If
f(x) = ax ³ + bx ² - 5x + 9
then
f '(x) = 3ax ² + 2bx - 5
Given that f (-1) = 12 and f '(-1) = 3, we get the system of equations
-a + b + 5 + 9 = 12
3a - 2b - 5 = 3
or
-a + b = -2
3a - 2b = 8
Multiply through the first equation by 2 and add it to the second one to eliminate b and solve for a :
2(-a + b) + (3a - 2b) = 2(-2) + 8
-2a + 2b + 3a - 2b = -4 + 8
a = 4
Substitute this into the first equation above to solve for b :
-4 + b = -2
b = 2
Answer is a = 4, b = 2.
First derivative of an equation:
The derivative formula is one of the basic concepts used in calculus and the process of finding a derivative is known as differentiation. The derivative formula is defined for a variable 'x' having an exponent 'n'. The exponent 'n' can be an integer or a rational fraction. Hence, the formula to calculate the derivative is:
[tex]\frac{d}{dx} x^{n} = n x^{n-1}[/tex]
(Given)
[tex]f(x) = ax^{3} + bx^{2} - 5x + 9[/tex]
And f'(x) we get , [tex]f'(x) = 3ax^{2} + 2bx-5[/tex]
Now, also given f(-1) = 12
=> [tex]f(-1) =a (-1)^{3} + b(-1)^{2} - 5 (-1) + 9[/tex]
=> 12 = -a + b +5 + 9
=> a = b + 2 ------( 1 )
Also given, f'(-1) = 3.
i.e., [tex]3 = 3a(-1)^{2} + 2b(-1) - 5[/tex]
3 = 3a -2b -5
From eq - (1) we can replace a.
3 = 3(b + 2) - 2b - 5
3 = 3b + 6 - 2b - 5
b = 2.
a = 4.
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Can someone please help me ?
Answer:
Um, I feel like I don't have enough info to solve this
Step-by-step explanation:
Say me how to on chulla
Evaluate: x + (x2 - xy) - y
if x = 5 and y = 4
When x = 5 and y = 4, the expression [tex]x + (x^2 - xy) - y[/tex] evaluates to 6.
To evaluate the expression [tex]x + (x^2 - xy) - y[/tex] when x = 5 and y = 4, we substitute the given values into the expression and perform the
calculations:
[tex]x + (x^2 - xy) - y\\x= 5 + (5^2 - 5*4) - 4\\x= 5 + (25 - 20) - 4\\x= 5 + 5 - 4\\x= 10 - 4\\x= 6\\[/tex]
It's crucial to remember that the expression in question is not an equation that represents a graph, nevertheless. It is merely an algebraic expression that, given the values of "x" and "y," evaluates to a single value. We need an equation that connects 'x' and 'y' and specifies the relationship between them if we are to construct a graph.
Therefore, when x = 5 and y = 4, the expression [tex]x + (x^2 - xy) - y[/tex] evaluates to 6.
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Correct Question is:
Evaluate: [tex]x + (x^2 - xy) - y[/tex] if x = 5 and y = 4.
help me with this please!!! :)
Answer:
C. 4x-4
Step-by-step explanation:
If you divide by 4 on the left side you get...
16x/4 - 16/4
4x - 4
We are dividing by 4 because it was factored out of the expression.
The Mean Corporation would like to invest in the booming health food industry. It is considering the creation of a health-drink franchise called Goose Juice. The investment department of the Mean Corporation wants to investigate the feasibility of this venture by examining the profits of similar franchises. It believes that the venture will be feasible if an average annual profit of more than $85,000 can be expected from each Goose Juice that is opened. It is known that the annual profits earned by health-drink franchises has a population standard deviation of $8,700.
The Mean Corporation's statisticians would like to construct a hypothesis test for the population mean annual profit earned by health-drink franchises. A random sample of 50 franchises was chosen and their annual profit for the previous financial year was recorded. The mean annual profit for the sample was calculated as $82,441.
The hypotheses that were used by the statisticians were
Null hypothesis: population mean = 81,000, Alternative hypothesis: population mean > 81,000 and the test statistic was found to be 1.29 (to 2 decimal places).
Required:
Calculate the p-value for this test, giving your answer as a decimal to 4 decimal places.
Answer:
The p-value is approximately 0.9015
Step-by-step explanation:
The statistic parameters are;
The population mean, μ₀ = $85,000
The population standard deviation, σ = $8,700
The size of the sample, n = 50
The sample mean annual profit, [tex]\bar x[/tex] = $82,441
The null hypothesis, H₀: μ = 81,000
The alternative hypothesis, Hₐ: μ > 81,000
Given that n > 30, a z-test is used
The test statistic ≈ 1.29
Therefore, we have;
[tex]z=\dfrac{\bar{x}-\mu_0 }{\dfrac{\sigma }{\sqrt{n}}} = 1.29[/tex]
From the z-score, the p value for a test statistic of 1.29 = 0.90147 which is 0.9015 after rounding up to 4 decimal places
Describe the shape of the data summarized in the histograms.
Answers:
5) Roughly symmetrical6) Skewed to the right (aka "right skewed" or "positively skewed")=======================================================
Explanation:
5) We don't have perfectly symmetrical data, as that would require the left half to be a perfect mirror copy of the right half. However, we have some semblance of symmetry going on. In the middle is 5 which is where the highest bar is, where the mode is located. The mean and median are likely to be around here as well. Then on either side of this highest peak are bars of shorter heights. The heights decrease as we move away from the center in either direction. We can draw an estimated or approximated bell curve (aka normal distribution curve or gaussian curve) to get a fairly good sense of how the data is roughly symmetric. The right-hand portion of this graph is shorter compared to the left side, but I don't think that's enough info to say if we have skewed data or not; so I would stick with "roughly symmetric" here.6) Unlike problem 5, we don't have symmetric data. Instead, we have data that is skewed to the right. The main cluster is grouped or centered on the left side, while we have some outliers to the right side. Draw a curve over each peak of the bars and you'll see that the right tail is pulled longer than the left tail is. We consider this a positively skewed distribution because there are outliers in the positive x direction compared to the main cluster. In contrast, a negatively skewed distribution would have outliers smaller than the main cluster. The mean is larger than the median for a right-skewed distribution. This is due to the mean being pulled on by the outlier, while the median is robust and isn't affected by outliers no matter how distant they are.Your parents car initially costs $18,000 and it depreciates at a rate of 12% a year. How much will the car be worth after 5 years.
Using this equation, when your parents give you the car when the value drops below $2,000, in what year of depreciation will you become the owner?
Answer:
Step-by-step explanation:
value after five years = $18,000×(1-0.12)⁵ = 18,000×0.88⁵ = $9,499.17
:::::
The value drops below $2,000 in the 17th year.
Jessie started a record collection with 8 records. Each week he added 3 records to his collection. Riley started her record collection with 23 records. Each week she gave away 2 records.
a) Write an equation to represent the number of records in Jessie's collection based on the number of weeks he has been collecting records.
3 per week + blank=8 Step-by-step explanation: brainly plz
If 5y+4y+y is completely simplified by combining like terms, what is the result?
Answer:
10y
Step-by-step explanation:
Answer:
10 y..
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please help me I need to get a good grade on this
7 Select the correct answer. A scientist is trying to predict the reglors of the world most likely to see a decrease in natural resources from population changes. Based on the evidence in the graph, what should the scientist conclude?
Answer:
A
Step-by-step explanation:
A system of inequalities is shown below.
y < -1
2x - y < 2
In which quadrants is the solution set of the system?
Answer:
C
I may be wrong sorry if I am
Answer:
The answer is C
Step-by-step explanation:
Since they both have a negative y and Quardant 4 has a positive x
Work out the number of cubes in the cuboid
Kennedy won $3,000 from a radio contest. If she puts this money in a bank account that earns 2.9% interest compounded annually, how much total interest will she earn in 10 years?
Determine if the following statements are true or false. If true give a reason or cite a theorem and if false, give a counter example.
a. If {a _n} is bounded, then it converges.
b. If {a _n} is not bounded, then it diverges.
c. If {a _n} diverges, then it is not bounded
Give an example of divergent sequences {a _n} and {b _n} such that {a _n + b _n} converges
Answer:
a. False the series [tex]\sum\limits_{i=1}^\infty (-1)^n[/tex]is bounded but does not converge
b. False, xₙ = n + (-1)ⁿ⁻¹(n - 1) does not diverge to infinity but it is not bounded for n ≥ 1
c. False some bounded sequences are divergent
An example of divergent sequences, aₙ, and bₙ, such that aₙ + bₙ converges is [tex]a_n = \sum\limits_{n} \dfrac{1}{n} , \, b_n = \sum\limits_{n} \dfrac{-1}{n}[/tex]
[tex]\sum\limits_{n} \dfrac{1}{n} + \sum\limits_{n} \dfrac{-1}{n}[/tex] is convergent
Step-by-step explanation:
For some constant c, the random variable X has probability density function
f(x)=(c(1-x)^9, 0≤x≤1
0, otherwise)
a) Find c.
b) Find P(X>0.6)
Answer:
b) Find P(X>0.6)
Explanation:
In order to find the product to the unknown variable you have to first solve the equation that has the parenthesis, The reason you should first find the parenthesis is because of The Order Of Operations, You have to first do parenthesis to find the unknown variable.
A business school is conducting a study to investigate whether a students’ scores on a placement test can be used to predict students’ starting salaries. Based on a random sample of 200 graduates of the business school, a 98 percent confidence interval for the slope of the linear regression line relating placement scores and starting salary is calculated to be (315,336). Assume the conditions for inference are met.
Which of the following is a correct interpretation of the confidence interval?
a. There is a 98 percent probability that the slope of the population regression line is between $315 per point and $336 per point.
b. Ninety-eight percent of the time, a 10-point increase in placement score will result in an average increase between $3,150 and $3,360 in starting salary.
c. We are 98 percent confident that a 10-point increase in placement score will result in a predicted increase in starting salary of between $3,150 and $3,360.
d. We are 98 percent confident that predicted starting salaries will be between $315,000 and $336,000.
e. We are 98 percent confident that the regression equation can be used to make accurate predictions for placement scores between 315 and 336.
Answer:
The answer is C
Step-by-step explanation:
I did it on college board
Express as a difference: a+5
The expression expressed as a difference is (a - 2) - (-7).
We have,
We can express a + 5 as a difference by subtracting a suitable term from it.
One way to do this is to subtract 2 and add 2, like this:
a + 5 = a + 5 - 2 + 2 (adding and subtracting 2)
= (a - 2) + 7 (rearranging)
Now,
We can express a + 5 as the difference between a - 2 and -7, like this:
a + 5 = (a - 2) - (-7)
Thus,
The expression expressed as a difference is (a - 2) - (-7).
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(2x -3) + (4c + 20) i need help
Answer:
=2x+4c+17
Step-by-step explanation:
(2x-3)+(4c+20)
=2x-3+4c+20
=2x+4c-3+20
=2x+4c+17
Hi food morning
What is 10 x 100
Answer:
1000
Step-by-step explanation:
Answer:
1,000
Step-by-step explanation:
pls give brainliest
how many people in the town of summit have jobs if there are 9,255 people in the town and 1/3 of them are employed? simplify the fraction if possible
Answer:
divide 9,255 divide 1/3 and you will get your answer hope this helps :)))
Step-by-step explanation:
In the town of Summit, 3,085 people have jobs. If there are 9,255 people in the town and 1/3 of them are employed.
To find the number of people in the town of Summit who have jobs, we can multiply the total population by the fraction representing the employed individuals.
Total population = 9,255 people
Fraction employed = 1/3
Number of people employed = Total population * Fraction employed
Number of people employed = 9,255 * (1/3)
To simplify the fraction (1/3), we can divide both the numerator and denominator by their greatest common divisor, which is 1 in this case.
Dividing 1 and 3 by 1, we get:
1/1 = 1
3/1 = 3
So, the simplified fraction is 1/3.
Continuing the calculation:
Number of people employed = 9,255 * (1/3)
Number of people employed = 9,255 / 3
Number of people employed = 3,085
Therefore, in the town of Summit, 3,085 people have jobs.
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The table represents temperatures for 9 days in February. What is the average temperature?
Answer:
35
Step-by-step explanation:
free points for me
Answer:
35- Yw Lovie <3
Step-by-step explanation:
Solve this system of equations:
y = x - 4
y = 6x - 9
Show your work in the text box below.
also Write your answer as an ordered pair.
Answer:
y=-3 x=1 (1,-3)
Step-by-step explanation:
y=x-4
y=6x-9
y+4=x
y+9=6x
difference = 5
x+5=6x
x=1
y=-3
1,-3
45 degrees and 6 find each variable
Will mark brainliest
Answer:
[tex]x = y = 3\sqrt{ 2[/tex]
Step-by-step explanation:
Given
The attached triangle
Required
Find x and y
The given triangle has 45 degrees as one of its angles, and it is also a right angle triangle.
For this kind of parameter, the opposite = the adjacent
i.e. x = y
Apply Pythagoras theorem
[tex]x^2 + y^2= 6^2[/tex]
Substitute x for y
[tex]y^2 + y^2= 6^2[/tex]
[tex]2y^2= 36[/tex]
Divide by 2
[tex]y^2 = 18[/tex]
Take square root
[tex]y = \sqrt{18[/tex]
[tex]y = \sqrt{9 * 2[/tex]
Split
[tex]y = \sqrt{9} *\sqrt{ 2[/tex]
[tex]y = 3*\sqrt{ 2[/tex]
[tex]y = 3\sqrt{ 2[/tex]
[tex]x = y = 3\sqrt{ 2[/tex]
there are 15 peices of fruit in a bowl and 6 of them are apples what percentage of the peices of fruit are apples
Answer:
40%
Step-by-step explanation:
6/15 = 0.4
0.4x100 = 40%
Why do you think adding and subtracting polynomial expressions is like adding and subtracting
expressions?
Answer:
Polynomials are closed under addition and subtraction, which is fancy mathspeak that means that whenever we add or subtract two polynomials, we always get another polynomial. In that way, they behave a lot like the numbers you're probably already familiar with. Adding and subtracting:
Two integers gives you another integerTwo rational numbers gives you another rational numberTwo real numbers gives you another real numberAnd it works the same with polynomials!
What is the volume of a rectangular prism with a height of 6 m, a length of 4 m, and a
width of 2 m?
A ladder is placed 7 feet from the base of a building and reaches a point on the building that is 24 feet above the ground. Find the length of the ladder.
Use the Pythagorean theorem:
7^2 + 24^2 = length^2
Simplify:
49 + 576 = length ^2
Add:
625 = length^2
Take the square root of both sides
Length = 25
The ladder is 25 feet long
For what value(s) of k will the relation not be a function?
#1: A = {(k^2, 16), (4k, 32)}
#2: B = {(k^2-5k, 10), (k+7, 4)}
#3: R = {(k^3-5k^2+3k, -5), (-k, 4)}
#4: S = {(|k+1|+2, 4), (8, 7)}
Will give 100 points and Brainliest!
Answer:
See belowStep-by-step explanation:
The relation is not a function when x -value is same but y- values are different.
#1
k^2 = 4kk = 0, k = 4#2
k^2 - 5k = k + 7k^2 - 6k = 7k^2 - 6k + 9 = 16k - 3 = 4 ⇒ k = 7k - 3 = -4 ⇒ k = -1#3
k^3 - 5k^2 + 3k = -kk^3 - 5k^2 + 4k = 0k(k^2 - 5k + 4) = 0k = 0, k = 1, k = 4#4
|k + 1| + 2 = 8|k + 1| = 6k = 5, k = -7cupcakes for a bake sale. He can bake 45
cupcakes in one hour. Which inequality shows the minimum number of hours that Hannah must bake to make at least 250
cupcakes?
Answer:
About 5 to 5.5 hours
Step-by-step explanation:
Get out of my swamp!