The required solution for the hypothesis testing is shown.
What is Statistic?Statistics is the study of mathematics that deals with relations between comprehensive data.
Here, we have,
Part A:
The null hypothesis (H0) is that the company's claim is true, and the proportion of defective batteries is 5% or less.
The alternative hypothesis (Ha) is that the company's claim is false, and the proportion of defective batteries is greater than 5%.
H0: p ≤ 0.05
Ha: p > 0.05
where p represents the proportion of defective batteries.
Part B:
A Type I error in this context would be rejecting the null hypothesis (i.e., finding significant evidence that the proportion of defective batteries is greater than 5%) when it is actually true (i.e., the proportion of defective batteries is 5% or less). This would be a false positive result.
A Type II error would be failing to reject the null hypothesis (i.e., not finding significant evidence that the proportion of defective batteries is greater than 5%) when it is actually false (i.e., the proportion of defective batteries is greater than 5%). This would be a false negative result.
Part C:
If the hypothesis is tested at a 5% level of significance instead of 1%, this means that the criteria for rejecting the null hypothesis will be less stringent. In other words, it will be easier to find significant evidence that the company's claim is false. Therefore, increasing the level of significance from 1% to 5% will increase the power of the test.
Part D:
If the hypothesis is tested based on the sampling of 500 boxes of batteries rather than 100 boxes of batteries, this means that the sample size is larger. As a result, the standard error of the estimate will be smaller, and the test will be more precise. This increased precision will increase the power of the test.
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A basketball player makes 39% of her shots from the free throw line. Suppose that each of her shots can be considered independent and that she takes 10 shots. Let x = the number of shots that she makes. What is the standard deviation for x?.
The standard deviation is 1.32
We can use the binomial distribution to calculate the probability of making a certain number of shots. The formula for the standard deviation of a binomial distribution is:
σ = √(np(1-p))
Where σ is the standard deviation, n is the number of trials (in this case, 10), p is the probability of success on each trial (0.39, or 39%), and (1-p) is the probability of failure on each trial (0.61, or 61%).
So, plugging in our values:
σ = √(10 * 0.39 * 0.61)
σ ≈ 1.32
In other words, if the player takes 10 free throws, we would expect her to make between 2 and 6 of them about 68% of the time.
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Please help me a soon as possible. See the graph.
The evaluation of the limits of the piecewise function at the specified intervals are as follows;
[tex]\lim\limits_{x\to2^+}\frac{f(x) -1}{f(x + 4)} = -2[/tex]
[tex]\lim \limits_{x\to 1^-}f(f(x) + 1) = 11[/tex]
[tex]\lim\limits_{h\to 0}\frac{f(6+h) - f(6)}{h} = 2[/tex]
What is a piecewise function?A piecewise function is a function with rules or definition of the function based on the interval of the function.
The equation representing the piece wise function at x → 2⁺, can be found as follows;
Points on the graph of the function are; (3, 2), and (4, 1)
Slope of the graph of the function = (1 - 2)/(4 - 3) = -1
Equation of the function is; y - 2 = -1·(x - 3) = 3 - x
y = 3 - x + 2 = 5 - x
y = 5 - x
y = f(x) = 5 - x
f(x) - 1 = 5 - x - 1 = 4 - x
f(x) - 1 = 4 - x
f(x + 4) = 5 - (x + 4) = 5 - x - 4 = 1 - x
f(x - 4) = 1 - x
[tex]\frac{f(x) - 1}{f(x + 4)} = \frac{4 - x}{1 - x}[/tex]
[tex]\lim\limits_{x\to 2^+}\frac{f(x) - 1}{f(x + 4)} = \frac{4 - (2)}{1 - 2} = \frac{2}{-1}= -2[/tex]The coordinate points on the piecewise function at x → 1⁻ are; (0, 3), and (1, 4)
The slope of the graph is; (4 - 3)/(1 - 0) = 1
The equation is; y - 3 = x
y = f(x) = x + 3
f(f(x) + 1) = f((x + 3) + 1) = f((x + 3) + 3 + 1) = f(x + 7)
f(x + 7) = (x + 7 + 3) = x + 10
[tex]\lim \limits_{x \to 1^{-1}} f(f(x) + 1) = 1 + 10 = 11[/tex]The points on the piecewise function at x = 6 are; (5, 2), and (7, 6)
The slope is; (6 - 2)/(7 - 5) = 2
The equation is; y - 2 = 2·(x - 5) = 2·x - 10
y = 2·x - 10 + 2 = 2·x - 8
y = f(x) = 2·x - 8
f(6 + h) = 2·(6 + h) - 8 = 12 + 2·h - 8 = 4 + 2·h
f(6) = 2 × 6 - 8 = 4
f(6 + h) - f(6) = 4 + 2·h - 4 = 2·h
[tex]\frac{f(6 + h) - f(6)}{h} = \frac{2\cdot h}{h}= 2[/tex]
The limits of the function is therefore;
[tex]\lim \limits_{h\to 0}\frac{f(6 + h) - f(6)}{h} = 2[/tex]Learn more on the limits of a function here: https://brainly.com/question/30460469
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g five cards are dealt from a standard deck of playing cards.what is the probability that the you dealt 5 cards from same suit.
Answer:
the probability of being dealt 5 cards from the same suit is approximately 0.00198, or about 0.198%.
Step-by-step explanation:
The total number of ways to choose 5 cards from a deck of 52 cards is given by the combination formula:
C(52, 5) = 52! / (5! (52 - 5)!) = 2,598,960
Now, we need to count the number of ways of choosing 5 cards from the same suit. There are 4 suits in a deck of cards (hearts, diamonds, clubs, and spades), so we need to count the number of ways to choose 5 cards from each of these suits and add them up.
For each suit, the number of ways of choosing 5 cards from that suit is given by the combination formula:
C(13, 5) = 13! / (5! (13 - 5)!) = 1,287
So the total number of ways of choosing 5 cards from the same suit is:
4 * 1,287 = 5,148
Therefore, the probability of getting 5 cards from the same suit is:
5,148 / 2,598,960 ≈ 0.00198
So the probability of being dealt 5 cards from the same suit is approximately 0.00198, or about 0.198%.
Solve for m.
Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
8m + 95 < -87m+5
The values of m for the given inequality should be in the interval
(-∞, -18/19).
What is meant by inequality?
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols. Typically, we use the "not equal" sign to indicate that two values are not equal. However several inequalities are utilised to compare the numbers, whether it is less than or higher than.
Given the inequality,
8m + 95 < -87m +5
We are asked to solve the inequality.
this means we have to find the value of m.
8m + 95 < -87m +5
8m + 87m < 5 - 95
95m < -90
m < -90/95
m< -18/19
Therefore the values of m for the given inequality should be in the interval (-∞, -18/19).
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6 In a school the ratio of teachers : male learners: female learners is 1 : 7:8. The total number of learners is 720. Find the number of teachers in the school.
Using the given ratio, we can see that there are 48 teachers.
How to find the number of teachers?Here we know that the ratio of teachers to male learners to female learners is:
1:7:8
So for each teacher there are 7 female learners and 8 male learners, for a total of 15.
So we can simplify this and say that there are 15 learners for each teacher.
Then if there are 720 learners, the number of teachers is:
720/15 = 48
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Determine the equation of the line of fit
Y= 15x+70
Y= 15x+40
Y=30x+70
Y=30x+40
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{70})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{100}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{100}-\stackrel{y1}{70}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{2}}} \implies \cfrac{ 30 }{ 2 } \implies 15[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{70}=\stackrel{m}{ 15}(x-\stackrel{x_1}{2}) \\\\\\ y-70=15x-30\implies {\Large \begin{array}{llll} y=15x+40 \end{array}}[/tex]
Someone please help me with this qiesrion pls
The true statement on the height of the ball when thrown from a building, given the equation, can be found to be A. The ball reaches the ground in 3 seconds.
How to find the height ?The equation given of the ball being thrown from a building, gives us the height when solved.
The height of the ball when it reaches the ground is 0 feet so we can insert this in the formula to find the time:
0 = - 5 ( t - 3 ) ( t + 5 )
We can use the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. So, we can set each factor equal to zero and solve for t:
t - 3 = 0 or t + 5 = 0
Solving for t in the first equation, we get:
t - 3 = 0
t = 3
Seeing as t is 3 seconds the first option is correct.
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What is the probability that a randomly selected person is male given the person is left handed?
Answer:
13/24
Step-by-step explanation:
13/11+13= 13/24
The probability that a randomly selected person is male given the person is left handed is 13/200.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.
Here, total number of outcomes = 200
Number of favorable outcomes = 13
Now probability of an event = 13/200
Therefore, the probability that a randomly selected person is male given the person is left handed is 13/200.
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Solve the following quadratic function by utilizing the square root method. simplify your answer completely (x)=81x^2 -16
The quadratic function has its solution to be x = 4/9 and x = -4/9
How to solve the quadratic functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = 81x^2 - 16
Express the expression as difference of two squares
So, we have the following representation
f(x) = (9x)^2 - 4^2
Apply the difference of two squares rule
So we have
f(x) = (9x - 4)(9x + 4)
This gives
(9x - 4)(9x + 4) = 0
So, we have
9x = 4 and 9x = -4
Evaluate
x = 4/9 and x = -4/9
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What is the equation of the midline for the function f(x)? f(x)=12sin(x)+6 enter your answer in the box.
The equation of the midline for the function f(x) = 12sin(x) + 6 is y = 12. The midline of a periodic function is a horizontal line that represents the average value of the function over one period.
For a sinusoidal function, the midline is the line that passes through the center of the graph, or the average of the maximum and minimum values of the function.
To find the midline equation for the function f(x) = 12sin(x) + 6, we first need to find the maximum and minimum values of the function. The amplitude of a sinusoidal function is half the difference between its maximum and minimum values. In this case, the amplitude is 12, so the maximum value is 12+6=18, and the minimum value is 6-12=-6.
The midline of the function is the line halfway between the maximum and minimum values, or at a height of (18 - 6)/2 + 6 = 12. Therefore, the equation of the midline is y = 12. This means that the function oscillates above and below this line by a maximum of 12 units.
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What is the volume of this figure?
80 cubic inches is the volume of the given prism'
Volume of a composite figureThe given figure is made of triangular prisms. The formula for calculating the volume of rectangular prism is expressed as:
Volume = length * width * height
The given composite figure is made of 2 prisms. The volume is calculated as:
V = (5*1*6) + (2*5*5)
V = 30. + 50
V = 80 cubic inches
Hence the required volume of the figure is 80 cubic inches
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A -foot tall monument is located in the distance. From a window in a building, a person determines that the angle of elevation to the top of the monument is , and that the angle of depression to the bottom of the monument is. How far is the person from the monument? round the answer to the nearest hundredth.
The distance between the man and the monument is 1060.16 feet.
Here we have the angle of elevation to be 18°
and the angle of depression to be 3°
Let the distance between the man and the monument be x feet
Now for any angle a, tana = opposite angle / adjacent angle
Hence we can sum up the building's height to be
x tan18 + x tan3 = 400
or, x(tan18 + tan3) = 400
or, x(0.3249 + 0.0524) = 400
or, 0.3773x = 400
or, x = 400/0.3773
or, x = 1060.16
Hence the distance between the man and the monument is 1060.16 feet.
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1.8A F. Flint is starting a business. Before starting to sell anything, he bought fixtures for £1,200, a van
for £6,000 and an inventory of goods for £2,800. Although he has paid in full for the fixtures and the van,
he still owes £1,600 for some of the inventory. B. Rub lent him £2,500. After the above, Flint has £200 in
the business bank account and £175 cash in hand. You are required to calculate his capital.
Flint is starting a business. Before starting to sell anything, he bought fixtures for £1,200, a van for £6,000 and an inventory of goods for £2,800. Although he has paid in full for the fixtures and the van, he still owes £1,600 for some of the inventory. B. Rub lent him £2,500. After the above, Flint has £200 in the business bank account and £175 cash in hand. Total capital is £10,375
What do you mean by capital?
Any employed financial asset might be considered capital. A company's capital is represented on its balance sheet as the earnings from its ongoing operations. The money in a bank account, the proceeds from the sale of stock shares, and the proceeds from the sale of bonds are a few examples.
A factory and its equipment, intellectual property like patents, or the financial assets of a company or a person are all examples of things that provide value or benefit to their owners and fall within the broad definition of capital.
Fixtures= £1,200, van= £6,000, inventory of goods= £2,800, cash =£375
So, Total assets= £10,375
Payable= £1,600, loan from Rub= £2,500, Balancing figure= £6,275
Total liabilities= £10,375
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The value went from $45.00 to $68.75. What was the percent change?
The percent change from $45.00 to $68.75 is approximately 52.8%.
What does the phrase "percent change" mean?Finding the difference between two values in a time series and multiplying it by 100 after dividing it by the initial value yields the percentage change between the two values.
We employ the following formula to determine the percentage difference between two values:
(New Value - Old Value) / Old Value * 100% is the formula for percent change.
The former value in this instance was $45.00, whereas the new value is $68.75.
Adding these values to the formula yields the following results:
($68.75 - $45.00) / $45.00 * 100% is the percent difference.
percent modification: (23.75% / (45.00%) * 100%
52.8% change in percentage
As a result, the percentage increase from $45.00 to $68.75 is almost 52.8%.
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The grade point average for college students is based on a weighted mean computation. For most colleges, the grades are given the following data values: A (4), B (3), C (2), D (1), and F (0). After 60 credit hours of course work, a student at State University earned 6 credit hours of A, 15 credit hours of B, 31 credit hours of C, and 8 credit hours of D.
a. Compute the student's grade point average. Round your answer to two decimal places.
b. Students at State University must maintain a 2.5 grade point average for their first 60 credit hours of course work in order to be admitted to the business college. Will this student be admitted?
The student's grade point average is 2.32.
The student will not be admitted to the business college.
What is a mean?It is the average value of the set given.
It is calculated as:
Mean = Sum of all the values of the set given / Number of values in the set
We have,
(a)
Total grade points earned
= (6 x 4) + (15 x 3) + (31 x 2) + (8 x 1)
= 24 + 45 + 62 + 8
= 139
Total credit hours.
= 6 + 15 + 31 + 8
= 60
Now,
The student's grade point average:
= Total grade points earned / Total credit hours taken
= 139 / 60
= 2.32
(b)
2.32 < 2.5
This means,
The student's grade point average is lower than the required 2.5 GPA for admission to the business college.
Thus,
The student's grade point average is 2.32.
The student will not be admitted to the business college.
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Drag one or more expression into each letter space (a,b,c,d) to create an equation that is true for all values of x. (Assume no denominator equals zero)
(3/x+2)+(4/x)+(2/x^2)=(3(a)+4(b)+2(c)/d)
X^2(x+2)
X(x+2)
X^2
X
(X+2)
The expression into each letter space (a,b,c,d) to create an equation that is true for all values of x is X(x+2),X,(X+2),X^2.
What is an expression?Expression in mathematics is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We are given that;
The equation with a,b,c,d=(3/x+2)+(4/x)+(2/x^2)=(3(a)+4(b)+2(c)/d)
Now,
=(3/x+2)+(4/x)+(2/x^2)
=3/x + 2x/2 + 4/x + 2/x^2
=(3+2x)/x+4/x+2/x^2
Therefore, the answer of the expression will be X(x+2),X,(X+2),X^2.
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Use a definition, postulate, or theorem to find the value of x in the figure described.
Point E is between points D and F. IfDE=x-1, EF = 4x + 5, and DF = 6x - 5, find x.
The solution is x =?
Thus, the value of x in the figure is 9.
What's collinear?Collinear refers to a term used in figure to describe a set of three or further points that lie on the same straight line. In other words, if you can draw a straight line that passes through two or further points, those points are said to be collinear.
We can use the member addition hypothetical to break for x. According to the member addition hypothetical, if three points A, B, and C are collinear, also AB BC = AC.
In this case, points D, E, and F are collinear, so we can write
DE EF = DF
Substituting the given values, we get
x- 1 4x 5 = 6x- 5
Simplifying the equation, we get
x 4 = 6x- 5
Abating 5x from both sides, we get
= x- 5
Adding 5 to both sides, we get
x = 9
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The altitude of an airplane coming in for a landing is represented by the equation shown below, where y represents the altitude,
in feet, of the airplane and x represents the number of minutes the plane has been descending:
y= -1025x + 30,750
Part A:
Create a table for the values when x = 0, 5, 8, 10, 30.
Include worked-out equations used to identify the values within the table.
Part B:
Identify the altitude after 5 minutes and after 30 minutes. Use 1-2 sentences to explain the altitude at these two times and
describe what is happening to the ajrplane at these time intervals.
Part C:
Which ordered pair(from the table in part A) represents the initial value? What does the initial value represent in this problem?
Part D:
What is the rate of change in this equation? What does the rate of change represent in this problem?
Answer:
Step-by-step explanation:
Part A:
To create the table, we substitute each of the given values of x into the equation and solve for y:
x y = -1025x + 30,750
0 30,750
5 25,375
8 21,050
10 18,725
30 -7,500
Part B:
The altitude after 5 minutes can be found by substituting x=5 into the equation:
y = -1025(5) + 30,750 = 25,375
The altitude after 30 minutes can be found by substituting x=30 into the equation:
y = -1025(30) + 30,750 = -7,500
After 5 minutes, the altitude of the airplane is 25,375 feet. After 30 minutes, the altitude of the airplane is -7,500 feet, which means the airplane is on the ground. This is because the altitude is decreasing by 1,025 feet every minute, and after 30 minutes, the altitude has decreased to 0 feet, which is the ground level.
Part C:
The ordered pair (0, 30,750) represents the initial value, where x=0. The initial value represents the altitude of the airplane before it started descending. In this problem, the initial value of 30,750 feet represents the altitude of the airplane when it was at cruising altitude.
Part D:
The rate of change in this equation is -1025. The rate of change represents the speed at which the altitude of the airplane is changing per minute. In this problem, the rate of change of -1025 feet per minute means that the altitude of the airplane is decreasing by 1025 feet every minute it descends.
In one day, there are two high tides and two low tides in equally spaced intervals. The high tide is observed to be 6 feet above the average sea level. After 6 hours pass, the low tide occurs at 6 feet below the average sea level. In this task, you will model this occurrence using a trigonometric function by using x as a measurement of time. Assume the first high tide occurs at x = 0
Create a trigonometric function that models the ocean tide for a period of 12 hours.
Answer:
The trigonometric function that models the ocean tide for a period of 12 hours is f(x) = 6 sin (2πx/12).
1. There is a chance that a bit transmitted through a digital transmission channel is received in error. Let X denote the number of bits in error in the next four bits transmitted. Suppose the probability mass function is given by:
Pr(X = 0) = 0.55
Pr{X = 1) = 0.22
Pr(X = 2) = 0.13
Pr(X = 3) = 0.08
Pr(X = 4) = 0.02
Determine the following:
a. the probability that two or fewer bits are transmitted in error
b.the probability that at least one bit is transmitted in error
c.the expected value of the number of bits transmitted in error
d.the standard deviation of the number of bits transmitted in error
2. Consider the following function:
f(x) = kx 0 less than or equal to x less than or equal to 8
a.Find the value of k that makes the function a valid probability density function (pdf). Report your answer as a fraction.
b. Determine Pr(2 less than or equal to x less than or equal to 3).Report your answer as fraction
c. Determine the expected value.
All the probabilities are solved and are mentioned below.
What is probability mass function?In probability and statistics, a probability mass function is a function that gives the probability that a discrete random variable is exactly equal to some value
Given is that there is a chance that a bit transmitted through a digital transmission channel is received in error. Let X denote the number of bits in error in the next four bits transmitted. Suppose the probability mass function is given by -
Pr(X = 0) = 0.55
Pr{X = 1) = 0.22
Pr(X = 2) = 0.13
Pr(X = 3) = 0.08
Pr(X = 4) = 0.02
We can find the probabilities as -
{ 1 } - the probability that two or fewer bits are transmitted in error :
P{E} = P(0) + P(1) + P(2)/∑P{n}
P{E} = 0.9/1
P{E} = 0.9
{ 2 } - the probability that at least one bit is transmitted in error -
P{E} = P(1) + P(2) + P(3) + P(4)/∑P{n}
P{E} = 0.45/1
P{E} = 0.45
{ 4 } - the expected value of the number of bits transmitted in error -
n = 0 + 1 + 2 + 3 + 4
n = 10
{ 4 } - the standard deviation of the number of bits transmitted in error -
σ = 1.0677
Therefore, all the probabilities are solved and are mentioned above.
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(a) The length of a rectangle is 6 cm more than its width, w cm. The perimeter of the rectangle is 37 cm. Form an equation in w and solve it to find the width of the rectangle.
The width of the rectangle whose perimeter is 37 cm is 6.25 cm.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
The length of a rectangle is 6 cm more than its width, w cm.
So, the length = w + 6
The perimeter of the rectangle is 37 cm.
Then, Perimeter of the rectangle = 37
2(l+ w) = 37
2( w+ 6 +w )= 37
2(2w + 6)= 37
4w + 12 = 37
4w = 25
w = 6.25 cm
and, length = w+ 6 = 6 + 6.25 = 12.25 cm
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If f is one-to-one and f(7)=3, then f^1(3)= ___, and (f(7))^-1= ___
Answer:
[tex]f^{-1}(3) = \boxed{7}[/tex]
[tex]f(f(7))^{-1} = \boxed{7}[/tex]
Step-by-step explanation:
These follow from two of the properties of inverse functions:
If [tex]f[/tex] is a one-to-one function then
[tex]if\; f(x) = y \;then\; f^{-1}(x) = y}[/tex][tex]f^{-1}(f(x) = x\\\\f^{-1}(f(x) \;is\;the\;same\;as; ((f(x))^{-1}[/tex]Which correctly describes how the graph of the inequality 6y − 3x > 9 is shaded?
Group of answer choices
Above the solid line
Below the solid line
Above the dashed line
Below the dashed line
HELP URGENT! LIMITED TIME TEST!!!
An ice cream truck tracks its sales for a year. They create a scatter plot using the data with the average monthly temperature temperature on the x-
axis and the sales along the y- axis.
The data in the graph (the photo added) suggest a linear association. Which of the functions best represents the equation of the line of best fit?
[Pay attention to the scale of the x and y axis]
Choose one,
y= 0.01x + 152
y= 0.5x + 100
y= x + 100
y = 30x - 159
A linear relationship between two quantities can be modeled using a mathematical function.
What is function?Function is the process or state of instruction that text inputs performance is specific tax and produce an output functional key components of programming language allowing the quarters to create complex commands with simple instruction for example a function can be used to add two numbers round together or to generate a random number function can also be combined to create more complex sequence of instruction.
The form of the function is generally expressed as y = mx + b, where y is the dependent variable, m is the slope of the line, x is the independent variable, and b is the y-intercept. The slope of the line, m, can be calculated from two points on the line using the formula m = (y2-y1)/(x2-x1). The y-intercept, b, can be calculated by substituting any point into the equation y = mx + b and solving for b.
Once the slope and y-intercept are known, the equation can be used to predict the value of the dependent variable given a certain value of the independent variable. For example, if the equation is y = 3x + 4, then for any given value of x, the corresponding value of y can be calculated. For x = 5, the corresponding value of y is 19 (5 x 3 + 4 = 19). This equation can also be used to graph the linear relationship between the two variables; by plotting the equation, a straight line is produced.
By using a function to model a linear relationship between two quantities, it is possible to calculate the relationship between them and predict values for either one given the other. This can be a useful tool for understanding the data and for making predictions about the data.
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Please help I need help so badly
Step-by-step explanation:
area3.14×18×18
1017.36ft²
circumference2×3.14×18
113.04ft
Hello. Please, help with a question below
The Average rate of change is defined as
r{average} = Δy/Δx = (y₂ - y₁/x₂ - x₁).
What is unit rate?The rate at which one quantity changes per unit change with the other quantity is called unit rate.
Given is the average rate of change.
Average rate of change is defined as the change in the value of a quantity over the interval change in the other quantity.
Mathematically -
r{average} = Δy/Δx = (y₂ - y₁/x₂ - x₁)
Therefore, the Average rate of change is defined as
r{average} = Δy/Δx = (y₂ - y₁/x₂ - x₁).
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Answer:
what basic business principle does the author of your reading material state that automakers igno red in recent years leading to the need for an industry bailout
7. Alexis has 145 stickers. She wants to divide the stickers evenly among 5 of her friends. How
many stickers will each friend get?
Write your answer in the box.
stickers.
8. There are 2,472 seats in the school auditorium. The seats are divided into 6 equal sections.
How many seats are in each section? Write your answer in the box.
seats
Explain how you found your answer. Show your work.
Answer: 7: 29 stickers for each friend
8: 412 seats in each section
Step-by-step explanation:
We will have to divide 145 (stickers) by 5 (friends) to get 29
We will have to divide 2472 by 6 to get 412
7.) 145 ÷ 5 = 29 → Each friend will get 29 stickers
8.) 2,472 ÷ 6 = 412 → There are 412 seats in each second.
I divided for both problems using the long division method and multiplied which is the inverse operation, to check my work.
Select the correct answer. What is the solution to this equation? 216 = 6 2 x − 1 A. x = 1 B. x = 2.5 C. x = 3 D.
Answer:
D. [If D is saying "x = 4"]
Step-by-step explanation:
We can start solving the equation 216 = 62x - 1 by adding 1 to both sides to isolate the term with x:
216 + 1 = 62x
Simplifying the left side, we get:
217 = 62x
To solve for x, we can divide both sides by 62:
217/62 = x
Using a calculator, we can evaluate the quotient:
3.5 = x
Therefore, the solution to the equation 216 = 62x - 1 is x = 3.5.
Since none of the answer choices match this result exactly, we can round 3.5 to the nearest integer. Rounding 3.5 up to the nearest integer gives us x = 4.
A carpenter who was installing a new roof on a garage noticed that for every 1-foot horizontal run, the roof was elevated by 4 inches. What is the pitch of this roof?
The pitch of the roof with one foot horizontal run and 4 inches elevation is 4 in per foot
What is an equation?
An equation is an expression that shows the relationship between two numbers and variables using mathematical operations like addition, subtraction, multiplication, exponents
The roof pitch (steepness) is given as a ratio of inch rise per horizontal foot, It is given by:
Pitch = rise / run
For every 1-foot horizontal run, the roof was elevated by 4 inches, hence:
Pitch = rise / run = 4 in / 1 ft = 4 in per foot
The pitch is 4 in per foot
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Match the following equation to the correct situation.
A + A(9%) = A(1.09)
A.
The amount Ryan paid for two shirts, one was full price for A, the other was discounted 9%.
B.
The amount donated by a company which gives 9% of A dollars collected at a charity banquet.
C.
The amount Tonya owes after putting 9% down on an A home.
D.
The amount Jess owes Julie from borrowing A with 9% interest.
A + A(9%) = A(1.09) is matching with the amount Jess owes Julie from borrowing A with 9% interest.
What is interest?
In the study of finance and economics, interest is the predetermined amount that a borrower or deposit-taking financial institution pays to a lender or depositor above and beyond the principal amount. It differs from any fees the borrower may be required to pay the lender or another entity.
Suppose here A is 100
We put the value of A in the equation
A + A(9%) = A(1.09)
100+ 100*9/100 = 100*1.09
Or,100+9=100*109/100
Hence the correct answer is D, amount Jess owes Julie from borrowing A with 9% interest.
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Answer:
Step-by-step explanation:
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