Similarity: Both are monotonous functions.
Difference: The parent radical function is a decreasing expression and the parent radical function is an increasing expression.
What are the difference and similarity between the parent radical and exponential functions?
Herein we must describe a difference and a similarity between the parent radical function and the parent exponential function, whose definitions are presented below:
Parent radical function
f(x) = √x
Parent exponential function
f(x) = eˣ
One similarity between these two parent functions is that are monotonous functions and one difference is that the parent radical function is a decreasing expression whereas the parent radical function is an increasing expression.
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44. the total cost for tuition plus room and board at state university is 2,584 dollars. tuition costs 704 dollars more than room and board. what is the tuition fee?
If total cost for tuition plus room and board at state university is 2,584 dollars and tuition costs 704 dollars more than room and board, then the tuition fees is 1644 dollars
Given,
The total cost for tuition plus room and board = 2584 dollars
Consider the cost for room and board as x
Tuition costs 704 dollars more than room and board.
Therefore the tuition fees = 704+x
Then the total cost = Cost for tuition fees+ Cost for room and board
2584 = (704+x)+x
2584= 704+2x
2x= 1880
x= 940 dollars
Then the tuition fees = 704+x
=704+940
=1644 dollars
Hence, if total cost for tuition plus room and board at state university is 2,584 dollars and tuition costs 704 dollars more than room and board, then the tuition fees is 1644 dollars
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Homework help please
Answer:
Step-by-step explanation:
180
Approximately 33 comma 200 citizens of a country died in automobile accidents in 2015. Express this toll in deaths per day
The toll of death per day in 2015 is 91.
We are given the approximate number of people who died in year 2015, which is 33,200. Now, as per the known fact, the year 2015 has 365 days. So, we can easily calculate the toll in deaths per day by performing division.
Number of deaths in 365 days = 33,200
Number of deaths each day = 33,200 ÷ 365
Performing division to find the number of deaths per day
Number of deaths each day = 90.96
Rounding off the digits to find number of deaths each day
Number of deaths each day = 91
Hence, this toll in deaths per day is 91.
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in a large population, 71% of the people have been vaccinated. if 5 people are randomly selected, what is the probability that at least one of them has been vaccinated?
The probability that AT LEAST ONE of them has been vaccinated is 0.9979.
Vaccination rate among the population: p = 0.71
Sample size = 5
Assume that X people have received vaccinations.
P(atleast one) = 1 - P (none)
By the binomial distribution, now,
P(none)= (⁵₀) 0.71° (1-0.71)⁵⁻⁰
= 1 × 1 (0.29)⁵
= 0.0021
So,
P(at least one) therefore equals 1 - P (none)
= 1 - 0.0021
= 0.9979
Therefore, the probability that AT LEAST ONE of them has been vaccinated is 0.9979
An explanation of probability theory?
Probability theory is a mathematical discipline that analyzes random encounters. A random event's outcome cannot be predicted before it occurs, but it could take any of several various forms. The end outcome is thought that it was determined by chance.
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1/3 ÷ 8 =
what s the answer
Answer:
0.0416¯
Step-by-step explanation:
after the 1 six is being repeated. Hope this helps! :)
Matthew scored −33 points in his turn at a video game. In Genevieve's turn, she scored fewer points than Matthew.
Use absolute value to describe Genevieve's score as a loss.
Genevieve lost more than 33 points in her turn at a video game.
Absolute value describes a number's distance from zero on the number line without taking direction into account. A number's absolute value is never negative.
Given that Matthew's score is −33 points.
In Genevieve’s turn, she scored lesser points than Matthew in her turn at a video game.
Let y be the points scored by Genevieve.
Then we have y < -33
⇒ | y | > | -33 | (Using absolute value on both sides)
⇒ | y | > 33
The absolute value of y can be any number greater than or equal to 34, while Genevieve's point in her video game turn is less than or equal to -34.
Therefore, Genevieve lost more than 33 points in her turn at a video game.
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Imagine that you are a teacher grading your students’ assignments. The following questions were turned in with incorrect answers. Trace through the process of solving them to discover where your students made a mistake in their order of operations. Which step of PEMDAS did they do out of order? Explain.
(6-2)^2+12-3^2
The correct answer is 19
student answer 97
The student did the subtraction step of PEMDAS out of order.
What is PEMDAS?PEMDAS is a rule regarding precedence of operations, given as follows, from highest to lowest precedence.
Parenthesis.Exponents.Multiplication/Division.Addition/Subtraction.In this problem, the expression is:
(6 - 2)² + 12 - 3².
The student reached an answer of 97 as follows:
(6 - 2)² + 9² = 4² + 9² = 16 + 81 = 97.
The student did the subtraction first, hence the student did the subtraction step of PEMDAS out of order.
The correct solution is:
(6 - 2)² + 12 - 3² -> Solve the Parenthesis.
4² + 12 - 3² -> Solve the Exponents.
16 + 12 - 9 -> Solve the Addition and Subtraction.
19.
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Find the LCM of
[tex]8 {a}^{2} {b}^{3} {f}^{4} [/tex]
and
[tex]3abg[/tex]
The LCM of 8a²b³f⁴ and 3abg is 24a²b³f⁴g.
What is defined by the term LCM?LCM is an abbreviation for "Least Common Multiple." The smallest multiple which two or even more numbers have in common is defined as the least common multiple.
Consider the following two integers: 2 and 3.2 multiples: 2, 4, 6, 8, 10, 12, 14....Multiples of three: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, and so on.The numbers 6, 12, and 18 are all common multiples of 2 and 3. The smallest number is six. As a result, the least common multiple of 2 and 3 is 6.The smallest number divisible both by numbers is the LCM of two numbers.Figuring the lowest common denominator (LCD) of 2 or even more fractions is a common application of LCM.
It is useful for adding, subtracting, as well as compare different or more fractions.
For the given question, the two numbers are given as; 8a²b³f⁴ and 3abg.
The least common multiple which will divide both the numbers are; all the values with their highest power.
LCM = 24a²b³f⁴g.
Thus, the LCM is found as 24a²b³f⁴g.
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See attachments!
Paolo wrote the following equation for the perimeter of a rectangle.
Which equation is equivalent to the equation Paolo wrote?
Answer:
p = 2 + l w
Step-by-step explanation:
Georgia is on the prom committee. She wants to hang a dozen congruent triangles from the ceiling so that they are parallel to the floor. She sketched out one triangle on a coordinate plane with coordinates (0,4),(3,8) , and (6,0) . If each triangle is to be hung by one chain, what are the coordinates of the point where the chain should attach to the triangle?
The coordinates of the point where the chain should attach to the triangle are (3, 4).
Given that, a triangle is on a coordinate plane with coordinates (0,4), (3,8), and (6,0).
We need to find the coordinates of the point where the chain should attach to the triangle.
What is the centroid of the triangle?The centroid is the centre point of the object. The point at which the three medians of the triangle intersect is known as the centroid of a triangle. It is also defined as the point of intersection of all three medians. The median is a line that joins the midpoint of a side and the opposite vertex of the triangle. The centroid of the triangle formula is G = ((x1+x2+x3)/3 , (y1+y2+y3)/3).
Now, centroid = ((0+3+6)/3, (4+8+0)/4)
=(3, 4)
Therefore, the coordinates of the point where the chain should attach to the triangle are (3, 4).
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Venus has switches at the top and bottom of her stairs to control the light for the stairwell. She notices that when the upstairs switch is up and the downstairs switch is down, the light is turned on.
b. If both the upstairs and downstairs switches are in the up position, will the light be on?
Explain your reasoning.
If both the upstairs and downstairs switches are in the up position, the light will be off
How to determine if the light will be on?The given parameters are
Switches = 2 i.e. top and bottom
Also, we have:
When the upstairs switch is up and the downstairs switch is down, the light is turned on.
This means that the light is only on when the upstairs switch is up and the downstairs switch is down
Any other position of the switches, the light is off
From the question, we have
Both the upstairs and downstairs switches are in the up position
This is different from the required position to on the light
Hence, the light will be off
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Heyy! Could you guys possibly help with the answer to this question? I’m stuck.
The codes of the countries are 34, 35 and 36
How to determine the codes of the countries?The given parameters are
Sum of codes = 105
Where the numbers are consecutive numbers
This means that
B = A + 1
C = A + 2
So, we have
A +A + 1 + A + 2 = 105
Evaluate the like terms
3A = 102
Divide through by 3
A = 34
So, we have
B = A + 1 = 34 + 1 = 35
C = A + 2 = 34 + 2 = 36
Hence, the codes of the countries are 34, 35 and 36
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Matt had 6 books to read. Each book has 11 pages. He has already read 60 pages. How many pages does he have left to read? The answer
Bob is interested in examining the relationship between the number of bedrooms in a home and its selling price. After downloading a valid data set from the internet, he calculates the correlation. The correlation value he calculates is only 0. 5. What does bob conclude?.
Bob after downloading the valid data set from the internet and calculating the correlation values as 0.5 concludes that as the number of bedrooms in a home increases its selling price also increases.
This happens because as there is an increased demand for the number of bedrooms in a home there should be enough supply in the market to fulfill the requirements. So, there should be a surplus of beds in the market and for that the selling price increases to maintain the surplus.
The law of Demand states that as the demand for a particular commodity or a product increases its price also increases. The above example of Bob gets verified according to the Law of Demand.
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Simplify an expression for the perimeter of the rectangle shown.
8.6x + 3
5.2
4
Write your answer with NO spaces:
The perimeter of the rectangle is P = (17.2x₊16.4).
Given that,
Length, l = 8.6x₊3
Width, b = 5.2
In the formula P=2l+2w, where l is the rectangle's length and w is its width, the perimeter P of a rectangle is determined. Using the formula A=l×w, where l is the length and w is the width, we can determine the area A of a rectangle.
We need to find the expression for the perimeter of the rectangle. The formula for the perimeter of the rectangle is given by :
P=2(l₊b)
Putting values of l and b in the above formula:
p = 2(8.6x ₊ 3 ₊ 5.2)
= 2(8.6x ₊ 8.2)
= 2(8.6x) ₊ 2(8.2)
= 17.2x ₊ 16.4
So, the required perimeter of the rectangle is 17.2x₊16.4.
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Pierce sold six gallons of paint for $75.78. What was the price per gallon of the paint?
Find the general indefinite integral. (use c for the constant of integration.) 8 x9 dx
[tex]$$\begin{aligned}&\text { (1) } \int \sqrt[8]{x^9} d x=\int x^{9 / 8} \cdot d x=\frac{(x)^{\frac{9}{8}+1}}{\frac{9}{8}+1}+c=\frac{8 x^{17 / 8}}{17}+c\\\\&\Rightarrow \int \sqrt[8]{x^9} d x=\frac{8}{17} \sqrt[8]{x^{17}}+c,(c \text { is constant })\\[/tex]
What is indefinite integral?In the previous two chapters, we were given a function and asked to determine its derivative. We are now going to reverse the situation, beginning with this part. We now want to know what function we discriminated in order to obtain the function. This previous example has two implications. The initial goal was to encourage you to start considering solutions to these difficulties. First, it's crucial to keep in mind that we are only asking what we differentiated to obtain the specified function. The second thing to keep in mind is that we could potentially employ an endless number of different functions, and they would all be different by a constant.
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The difference in the x-coordinates of two points is 3, and the difference in the y-coordinates of the two points is 6. What is the slope of the line that passes through the points? 2 3 6 9
Solution :
the differences in the X coordinates and Y coordinates:
The x-coordinate tells you how many steps you have to take to the right (positive) or left (negative) on the x-axis. And the y-coordinate tells you have many steps to move up (positive) or down (negative) on the y-axis.
Given : difference in the x-coordinates of two points is 3
the difference in the y-coordinates of the two points is 6
The slope of the line :
In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate.
The net change in the y-coordinate is represented by Δy and the net change in the x-coordinate is represented by Δx.
Hence, the change in y-coordinate with respect to the change in x-coordinate is given by,
m = change in y/change in x = Δy/Δx
Where “m” is the slope of a line.
Tan θ = Δy/Δx can also represent the slope of the line
So, tan θ to be the slope of a line.
Generally, the slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says (x1,y1) and (x2,y2) can be easily determined by finding the difference between the coordinates of the points. The letter ‘ m’ usually represents the slope.
If P(x1,y1) and Q(x2,y2) are the two points on a straight line, then the slope formula is given by:
Slope,
m = Change in y-coordinates/Change in x-coordinates
m = (y2 – y1)/(x2 – x1)
Therefore, based on the above formula, we can easily calculate the slope of a line between two points.
In other terms, the slope of a line between two points is also said to be the rise of the line from one point to another (along the y-axis) over the run (along the x-axis). Therefore,
Slope, m = Rise/Run
Use the slope formula.
the slope of a line given the coordinates of two points on the line. The slope formula is m=(y2-y1)/(x2-x1), or
the change in the y values over the change in the x values.
The coordinates of the first point represent x1 and y1. The coordinates of the second points are x2, y2. It does not matter which point you label as the first point and which you label as the second. Don't forget to include the correct sign of each value. Simplify to get the value of the slope. Check the your answer by graphing the points and verifying that the vertical distance between the two points and the horizontal distance between the two points is captured by the numerator and denominator of the slope
Ponit (2,3) & (6,9)
Slope of Line = y2-y1/x2-x1
= 9-3/3-2
=6/1
Slope of Line = 6
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REWRITE USING SET BUILDER NOTATION
a) the set of natural numbers less than 10
b) the set of integers greater than -7 but less than 7
c) the set of whole numbers greater than zero but less than or equal to 20
Answer:
See explanation
Step-by-step explanation:
n=number
a. { n ∈ N | n<10 } ==> N denotes natural numbers
b. { n ∈ Z | -7<n<7 } ==> Z denotes integers
c. {n ∈ W | 0<n<=20 } ==> W denotes whole numbers
A road sign in Canada gives the distance to Toronto as 140 kilometers. What is this distance to the nearest mile?
Converting 140 kilometers to miles, the distance from a road sign in Canada to Toronto is 87 miles.
In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.
A conversion factor is a number used to change one set of units to another, either by multiplying or dividing.
From the problem, we must convert the distance of 140 kilometers into miles.
Converting kilometers to miles, we must use the conversion
1 kilometer = 0.621371 mile
140 kilometers = 140 (0.621371 mile)
140 kilometers = 86.992 miles
Rounding off to the nearest mile,
140 kilometers = 86.992 miles = 87 miles
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PLEASE I NEED HELP!! URGENT!!!
please don't put in any spam answers :/
Answer:
hope this helped
Step-by-step explanation:
fluid ounces row 1) 64, row 2) 2
Cups row 2) 14
quarts row 1) 2
Spam Answer- Will the Wise
Find the distance between the two points rounding to the nearest tenth (if necessary).
(-6, 5) and (3,-7)
Answer: 15
Step-by-step explanation:
Distance formula: a^2+b^2=c^2 where c is the distance.
a^2=
(-6-3)^2=
(-9)^2=81
b^2=
(5-(-7))^2=
(5+7)^2=
12^2=144
c^2=81+144=225
If c^2=225, then what's c?
c=15
Help me with this question please
Answer: (1,0)
Step-by-step explanation:
Point is located on the x-axis
Hence, y=0
Thus, (1,0)
NEED HELP
Which of the following is and isn't a function? ( There may be more than one answer ). Explain Clearly
Using the function concept, we have that:
Items, a, and d are functions.Item b and c are not functions.When does a relation represents a function?A relation represents a function when each value of the input is mapped to only one value of the output.
On a graph, it means that each value of x is mapped to only one value of y, that is, there are no vertically aligned points on the graph.
For this problem, relation c does not represent a function, as there are multiple values of x are related to two values of y, and there are vertically aligned points on the graph.
In item b, when x = 6, there are two values of y, hence this is also not a function. For items a and d, each value of x is mapped to only one value of y, hence they are functions.
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find the area and circumference of each circle. Use pi in your answer (example: radius = 8, or diameter = 14).
The area of the circle is 64π square unit and the circumference is 16π units
Calculating area and circumference of a circleFrom the question, we are to find the area and circumference of the circle
The area of a circle is given by the formula,
A = πr²
Where A is the area
and r is the radius
Using the parameter, radius = 8
Then,
A = π × 8²
A = 64π square unit
Calculating the circumference
The circumference of a circle is given by the formula
C = 2πr
Where C is the circumference
and r is the radius
Thus,
C = 2 × π × 8
C = 16π units
Hence, the area of the circle is 64π square unit and the circumference is 16π units
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a traffic study has shown that the probability that 55 cars will pass over a small bridge in a 4-4-minute period is 0.16.0.16. what are the odds against exactly 55 cars passing over the bridge in that time?
How do you do order of operations?
Use the graph of each function to estimate intervals to the nearest 0.5 unit on which the function is increasing, decreasing, or constant. Support the answer numerically.
f(x)=x^3-x^2-2x+3
It appears that from graph that the function is increasing in the interval (-∞,-1) and (1,∞). Also the function is decreasing in the interval (-1,1) and (0.0.5).The function is not constant anywhere.
To check if this is correct, we will find the relative extrema of the function,
f(x) = x³-x²-2x+3
Find it derivative f'(x) = 3x²-2x-2
f'(x) = 0
⇒ x = 2 ± √(4+24)/3
= 3.77 , -1.1
Find the second derivative f''(x) = 6x -2
f''(3.77) = 20.62>0
So the function has a relative minimum at x = 3.77.
f''(-1.1) = -8.6<0
So the function has a relative maximum at x = -1.1
Now we can conclude with the intervals where the function is increasing is before the relative maximum and after the relative minimum.
i.e., the intervals (-∞,-1) and (3.5,∞) [rounding to the nearest 0.5 unit]
So the interval in which the function is decreasing is between the relative maximum and minimum. i.e., the interval (-1, 3.5)
The function is nowhere constant.
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Which number appears farther to the right on the number line?
a) -53/2
b) -1
c) -100
Answer:
-1
Step-by-step explanation:
-1 has the greatest value
For each pair of figures below, choose how they are related.
Translation
Reflection
Rotation
None of these
1 t
Translation
Reflection
O Rotation
None of these
M
1
O Translation
O Reflection
Rotation
O None of these
S
Translation
Reflection
O Rotation
O None of
Figure 1, 2,3and 4 are the cases of rotation, reflection, not the case of any options and rotation respectively
Figure 1 is the case of rotation as the two figures are of exact same size and same shape and are rotated at a angle
Figure 2 is the case of reflection as both the figures are mirror reflection of each other and are of exact same size and same shape
Figure 3 is a case of neither transition, refection nor rotation as the two figures are not of exact same size or shape
Figure 4 is a case of rotation as the two figures are of exact same size and same shape and are rotated at a angle
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