Find the exact value of the integral fx=-2² dx. -2x² 500 dx
Answers
The given integral is: $$\int (-2x^2 + 500)dx$$
To solve the above integral, we integrate both terms separately. Using the integral formulas, $$\int x^n dx= \frac{x^{n+1}}{n+1}+ C$$$$\int kf(x)dx= k\int f(x)dx$$
where C is a constant of integration and k is a constant.
The integral $\int -2x^2 dx$ is:\begin{align*} \int -2x^2 dx &= -2\int x^2 dx\\&= -2\times \frac{x^{2+1}} {2+1} + C\\&= -\frac {2}{3}x^3+ C\end{align*}
The integral $\int 500 dx$ is:\begin{align*}\int 500 dx &= 500\int dx\\&= 500\times x + C\\&= 500x + C\end{align*}
Thus, the integral $\int (-2x^2 + 500) dx$ is:\begin{align*}\int (-2x^2 + 500) dx &= \int -2x^2 dx + \int 500 dx\\&= (-\frac {2}{3}x^3+ C_1) + (500x + C_2)\\&= -\frac {2}{3}x^3+ 500x + C\end{align*}
where C is a constant of integration and $C=C_1+C_2$.
Therefore, the exact value of the integral is $-\frac {2}{3}x^3+ 500x + C$.
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Related Questions
How many different batting orders can be formed for a 9-member baseball team?
Hint: Assume all team members are in the batting order
Answers
Answer:
362,880 different
Step-by-step explanation:
Use the permutation 9*8*7*6*5*4*3*2*1. Since there are 9 possible players for the first position, 8 for the 2nd (1 is taken off), 7 for the 3rd, etc. So you would multiply these numbers together. So there are 362,880 different possible batting orders.
Thaddeus traded $3750 for British pounds, immediately changed his mind,
and then promptly traded his British pounds back into dollars. Which of these
amounts is he most likely to have?
O A. $3750
B. More than $3750
O c. $0
O D. More than $0 but less than $3750
SUBMIT
Answer us D ladies and gents?
Answers
Answer:
[See Below]
Step-by-step explanation:
✦ 1$ = 0.78£
✧ So do 3750 x 0.78 = 2925£
✦ 1£ = 1.28$
✧ 2925 / 1.28 = 2285$
So it'd be D, More than 0$ but less than 3750$.
~Hope this helps Mate. If you need anything feel free to message me.
Given that the probability of a company having a section in the newspaper is 0.43, and the probability of a company having a website given that the company has a section in the newspaper is 0.84, what is the probability of a company having a website and a section in the newspaper
Answers
To find the probability of a company having both a website and a section in the newspaper, we can use the formula for conditional probability.
Let's denote the events as follows:
A: A company has a section in the newspaper
B: A company has a website
We are given the following probabilities:
P(A) = 0.43 (Probability of a company having a section in the newspaper)
P(B|A) = 0.84 (Probability of a company having a website given that it has a section in the newspaper)
The probability of both events A and B occurring can be calculated as:
P(A and B) = P(A) * P(B|A)
Substituting in the values we have:
P(A and B) = 0.43 * 0.84
P(A and B) = 0.3612
Therefore, the probability of a company having both a website and a section in the newspaper is 0.3612 or 36.12%.
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The given lengths are two sides of a right triangle. All three side lengths of the triangle are integers, and together they form a Pythagorean triple. Find the length of the third side, then indicate whether it is a leg or a hypotenuse.
Answers
Answer:
C) 92, leg
Step-by-step explanation:
a² + 28² = 96² *the hypotenuse is always the longest side
a² + 784 = 9216
a² = 8432
a = √8432
'a' is approximately 92, and is a leg
WILL MARK BRAINLIEST
Answers
Answer:c
Step-by-step explanation:
Answer:
I think it is 19.7
Step-by-step explanation:
27) Suppose the price elasticity of supply for shampoo is 20. If the price of shampoo increases by 0.7%, what would we expect to happen to the quantity of shampoo supplied?
a) Increase by 27%
b) Increase by 14%)
e) Increase by 13%
d) Decrease by 13%
28)
e) Decrease by 27%
If pasta is a Giffen good, then....
a) pasta is also a normal good.
b) pasta is also a luxury good.
e) an decrease in the price of pasta will increase the quantity demanded. d) an increase in the price of pasta will increase the quantity demanded. e) pasta must make up a small portion of consumers' total expenditures.
20)
An inferior good in which the income effect dominates the substitution effect is called....
a) a normal good.
b) a luxury good.
30)
a) a Giffon good.
d) a mass-produced good.
e) a favored good.
The cross elasticity of demand measures the responsiveness of the quantity demanded of a particular good to changes in the prices of
a) its complements but not its substitutes.
b) Its substitutes but not ita complements.
c) its substitutes and its complements.
d) neither its substitutes nor its complements. e) None of the above..
Answers
In question 27, the price elasticity of supply for shampoo is given as 20, and the price of shampoo increases by 0.7%. The expected change in the quantity of shampoo supplied can be determined using the concept of price elasticity of supply. However, the specific percentage change in quantity supplied is not provided, so a precise answer cannot be given based on the given information.
In question 20, an inferior good in which the income effect dominates the substitution effect is referred to as a Giffen good. It is not classified as a normal good, luxury good, mass-produced good, or favored good.
In question 30, the cross elasticity of demand measures the responsiveness of the quantity demanded of a particular good to changes in the prices of its substitutes and complements. The correct answer is that the cross elasticity of demand measures the responsiveness to changes in both substitutes and complements.
In question 27, without the specific percentage change in quantity supplied, we cannot determine the exact outcome based on the given information. The price elasticity of supply of 20 suggests that the quantity supplied is highly responsive to changes in price, but the specific percentage change in quantity supplied cannot be calculated without additional data.
In question 28, the relationship between pasta being a Giffen good and other characteristics is not specified. While pasta being a Giffen good indicates that the quantity demanded increases as the price increases, it does not imply whether pasta is a normal good, luxury good, or how price changes affect quantity demanded.
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What are some 3 out of the six questions you can ask about the statistical validity of a bivariate correlation? Do all the statistical validity questions apply the same way when bivariate correlations are represented as bar graphs? Explain.
Answers
Three out of six questions that you can ask about the statistical validity of a bivariate correlation are: All the statistical validity questions do not apply in the same way when bivariate correlations are represented as bar graphs because statistical validity questions address issues of internal validity (causality) rather than issues of external validity (generalizability).
Statistical validity questions are concerned with establishing whether the relationship between the two variables is likely to be a true relationship or just a chance occurrence. Statistical validity can be assessed by determining whether the correlation coefficient is statistically significant (i.e., whether the relationship observed is likely to be a true relationship or just a chance occurrence) and the strength of the correlation.
Statistical significance testing requires a large sample size, and as a result, the correlation coefficient may be statistically significant even if the effect size is small. Therefore, it is important to consider both statistical significance and effect size when evaluating the statistical validity of a bivariate correlation.
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find all the expressions that are equal to 4*10^-3
Answers
Answer:
Attached to this answer are some of the ways you could rewrite \(4*10^{-3}\)
hey its mathematics please and thank you
Answers
which do you press while dragging to maintain the height and width proportion of a shape?
Answers
To maintain the height and width proportion of a shape while dragging, you would typically hold down the Shift key on your keyboard.
When you select and drag a shape, holding down the Shift key constrains the proportions of the shape and ensures that the height and width change proportionally.
This technique is commonly used in graphic design and image editing software, as well as in various drawing and design applications. By holding down the Shift key while dragging a shape, you can prevent it from being distorted or skewed, preserving its original aspect ratio.
This feature is especially useful when you want to maintain the shape's original proportions or when you need consistency in the size and dimensions of multiple shapes. It helps ensure that the height and width remain in the same ratio as the original shape, regardless of how you adjust its size.
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select the two values of x that are roots of this equation x^2-5x+5=0
Answers
The solution of the quadratic equation is \(x = \dfrac{5\pm\sqrt5}{2}\).
What is a quadratic equation?
A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Given that the quadratic equation is x²-5x+5=0. The equation can be solved as below:-
x²-5x+5=0
a = 1 , b = -5 , c = 5
\(x = \dfrac{-b \pm\sqrt{(b^2-4ac}}{2a}\)
\(x=\dfrac{5\pm\sqrt{25 - 4\times1\times5}}{2}\)
\(x = \dfrac{5\pm\sqrt5}{2}\)
The value of x for the quadratic equation will be \(x = \dfrac{5\pm\sqrt5}{2}\).
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Maggie buys 1 1/2 pounds of walnut, 8 ounces of pecans and 3/4 pound of almonds. How much do the nuts weigh in all?? Show how you solved it.
Answers
Answer:
2 3/4
Step-by-step explanation:
There are 16 ounces in a pound so 8 ounces is 1/2 a pound.
1 1/2 + 1/2 + 3/4
2 + 3/4
2 3/4
is this correct? if not what is the correct answer?
Answers
6 soaps comparing to the other 5 = 30 different comparisons:
30 x 2,000 = 60,000
Answer: H. $60,000
Find the equation of the line that
- is perpendicular to the line y=3x-1
and
-passes through the point (7,4)
Answers
Answer:
y = -1/3x + 19/3
Step-by-step explanation:
let the equation of the line be y = mx + b
since it is perpendicular to y = 3x - 1, these two lines's gradient when producted gives -1.
hence, 3 x m = -1
m = -1/3
sub m = -1/3 and (7, 4):
4 = -1/3(7) + b
b = 19/3
therefore, equation of the line is y = -1/3x + 19/3
Topic: coordinate geometry
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Simplify the following question:
Answers
yea here is another q
Answers
The graphs below have the same shape. What is the equation of the red
graph?
5
Answers
Answer:
A is ur answer
Porcupines can cause damage to wood structures by chewing them. Researchers studied a liquid repellent designed to reduce such damage. A sample of 20 wooden blocks of the same size were treated with the repellent and left outside in an area where porcupines are known to live. After a certain amount of time, the blocks were inspected for the number of porcupine teeth marks visible. The data were used to create the 95 percent confidence interval (4.9,5.8).Which of the following claims is supported by the interval?The mean number of porcupine teeth marks on all wooden blocks treated with the repellent is less than 6.
Answers
The given interval suggests that the mean number of porcupine teeth marks on all wooden blocks treated with the repellent is less than 6 since the upper limit of the interval is 5.8. This claim falls within the given interval and is supported by the data. Therefore, we can say that the mean number of porcupine teeth marks on all wooden blocks treated with the repellent is less than 6 based on the 95 percent confidence interval (4.9,5.8).
In the given scenario, a sample of 20 wooden blocks treated with a liquid repellent designed to reduce damage caused by porcupines were left outside in an area where porcupines are known to live. After some time, the blocks were inspected for the number of porcupine teeth marks visible. The data collected was then used to create the 95 percent confidence interval (4.9,5.8).
The 95 percent confidence interval can be defined as a range of values that we can be 95 percent confident the true population parameter falls within. In this case, the true population parameters is the mean number of porcupine teeth marks on all wooden blocks treated with the repellent.
From the given interval, we can conclude that we are 95 percent confident that the true mean number of porcupine teeth marks on all wooden blocks treated with the repellent is between 4.9 and 5.8.
Therefore, any claim that falls within this interval is supported by the data.
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please help
answer choices are:
A. (3, -3)
B. (1,-6)
C. (8,-6)
D. (-1, 3)
Answers
Answer:
C ( 8,-6)
Because you move the points according to the rule.
Find the measure of angle A.
A
7x-1
12x
489
Answers
Answer:
48 degrees
Step-by-step explanation:
7X-1+12x+48=180
19x+47=180
19x=133
x=7
7(7)-1=A
49-1=A
48=A
A is 48 degrees
standard error of an estimator is not affected by the multiple choice question. population standard deviation. sample size. population size
Answers
The term that is not affected the standard error of an estimator is population size, from the provide data in options. So, option (c) is right one.
The standard error is a statistical term that used to measured the accuracy that a sample distribution represents a population by using standard deviation. The standard error(SE) is very similar to standard deviation of a distribution. Both are used to measure the spread of distribution. Higher the value SE, the more spread out your data is. In statistical way, standard error is also called standard error of mean, SEM, it represents the deviation of sample mean deviates from the actual mean of a population.
It is calculated simply by dividing the standard deviation by the square root of the sample size. That is \(SE = \frac{σ }{\sqrt{n}}\)
where , n --> sample size
σ --> population standard deviations
Now, from the above formula it is clearly seen that standard error term or an estimator affected by sample size (n) and population standard deviations ( σ). So, right choice for answer is population size.
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Complete question:
standard error of an estimator is not affected by the multiple choice question.
a) population standard deviation
b) sample size
c) population size
What is the slope of the line that passes through the points (6, 4) and (3, 8)?
-4/3
-3/4
3/4
4/3
Answers
(8-4)/(3-6) = 4/-3
The slope is -4/3
Question to this please not sure
Answers
Answer:
6
Step-by-step explanation:
Answer:
6 miles
Step-by-step explanation:
d = 2xr
2x3 = 6
hope this helps
394.82−55.75 helppppppppppp
Answers
Answer: 339.07
Step-by-step explanation:
Answer:
339.07.
Step-by-step explanation:
I've attached an image to help break down this problem. (credit to cymath.com)
Hope this helps! :)
absorption costing net income is calculated by subtracting selling and administrative expenses from . (enter only one word per blank.)
Answers
Absorption costing net income is calculated by subtracting selling and administrative expenses from gross profit.
Gross Profit: Gross profit is the revenue generated from sales minus the cost of goods sold (COGS). The COGS includes all the direct production costs associated with manufacturing or acquiring the products sold. It typically includes costs such as raw materials, direct labor, and direct overhead expenses. Gross profit represents the profit earned from the core operational activities of a company before accounting for selling and administrative expenses.Selling and Administrative Expenses: These are the expenses incurred in the process of selling the products or services and managing the overall operations of the company. Selling expenses include costs such as sales commissions, advertising expenses, and marketing costs. Administrative expenses include items like salaries of management personnel, office rent, utilities, and other general administrative costs.Calculation: To calculate the net income using absorption costing, we subtract the selling and administrative expenses from the gross profit. This calculation reflects the profit remaining after deducting both the direct production costs (COGS) and the selling and administrative expenses from the total revenue generated by the company.By subtracting the selling and administrative expenses from the gross profit, we arrive at the absorption costing net income. This net income figure reflects the overall profitability of the company, considering both the operational costs of production and the expenses associated with selling and administration.
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Can someone help me with this question? If I can get an equation for it and an explanation of how to do it then I should be able to do the rest of them.
The problem wants me to:
"write the equation of the parabola in intercept form."
Answers
Please help me with this question im too slow to answer
Answers
Answer:
92
Step-by-step explanation:
w=7
x=4
y=8
z=1
8^2 + 2(4) + 3 (7) -1
64 + 2 * 4 + 3 * 7 -1
64 + 8 + 21 - 1
72 + 20
92
y2+2x+3w-z
(8x8)+(2x4)+(3x7)-1
64+8+21-1
=92
4. A box contains cards that are numbered from 1 to 100. What is the
probability of randomly selecting a number that is less than 12? *
1/100
1/12
11/100
12/100
Answers
Answer:
Hey! The answer would be 12/100
Step-by-step explanation:
Because you dont need to simplify the fraction, the only right answer there is 12/100.
suppose that 75% of the applicants for a certain industrial job possess advanced training in computer programming. applicants are interviewed sequentially and are selected at random from the pool. find the probability that the first applicant with advanced training in programming is found on the third interview. (round your answer to four decimal places.)
Answers
The probability that the first applicant with advanced training in programming is found on the third interview is 0.0469
Let X denote the number interviewed until 1 has advanced training and follows a geometric distribution with parameter 75%, so
Geometric distribution is: (1-75%)
=0.75
The density function of geometric distribution is,
\(P(X=x)=p(1-p)^{x-1}\), for all x = 1,2,3,....
Now, we calculate the probability that the first applicant with advanced training in programming is found on the third interview:
P(X=3) =\(0.75(1-0.75)^{3-1}\)
=\(0.75(1-0.75)^{2}\)
=0.75×0.0625
=0.0469
Hence, the required probability is 0.0469
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These marbles are placed in a bag and two of them are randomly drawn what is the probability of drawing two blue marbles if the first one is placed back in
Answers
Answer:
2/9
Step-by-step explanation: