The graph of a function is shown below. Use the graph of the function to find its average rate of change from x=-4 to x=2
Based on the interval, the average rate of change of the function is 4.0
How to estimate the average rate of change of the function f?The graph that completes the question is added as an attachment
From the graph, we can see that the equation of the graph is a quadratic equation
Also, from the question:
We have the interval to be:
The interval is given as
x = -4 to x = 2
This can be represented as
(a, b) = (-4, 2)
From the attached graph, we have
f(-4) = 22
f(2) = -2
The estimate of the average rate of change f is calculated as(to one decimal place)
Rate = [f(b) - f(a)]/[b - a]
Substitute the known values in the above equation
This gives
Rate = [f(2) - f(-4)]/[2 + 4]
Substitute the known values in the above equation
So, we have
Rate = [-2 - 22]/[2 + 4]
Evaluate
Rate = -4.0
Hence, the estimate (to one decimal place) of the average rate of change of the graph is 4.0
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simplify 5x -6y - x + 3y
Step-by-step explanation:
collect like terms
[tex]5x - x - 6y + 3y \\ 4x - 3y [/tex]
For the right triangle below, find the measure of the angle. Please show your answer to one decimal place.
6
13
The measure of the angle is 1.0 when rounded to one decimal places.
What is right triangle ?If one of the triangle's angles is 90 degrees, the triangle is said to have right angles. The triangle with a right angle is known as a right triangle because a right angle is 90 degrees. Using the Pythagorean rule, it is simple to understand how the different sides of this triangle relate to one another. The greatest side of a right angle is known as the hypotenuse, and it is opposite the right angle. In addition, the right triangles are categorized as isosceles right triangles and scalene right triangles based on the other angle values. Pythagorean triples are another name for the right triangle's side lengths, which include 3, 4, and 5.
Given that : right triangle, we're provided the hypotenuse and the leg next to. We can use the cosine ratio to determine :
Cosθ =[tex]\frac{adjacent}{hypotenuse}[/tex]
Plug in the given information
Cosθ =[tex]\frac{4}{7}[/tex]
Use the inverse cosine ratio
θ = [tex]cos^{-1} \frac{4}{7}[/tex]
Plug this into your calculator (and ensure you're solving for radians instead of degrees in the settings)
θ =0.9626
Therefore, θ = 1.0 when rounded to one decimal places.
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This is a file of basic probability, as I start to study this subject I realize that I have forgotten all the basic knowledge, can someone please show me how to do questions (b) and (c)
The probability that a ball is not red is 3/5 and the probability that the ball is red or white is 2/3 .
Mathematical descriptions of the likelihood that an event will happen or that a proposition is true are dealt with in the discipline of mathematics known as probability.
The probability of an event is a number between 0 and 1, where 1 denotes a certainty and 0 denotes an impossibility of the event.Simply put, probability is the likelihood that something will occur. We may discuss the chances of various outcomes when we are unsure of how an event will turn out.Statistics is the study of events subject to probability.In the given question there are 6 red balls, 4 white balls, and 5 blue
balls.
Total number of balls = 6+4+5 = 15 balls (sample space)
Red balls = 6
Not red balls = 15 - 6 = 9
Probability that the ball is red = 9/15 = 3 /5
Red and white balls = 6 + 4 =10
Probability that the ball is red or white = 10 / 15 = 2 / 3
Hence the probability that a ball is red or white is 2 / 3.
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Disclaimer : The complete question is :
A ball is drawn at random from a box containing 6 red balls, 4 white balls, and 5 blue balls. Determine the probability that it is
(a) not red
(b) red or white
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Change 4x + 7y= 14 to slope intercept form
(y=mx+b)
The length of a rectangle is four times its width.
If the area of the rectangle is 144 cm^2 , find its perimeter.
Answer:
Let width of rectangle be x cm.
Width = x cm
Length = 4x cm
Area of rectangle = length x width
4x × x = 144
4x² = 144
x² = 144 ÷ 4 = 36
x = √36 = 6
Width = 6 cm
Length = 6 × 4 = 24cm
Perimeter = 6 + 24 + 6 + 24 = 60 cm
A random sample of individuals at an airport were asked, "Is your flight on time or delayed?" Below are the results of the survey in a joint relative frequency table.
On Time Delayed Total
Domestic 94 418
International 73
Total 145
Part A: Draw and complete the frequency table. (3 points)
Part B: What is the smallest joint frequency, and what does it represent in the context? (3 points)
Part C: Does the data show an association between the flight being on time and flying domestic? If so, is it positive or negative? Justify your answer mathematically. (4 points)
For the frequency table for a random sample answer of the following are given below:
A. Complete frequency table:
On Time Delayed Total
Domestic 324 94 418
International 73 51 124
Total 397 145 542
B. Smallest joint frequency is 51. It represent international flight has lowest number of delays.
C. Domestic flight has highest number of on time flight. It is positive.
As given,
From the random sample of the survey of joint relative frequency table.
On Time Delayed Total
Domestic ? 94 418
International 73 ? ?
Total ? 145 ?
A. Domestic on time = 418 -94
=324
International delayed =145 -94
=51
On time total =324 + 73
=397
International total =73+ 51
=124
Total = 418 + 124
=542
=397 +145
B. Smallest joint frequency is 51. It represent international flight has lowest number of delays.
C. Domestic flight has highest number of on time flight. It is positive as on time flights are more than the delayed.
Therefore, For the frequency table for a random sample answer of the following are given below:
A. Complete frequency table:
On Time Delayed Total
Domestic 324 94 418
International 73 51 124
Total 397 145 542
B. Smallest joint frequency is 51. It represent international flight has lowest number of delays.
C. Domestic flight has highest number of on time flight. It is positive.
The complete question is:
A random sample of individuals at an airport were asked, "Is your flight on time or delayed?" Below are the results of the survey in a joint relative frequency table.
On Time Delayed Total
Domestic ? 94 418
International 73 ? ?
Total ? 145 ?
Part A: Draw and complete the frequency table. (3 points)
Part B: What is the smallest joint frequency, and what does it represent in the context? (3 points)
Part C: Does the data show an association between the flight being on time and flying domestic? If so, is it positive or negative? Justify your answer mathematically. (4 points)
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Answer:
Step-by-step explanation:
Be sure to contact your instructor if you have questions. :)
4) Jim and Edna are planting a rectangular garden with 6 rows of equal numbers of pepper
plants. Each row will be 60 feet long. They set the plants 3 feet apart and start planting at one
corner of the garden. How many plants will they need?
Answer:
120
Step-by-step explanation:
They need six rows with an equal amount of peppers on each row, luckily, everything we need to solve is problem is right in front of us.
First we divide the amounts below
How long the rows will be / How far apart the peppers will be spread.
As we can see that gives us 60 / 3, which should be 20.
Now that we’ve completed this portion we can move on.
Multiply your answer from the division, by how many rows there are.
Our answer from the division was 20, and as we can see there are six rows.
20 x 6 = 120.
Which should give you your answer!
What is [tex]lim_{x-0} (f(f(x))[/tex] closest to?
a. DNE
b. 1
c. 3
d. 5
Answer:
c. 3
Step-by-step explanation:
You want to know the limit of the composite function f(f(x)) as x approaches zero.
LimitThe function f(x) can be evaluated at x=0. The graph shows the value to be ...
f(0) = 2
The function f(x) can also be evaluated at x=2. The graph shows the value to be ...
f(2) ≈ 3
The nearest value to f(f(0)) is 3.
__
Additional comment
For a continuous function, the limit at a point is simply the value at that point. F(x) is continuous in the neighborhoods of the points of interest, so we simply need to find the function value.
Marie is choosing a bag of apples to make into a pie. She thinks the pie will be tastier if it has more apples. The bag of green apples weighs 4.75, point, 75 pounds. The bag of red apples weighs 4.54, point, 5 pounds.
Which bag of apples should she buy?
red apples or green?
(from khan academy)
Marie should buy the bag with green apples as it has more weight hence it will have more apples eventually making her pie tastier
Comparison: When we compare, we look for similarities among the characteristics of other items or objects. Mathematicians use the concept of comparing and ranking numbers to identify the smaller and larger numbers and to determine whether they should be arranged in ascending or descending order.
Weight of bag with green apples = 4.75 pounds
Weight of bag with red apples = 4.54 pounds
Since the bag with green apples weighs heavier and contains more apples overall, Marie should purchase it because it will make her pie taste better.
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If you divided a positive number by a negative number and then divided the result by another negative number, what would the sign of the final result be? Explain your reasoning.
Answer: Positive
Step-by-step explanation:
If a positive number is divided ( or multiplied ) by a negative number it is always a negative number. If you divide ( or multiplied) two negative numbers its always a positive so,
+/- = -
- / - = +
Suppose the current cost of gasoline is $3.10 per gallon. Find the current price index number, using the 1975 price of 56.7 cents as the reference value.
The current price index is _____
(Round to one decimal place as needed.)
The current price index is mathematically given as,$538.194
What is the current price index?By increasing the ratio of the current value to the reference value by 100, one can determine the index value.
Given that the current cost of gasoline is $3.10 per gallon. we need to find the current price index number, using the 1975 price of 56.7 cents as the reference value.
In regard to this issue, we have that:
Current value = $3.10
Reference value: $0.576
Typically, the mathematical formula for the Index price is,
I = (3.10/0.576) x 100
I= $538.194
The current price index number is 538.194
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What is 7 x 10 ^-4 in standard notation?
Answer: 0.007
Step-by-step explanation: 70 x 10^-4= 0.0001
70 x 0.0001
7 x 0.001
0.007
Hope this helps!
The standard notation of 7 x [tex]10^{-4}[/tex] is 0.0007.
The given expression is;
7 x [tex]10^{-4}[/tex]
To write 7 x [tex]10^{-4}[/tex] in standard notation,
When multiplying an integer by a power of ten, the decimal point is moved to the right or left by the number of zeroes in the exponent.
So, for7 x [tex]10^{-4}[/tex],
Move the decimal point 4 places to the left.
Starting with 7, Move the decimal point 1 place to the left to get 0.7.
Move it another 3 places to the left to get 0.0007.
Therefore,
7 x [tex]10^{-4}[/tex] in standard notation is 0.0007.
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CONFUSED ON THIS PLEASE HELP!! QUESTION DOWN BELOW!
many thanks!!!
Answer:
(a) ∠e +∠d = 180° is false
Step-by-step explanation:
You want to know which angle expression is not true.
Angle SolutionWe can figure the measures of all of the unknown angles, then check the given expressions.
Angles 'a' and 130° are corresponding angles, so congruent:
a = 130°
Angles 'a' and 'e' are vertical angles, so congruent:
e = a = 130°
Angle 'd' and 62° are vertical angles, so congruent:
d = 62°
Angles 'b' and 'd' are corresponding angles, so congruent:
b = d = 62°
Angles 'f' and 62° are corresponding angles, so congruent:
f = 62°
Angles 'c' and 130° are a linear pair, so supplementary:
c + 130° = 180°
c = 50° . . . . . . subtract 130°
Statement check(a) ∠e +∠d = 180° ⇒ 130° +62° = 180° . . . . false
(b) ∠d +∠b = 124° ⇒ 62° +62° = 124° . . . . true
(c) ∠a +∠c = 180° ⇒ 130° +50° = 180° . . . . true
(d) ∠ 180° -∠f = 118° ⇒ 180° -62° = 118° . . . . true
I am very confused on how to get i, how do you do this problem?
given polynomial is,
[tex](x-2)(x^2-12x+40)=0_{}[/tex]let us find thefactors of the polynomial,
[tex]\begin{gathered} x-2=0 \\ x=2 \\ \\ \end{gathered}[/tex]for the polynomial,
[tex]x^2-12x+40=0[/tex]use the formula to find the factors,
[tex]\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where,
[tex]\begin{gathered} a=1 \\ b=-12 \\ c=40 \end{gathered}[/tex]thus,
[tex]\begin{gathered} =\frac{-\mleft(-12\mright)\pm\sqrt[]{(-12)^2-4\times1\times40}}{2\times1} \\ =\frac{12\pm\sqrt[]{144-160}}{2} \\ =\frac{12\pm\sqrt[]{-16}}{2} \\ =\frac{12\pm\sqrt[]{2\times8}}{2} \\ =\frac{12\pm4i}{2} \\ =\frac{2(6\pm2i)}{2} \\ =6\pm2i \end{gathered}[/tex]thus,
[tex]\begin{gathered} x=6+2i \\ x=6-2i \end{gathered}[/tex]the factors are,
[tex]\begin{gathered} x=2 \\ x=6+2i \\ x=6-2i \end{gathered}[/tex]Finding the coordinate that yields a given slope
The points (6, 4) and (r, -11) lie on a line with slope -5. Find the missing coordinate r.
Answer:
Step-by-step explanation:
Help.
A. 6.5
B. 18
C. 36
D. 6
Answer: The answer is D: 6
(CO 5) A company claims that its heaters last more than 5 years. Write the null andalternative hypotheses and note which is the claim.O H: = 5, H: 4 < 5 (claim)wO Hou = 5 (claim), H: 25O Hou = 5, H.: > 5 (claim)O Hou > 5 (claim), H: 35
Given:
The company claims that its heaters last more than 5 years.
Find: null alternative hypotheses.
Sol:
[tex]H_0:\mu=5,H_a|:\mu>5\text{ \lparen claim\rparen}[/tex]what is the percent chance from 450 To 1188
Answer:
738
Step-by-step explanation:
1188 - 450 = 738
pls help i dont get it
Create an In-Out table with your findings. Make a table with the number of bagels she has when she gets home as the In and the number she had to start with as the Out.
How does the solution to Marcella’s Bagels depend on the number of bagels she has when she gets home?Try several numbers for the number she has when she arrives home to explore this expansion, such as 3, 4, 5, or even 0. You should presume that, other from this number, everything in the problem is the same as it was in the original problem.
Create an In-Out table with your findings. Make a table with the number of bagels she has when she gets home as the In and the number she had to start with as the Out. Once you've added numerous entries to the table, search for a connection between the Out and the In before attempting to identify a rule that can explain this connection.
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A phone keeps track of the number of steps taken and the distance traveled. based on the information in the table, is there a proportional relationship between the two qualities?
there is no proportional relationship between the two qualities
Explanation:For two quantities to be proportional, it must follow the formula:
y = kx
where k = proiportionality constant
k = y/x
if y = 950, x = 1
inserting in the equation:
950= 1k
k = 950
The equation becomes: y = 950 × x
We check for other values. if k is the same, it is proportional
when y = 2852, x = 3
2852 = k × 3
k = 2852/3 = 950.67
when y = 5.1, x = 4845
4845 = k × 5.1
k = 4845/5.1 = 950
From the above, the value of k which is different is for the 2nd value.
Since they are not all the same, we say there is no proportional relationship between the two qualities
A number is divided by 3, and then 4 is added to the quotient. The result is 8. Find the number
Answer: 4/3 or 1.33
Step-by-step explanation:
pls help i dont get it this is due today
Answer:
Part a: x + 17 = 52 Part b: He should guess the number 35.
Step-by-step explanation:
In the equation, x stands for the number he has to guess. He is given the clue, "17 more than the number is 52." Therefore x + 17 = 52. Another equation you could use is 52 - 17 = x. This equation would be used to solve the problem. 52 - 17 = 35
What is an equation of a line that passes through the given point and is perpendicular to the given line. (-2, 5) and x = 3
The equation of the line passing from found as y = 5.
What is referred as the slope of line?The slope of the line is a measurement of its steepness and direction. A line's slope is classified as the change in y coordinate with regard to the shift in x coordinate. The net y coordinate change is Δy, whereas the net x coordinate change is Δx. So the transformation in y coordinate in relationship to the shift in x coordinate is written as m.The formula for finding the slope is;
m = Δy/Δx
Where, m is the slope
The given equation of line is;
x = 3 comparing it with standard form of equation;
y = mx + c
As, the equation is a straight line passing parallel to x axis, the slop of line x = 3 is ∞.
Thus, m₁ = ∞.
Now, let the slops of the line passing from (-2, 5) is m₂,
The, as both line are perpendicular.
Thus,
m₁ x m₂ = -1
m₂ = -1/∞
m₂ = 0
The equation of line is found by
y - y₁ = m₂(x - x₁)
Put the values;
y - 5 = 0(x + 2)
y = 5
Therefore,the equation of the line passing from found as y = 5.
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y=x+6
how do i graph this?
Answer:
y=mx+b, where x and y are variables, m is the slope, and b is the y-int
Since there is no m value, it is 1/1 or simply 1. Therefore you rise 1 point for every 1 you move right.
Your graph needs to intercept the y-axis at point (0,6).
The easiest way to graph this equation is to plot a point at (0,6) and then start your slope of 1/1.
I have attached an image of the graph.
Hope that helps.
This is an assignment may someone help me but not give me the answers just explain the steps I need to take
See explanation below
Explanation:
From the question, we are told line TV is perpendicular to line US.
This means the point which they intersect has an angle of 90°.
We are also told line TV bisects STU.
For a line to bisect an angle, it means it divided the angle into two equal parts.
When line TV bisects STU, it divided it into angle STR and angle UTR
Hence, ∠STR = ∠UTR
Also line SU and line and line VT intersect to give vertical angles.
Angle R and the angle opposite it are vertical angles.
Vertical angles are equal.
The angle with 90° and the angle opposite it is also a vertical angle.
you can see from the illustration. The two angles opposite each other are equal to 90°.
Since angle on a straight line = 180°
angle R + 90° = 180°
angle R = 180-90
angle R = 90°
All the 4 angles that result from the intersection line VT and line SU are equal to 90°
if explain this question to me give those crown thingy points
it two pages
please help 20points
Answer:
1.) 12 yards (the one you selected is correct)
2.) 1.1 with the bar over the decimal (the one you selected is correct)
Step-by-step explanation:
1.) It looks like Aaron dropped back 5 yards from the line of scrimmage and threw to the 7 yard line for a total of 12 yards.
2.) If you enter 10 divided by 9 into your calculator you will get back 1.11111111111111 that keeps repeating for how ever many digits your calculator can show. We write this as 1.1 with the bar over the decimal.
Which of the following expression gives a fine in dollars for a book that is n days overdue
The rate is given by
[tex]\text{ \$0.10 per day}[/tex]and since the one-time charge is $0.25, the expression is
[tex]0.25+0.10n[/tex]where n denotes the number of days. Then, the answer is the second option
If we wanted to analyze the variables GNP (Gross National Product) and Region at the same time, what would be appropriate to use?
If we wanted to analyze the variables GNP (Gross National Product) and Region at the same time, bargraph, pie chart, one way table would be appropriate to use.
What exactly do you mean by Gross National products?Gross national product (GNP), calculated without taking into account the depreciation or consumption of capital utilized in the manufacturing process, is the total market value of the final goods and services generated by a country's economy during a given time period (often a year).
What distinguishes the GDP from the GNP?The value of the final domestic goods and services generated inside a country's boundaries is known as the gross domestic product (GDP).
The value of all the finished goods and services that are owned by a nation's citizens, regardless of whether those kinds of goods were made in that nation, is what is known as its gross national product (GNP).
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Question: 7 divided by 4 5/11
The answer to your question is =
1.57142857