Using simultaneous equations, each small candle costs $1.00 and each large candle costs $5.00.
What are simultaneous equations?Simultaneous equations are two or more equations solved concurrently.
Simultaneous equations are also known as a system of equations.
Small Candle Large Candle Total Cost
You buy 4 2 $14
A friend buys 5 3 $20
Let the cost of the small candle each = s and the cost of the large candle each = l
Equations:Equation 1: 4s + 2l = 14
Equation 2: 5s + 3l = 20
Multiply Equation 1 by 1.5:
Equation 3: 6s + 3l = 21
Subtract Equation 2 from Equation 3:
6s + 3l = 21
-
5s + 3l = 20
s = 1
= $1
From Equation 1:
4s + 2l = 14
4 + 2l = 14
2l = 10
l = 5
= $5
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HELP PLS What is the mean absolute deviation of Leo's test scores?
The mean of the data is 31. Then the mean absolute deviation of Leo's test scores will be 9.
What is the mean absolute deviation?It is the average distance between each data point and the mean.
The mean absolute deviation is given as
[tex]\rm MAD = \dfrac{\Sigma _{i = 1}^n|x_i - \mu|}{n}[/tex]
The data is given below.
18, 26, 38, 42
The mean of the data is given as,
μ = (18 + 26 + 38 + 42) / 4
μ = 124 / 4
μ = 31
Then the mean absolute deviation is given as,
MAD = (|18 - 31| + |26 - 31| + |38 - 31| + |42 - 31|) / 4
MAD = (13 + 5 + 7 + 11) / 4
MAD = 36 / 4
MAD = 9
The mean absolute deviation will be 9.
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a teacher is lecturing on excel macros. they plan to divide the class into groups of 5 and want each group to work on a unique exercise. to determine the number of exercises needed, model this situation with an equation, using x as the independent variable and y as the dependent variable.
In this situation, the independent variable is x, which is the number of groups, and the dependent variable is y, which is the number of exercises needed.
To model this situation with an equation, we need to calculate the number of exercises needed for each group. Since we have x groups, and each group needs a unique exercise, we can calculate the number of exercises needed by multiplying the number of groups by 5, since each group has 5 members. Thus, the equation would be y = 5x. This equation uses the fact that each group is made up of 5 members, so each group needs a unique exercise. In order to determine the number of exercises needed, we can solve the equation for x by dividing both sides by 5. This gives us x=y/5, which indicates that the number of exercises (x) is equal to the number of groups (y) divided by 5.For example, if we have 8 groups, then the number of exercises needed would be 5*8 = 40.In this situation, the independent variable is x, which is the number of groups, and the dependent variable is y, which is the number of exercises needed.
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Determine whether each claim about the properties of A’ B’ C’ D’ and ABCD is true or false quadrilateral A’B’C’ D’ is the result of dilating quadrilateral ABCD about point P by a scale of factor 3
The lengths of AD and A'D' are equal False
The area of ABCD and A'B'C'D' are equal False
How to determine the true statements
The complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The quadrilateral A’B’C’ D’ is the result of dilating quadrilateral ABCD about point P by a scale of factor 3
When a shape is dilated by a scale factor other than 1 or -1, the resulting shape would have a different area and a different side length
This implies that ABCD and its image do not have equal side length and equal area
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Recent findings lend strong support to the theory that a black hole lies at the center of the Milky Way and of many of the 100 billion other galaxies estimated to exist in the universe.
(A) that a black hole lies at the center of the Milky Way and of
(B) that a black hole lies at the Milky Way's center and
(C) that there is a black hole lying at the Milky Way’s center and
(D) of a black hole lying at the Milky Way's center and
(E) of a black hole that lies at the center of the Milky Way and of
Recent findings have revealed strong evidence amount for the theory that there is a black hole that lies at the center of the Milky Way and of many other galaxies in the universe.
Recent scientific studies have provided strong evidence for the theory that there is a black hole lying at the center of the Milky Way and of many other galaxies in the universe. This theory is supported by findings such as the detection of gravitational waves caused by the collision of two black holes, which is indicative of the existence of black holes in the universe. Additionally, the discovery of high-energy X-ray emissions from regions near the center of the Milky Way suggests the presence of a supermassive black hole. These findings, combined with other evidence, provide strong support for the theory that a black hole lies at the center of the Milky Way and of many other galaxies in the universe.
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3. write an equation in standard form to represent the amount charged, c, for m number of miles by the company in charlotte. (remember a cannot be negative and no fractions or decimals for any of the values) * 1 point your answer
The equation for the amount charged by the company in Charlotte for m number of miles is c = 2m + 25.
The equation in standard form to represent the amount charged, c, for m number of miles by the company in Charlotte is c = 2m + 5. This means that the cost of utilizing the company is $2 per mile plus a flat fee of $5.This equation is in standard form, in which c represents the amount charged, m represents the number of miles and 25 represents the flat rate fee. To calculate the cost of a certain number of miles, we first multiply the number of miles by 2, then add 25 to the result. For example, if m = 10, then c = 2(10) + 25 = 45. In other words, if someone in Charlotte wanted to travel 10 miles, they would be charged 45 dollars.
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What do these have in common?
20Ne 19F- Mg2+
20Ne, 19F and Mg₂+ are all examples of species or chemical ions.
How will you describe these ions?20Ne is a stable isotope of Neon, 19F- is a negatively charged fluoride ion, and Mg₂+ is a positively charged magnesium ion. They all have a specific number of protons and electrons, which gives them their chemical properties and their unique behavior.
Chemical ions are atoms or molecules that have gained or lost one or more electrons, resulting in a net electrical charge. This charge can be positive (cation) or negative (anion). Examples of common ions include sodium (Na+) and chloride (Cl-), which combine to form table salt (NaCl).
Therefore, the correct answer is as given above
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What equation(s) represent the vertical asymptote(s) of the graph of y = 1/x^2 - 4? J) x = -4 and x = 4 K) x = - 2 and x = 2 L) x = 0 only M) x = 2 only N) x = 4 only
Answer:
K) x = - 2 and x = 2
Step-by-step explanation:
Vertical asymptotes occur when the denominator of a fraction equals to zero, but the numerator does not. In the case of y = 1/x^2 - 4, the denominator is x^2 - 4.
The equation x^2 - 4 = 0 represents the points at which the denominator equals to zero, so we can find the solutions for x by solving this equation:
x^2 - 4 = 0
x^2 = 4
x = ±2
So x = 2 and x = -2 represents the vertical asymptote of the graph of y = 1/x^2 - 4
This means that the graph of the function approaches zero as x approaches 2 and -2 from the left and right respectively, but it never touches the x-axis at those points.
What is 4(-8)+8= and how can I find it
Answer: -24
Step-by-step explanation:
⇒4(-8)+8
in such questions, first solve the bracket. In this question there is only a single term within the bracket, -8. Brackets usually mean multiplication. So we multiply 8 by 4 to get 32. Now since we need to give 32 a sign as well, so in case of multiplication we multiply the sign of 8 and 4 together i.e negative and positive respectively. Negative positive multiplied give us negative. Therefore the sign of 32 will be negative.
⇒- 32 + 8
now again we are stuck with the sign issue. Notice that we have both a negative and a positive sign as well. How do we know if we are supposed to add or subtract? In order to decide which operation we apply on the two numbers, we first multiply the signs. Negative positive multiplied give negative, therfore we will do subtraction. 32 subtracted from 8 gives 24. Now again we are supposed to give 24 a sign. Unlike in multiplication, when we do addition or subtraction, instead of multiplying the signs to give the result a sign, we look for the sign of the greater operand, i.e 32, because 32 is greater than 8 and has a negative sign, so we give 24 a negative sign. H
⇒-24 answer
⇒4(-8)+8
⇒- 32 + 8
⇒-24 answer. hope the helps ...
just before a presidential election, a national opinion poll increases the size of its weekly sample from the usual 1500 people to 4000 people. (a) Does the larger random sample reduce the bias of the poll result? Explain. (b) Does it reduce the variability of the result? Explain.
The larger random sample of 4000 people can reduce the bias and variability of the poll result by increasing the chances that the sample reflects the population accurately, reducing the effect of chance on the sample drawn, and increasing the precision of the estimate.
(a) Yes, the larger random sample can reduce the bias of the poll result. A larger sample size increases the chances that the sample accurately reflects the population by reducing the effect of chance on the sample drawn. This in turn reduces the likelihood of sampling bias, which occurs when a sample is unrepresentative of the population being studied.
(b) Yes, the larger random sample can reduce the variability of the result. A larger sample size increases the chances that the sample accurately reflects the population, which reduces the variability of the results. A larger sample size also increases the precision of the estimate, which reduces the variability of the results.
The larger random sample of 4000 people can reduce the bias and variability of the poll result by increasing the chances that the sample reflects the population accurately, reducing the effect of chance on the sample drawn, and increasing the precision of the estimate.
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sum of the digits of a 2 digit number is 8.when the digits of the number are interchanged the resulting new number is smaller than the original number by 36. what is the original number.
Answer:
The original number is 62.
Step-by-step explanation:
Solution :
Let,
Units digit = x
Tens digit = 8 - x
★ Original number :
10 (8 - x) + x
80 - 10x + x
80 - 9x
When the digits of the number are interchanged :
10 (x) + 8 - x
10 x + 8 - x
9x + 8
(80 - 9x) - 36 = 9x + 8
80 - 36 - 9x = 9x + 8
44 - 9x = 9x + 8
44 - 8 = 9x + 9x
36 = 18x
x = 36/18
x = 2
Units digit = 2
Tens digit = 8 - x
8 - 2 = 6
Therefore, the original number is 62.
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Suppose you wanted to reach Alpha Centauri (4.4 ly from the Solar system) in 160 years How fast would you have to go, in km/hr?
If you want to reach Alpha Centauri you will need to go at a speed of 29,666,095,890,410 km/hr.
What is the distance to Alpha Centauri?Alpha Centauri is 4.4 lightyears away from your location, now let's convert this distance into kilometers:
1 lightyear = 9.46 trillion kilometers
4.4 x 9.45 trillion kilometers = 41.58 trillion kilometers
What should be the speed?Now, let's calculate the time available:
If there are 24 hours in a day, then in a year there are 24 x 365 = 8760, hours, which means in 160 years there are 1,401,600. Using this, calculate the speed:
41.58 trillion kilometers/ 1,401,600 hours = 29,666,095,890,410 kilometers per hour.
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Professor A. has 40 students in her class. After giving a first quiz, she calculated 5 measures of relative standing:
min =3, Q1 = 12, Median = 14, Q3 = 16, Max = 20.
1. Draw a box plot for quiz scores of her class.
2. What are the highest and the lowest quiz score?
3. What is the score that separates the bottom 75% from the top 25%?
4. How many students scored more than the median?
5. How many students scored more than 14 points?
6. What percent of her students received less than 12 points?
7. Would the score of 4 be an outlier? (use the IQR method to explain)
To draw a box plot for the quiz scores of Professor A's class, you would start by drawing a number line along the horizontal axis and marking the minimum, Q1, median, Q3, and maximum scores.
Then, you would draw a box from Q1 to Q3 to represent the middle 50% of the data in professor A's class. The median score would be marked within the box, and a line would be drawn from either end of the box to the minimum and maximum scores to represent the lower and upper extremes of the data.
The highest quiz score is 20, and the lowest quiz score is 3.
The score that separates the bottom 75% from the top 25% is Q3, which is 16.
By definition, half of the class should have scored more than the median, so 20 students scored more than 14 points.
By definition, the median is 14, so half of the class should have scored more than 14 points, so 20 students scored more than 14 points.
Using the min value and Q1 value, we know that 25% of the students scored less than 12 points.
To determine if 4 is an outlier, we can use the IQR (interquartile range) method, which is calculated by subtracting Q1 from Q3. In this case, the IQR is 4 (16 minus 12). We can then use the IQR to find the lower and upper bounds of the data, which are determined by subtracting 1.5 IQR from Q1 and adding 1.5 IQR to Q3. In this case, the lower bound is 8 (12 minus 1.54) and the upper bound is 20 (16 plus 1.54). 4 is lower than the lower bound; therefore, it is considered an outlier.
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P(x) =2x³ + 2x² - 3x - 3 is divisible by:
A. x - 1
B. x + 1
C. x + 2
D. x + 3
E. x - 2
Answer:
Option B
Step-by-step explanation:
If you replace the X in the P(X) it becomes -1 and then you'll change every x in the equation to -1
2(-1)³ + 2(-1)² -3(-1) -3
which = -2 +2 +3 -3
= 0
Since the answer is 0 it means x + 1 is a factor of 2x³ + 2x² - 3x -3
Answer:
B. x + 1-----------------------
Factorize the given polynomial:
P(x) =2x³ + 2x² - 3x - 3 = 2x²(x + 1) - 3(x + 1) =(x + 1)(2x² - 3)As we see the polynomial is divisible by x + 1.
Correct choice is B.
Question 2
Given the following information, find the probability that a randomly selected student will be short or very short. Number of students who are very short: 45, short: 60, tall: 82, very tall: 21
2DB. Probabilities from a given distribution of frequencies (Links to an external site.) (DOCX)
Group of answer choices
50.5%
21.0%
49.5%
28.8%
The probability of the number of students to be selected randomly short or very short is 0.5048 or 50.48% = 50.5%.A is correct option
Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
Number of students who are.
very short: 45,
short: 60,
tall: 82,
very tall: 21
The total number of students will be
Total sample = 45 + 60 + 82 + 21 = 208
The probability that a randomly selected student will be short or very short will be
Favorable sample = 45 + 60 = 105
Then the probability will be
P=105÷208
P=0.5048=50.48%
p=50.5%
option A is correct choice
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Calculate the bill total for the week by summing the daily bill amounts. In cell B26, enter a formula using the SUM function. The function argument should be the range of cells representing the daily bill totals (B25:H25).
The formula for the bill total for the week by summing the daily bill amounts is (=sum(B25:H25)).
What are excel math functions?Numerous common mathematical operations are carried out by the Excel Math Functions, such as fundamental arithmetic, conditional sums and products, exponents and logarithms, and trigonometric ratios. Please take note that the Excel Statistical Operations and Excel Engineering Functions categories also offer other math-related Excel functions.
Given finding the bill total for the week in cell B26
To sum the daily bill amounts, use Excel's Sum function, which is a pretty simple mathematical procedure. You can manually input the sum function by typing (=sum) in the field designated for the sum, after which you provide the parameters (=sum(B25:H25)). When you hit "enter," the outcome is presented immediately. By selecting the Sum Function from the Ribbon or by hitting Alt + =, this can also be done automatically.
Hence the formula is (=sum(B25:H25)).
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Find the slope of the line that contains the points (2, -1) and (4, 7)?
Answer:
mx=4
Step-by-step explanation:
Following the slope formula y2-y1/x2-x1, we can find our solution. Follow steps in image.
-Hope this helped
Calculate s20 for the arithmetic sequence in which a=32 and the common difference is d=2.9
It is possible to find the value of S20 by applying arithmetic progression. similar by applying the sum formula.
Formula is used to determine S20.
First term (a) here equals 32, and common difference (d) is equal to 2.9
Sn = n/2 × ( 2a + (n-1) × d)
S20 = 20/2 × ( 2×32 + ( 20 - 1 ) × 2.9 )
S20 = 20/2 × ( 64 + (19 × 2.9) )
S20 = 20/2 × ( 64 + 55.1 )
S20 = 20/2 × 119.1
S20 = 1191
Therefore, value of S20 is 1191
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Answer:
Step-by-step explanation:
[tex]s_{n}=\frac{n}{2} [2a+(n-1)d]\\s_{20}=\frac{20}{2} [2 \times 32+(20-1)\times 2.9]\\=10[64+19\times 2.9]\\=640+551\\=1191[/tex]
Which of the following has an answer that is a whole number?
1. v20
2. v15
3. v25
Answer:
3
Step-by-step explanation:
√25 = .5
Answer:
the answer is Number 3 = v25
What is the value of X
Answer:
A) 540
B) x = 115/3
Step-by-step explanation:
A) to find the sum of the interior angles of any gon, use this formula: 180(n-2); n = the number of sides of the gon you are given (ex. octagon will be n=8). Therefore, a pentagon will be: 180(5-2) = 540
B) To find x, we can add all the angles and make them equal to 540.
(3x+50) + (2x+60) + (3x-30) + 2x + 2x = 540
12x = 460
x = 115/3
C) Plug-in x for every angle
When a customer buys a family-sized meal at a certain restaurant, they get to choose 3 side dishes from 9 options. Suppose a customer is going to choose 3 different side dishes.
How many groups of 3 different side dishes are possible?
There amount are 504 different groups of 3 side dishes that a customer can choose from.
There are 9 possible side dishes, and the customer can choose any 3 of them. The number of different groups of 3 side dishes can be determined using the formula:
nCr = n!/(r!(n-r)!).
In this case,
n = 9 and r = 3,
so the number of possible groups is
9!/(3!(9-3)!) = 504.
When a customer buys a family-sized meal at a certain restaurant, they get to choose 3 side dishes from 9 options. The number of different groups of 3 side dishes possible for the customer to choose from can be determined using the formula for combination: nCr = n!/(r!(n-r)!). In this case, n = 9 (the number of possible side dishes) and r = 3 (the number of side dishes chosen). Applying the formula, the number of possible groups of 3 side dishes is 9!/(3!(9-3)!) = 504. This means that there are 504 different groups of 3 side dishes that a customer can choose from.
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Substitute given values of variables and evaluate expression
The value of the the expression 3x - 2y when x = 2 and y = 1 is 4
How to calculate the expression?It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.
In this case, we want to find the expression 3x - 2y when x = 2 and y = 1. This will be:
= 3x - 2y
= 3(2) - 2(1)
= 6 - 2
= 4
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Complete question
Find the expression 3x - 2y when x = 2 and y = 1. Substitute given values of variables and evaluate expression
Enter the quotient of 4 2/3 and 3/4 in fraction form
The quotient of 4 2/3 and 3/4 in fraction form is 6 2/9.
An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
There are three main categories of fractions in mathematics. Proper fractions, incorrect fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions. We categorize its types based on these two terms.
14/3 ÷ 3/4
⇒ 14/3 × 4/3
⇒ 56/9
⇒ 6 2/9
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Convert 25 dollars to dimes
Answer:
Step-by-step explanation:
250
Answer:250
Step-by-step explanation: just add 10 till you get 250
Help with math! (Picture attached)
You can find the sales price history of a car by looking up the VIN
How do I find the original price of my car?D=P(1−E%) 2
Or equivalently:
D=P(1− E/100 )^ 2
The exponential depreciation equation is of the form y=P(1-r)^xy=P(1−r) X With PP the original value, rr the depreciation rate per period and xx the number of periods.
The Kelley Blue Book, as well as its equally prominent website, is one of the most reliable sources for vehicle price, utilized by individuals buying or selling cars. Kelley evaluates the following values: private party, trade-in, recommended retail, and certified pre-owned (CPO). Check the vehicle history record while looking for a secondhand automobile online. If the original car window sticker is submitted with the report, you may sometimes figure out the MSRP of a vehicle.
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We want to know how many people plan on buying a new car this year. Determine the sample size needed for a one proportion confidence interval to estimate this with a margin of error of 0.06 and a 95% confidence interval. We don't have any idea what the population proportion would be.
The required sample size for the confidence interval is given as follows:
n = 267.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The margin of error is defined as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The parameters for this problem are given as follows:
[tex]M = 0.06, \pi = 0.5[/tex]
The estimate is of 0.5 as it is when the highest sample size is needed, and the sample size is obtained as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.06 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.06\sqrt{n} = 1.96 \times 0.5[/tex]
[tex]\sqrt{n} = \frac{1.96 \times 0.5}{0.06}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96 \times 0.5}{0.06}\right)[/tex]
n = 267.
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please help! Thank you!
The painting crew will take approximately 38 hours to complete the 24-mile stretch of road.
What is painting crew?Painting crew is a group of professional painters responsible for completing painting projects. They typically work on both interior and exterior painting projects and often specialize in specific types of paint finishes, such as faux finishes or specialty finishes. Painting crew members typically have a good understanding of painting techniques and tools, such as brushes and rollers, as well as a basic understanding of the chemistry involved in mixing paints.
This is calculated by taking the remaining miles (24 miles - 9.5 miles = 14.5 miles) and
dividing it by the rate at which they are painting (14.5 miles / 0.25 miles per hour = 58 hours).
Then we subtract the amount of hours they have already worked (58 hours - 9.5 hours = 38 hours).
Therefore, the painting crew will take approximately 38 hours to complete the 24-mile stretch of road.
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HELP PLEASE FAST!!!!!
Answer:
part a: y = -5/2 + 100
part b: because the line is descending from left to right, moving down by 5 units, and moving across by 2 units, the slope is -5/2. the y-intercept can be found by looking at the y-value where the line crosses the y-axis- which is 100.
part c: the slope represents the relation of a cellphone's battery percentage with the number of hours that pass.
Step-by-step explanation:
hope this helped, good luck!
Question 1 Integrate each of the following:
(a) x² - 2x + 1/x²
(b) x(x + 3)²
Step-by-step explanation:
I've skipped some steps. Hope you get this.
Answer:
(a) [tex]\displaystyle{\int \left(x^2-2x+\dfrac{1}{x^2}\right) \, dx} = \dfrac{x^3}{3} - x^2 - \dfrac{1}{x} + \text{C}}[/tex]
(b) [tex]\displaystyle{\int x\left(x+3\right)^2 \, dx = \dfrac{x^4}{4} + 2x^3 + \dfrac{9x^2}{2} + \text{C}}[/tex]
Step-by-step explanation:
Part A
Consider the indefinite integral with respect to x:
[tex]\displaystyle{\int \left(x^2-2x+\dfrac{1}{x^2}\right) \, dx}[/tex]
We can separately integrate each terms as they are in addition and subtraction:
[tex]\displaystyle{\int x^2 \, dx - \int 2x \, dx + \int \dfrac{1}{x^2} \, dx}[/tex]
For the last term, we can rewrite in negative exponent as [tex]x^{-2}[/tex] so we can apply power rules to all these terms (making it easier):
[tex]\displaystyle{\int x^2 \, dx - \int 2x \, dx + \int x^{-2} \, dx}[/tex]
The middle term -- we can separate the constant out of integral:
[tex]\displaystyle{\int x^2 \, dx - 2\int x \, dx + \int x^{-2} \, dx}[/tex]
Apply the power integration rule (for n ≠ 1):
[tex]\displaystyle{\int x^n \, dx = \dfrac{x^{n+1}}{n+1} + \text{C} \ \ \left(\text{where C is a constant}\right)}[/tex]
But we can add C later after we integrate all these terms, therefore:
[tex]\displaystyle{\dfrac{x^{2+1}}{2+1} - 2\cdot \dfrac{x^{1+1}}{1+1} + \dfrac{x^{-2+1}}{-2+1}}\\\\\displaystyle{\dfrac{x^{3}}{3} - 2\cdot \dfrac{x^{2}}{2} + \dfrac{x^{-1}}{-1}}\\\\\displaystyle{\dfrac{x^3}{3} - x^2 - x^{-1}}[/tex]
Rewrite the negative exponent back to fraction form:
[tex]\displaystyle{\dfrac{x^3}{3} - x^2 - \dfrac{1}{x}}[/tex]
After integrating all terms, we add + C every time. Hence:
[tex]\displaystyle{\int \left(x^2-2x+\dfrac{1}{x^2}\right) \, dx} = \dfrac{x^3}{3} - x^2 - \dfrac{1}{x} + \text{C}}[/tex]
Part B
Consider the indefinite integration with respect to x of:
[tex]\displaystyle{\int x\left(x+3\right)^2 \, dx}[/tex]
First, expand (x + 3)² to x² + 6x + 9:
[tex]\displaystyle{\int x\left(x^2+6x+9\right) \, dx}[/tex]
Then disribute the x inside the brackets:
[tex]\displaystyle{\int \left(x^3+6x^2+9x\right) \, dx}[/tex]
Integrate separately:
[tex]\displaystyle{\int x^3 \, dx + \int 6x^2 \, dx + \int 9x \, dx}[/tex]
Separate the constants:
[tex]\displaystyle{\int x^3 \, dx + 6\int x^2 \, dx + 9\int x \, dx}[/tex]
For the power integration formula, recall above. Thus:
[tex]\displaystyle{\dfrac{x^{3+1}}{3+1} + 6 \cdot \dfrac{x^{2+1}}{2+1} + 9 \cdot \dfrac{x^{1+1}}{1+1}}\\\\\displaystyle{\dfrac{x^{4}}{4} + 6 \cdot \dfrac{x^{3}}{3} + 9 \cdot \dfrac{x^{2}}{2}}\\\\\displaystyle{\dfrac{x^4}{4} + 2x^3 + \dfrac{9x^2}{2}}[/tex]
Add + C after finishing the integration process, hence:
[tex]\displaystyle{\int x\left(x+3\right)^2 \, dx = \dfrac{x^4}{4} + 2x^3 + \dfrac{9x^2}{2} + \text{C}}[/tex]
Let me know if you have any questions!
evidence of climate change indicates each of the following earth vital signs have been on the rise except:
Climate change is causing an increase in air temperature, sea surface temperature, sea level, ocean acidity, and snow cover, but not humidity.
Humidity
Climate change is the long-term change in average weather patterns, and is caused by increased atmospheric concentrations of greenhouse gases. Earth's vital signs that have been on the rise due to climate change include air temperature, sea surface temperature, sea level, ocean acidity, and snow cover. Humidity is not one of these vital signs, and actually is expected to decrease in some areas due to climate change.
Climate change is causing an increase in air temperature, sea surface temperature, sea level, ocean acidity, and snow cover, but not humidity.
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Vincent makes handcrafted dining tables, and he is trying to decide how many tables to produce. He can sell each dining table for $1,000. The cost of the first table is $900, for the second it's $1,100. For each additional table he produces, the marginal cost of each table increases by $200. How many dining tables should Vincent produce, and what is the total cost of his production?
The total cost of production of six dining tables is $1300.
How many tables to be produced?Production is the act of combining a variety of material and immaterial inputs to create an output. In a perfect world, this output would be a good or valuable good or service for people to use. The three main production factors of land, labor, and capital are known as primary producers of goods or services.
These crucial inputs are not significantly altered by the output process or the end product, nor are they made a crucial component of it. In classical economics, materials and energy are regarded as secondary factors because they are byproducts of land, labor, and capital. Technology and entrepreneurship are sometimes seen as evolved variables in production in addition to the conventional components of production.
Each dining table for $1,000
The second it's $1,100.
The marginal cost of each table increases by $200
The total cost of his production is
Fixed cost + Variable cost
= $1000 + 300= $1300
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