A table of values, rounded to the nearest hundredth, for the function y = is given for
0≤x≤8.
What is the average rate of change of the function over the interval [2, 7] to the nearest
hundredth?
Answers
Answer:
A) [tex]0.13[/tex]
Step-by-step explanation:
If a function [tex]f(x)[/tex] is continuous over the interval [tex][a,b][/tex], then the average rate of change over that interval is [tex]\displaystyle \frac{f(b)-f(a)}{b-a}[/tex]:
[tex]\displaystyle \frac{f(b)-f(a)}{b-a}\\\\\frac{f(7)-f(2)}{7-2}\\ \\\frac{1.91-1.26}{5}\\ \\\frac{0.65}{5}\\ \\0.13[/tex]
Thus, the average rate of change over the interval [tex][2,7][/tex] to the nearest hundredth is [tex]0.13[/tex].
Related Questions
What is the domain of the function shown in the graph?
Answers
Answer:
the answer is b you have it right
Step-by-step explanation:
your welcome
NEED TO PASS HELP WILL GIVE BRAINLY!!!
Answers
Answer:
[tex]\bigodot[/tex] None of the other answers are correct.
Step-by-step explanation:
[tex]2b^2-3b+85=-5[/tex] (Given)[tex]\implies 2b^2-3b+85+5=0[/tex][tex]\implies 2b^2-3b+90=0[/tex]Comparing it with the general form of quadratic equation [tex]ax^2+bx+c=0,[/tex] we find:a = 2, b = -3, c = 90Next, we find the value of the discriminant [tex] b^2-4ac[/tex][tex] b^2-4ac= (-3)^2-4(2)(90)=9-720=-711<0[/tex][tex] \because b^2-4ac<0[/tex], which means the roots of the given quadratic equation are non-real or imaginary.Thus, last option is the correct answer.I need help I don’t know the answer
Answers
Answer:
Option 2
Step-by-step explanation:
Height of lemon tree = 8
Height of date tree = 8 x 3
On comparing, we understand that the date tree is 3 times as tall as the lemon tree.
Answer:
the answer is B or the second one
Step-by-step explanation:
8 x 3 = 24
the data tree is 3 times as tall as the lemon tree
The rectangular room shown 20 feet long, 48 feet wide, and 10 feet tall. Use the Pythagorean Theorem to find the distance from A to C and the distance from A to B. Round to the nearest tenth, if necessary.
(Only really need A to B though)
Answers
Using Pythagorean theory
10^2 + 52^2 = c^2 (hypotenuse)
2704 = c^2
52 = c (A to B)
Amber is solving the inequality |x+6| - 12 < 13 by graphing. Which equations should Amber graph?
Answers
Answer:
y₁ = |x+6| ; y₂ = 25
Step-by-step explanation:
|x+6| - 12 < 13
⇔ |x+6| < 25
Equation for the given inequality is equals to [tex]y_{1} =| x+ 6| , y_{2} =25[/tex]
What is inequality?" Inequality is defined as the algebraic expression which represents the relation between two variables using sign of inequality."
According to the question,
Given inequality,
|x+6| - 12 < 13
Add both the side of the inequality 12 we get ,
|x+6| - 12+12< 13 + 12
⇒ |x+6| < 25
As represent in the graph equation for the given inequality are,
[tex]y_{1} =| x+ 6| , y_{2} =25[/tex]
Hence, equation for the given inequality is equals to [tex]y_{1} =| x+ 6| , y_{2} =25[/tex].
Learn more about inequality here
https://brainly.com/question/20383699
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what is the surface area of a rectangular prism that has a length of 5 cm, a height of 14 cm, and a width of 12 cm? a. 298 cm2 b. 378 cm2 c. 616 cm2 d. 596 cm2
Answers
Answer:
sorry for being late but the answer is c 616 cm
Step-by-step explanation:
Write a cosine function that has a midline of 3, an amplitude of 4 and a period
of pi.
Answers
Answer:
[tex]f(x)=4\cos(2x)+3[/tex]
Step-by-step explanation:
Using the general equation [tex]f(x)=a\cos(bx+c)+d[/tex], we already know that [tex]a=4[/tex] and [tex]d=3[/tex], but we need to find [tex]b[/tex] from the period:
[tex]\frac{2\pi}{|b|}=\pi\\ 2\pi=b\pi\\2=b[/tex]
Hence, the cosine function is [tex]f(x)=4\cos(2x)+3[/tex]
please can someone do this for me? thanks alot x
Answers
Answer:
Learning Objective: Use the mean and range to compare the spread and averages.
a) Sarah Mean = 70.9, Katie Mean = 78.9
b) Sarah Range = 15, Katie Range = 25
c) Sentences
- The mean shows, on average, Sarah was 8 seconds quicker than Katie.
- The range shows that Sarah was more consistent with her times. Katie had a larger spread of times which shows she was less consistent.
Step-by-step explanation:
Given:
Sarah's Data Set:
79, 70, 68, 75, 69, 64, 69, 75, 64, 76Katie's Data Set:
79, 79, 76, 81, 89, 76, 64, 85, 82, 78To Find:
The mean and range of both data sets separately.Work:
The mean of a data set is commonly known as the average. You find the mean by taking the sum of all the data values and dividing that sum by the total number of data values. The formula for the mean of a population is [tex]\mu = \frac{{\sum}x}{N}[/tex].
The formula for the mean of a sample is [tex]\bar{x} = \frac{{\sum}x}{n}[/tex].
Both of these formulas use the same mathematical process: find the sum of the data values and divide by the total. For the data values given above, the solution is: [tex]\frac{709}{10} = 70.9[/tex]
Therefore, the mean of Sarah's data set is 70.9.
For Katie's Data Set, [tex]\frac{789}{10} = 78.9[/tex].
Therefore, the mean of Katie's data set is 78.9.
To fill in the summary, we have to use the data we just calculated.
That summary can be found in the answer section.
Answer:
Sarah's mean = 70.9
Katie's mean = 78.9
Sarah's range = 15
Katie's range = 25
The mean shows that on average Sarah was 8 seconds faster than Katie. The range shows that Sarah was more consistent with her times. Katie had a larger spread of times which shows she was less consistent.
Step-by-step explanation:
Identifying the mean time for Katie and Sarah
The mean ( average ) is equal to the sum of the numbers in the data set ( the sum of the swimming times ) divided by the number of values in the data set ( which is given as 10 )
Mean for Sarah : Sum of her swimming times : 79 + 70 + 68 + 75 + 69 + 64 + 69 + 75 + 64 + 76 = 709
Number of values = 10
So mean = 709 / 10 = 70.9 seconds.
Mean for Katie : Sum of her swimming times : 79 + 79 + 76 + 81 + 89 + 76 + 64 + 85 + 82 + 78 = 789
number of values = 10
so mean = 789 / 10 = 78.9
Using this information we can identify what the first to blanks are. The mean shows that on average Sarah was ___ seconds ____ than Katie.
The mean time for Sarah was 70.9 seconds and the mean time for Katie was 78.9 seconds. So on average Sarah was faster and by 8 seconds ( which can be found by subtracting Sarah's mean from Katie's )
Identifying the range
The range is equal to the largest value ( longest swim time ) subtracted by the smallest value ( or quickest swim time )
Range for Sarah : Sarah's highest swim time is 79 seconds and her lowest is 64 seconds.
So her range = 79 - 64 = 15 seconds
Range for Katie : Katie's highest swim time is 89 seconds and her lowest time is 64 seconds
So her range = 89 - 64 = 25
Using this information we can fill out the remaining blanks.
The range shows that ____ was more consistent with her times. ___ had a larger spread of times which shows she was ____ consistent.
The higher the range the less consistent you are vise versa. Katie had a larger range hence, Sarah was more consistent and Katie was less consistent.
The description for a certain brand of house paint claims a coverage of 410 ft2/gal. How many liters of paint are required to apply a single coat of paint to the (4) walls of a 7.7 m by 14.8 m room with a height of 2.4 m
Answers
Answer:
10.7 liters of paint requiredStep-by-step explanation:
Dimensions of the room
7.7 m by 14.8 m with the height of 2.4 mFind the surface area of the 4 walls
A = Ph = 2(l + w)h = 2(7.7 + 14.8)*2.4 = 108 m²Convert the area to ft²
108 m² = 108*10.7639 ft² = 1162.5012 ft²Find the amount of paint required
1162.5012/410 = 2.84 gal (rounded)Covert the volume to liters
2.84 gal = 2.84*3.76 l = 10.7 l (rounded)What is the slope of the line that passes through the points (-8, 6) and (-8, 2)?
Write your answer in simplest form.
Answers
Answer: Undefined or Vertical Slope.
AABC and AXYZ are similar. Find the missing side length.
Y
21
AA
3
6
4
Z
C X
28
(The triangles are not drawn to scale.)
Answers
Answer:
42
Step-by-step explanation:
it is stated that the triangle are similar so their side lengths must be proportional, we can use this to find the missing side length
AB/XY = BC/YZ write this with the side lengths
3/21 = 6/? cross multiply expressions
3? = 126 divide both sides by 3
? = 42
Evaluate the following expression. You should do this problem without a calculator. log 5 125
Answers
Answer:
3
Step-by-step explanation:
log(5) 125 =x
5^x = 125
5^x = 5^3
x=3
#76 will give brainliest! please help
Answers
Answer:
2nd option, (6x + 8)(x - 1) = 0
Step-by-step explanation:
Answer:
[tex](6x+8)(x-1)[/tex]
Step-by-step explanation:
We can separate the 2x into -6x + 8x. Then this will give us [tex]6x^2 - 6x + 8x - 8 = 0[/tex]. Now we can factor out a 6x and an 8 to give us [tex]6x(x-1) + 8(x-1) = (6x+8)(x-1)[/tex] by the distributive property.
Hope this helps! :)
10 units
What is the approximate area of the circle?
Answers
Because pi r ^2
Hi, I need help with arithmetic sequence and I don't really know what to do.
Answers
Answer:
Step-by-step explanation:
Answer:
choice 2
Step-by-step explanation:
Arithmetic sequences arare linear. The common difference is the slope. The points given are (3,10) And (5,26).
The slope is the change of y (26-10=16) over the change of x (5-3=2); this is 16/2=8.
The equation of line in slope-intercept form whose slope is given as 8 is y=8x+b.
We may plug in a point to solve for b.
Let's plug in (3,10):
10=8(3)+b
10=24+b
10-24=b
-14=b
So the equation we are lookinlooking for is y=8x-14 which is choice 2.
which expression has a value of 2/3?
(8+24) (12 × 4)
824 12 x 4
8+ (2412) × 4
8+24 (12 x 4)
Answers
Answer:
(8 + 24) ÷ (12 x 4) = 2/3
Step-by-step explanation:
To Find: an expression that has a value of 2/3
Solution :
A. [8 + (24 ÷ 12)] x 4
= [8 + (2)] x 4
= 10 x 4
= 40
B. (8 + 24) ÷ (12 x 4)
= 32 ÷ 48
= 2 ÷ 3
= 2/3
C. 8 + (24 ÷ 12) x 4
= 8 + 2 x 4
= 8 + 8
= 16
D. 8 + 24 ÷ 12 x 4
8 + 2 x 4
= 8 + 8
= 16
The correct option is :
(8 + 24) ÷ (12 x 4) = 2/3
A ramp rises 3.5 feet & has an angle of elevation
of 24 degrees. How long is the ramp?
Answers
Check the picture below.
Make sure your calculator is in Degree mode.
A baseball team is hosting a dance as a fundraiser. the cost of 1 individual ticket is $7. the cost of 1 group ticket is $16. the baseball team sold 36 more individual tickets than group tickets. the fundraiser raised $574 as a result of all ticket sales. if x is the number of the individual tickets that were sold and y is the number of group tickets that were sold, how many individual tickets were sold (what is the value of x)?
Answers
To form equations from word problems, we can do the following:
Identify variablesFind key informationIdentify word equations and translate into numerical equationsSolveSolving the QuestionWe're given:
Let x be the number of individual tickets that were soldLet y be the number of group tickets soldCost of 1x = 7 dollarsCost of 1y = 16 dollarsBaseball team: 36 more x than y⇒ x = 36 + yFundraiser raised 574 dollars in total
⇒ 7x + 16y = 574 dollars
Question: How many individual tickets were sold? (What is the value of x?)
Here are all the equations we have created:
x = 36 + y7x + 16y = 574We can solve for the value of x using systems of equations.
First, isolate y in the first equation:
[tex]x = 36 + y\\y=x-36[/tex]
Now, plug this into the second equation:
[tex]7x + 16y = 574\\7x + 16(x-36)= 574\\7x+ 16x-586= 574\\23x=1150\\\\x=\dfrac{1150}{23}\\\\x=50[/tex]
Therefore, x is equal to 50.
Answer50 individual tickets were sold.
Move a phrase and number to the blanks to complete the sentence.
Answers
2nd blank- 75 min
Answer:
The sophomore in her school is 75
Step-by-step explanation:
Solution
The plot shows the distribution of 30 sophomores
We can see that there are 3 main vertical
line in red pen in the picture above.( distribution)
The first line means Minimum
The third line means the maximum
The second line means the medium
So the Medium is 75. And 30 sophomores in her
School took the survey.
So the medium belongs to them
length of a rectangular garden is 9m and breadth is 6m calculate it's area in mm2
Answers
Given
Length =9 m
Breadth =6 m
Area of the rectangle= (length × breadth) sq. units
=(9×6) m
2
=54 m
2
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Determine the interquartile range for the following data 1,15,16,16,19,24,25
Answers
Answer:
IQR = 9
Step-by-step explanation:
Q3 = 24
Q1 = 15
24-15=9
Give brainliest, please!
Hope this helps :)
Describe the transformations necessary to transform the graph of f(x) into that of g(x).
Answers
Using translation concepts, it is found that the necessary transformations are given as follows:
Reflection over the y-axis. Horizontal stretch by a factor of 2.Shift left 3 units.Reflection over the x-axis.Shift down 1 unit.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The original function f(x) is given by:
[tex]f(x) = \sqrt{x}[/tex]
The transformations are as follows:
For the values of x, the function was multiplied by -1/2 and then 3 was added. Thus it was reflected over the y-axis, horizontally stretched by a factor of 2 and shifted left 3 units.Outside the domain, in the values of y, the function was multiplied by -1 and then subtracted by 1, hence it was reflected over the x-axis and shifted down one unit.More can be learned about translation concepts at https://brainly.com/question/4521517
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A system of equations is graphed on the coordinate plane.
y = 1/2+2
y = x + 1
What is the solution to the system of equations?
Answers
Answer:
y=2.5, x=1.5
Step-by-step explanation:
y=1/2+2 ---(1)
y=x+1 ---(2)
y=1/2+2=2.5
Substitute y=2.5 into equation (2)
y=x+1
2.5=x+1
2.5-1=x
x=1.5
5 points and brainliest to the best correct answer, questions in photo, thank you
Answers
Answer:
C) 150
Step-by-step explanation:
A decrease of 50% every two days can be predicted with the formula
x * 0.5^t
x being the start amount
t being time
5 days with periods of 2.5 days, 5 / 2.5 = 2
start amount of 600
600 * 0.5^2
600 * 0.25
150 so C
Multiply. 2 5/8⋅(−4 3/4)
A. −12 15/32
B. −8 15/32
C. −7 3/8
D. −2 1/8
Answers
option b
see attachment for solution
hope it helps...!!!
A soup can has a diameter of 8 cm and a height of 12 cm. What is the volume of the soup can? Use 3. 14 for Pi. A cylinder has a height of 12 centimeters and diameter of 8 centimeters. 192. 00 cubic centimeters 301. 44 cubic centimeters 602. 88 cubic centimeters 2,411. 52 cubic centimeters.
Answers
Answer:
The volume of the soup can is 602. 88 cubic centimeters
Step-by-step explanation:
Volume of a cylinder = π {r} ^{2} h
Where π = 3.14
r = diameter ÷ 2
r= 8 ÷ 2
r= 4 cm
h= 12 cm
Volume of the soup can= 3.14 × 4 × 4 × 12
= 602. 88 cubic centimeters
PLEASE ANSWER PLEASEEEEEEEEE
Answers
Answer:
C
Step-by-step explanation:
11 | 2 means 112
A is wrong because 11 | 2 cannot mean 12.
B is wrong because stem with value 1 doesn't exist.
D is wrong because stems and leaves are not added to give real value.
Hope this helps!
In one day, a toy store sold 15 toy cars and 20 yo-yos for a total of $190. the next day, the toy store sold 3 toy cars and 12 yo-yos for a total of $102. what is the cost of one toy car? $1 for one car $2 for one car $4 for one car $8 for one car
Answers
Answer:
$2
Step-by-step explanation:
see photo for solution
#79 will give brainliest please help!
Answers
Step-by-step explanation:
this means the factors of the various terms of x and the constant.
a = 4
b = 1
c = 9
and yes, if there would be negative factors, the signs wold be part of a, b and c too.
overall, this is then used to solve the quadratic equation.
the general solution is
x = (-b ± sqrt(b² - 4ac))/(2a)
students from a class of 15 are going to be chosen to be on the dance committee. Find the number of different 4-person committees that can be made.
Answers
we know that
The formula for combinations is
[tex]C=n!/[(n-r)!*r!][/tex]
where
[tex]n[/tex] is the total number of objects you choose from
[tex]r[/tex] is the number that you choose to arrange
in this problem
[tex]n=15[/tex] students
[tex]r=4[/tex] students
[tex]C=15!/[(15-4)!*4!][/tex] → [tex]C=15!/[11!*4!][/tex] → [tex](15*14*13*12*11!)/(11!*4*3*2*1)[/tex]
[tex]C=(15*14*13*12)/(24)[/tex] → [tex]C=1365[/tex]
the answer is
1,365