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]
A recent article1 claims that "Green Spaces Make Kids Smarter." The study described in the article involved
2623 schoolchildren in Barcelona. The researchers measured the amount of greenery around the children's schools, and then measured the children's working memories and attention spans. The children who had more vegetation around their schools did better on the memory and attention tests.
(a) What are the cases in this study?
(b) What is the explanatory variable?
(c) What is the response variable?
(d) Does the headline imply causation?
(e) Is the study an experiment or an observational study?
(f) Is it appropriate to conclude causation in this case?
Answer:
Cases : 2623 school children , Explanatory Variable : Greenery or Vegetation around school , Response Variable : Children's Memory & attention spans , Yes causation, Observational study
Step-by-step explanation:
a) Cases refers to the people or units of population studied in the research. In this case, it is sample of 2623 school children in Barcelona
b) Explanatory variable is variable which leads to, or causes the change in other variable. In this case, it is greenery or vegetation around researched students' schools
c) Response variable is the variable which is affected due to change in independent explanatory variable. In this case, it is children's working memory & attention spans
d) Yes, the headline implies causation. As it implies cause effect relationship of greenery around children's school on their working memory & attention spans.
e) It is an observational study, as it observes the variables relationship as it is, without any specific experimental intervention.
sider F and C below. F(x, y, z) = yz i + xz j + (xy + 4z) k C is the line segment from (1, 0, −2) to (6, 4, 1) (a) Find a function f such that F = ∇f. f(x, y, z) = xyz+2z2+c (b) Use part (a) to evaluate C ∇f · dr along the given curve C.
Answer:
a) The function is [tex]f(x,y,z) = xyz+2z^2[/tex]
b) The value of the integral is 18
Step-by-step explanation:
a) We are given that [tex] F(x,y,z) (yz,xz,xy+4z)[/tex]. We want to find a function f such that the gradient of f is F. That is [tex]\nablda f = F[/tex] . Suppose that such f does exist, if that is the case, then by definition of the gradient, we have that
[tex] F(x,y,z) = (\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z})[/tex]
From here, we have that
[tex] yz = \frac{\partial f}{\partial x}[/tex]
if we integrate both sides with respect to x, we get that
[tex] f(x,y,z) = xyz+ g(y,z)[/tex]
where g is a function that depens on y and z only. Now, we differentiate this equation with respect to y and make it equal to the 2nd component of F. That is
[tex] xz + \frac{\partial g}\partial{y} = xz[/tex]
This implies that [tex]\frac{\partial g}{\partial y} =0[/tex]. This means that g actually depends only on z. Until now, f is of the form
[tex] f(x,y,z) = xyz+g(z)[/tex]
If we repeat the previous step, by differentiating with respect to z and making it equall to the third component of F we get
[tex] xy + \frac{\partial g}{\partial z} = xy + 4z[/tex]
This implies that [tex] \frac{\partial g}{\partial z} = 4z[/tex] . If we integrate both sides with respect to z, we get that [tex] g(z) = 2z^2[/tex]
So f is of the form [tex] f(x,y,z) = xyz+2z^2[/tex]
b) To calculate the integral over the given segment, we can use the function f. Since the path is from (1,0,-2) to (6,4,1), then the value of the integral is given by evaluatin f at the end point and the substracting the value of f at the start point, that is
[tex] \int_C F \cdot dr = f(6,4,1) -f(1,0,-2) = 24+2(1)^2- (0+2(-2)^2)) = 18[/tex]
................
...
...
Answer:
C............PAC-MAN
Step-by-step explanation:
In 1990, there were 4,500 deaths due to lung diseases in miners aged 20 to 64 years. The expected number of deaths in this occupational group, based on age-specific deaths rates from lung diseases in all males aged 20 to 64 years, was 1,800 during 1990. What is the standardized mortality ratio (SMR) for lung disease in miners
Answer:
2.5
Step-by-step explanation:
We have that the standardized mortality ratio (SMR) is the relationship between the number of deaths observed in a year, that is, those that occurred and the number of expected deaths, that is, those that were predicted.
SMR = observed / expected
therefore if we replace we have:
SMR = 4500/1800
SMR = 2.5
Which means that the standardized mortality ratio (SMR) is 2.5
In a car dealership there are 5 models that get displayed in a line in the front of the parking lot for prime viewing. The dealership sells 15 different models. In how many ways can the 5 models be displayed
Answer:
360360
Step-by-step explanation:
We have the following information:
Number of ways of choosing 5 car models from 15 different models = 15C5
Number of arranging above 5 models = 5!
Therefore, the total number of displayong 5 models would be:
15C5 * 5!
nCr = n! / (r! * (n-r)!)
we replace:
15! / (5! * (15-5)!) * 5! = 15! / 10! = 360360
So there are a total of 360 360 ways to display the 5 car models.
Answer: 360,360
Step-by-step explanation:
4. The Navarro family uses an average of 225 gallons of water per day, 5 gallons of water per day, 5 gallons of water which goes through the family’s water filter. The Navarros’ water filter can process 450 gallons before it needs to be replaced. After how many days of average water use will the family need to replace their filter?
Answer:
90
Step-by-step explanation:
The family filters 5 gallons per day, so can expect to use the filter for ...
(450 gal)/(5 gal/day) = 90 day
After 90 days of average water use, the family will need to replace the filter.
9. In 2002 the Georgia department of education reported a mean reading test score of 850 from Tattnall County Career Academy with a standard deviation of 50. The sample was taken from 100 11th grade students. Assuming the test scores are normally distributed, what is the standard error
Answer:
The standard error = 5
Step-by-step explanation:
Explanation:-
Given sample size 'n' = 100
Given mean reading test score μ = 850
Given standard deviation of the population 'σ' = 50
The standard error is determined by
Standard error = [tex]\frac{S.D}{\sqrt{n} }[/tex]
S.E = σ/√n
[tex]S.E = \frac{S.D}{\sqrt{n} } = \frac{50}{\sqrt{100} } = 5[/tex]
Final answer:-
The standard error ( S.E) = 5
What’s the correct answer for this question?
Answer:
A.
Step-by-step explanation:
Volume of sphere = (4/3)πr³
= 4/3(3.14)(d/2)³
= 4/3(3.14)(7/2)³
= 4/3(3.14)(3.5)³
= 4/3(3.14)(42.875)
= (1.33)(3.14)(42.875)
= 179.5 cm³
Answer:
The answer is 179.5 cm^2
g You run a regression analysis on a bivariate set of data ( n = 14 ). With ¯ x = 27.7 and ¯ y = 26.5 , you obtain the regression equation y = 0.495 x − 14.914 with a correlation coefficient of r = 0.39 . You want to predict what value (on average) for the response variable will be obtained from a value of 110 as the explanatory variable. What is the predicted response value?
Answer:
Predicted response value = 39.536
Note that this predicted response value will most likely be far from the actual response value because the correlation coefficient of the regression equation used (r = 0.39) is too far away from 1.
Step-by-step explanation:
The response variable is the dependent variable (y) whose value is obtained from the expression involving the independent variable (x).
For this question, although the correlation coefficient, r = 0.39, is far from 1, the regression equation is
y = 0.495x - 14.914
The predicted response value will be obtained from the explanatory variable and the regression equation
x = 110
y = 0.495x - 14.914
y = (0.495×110) - 14.914 = 39.536
Note that this predicted response value will most likely be far from the actual response value because the correlation coefficient of the regression equation used (r = 0.39) is too far away from 1.
Hope this Helps!!!
What is the square root of -1?
Answer:
i
Step-by-step explanation:
Why is i the square root of negative one?
The term "imaginary" is used because there is no real number having a negative square. There are two complex square roots of −1, namely i and −i, just as there are two complex square roots of every real number other than zero, which has one double square root.
An investigative bureau uses a laboratory method to match the lead in a bullet found at a crime scene with unexpended lead cartridges found in the possession of a suspect. The value of this evidence depends on the chance of a false positive positive that is the probability that the bureau finds a match given that the lead at the crime scene and the lead in the possession of the suspect are actually from two differant melts or sources. To estimate the false positive rate the bureau collected 1851 bullets that the agency was confident all came from differant melts. The using its established ctireria the bureau examined every possible pair of bullets and found 658 matches. Use this info to to compute the chance of a false positive.
Answer:
Step-by-step explanation:
Given that, we have 1851 bullets that we KNOW are NOT MATCHES of one another. One by one they examine two bullets at a time.
So, there are 1851 bullets but each time we choose 2.
We have, N choose K = N! / K! (N-k)!
Here, N = 1851 and K = 2
Therefore, 1851 choose 2 = 1851! / 2! (1851-2)!
= 1851! / 2! * 1849!
= 1712175 Possible Combinations
Out of these 653 are false positive.
The chance of getting false positive is = 658 / 1712175
= 0.000384
= 0.0384 %
Therefore, The correct option is
The chance of false positive is 0.0384% Because this probability is sufficiently small (< or = 1%) There is high confidence in the agency's forensic evidence.
a consumer affairs company is interested in testing at the 5% level of significance that the average weight of a package of butter is less than 16 oz if the p value is 0.003 the conclusion is
A laptop producing company also produces laptop batteries, and claims that the batteries
it produces power a laptop for about 4:00 hours. But, you doubted the claim and collected
data from 500 laptop users of the same brand and battery, and you found out the battery
powers the laptop for about 3:00 hours and 30 minutes. Considering an alpha of 0.05,
prove the claim of the company is true or false or show whether you accept the
company’s claim or reject it? Please also write H0 and Ha statements for testing your
hypothesis
Answer:
There is enough evidence to support the claim that the batteries power the laptops for significantly less than 4 hours. (P-value = 0).
The null and alternative hypothesis are:
[tex]H_0: \mu=4\\\\H_a:\mu< 4[/tex]
Step-by-step explanation:
The question is incomplete: To test this claim a sample or population standard deviation is needed.
We will estimate that the sample standard deviation is 2 hours, and use a t-test to test that claim.
NOTE (after solving): The difference between the sample mean and the mean of the null hypothesis is big enough to reject the null hypothesis, even when we have a sample standard deviation of 3.5 hours, which can be considered bigger than the maximum standard deviation for the sample.
This is a hypothesis test for the population mean.
The claim is that the batteries power the laptops for significantly less than 4 hours.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=4\\\\H_a:\mu< 4[/tex]
The significance level is 0.05.
The sample has a size n=500.
The sample mean is M=3.5.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=2.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{2}{\sqrt{500}}=0.0894[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{3.5-4}{0.0894}=\dfrac{-0.5}{0.0894}=-5.5902[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=500-1=499[/tex]
This test is a left-tailed test, with 499 degrees of freedom and t=-5.5902, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=P(t<-5.5902)=0[/tex]
As the P-value (0) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the batteries power the laptops for significantly less than 4 hours.
SL Part 1: Function Families > 01: Graphs and Functions
22. Find the constant of variation k for the direct variation.
х
f(x)
2
-1
7
-3.5
Ok= -2
Ok=0
Ok=0.5
Ok= -0.5
Civil engineers often use the straight-line equation, y Bo +B1x, to model the relationship between the mean shear strength of masonry joints and precompression stress, x. To test this theory, a series of stress tests were performed on solid bricks arranged in triplets and joined with mortar. The precompression stress was varied for each triplet and the ultimate shear load just before failure (called the shear strength) was recorded. The stress results for n 7 triplet tests is shown in the accompanying table followed by a printout of the regression analysis. Give a practical interpretation of the estimate of the slope of the least squares line. Round to three decimal places if needed.
Click the icon to view the table of results and the regression analysis
A. or every 1 ton increase in precompression stress, the shear strength of the joint is estimated to increase by 0.987 tons.
B. For a triplet test with a precompression stress of o tons, the shear strength of the joint is estimated to be 1.192 tons.
C. For a triplet test with a precompression stress of 1 ton, the shear strength of the joint is estimated to be 0.987 tons.
D. For every 0.987 ton increase in precompression stress, the shear strength of the joint is estimated to increase by 1 ton.
Answer:
A. or every 1 ton increase in precompression stress, the shear strength of the joint is estimated to increase by 0.987 tons.
Step-by-step explanation:
Hello!
The engineers created a regression model to estimate the relationship between the "shear strength of masonry joints" (Y), measured in tons, and the "precompression stress" (X), measured in tons.
^Y= a + bXi
Using the regression output:
Estimate of the y-intercept: a= 1.192
Estimate of the slope: b= 0.987
In general terms you can interpret the slope as:
"Is the modification of the estimated mean of Y when X increases one unit"
In this case it means that every time the precompression stress increases one ton, the shear strength of the joint is estimated to increase 0.987 tons.
I hope this helps!
WILL GIVE BRAINLIEST HURRY
Answer: C
Step-by-step explanation:
To get all the constant terms on one side and variable terms on another, all we have to do is to add or subtract them on both sides.
3x+2x=10+5
Now that the like terms are on one side, we can combine them.
5x=15
To get x alone, we divide both sides by 5.
x=3
Now, we notice that x=3 is not an answer choice, but the next option that is equivalent to x=3 is C.
For C, if you divide both sides by -5, you still get x=3.
-15=-5x
x=3
Find sin 2x, cos 2x, and tan 2x if sinx =
5
13
and x terminates in quadrant I.
ala
sin 2x
U
х
cos 2x
=
tan 2x
10
Answer:
12/13 ; 5/13; 12/5
Step-by-step explanation:
sinx =5/13 =opposite/ hypothenus
By Pythagoras rule the hypothenus side can be obtained as
√ 13^2 -5^2 = √169 -25 = √144 = 12
cos x= adjacent/ hypothenus = 12/13
Now Cos2x= Sinx
And Sin2x = Cosx
Hence ;
Sin2x=12/13
Cos2x =5/13
Tan2x= Sin 2x/ Cos 2x
= 12/13 ÷ 5/13
= 12/13 × 13/5 = 12/5
The probability that an event will happen is P(E)=34. Find the probability that the event will not happen.
Answer:
.66
Step-by-step explanation:
1minus .34
Correct me if I am wrong
Which ordered pair is a solution of the equation? y=-6x+1y=−6x+1y, equals, minus, 6, x, plus, 1 Choose 1 answer: Choose 1 answer:Only (-2,13)(−2,13)left parenthesis, minus, 2, comma, 13, right parenthesis (Choice B) B Only (-1,7)(−1,7)left parenthesis, minus, 1, comma, 7, right parenthesis (Choice C) C Both (-2,13)(−2,13)left parenthesis, minus, 2, comma, 13, right parenthesis and (-1,7)(−1,7)left parenthesis, minus, 1, comma, 7, right parenthesis (Choice D) D Neither
Answer:
C Both (-2,13) and (-1,7)
Step-by-step explanation:
Try the offered points in the equation and see if they work
y = -6x +1
For (-2, 13):
13 = -6(-2) +1 = 12 +1 . . . . true
For (-1. 7):
7 = -6(-1) +1 = 6 +1 . . . . true
Both ordered pairs are solutions.
Mai is making personal pizzas. For 4 pizzas, she uses 10 ounces of cheese.
Complete question:
Mai is making personal pizzas. For 4 pizzas, she uses 10 ounces of cheese.
a. How much cheese does Mai use per Pizza
b. At this rate how much cheese will she need to make 15 Pizza's
Answer:
a. ounces of cheese per pizza = 10/4 = 2.5 ounces of cheese
b. amount of cheese to make 15 pizzas= 2.5 × 15 = 37.5 ounces of cheese
Step-by-step explanation:
Mai is making a personal pizzas .For 4 pizza she uses 10 ounces of cheese. This means Mai uses 10 ounces of cheese in weight to make just 4 pizzas.
a. How much cheese does Mai use per Pizza
Not she uses 10 ounces of cheese to make 4 pizzas. Therefore,
If 4 pizzas requires 10 ounces of cheese
1 pizza will require ? ounces of cheese
cross multiply
ounces of cheese per pizza = 10/4 = 2.5 ounces of cheese
b. At this rate how much cheese will she need to make 15 Pizza's
Since she requires 2.5 ounces of cheese to make 1 pizza
? ounces of cheese will be required to make 15 pizzas
cross multiply
amount of cheese to make 15 pizzas = 2.5 × 15 = 37.5 ounces of cheese
Real Estate One conducted a recent survey of house prices for properties located on the shores of Tawas Bay. Data on 26 recent sales, including the number of bathroom, square feet and bedrooms are below.
Selling Price Baths Sq Ft Beds
160000 1.5 1776 3
170000 2 1768 3
178000 1 1219 3
182500 1 1568 2
195100 1.5 1125 3
212500 2 1196 2
245900 2 2128 3
250000 3 1280 3
255000 2 1596 3
258000 3.5 2374 4
267000 2.5 2439 3
268000 2 1470 4
275000 2 1678 4
295000 2.5 1860 3
325000 3 2056 4
325000 3.5 2776 4
328400 2 1408 4
331000 1.5 1972 3
344500 2.5 1736 3
365000 2.5 1990 4
385000 2.5 3640 4
395000 2.5 1918 4
399000 2 2108 3
430000 2 2462 4
430000 2 2615 4
454000 3.5 3700 4
Action:
Use the data above and multiple regression to produce a model to predict the average sale price from other variables. Comment on the following:
a. Regression equation
b. R, R2 and 1-R2, adjusted R2
c. Standard error of estimate
d. Report the t's for each value and the corresponding p-values
e. Overall test of hypothesis and decision
f. Use a .05 level of significance. Cite which variables are significant and which are not significant, based on the t values and p values for each independent variable.
Answer:
Step-by-step explanation:
Hello!
Given the data for the variables:
Y: Selling price of a house on the shore of Tawas Bay
X₁: Number of bathrooms of a house on the shore of Tawas Bay.
X₂: Square feet of a house on the shore of Tawas Bay.
X₃: Number of bedrooms of a house on the shore of Tawas Bay.
The multiple regression model is Y= α + β₁X₁ + β₂X₂ + β₃X₃ + εi
a. Using software I've entered the raw data and estimated the regression coefficients:
^α= a= -5531.01
Represents the mean selling price of the houses when 0 bathrooms, 0 square feet and 0 bedrooms.
^β₁= b₁= -1386.21
Represents the modification of the mean selling price of the houses when the number of bathrooms increases in one unit and the square feet and number of bedrooms remain unchanged.
^β₂= b₂= 60.28
Represents the modification of the mean selling price of the houses when the square feet increase in one unit and the number of bathrooms and bedrooms remain unchanged.
^ β₃= b₃= 54797.08
Represents the modification of the mean selling price of the houses when the number of bedrooms increase in one unit and the number of bathrooms and square feet of the houses remain unchanged.
^Y= -5531.01 -1386.21X₁ + 60.28X₂ + 54797.08X₃
b)
R²= 0.55
R²Aj= 0.49
The coefficient of determination gives you an idea of how much of the variability of the dependent variable (Y) is due to the explanatory variables. Each time you add another explanatory variable to the regression the coefficient increases regarding of real contribution of the new variable. This could lead to thinking (wrongly) that the new variables are good to explain the dependent variable.
The adjusted coefficient of determination is a correction made to the raw coefficient of determination to have a more unbiased estimation of the effect the independent variables have over the dependent variable.
⇒ As you can see both coefficient are around 50%, which means that these explanatory variables
c)
The standard error estimate, this is the estimate of the population variance of the errors. In the ANOVA is represented by the Mean Square of the errors (MME)
Se²= MME= 3837640577.01
Se= 61948.6931
d) and f)
For the hypotheses tests for each slope the t- and p-values are:
α: 0.05
β₁: [tex]t_{H_0}= \frac{b_1-\beta_1 }{Sb_1}[/tex] t= -0.06; p-value: 0.9528 ⇒ Do not reject H₀, the test is not significant.
β₂: [tex]t_{H_0}= \frac{b_2-\beta_2 }{Sb_2}[/tex] t= 2.56; p-value: 0.0180 ⇒ Reject H₀, the test is significant.
β₃: [tex]t_{H_0}= \frac{b_3-\beta_3 }{Sb_3}[/tex] t= 2.28; p-value: 0.0326 ⇒ Reject H₀, the test is significant.
e)
H₀: β₁= β₂= β₃
H₁: At least one βi is different from the others ∀ i=1, 2, 3
α: 0.05
F= 9.03
p-value: 0.0004
⇒ Reject H₀, the test is significant.
I hope it helps!
Ten teaching assistants are available for grading papers in a particular course. The first exam consists of four questions, and the professor wishes to select a different assistant to grade each question (only one assistant per question). In how many ways can assistants be chosen to grade the exam
Answer:
There are 210 ways
Step-by-step explanation:
The number of ways or combinations in which we can select x elements from a group of n elements where the order doesn't matter can be calculated as:
[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]
So, we have 10 teaching assistants and we need to choose 4 (one assistant per question) to grade each question. It means that n is equal to 10 and x is equal to 4.
Therefore, the number of ways that the assistants can be chosen to grade the exam are calculated as:
[tex]10C4=\frac{10!}{4!(10-4)!}=210[/tex]
NEED HELP ASAP!!! a hexagon-based pyramid has a height of 54cm. The volume of the pyramid is 1080cm3. What is the area of the base?
Answer:
32
Step-by-step explanation:
(07.01 MC)Of the following sets, which numbers in {0, 1, 2, 3, 4} make the inequality 7x + 3 < 17 true? {0} {0, 1} {0, 1, 2} {2, 3, 4}
Answer:
{0, 1}
Step-by-step explanation:
Solving for 'x' in the inequality:
[tex]7x+3<17\\7x+3-3<17-3 \leftarrow \text{Subtraction Property of Equality}\\7x<14\\7x/7<14/7 \leftarrow \text{Division Property of Equality}\\\boxed{x<2}[/tex]
X's value has to be less than two to make the inequality true. So, {0, 1} should be the correct answer.
Answer:
I took the quiz and the answer is B
Step-by-step explanation:
help help help help help
Answer:
See below
Step-by-step explanation:
a.
[tex]\dfrac{10}{4}=\dfrac{5(2)}{2(2)}=\dfrac{5}{2}[/tex]
b.
[tex]\dfrac{20}{15}=\dfrac{4(5)}{3(5)}=\dfrac{4}{3}[/tex]
c.
[tex]\dfrac{-24}{42}=\dfrac{-4(6)}{7(6)}=\dfrac{-4}{7}[/tex]
d.
[tex]\dfrac{-18}{-14}=\dfrac{-2(9)}{-2(7)}=\dfrac{9}{7}[/tex]
Hope this helps!
Arun’s restaurant bill is $58, and he wants to leave the waiter an 18 percent tip. What will Arun’s total bill be? $10.44 $47.56 $68.44 $76.00
Answer:
The Answer is 68.44. I wish it helpsAnswer:
68.44$
Step-by-step explanation:
x=18*58/100=10.44 $(the tip)
58+10.44=68.44 ( the bill )
f(x)=x^3-3x^2-9x+4 find the intervals on which f is increasing or decreasing b. find the local maximum and minimum values of f. c. find the intervals of concavity and inflection points
Answer:
Please read the complete answer below!
Step-by-step explanation:
You have the following function:
[tex]f(x)=x^3-3x^2-9x+4[/tex] (1)
a) To find the interval on which f is increasing or decreasing, you first calculate the critical points of f(x).
You calculate the derivative f(x) respect to x:
[tex]\frac{df}{dx}=3x^2-6x-9[/tex] (2)
Next, you equal the derivative to zero, and then you find the roots of the polynomial by using the quadratic formula:
[tex]3x^2-6x-9=0\\\\x_{1,2}=\frac{-(-6)\pm\sqrt{(-6)^2-4(3)(-9)}}{2(3)}\\\\x_{1,2}=\frac{6\pm12}{6}\\\\x_1=-1\\\\x_2=3[/tex]
Then, the critical points are x=-1 and x=3
Next, you calculate df/dx for a values of x to the left and to the right of the critical points x1 and x2. If df/dx < 0 the function is decreasing, if df/dx > 0 the function is increasing.
for x = -1.01
[tex]\frac{df(-1.01)}{dx}=3(-1.01)^2-6(-1.01)-9=0.12[/tex]
Then, in the interval (-∞,-1), the function is increasing
for x = -0.99
[tex]\frac{df(-0.99)}{dx}=3(-0.99)^2-6(-0.99)-9=-0.11[/tex]
In the interval (-1,3) the function is decreasing
for x = 3.01
[tex]\frac{df(3.01)}{dx}=3(3.01)^2-6(3.01)-9=0.12[/tex]
In the interval (3,+∞) the function is increasing
b) To find the local minimum and maximum you use the second derivative of the function:
[tex]\frac{d^2f}{dx^2}=6x-6[/tex] (3)
you evaluate the second derivative for the critical points x1 and x2, if the second derivative is positive, you have a local minimum. If the second derivative is negative, you have a local maximum:
for x1 = -1
[tex]6(-1)-6=-12<0[/tex]
x=-1 is a local maximum
for x2 = 3
[tex]6(3)-6=12>0[/tex]
x=3 is a local minimum
c) upward concavity: (-1,3)
downward concavity: (-∞,-1)U(3,+∞)
The inflection points are calculated with the second derivative equal to zero:
[tex]6x-6=0\\\\x=1[/tex]
For x = 1 you have an inflection point
Write an equation of the line containing the point (2,1) and perpendicular to the line 5x – 2y = 3.
So first, you want to isolate your Y. To do this, you must get it alone on ONE SIDE of the equation.
5x - 2y = 3
-5x -5x
[tex]\frac{-2y}{-2}[/tex] = [tex]\frac{3-5x}{-2}[/tex]
ANSWER: y = \frac{3-5x}{-2}
You invest $2,000 in an account that is compounded annually at an interest rate of 5%. You never withdraw money fro
the account. Which equation below gives the amount of money you will have in the account after tyears?
Al = 2,000 20.05
Al = 2,000(1.5)
A10 = 2,000(105)
A1 = 2.000 e5
Answer:
[tex]A(t) = 2,000(1.05)^{t}[/tex]
Step-by-step explanation:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
You invest $2,000
This means that [tex]P = 2,000[/tex]
Compounded anually
Once a year, so [tex]n = 1[/tex]
Interest rate of 5%.
This means that [tex]r = 0.05[/tex]
Amount after t years:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(t) = 2,000(1 + \frac{0.05}{1})^{t}[/tex]
[tex]A(t) = 2,000(1.05)^{t}[/tex]
The function g is defined by g(x) = 1/2x - 1. What is
the value of g(6) ?
Answer:
2
Step-by-step explanation:
g(x) = 1/2x - 1
g(6= 1/2*6-1= 3-1= 2