Given the following information about f(x) and f '(x), determine which points are local minimums. f(-1) = -1, f(1) = 2, f(2) = 0 f '(-1) = 0 and f '(1) = 0 and f '(2) = undefined Note: f '(x) > 0 on - 1 < x < 1 or x > 2 Note: f '(x) < 0 on x < -1 or 1 < x < 2
Answers
The only local minimum of f(x) is at x = -1.
To determine the local minimums of f(x), we need to find the points where the derivative f '(x) changes sign from negative to positive. From the given information, we know that f '(x) < 0 on the interval x < -1 or 1 < x < 2, and f '(x) > 0 on the interval -1 < x < 1 or x > 2.
At x = -1, we have f '(-1) = 0, which means that the derivative changes sign from negative to positive at this point. Therefore, f(-1) = -1 is a local minimum.
At x = 1, we have f '(1) = 0, but the derivative does not change sign at this point. Therefore, f(1) = 2 is not a local minimum.
At x = 2, we have f '(2) = undefined, which means that the function is not differentiable at this point. Therefore, we cannot determine whether f(2) = 0 is a local minimum or not.
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Related Questions
How many gallons of a 50% antifreeze solution must be mixed with 80 gallons of 10% antifreeze to get a mixture that is 40% antifreeze?
Answers
240 gallons of a 50% antifreeze solution must be mixed with 80 gallons of 10% antifreeze to get a mixture that is 40% antifreeze.
Let's call the amount of 50% antifreeze solution that we want to mix with the 80 gallons of 10% antifreeze "x".
The total volume of the mixture after mixing x gallons of 50% antifreeze solution with 80 gallons of 10% antifreeze solution is given by (x + 80) gallons.
The concentration of antifreeze in the mixture is given by the weighted average of the antifreeze concentrations in the two solutions, where the weight for each solution is proportional to its volume:
(0.5x) + (0.1 * 80) = (0.4 * (x + 80))
Expanding and solving for x, we get:
0.5x + 8 = 0.4x + 32
0.1x = 24
x = 240
Therefore, we need to mix 240 gallons of 50% antifreeze solution with 80 gallons of 10% antifreeze solution to get a mixture that is 40% antifreeze.
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Lab 1: Statistics Homework Assignment The following assignment is designed to give you more practice interpreting data. Refer to Lab 3 if you have any questions. You must show ALL your work 'organized' on a separate sheet of paper and have complete answers (ANSWER THE WHY/WHAT PART OF THE QUESTIONs). Part 1: The General Biology final was difficult for the 30 students. Use the scores below to answer questions 1 through 6. (1). You, as the teacher, wish to group the students into categories to create a histogram for the data Bins =(40−49,50−59,60−69,70−79,80−89). Create a histogram (Figure) of the data set with properly labeled axes and caption. Are the data normally distributed, skewed right, or skewed left? How do you know? (2). Calculate the Mean and Median values for the data set (show your work!!!). Are the two values the same? Why or why not? (3). State the Range for the data set. (4). Calculate the Standard Deviation. What does this value tell you about how the data points are related to the estimated mean? (5). Calculate the Standard Error of the Mean. What does this value tell you about your estimation of the true mean? (6). Calculate the Confidence Limits. What does this value tell you about your mean? Part 2: Use an online calculator (https://www.graphpad.com/quickcalcs/ttest1/) to calculate descriptive statistics and run a student t-test (7) State a null and alternative hypothesis (8) Record the means, SD (standard deviation), SEM (standard error of means), calculated t, and p-value, and use the provided t-table to find the t-table value. (do not just send me a printout or screen shot) (9) Interpret your results (t-value) using the sentence format from page 8. (10) Provide a 3-4 sentence explanation of the results. What are the tradeoffs for different leaf size?
Answers
(2) The values of mean and median are not the same because the distribution of data is skewed right. (3) The value of Range is 40.
(2) Mean and Median values for the given data set are:
Mean = $\frac{1880}{30}$ = 62.67Median = (60 + 62) / 2 = 61
The values of mean and median are not the same because the distribution of data is skewed right.
(3) Range = Maximum value – Minimum value
Range = 81 - 41 = 40
(4) Standard deviation for the given data can be calculated by using the following formula:
\(\(s=\sqrt{\frac{\sum_{i=1}^{n}(x_{i}-\overline{x})^{2}}{n-1}}\)\)
The calculated standard deviation is s = 11.38.
This value tells that how much the data points deviate from the estimated mean.
(5) Standard Error of Mean (SEM) can be calculated using the following formula:
SEM = $\frac{s}{\sqrt{n}}$The calculated SEM is 2.07.
This value tells about the accuracy of the estimated mean.
(6) Confidence Limits can be calculated as:
Confidence limits = $\overline{x}$ ± (t)(SEM) = 62.67 ± (2.045)(2.07)
Confidence limits = (58.57, 66.77)
This value tells about the range in which the true mean is expected to lie.
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2. A recipe calls for 2 3/4
Cups of milk. How much is this in mL?
Answers
The hypotenuse of a right triangle measures 3 cm and one of its legs measures 2 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answers
The required length of the other leg is \($\sqrt{5}$\) cm. If we need to round to the nearest tenth, we get: \($b \approx 2.2$\) cm
How to use Pythagoras theorem to find sides of right angled triangle?Let's use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. So we have:
\($c^2 = a^2 + b^2$\)
where c is the length of the hypotenuse, a and b are the lengths of the legs.
We are given that the length of the hypotenuse is 3 cm and the length of one leg is 2 cm. Let's substitute these values into the equation above:
\($3^2 = 2^2 + b^2$\)
\($9 = 4 + b^2$\)
\($b^2 = 5$\)
\($b = \sqrt{5}$\)
So the length of the other leg is \($\sqrt{5}$\) cm. If we need to round to the nearest tenth, we get: \($b \approx 2.2$\) cm (rounded to one decimal place).
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Find the lowest common denominator (multiple). Type the equivalent fractions. Then, add or subtract. Simplify your answer. 1
2
1
3
Answers
Answer:what
Step-by-step explanation:what does this mean
Important Please Help!!!!
Answers
Answer:
angle bisector
Step-by-step explanation:
the construction shows an angle bisector.
the line EG bisects ∠ FED
what dx gets doxy no matter what age?
Answers
It is important to consult a healthcare provider to determine if doxycycline is appropriate for a particular individual, regardless of their age.
Doxycycline is a broad-spectrum antibiotic that is used to treat a variety of bacterial infections. However, there are certain medical conditions and factors that may contraindicate the use of doxycycline.
Some of the common medical conditions that may prevent the use of doxycycline include:
Allergy or hypersensitivity to doxycycline or other tetracycline antibiotics.
Severe liver disease or impairment.
Pregnancy or breastfeeding.
Children under the age of 8 (because doxycycline can cause permanent discoloration of teeth and affect bone growth).
Kidney disease, because doxycycline is excreted through the kidneys and may accumulate to toxic levels.
In general, the use of doxycycline is based on the patient's medical history, the severity of the infection, and other factors such as age and weight. Therefore, it is important to consult a healthcare provider to determine if doxycycline is appropriate for a particular individual, regardless of their age.
Complete question : It is important to consult a healthcare provider to determine if doxycycline is appropriate for a particular individual, regardless of their age. what dx gets doxy no matter what age?
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URGENT PLEASE HELP!!
7 = 2k + 1
Step 1:
Subtract
from each side.
Step 2:
Divide each side into
groups.
Show work:
Answers
Answer:
k = 3
Step-by-step explanation:
Subtract that one from the right side and then from the left side, so the equation should now look like (6 = 2k). Now you need to make the k be by itself to find what number it represents. So divide 2k by 2 and 6 by 2. So now the equation should look like (3 = k). (k = 3)
popular magazine tests cars and trucks for mileage on the road and around the city. the magazine reports that 50% of the cars tested had mileages below 24.7 mpg on the road, and the other 50% of the cars tested had mileages above 24.7 mpg. which statistic does this 24.7 represent? question 9 options: the interquartile range (iqr) of the gas mileages for the cars tested. the mode of the gas mileages for the cars tested. the median of the gas mileages for the cars tested. the mean of the gas mileages for the cars tested.
Answers
The statistic that the value 24.7 represents in this context is the median of the gas mileages for the cars tested.
Popular magazine that tests cars and trucks for mileage on the road and around the city. They report that 50% of the cars tested had mileages below 24.7 mpg on the road, and the other 50% had mileages above 24.7 mpg. The 24.7 mpg statistic represents the median of the gas mileages for the cars tested. This is because the median is the middle value when the data is arranged in ascending order, and in this case, it separates the lower 50% from the upper 50% of the mileages.
The median is the value that separates the data set into two halves. In this case, the magazine reports that 50% of the cars tested had mileages below 24.7 mpg on the road and the other 50% of the cars tested had mileages above 24.7 mpg. This means that 24.7 mpg is the exact middle value of the distribution of the gas mileages for the cars tested.
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If x = 3 and y = 5 then which of the following expression has the value ( -8)
Answers
당신에게 도움이됩니다
\(( - 3) - 5 \\ = ( - 8)\)
the term to term rule is half then add 10 the 2nd term of the sequence is 44 wok out the 1st term
Answers
The first term of the sequence is 68.
How to find the first term of the sequence?The term to term rule of a sequence is halve then add 10.
The 2nd term of the sequence is 44.
Therefore, the first term of the sequence can be calculated as follows:
let
the first term = x
Hence, the rule to get the next term in the sequence is as follows:
1 / 2 x + 10 = 44
1 / 2 x = 44 - 10
1 / 2x = 34
cross multiply
x = 34 × 2
x = 68
Therefore, the first term is 68.
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Both the ranges and the interquartile ranges for the data sets are the same.
Neither the ranges nor the interquartile ranges for the data sets are the same.
The interquartile ranges for the box plots are the same, but their ranges are different.
The ranges for the box plots are the same, but their interquartile ranges are different.
Answers
Answer:
to find range of interquartile sets of data
you see 5 vertical lines 1 is start point 2 is start of 2nd quartile 3 is start of 3rd quartile and also represents the median. the 4th start of 4th quartile and 5th is very end point.
Therefore the interquartile is from start line 2 to start line 4
apply to each by if it says 10 and 34 then we show workjings 34-10 = 24 and that is the range once we deduct data from each other.
Therefore full range is start line 1 to end line 5
if this says 2 to 45 then full range is 45-2 = 43 and apply to each boxplot.
Step-by-step explanation:
please help me solve this and what are the answers
Answers
Answer:
5y=-2x - 3x
5y = -5x
5y + 5x = 0
5(y + x ) = 0
maybe
Which of the following correctly expresses the limit lim n rightarrow infinity sigma i = 1 to n i^4/n^5 , as a definite integral? Integral 0 to 1 x^4 dx integral 1 to 2 x^3 dx integral 1 to 2 x^2 dx integral 0 to 1 x^2 dx integral 1 to 2 x^4 dx integral 0 to 1 x^3 dx
Answers
The answer is integral 0 to 1 x^4 dx. To convert the sum to a definite integral, we use the fact that the width of each rectangle in the sum is 1/n and the height is i^4/n^5. We can write this as i^4/n^4 * 1/n, which can be interpreted as the area of a rectangle with base 1/n and height i^4/n^4.
Taking the limit as n goes to infinity, we can see that the sum becomes the definite integral of x^4 dx from 0 to 1. This is because the height of the rectangles approaches the value of the function at the left endpoint of each interval (since the intervals have width 1/n and we are taking the limit as n goes to infinity).
So the long answer is:
lim n rightarrow infinity sigma i = 1 to n i^4/n^5
= lim n rightarrow infinity (1/n) * sigma i = 1 to n i^4/n^4
= integral 0 to 1 x^4 dx
To find the definite integral that represents the limit, you need to convert the given limit of a Riemann sum to a definite integral using the following formula:
lim n→∞ Σ(i=1 to n) [f(a + iΔx)]Δx = ∫(a to b) f(x) dx
In this case, the function f(x) is x^4, Δx is 1/n, and the interval [a, b] is [0, 1]. So, the definite integral representing the limit is:
∫(0 to 1) x^4 dx
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a) simplify 4 x 5p
b) simplify 9y-6y + y
Answers
Answer:
20p & 4y
Step-by-step explanation:
combine like terms yk
Help! I got 3,593 but that doesn’t make sense
Answers
Because the number increase by a percentage this is an exponential growth problem.
The equation for exponential growth is :
Total = start value x ( 1 + percent) ^ time
Using the information from the problem:
2011-2005 = 6 years.
Total = 23 x (1 + 0.72)^6
Total = 23x 1.72^6
Total = 595.52 = 596 total people
If ∫0-4f(x)dx=−2 and ∫2-3g(x)dx=−3 , what is the value of ∫∫Df(x)g(y)dA where D is the square: 0≤x≤4, 2≤y≤3
Answers
The value of the double integral is 6.
To find the value of the double integral, we need to use Fubini's theorem to switch the order of integration. This means we can integrate with respect to x first and then y, or vice versa.
Using the given integrals, we know that the integral of f(x) from 0 to 4 is equal to -2. We also know that the integral of g(x) from 2 to 3 is equal to -3.
So, we can start by integrating g(y) with respect to y from 2 to 3, and then integrate f(x) with respect to x from 0 to 4.
∫∫Df(x)g(y)dA = ∫2-3∫0-4f(x)g(y)dxdy
We can use the given values to simplify this expression:
∫2-3∫0-4f(x)g(y)dxdy = (-2) * (-3) = 6
Therefore, the value of the double integral is 6.
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Assuming that the set of integers is closed under addition, prove that the set of integers that are multiples of 5 is closed under addition. (b) Is the set of integers that are not multiples of 5 closed under addition? Justify your answer with one or two sentences. (c) In JFLAP, construct a DFA over the alphabet {a,b} that recognizes the language {w∣∣w∣ is a multiple of 5} and that has at most 6 states. Along with the JFLAP diagram, include a brief description (in English) of why each state is included and why you chose to make each state either accepting or non-accepting.
Answers
The set of integers that are not multiples of 5 is not closed under addition.
(a) To prove that the set of integers that are multiples of 5 is closed under addition, we need to show that if we take any two integers that are multiples of 5, their sum will also be a multiple of 5.
Let's assume that we have two integers, a and b, which are both multiples of 5. This means that a = 5n and b = 5m, where n and m are integers.
Now, let's find the sum of a and b: a + b = 5n + 5m = 5(n + m).
Since (n + m) is also an integer, we can see that a + b is a multiple of 5.
Therefore, the set of integers that are multiples of 5 is closed under addition.
(b) The set of integers that are not multiples of 5 is not closed under addition. To justify this, we can provide a counterexample.
Let's take the integers 2 and 3, which are not multiples of 5. Their sum is 2 + 3 = 5, which is a multiple of 5.
Since we found a sum that is a multiple of 5, but the two integers were not multiples of 5, we can conclude that the set of integers that are not multiples of 5 is not closed under addition.
(c) Unable to provide a JFLAP diagram as I am a text-based bot. However, to construct a DFA over the alphabet {a,b} that recognizes the language {w∣∣w∣ is a multiple of 5} and that has at most 6 states, you can follow these steps:
1. Start with an initial state.
2. Create 5 more states to represent the remainder when dividing the length of the input string by 5.
3. For each state, determine the transitions based on the next input symbol. For example, if the current state represents a remainder of 0 and the next input symbol is 'a', transition to the state that represents a remainder of 1.
4. Designate one state as the accepting state, which represents a remainder of 0 when the entire input has been read.
5. Make all other states non-accepting.
6. Connect all states with transitions for both 'a' and 'b' inputs.
7. Ensure that the DFA transitions to the accepting state when the entire input has been read and the remainder is 0.
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The formula to compute a person's body mass index is B= 703x w/h2. B represents the body mass index, is the person's weight in pounds and represents the person's height in inches.
a. Solve the formula for w.
b. Find the weight to the nearest pound of a person who is 64 inches tall and has a body mass index of 21.45.
Answers
a. The formula B = 703w/h^2 can be solved for w by rearranging the equation as w = B * h^2 / 703.
b. For a person who is 64 inches tall and has a body mass index of 21.45, the weight can be calculated by substituting the values into the formula w = B * h^2 / 703, where B is 21.45 and h is 64 inches.
a. To solve the formula B = 703w/h^2 for w, we can rearrange the equation to isolate w on one side of the equation. Multiply both sides of the equation by h^2, then divide both sides by 703. The resulting equation is w = B * h^2 / 703.
b. To find the weight of a person who is 64 inches tall and has a body mass index of 21.45, we can substitute the values into the formula w = B * h^2 / 703. In this case, B is 21.45 and h is 64 inches. Plugging these values into the equation, we get w = 21.45 * 64^2 / 703. Evaluating this expression will give us the weight in pounds.
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7. Mr. Grover bought a house for ₹30,00,000 in the year 2000. In 2004, the price of that house increased by 10%. In the year 2008, the price increased further by 20%. Calculate the price of the house at the end of 2008.
Answers
The price of the house at the end of 2008 will be 39,60,000
We must determine the price following each rise in order to determine the cost of the house at the end of 2008.
First of all, in 2004 the price jumped by 10%.
10% of 30,00,000 = 0.1 x 30,00,000 = 3,00,000
As a result, the house's new price in 2004 was:
30,00,000 + 3,00,000 = 33,00,000
The price then rose by 20% in 2008.
20% of 33,00,000 = 0.2 x 33,00,000 = 6,60,000
The home's total price at the end of 2008 was therefore: 33,00,000 + 6,60,000 = 39,60,000.
As a result, the house cost 39,60,000 at the end of 2008.
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2 7/4 - 7 3/8
○ 10 1/8
○ 10 9/8
○ 11 1/8
○ 11 7/8
Answers
Answer:
no choise
Step-by-step explanation:
=54/8-73/8
=-19/8
so no choise
Frank keeps his pet iguana in a glass tank that is shaped like a rectangular prism.
The height of the tank is 11 inches, the width is 34.5 inches, and the length is 25 inches.
What is the best estimate for the volume of the tank in cubic feet?
Remember 12 inches = 1 foot.
A. 4 ft3
B. 6 ft3
C. 9 ft3
D. 12 ft3
Answers
Answer: D. 12 ft3
Step-by-step explanation:
Find the volume of the solid above the region D={(x,y): 05 xs 39, os ys 39-x2} and between the planes z=39-y, z=0.
Answers
The volume of the solid above the region D, bounded by the planes z = 39 - y and z = 0, can be found using a triple integral. By integrating over the region D and between the two given planes, we can calculate the volume.
To find the volume, we set up the triple integral as follows: ∭ D (39 - y) dA, where D represents the region in the xy-plane bounded by the inequalities 0 ≤ x ≤ 39 and 0 ≤ y ≤ 39 - x^2, and dA represents the differential area element.
The integration is done in the order dzdydx. The limits of integration for z are from 0 to 39 - y, the limits for y are from 0 to 39 - x^2, and the limits for x are from 0 to 39. By evaluating this triple integral, we can find the volume of the solid.
The second paragraph can be the detailed calculation of the triple integral, but due to the word limit, I am unable to provide that here. The process involves solving the triple integral iteratively, integrating with respect to z first, then y, and finally x, while respecting the given limits. The evaluation of the integral will give the exact volume of the solid above the region D and between the two planes z = 39 - y and z = 0.
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True/False based on the t-test assuming equal variances on the t-testequal worksheet, it is reasonable to assume that the variances are equal?
Answers
Based on the t-test assuming equal variances a. Examining the ratio of the variances, it is reasonable to conclude that the variances are unequal."
It is vital to establish whether or not the variances of the two groups being compared are indeed identical before performing a t-test under the assumption of equal variances. This is significant since the t-calculation statistic depends on the assumption that variances are equal.
One can look at the ratio of the variances between the two groups to evaluate the assumption of equal variances. Typically, it is acceptable to infer that the variances are not equal if the ratio of the variances is more than two or lower than half. One can presume that the variances are equal in the absence of such proof. Since the variances are not equal, it is not logical to infer that they are.
Complete and correct Question:
Based on the t-test assuming equal variances on the T-Test Equal worksheet, is it reasonable to assume that the variances are equal?
a. Examining the ratio of the variances, it is reasonable to conclude that the variances are unequal.
b. Whether the variances are equal or not is not relevant for this situation.
c. Examining the ratio of the variances, it is reasonable to conclude that the variances are equal.
d. It is impossible to determine if the variances are equal given the data we have.
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A home has a rectangular kitchen. If listed as ordered pairs, the corners of the kitchen are (8, 4), (−3, 4), (8, −8), and (−3, −8). What is the area of the kitchen in square feet?
20 ft2
46 ft2
132 ft2
144 ft2
Answers
If the corners of the kitchen are (8, 4), (−3, 4), (8, −8), and (−3, −8), the area of the kitchen is 132 square feet. So, the correct option is C.
To find the area of the rectangular kitchen, we need to use the formula for the area of a rectangle, which is A = L x W, where A is the area, L is the length, and W is the width.
From the given ordered pairs, we can determine the length and width of the rectangle. The length is the distance between the points (8,4) and (-3,4), which is 8 - (-3) = 11 feet. The width is the distance between the points (8,4) and (8,-8), which is 4 - (-8) = 12 feet.
Now that we know the length and width, we can find the area by multiplying them together:
A = L x W = 11 x 12 = 132 square feet
Therefore, the correct answer is C.
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Answer C. 132 fT2
Step-by-step explanation:
(please help!!!) For each subject, choose an appropriate scale for a drawing that fits on a regular sheet of paper. Not all of the scale on the list will be used.
Answers
Answer:
590
Step-by-step explanation:
What is the radius of a hemisphere with a volume of 8231 cm", to the nearest tenthof a centimeter?
Answers
Answer:
The radius of the Hemisphere is 15.8 cm.
\(r=15.8\operatorname{cm}\)Explanation:
The formula for the volume of an hemisphere can be written as;
\(V=\frac{2}{3}\pi r^3\)Given that the volume of the hemisphere is;
\(8231\operatorname{cm}^3\)We can get the radius of the hemisphere using the formula above.
Firstly let us make r the subject of formula;
\(\begin{gathered} V=\frac{2}{3}\pi r^3 \\ \text{multiply through by 3/2} \\ \frac{3}{2}V=\pi r^3 \\ \text{divide through by pi} \\ \frac{3}{2}\frac{V}{\pi}=r^3 \\ \text{cube root both sides} \\ \sqrt[3]{\frac{3}{2}\frac{V}{\pi}}=r \\ r=\sqrt[3]{\frac{3}{2}\frac{V}{\pi}} \end{gathered}\)Lastly let us substitute the given volume V into the derived formula for radius r.
\(\begin{gathered} r=\sqrt[3]{\frac{3}{2}\frac{V}{\pi}} \\ r=\sqrt[3]{\frac{3\times8231}{2\times\pi}}=\sqrt[3]{\frac{24693}{2\times\pi}} \\ r=15.78\operatorname{cm} \\ r=15.8\operatorname{cm}\ldots\ldots.(to\text{ the nearest tenth of a centimeter)} \end{gathered}\)Therefore, the radius of the Hemisphere is 15.8 cm.
\(r=15.8\operatorname{cm}\)here is a easy question :- if -25/5 x p/q =1 , then p/q is equal to ?
Answers
9514 1404 393
Answer:
-1/5
Step-by-step explanation:
Divide by the coefficient of p/q:
-25/5 × p/q / (-25/5) = 1 / (-25/5)
p/q = -5/25
p/q = -1/5 . . . . in reduced form
Manny is watching the past three seasons of a The Big Bang Theory. He watched 8
episodes in 6 hours. At this rate, how many episode will he watch in 15 hours?
90
48
20
3.2
Answers
Answer:
20 episodes
Step-by-step explanation:
In the 21st century, people measure length in feet and meters. At various points in history, people measured length in hands, cubits, and paces. There are 9 hands in 2 cubits. Write an equation to express the relationship between hands, LaTeX: hh, and cubits, LaTeX: cc. Explain your reasoning under your equation.
Answers
Answer: 1 hand = 0.22... cubits.
Step-by-step explanation:
We want to write the relation between hands and cubits.
We know that there are 9 hands in 2 cubits.
So we can write:
9 hands = 2 cubits.
Now, we want to have an unit in the left side (so we can see how many cubits are equal to exactly one hand).
Then we can divide by 9 in both sides of the equality.
(9 hands)/9 = (2 cubits)/9
1 hand = 0.22... cubits.
Answer:
22.5 hands = 3 paces
Step-by-step explanation:
Nobody answered b yet again.