PLEASE HELP
The table above gives selected values for the differentiable function f. in which of the following intervals must there be a number c such that f’(c)=2 PHOTO ATTACHED
Answers
Answer:
C.
Step-by-step explanation:
We need to apply Mean Value theorem here.
We just need to calculate the average rate of change for each interval.
A) x=0 to x=4
We have the points (0,8) and (4,0) are the points that correspond to the endpoints of the given interval.
(8-0)/(0-4)
8/-4
-2
Not this choice
B) x=4 to x=8
We have the points (4,0) and (8,2) are the points that correspond to the endpoints of the given interval.
(2-0)/(8-4)
2/4
1/2
Not this choice
C) x=8 to x=12
We have the points (8,2) and (12,10) are the points that correspond to the endpoints of the given interval.
(10-2)/(12-8)
8/4
2
This one works.
D) x=12 to x=16
We have the points (12,10) and (16,1) are the points that correspond to the endpoints of the given interval.
(1-10)/(16-12)
-9/4
The table is an illustration of mean value theorem
\(\mathbf{f'(c) =2}\) on the interval (8,12)
If a function is differentiable, then:
\(\mathbf{f'(c) =\frac{f(b) - f(a)}{b - a}}\)
(a) (0,4)
This gives
\(\mathbf{f'(c) =\frac{f(4) - f(0)}{4 - 0}}\)
\(\mathbf{f'(c) =\frac{f(4) - f(0)}{4}}\)
From the table, we have:
\(\mathbf{f'(c) =\frac{0 - 8}{4}}\)
\(\mathbf{f'(c) =\frac{- 8}{4}}\)
\(\mathbf{f'(c) =-2}\)
(b) (4,8)
This gives
\(\mathbf{f'(c) =\frac{f(8) - f(4)}{8 - 4}}\)
\(\mathbf{f'(c) =\frac{f(8) - f(4)}{4}}\)
From the table, we have:
\(\mathbf{f'(c) =\frac{2-0}{4}}\)
\(\mathbf{f'(c) =\frac{2}{4}}\)
\(\mathbf{f'(c) =\frac{1}{2}}\)
(c) (8,12)
This gives
\(\mathbf{f'(c) =\frac{f(12) - f(8)}{12 - 8}}\)
\(\mathbf{f'(c) =\frac{f(12) - f(8)}{4}}\)
From the table, we have:
\(\mathbf{f'(c) =\frac{10-2}{4}}\)
\(\mathbf{f'(c) =\frac{8}{4}}\)
\(\mathbf{f'(c) =2}\)
Hence, \(\mathbf{f'(c) =2}\) on the interval (8,12)
Read more about mean value theorems at:
https://brainly.com/question/3957181
Related Questions
A chessboard has 64 squares on it. If each square is 1 inch by 1 inch, what is the area of the entire
chessboard covered by the squares?
Answers
Answer:
64 inches squared
Step-by-step explanation:
How do you find Exponential Decay Rate?
1+b
1-b
Answers
Answer:
Exponential decay is represented by the equation:
y = a * e^(-bx)
where:
y is the final value
a is the initial value
b is the decay rate
x is the time variable
The exponential decay rate, b, can be found by taking the natural logarithm (ln) of both sides of the equation, then rearranging to isolate the decay rate:
ln(y/a) = -bx
b = -ln(y/a)/x
So, to find the exponential decay rate, you would need to know the initial value (a), the final value (y), and the time elapsed (x). Then, you can use the formula above to calculate the decay rate, b.
The expressions "1+b" and "1-b" are not sufficient to find the exponential decay rate, as they do not contain enough information about the specific scenario or data set.
if this helps, can you please mark my answer brainliest?
you sailed 0.032 units to the left and found treasure at 0.248 units find where the ship started
Answers
Please answer ASAP I will brainlist
Answers
I can't really see the graph clearly but I think that the x-intercepts should be (-16/7, 0) and (32/7, 0).
Answer:
x-intercepts: -2, 4
Step-by-step explanation:
The given graph shows a parabola that opens downwards.
The y-intercept is the point at which the curve crosses the y-axis, so when x = 0. From inspection of the given graph, we can see that the parabola crosses the y-axis when y = 8. Therefore, the y-intercept is (0, 8).
The x-intercepts are the points at which the curve crosses the x-axis, so when y = 0. From inspection of the given graph, we can see that the parabola crosses the x-axis when x = -2 and x = 4. Therefore, the x-intercepts are (-2, 0) and (4, 0).
Charges for advertising on a TV show are based on the number of viewers, which is measured by the rating. The rating is a percentage of the population of 110 million TV households. The CBS television show 60 Minutes recently had a rating of 7.8, indicating that 7.8% of the households were tuned to that show. An advertiser conducts an independent survey of 100 households and finds that at least b+1 were tuned to 60 Minutes. Assuming that the 7.8 rating is correct, find the probability of surveying 100 randomly selected households and getting at least 5+1 tuned to
60 Minutes.
Answers
The probability of surveying 100 randomly selected households and getting 4 or fewer tuned to 60 minutes is only 0.02%.
How to calculate the probabilityP(X <= 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)
P(X = k) = (100 choose k) * 0.078^k * (1 - 0.078)^(100-k)
P(X <= 4) = (100 choose 0) * 0.078^0 * (1 - 0.078)^(100-0) + (100 choose 1) * 0.078^1 * (1 - 0.078)^(100-1) + (100 choose 2) * 0.078^2 * (1 - 0.078)^(100-2) + (100 choose 3) * 0.078^3 * (1 - 0.078)^(100-3) + (100 choose 4) * 0.078^4 * (1 - 0.078)^(100-4)
Using a calculator or software, we can find that:
P(X <= 4) = 0.000203
This means that the probability is 0.02%.
Learn more about probability on
https://brainly.com/question/24756209
#SPJ1
Charges for TV advertising on a TV show are based on the number of viewers, which is measured by the rating. The rating is the percentage of population of 110 million TV households.The CBS television show 60 minutes recently had a rating of 7.8, indicating that 7.8% of the household were tuned to that show.An advertiser conducts an independent survey of 100 households and finds that only 4 were tuned to 60 minutes. Assuming that the 7.8 rating is correct, find the probability of surveying 100 randomly selected households and getting 4 or fewer tuned to 60 minutes.Does the result suggest that the rating of 7.8 is too high?
PLEASE HELP IM GIVING BRAINLYEST FOR ANYONE WHO CAN AWNSER THIS!?!
For questions 1 – 10, find the slope of the line.
Answers
If I did this correct, it should be 7,5 hope ot helps
A bag contains 3 green marbles and 5 white marbles. Paul picks a marble at random from the
bag and does not put it back in the bag. He then picks another marble from the bag.
a. Construct a probability tree of the problem.
Answers
A probability tree is a visual representation of the possible outcomes of an event or series of events. In this case, the event takes a marble out of the bag.
How to create the tree?The first step in building a probability tree is to create a starting point that represents the first state of the problem. In this case, the starting point is a bag containing 3 green marbles and 5 white marbles.
The next step is to branch from the starting point and show the possible results of the first event. This includes taking out the marble out of the bag. The probability of getting a green marble is 3/8 and the probability of getting a white marble is 5/8.
After the first event, the issue status changes. In this case, the bag contains 2 green marbles and 4 white marbles.
The next step is to branch out from the state after the first event and show the possible outcomes of his second event involving pulling another marble out of his pocket. The probability of getting a green marble is 2/6 and the probability of getting a white marble is 4/6. The final step is to label the endpoints of the tree with the possible outcomes of the problem and the probabilities of each outcome.
The probability tree starts with an sack of 3 green marbles and 5 white marbles, as shown in the design showing the possible outcomes of selecting a marble, the new state of the sack after each selection, and the probability of each outcome
To know more about probability tree visit:
https://brainly.com/question/28916734
#SPJ1
Which statement is not one of the axioms of Euclidean geometry?
A. If two points lie in space, there is only one line that can pass through them.
B. If three points lie on the same line, there is only one plane that can pass through them.
C. If two points lie on a plane, the line containing them also lies on the plane.
D. If two planes intersect, their intersection is a line.
Answers
Answer:
B. if three points lie on the same line there is only one plane that can pass through them.
Step-by-step explanation:
10. Prime numbers from 1 to 100 are running a restaurant - PRIME SPOT, near a tourist point. On a winter holiday, 1 and the composite numbers up to 100 enter the restaurant for dinner after their picnic at the same point. The dining hall has tables with seating capacity 15 for each. If they occupy tables without leaving any chair free, how many tables are required? If each prime number attender has to serve equal number of customers, how many customers should each one get to serve?
Answers
6 tables are required. Each prime number attender should serve 3 customers each.
The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
All the numbers other than prime numbers are composite numbers.
The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.
Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.
Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables
Therefore, 6 tables are required.
Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.
Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.
Thus, each prime number attender should serve 3 customers each.
For more questions on prime number
https://brainly.com/question/145452
#SPJ8
Students in a classroom have eaten 20% of jellybeans from a jar. There are now only 100 jellybeans left! How many jellybeans
were in the jar to begin with?
Answers
Answer:
125 to start with
Step-by-step explanation:
Find the side length of a cube with a volume of 141 f3 If necessary, round your answer to the nearest tenth.
Answers
The side length of the cube is 5.6 feet (rounded to the nearest tenth).
We can calculate the side length of a cube with a volume of 141 cubic feet using the formula for cube volume , which is \(V = s^3\), where V is the volume and s is the side length.
We can calculate s by taking the cube root of both sides of the equation:
\(s = (V)^{(1/3)\)
Substituting V = 141, we get:
\(s = (141)^{(1/3)\)
By using a calculator to evaluate this expression, we may determine:
s ≈ 5.6
As a result, the cube's side length is roughly 5.6 feet (rounded to the closest tenth). This indicates that if we increase the side length by three, it will become longer. (\(s^3\)), we will get the volume of the cube, which is 141 cubic feet.
for such more question on length
https://brainly.com/question/20339811
#SPJ11
Please help me for 15 points
Answers
13 12 28 candy bars and 42 packs of gum were put in gift bags. The same number of candy bars and the same number of packs of gum were put in each bag. What is the greatest number of gift bags that could be made?
Answers
Answer:
Step-by-step explanation:
Please help me with find the product
Answers
Answer: 4a+6b=ab
Step-by-step explanation:
An investment portfolio is shown below.
Investment Amount Invested ROR
Money Market Account $3,200 2.1%
Government Bond $1,750 4.4%
Preferred Stock $1,235 −7.8%
Common Stock $2,300 10.5%
Using technology, calculate the difference between the arithmetic average ROR and the weighted average ROR. Round to the nearest tenth of a percent.
0.5%
1.1%
2.3%
3.5%
Answers
Using technology, the difference between the arithmetic average ROR and the weighted average ROR is 0.52%
What is arithmetic mean?The Arithmetic Mean will be called the Simple Arithmetic Mean when it is calculated as the quotient between the sum of all the different related values and the number of observations involved in this sum.
Given An investment portfolio
Since arithmetic average ROR:
The average arithmetic average ROR is the sum of the rate of returns divided by the number of investments arithmetic average:
ROR = (2.1%+ 4.4%+ 7.8% + 0.5%)/4
arithmetic average ROR=6.20%
total amount invested=$3200+$1750+$1235+$2,300
total amount invested=$8,485
weighted average:
ROR = (3200/8485 * 2.1%+ 1750/8485 * 4.4%+ 1235/8485 *7.8% + 2300/8485 *0.5%)
weighted average:
ROR=5.68%
difference=6.20%-5.68%
difference=0.52%
Learn more about ROR on:
brainly.com/question/28683603
#SPJ1
Answer: it’s 1.1%
Step-by-step explanation: just got it right on the test
Elsevier logo el Home
Find the area of the combined rectangles.
9 ml
1 2 3 4
The area is
11 ml
19 ml
square miles.
2 ml
8 ml
5
7 ml
Answers
To find the area of the combined rectangles, we need the dimensions (length and width) of each rectangle. However, the provided text and numbers do not seem to correspond to a clear description of the rectangles or their dimensions. Could you please provide more specific information or clarify the question?
Given m||n, find the value of x.
(7x-1)º
(9x+5)º
Answers
The value of x is 11 for the given condition that m||n.
What are parallel lines?Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.
Numerous pairs of angles are created whenever any two parallel lines are intersected by a third line known as a transversal. The other angles are supplementary while some are congruent (equal).
Angles on a straight line sum up 180°
Let us take the line t as our straight line
(7x – 1)° + (9x + 5)° = 180°
(7x + 9x + 5 – 1) = 180
16x + 4 = 180
16x = 180 – 4
16x = 176
(16x)/16 = (176/16)
x = 11
Hence, the value of x is 11.
Learn more about parallel lines here:
https://brainly.com/question/16701300
#SPJ1
The population of a city has increased by 35% since it was last measured. If the current population is 29,700 , what was the previous population?
Answers
Answer:
19305
Step-by-step explanation:
We simply take the percentage of 29700 to find how many people were added.
29700(0.35) = 10395 <== so 10395 people have been added
Subtract it from the current:
28700 - 10395 = 19305 people before.
Jennifer is a lifeguard at the same pool. She earns $137.25 for 15 hours of lifeguarding how much does Jennifer earn per hour?
Answers
Jennifer earns $9.15 per hour as a lifeguard at the pool.
Given that,
Jennifer is a lifeguard at the same pool. She earns $137.25 for 15 hours of lifeguarding how much does Jennifer earn per hour is to be determined.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
She earned $137 in 15 hours,
Per hour earning = 137 / 15 = $9.15
Thus, Jennifer earns $9.15 per hour as a lifeguard at the pool.
Learn more about simplification here:
https://brainly.com/question/12501526
#SPJ2
3^4 x 10^6
What is the answer ??
Answers
p(x)=5x^4+7x^3-2x^2-3x+c divided by (x+1)
Answers
The remainder is 5 + c, which means that the expression P(x) = \(5x^4 + 7x^3 - 2x^2 - 3x + c\) divided by (x + 1) results in a quotient of\(5x^3 + 2x^2 - 4x + 4\) and a remainder of 5 + c.
To divide the polynomial P(x) = \(5x^4 + 7x^3 - 2x^2 - 3x + c\) by the binomial (x + 1), we can use polynomial long division.
Let's set up the long division:
\(5x^3 + 2x^2 - 4x + 4\)
_______________________
x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)
We start by dividing the highest degree term of the dividend (5x^4) by the divisor (x + 1), which gives us 5x^3. We then multiply this quotient by the divisor (x + 1) and subtract it from the dividend:
\(5x^3(x + 1)\)
_______________________
x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)
- (\(5x^3 + 5x^2)\)
This leaves us with a new polynomial:\(2x^3 - 7x^2 - 3x + c\). We repeat the process by dividing the highest degree term of this polynomial (2x^3) by the divisor (x + 1), resulting in 2x^2. We then multiply this quotient by the divisor and subtract it from the polynomial:
\(5x^3(x + 1) + 2x^2(x + 1)\)
_______________________
x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)
-\((5x^3 + 5x^2)\)
_______________________
\(2x^2 - 3x + c\)
We continue this process until we reach the constant term, resulting in the remainder of the division.
At this point, we have:
\(5x^3(x + 1) + 2x^2(x + 1)\)
_______________________
x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)
- \((5x^3 + 5x^2)\)
_______________________
\(2x^2 - 3x + c\)
-\((2x^2 + 2x)\)
_______________________
- 5x + c
- (-5x - 5)
_______________________
5 + c
For more such questions on remainder visit:
https://brainly.com/question/29347810
#SPJ8
Which car’s price is less than 2 times the price of Car 1?
Answers
Answer:
car 2
Step-by-step explanation:
2×car1 = $30,000
car2 costs less than $30,000
Original price of a sled: $99.50
Discount: 50%
Answers
Answer:
49.75
Step-by-step explanation:
1/2 (50%) of 99.50 is 49.75
which of the following sets represents the tangeof the function shown? {(-3,4),(5,11),(9,-1),(10,13)}
Answers
Explanation:
The range is the set of y outputs of a relation. So we just list the y coordinates of the points shown.
We could sort the values to get {-1, 4, 11, 13}, but order doesn't matter in a set. So this step is optional.
HELP ASAP HELP ASAP
A map has a scale of 3 cm:20 km. If two cities are 6 cm apart on a map,
how far are the cities actually apart?
6 cm
3 cm
20 km
x km
Cross multiply and solve for "x."
А
30 km
B
40 km
С
60 km.
D
100 km
Answers
At the city museum, child admission is $5.50 and adult admission is $9.90. On Saturday , 146 tickets were sold for a total sales of 1216.60 How many adult ckets were sold that day?
Answers
84 adult tickets were consequently sold on that day.
To solve this problemLet's fix this issue using a set of equations. Let x represent how many adult tickets were sold, and y represent how many kid tickets were sold.
We learn the following from the issue:
Total number of tickets sold = x + y
Total sales equal 9.9x + 5.5y = 1216.6.
To find y, we can utilize the first equation:
y = 146 - x
We obtain the following by substituting this into the second equation: 9.9x + 5.5(146 - x) = 1216.6
The result of simplifying and finding x is: 4.4x = 369.6 x = 84
Therefore, 84 adult tickets were consequently sold on that day.
Learn more about equations here : brainly.com/question/25976025
#SPJ1
Kevin drove 18 1/2 miles in 2/3 hours. If he drove at a constant rate, how far did he travel in one hour
Answers
Answer:
27.75 miles
Step-by-step explanation:
(18 1/2 miles) / (2/3 hours) = (37/2 miles) × (3/(2 hours)) = 111/4 miles/hour
111/4 miles/hour = 27.75 miles/hour
Answer: 27.75 miles
Jeremy spent $33 on 3 CDs. At This rate. how much would 6 CDs cost ?
Answers
33/3=11.
It costs $11 per CD.
6*11=66.
It would be $66 for 6 CDs.
Answer:
It would cost Jeremy $66 for 6 CDs
Step-by-step explanation:
3 CDs for $33
3(2)=6
$33(2)=$66
The function C gives the production cost for a bakery to produce cakes of a certain type, where C(x) is the cost, in dollars, to produce x of the cakes. The function M defined by M(x)=C(x+1)−C(x) gives the marginal cost, in dollars, to produce cake number x+1. Which of the following gives the best estimate for the marginal cost, in dollars, to produce the 40th cake?
Answers
Answer:
To find the marginal cost, in dollars, to produce the 40th cake, you can use the function M(x) = C(x+1) - C(x). Substituting 40 for x in this function gives:
M(40) = C(40+1) - C(40)
This expression represents the cost to produce the 41st cake minus the cost to produce the 40th cake, which is the marginal cost of producing the 40th cake. To find the best estimate for this marginal cost, you would need to know the values of C(41) and C(40) and substitute them into the expression above. Without knowing these values, it is not possible to determine the marginal cost of producing the 40th cake.
Step-by-step explanation:
Two data sets are summarized in the box plots shown.
Plot A
Plot B
H
H>
9 10 11 12 13 14
4 5
6
7
8
9 10 11 12 13 14 15 16
45
6
Z
8
Which statements comparing the two box plots are correct? Choose all the correct statements.
A. The mean of plot B is greater than the mean of plot A.
B. The range of plot B is greater than the range of plot A.
C. The median of plot B is the same as the median of plot A.
D. The interquartile range of plot B is the same as the interquartile range of plot A.
Answers
Answer: A,D
Step-by-step explanation:
I took the test