Answers
[tex]R_{ave}=\frac{f(b)-f(a)}{b-a}[/tex]
[tex]R_{ave}=\frac{f(3)-f(1)}{3-1}[/tex]
[tex]R_{ave}=\frac{(2(3^{2})-20(3))-(2(1^{2})-20(1))}{2}[/tex]
[tex]R_{ave}=\frac{(2(9)-60)-(2(1)-20)}{2}[/tex]
[tex]R_{ave}=\frac{(18-60)-(2-20)}{2}[/tex]
[tex]R_{ave}=\frac{(-42)-(-18)}{2}[/tex]
[tex]R_{ave}=\frac{-24}{2}[/tex]
[tex]R_{ave}=-12[/tex]
Related Questions
Which of the following statements best describes the effect of replacing the graph of y = f(x) with the graph of y = f(x) − 9?\
The graph of y = f(x) will shift up 9 units.
The graph of y = f(x) will shift down 9 units.
The graph of y = f(x) will shift left 9 units.
The graph of y = f(x) will shift right 9 units.
Answers
Answer:
The graph of y = f(x) will shift down 9 units.
Step-by-step explanation:
With the graph of y = f(x)-9 the graph of y=f(x) will shift down 9 units. For example:
if f(0) = 0, then y = f(0) -9 = -9.
if f(1) = 9, then y= f(1) - 9 = 9-9 = 0.
The same proccess with all x in the domain of f(x).
A rope is 66 feet long. It is cut into two pieces such that one piece is half the length of the other. What is the length of the longer piece of rope?
Answers
Then the other piece is 0.5x feet long
In total: x + 0.5x = 66 -> x = 44
So the longer piece is 44 feet, shorter piece is 22 feet
Rope Length = 1st Piece + 2nd Piece
Where 1st Piece = 1/2 the 2nd Piece.
Therefore.
Rope Length = 1/2x + x
Now substitute and solve for x.
66 = 1/2x + x
66 = 3/2x
/1.5 /1.5
44 = x
Therefore the longer piece is 44.
Proof.
First Piece: 1/2 x = 44 / 2 = 22
Second Piece = x = 44
22 + 44 = 66
You have three $1 bills, four $5 bills, and two $10 bills in your wallet. You select a bill at random. Without replacing the bill, you choose a second bill at random. Find P($5 then $10).
Answers
P(5,10)=8/72
P(5,10)=1/9
write an equation thats parellel to the given line & that passes through the given point y=5/2x-10;(6,-29)
Answers
Explanation: Any lines that are parallel to each other share the same slope but have different y-intercepts. To solve for this problem, keep you would first need to find out the b-value or the y-intercept. To do this, set up the y=mx+b equation and plug the slope into m (5/2). Then, since you know the line has to pass through points (6, -29) you would plug those points into the equation: -29=5/2(6) + b . You will then solve for b and your b-value will be -44. Now, since you know your slope and your y-intercept, you now know your answer is y= 5/2x-44.
Solve 10p + 9 - 11 - p = -2(2p + 4) - 3(2p - 2)
Answers
9p - 2 = -4p - 8 - 6p + 6
9p - 2 = -10p - 2
9p + 10p = -2 + 2
19p = 0
p = 0 <===
The value of p is 0.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
Example:
33 + 3x + 4y = 7 is an expression.
24 - 87 is an expression.
We have,
10p + 9 - 11 - p = -2(2p + 4) - 3(2p - 2)
Simplifying we get,
10p - 2 - p = -4p - 8 - 6p + 6
Combining like terms.
9p - 2 = -10p - 2
Add 2 on both sides.
9p + 10p = -2 + 2
Divide 19 on both sides.
19p = 0
p = 0
Thus,
The value of p is 0.
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Help please on that one
Answers
the circle is divided into 8 sections
5 are shaded
so 5/8 are shaded
5 divided by 8 = 0.625
0.625 = 62.5%
Round to 63% if you need to.
Dominick is planning to take a vacation to either Orlando or Tampa Bay. He wants to go to the city that is warmer, on average. The box plot below shows the temperatures from the previous year during the time that Dominick will take his vacation: box plot labeled Orlando with min at 64.5, Q1 at 65.5, median at 67.5, Q3 at 71.5, max at 72.5. Box plot labeled Tampa Bay with min at 60, Q1 at 63.5, median at 66.25, Q3 at 72.5, max at 74 Which city should Dominick visit, and why? He should visit Orlando. It has a greater IQR. He should visit Orlando. The median is higher and the range is smaller, so the temperature is higher on average. He should visit Tampa Bay. The highest temperature occurred there. He should visit Tampa Bay. The range is very large, so there is a better chance that any given day will be warm.
Answers
He should visit Orlando. The median is higher and the range is smaller, so the temperature is higher on average. This is the correct answer, as we are only interested in the average temperature in both cities in deciding which to go to. The larger the range (max - min values) or interquartile range (range of central box), the more spread out the temperatures are around the median. As Orlando's range and interquartile range is lower than Tampa Bay's, and its median (middle value in the data set of temperatures) is higher, Dominick would, on average, have more chance of visiting Orlando on a day when it was warmer than Tampa Bay than the other way around.
The correct answer is option b. Dominick should visit Orlando. The median is higher and the range is smaller, so the temperature is higher on average.
Option b is correct because if Orlando has a higher median temperature, this suggests that the middle value of the temperatures in Orlando is higher than in Tampa Bay. Additionally, a smaller range indicates less variability, suggesting more consistent warm temperatures. Therefore, the higher median and smaller range are strong indicators that, on average, the temperatures in Orlando are warmer.
Why other options are incorrect:
Option a is incorrect because the Interquartile Range (IQR) represents the middle 50% of the data. While a greater IQR indicates a larger spread in the middle 50% of the temperatures, it doesn't necessarily mean the average temperature is higher.
Option c is incorrect while Tampa Bay having the highest temperature might indicate that it reached the highest peak temperature, this single data point does not provide enough information about the overall average or consistency of warm temperatures. The highest temperature alone doesn't guarantee that the city is warmer on average.
Option d is incorrect because a larger range indicates a wider spread of temperatures, which could mean more variability. This does not necessarily mean that any given day will be warm; it could also mean that there are very low temperatures included in that range.
The complete question is
Dominick is planning to take a vacation to either Orlando or Tampa Bay. He wants to go to the city that is warmer, on average. The box plot shows the temperatures from the previous year during the time that Dominick will take his vacation:
Which city should Dominick visit, and why?
a. He should visit Orlando. It has a greater IQR.
b. He should visit Orlando. The median is higher and the range is smaller, so the temperature is higher on average.
c. He should visit Tampa Bay. The highest temperature occurred there.
d. He should visit Tampa Bay. The range is very large, so there is a better chance that any given day will be warm.
A rectangular area is to be fenced in with 600 feet of chicken wire. find the maximum area that can be enclosed.
Answers
the area of the area is max when it's a square
the length of the square is 600/4 = 150
so the max area that can be enclosed is:
150×150 = 22500 ft square
The maximum area that can be enclosed is 22500 feet²
A rectangle is a quadrilateral in which opposite sides are equal and parallel to each other.
Let x represent the length and y represent the width. Hence:
perimeter = 2(length + width)
600 = 2(x + y)
300 = x + y
y = 300 - x
The area of a rectangle (A) = length * width
A = x * (300 - x)
A = 300x - x²
The maximum area is at dA/dx = 0, hence:
dA/dx = 300 - 2x
300 - 2x = 0
2x = 300
x = 150 feet
y = 300 - x = 300 - 150 = 150 feet
The maximum area = x * y = 150 * 150 = 22500 feet²
The maximum area that can be enclosed is 22500 feet²
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Write any algebraic expression with at least two operations and the word phrase it represents.
Answers
Word Phrase: 5 times x plus 3 times y divided by 2 equals z
______________________________________________________________
I am 99.9% sure that this is correct, if not, I am truly sorry, and please forgive me. Thank You!
How do I solve this (step-by-step preferred) using common denominators?
Answers
[tex]\bf \textit{and now, if you recall }\textit{difference of squares} \\ \quad \\ (a-b)(a+b) = a^2-b^2\qquad \qquad a^2-b^2 = (a-b)(a+b)\\\\ -------------------------------\\\\ \textit{then we can combine }(x+1)(x-1)\implies x^2-1 \\\\\\ \cfrac{x^4+2x^3-x^2-2}{x(x+1)(x-1)}\implies \cfrac{x^4+2x^3-x^2-2}{x(x^2-1)}\implies \cfrac{x^4+2x^3-x^2-2}{x^3-x}[/tex]
Find the area of each regular polygon. Round your answer to the nearest tenth. Show your work.
a. Octagon with side lengths 5in.
b. Hexagon with radius 5in
Answers
a) approx. 120.71 in^2
b) approx. 86.603 in^2 (if 5 = INRADIUS)
approx. 64.952 in^2 (if 5 = CIRCUMRADIUS)
Plenty of sources and calculators online
A mathematics journal has accepted 14 articles for publication. However, due to budgetary restraints only 9 articles can be published this month. How many ways can the journal editor assemble 9 of the 14 articles for publication? A. 726,485,760 B. 14 C. 2,002 D. 126
Answers
Answer:
A. 726,485,760
Step-by-step explanation:
A mathematics journal has accepted 14 articles for publication.
However, due to budgetary restraints only 9 articles can be published this month.
As the journals are published one by one (arranged combination), so the order matters in this case.
So permutation should be used in this case, rather than combination.
Hence, the number of ways the journal editor can assemble 9 of the 14 articles for publication is,
[tex]=\ ^{14}\text{P}_9=\dfrac{14!}{(14-9)!}=\dfrac{14!}{6!}=726,485,760[/tex]
Show all work to write the equations of the lines, representing the following conditions, in the form y = mx + b, where m is the slope and b is the y-intercept:
Part A: Passes through (−2, 1) and parallel to 4x − 3y − 7 = 0
Part B: Passes through (−2, 1) and perpendicular to 4x − 3y – 7 = 0
Answers
-3y = -4x + 7
y = 4/3x - 7/3....slope here is 4/3
A. a parallel line will have the same slope
y = mx + b
slope(m) = 4/3
(-2,1)...x = -2 and y = 1
sub and find b, the y int
1 = 4/3(-2) + b
1 = -8/3 + b
1 + 8/3 = b
3/3 + 8/3 = b
11/3 = b
so ur parallel line is : y = 4/3x + 11/3
B. A perpendicular line will have a negative reciprocal slope. To get the negative reciprocal of a number, u flip the number and change the sign. So our perpendicular line will need a slope of -3/4
y = mx + b
slope(m) = -3/4
(-2,1)...x = -2 and y = 1
sub and find b, the y int
1 = -3/4(-2) + b
1 = 3/2 + b
1 - 3/2 = b
2/2 - 3/2 = b
-1/2 = b
so ur perpendicular equation is : y = -3/4x - 1/2
Final answer:
The equation of the line for Part A is y = (4/3)x + 11/3, since it is parallel to the given line with a slope of 4/3. The equation for the line in Part B is y = (-3/4)x - 1/2, as it is perpendicular to the given line and the slope is the negative reciprocal of 4/3.
Explanation:
Writing Equations of Lines
To find the equation of a line in the form y = mx + b, we first need to determine the slope (m) and the y-intercept (b). For Part A, since the line needs to be parallel to 4x - 3y - 7 = 0, the slope of our line must be the same as the slope of this given line. To find the slope of the given line, we can rewrite it in slope-intercept form:
4x - 3y = 7
-3y = -4x + 7
y = (4/3)x - 7/3
The slope is 4/3. Since parallel lines have the same slope, our line's slope is also 4/3. Using the point (-2, 1) it passes through, we can substitute into the equation y = mx + b to find b:
1 = (4/3)(-2) + b
1 = -8/3 + b
b = 1 + 8/3
b = 11/3
Thus, the equation of the line for Part A is y = (4/3)x + 11/3.
For Part B, to find a line perpendicular to the given line, we need the negative reciprocal of its slope. The negative reciprocal of 4/3 is -3/4. We then use the given point (-2, 1) to find the y-intercept:
1 = (-3/4)(-2) + b
1 = 3/2 + b
b = 1 - 3/2
b = -1/2
So, the equation for the line in Part B is y = (-3/4)x - 1/2.
Find the point P along the directed line segment from point A(-8,-3) to point B(6,12) that divides the segment in the ratio 1 to 7
Answers
I think that it is c - P[-3/4, - 1/8]
BMK
Jillian’s begins to solve a linear equation that results in a variable expression set equal to the same variable as expression. Which is the best interpretation of this solution
Answers
the equation has infinite solutions
Answer:
infinity solutions
Step-by-step explanation:
On the evening news, the meteorologist states that there is a 70% chance that it will rain the next morning. Select all the statements that are true.
YOU CAN PICK MORE THAN ONE
A. It is neither unlikely nor likely that it will rain the next day.
B. It is certain that it will rain the next day.
C. It is likely that it will not rain the next day.
D. It is unlikely that it will rain the next day.
E. It is unlikely that it will not rain the next day.
F. It is likely that it will rain the next day.
Answers
Answer:
E. It is unlikely that it will not rain the next day.
F. It is likely that it will rain the next day.
Which function has the range (-infinity,0)u(2,infinity)?
A. y = sex x
B. y = cot (2x) - 1
C. y = cos (x+1)
D. y = csc(x) + 1
Answers
Answer:y=csc(x) -1
Step-by-step explanation:
The correct answer is option D. y = csc(x)+1
To determine which function has the range (-infinity, 0) U (2, infinity), we need to analyze each option:
A. y = sec(x): The range of sec(x) is [tex](-\infty,-1] \cup[1,\infty)[/tex], not matching our target range.B. y = cot(2x) - 1: The range of cot(x) is [tex](-\infty,\infty)[/tex], so cot(2x) also has a range of [tex](-\infty,\infty[/tex]). Shifting it down by 1 unit, the range becomes [tex](-\infty, \infty) - 1 = (-\infty, \infty)[/tex], also not matching.C. y = cos(x + 1): The range of cos(x) is [-1, 1], so cos(x + 1) still has a range of [-1, 1] after translating horizontally, which does not match.D. y = csc(x) + 1: The range of csc(x) is [tex](-\infty,-1]\cup[1,\infty)[/tex]. When we add 1 to it, we get [tex](-\infty,0]\cup[2,\infty)[/tex] - which simplifies to our target range of [tex](-\infty,0]\cup[2,\infty)[/tex].Therefore, the function is y = csc(x) + 1.
I need help answering number 8 please
Answers
One interior angle is 56°
One exterior angle is 103° ⇒ we can work out one interior angle 180°-103° = 77°
The other interior angle is 180° - (56°+77°) = 44°
Find the area under the standard normal curve to the left of z = −2.8 and to the right of z = 2.06
Answers
z₂ = 2.06 correspond to an area of = 0.9750
z₁ ≤ Area ≤ z₂ ↔ z₂ - z₁ = 0.9750 - 0.0026 = 0.9724
Answer Area = 0.9724
The area under the standard normal curve to the left of z = −2.8 and to the right of z = 2.06 is 0.9776.
Given that, z₁ = -2.8 and z₂ = 2.06.
What is normal a distribution?It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.
The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.
The area under the standard normal curve to the left of z = −2.8 and to the right of z = 2.06 will be calculated as follows:
The standard normal table represents the area under the curve.
P(z<-2.8) ∩ P(z>2.06)=P(z<-2.8) + P(z>2.06)------(1)
According to the standard normal table, we have
z = -2.8 correspond to an area of = 0.0026
z = 2.06 correspond to an area of = 0.9750
Substitute these values in equation 1, we have
P(z<-2.8) + P(z>2.06) = 0.9750 + 0.0026 = 0.9776
Therefore, the area under the standard normal curve to the left of z = −2.8 and to the right of z = 2.06 is 0.9776.
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The graph of f(x) = x3 − 7x − 6 is shown. Based on the graph, what are all of the solutions to f(x) = x3 − 7x − 6? x = −6 x = −2, −1 x = −2, −1, 3 x = −6, −2, −1, 3
Answers
x-(f(x)/(dy/dx))
x-(x^3-7x-6)/(3x^2-7)
(2x^3+6)/(3x^2-7), letting x1=0
0, -6/7, -.988, -.9999, -.99999999999, -1
(x^3-7x-6)/(x+1)
x^2 r -x^2-7x-6
-x r -6x-6
-6 r 0
(x+1)(x^2-x-6)=0
(x+1)(x-3)(x+2)=0
x= -2, -1, 3
Answer:
c
Step-by-step explanation:
e2020
HELP! 20 POINTS!!! Graph the system of inequalities on your paper. Please provide only one ordered pair (x, y) that will work for both system of inequalities.
To earn full credit you must prove your answer by substituting the (x, y) order pair into both inequalities. Show all work for each inequality.
y < 4x + 3
y > -3x - 3
Answers
The sides of a rhombus with angle of 60° are 6 inches. find the area of the rhombus. 9√3 in2 18√3 in2 36 in2
Answers
Drop a perpendicular from an obtuse vertex.
That makes a 30 - 60º right triangle, with
hypotenuse 6 and short leg 3. So the long leg,
which is the height of the rhombus, is 3√3 .
Since a rhombus is a parallelogram, its area
is base x height = 6 x 3√3 = 18√3 .
Drop a perpendicular from an obtuse vertex.
That makes a 30 - 60º right triangle, with hypotenuse 6 and short leg 3. So the long leg, which is the height of the rhombus, is 3√3 .
Since a rhombus is a parallelogram, its area is base x height = 6 x 3√3 = 18√3
what is the area of this rhombus?
Answers
(6 1/2 * 12 3/4)/ 2= 41 11/25
area= 41 11/25
****to make things make things easier when solving convert the fractions into decimals****
HELP PLEASE !!! Find the measure of <2
Answers
answer
40 - last choice
Answer:
40
Step-by-step explanation:
At an airport, its costs $7 to park for up to one hour and $5 per hour for each additional hour. Let x represent the number of hours parked. Write a function that models the cost, C(x), of parking x hours, where x is an integer greater than 1.
A: C(x)=5x+12
B: C(x)=5(x+1)+7
C: C(x)=5(x-1)+7
D: C(x)=5x+7
Answers
the answer would be C
because it is taking the total hours ( x) and subtracting 1 ( the first hour that cost $7
and then multiplying x by the $5 per minute and then adding the $7 for the first hour
What reduced fraction corresponds to 92%?
Answers
WILL GIVE A BRAINLIEST IF UR 100% CORRECT PLEASE HELP!!
On which of the following lines does the point (8, 41) lie?
a.
y=5x+1
b.
y=3x-2
c.
y=-x-7
d.
y=4x-5
Answers
41 = 5(8) + 1
41 = 40 + 1
41 = 41
So, A y = 5x + 1 is the answer.
Factor: 100x^2−121
x^2 is x to the second power
Answers
100x² - 121
= (10x +11)(10x-11)
I hope that helps!
4x=(cd)/(yz) solve for z
Answers
If angle SUT is 39, what does that tell us about angle TUV? What arc measure describes arc VTS? How can we make any assertions about these angle and arc measures? b. Which line segments’ length can be calculated based on knowing the radius length? Explain. c. If angle MOP is 49, which other angle measures can we calculate? What arc measures can we calculate? Describe which lesson concepts allow us to make these calculations.
Answers
In a circle, corresponding arc measures are equal to the angle at the center, while any chord, secant, or tangent length can be determined with a known radius. Furthermore, other angles and arcs can be obtained via properties of circles such as vertical angles, linear pairs, or the properties of quadrilaterals inscribed in circles.
Explanation:You've asked about the properties of angles, lines, and arc measures within a circle. For the first part, if angle SUT is 39 degrees, then since angle TUV is a vertical angle to it, angle TUV is also 39 degrees because vertical angles are equal. For the arc measure of VTS, since we know the measure of angle SUT, arc VTS will be 2 times that, or 78 degrees, due to the concept of inscribed angles.
Next, the lengths of any chord, secant, or tangent line segments can be calculated knowing the radius length, as they all relate back to the radius in some way. This knowledge comes from our study of circles.
For the third part, if angle MOP is 49 degrees, we can find other angle and arc measures because of the properties of circles. Other angle measures can be found using concepts like vertical angles, linear pairs, or the properties of quadrilaterals inscribed in circles, while arc lengths can be determined by the concept of inscribed angles or central angles. Understanding these concepts allows us to make calculated assertions on angles and arcs within circles.
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