Answer:
All you have to do is divide by -2 on both sides. You're trying to get x by itself, so divide by a number by cancels itself out. Don't forget the negative sign as well, or else you'll be left with -x instead of just x. A positive number divided by a negative number will become negative.
-2x=8
x=-4
Marty buys 12 ounces of granola what fraction of a pound did Marty buy?
The fraction of a pound of granola that Marty bought is 3/4 pounds.
How many pounds of granola did Marty buy?A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below. An example of a fraction is 3/4.
The unit of conversion of ounces to pounds is :
1 pound = 16
12 ounces of granola = 12/16 pounds = 3 /4 pounds
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HELP PLEASE 100 POINT WILL GIVE BRAINLIEST
Answer:
no clue sorry I was not able to help
A commission of $300 was paid to a broker's agent for the sale of a bond. If the commission was 3/4% of the sales value of the bond, how much was the bond sold for?
Answer:
Look below
Step-by-step explanation:
Sale prince is $300
the commission is 3/4%
Commission amount is $2.25
Price + commission $302.25
Price - commission $297.95
I hope this gives you the answer you where looking for
a company has offices in 3 different cities and a total of 480 workers. there are 90 workers in new york and 130 workers are in san diego. which number line represents the numbe line represents the number of workers in san diego
Using the arithmetic operation, the number of worker in San Diego is obtained as 260, and the number line which represents the same is option 1.
What is arithmetic operation?
A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
The number of offices are = 3
The number of workers in the company is = 480
The number of workers in New York city = 90
The number of workers in Denver city = 130
The number of workers in San Diego city = x
To find the number of workers in San Diego use the formula -
Number of workers in San Diego = Total Number of Workers - (Number of workers in New York + Number of workers in Denver)
The arithmetic operation of addition and subtraction is used.
Substitute the values into the equation -
Number of workers in San Diego = 480 - (90 + 130)
Number of workers in San Diego = 480 - 220
Number of workers in San Diego = 260
The number line which represents the number of workers in San Diego is option 1.
Therefore, the number of workers in 260.
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A company has offices in 3 different cities and a total of 480 workers. There are 90 workers in New York and 130 workers are in Denver. Which number line represents the number line represents the number of workers in San Diego?
The graph of (c•d)(x) is shown.
Plot a point at the ordered pair that represents (c•d)(4) on the graph of the combined function.
The ordered pair that represents (c•d)(4) on the graph of the combined function is (4, -12)
How to determine the graph of the ordered pair?From the question, we have the following parameters that can be used in our computation:
The graph
The function of the graph is a combined function (c . d)(x)
To calculate (c . d)(4), we trace the point x = 4 to the curve
So, we have
(c . d)(4) = -12
See attachment for the graph
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Question content area top Part 1 Compare A and B in three ways, where A=52093 is the number of deaths due to a deadly disease in the United States in 2005 and B=17821 is the number of deaths due to the same disease in the United States in 2009.
In the below we have compared deaths in A and B in terms of ratio, percentage and in terms of proportion.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
The first comparison is in terms of rato.
The ratio of deaths due to a deadly disease in the United States at A and B is A : B = 17821 : 52093.
The second comparison in terms of percentage,
The percentage of people died in A is (52093/17821)×100 = 292.31% more than people died in B.
The third comparison is in terms of fractions.
The fraction of people died in A is (52093/17821) = 2.92 times more than people died in B.
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what is the angle (in degrees) north of east from the post office to the grocery store in centralburg? express your answer in degrees to two significant figures.
The angle θ measures 53.13⁰ with the east direction.
What is tangent of any angle?The tangent of an angle is a trigonometric function that is defined as the ratio of the side opposite the angle to the side adjacent to the angle in a right triangle. In other words, it is a measure of the steepness of a line that is tangent to a point on a function's graph and is represented by the symbol tan. It is one of the three main trigonometric functions, along with sine and cosine. The value of tangent is always positive in the first and fourth quadrants.
let the angle made be θ degree to the north of east from the post office to the grocery shop
so tan θ = p/b
where p is perpendicular , b is base of the triangle
so tan θ = 3/4
=> θ = 53.13 degree
so the angle θ measures 53.13⁰ with the east direction.
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Complete question :
what is the angle (in degrees) north of east from the post office to the grocery store in centralburg? express your answer in degrees to two significant figures.
When looking east, the angle is 53.[tex]13^{0}[/tex] degrees.
What does a tangent to any angle mean?
The ratio of a right triangle's side opposite to its side next to the angle is known as the tangent of an angle, which is a trigonometric function. It is a measurement of the steepness of a line that is tangent to a point on the graph of a function, and it is denoted by the symbol tan. One of the three primary trigonometric functions, together with sine and cosine, is it. In the first and fourth quadrants, tangent's value is always positive.
Let the angle formed between the post office and the grocery store be degrees to the north of east.
so tan θ = p/b
where p is perpendicular , b is base of the triangle
so tan θ = 3/4
=> θ = 53.13 degree
so the angle θ measures 53.13⁰ with the east direction.
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Complete question :
What is the angle (in degrees) north of east from the post office to the grocery store in centralburg? express your answer in degrees to two significant figures.
An alloy is a mixture of metals. Suppose that a certain alloy is made by mixing 120 g of an alloy That contains 42% copper with 200 g of pure copper
The mixture is 78.25% copper for the given alloy.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
To solve the given situation, we utilize material balancing before and after mixing.
Let the total amount of material after mixing is 320.
Let x be the percent copper of the mixture and applying copper balance,
⇒ (0.42)(120 g) + (1)(200) = 320x
Solving the above equation, we get the value as
⇒ x = 0.7825
Thus, the mixture is 78.25% copper.
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d 8, write the equation of the plane passing through p with normal vector n in (a) normal form and (b) general form.
The equation of the plane passing through point P with normal vector n A(x-2) + B(y-3) + C(z-4) = 0
(a) Normal Form:
The equation of the plane passing through point P with normal vector n can be written in normal form as:
n • (r - p) = 0
where r is a position vector in three-dimensional space and n is the normal vector of the plane.
Given n = (1,2,3) and p = (2,3,4).
Therefore, n • (r - p) = (1,2,3) • (r - (2,3,4)) = r1 + 2r2 + 3r3 -2 - 3 - 4 = 0
=> r1 + 2r2 + 3r3 - 8 = 0
=> Plane equation in normal form: 1x + 2y + 3z - 8 = 0
(b) General Form:
The equation of the plane passing through point P with normal vector n can also be written in general form as:
A(x-x0) + B(y-y0) + C(z-z0) = 0
where A, B and C are the components of the normal vector n and (x0,y0,z0) are the coordinates of the point p.
Given n = (1,2,3) and p = (2,3,4).
Therefore, A(x-2) + B(y-3) + C(z-4) = 0
=> 1(x-2) + 2(y-3) + 3(z-4) = 0
=> Plane equation in general form: x - 2y + 3z - 8 = 0
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Provide complete question here:Write the equation of the plane passing through p with normal vector n in (a) normal form and (b) general form.
is x-3y =15 and y = -3y + 4 perpindiculad paralleled or neither
The two lines are perpendicular because the product of their slopes is equal to 1
What is the slope-intercept form of a line?The slope-intercept form of a line is represented by y=mx+c where m=slope and c is the y-intercept of the line
Given here: The two lines x-3y =15 and y = -3y + 4
Rewriting the given expressions in slop-intercept form we get
y=x/3-5
y = -3y + 4
The respective slopes are given as 1/3 and -3
Thus the product of the two slopes is 1/3×-3=-1
Hence, The given lines are perpendicular.
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Jessica makes $10 an hour babysitting. She babysat 4 hours on Friday
and 7 hours on Saturday. Write an expression and use the distributive
property to find how much Jessica made.
Equivalent Expression =
Evaluate =
An expression using the distributive property to find the earnings Jessica made on Friday and Saturday is 10(4 + 7).
What is distributive property?The distributive property postulates that multiplying the sum of two or more addends by a number gives the same result as multiplying each addend by the number and then adding the products together.
The distributive property helps to solve mathematical expressions written in the form of a(b + c).
The amount Jessica makes per hour babysitting = $10
The number of hours of babysitting on Friday = 4 hours
The number of hours of babysitting on Saturday = 7 hours
According to the distributive property, the results from 'a' and 'b' below are the same.
a) 10(4 + 7) = 40 + 70 = 110
b) 10(4 + 7) = 10 x 11 = 110
Thus, using the distributive property, Jessica will make $110 for babysitting on Friday and Saturday, notwithstanding whether process A or B was followed.
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Please answer this question for me
The student is trying to construct a bisector of a given Angle i.e. A.
what is a bisector?
In Geometry, a “Bisector” is a line that divides the line into two different or equal parts. It is applied to the line segments and angles. A line that passes through the midpoint of the line segment is known as the line segment bisector, whereas the line that passes through the apex of an angle is known as the angle bisector. The bisector of a segment always contains the midpoint of the segment. There are two types of bisectors based on what geometrical shape it bisects.
Line Segment Bisector (Perpendicular Bisector Theorem)
Angle Bisector (Triangle Bisector Theorem)
Now,
As we can see from the figure given that the bisector is dividing the angle in two equal segments.
Hence,
The student is trying to construct a bisector of a given Angle.
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Water leaks from a tank at the rate of r(t) gallons per hour. The rate decreased as time passed, and values of the rate at two-hour time intervals are shown in the table below. The total amount of water that leaked out is evaluated by a Riemann sum. Find the upper estimate (left end-points of each rectangle) for the total amount of water that leaked out by using five rectangles.
Give your answer with one decimal place
t(hr) r(t) (gal/hr)
0 10.7
2 8.6
4 6.6
6 5.2
8 5.0
10 4.5
The upper estimate (left end-points of each rectangle) for the total amount of water that leaked out by using five rectangles is 72.2 gallons.
R(t) gallons per hour of water leak from a tank. The values of the rate at two-hour intervals are shown in the table below. As time went on, the rate decreased. A Riemann sum is used to determine the overall volume of water that has leaked out.
An integral representation of the rate function would be the amount of water. Estimation with the Riemann sum and left endpoints:
F(x) ≅ ∑f(xi-1)Δx where Δx=10/5 = 2 for this case and i = 1 to 5
W = (10.7 + 8.6 + 6.6 + 5.2 + 5.0)2
= 36.1•2
= 72.2 gallons
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What is the answer for
15 + x = 28
Answer: x = 13
Step-by-step explanation:
First you have to move 15+ to the other side to 28.Then when 15+ moves to the other side it will be 15-. After that you subtract 28 with 15 that will make 13. So x is equal to 13.
By numbers:
15+x=28
x=28-15
x=13
Find the domain and range of the function represented by the graph.
The function represented in Cartesian plane have the following features: Domain of function: - 4 ≤ x ≤ 2, Range of function: - 4 ≤ y ≤ 4. (Right choice: B)
How to determine the domain and range of a function
In this question we find the representation of a function on Cartesian plane. There are two important hints to answer this question:
Domain of the function is the set of x-values such that function exists. Range of the function is the set of y-values such that function exists.Then, by direct inspection we find the following results: Domain: - 4 ≤ x ≤ 2, Range: - 4 ≤ y ≤ 4.
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? ÷ 2/5 = 4
Draw a diagram to represent the situation.
Given expression ?/(2/5)=4 where ?=x gives x=8/5.
what are expressions?
Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.
e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.
Now,
Given expression ? ÷ 2/5 = 4
let x=?
Therefore,
x=4*2/5
x=8/5
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Please help me out. I Need it today
The absolute values of inequality equations totally depend on the symbols.
x+1 = 3, x = 2x+1 > 3 , x > 2 x+1 < 3 , x< 2x+1 ≥ 3 , x ≥ 2 x+1 ≤ 3, x ≤ 2What is inequality?An inequality in mathematics is a relationship that compares two numbers or other mathematical expressions in unequal absolute values. By comparing the absolute valuesof two numbers on the number line, inequality is most frequently utilized. Different types of inequality are represented by a variety of different notations, including:
The symbol a b indicates that an is less than b.
A bigger value for a than a lesser value for b is indicated by the notation a > b.
a is not equal to b in either situation. These relationships are referred to be stringent inequalities since an is either strictly less than or strictly greater than b. Equivalence is not included.
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What is the value of x in this triangle?
[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]
83°Step-by-step explanation:
As it is a triangle , so we know that sum of all angles of a triangle = 180°
therefore,=> 44 + 53 + x = 180
=> 97 + x = 180
=> x = 180 - 97
=> x = 83°
______________________________Hope it helps you ~The area of a circle is 4/pi cm. What is the circumference in centimeters express your answers in terms of pi
Answer:
4 cm.
Step-by-step explanation:
Area = pi r^2, so:
pi r^2 = 4 / pi
(pi)^2 r^2 = 4
r^2 = 4/ (pi^2)
r = 2/pi
Therefore, the circumference
= 2 pi r
= 2* pi * 2/pi
= 4
USING SIMULATIONS TO CALCULATE ESTIMATED PROBABILITIES
3. A scientist wants to estimate the probability that a drought will happen in an area at least once over the next 4 years. The chances of a drought happening in a given year is 12%. She has generated 20 sets of 8 random numbers to help estimate the probability.
Part A: Before doing any calculations, use your intuition to predict the probability of a drought within the next 4 years if the probability of a drought in any one year is 12%. (1 point)
Scoring Notes: 1 point for any reasonable answer.
Part B: Which pairs of digits, starting at 00, represent a drought happening? Which pairs of digits, ending at 99, represent a drought not happening? (2 points)
Part C: Use the random numbers to estimate the probability that a drought happens at least once over the next 4 years. (7 points)
Part D: Is the probability that you calculated greater than or less than you predicted? Explain. (2 points)
Part E: If you change the pairs of digits that represent a drought happening so that they start at 10 instead of 00, does the estimated probability change? Calculate the estimated probability using the new ranges of numbers. (8 points)
Estimated probabilities are predictions made based on past data, trends, and patterns. They provide an idea of the likelihood that an event will occur in the future.
Calculate estimated probabilitiesPart A:
Answer: The probability of a drought within the next 4 years if the probability of a drought in any one year is 12% is approximately 48%.
Part B:
Answer: Pairs of digits starting at 00 and ending at 11 represent a drought happening. Pairs of digits starting at 88 and ending at 99 represent a drought not happening.
Part C:
Answer: Using the random numbers, the estimated probability that a drought happens at least once over the next 4 years is 68%.
Part D:
Answer: The probability that was calculated is greater than the probability predicted. This is because the sample size of 20 sets of 8 random numbers provided a more accurate and precise estimate than the intuition-based prediction.
Part E:
Answer: Yes, the estimated probability changes when the pairs of digits that represent a drought happening are changed so that they start at 10 instead of 00. Using the new ranges of numbers, the estimated probability that a drought happens at least once over the next 4 years is 64%.
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Estimated probabilities are predictions made based on past data, trends, and patterns. They provide an idea of the likelihood that an event will occur in the future.
Calculate estimated probabilitiesPredictions based on historical data, patterns, and trends are known as estimated probability. They give a sense of how likely it is that a certain occurrence will take place in the future.
Estimated probabilities calculation Part A:
If the likelihood of a drought in any given year is 12%, the likelihood that one will occur within the next four years is roughly 48%.
Part B:
Answer: The drought is represented by pairs of numerals beginning at 00 and ending at 11. A drought that is not occurring is represented by pairs of digits that begin at 88 and terminate at 99.
Part C:
According to the random numbers, there is a 68% chance that a drought will occur at least once over the next four years.
Part D:
Answer: The calculated probability is higher than the expected probability. This is due to the fact that the estimate produced by the sample size of 20 sets of 8 random numbers was more precise and accurate than the intuition-based prediction.
Part E:
Answer: When the pairs of digits that represent the occurrence of a drought are modified so that they begin at 10 instead of 00, the predicted likelihood does indeed change. According to the revised ranges of figures, there is a 64% chance that a drought will occur at least once over the next four years.
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At a grocery store, a sign says that if you buy three bottles of water, you will pay 1/4 of the regular price per bottle. Which expression shows the amount of money saved on 3 bottles of water at the regular price of d dollars? Select three correct expressions.
Answer:
Step-by-step explanation:
the fourth one
Answer:
first three answers.
Step-by-step explanation:
each bottle is 1/4d. so all three are 3*1/4d
HELP ASAP (BRAINLIEST)
The table shows the relationship between the participants walking and running for the week's cross-country practices.
Walk (laps) 3 B 15
Run (laps) 5 10 D
Total (laps) A C 40
At this rate, how many laps will the participants walk if the total distance is 24 miles? How many miles will they run?
They will walk 7 laps and run 17 laps for a total of 24 miles.
They will walk 15 laps and run 9 laps for a total of 24 miles.
They will walk 9 laps and run 15 laps for a total of 24 miles.
They will walk 6 laps and run 18 laps for a total of 24 miles.
Option C. They will walk 9 laps and run 15 laps for a total of 24 miles.
How to calculate for the tableThe table is given as Walk (laps) 3 B 15
Run (laps) 5 10 D
Total (laps) A C 40
The total for walk and run is 3 + 5 = 8
Walk is 3
Run is 5
We are to find the laps of both categories with respect to the total distance of 24 miles
for walk = 3/8 * 24
= 9
For run we would have 5 / 8 * 24 = 15
Hence They will walk 9 laps and run 15 laps for a total of 24 miles.
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How do I do this I am stuck on this question please and thank you
A rectangle has a length of 8.2cm and a height of 42mm. The area of the rectangle is mm2
Answer: To find the area of a rectangle, you can use the formula:
Area = Length x Height
In this case, the length is given in cm and the height is given in mm. Therefore, you need to convert the length to mm before you can calculate the area.
1cm = 10mm.
So, 8.2 cm = 8.2 x 10 = 82mm
Now you can find the area of the rectangle:
Area = Length x Height = 82mm x 42mm = 3,444 mm^2
So, the area of the rectangle is 3,444 mm^2
Step-by-step explanation:
Question 4Multiple Choice Worth 2 points)
(04.05 MC)
A chess player ran a simulation twice to estimate the proportion of wins to expect using a new game strategy. Each time, the simulation ran a trial of 1,000 games. The first
simulation returned 212 wins, and the second simulation returned 235 wins. Construct and interpret 95% confidence intervals for the outcomes of each simulation.
The confidence interval from the first simulation is (0.187, 0.237), and the confidence interval from the second simulation is (0.209, 0.261). For the first trial, we are
95% confident the true proportion of wins with the new game strategy is between 0.187 and 0.237. For the second trial, we are 95% confident the true proportion of
wins with the new game strategy is between 0.209 and 0.261.
The confidence interval from the first simulation is (0.187, 0.237), and the confidence interval from the second simulation is (0.209, 0.261). For the first trial, we are
90% confident the true proportion of wins with the new game strategy is between 0.187 and 0.237. For the second trial, we are 90% confident the true proportion of
wins with the new game strategy is between 0.209 and 0.261.
The confidence interval from the first simulation is (0.191, 0.233), and the confidence interval from the second simulation is (0.213, 0.257). For the first trial, we are
95% confident the true proportion of wins with the new game strategy is between 0.191 and 0.233. For the second trial, we are 95% confident the true proportion of
wins with the new game strategy is between 0.213 and 0.257.
The confidence interval from the first simulation is (0.191, 0.233), and the confidence interval from the second simulation is (0.213, 0.257). For the first trial, we are
90% confident the true proportion of wins with the new game strategy is between 0.191 and 0.233. For the second trial, we are 90% confident the true proportion of
wins with the new game strategy is between 0.213 and 0.257.
2
By constructing 95% confidence intervals for each simulation, we can be 95% confident that the true proportion of wins lies within the range of each interval.
What is Confidence Intervals?A confidence interval is a set of values that, given a specific level of certainty, are likely to include a population parameter like a mean or proportion.
The interval is derived using data drawn from a sample of the population and is frequently presented as a range of values with a 95% confidence level.
The probability that the range of values contains the genuine population parameter is quantified by the confidence level.
In the case of a 95% confidence interval, for instance, it means that 95% of the intervals would contain the real population parameter if we sampled the same population more than once and calculated a confidence interval each time.
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Find the solutions to the equation:
2x² - 10x + 15 = x
5/2 and 3 are the solutions to the equation 2x² - 10x + 15 = x.
What is equation?An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.
Here,
2x² - 10x + 15 = x
2x² - 11x + 15 = 0
2x² -6x -5x + 15 = 0
2x(x-3)-5(x-3)=0
x=5/2, 3
The solutions to the equation 2x² - 10x + 15 = x is 5/2 and 3.
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Can someone show the steps please and thank you
y=ax+3
y=3x+5
A solution to the given system of equations include the following:
x = -2.
y = -1.
How to solve this system of equations?In order to solve the given system of equations, we would apply the substitution method. From the information provided in the image attached above, we have the following system of equations:
y = 2x + 3 .......equation 1.
y = 3x + 5 .......equation 2.
By using the substitution method to substitute equation 1 into equation 2, we have the following:
2x + 3 = 3x + 5
By re-arranging and collecting like terms, we have the following:
3x - 2x = 3 - 5
x = -2.
For the value of y, we have the following:
y = 2x + 3
y = 2(-2) + 3
y = -4 + 3
y = -1.
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