(a) Use a linear approximation to estimate f(0.9) and f(1.1). f(0.9) ≈ f(1.1) ≈ (b) Are your estimates in part (a) too large or too small? Explain. The slopes of the tangent lines are negative, but the tangents are becoming steeper. So the tangent lines lie below the curve f. Thus, the estimates are too large. The slopes of the tangent lines are negative, but the tangents are becoming steeper. So the tangent lines lie below the curve f. Thus, the estimates are too small. The slopes of the tangent lines are positive, but the tangents are becoming less steep. So the tangent lines lie above the curve f. Thus, the estimates are too large. The slopes of the tangent lines are positive, but the tangents are becoming less steep. So the tangent lines lie above the curve f. Thus, the estimates are too small.
Answers
Answer:
(Missing part of the question is attached)
[tex]L(x)=2x+3[/tex]
Estimates are too large.
Step-by-step explanation:
Suppose the only information we know about the function is:
[tex]f(1)=5[/tex]
where the graph of its derivative is shown in the attachment
(a)If the function [tex]f\\[/tex] is differentiable at point [tex]x=1[/tex] , the tangent line to the graph of [tex]f[/tex] at 1 is given by the equation:
[tex]y=f(1) +f'(1)(x-1)[/tex]
So we call the linear function:
[tex]L(x)=f(1) +f'(1)(x-1)[/tex]
We know the [tex]f(1)=5[/tex] as it is given in the question, and [tex]f'(1)=2[/tex] from the graph attached. Substitute in the equation of [tex]L(x)[/tex].
[tex]L(x)=5+2(x-1)\\L(x)=5+2x-2\\L(x)=2x+3\\[/tex]
(b)At x=1, [tex]f'(x)[/tex] is positive but it is decreasing. However. if we draw the tangent lines, we see that the tangent lines are becoming less steeper, so the tangent lines lie above the curve [tex]f[/tex]. Thus, The estimates are too large.
Related Questions
A fuel oil company claims that one-fifth of the homes in a certain city are heated by oil. Do we have reason to believe that fewer than one-fifth are heated by oil if, in a random sample of 1000 homes in this city, 136 are heated by oil? Please show all 4 steps of the classical approach clearly using α = 0.05.
Answers
Answer:
Yes, we have reason to believe that fewer than one-fifth are heated by oil.
Step-by-step explanation:
A one-sample proportion test is to be performed to determine whether fewer than one-fifth of the homes in a certain city are heated by oil.
The hypothesis can be defined as follows:
H₀: The proportion of homes in a certain city that are heated by oil is not less than one-fifth, i.e. p ≥ 0.20.
Hₐ: The proportion of homes in a certain city that are heated by oil is less than one-fifth, i.e. p < 0.20.
The information provided is:
n = 1000
x = 136
α = 0.05
Compute the sample proportion as follows:
[tex]\hat p=\frac{x}{n}=\frac{136}{1000}=0.136[/tex]
Compute the test statistic as follows:
[tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]=\frac{0.136-0.20}{\sqrt{\frac{0.136(1-0.136)}{1000}}}\\\\=-5.9041\\\\\approx -5.90[/tex]
The test statistic value is, -5.90.
Decision rule:
Reject the null hypothesis if the p-value of the test is less than the significance level.
Compute the p-value as follows:
[tex]p-value=P(Z<-5.90)\\\\=1-P(Z<5.90)\\\\=1-(\approx 1)\\\\=0[/tex]
The p-value of the test is, 0.
p-value = 0 < α = 0.05
The null hypothesis will be rejected at 5% level of significance.
Conclusion:
The proportion of homes in a certain city that are heated by oil is less than one-fifth.
Suppose the demand for a certain brand of a product is given by D(p)equals=StartFraction negative p squared Over 116 EndFraction−p2116plus+200200, where p is the price in dollars. If the price, in terms of the cost c, is expressed as p (c )equals 2 c minus 10p(c)=2c−10, find the demand function in terms of the cost.
Answers
Answer:
The demand function in terms of cost is [tex]D(c) = [\frac{[40c- 100 -4c^2 \ ])}{116} ] + 200[/tex]
Step-by-step explanation:
From the question we are told that
The demand for a certain brand of a product is
[tex]D(p) = \frac{-p^2}{116} + 200 ----(1)[/tex]
The price, in terms of the cost c, is expressed as
[tex]p(c) = 2c -6 -----(2)[/tex]
Now substituting equation 2 into equation 1
So
[tex]D(c) = - [\frac{(2c -10 )^2)}{116} ] + 200[/tex]
[tex]D(c) = - [\frac{[4c^2 + 100 -40c \ ])}{116} ] + 200[/tex]
[tex]D(c) = [\frac{[40c- 100 -4c^2 \ ])}{116} ] + 200[/tex]
y=2x−4y=−12x+1 Question 1 options: a) (3, 2) b) (0, 2) c) (2, 0) d) (2, 3)
Answers
Which data collection method would provide an unbiased sample?
Answers
Answer:
The best data collection method or sampling method to provide an unbiased sample is the random sampling method.
Step-by-step explanation:
There are 5 popular known sampling methods or data collection methods.
1) Random Sampling
In random sampling, each member of the population would have an equal chance of being surveyed. One of the best ways to use random sampling is to give all the members of the population numbers and then use computer to generate random numbers and pick the members of the population with those random numbers.
2) Systematic sampling is easier than random sampling. In systematic sampling, a particular number, n, is counted repeatedly and each of the nth member is picked to be sampled.
3) Convenience Sampling
This is the worst sampling technique. It is also the easiest. In Convenience sampling, the surveyor just picks the first set of members of the population that they find and surveys.
4) Stratified Sampling
Stratified sampling divides the population into groups called strata. A sample is taken from each of these strata using either random, systematic, or convenience sampling.
5) Cluster sampling
Cluster Sampling divides the population into groups which are called clusters or blocks. The clusters are selected randomly, and some members or every element/member in the selected clusters is surveyed.
Hope this Helps!!!
Classify the following triangle .check all that apply
Answers
Answer:
Isosceles right triangle
Answer:
It is a scalene triangle because 2 angles are equal and one angle is different .
Step-by-step explanation:
please mark as brainliest and follow me!!!!!...
is –68 + 90 positive or negative?
Answers
Answer:
22. positive
Step-by-step explanation:
–68 + 90
22
Therefore meaning it goes into the positive numbers and making the answer 22!
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
PLEASE HELP
Answers
Answer: [tex]y=\frac{3}{2} x - 3[/tex]
Step-by-step explanation:
Looking at the graph we could locate the y intercept at point (0,-3) and we can locate another point (4,3) which also passes through the line. So using these coordinates we already know the the y-intercept as -3 but we need to find the slope to write it in slope intercept form.
To find the slope, we will need to find the difference in the y values and divide it by the difference in the x values.
(0,-3)
(4,3)
-3 - 3 = -6
0-4 = -4
-6 /-4 = 3/2 so now we know that the slope is 3 over 2
so we could write the equation as y = 3/2x -3
Answer: Thank you (nermay7)
Step-by-step explanation: They are correct!!!!!!!
To ______ a function, you need to stretch or compress it
Answers
Answer: It’s to change the shape of a function
Step-by-step explanation:
To change the shape of a function, you need to stretch or compress it.
How to stretch or compress a function?In math terms, you can stretch or compress a function horizontally by multiplying x by some number before any other operations. To stretch the function, multiply by a fraction between 0 and 1. To compress the function, multiply by some number greater than 1.
Is there a function for every shape?By definition, a function has one possible output for any given input. So if you want your function defined as some y=f(x), then not every shape can be written as a function. Any shape that has two points directly above each other (relative to the x-axis) cannot be written as a function, even a piecewise one.
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A stack of 4 identical books is 6.28 high. What is the heigh of 30 of these books?
Answers
Answer:47.1
Step-by-step explanation:6.28/4=x/30
188.4=4x
47.1=x
Answer:
47.1
Step-by-step explanation:
height of 1 book=6.28÷4=1.57
height of 30 books=1.57×30=47.1
You are testing the claim that the mean GPA of night students is different from the mean GPA of day students. You sample 30 night students, and the sample mean GPA is 2.35 with a standard deviation of 0.46. You sample 25 day students, and the sample mean GPA is 2.58 with a standard deviation of 0.47. Test the claim using a 5% level of significance. Assume the sample standard deviations are unequal and that GPAs are normally distributed. Give answer to exactly 4 decimal places.Hypotheses:sub(H,0):sub(μ,1) = sub(μ,2)sub(H,1):sub(μ,1) ≠ sub(μ,2)**I'm not sure how to calculate this in excel***Enter the test statistic - round to 4 decimal places.A=Enter the p-value - round to 4 decimal places.A=
Answers
Answer:
Step-by-step explanation:
This is a test of 2 independent groups. The population standard deviations are not known. Let μ1 be the mean GPA of night students and μ2 be the mean GPA of day students.
The random variable is μ1 - μ2 = difference in the mean GPA of night students and the mean GPA of day students.
We would set up the hypothesis.
The null hypothesis is
H0 : μ1 = μ2 H0 : μ1 - μ2 = 0
The alternative hypothesis is
H1 : μ1 ≠ μ2 H1 : μ1 - μ2 ≠ 0
This is a two tailed test.
Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is
(x1 - x2)/√(s1²/n1 + s2²/n2)
From the information given,
μ1 = 2.35
μ2 = 2.58
s1 = 0.46
s2 = 0.47
n1 = 30
n2 = 25
t = (2.35 - 2.58)/√(0.46²/30 + 0.47²/25)
t = - 1.8246
The formula for determining the degree of freedom is
df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²
df = [0.46²/30 + 0.47²/25]²/[(1/30 - 1)(0.46²/30)² + (1/25 - 1)(0.47²/25)²] = 0.00025247091/0.00000496862
df = 51
We would determine the probability value from the t test calculator. It becomes
p value = 0.0746
Since alpha, 0.05 < than the p value, 0.0746, then we would fail to reject the null hypothesis.
average of a data set was 40, and that standard deviation was 10, what else could you derive from that information.
Answers
Answer:
[tex] \bar x = 40, s =10[/tex]
And from these values we can estimate the sample variance like this:
[tex] s^2 = 10^2 =100[/tex]
And we can also estimate the coeffcient of variation given by:
[tex] \hat{CV} =\frac{s}{\bar x}[/tex]
And replacing we got:
[tex] \hat{CV} = \frac{10}{40}= 0.25[/tex]
And this coefficient is useful in order to see the variability in terms of the mean for this case since is lower than 1 we can conclude that this variation around the mean is low.
Step-by-step explanation:
For this case we have the following info given:
[tex] \bar x = 40, s =10[/tex]
And from these values we can estimate the sample variance like this:
[tex] s^2 = 10^2 =100[/tex]
And we can also estimate the coeffcient of variation given by:
[tex] \hat{CV} =\frac{s}{\bar x}[/tex]
And replacing we got:
[tex] \hat{CV} = \frac{10}{40}= 0.25[/tex]
And this coefficient is useful in order to see the variability in terms of the mean for this case since is lower than 1 we can conclude that this variation around the mean is low.
334% of what number is 33,400
Answers
Answer:
10000
Step-by-step explanation:
3.34x=33400
x=10000
The number is x=10000.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
let, the number = x
now, we get,
3.34x=33400
x=10000
Hence, The number is x=10000.
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Colgate claims that 90% of dentists recommend Colgate toothpaste. Suppose you randomly choose 10 dentists and ask whether they recommend Colgate toothpaste. What is the probability that exactly 8 dentists in your sample recommend Colgate toothpaste
Answers
Answer:
the probability that exactly 8 dentists in 10 samples recommend Colgate toothpaste is;
P(X) = 0.0043
P(X) = 0.43%
Step-by-step explanation:
The probability that a dentist recommend Colgate is;
P = 90% = 0.9
The probability that a dentist doesn't recommend Colgate is;
P' = 1 - P = 1 -0.9 = 0.1
Of 10 sample dentists, the probability that exactly 8 dentists recommend Colgate toothpaste is;
8 will recommend and two will not recommend it.
P(X) = P^8 × P'^2
P(X) = (0.9)^8 × (0.1)^2
P(X) = 0.0043
P(X) = 0.43%
The Probability of exactly 8 dentists in sample recommend Colgate toothpaste is 0.0043.
Since, Colgate claims that 90% of dentists recommend Colgate toothpaste.
Probability of dentist, who recommend Colgate toothpaste = 0.9
Probability of dentist, who does not recommend Colgate toothpaste,
= 1 - 0.9 = 0.1
When 10 dentist randomly choose , out of which 8 dentists recommend Colgate toothpaste. It means that 8 recommend Colgate toothpaste and 2 recommend other tooth paste.
Thus, The Probability of exactly 8 dentists in sample recommend Colgate ,
[tex]=(0.9)^{8}*(0.1)^{2} =0.0043[/tex]
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{(1,3),(2,5)(3,-4),(4-3),(5,1)} a function or not a function
Answers
Answer:
yes the above is a function.
Given cot ø = 4/3. Find the other two reciprocal trigonometic ratios. 1) scs 2) sec
Answers
Answer:
csc ø = 5/3 ; sec ø = 5/4
Step-by-step explanation:
cot ø = adj/opp
adj = 4
opp = 3
after that, we must find the hypotenuse by using phytagoras theorem
hpy² = adj² + opp²
hpy² = 4² + 3²
hpy² = 25
hpy = 5
now let's find the other
csc ø (not scs) = hyp/opp = 5/3
sec ø = hyp/adj = 5/4
SOLVE THE EQUATION SHOW YOUR WORK 3x = 45
Answers
Answer:
x = 15
Step-by-step explanation:
3x = 45
x = 45/3
x = 15
Answer:
15
Step-by-step explanation:
3x = 45
Dividing 3 from both sides gives you
[tex]x = 45/3\\\\[/tex]
Now that isolated x.
[tex]45/3 = 15[/tex]
So x = 15
:D
How do I explain this answer
Answers
Answer:
199
Step-by-step explanation:
i dont know
3.14 The waiting time, in hours, between successive speeders spotted by a radar unit is a continuous random variable with cumulative distribution function F(x) = 0, x< 0, 1 − e−8x, x ≥ 0. Find the probability of waiting less than 12 minutes between successive speeders (a) using the cumulative distribution function of X; (b) using the probability density function of X.
Answers
Answer:
(a) The probability of waiting less than 12 minutes between successive speeders using the cumulative distribution function is 0.7981.
(b) The probability of waiting less than 12 minutes between successive speeders using the probability density function is 0.7981.
Step-by-step explanation:
The cumulative distribution function of the random variable X, the waiting time, in hours, between successive speeders spotted by a radar unit is:
[tex]F(x)=\left \{ {{0;\ x<0} \atop {1-e^{-9x};\ x\geq 0}} \right.[/tex]
(a)
Compute the probability of waiting less than 12 minutes between successive speeders using the cumulative distribution function as follows:
[tex]12\ \text{minutes}=\frac{12}{60}=0.20\ \text{hours}[/tex]
The probability is:
[tex]P(X<0.20)=|F (x)|_{x=0.20}[/tex]
[tex]=(1-e^{-8x})|_{x=0.20}\\\\=1-e^{-8\times 0.20}\\\\=0.7981[/tex]
Thus, the probability of waiting less than 12 minutes between successive speeders using the cumulative distribution function is 0.7981.
(b)
The probability density function of X is:
[tex]f_{X}(x)=\frac{d F (x)}{dx}=\left \{ {{0;\ x<0} \atop {8e^{-8x};\ x\geq 0}} \right.[/tex]
Compute the probability of waiting less than 12 minutes between successive speeders using the probability density function as follows:
[tex]P(X<0.20)=\int\limits^{0.20}_{0} {8e^{-8x}} \, dx[/tex]
[tex]=8\times [\frac{-e^{-8x}}{8}]^{0.20}_{0}\\\\=[-e^{-8x}]^{0.20}_{0}\\\\=(-e^{-8\times 0.20})-(-e^{-8\times 0})\\\\=-0.2019+1\\\\=0.7981[/tex]
Thus, the probability of waiting less than 12 minutes between successive speeders using the probability density function is 0.7981.
PLEASE HELPPPPPPPPPP <3
Answers
Answer:
y = 1/2x + 4
Step-by-step explanation:
Slope intercept form is y = mx + b, where m is the slope and b is the y-intercept.
When we count rise over run, we find that the slope is 1/2
y = 1/2x + b
The line intersects the y-axis at 4, so the y-intercept is 4.
y = 1/2x + 4
I hope this helps :))
What role did youth play in the Civil Rights Movement?
Answers
Answer:
they played the pivotal role
Find the mode for the following distribution.
Number Frequency
16
3
20
5
24
9
28
7
32
7
36
5
40
3
24
28
32
28 and 32
Answers
Answer:
28 and 32
Step-by-step explanation:
they have the most
Observe the expression below and select the true statement(s).
3y(7 + 2x) + 9ry - 10
The "(7 + 2x)" in the first term is a factor.
The "9" in the second term is a coefficient.
The "By" in the first term is a factor.
The "10" in the third term is a coefficient.
The "2" in the first term is a constant.
The "x" in the second term is an exponent
Answers
Answer: The 9 in the second term is a coefficient that is true. I think that is the only thing that is true. There may be one more thing that is true.
The 10 in the third term is not a coefficient.
The 2 is not a constant
the x is not an exponent.
those are the ones that I'm sure about.
Please correct anything if i'm wrong.
:)
Which operation is the default operation in algebra?
Answers
Step-by-step explanation:
in mathematics, a basic algebra corporation is there any one of the traditional operation of arithmetic, which are addition, subtraction, multiply, division, rising to an integer power, and taking root (fractional power ).
If the captain has a 3/4 probability of hitting the ship and the pirate has a 1/4 probably what is the probability the pirate hits and the captain misses
Answers
Answer:
9/16
Step-by-step explanation:
captain has a 3/4 probability of hitting the ship
pirate has a 1/4 probability of hitting the ship
This means he has a 3/4 probability of missing the ship
P (captain hitting and pirate missing) = 3/4*3/4 = 9/16
A sinusoid is any function whose values repeat in a periodic manner.
A. True
B. False
SUBMIT
Answers
Answer: short answer
Just checked it’s False
Hope this helps :))
Step-by-step explanation:
Answer:
B. False
Step-by-step explanation:
A P E X
What value of b will cause the system to have an infinite number of solutions?
A system of equations. y equals 6 x plus b. negative 3 x plus StartFraction one-half EndFraction y equals negative 3.
A coordinate grid with a line labeled negative 3 x plus StartFraction one-half EndFraction y equals negative 3 and passes through the points (1, 0) and (0, negative 6).
-6
-3
3
6
Answers
Answer:
-6 on edge
Step-by-step explanation:
The value of b that causes the system of equations to have infinite solutions will be: b = -6
System with infinite solutions:A system of linear equations will have infinite solutions only when both equations represent the same line.
In this case our equations are:
y = 6x + b
-3x + (1/2)*y = -3
So the value of b needs to be such that these two equations are equal
Let's isolate y in the second equation:
(1/2)*y = -3 + 3x
y = -3*2 + 3x*2 = -6 + 6x
Then we must have:
6x - 6 = 6x + b
-6 = b
Thus, the value of b that causes the system to have infinite solutions is b = -6.
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What is the average rate of change of f over the interval [-1, 4] Give an exact number.
Answers
Answer:
1.4
Step-by-step explanation:
The average rate of change is the "rise" divided by the "run".
rise/run = (f(4) -f(-1))/(4 -(-1)) = (0 -(-7))/(4+1)
rise/run = 7/5 = 1.4
The average rate of change on the interval [-1. 4] is 1.4.
We will see that the average rate of change in the given interval is 1.4
How to find the average rate of change?
For a given function f(x), the average rate of change on an interval [a, b] is given by:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
In this case the interval is [-1, 4], using the graph we can see that:
f(-1) = -7
f(4) = 0
replacing that in the formula we get:
[tex]r = \frac{0 - (-7)}{4 - (-1)} = \frac{7}{5} = 1.4[/tex]
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IQ levels: A study investigated whether there are differences between the mean IQ level of people who were reared by their biological parents and those who were reared by someone else. What is the null hypothesis in this case
Answers
Answer:
The null hypothesis: there is no difference between the mean IQ level of people who were reared by their biological parents and those who were reared by someone else.
Step-by-step explanation:The null hypothesis can be a general statement mostly in statistics that proposes no difference or no relationship between 2 phenomena etc
Researchers always carry out a study to test against the null hypothesis ie the opposite of the null hypothesis showing that there is a difference. In this study, the researchers aim is to establish that there is a difference between the mean IQ level of people who were reared by their biological parents and those who were reared by someone else. This goes against the null which states that
there is no difference between the mean IQ level of people who were reared by their biological parents and those who were reared by someone else.
Kimberly goes on a road trip; her car gets 25 miles per gallon (mpg) and gas costs $3.24 per gallon. Let n represent the number of miles Kimberly has traveled since she started driving.
a. Suppose Kimberly has traveled 252 miles (n 252) since she started driving. i. How many gallons of gasoline has she used since she started driving? gallons Preview i. What is the cost of the gasoline that she has used since she started driving?
b. Write an expression in terms of n that represents the number of gallons of gasoline she has used since she started driving.
c. Write an expression in terms of n that represents the cost of the gasoline that she has used since she started driving.
Answers
Answer:
a) 10.08 gallons and $32.66 of gas
b) gallons used = n/25
c)cost of the gasoline = [tex]\frac{n}{25}(3.24)[/tex]
Step-by-step explanation:
a) We know that Kimberly has traveled 252 miles and we also know that her car gets 25 miles per gallon. We can apply proportions and rule of three:
25 miles ------ 1 gallon
252 miles ----- x gallons
Solving for x:
x gallons = 252 miles(1 gallon)/25 miles= 10.08 gallons.
Thus, she has used 10.08 gallons since she started driving.
Now we need to know the cost of the gasoline that she has used.
We know that each gallon of gas costs $3.24 and she has used 10.08 gallons. Again, we can apply proportions and rule of three:
1 gallon ------ 3.24 dollars
10.08 gallons---- x dollars.
Solving for x we get:
[tex]x=(10.08)(3.24)[/tex]= 32.659=32.66 dollars.
Thus, she has used $32.66 of gas since she started driving.
b) Write an expression in terms of n that represents the number of gallons of gasoline she has used since she started driving.
If we know that n is the number of miles that she drives, from what we wrote above, an expression to know the number of gallons she has used would be:
Gallons used = n/25 (since her car gets 25 miles per gallon) where n is the number of miles.
c) Write an expression in terms of n that represents the cost of the gasoline that she has used since she started driving.
Again, to know the cost of the gasoline we first need to know how many gallons she has used. From b) we know that the expression to know how many gallons she has used is n/25. Since each gallon costs $3.24 we will multiply this number by n/25 and we will get the cost (like we did in a))
Therefore, the cost of the gasoline = [tex]\frac{n}{25}(3.24)[/tex] where n is the number of miles.
The radius of a circle is 2.6 in. Find the circumference
to the nearest tenth.
Answers
Answer:
16.
Step-by-step explanation:
since given the radius and the formula of the circumference of a circle is 2pie*r