Find the average rate of change of f(x) = - 2x ^ 2 - x from x = 1 to x = 6 . Simplify your answer as much as possible .
Answers
The average rate of change of a function in the interval [a,b] is given by:
[tex]\frac{f(b)-f(a)}{b-a}[/tex]In this case we have that a=1 and b=6; plugging these values in the formula above we have:
[tex]\begin{gathered} \frac{-2(6)^2-6-(-2(1)^2-1)}{6-1}=\frac{-2(36)-6-(-2(1)-1)}{5} \\ =\frac{-72-6-(-2-1)}{5} \\ =\frac{-78-(-3)}{5} \\ =\frac{-78+3}{5} \\ =\frac{-75}{5} \\ =-15 \end{gathered}[/tex]Therefore, the average rate of change in the interval is -15
Related Questions
Suppose a hospital would like to estimate the proportion of patients who feel that physicians who care for them always communicated effectively when discussing their medical care. A pilot sample of 40 patients found that 28 reported that their physician communicated effectively. Determine the additional number of patients that need to be sampled to construct a 90% confidence interval with a margin of error equal to 2% to estimate this proportion.
Part 1
The additional number of patients that need to be sampled is
(Round up to the nearest integer.)
Answers
174 more patients need to have their samples taken than were originally anticipated. This is further explained below.
What is a Marginal error?Generally, the equation for the margin of error is mathematically given as
[tex]{Margin\ of \ error } & \ amp;=Z_{o \text { it }} \text { at } 5 \% \text { lo.s } \times S E(p)[/tex]
Where
Z is the distributionSE is the standard deviationGiven that the margin of error should be 7%, or 0.07, the total number of extra patients is denoted by n.
sample proportion = 11/20 = 0.55
q =0.45
Margin of error = Zo at 5% lo.s * S E(p)
To solve for the 0.07amp
[tex]\\\\0.07 =1.96 \times \sqrt{\frac{p q}{n}}[/tex]
[tex]\\\\&0.07=1.96 \sqrt{\frac{0.55 \times 0.45}{20+n}} \\\\0.07 =\frac{0.97508}{\sqrt{20+n}} \\\\\sqrt{20+n} =\frac{0.97508}{0.07} \\\\\end{aligned}[/tex]
20+n =194.04
n =174.04
n=174
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Evaluate : limx→ tan2-sin2x x3
Answers
Given:
[tex]\lim _{x\to0}\frac{\tan 2x-\sin 2x}{x^3}[/tex]Solve:
[tex]\lim _{x\to0}\frac{\tan 2x-\sin 2x}{x^3}[/tex]Use l'hopital's rule:
[tex]\begin{gathered} =\lim _{x\to0}\frac{\frac{d}{dx}(-\sin 2x+\tan 2x)}{\frac{d}{dx}(x^3)} \\ =\lim _{x\to0}\frac{-2\cos (2x)+2\tan ^2(2x)+2}{3x^2} \end{gathered}[/tex]Simplify:
[tex]\begin{gathered} =\lim _{x\to0}\frac{-2\cos (2x)+2\tan ^2(2x)+2}{3x^2} \\ =\lim _{x\to0}\frac{2(-\cos (2x)+\tan ^2(2x)+1)}{3x^2} \end{gathered}[/tex]Apply the constant multiple rule:
[tex]\begin{gathered} \lim _{x\to0}cf(x)=c\lim _{x\to0}f(x) \\ \text{With c=}\frac{2}{3} \\ f(x)=\frac{-\cos (2x)+\tan ^2(2x)+1}{x^2} \end{gathered}[/tex][tex]\begin{gathered} =\frac{2\lim _{x\to0}\frac{-\cos (2x)+\tan ^2(2x)+1}{x^2}}{3} \\ =\frac{2\lim _{x\rightarrow0}\frac{(4\tan ^2(2x)+4)\tan (2x)+2\sin (2x)}{2x}}{3} \end{gathered}[/tex]Similary :
[tex]\begin{gathered} =\frac{2\lim _{x\to0}(2\cos (2x)+12\tan ^4(2x)+16\tan ^2(2x)+4)}{3} \\ =\frac{2(6)}{3} \\ =4 \end{gathered}[/tex]The office floor is 250 ft. X 80 ft. The conference room floor is 50 ft. X 20 ft. , which covers __?__ of the office
Answers
The percentage of area covered by the conference room is 5%.
What is area?
A region's size on a flat or curved surface is expressed in terms of area, a unit of measurement. A surface region or plane area is the area of an open surface or the boundary of a three-dimensional object, whereas a plane region or area refers to the area of a form or planar lamina.
The quantity of unit squares necessary to completely encompass a form is its area. In order to express and measure it, square units are used.
Given, the dimension of office as
Length= 250 ft and breadth is 80 ft
Area of office = length ×breadth = 250 ×80 = 20,000
Length of conference room = 50 ft
Breadth of conference room = 20 ft
Area = 50 (20) = 1000
Percentage of office covered by conference room is given as:
1000/20000×100=5
Hence, 5% is occupied
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Selwyn wanted to place point V on the same number line to represent the opposite number of point W . Which instruction should he follow to place point V
Answers
Move ten units to the left of point W.
1) Counting the marks on the number line, we can tell that Selwyn placed point V 5 units to the right of zero.
2) Since we need to find the opposite number, we need to find the negative 5 ( -5). Hence, we need to:
Move ten units to the left of point W.
Because we need to remember that the reference is not zero but W.
HELP!
Do units affect significant figures? For example, I know that the number 5600 has two significant figures. But if I wrote it as 5600 L, would the unit "L" count as a sig fig? Please help me!!
Answers
Gourmet in Italy has a policy of automatically adding an 18% tip to a restaurant bill. How much would a restaurant bill be if it had a tip of $3.20 added to it?
Answers
The restaurant charger a tip of the 18% of the bill
So the total amount charged is the money spent + 18%
The bill had a tip of $3.20 this is the 18% of the amount spent.
Using cross multiplication you can calculate the amount of the bill as:
Bill without tip: 100%
Tip: 18%
Total amount (bill + tip): 118%
If 18% ____ $3.20
Then 118%___$x
[tex]undefined[/tex]If a 1/3 cup serving of cheese provides your fully daily value of calcium, then what percentage of your daily value of calcium is provided by 3/4 cup of the cheese?
Answers
If a 1/3 cup serving of cheese provides your full daily value of calcium, then 225% of your daily value of calcium is provided by ¾ cup of the cheese.
What are the ratios rules?Between amounts of the same sort, the ratio should exist. The units used to compare two items should be comparable.
Terms should be in a meaningful sequence. If two ratios are comparable to one another like fractions, they may be compared.
An easy ratio Is what?When both sides are whole numbers and cannot be split by another
whole number, a ratio is considered to be in its simplest form.
Think about full number ratios, such as 6:4. The fraction 64 can be used to represent it.
What proportion of your daily intake of calcium is delivered by 3/4 cup of the food if a serving of cheese that is 1/3 cup in size delivers your whole daily value of calcium?Daily value of calcium= (3/4)/(1/3) = 9/4
3/4 cup gives you 9/4 of your daily value of calcium.
We can convert fractions to percentages, we will get
9/4= 2.25
2.25*100=225%
Then the percentage of your daily value of calcium is 225%.
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Round 18,792 to the nearest thousand is the answer 18,790 or 00019 or 00018 or 18800 please due today please give brainiest.
Answers
Answer:
The answer is 19,000
Step-by-step explanation:
18,792 you round to the thousand which is 8 and the number after is 7 which is above 5 so the 8 turns into a 9
Answer:
19000
Step-by-step explanation:
18,792
Rounding to the nearest thousand
The 8 is in the thousands place
We look at the number in the hundreds place, 7
It is 5 or higher so we will round the 8 up to 9 and everything else to the right will become zeros
18,792 becomes 19000
Sue used 4 ounces of dark chocolate chips for every 3 ounces of white chocolate chips if she uses 21 ounces of chips altogether how many ounces of dark chocolate chips did she use
Answers
Answer: 12 oz
Step-by-step explanation:
Answer: 12
Step-by-step explanation:
PLEASEE I NEED HELP!!
Figure 3 can also be created by transforming figure 1 with a sequence of two transformations. Which statement describes a possible sequence of transformations that transforms figure 1 into figure 3?
A. a rotation 180 degrees clockwise about the origin, followed by translation 2 units to the left.
B. a rotation 90 degrees clockwise about the origin, followed by a reflection across the x-axis.
C. a rotation 180 degrees clockwise about the origin, followed by a reflection across the y-axis.
D. a rotation 90 degrees clockwise about the origin, followed by a translation 3 units to the right.
Answers
the correct answer is A. Option A describes a rotation of 180 degrees clockwise, which would result in figure 1 being upside down, and then a translation of 2 units to the left.
What is triangle?
A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.
To transform figure 1 into figure 3, we need to apply two transformations. We can eliminate option B because a rotation of 90 degrees followed by a reflection across the x-axis would transform figure 1 into a mirror image of figure 2, not figure 3.
Option A describes a rotation of 180 degrees clockwise, which would result in figure 1 being upside down, and then a translation of 2 units to the left. This would transform figure 1 into figure 3, so option A is a possible sequence of transformations.
Option C describes a rotation of 180 degrees clockwise followed by a reflection across the y-axis. This would transform figure 1 into a mirror image of figure 2, not figure 3.
Option D describes a rotation of 90 degrees clockwise followed by a translation of 3 units to the right. This would transform figure 1 into a position that is similar to figure 3, but the orientation of the triangle would be different.
Therefore, the correct answer is A.
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Borrowed $30000 four year loan at 7% what’s monthly payment? And what’s the intrest I will pay on loan?
Answers
given:
There are given that the Borrowed is $30000.
Explanation:
To find the monthly amount, we need to use the formula:
[tex]R=\frac{P}{1-(i+1)^{-n}}[/tex]Where,
[tex]\begin{gathered} P=30000 \\ r=0.07 \\ m=12\text{ Thenn} \end{gathered}[/tex][tex]\begin{gathered} i=\frac{r}{m}=\frac{0.07}{12} \\ =0.0058 \end{gathered}[/tex]Ans,
[tex]\begin{gathered} n=mt=12(4) \\ =48 \end{gathered}[/tex]Then,
From the formula:
[tex]\begin{gathered} R=\frac{Pi}{1-(1+i)^{-n}} \\ R=\frac{30000(0.0058)}{1-(1+0.0058)^{-48}} \\ R=\frac{30,000(0.0058)}{1-(1.0058)^{-48}} \\ R=\frac{30000(0.0058)}{0.24} \\ R=725 \end{gathered}[/tex][tex]\begin{gathered} S.I=\frac{P\times r\times t}{100} \\ =\frac{30000\times7\times4}{100} \\ =4800 \end{gathered}[/tex]Final answer:
Hence, the monthly payment is $725 and the interest will be: $4800
Find 98.6% of 343.7. Round to the nearest thousandth.
Answers
Percentage, a relative value indicating hundredth parts of any quantity.
98.6% of 343.7 is in nearest thousandth 338.888
What is Percentage?Percentage, a relative value indicating hundredth parts of any quantity.
We need to find 98.6% of 343.7.
Ninty eight point six percentage of three hundred forty three point seven.
Ninty eight point six percentage we need to convert into decimal number this can be achieved by dividing with 100.
98.6% =98.6/100
When ninty eight point six is divided by hundred we get zero point nine eight six.
=0.986
We need to find what is 98.6% of 343.7.
To find ninty eight point six percentage of three hundred forty three point seven. we are required to multiply the converted value of 98.6% with three hundred forty three point seven.
Simply we need to multiply 0.986 with 343.7.
=0.986×343.7
=338.888
Hence 98.6% of 343.7 is 338.888
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Please help me brainly!!!<3
Answers
The domain of a function f(x) is x< 4, and the range is y≤ 0. What are the
domain and range of its inverse function, f-¹ (x)?
A. Domain: x≤0
Range: y< 4
B. Domain: x<0
Range: y≤ 4
C. Domain: x24
Range: y> 0
D. Domain: x < 4
Range: y≤ 0
Answers
Answer:
Step-by-step explanation:
d
How could you correctly rewrite the equation 6(11-3) = 4(7 + 5) using the distributive property?
66-3 = 28 +35
Answers
Answer:
The formula for the distributive property is expressed as, a × (b + c) = (a × b) + (a × c );
Step-by-step explanation:
6(11-3) = 4(7 + 5)
(6×11)-(6×3)=(4×7)+(4×5)
66 - 18 = 28 + 20
Mr. Connor's physics class has 105 students, classified by academic year and gender, as illustrated in the table. Mr. Connor randomly chooses one student to collect yesterday's work
Academic Year male female
Junior 8 11
senior 19 19
freshman 9 12
sophomore 19 8
Answers
The probability that he selects a Mel given that he chooses randomly from only the Juniors is 0.076.
How to calculate the probability?It should be noted that the probability is the likelihood that something will happen. The table shows that Connor's physics class has 105 students, classified by academic year and gender.
The probability will be:
Fraction of males that are junior / Fraction if Junior
= 8/105 / 19/105
= 0.076
The probability is 0.076.
The complete question is written below.
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What is the probability that he selects a Mel given that he chooses randomly from only the Juniors.
What is the answer to m
Answers
the sum of the internal angles of a quadrilateral is 360, therefore:
[tex]\begin{gathered} m\angle A+m\angle B+m\angle C+m\angle D=360 \\ \text{and} \\ m\angle A+m\angle C=180 \\ m\angle B+m\angle D=180 \end{gathered}[/tex]so
[tex]\begin{gathered} a+5+a-25=180 \\ 2a-20=180 \\ 2a-20+20=180+20 \\ 2a=200 \\ \frac{2a}{2}=\frac{200}{2} \\ a=100 \end{gathered}[/tex]mm
mm
Show all work for full credit.
Sketch the following curves, indicating all relative extreme points and inflection points. (10 pts)
a. y= x^3-6x^2+9x+3
Answers
For the given function, it is found that:
The extreme points are given by: (3,3) and (1,7).The inflection point is: (1,7).What are the extreme points of a function?The extreme points of a function happen at the values for x for which the first derivative is zero, that is:
y' = 0.
In this problem, the function is:
y = x³ - 6x² + 9x.
Hence the first derivative is:
3x² - 12x + 9.
The extreme values of x are:
3x² - 12x + 9 = 0.
3(x² - 4x + 3) = 0
x² - 4x + 3 = 0
(x - 3)(x - 1) = 0.
Then:
x - 3 = 0 -> x = 3.x - 1 = 0 -> x = 1.The numeric value of the function at these points is:
x = 3: y = 3³ - 6(3)² + 9(3) + 3 = 3.x = 1: y = 1³ - 6(1)² + 9(1) + 3 = 7.Hence the points are:
(3,3) and (1,7).
What are the inflection points of a function?The extreme points of a function happen at the values for x for which the second derivative is zero, that is:
y'' = 0.
For this problem, the second derivative is given by:
y'' = 6x - 12.
Hence the x-coordinate of the inflection point is:
6x - 12 = 0
6x = 12
x = 2.
The numeric value at x = 2 is:
2³ - 6(2)² + 9(2) + 3 = 5.
Then the inflection point is:
(2,5).
The graph with these points labeled is given at the end of the answer.
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Use the point-slope formula to write an equation of the line that passes through (0,6) and (-2,0) write answer in slope intercept form
Answers
Equation using slope intercept form is 3y = x + 18
What is slope intercept form?An intercept in mathematics is a location on the y-axis through which the line's slope passes. It is a place on the y-axis where a straight line or a curve crosses. This is reflected in the equation for a line, which is written as y = mx + b, where m denotes slope and c denotes the y-intercept. Y = mx + b is the general formula for the slope-intercept form, where m stands for the line's slope and b for the y-value of the line's y-intercept. We may more easily determine a line's slope and its y-axis intersection using the slope-intercept form of a linear equation.
Given Data
Points(0,6) and (-2,0)
The slope formula = [tex]\frac{y_{2}-y_{1 } }{x_{2}-x_{1} }[/tex]
y₂= 0
y₁=6
x₂=-2
x₁=0
Slope = (-2-0)/(0-6)
Slope = -2/ -6
Slope = 1/3
Slope intercept form
y = mx + b
y = (1/3)x + 6
y = (x+18)/3
3y = x + 18
Equation using slope intercept form is 3y = x + 18
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help
fast 20 point
please
Answers
x * 2 = y
Answer:
A. 2
Step-by-step explanation:
Hope this helps
the phone sells Jan a bicycle for $175 and a helmet for $17. The total cost for Jin is 160% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin
Answers
Jin
The bicycle selling price was : $175
The helmet was for : $17
Jin total cost was 160% of what Stefan spent originally to buy the two items
This means ; 160/100 * x = { 175+17} -----where x is the original amount stefan spent to buy the two items
1.6 x = 192
x = 192 /1.6
x=120
Stefan originally spent $120
The money he made after the sell is: $192-$120 =$72
Answer
a) $120
b) $72
I need help
There are 3 consecutive even integers with a sum of 72. Which equation can be used to find such integers?
x + 2 = 24
x + 2 = 12
x + 1 = 12
x + 1 = 24
Answers
The equation used to find the 3 consecutive even integers with a sum of 72 is x + 2 = 24.
What is defined as the even integers?An even integer is one that is divisible by two, i.e. a multiple of two.For eg:- 2,4,6,... and −2,−4,−6,.... are divided by twoAs a result, the integers 2,4,6,... and −2,−4,−6,.... are all even integersThus, the integer of a form 2k is a even integer, in which k is an integer.For the given data in question.
Let the first even integer be 'x'.
Second even integer will be 'x + 2'.
Thirst even integer will be 'x + 4'.
The sum is 72
x + x + 2 + x + 4 = 72
Simplifying;
3x + 6 = 72
Divide whole equation by 3.
x + 2 = 24
Thus, the equation used to find the 3 consecutive even integers with a sum of 72 is x + 2 = 24.
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How many solutions does -14 + 6b + 7 - 2b = 1 + 5b have
Answers
The number of solutions that -14 + 6b + 7 - 2b = 1 + 5b has is 1 solution.
How to illustrate the information?It should be noted a equation is important to illustrate the relationship between the variables. In this case, the equation given is illustrated as:
-14 + 6b + 7 - 2b = 1 + 5b
Collect like terms
-8 + 6b - 2b = 5b
b = -8
Therefore, it has only one solution.
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A test was given to a group of students. The grades and gender are summarized below A B C TotalMale4192043Female1116532Total15352575If one student is chosen at random from those who took the test,Find the probability that the student got a 'B' GIVEN they are male.
Answers
please quick I need this
Answers
Answer:
The remainder is [tex]4[/tex].
The quotient is [tex]3x^{2}+6x+1[/tex]
Step-by-step explanation:
Step 1: Do long division
To divide these expressions, we will have to make use of long division, which is shown in the picture.
Step 2: Identifying the remainder and quotient
The remainder is [tex]4[/tex].
The quotient is [tex]3x^{2}+6x+1[/tex]
A DVD is available at a store for $16.99. The list price of this DVD was $18.75. What was the percent discount? % (Round to the nearest tenth as needed.)
Answers
The cost of DVD = $16.99
The list price of this DVD was $18.75
So, the discount =
[tex]18.75-16.99=1.76[/tex]And the percent discount =
[tex]\frac{1.76}{18.75}\cdot100=9.3866\%[/tex]Rounding the answer to the nearest tenth
So, the answer will be : the percent discount = 9.4%
Find the area of the circle A) 12.56 mm^2B) 25.12 mm^2C) 37.17 mm^2D) 50.24 mm^2
Answers
The formula in getting the area of the circle is:
[tex]A=\pi r^2[/tex]where r = the radius of the circle and the value of π = 3.14
In the diagram, the radius of the circle is 4 mm. Let's replace the "r" in the formula with 4 mm and "π" with 3.14
[tex]A=(3.14)(4mm)^2[/tex]Then, simplify.
[tex]\begin{gathered} A=(3.14)(16mm^2) \\ A=50.24\text{ }mm^2 \end{gathered}[/tex]Therefore, the area of the circle is 50.24 mm². (Option D)
We have π = 3.14 and the radius is 4 mm. Therefore we apply the following formula:
A = π * r²Replacing values in the equation.
A = 3.14 * (4 mm)²We calculate potentiation.
A = 3.14 * 16 mm²We multiply
A = 50.24 mm²
Answer: The circle area is 50.24 mm^2 (option D)✅ .
To learn: https://brainly.com/question/23422024To learn: https://brainly.com/question/16612428To learn: https://brainly.com/question/28570984To learn: https://brainly.com/question/24048237The measures of the angles of a triangle are shown in the figure below. Solve for x.
50°
(6x-18)°
70°
Answers
Answer:
x=13
Step-by-step explanation:
We add all the numbers together, and all the variables
6x-78
We move all terms containing x to the left, and all other terms to the right
6x=78
x=78/6
which should equal 13
3. Compute the derivatives of the following functions. Do not simplify.
a) f(x)=tanx/e^3
b) f(x)= tan -¹(x³)(x^5)(ln x) c) f(x)=^7√x^5+ 5^x d) g(x)=x^sec(x)
Answers
Answer:
A im sure
Example
hope itz helpppp
f(x)=x^2+6x+7
f(x+h)=?
f(x+h)-f(x)=?
f(x+h)-f(x)/h=?
Answers
The values are;
f (x + h) = x² + 2xh + h² + 6x + 6h + 7
f (x + h) - f (x) = h² + 2xh + 6h
f (x + h) - f (x) / h = h + 2x + 6
What is substitution method?
Find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.
Given that;
The value of the function is;
f (x) = x² + 6x + 7
Now, Find the given values of f (x + h) , f (x + h) - f (x) and f (x + h) - f (x) / h by substitution method.
The value of the function is;
f (x) = x² + 6x + 7
Substitute x = x + h;
The value of the function is;
f (x + h) = (x + h)² + 6(x + h) + 7
= x² + 2xh + h² + 6x + 6h + 7
Thus, The value of f (x + h) = x² + 2xh + h² + 6x + 6h + 7.
Now,
f (x + h) - f (x) = (x² + 2xh + h² + 6x + 6h + 7) - (x² + 6x + 7)
= x² + 2xh + h² + 6x + 6h + 7 - x² - 6x - 7
= h² + 2xh + 6h
Thus, The value of f (x + h) - f (x) = h² + 2xh + 6h.
Now,
f (x + h) - f (x) / h = h² + 2xh + 6h / h
= h (h + 2x + 6) / h
= h + 2x + 6
Thus, The value of f (x + h) - f (x) / h = h + 2x + 6.
Therefore, The values are;
f (x + h) = x² + 2xh + h² + 6x + 6h + 7
f (x + h) - f (x) = h² + 2xh + 6h
f (x + h) - f (x) / h = h + 2x + 6
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