Find the average rate of change of each function on the interval specified.
i only need #5 thank you :)
Answers
The average rate of change (AROC) of a function f(x) on an interval [a, b] is equal to the slope of the secant line to the graph of f(x) that passes through (a, f(a)) and (b, f(b)), a.k.a. the difference quotient given by
[tex]f_{\mathrm{AROC}[a,b]} = \dfrac{f(b)-f(a)}{b-a}[/tex]
So for f(x) = x² on [1, 5], the AROC of f is
[tex]f_{\mathrm{AROC}[1,5]} = \dfrac{5^2-1^2}{5-1} = \dfrac{24}4 = \boxed{6}[/tex]
Related Questions
25. Anthropologists use a linear model that relates human femur (thighbone) length to height. The model allows an anthropologist to determine the height of an individual when only a partial skeleton (including the femur) is found. Here we find the model by analyzing the data on femur length and height for the eight males given in the following table.
(c) An anthropologist finds a human femur of length [tex]53 \mathrm{~cm} .[/tex] How tall was the person?
Answers
The height of the person when an anthropologist finds a human femur of length will be 183.94cm.
How to calculate the height?In order to calculate the height, the expression to use will be:
h = 1.876l + 84.512
h = 1.876(53) + 84.512
h = 99.428 + 84.512
h = 183.94
Therefore, the height is 183.94cm.
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The Music Express has $72,000 to spend on the music bundles. If it buys
more pop bundles than rock bundles, how many bundles of each type of
music can The Music Express buy while getting closest to the budget of
$72,000? Explain.
Answers
Answer:
It Depend on how much the pop bundles/ rock bundles cost you need those numbers before you can dertermine the answer.
Step-by-step explanation:
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answers
Answer:
x=19, y=[tex]19\sqrt{3}[/tex]
Step-by-step explanation:
This triangle is a 30-60-90 triangle.
This means the hypotenuse (38) is double the short leg (x)
x=19
Then use the pythagorean theorem
a^2+b^2=c^2
19^2+y^2=38^2
361+y^2=1444
Subtract 361 from both sides
y^2=1083
put it in square roots and simplify
[tex]\sqrt{1083} =19\sqrt{3}[/tex]
y=[tex]19\sqrt{3}[/tex]
To solve this problem:
⇒ need to use a special right triangle theorem:
Let's consider the information given:
⇒ one angle is 30 degrees
⇒ one angle marked with a little square signifies that it is 90
degrees
⇒ (all the angles added up are 180 degrees) so the last angle is
60 degrees
Therefore we have a '30-60-90' triangle which states:
the side opposite the 30-degree angle⇒ half the length of the hypotenuse (longest side of the triangle)
⇒ x = 38/2 = 19
the side adjacent to the 30-degree angle⇒ is the square root of 3 divided by 2 of the hypotenuse
⇒ y = [tex]\frac{\sqrt{3} }{2} *38=19\sqrt{3}[/tex]
Therefore:
x = 19
y = [tex]19\sqrt{3}[/tex]
Hope that helps!
what is the slope of the line that passes through (2,5) and (-3,15)
Answers
Answer:
The slope is -2, or -2/1.
Step-by-step explanation:
[tex]m = \frac{15 - 5}{ - 3 - 2} = \frac{10}{ - 5} = - 2 = - \frac{2}{1} [/tex]
Write the expression represented by the following: 8 less than twice a number
Answers
Answer:
2x<8
Step-by-step explanation:
we don't know the number so let the number be x then 2*x=2x therefore 2x<8
Writing 0.0725 in simplest fraction form gives the result: 29 29 (A) (B) 4000 400 129 (C) 29 40 (D) 400
Answers
Answer:
29/400
Step-by-step explanation:
Converting 0.0725 to a fraction
0.0725725/10000 [Divide by 25]29/400The simplified fraction form of 0.0725 is 29/400.
FractionA fraction is used to indicate a piece of something larger. It depicts the whole's equal pieces. The numerator and denominator are the two elements of a fraction.
How to find the simplest fraction?The given value is 0.0725.
Multiply numerator and denominator by 10000
then 0.0725 = 725/10000
To simplify divide numerator and denominator by 25
then 725/10000 =29/400
Hence the simplify fraction form is 29/400.
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A training field is formed by joining a rectangle and 2 semicircles. The rectangle is 89 m long and 66 m wide. Find the area of the training field. Use the value 3.14 for pie, and do not round your answer. Be sure to include the correct unit in your answer.
Answers
Step 1: break the shape into 2, a rectangle and a circle and first find the area of the rectangle ( l x w or 89 x 66)
Step 2: now that we know that the area of the rectangle is 5874 we find the area of the circle (3.14 x radius^2), the diameter is 66, and the radius is 33 (diameter divided by 2)
Now that we know both the rectangle (5874 meters) and circles (1092.14 meters) we add them and get 6966.14
I hope this helps if I made a mistake pls let me know
What is the value of x? Enter your answer in the box.
Answers
Answer: x = 4
Step-by-step explanation:
this is just easier to show work for so i hope this helps :)
Chapman's Cheese factory packs assorted cheese into 100-slice boxes.
The factory has 150 slices of cheddar, 309 slices of swiss, and 147 slices of
parmesan.
How many boxes of cheese can it make?
Answers
hello,
the answer would be 6 boxes
What might factor into a cost of your house that would not factor into the cost for of rebuilding it?
Answers
Can someone please help
Answers
Answer:
12
Step-by-step explanation:
Volume of a sphere = 4/3 pi r^3 r = 3 for this one
volume = 4/3 pi (3^2) = 36/3 pi = 12 pi units^3
A function, f(x), has a domain of −10≤x≤20 and range −40≤f(x)≤−10.
f(1)=−13
f(−10)=−40
Select each statement that must be false about f(x).
f(5)= - 40
f(0)=0
f(−15)=−20
f(1)=13
f(−9)=88
Answers
Answer:
all of them are false
Step-by-step explanation:
i know
Determine the solution to each of the following single variable equations. A. x-4=1/2(x+3) B -4x=1/2(-8+2) C. 3-2(-3x+1)=6x+1 D. 0.5(x+3)=-3(x-0.5)
Answers
Answer:
A. x = 11
B. x = 3/4 (or 0.75)
C. any value
D. x = 0
Step-by-step explanation:
hope this helps:)
Graph a line with a slope of 4 that contains the point (3, 0)
Answers
[tex]\text{view explanation pls}[/tex]
Calculation ↓The first step is to write the line's equation in point-slope form
y-y1=m(x-x1)
y-0=4(x-3)
use the distributive property
y-0=4x-12
y=4x-12
Now that we have the equation of the line, we need to determine it's graph. how do we actually graph the line?Well, let's start with the y-intercept, which is -12 or (0, -12)
After plotting the point (0, -12) move up 4, over 1, up 4, over 1, up 4, over 1.
Do the same on both sides of the y-intercept.
hope helpful ~
The ages of members of a stamp collecting group are normally distributed with a mean of 56 years and a standard deviation of 3 years there are 82 members in the group about how many members are expected to be between 53 years old and 59 years old
Answers
Answer:
all of them
Step-by-step explanation: Because the age bracket id between 56 and 59.
PLEASE HELP!
which of the following choices is the area if the length is 8x and the width is 3y-2
Answers
Answer:
None of them are correct.
Step-by-step explanation:
The correct one would be 8x - 3y-2
PLEASE I NEED HELP!!!!!
Answers
Answer:
-5, -8, -4, -7, 0
Step-by-step explanation:
The diagram shows a square pizza box with side lengths of 18 inches. In the box is a circular pizza with a radius of 8 inches. What is the difference between the area of box and the pizza?
Answers
18x18=324
pi8^2=201.0619
324-201=123
Write a function to represent the set of ordered pairs. {(2, -1), (4, 5), (6, 15), (8, 29)}
Answers
Answer:
(7, 32), In this situation you could put any ordered pair but it just has to be different than the x variables shown. The y values can be the same, only the x values really count ♀️
Which of the following are square roots of 576
A. -24
B. 5761/2
C. 48
D. 24
E. 12
F. -5761/2
Answers
The square root of 576 is the inverse of the mathematical operation of squaring the number 24. The square root of a number implies a number whose product with itself gives the initial number. Now we will calculate the square root of 576 using various methods and a few interesting facts and problems too.
Square root of 576: 24Square of 576: 331776What Is the Square Root of 576?The square root of 576 can be written as √576 and (576)1/2
The square of 576 will be a number(a) such that a × a = 576
And 24 × 24 = 576 also -24 × -24 = 576
Therefore, +24 and -24 are the square root of 576
Is Square Root of 576 Rational or Irrational?The square root of 576 are +24 and -24.
Both numbers are integers and we know that all integers are rational numbers.
Hence, the square root of 576 is a rational number.
Is this correct?
Draw and label a triangle that is similar to the one pictured below.
Answers
im not quite sure how to do this pls if anyone could help thanks
Answers
Answer:
a, 10% of 300 = 30 b, 300 - 30 = 270
Step-by-step explanation:
1. 300 x 10 = 3,000
2. Move decimal place 2 to the left = 30.00
3. Subtract 30 from 300 which is 270
There are 35,783 police officers in the city. 1/5 of them are females. There are about ___ male police officers in the city.
Answers
Answer:
7156.6 Women. 28624 Men.
Step-by-step explanation:
I used a web browser and typed "35783/5" That answers the woman part. "4/5 of 35783" Solves the male part.
There are about 4/5th = 28626 male police officers in the city.
What is a percentage?Percentage is defined as "out of 100." Similar to fractions and decimals, percentages are used in mathematics to represent subsets of a whole.
Given, there are 35,783 police officers in the city.
1/5 of them are females.
That means, 1/5th = 20%
20% are female police officers.
And 100 -20 = 80% are the male police officers.
To find the number of male police officers:
80% of 35,783
= 35783 x 80 / 100
= 28626.4
= 28626 approximated
Therefore, 4/5th male police officers in the city are 28626.
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Write 2 as a complex number.
Answers
Answer:
2 + 0i
Step-by-step explanation:
Our real number in this scenario would be 2. And since we don't need an imaginary part because we are just converting 2 by itself, we plug in 0 for the imaginary number.
What is the mean for the set of data?
Rubric Test Score
xx. X. Xx. Xx. Xxx
1 2 3 4 5
Score
Answers
Steps: 1) 1+1+2+3+3+4+4+5+5+5=33
2) 33/10=3.3
find the value of this answer
Answers
Answer:
3
Step-by-step explanation:
[tex]\sqrt[3]{27} =\sqrt[3]{(3)(3)(3)} =\sqrt[3]{(3)^3}= 3[/tex]
BRAINLIEST please if this helped!Answer: 3.............
Step-by-step explanation:
What primarily drew early civilizations to the places they first populated?
A. Religious freedom
B. Governmental policies
C. Economic development
D. Physical geography
Answers
Answer:
gg8jhytufgkl
Step-by-step explanation:
What is the value of X?
Answers
Answer:
x is 54˚
Step-by-step explanation:
Opposite angles are equalTherefore [tex]2x+2=3x-52[/tex]Subtract 2x from both sides[tex]2=x-52[/tex]Add 52 to both sides[tex]x=54[/tex]Answer:
x = 54°
Step-by-step explanation:
Forming the equation,
→ (2x + 2)° = (3x - 52)°
Now the value of x will be,
→ (2x + 2)° = (3x - 52)°
→ 2x - 3x = -52° - 2°
→ -x = -54°
→ [ x = 54° ]
Hence, the value of x is 54°.
¿Cuál es el dominio de esta función?
Answers
Help urgently tired of post every 5 min
Answers
Answer:
A. 12.78
Step-by-step explanation:
4 shirts for 21.83 = 87.32
87.32 + 42.38 + 74.78 = 204.48
204.48 x 0.0625 = 12.78
The complete total of the items is $204.48.
And 6.25% of that would be $12.78. I hope this helped.