What does the problem asks for:
--> mean and median
Let's calculate the mean:
[tex]\text{Mean}=\dfrac{\text{sum of all the numbers}}{\text{number of numbers given}}[/tex]
--> the sum of all the numbers = 21 + 40 + 48 + 26+ 32 + 31 = 198
--> number of numbers given: 6
==> let's calculate
[tex]\text{Mean}=\dfrac{198}{6} =33[/tex]
Let's calculate the median
--> Median definition: middle number in an ordered sequence
==> let's order the sequence: 21, 26, 31, 32, 40, 48
--> since there are an even number of numbers, there isn't an exact
middle number
--> thus, we must find the mean of the two numbers closest to the
middle
[tex]\text{Median} = \dfrac{31+32}{2} =\dfrac{63}{2} =31.5[/tex]
Answer: 31.5
Step-by-step explanation:
21, 26, 31, 32, 40, 48
Median
31+32= 63
63÷2= 31.5
Mean
21+26+31+32+40+48=198
198÷6=33
If the slope of line a is -4, then the slope of a line parallel to it is: 4. -4. -. None of these choices are correct.
Considering the definition of parallel line, the correct answer is the second option: if the slope of line a is -4, then the slope of a line parallel to it is -4.
What is Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin.Parallel lineParallel lines are two lines that are always at the same distance from each other and that prolonged towards infinity never touch.
Two lines are parallel if they have the same slope "m" and different y-intercepts "b".
Slope of a line parallel in this caseIf the slope of line a is -4, then the slope of a line parallel to it is -4 because two lines are parallel have the same slope "m".
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You, are a loan officer at West Elm Savings and Loan. Mr. and Mrs. Brady are in your office to apply for a mortgage loan on a house they want to buy. The house market value of $209,900, the median price of a house in Champaign. Your bank requires 1/5 of the market value as a down payment.
The amount of the down payment, considering the median house price, is given as follows:
$41,980.
How to obtain the down payment?The down payment is obtained applying the proportions in the context of this problem.
A proportion is applied because the down payment is obtained with the multiplication of the median house price by the fraction.
The parameters are given as follows:
Fraction of 1/5.Median price of $209,900.Hence the down payment is obtained as follows:
1/5 x 209900 = $41,980.
Missing Information
The problem asks for the amount of the down payment, considering the median house price.
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A rocket is launched from the top of a building. The flight path is modelled by h = -4t2 + 16t + 24
where h is the height of the rocket from the ground in metres, and t is the time in seconds. What is the initial height of the rocket, when will the rocket hit the ground and what is the height of the rocket after 4 seconds
The initial height of the rocket is 24 metres, the rocket hit the ground in 0.88 seconds and the height of the rocket after 4 seconds is 24 metres.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
The initial height of the rocket is given by the value of h when t = 0:
h(t)=-4t² + 16t + 24
h(0)=-4(0)² + 16(0) + 24
h(0)=24
So the initial height of the rocket is 24 metres.
The rocket will hit the ground when its height is 0 metres, so we can set h = 0 in the equation and solve for t:
0 = -4t²+ 16t + 24
-4t² + 16t + 24 = 0
t=-0.88 seconds
So the rocket will hit the ground after approximately 0.88 seconds.
The height of the rocket after 4 seconds is given by:
h(4)== -4(4)²+ 16(4) + 24
=-64+64+24
=24
So the height of the rocket after 4 seconds is 24 metres.
Hence, the initial height of the rocket is 24 metres, the rocket hit the ground in 0.88 seconds and the height of the rocket after 4 seconds is 24 metres.
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A business magazine mailed a questionnaire to the chief executive officerschief executive officers of the top 400400 profitable companies, and received responses from 66% of them. Among those who responded, 40% reported that they did not find that such surveys intruded significantly on their workday.
What is the population?
Using percentages we know that 106 people stated they didn't think these questions seriously interrupted their ability to do their jobs.
What is the percentage?In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100.
Although "pct," "pct," and occasionally "pc" are also used as abbreviations, the percent symbol "%" is most usually used to denote it.
A% is a number that has neither dimensions nor a defined unit of measurement.
The percentage can be calculated by dividing the value by the total value and multiplying the result by 100.
(Value/Total Value)100% is the formula for calculating percentages.
So, the percentage of people who answered the questionnaire is 66%.
That will be,
= 400/100 * 66
= 264
Of the 264 respondents, 40% said that they did not feel that these questionnaires significantly disrupted their workday.
= 264/100 * 40
= 105.6
= 106
Therefore, using percentages we know that 106 people stated they didn't think these questions seriously interrupted their ability to do their jobs.
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Try This question out and I’ll give you brainliest
Answer:
p = -6, 7
Step-by-step explanation:
To find the solutions to the equation p^2 = p + 42, we are going to need to solve for p. So, let's do just that!
p^2 = p + 42 [Subtract p^2 from both sides]
0 = -p^2 + p + 42 [Factor out the -]
0 = - ( p^2 - p - 42 ) [Factor p^2 - p - 42]
0 = - ( p + 6 ) ( p - 7 ) [Set both pair of parentheses equal to 0}
p + 6 = 0
p = -6
p - 7 = 0
p = 7
So, the solutions to the equation are p = -6, 7
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Which one of the following compound inequalities has no solution?
[A]3x + 4 < x-8 and -5x +4> 3x - 10
[B]4x-6 ≤ 5x + 6 and -3x - 2 > 2x+8
[C]-4x-3 ≤ 2x +9 and -3x+2> - 2x + 5
[D]4(x + 1) ≥ 3(x + 2) and -3(x - 1) <5(x + 2)
The compound inequality that has no solution, according to the query, is B.
What are the two inequalities' rules?Rule 1: When the same quantity is applied to or subtracted on both sides, an inequality sign does not change. Rule 2: Once both ends are duplicated or halved by a positive value, the inequality sign does not change.
[A] 3x + 4 < x - 8 and -5x + 4 > 3x - 10
Solving for x, we get:
3x + 4 < x - 8 => 2x > 12 => x > 6
-5x + 4 > 3x - 10 => 2x < 14 => x < 7
The correct solution to x is 6 < x < 7, which is the overlapping answer.
Since this two inequalities don't have any common solutions, when we solve all of the 2 inequality in [B], we find there is no solution.
In the actual number system, the equation 4x - 6 ≤ 5x + 6 can be resolved as -x ≥ 12, with no answer.
-3x - 2 > 2x + 8 can be solved as -5x > 10, which has no solution in the real number system.
[C] -4x-3 ≤ 2x +9 and -3x+2> - 2x + 5
Solving for x, we get:
-4x - 3 ≤ 2x + 9 => -6x ≤ 12 => x ≥ -2
-3x + 2 > -2x + 5 => -x > 3 => x < -3
which is an empty set and has no solution.
[D] 4(x + 1) ≥ 3(x + 2) and -3(x - 1) < 5(x + 2)
Solving for x, we get:
4(x + 1) ≥ 3(x + 2) => x ≥ -3
-3(x - 1) < 5(x + 2) => x > -2
The overlapping solution for x is x > -2 and x ≥ -3, which is a valid solution of x > -2.
Therefore, B has no solution.
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true/false. the following histogram shows the distribution of house values in a certain city. the mean of the distribution is $403,000 and the standard deviation is $278,000 .
False. The histogram shows the frequency of house values, not the values themselves.
The histogram in the question does not show the actual values of house values in a certain city. It instead shows the frequency of house values. The histogram has the house values on the x-axis and the frequency of house values on the y-axis. The frequencies are shown as bars and the height of each bar represents the number of houses with that value. The mean and standard deviation mentioned in the question are statistical measures of the actual house values in the city. The mean is the average of all the house values in the city and the standard deviation is a measure of the variation in the house values. Therefore, the statement that the histogram shows the distribution of house values in a certain city with the mean of $403,000 and the standard deviation of $278,000 is false.
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The
equation C= 5.75b represents the cost. C, for b used books at Pickwick Books.
At Dickens Books, a customer can buy 3 used books for $16.50, with each book having the same price.
Who charges less per used book, and how much less? Move the correct name and dollar amount to the blanks to complete the sentence
charges less per used book. The cost is
Pickwick Books
Dickens Books
$0.15
$0.25
$0.35
The cost at Pickwick Books is $5.75 and the cost at Dickens Books is $5.50, so the books are cheapre in Dickens Books.
Who charges less per book?We know that the equation:
C = 5.75*b
Repersents the cost for b books at Pickwick Books.
Then the cost of each book there is $5.75
We also know that at Dickens Books, a customer can buy 3 used books for $16.50, then the cost of each book there is given by:
C = $16.50/3 = $5.50
So the books are cheaper, by $0.25, in Dickens Books.
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which does not demonstrate the addition property of equality or the subtraction property of equality? multiple choice question. a) 16
Neither the addition property of equality nor the subtraction property of equality can be demonstrated by themselves. They are properties that must be satisfied by the operations of addition and subtraction respectively, in order for equality to hold.
The addition property of equality states that if two quantities are equal.
(a = b), then their sum with any other quantity (c) will also be equal (a + c = b + c). The subtraction property of equality states that if two quantities are equal (a = b), then their difference with any other quantity (c) will also be equal (a - c = b).
In other words, both properties say that when two quantities are equal, then the result of adding or subtracting the same quantity from both will also result in equal quantities.
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two classes were asked what was their favorite food at a local restaurant. The results are shown in the table below.
Based on the result shown in the table below, a statement which is true include the following: A. exactly 1/5 of the students chose pizza as their favorite food.
What is a fraction?In Mathematics, a fraction simply refers to a numerical quantity which is not expressed as a whole number. In order to determine the true statement, we would evaluate them as follows;
"Exactly 1/5 of the students chose pizza as their favorite food."
Total number of students that chose pizza = 6 + 4
Total number of students that chose pizza = 10 students.
Total number of students = 26 + 24
Total number of students = 50 students.
Therefore, the fraction of students that chose pizza as their favorite food is given by:
Fraction = 10/50
Fraction = 1/5.
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Complete Question:
Two classes were asked what was their favorite food at a local restaurant. The results are shown in the table below.
Which statement is true?
Exactly 1/5 of the students chose pizza as their favorite food.
Less than 25% of students chose tacos as their favorite food.
More students prefer French fries than prefer tacos.
Exactly 1/2 of students prefer either pizza or hamburgers.
Anthony bikes a 16.2-mile long trail. If he bikes it 4 times, how faw will he have traveled
64.8 miles will be the distance travelled by Anthony.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that Anthony bikes a 16.2-mile long trail.
If Anthony bikes it 4 times we need to find how far Anthony traveled.
By means of multiplication we find the distance traveled by Anthony.
Multiplication is a method of finding the product of two or more numbers
Now multiply 16.2 with 4
16.2×4
64.8 miles
Hence, 64.8 miles will be the distance travelled by Anthony.
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Three softball players discussed their batting averages after a game.
Probability
Player 1 seven elevenths
Player 2 six ninths
Player 3 five sevenths
Compare the probabilities and interpret the likelihood. Which statement is true?
Player 1 is more likely to hit the ball than Player 2 because P(Player 1) > P(Player 2)
Player 2 is more likely to hit the ball than Player 3 because P(Player 2) > P(Player 3)
Player 1 is more likely to hit the ball than Player 3 because P(Player 1) > P(Player 3)
Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2)
The correct statement regarding the probabilities is given as follows:
Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2).
How to obtain a probability?A probability is obtained with the division of the number of desired outcomes by the number of total outcomes in the context of a problem.
The probabilities for each player are given as follows:
Player 1: 7/11 = 0.636 (converting to decimal).Player 2: 6/9 = 0.6667.7Player 3: 5/7 = 0.714.Hence the correct statement is given by the last option among those presented in this problem.
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let x denote the time in minutes (rounded to the nearest half minute) for a blood sample to be taken. the probability mass function for x is x 0 0.5 1 1.5 2 2.5 f(x) 0.1 0.2 0.3 0.2 0.1 0.1 determine the following: (a) p(x 2.25) (b) p(0.75
The probability of the time being 2.25 minutes is 0.9, and the probability of the time being 0.75 minutes is 0.1.
(a) p(x ≤ 2.25) = P(x = 0) + P(x = 0.5) + P(x = 1) + P(x = 1.5) + P(x = 2) + P(x = 2.5) = 0.1 + 0.2 + 0.3 + 0.2 + 0.1 + 0.1 = 0.9
(b) P(x = 0.75) = 0.1
The probability mass function is a function of discrete random variables that provides a probability for each value of the random variable. In this case, the random variable is the time in minutes (rounded to the nearest half minute) for a blood sample to be taken, and the probability mass function provides the probability of the time being a certain value. For example, the probability of the time being 2.25 minutes is 0.9, and the probability of the time being 0.75 minutes is 0.1.
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Nikhil and Mae work at the same company. Nikhil has been at the company 6 times as long as Mae. Nikhil's time at the company is 8 more than 4 times Mae's. The following system of equations models the scenario:
x = 6y
x = 8 + 4y
How many years has each person been employed by the company?
A) Nikhil has been with the company for 36 years, while Mae has been there for 6 years.
B) Nikhil has been with the company for 30 years, while Mae has been there for 5 years.
C) Nikhil has been with the company for 24 years, while Mae has been there for 4 years.
D) Nikhil has been with the company for 18 years, while Mae has been there for 3 years.
Nikhil has been with the company for 24 years, while Mae has been there for 4 years.
Option C is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 2 = 8 is an equation.
We have,
Number of years Nikhil worked = x
Number of years Mae worked = y
x = 6y ______(1)
x = 8 + 4y ______(2)
Substituting (1) in (2)
6y = 8 + 4y
Subtract 4y on both sides.
6y - 4y = 8
2y = 8
Divide 2 into both sides.
y = 4
Now,
x = 6y
x = 6 x 4
x = 24
Thus,
The number of years Nikhil worked is 24 years.
The number of years Mae worked 4 years.
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The quotient of (x4 – 3x2 + 4x – 3) and (x2 + x – 3) is a polynomial. What is the quotient?
x4 – 2x2 + 5x – 6
x2 – x + 1
x6 + x5 – 6x4 + x3 + 10x2 – 15x + 9
x4 – 4x2 + 3x
Answer:
B
Step-by-step explanation:
Got it right on the exam
TRUE OR FALSE Is the following proposition a tautology for all predicates P(x) and Q(x)? [Is it true for any predicates P(x) and Q(x)?] Va € Z, [P(x) VQ(x)] HW € Z,P(x)] V[Wx € Z, Q(x)]
True. The proposition "for all x in set Z, either P(x) or Q(x) if and only if for all x in set Z, either P(x) or Q(x)" is a tautology. This means that the statement is always true, regardless of what predicates P(x) and Q(x) are.
The logical connective "if and only if" (written as "iff") is used to express that the two statements are logically equivalent. The symbol "V" represents the logical operator "or".
The tautology states that if either P(x) or Q(x) is true for some x in set Z, then the other statement, either P(x) or Q(x), must also be true. It follows that if either P(x) or Q(x) is false, then the other statement must also be false.
This implies that the two statements are logically equivalent and that one statement can be substituted for the other without affecting the truth value of the overall proposition.
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Juan and Laura are 220 feet apart when they begin walking directly toward one another. Juan travels at a constant speed of 3.5 feet per second and Laura travels at a constant speed of 5 feet per second. How many seconds after Juan and Laura started walking will they reach each other?
The time it will take Juan and Laura to meet each other is 25.88seconds
What is velocity?Velocity is the rate of change of velocity with time. It is a vector quantity and it is measured in meter per second. It can also be measured in Mikes per hour and so on.
Velocity = displacement /time
displacement = velocity × time
The total distance traveled = 220feet
220 = v1t + v2t
220 = (v1+v2) t
220 = ( 3.5 + 5) t
220 = 8.5 t
divide both sides by 8.5
220/8.5 = t
t = 25.88 seconds
therefore it will take Juan and Laura 25.88 seconds to meet each other
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Why is the graph shown a line of best fit?
The points are evenly distributed above and below the line, which provides the best explanation for why the graph displays a line of best fit.
What is the regression line?A statistical tool that shows the relationship between two variables is a regression line. It is employed specifically when a change in one (the dependent variable) is dependent on a change in the value of the other (the independent variable).
Given the graph,
for the line of best fit, A graph's nodes are connected by a mathematical concept known as the line of greatest fit. It is a kind of linear regression that uses scatter data to determine how to best define the relationship between the dots.
A change in the value of X causes a change in the value of the equation, which is written as Y on X.
X on Y is the equation, and the deviation of the Y variable determines how the X variable changes.
The graph shows a line of greatest fit because the spots are equally spaced above and below the line.
Hence the points are drawn uniformly above and below the line, thus the best explanation is that the graph displays a line of best fit.
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Which set of numbers includes only integers?
A Venn diagram. A large box is labeled rational numbers. A box inside the rational numbers box is labeled integers. A box inside the integers box is labeled whole numbers.
Negative 5, negative 3 and one-fourth, 1, one-eighth
Negative 3, negative 2, 2, 3
Negative 6, negative 4, negative 2, negative one-half
One-half, two-thirds, StartFraction 6 Over 7 EndFraction, 0
The required set of numbers includes is given as {-3, -2, 2, 3}. Option B is correct.
What is set?Sets are an orderly collection of items in mathematics that can be expressed in set-builder or roster form.
Here,
Integers are whole numbers, both positive and negative, including zero. For example -4, -3, -2, -1, 0, 1, 2, 3, 4, etc. They are used to represent whole quantities and are a basic type of number in mathematics.
Thus, from the options set of numbers includes is given as {-3, -2, 2, 3}. Option B is correct.
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The lateral height of a cone is 4 inches and the area of the base of the cone is 49π in². It requires 2.5 minutes to paint the cone.
The area of the base is doubled.
How long will it take to paint this cone if it can be painted at the same rate? Use π≈3.14.
Enter your answer, rounded to the nearest tenth, in the box.
min
Answer:
100.2
Step-by-step explanation:if its the lateral height of 4 it has to 420
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x + 1, y = 0, x 0, x = 5; about the x-axis v=| 17.5 17.5x Sketch the region. 7 6 6 3
The volume of the solid is 17.5 . In general, finding the volume of a solid of revolution involves finding the volume of each infinitesimal cylindrical shell.
To find the volume of the solid obtained by rotating the region bounded by the curves y = x + 1, y = 0, x = 0, and x = 5 about the x-axis, we can use the method of cylindrical shells. The volume of the solid is given by the formula:
V = ∫ 2πrh dr
Where r is the radius of the cylindrical shell, h is the height of the shell, and dr is the incremental change in the radius as we move from one shell to the next. The radius of the cylindrical shell is equal to the distance from the line of rotation (in this case, the x-axis) to the point on the boundary curve that is vertically above the point where the shell intersects the x-axis.
In this case, the boundary curves are y = x + 1 and y = 0. For the interval 0 < x < 5, the height of the cylindrical shell is given by x + 1, and the radius of the shell is x. Therefore, the volume of the solid is given by:
V = ∫ 0 to 5 2π(x)(x + 1) dx = 17.5
The units of volume would be cubic units, determined by the units used for the variables x and π.
The choice of the method of integration, either by using disks/washers or cylindrical shells, depends on the geometry of the region being rotated and the axis of rotation.
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Please help me!! (30 points)
Answer:25.5
Step-by-step explanation:
64.5+90=154
180-154=25.5
Select the correct equation for the following sentence: Twenty-four is the same as 31.4 times a number plus negative 8.4. 31.4n + 8.4 = 24 –8.4n + 31.4 = 24 24 = 31.4n + (–8.4) 24 – 31.4 = –8.4n
The correct equation for the following sentence:
24 = 31.4n + (–8.4).
The correct option is C.
What is an expression?One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.
Given:
A phrase:
Twenty-four is the same as 31.4 times a number plus negative 8.4.
Let the number is n.
The phrase can be expressed as,
24 = 31.4n + (–8.4).
Therefore, the expression is 24 = 31.4n + (–8.4).
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Analyze the graph below to identify the key features of the logarithmic function. Graph begins in the third quadrant near the line x equals negative 6 and increases rapidly while crossing the ordered pair negative 5, 0. The graph then begins to increase slowly throughout the second and first quadrants. Group of answer choices The x‐intercept is x = −5, and the graph approaches a vertical asymptote at x = −6. The x‐intercept is y = −5, and the graph approaches a vertical asymptote at y = −6. The x‐intercept is x = 5, and the graph approaches a vertical asymptote at x = 6. The x‐intercept is y = 5, and the graph approaches a vertical asymptote at y = 6.
The x‐intercept is x = −5, and the graph approaches a vertical asymptote at x = −6. Then the correct option is A.
How to draw the graph of the function?The collection includes all locations on the surface of the shape (x, f(x)) that make up a function of f's graph. We may alternatively say that the graph of f is the curve of y = f. (x). As a result, the diagram of an equation is a particular instance of the graphs of functions.
The x-intercept is at (-5, 0). Then the value of the abscissa is given as,
x = -5
The graph begins in the third quadrant near the line x = - 6. Then the equation x = - 6 represents the asymptote.
The x‐intercept is x = −5, and the graph approaches a vertical asymptote at x = −6. Then the correct option is A.
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Shannon manages a small zoo and she has been analyzing the attendance data. Shannon finds that the number of visitors increases exponentially as the temperature increases, and this situation is represented by the function f(x) = 3x. Shannon also finds a linear equation that models the number of people who leave the park early depending on the change in temperature, and it is represented by g(x) = −x + 4. The graph of the two functions is below. Find the solution to the two functions and explain what the solution represents. Graph increasing exponentially from the left, crosses the y axis at one and goes to infinity and intersects a linear graph that decreases and crosses the y axis at four and the x axis at four.
The solution to the two functions f(x) = 3ˣ and g(x) = -x + 4 is, 1
What are functions?Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).
Vertical line test:-
Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.
If we get more images then it will not be a function.
For example, let us take, y² = 4ax
y = ±√4ax
For single value of x we get two values of y
Hence, it will not be a function.
Given that,
The number of visitors increases exponentially as the temperature increases, and this situation is represented by the function
f(x) = 3ˣ
The number of people who leave the park early depending on the change in temperature, and it is represented by
g(x) = −x + 4
the solution of both the graphs = ?
the intersection of the two curves of graphs of the functions is the solution,
Basically, it represent that,
both function have same value for particular value of x,
So,
when both functions have same value that will be our solution,
f(x) = 3ˣ
g(x) = −x + 4
It can be seen in the graph that both the functions intersects at x = 1,
f(1) = 3
g(1) = −1 + 4 = 3
Hence, the solution is 1
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Employees were asked how many times per week they exercised. The frequency table shows the results of the survey.
The answers include the following:
The total frequency is 22 + 16 + 18 + 22 + 9 + 13 + 6 + 3 + 1 = 110
We have given the frequency table
Number: 0 1 2 3 4 5 6 7 8
Frequency: 22 16 18 22 9 13 6 3 1
Probability distribution table
Number: 0 1 2 3 4 5 6 7 8
Frequency: 22/110 16/110 18/110 22/110 9/110 13/110 6/110 3/110 1/110
Probability P (x ≥ 7 ) = 3/110 + 1/110 = 4/110 = 2/55
P (x = 3 ) = 22/110 = 11/55
P (x < 4) = 22/110 + 18/110 + 16/110 + 22/110 = 78/110 = 39/55
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One leg of a triangle has a length of 3m. The other sides have lengths that are consecutive integers find these lengths
The length of the other two sides are 4m and 5m
How to determine the lengthsUsing the Pythagorean theorem, we have that the square of the hypotenuse sides is equal to the sum of the squares of the other two sides of the triangle
This is represented as;
x² = y² + z²
From the information given, we have that;
z = 3m
x = x + 1
y = x
Substitute the values, we get
(x + 1)² = x² + 3²
Find the squares
(x + 1) ² = 9 + x²
expand the bracket
(x + 1) ( x + 1) - x² = 9
x² + x + x + 1 - x² = 9
collect like terms
2x = 8
x = 4
Then,
x + 1 = 5
x = 4
Hence, the values are 4m and 5m
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copy and paste the descriptive statistics for the prices variable for all 75 observations in the box to the right. make sure the output contains the n, mean, median, standard deviation, min/max, and the quartiles of the variable specified. interpret in the words of the problems the following statistics that you generated:
The shape of the distribution, is symmetric, is the best description of statistics about scores.
What is standard deviation ?
The standard deviation is the positive square root of the variance of this data set. Variance of a data set is the sum of squared differences of the data values from its mean to the total count of data values.
The given data in the problem is;
Mean = 78%
Standard deviation = 4%
Min = 64
Median = 78
Q1 = 72
Q3 = 84
Max = 99
The condition for the symmetric distribution is found as;
Q2-Q1 = Q3 - Q2
From the data we have;
Q2-Q1 = 6
Q3 - Q2= 6
So that , both are equal
Hence, the condition of symmetry is followed.
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The points Q (7, 6), R(-1,5), S(-5, -2), and T(3, -1) form a quadrilateral.
Find the desired slopes and lengths, then fill in the words that BEST identifies the type of quadrilateral.
The slope of QR is 1/8.
The length of QR is 8.06 unit.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
Given:
The points Q (7, 6), R(-1,5), S(-5, -2), and T(3, -1) form a quadrilateral.
A quadrilateral in geometry is a four-sided polygon with four edges and four corners.
The slope of QR,
= (5 - 6)/(-1-7)
= 1/8.
The length of QR = √{(5 - 6)² + (-1-7)²} = 8.06 unit.
Therefore, 1/8 is the slope and 8.06 unit is the length.
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to isolate a single variable when rearranging equations, move all other variables to the other side of the equation by using the opposite function on them and remembering to perform that operation on both sides of the equation . make sure the rearrangement has the target variab
Make that the target variable is in the numerator, not the denominator, of the rearrangement.
Variable
A variable is a placeholder sign for a varying quantity or other mathematical entity.
Move all other variables to the other side of the equation by applying the opposite function to them, keeping in mind to carry out that operation on both sides of the equation, in order to isolate a single variable when rearranging equations. Make that the target variable is in the numerator, not the denominator, of the rearrangement.
Move all other variables to the other side of the equation by applying the opposite function to them, keeping in mind to carry out that operation on both sides of the equation, in order to isolate a single variable when rearranging equations. Make that the target variable is in the numerator, not the denominator, of the rearrangement.
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