The average rate of change of f(x) = x - 2√x on the interval [1, 9] is 1/2.
What is average rate of change?It is a measure of how much the function changed per unit, on average, over that interval.
We have,
f(x) = x - 2√x
On the interval [1,9].
[1, 9] = [a, b]
The average rate of change:
= f(b) - f(a) / b - a
= f(9) - f(1) / 9 - 1
= [(9 - 2√9) - (1 - 2√1)] / 8
= [ (9 - 6) - (1 - 2) ] / 8
= (3 + 1) / 8
= 4 / 8
= 1/2
Thus the average rate of change of f(x) = x - 2√x on the interval [1, 9] is 1/2.
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Solving quadratic equations problem
Which proportions can be used to find the length of side YZ?
Answer:
The two shapes are similar, therefore, [tex]\frac{\text{KJ}}{\text{WZ}} = \frac{\text{JM}}{\text{YZ}}[/tex]
[tex]\frac{12}4 = \frac6n\\\to 3n = 6\\\to n =2[/tex]
The side length YZof a trapezoid WXYZ will be 2 cm.
What is a trapezoid?It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezoid, one pair of opposite sides are parallel.
The side lengths are given as:
JK = 12 cm
MJ = 6 cm
WX = 4 cm
WZ = n cm
From the diagram, the trapezoid JKLM is similar to the trapezoid WXYZ.
If the two polygons are similar then the ratio of the corresponding sides of the polygon is constant. The ratios are written as,
JK/WX = KL/XY = LM/YZ = MJ/ZW
JK/WX = MJ/ZW
12/4 = 6/n
3 = 6/n
n = 6/3
n = 2
The side length YZof a trapezoid WXYZ will be 2 cm.
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f(t) = 10.72(0.9t + 10)0.3 (0 ≤ t ≤ 20)
where t is measured in years, with t = 0 corresponding to the year 2000.† At what rate was the percentage of Americans age 55 and older changing at the beginning of 2008? (Round your answer to four decimal places.)
____ % per year
At what rate was the percentage of Americans age 55 and older changing in 2017? (Round your answer to four decimal places.)
____% per year
What was the percentage of the population of Americans age 55 and older in 2017? (See Note on page 168. Round your answer to two decimal places.)
____%
a) The rate % at the beginning of 2008 rounded off to four decimal places will be 25.1682 % per year.
b) The rate % at the beginning of 2017 rounded off to four decimal places will be 28.2573 % per year .
c) The rate % at the beginning of 2017 rounded off to two decimal places will be 28.26% per year.
What is a function ?
A function is a relationship between inputs and outputs where each input has precisely one output and the output can be linked to its input.
It is given that , a function which represents rate % is f(t) = 10.72 × [tex](0.9t + 10)^{0.3}[/tex]. Also , t = 0 corresponding to the year 2000.
The rate % of Americans age 55 and older changing at the beginning of 2008 i.e., t = 8 , rounded off to four decimal places will be :
So : f(t) = 10.72 × [tex](0.9* 8 + 10)^{0.3}[/tex]
f(t) = 10.72 × [tex](7.2+ 10)^{0.3}[/tex]
f(t) = 10.72 × [tex](17.2)^{0.3}[/tex]
f(t) = 10.72 × 2.347
f(t) = 25.1682 % per year
The rate % of Americans age 55 and older changing at the beginning of 2017 i.e., t = 17 , rounded off to four decimal places will be :
f(t) = 10.72 × [tex](0.9* 17 + 10)^{0.3}[/tex]
f(t) = 10.72 × [tex](15.3 + 10)^{0.3}[/tex]
f(t) = 10.72 × [tex](25.3)^{0.3}[/tex]
f(t) = 10.72 × 2.6359
f(t) = 28.2573 % per year
The rate % of Americans age 55 and older changing at the beginning of 2017 rounded off to two decimal places will be :
f(t) = 28.26% per year
Therefore , the answers are :
a) The rate % at the beginning of 2008 rounded off to four decimal places will be 25.1682 % per year.
b) The rate % at the beginning of 2017 rounded off to four decimal places will be 28.2573 % per year .
c) The rate % at the beginning of 2017 rounded off to two decimal places will be 28.26% per year.
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What point in the feasible region maximizes the objective function?
For the given maximization problem there is no the point in the feasible region which maximizes objective function C = 7x -3y.
What is feasible region ?A feasible region in any optimization problem is the collection of all the points where all the given constraints are satisfied.
For maximization problem, we will use the corner points of the feasible region and then we will check that on which corner point the objective function is maximum.
Given problem is:
Maximize Objective function C = 7x-3y
When the constraints are (i) x≥0 , (ii) y≥0 , (iii) -x+5 ≤y
(iv) y ≤ (1/3)x +1
We will graph these constraints and find the common shaded area.
x≥0,y≥0 represents that the point is in 1st quadrant
For -x+5 ≤y, we will use -x +5 =y
When x= 0 then y=5 and when y=0 then x=5 , then -x +5 =y is a line passing through (0,5) and (5,0)
and on putting (0,0) in -x+5 ≤y we get 5≤0 which is a false statement .
Therefore -x+5 ≤y is region starting with line -x +5 =y and going in direction to opposite to that of (0,0)
For y ≤ (1/3)x +1, we will use y = (1/3)x +1
When x= 0 then y=1 and when y=0 then x=-3 , then y= (1/3)x +1 is a line passing through (0,1) and (-3,0)
and on putting (0,0) in y ≤ (1/3)x +1 we get 0≤1 which is a true statement .
Therefore, y ≤ (1/3)x +1 is region starting with line y = (1/3)x +1 and going in direction of (0,0).
Thus we got the feasible region as shaded in the below attached figure.
The shaded area is unbounded , therefore no point of maximum exist on the feasible region.
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abby can buy an 8-pound bag of dog food for7.40 or a 4-pound bag of the sane dog for 5.38 which is the better buy
Cynthia Besch wants to buy a rug for a room that is 18 ft wide and 32 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 176 square feet of carpeting. What dimensions should the rug have?
The rug will have dimension of 8ft. wide and 22ft. long.
Dimensions of room :
Wide (w) = 18 ft.
Long (l) = 32 ft.
Area of the room = l × w
= 32 × 18 = 576 ft²
Cynthia wants to leave a uniform strip of floor around the rug.
Let the width of the rug = x ft.
Then the dimensions of the rug will be = (18- 2x)ft. × (32- 2x)ft.
Area of the rug = (18 - 2x) × (32 - 2x) ft²
176 = (18 - 2x) × (32 - 2x)
176 = 576 - 36x - 64x + 4x²
4x² - 100x + 400 = 0 ( Divide the equation by 4 )
x² - 25x + 100 = 0
x² - 20x - 5x + 100 = 0
x(x - 20) -5(x - 20) = 0
(x - 20) (x - 5) = 0
x = 20, 5
If we take 20 as x then it will become a negative number when we will substract it from dimensions of the rug.
Therefore, The width of the rug will be 5 ft.
Thus, The Dimension of the rug = (18- 2x)ft. × (32- 2x)ft.
= (18 - 10) × (32 - 10)
= 8ft. × 22ft.
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Find the total cost to the nearest cent.
$20 haircut; 10% tip
Answer:
$22.00
What is a tip in sales?A tip in sales is an added monetary contribution to the worker responsible for your bill. Tips are usually in percentage form and represent a portion of the total before you add a tip.
To find a tip in sales, convert the percentage to a decimal and then add 1 to that decimal. Finally, multiply the total by this sum.
SolveTo solve, first convert the percentage into a decimal by dividing by 100.
[tex]\displaystyle \frac{10}{100}[/tex]
[tex]0.1[/tex]
Then, add 1 to this quotient.
[tex]1+0.1 =1.1[/tex]
Finally, multiply the total ($20) by this sum.
[tex]20\times 1.1[/tex]
[tex]22[/tex]
Therefore, the total cost is $22.00.
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The total cost to the nearest cent is $22.00 when haircut is $20 and tip is 10%.
To find the total cost, we need to add the cost of the haircut and the tip amount.
Given:
Haircut cost = $20
Tip percentage = 10%
First, calculate the tip amount:
Tip = (10/100) × Haircut cost
Tip = (10/100) × $20
Tip = $2
Add the haircut cost and the tip amount to find the total cost:
Total cost = Haircut cost + Tip
Total cost = $20 + $2
Total cost = $22
Therefore, the total cost to the nearest cent is $22.00.
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Explain why you use addition to
check subtraction.
Answer: The reason that you would use addition to check subtraction is because it is the easiest, fastest, and most reliable way to check your subtraction problem.
Step-by-step explanation:
for example. you do something like: 42 - 19 = 23
you just add 19 and 23. if you get 42 then that means your answer if correct.
hope it helps
in terms of height.
9 Modelling The inside of a saucepan has diameter 20 cm and height 13 cm.
The manufacturer claims that the pan has a capacity of 4 litres.
Is the claim correct?
Explain your answer.
Step-by-step explanation:
this is practically a cylinder.
the volume of a cylinder is
ground area × height = pi×r² × height.
r being the radius (half of the diameter).
so, we have here
V = pi×10² × 13 = pi × 100 × 13 = 1300pi =
= 4,084.07045... cm³
1 liter = the content of a cube with 10 cm side length.
10×10×10 cm³ = 1000 cm³ = 1 liter.
the pan has a volume of 4,084.07045... cm³, so, yes, it has the capacity of 4 liters as 4×1000 cm³ (and a little bit extra).
What is the area, in squared feet, of a rectangle whose length is three times its
width which is 4 feet?
Value: 2
Looking at the list of equalities below, which property does equality 2 demonstrate?
Equality 1: 8x5 = 5x8
Equality 2: (8x5) x 6.75 = 8 x (5x6.75)
Equality 3: 8 x (5+6.75) = 8 x 5 +8 x 6.75
Equality 4: 8x1 = 8
a. Commutative property of multiplication
O b. Distributive property
O c. Identity property of addition
O d. Associative property of multiplication
Check Answer
The property which equality 2 demonstrate is: d. Associative property of multiplication.
What is the associative property of multiplication?The associative property of multiplication states that when three (3) numbers are multiplied, the end result (output) would always be the same regardless of the way the numbers are arranged (grouped).
This ultimately implies that, the associative property of multiplication suggest that the way in which factors are arranged (grouped) when multiplying three (3) numbers does not change the product.
Mathematically, the associative property of multiplication can be represented by this expression:
(a × b) × c = a × (b × c) ≡ (8 × 5) × 6.75 = 8 × (5 × 6.75)
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When you subtract a constant from y=x2 what happens to the graph? Eg y = x2 - 2
When you subtract a constant from y = x², the following happens to the graph: C. graph moves DOWN.
What is a graph?
A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
In Mathematics, the graph of any quadratic function is parabolic because it is a u-shaped curve. For the given quadratic function, the graph is a upward parabola because the coefficient of x² is positive.
In conclusion, when a constant is subtracted from y = x², we can reasonably infer and logically deduce that the graph moves down as shown in the image attached below.
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Complete Question:
When you subtract a constant from y = x² what happens to the graph? Eg y = x² - 2
answer choices
Graph moves UP
Graph moves to the RIGHT
Graph moves DOWN
Graph moves to the LEFT
The number -3 is an integer and a rational number.
Answer:yes
Step-by-step explanation:
Shoreside Bikes is a bike rental company that charges tourists by the hour as
shown in the table. Use the table to fill in the missing representations.
Suppose you go shopping for a new futon bed for your room. The model you really like happens to be on sale for $200. It's original price is $500. What percent of the original price will you save if you purchase it?
Round your percentage to one decimal place.
Do not include
%
sign with your answer.
60 percent of the original price is saved if the futon bed is purchased.
The percent of the original price that will be saved can be calculated as followsThe original price of the futon bed is $500
The new price is $200
The first step is to calculate the price change
Price change= 500-200
= 300
The amount saved can be calculated as follows
300/500 × 100
= 0.6 × 100
= 60
Hence 60 percent of the original price which is $500 will be saved
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Two boxes are shown below. What is the combined volume? Show your work
Check the picture below.
The solution is, the combined volume of the boxes is 180 unit cube.
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
here, we have,
from the given diagram, we get,
there is two boxes in the diagram.
now, we have to find the combined volume.
here, we get,
the boxes are cuboids.
we know that,
Volume of cuboid = length * width * height
V = l*w*h
here, we get, from the figure,
for 1st box, l = 3, w = 5 , h = 8
so, V = 3 * 5 * 8 = 120
and, for 2nd box, l = 4, w = 5, h = 3
so, V = 4*5*3 = 60
we get, the combined volume 120 + 60 = 180
Hence, The solution is, the combined volume of the boxes is 180 unit cube.
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$7.99 by 16.2 ounces
Answer:
.49 if you're dividing them.
Step-by-step explanation:
2x-2(5x-3)=4x-6
Solve for X
Step-by-step explanation:
2x-10x+6=4x-6
2x-10x-4x=-6-6
-12x=-12
x=1
how do i simplify 4² X 4 ^4 / 4^3
Answer:
4³
Step-by-step explanation:
using the rules of exponents
• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
• [tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]
then
4² × [tex]4^{4}[/tex] / 4³
= [tex]4^{(2+4)}[/tex] / 4³
= [tex]4^{6}[/tex] / 4³
= [tex]4^{(6-3)}[/tex]
= 4³
what is the greatest common factor of 28 and 91
Find the greatest common factor: 9ab2, 108ab3
The greatest common factor of 9ab², 108ab³ is 9ab².
What is the greatest common factor?The factor of a number is the number that divides a number evenly; without any remainders. The factors of a number can either be positive or negative. For example, a factor of 10 is 2. This is because 10 divided by 2 is 5. 2 divides 10 evenly.
The greatest common factor is the highest factor that is common to two or more numbers. The highest common factor of 10 and 20 is 10. This is because it is the greatest common factor that is common to both numbers.
Factors of 9ab², 108ab³ = 3ab², 9ab²
The greatest common factor = 9ab²
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chapter 8
2.Find the volume of each figure. Round your answers to the nearest hundredth, if necessary.
The volume of the figure in the nearest hundredth is 67 mi³
How to determine the volume
The formula for determining the volume of a sphere is expressed as;
Volume = 4/ 3 πr³
Where;
π takes the value = 3. 14r is the radius of the sphere = 4 miTo determine the volume, we have to substitute the values of the parameters into the formula
Volume = 4/ 3 × 3. 14 × (4)²
Find the value of the square
Volume = 4/ 3 × 3. 14 × 16
Multiply through
Volume = 200. 96/ 3
Find the quotient
Volume = 66. 98
Volume = 67 mi³
Thus, the volume of the figure in the nearest hundredth is 67 mi³
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For each polynomial function, rewrite the polynomial in standard form. Then state its degree and constant term.
a. f(x) = (x + 1)(x+3)(x-4)
b. g(x) = 3(x + 1)(x+3)(x-4)
a. The stand form is f(x) = x^3 - 13x - 12
degree = 3
constant term = - 12
b. The stand form is g(x) = 3 x^3 - 39x - 36
degree = 3
constant term = - 36
Given data
f(x) = (x + 1)(x+3)(x-4)
g(x) = 3(x + 1)(x+3)(x-4)
How to find the standard form of the polynomialsfor f(x) = (x + 1)(x+3)(x-4) we have
f(x) = (x + 1)(x+3)(x-4)
f(x) = ( x + 1 ) ( x^2 - 4x + 3x - 12 )
f(x) = (x + 1) ( x^2 - x - 12 )
f(x) = x^3 - x^2 - 12x + x^2 - x - 12
f(x) = x^3 - 13x - 12
degree = 3
constant term = -12
g(x) = 3(x + 1)(x+3)(x-4)
g(x) = 3(x + 1) ( x^2 - 4x + 3x - 12 )
g(x) = 3(x + 1) ( x^2 - x - 12 )
g(x) = 3 ( x^3 - x^2 - 12x + x^2 - x - 12 )
g(x) = 3 ( x^3 - 13x - 12 )
g(x) = 3 x^3 - 39x - 36
degree = 3
constant term = - 36
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Jack is 29 of age he weighs 81kg he works out in a hot day what is the amount of water he will need to drink
Answer:
8 gallons
Step-by-step explanation:
8:50+ 7 hours and 35 minutes
Answer:
4:25 I think
Step-by-step explanation:
just added them all up I don't know if that's what you needed yho
Answer:
15:85 or 4:25
Step-by-step explanation:
jfhfjfjfjfjfndndndndndjdjfjfnnfjfjdjfjfjf
Eight less than five times a number is four more than eight times the number. Find the number.
Answer:
n = -4
Step-by-step explanation:
let the number = n
eight less than = .... minus 8
five times a number =n * 5
eight less than five times n = n * 5 minus 8 = n*5 -8
is means equal to
four more than = .... plus 4
eight times the number = n* 8
four more than eight times the number = n*8+4
n*5-8 is n*8 +4
n*5-8=8n+4
subtract 5n from both sides to put all variables and coefficients on one side
-8 = 3n + 4
subtract 4 from both sides to isolate the variable and coefficient
-12 = 3n
divide both sides by 3 to get n
n = -4
PLEEEEZZ HALP 50 POINTS
what is the inverse of the function
Answer:
the first one
Step-by-step explanation:
2.28times10^9 3times10^8
Mrs. Burke’s geography class has 106 students, classified by academic year and major, as illustrated in the table. Mrs. Burke randomly chooses one student to collect yesterday’s work.
Mrs. Burke’s Geography Class
Academic Year Geography Majors Non-Geography Majors
Freshmen 15 14
Sophomores 11 16
Juniors 13 11
Seniors 14 12
Step 2 of 2 : What is the probability that she selects a senior, given that she chooses a non-geography major? Enter a fraction or round your answer to 4 decimal places, if necessary.
Probability is the measure of the likelihood that an event will occur in a Random Experiment. The probability of selecting a senior from non geography is 0.1132
What is probability?Probability is the measure of the likelihood that an event will occur in a Random Experiment
Given
Geography Majors Non Geography Majors
Freshmen 15 14
Sophomores 11 16
Juniors 13 11
Seniors 14 12
The total number of students are 106
The number of seniors in non geography is 12
So probability of selecting one senior from 106 is 12/106
Probability(senior of non geography)=12/106=0.1132
Therefore required probability is 0.1132.
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PLSSS I NEED AN ANSWERR
find the midpoint of the segment with the given endpoints. (-1,5) and (-6,-8)
Answer: The midpoint is 1/2
Step-by-step explanation: The formula we are using for this problem is (x1+x2/2, y1+y2/2) I substitute the points for the equation and it looked likes this (-1-6/2)(5-8/2) and got 5/2-3/2 and the final answer is 1/2!
Hope this helped C:
Answer:
( -3 1/2, -1 1/2) or as a desimal (-3.5, -1.5)
Step-by-step explanation:
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