The sum of the 3rd triangular, 4th square, 5th pentagonal, 6th hexagonal, 7th heptagonal, and 8th octagonal numbers is 384.
What is triangle ?
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted triangle ABC.
The nth triangular number is given by the formula: n(n+1)/2
The nth square number is given by the formula: n^2
The nth pentagonal number is given by the formula: n(3n-1)/2
The nth hexagonal number is given by the formula: n(2n-1)
The nth heptagonal number is given by the formula: n(5n-3)/2
The nth octagonal number is given by the formula: n(3n-2)
So, the sum of the 3rd triangular number, 4th square number, 5th pentagonal number, 6th hexagonal number, 7th heptagonal number and 8th octagonal number can be calculated as follows:
Triangular number: 3 * (3 + 1) / 2 = 6
Square number: 4^2 = 16
Pentagonal number: 5 * (3 * 5 - 1) / 2 = 35
Hexagonal number: 6 * (2 * 6 - 1) = 91
Heptagonal number: 7 * (5 * 7 - 3) / 2 = 98
Octagonal number: 8 * (3 * 8 - 2) = 128
The sum of these numbers is: 6 + 16 + 35 + 91 + 98 + 128 = 384.
So, the sum of the 3rd triangular, 4th square, 5th pentagonal, 6th hexagonal, 7th heptagonal, and 8th octagonal numbers is 384.
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The sum of the 3rd triangular, 4th square, 5th pentagonal, 6th hexagonal, 7th heptagonal, and 8th octagonal numbers is 384.
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted triangle ABC.
The nth triangular number is given by the formula: n(n+1)/2
The nth square number is given by the formula: n^2
The nth pentagonal number is given by the formula: n(3n-1)/2
The nth hexagonal number is given by the formula: n(2n-1)
The nth heptagonal number is given by the formula: n(5n-3)/2
The nth octagonal number is given by the formula: n(3n-2)
So, the sum of the 3rd triangular number, 4th square number, 5th pentagonal number, 6th hexagonal number, 7th heptagonal number and 8th octagonal number can be calculated as follows:
Triangular number: 3 * (3 + 1) / 2 = 6
Square number: 4² = 16
Pentagonal number: 5 * (3 * 5 - 1) / 2 = 35
Hexagonal number: 6 * (2 * 6 - 1) = 91
Heptagonal number: 7 * (5 * 7 - 3) / 2 = 98
Octagonal number: 8 * (3 * 8 - 2) = 128
The sum of these numbers is: 6 + 16 + 35 + 91 + 98 + 128 = 384.
So, the sum of the 3rd triangular, 4th square, 5th pentagonal, 6th hexagonal, 7th heptagonal, and 8th octagonal numbers is 384.
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The lifetime of the timing belt of a certain make of cars is normally distributed with mean 125,000 miles and standard deviation 10,000 miles.
a) Find the probability that a timing belt lasts until the car runs 140,000 miles.
b) The auto maker recommends that owners have the timing belt replaced when the mileage reaches 90,000 miles. What is the probability that the timing belt fails before the car reaches the manufacturer’s recommended mileage?
c) An owner of this type of car wants to take a chance and replace the timing belt at the 1st percentile of the distribution. What should be the mileage of the car when he has the timing belt replaced?
The probability that a timing belt lasts until the car runs 140,000 miles is 0.9332.
a) The probability that a timing belt lasts until the car runs 140,000 miles can be found using the Z-score formula. The Z-score is calculated as (140,000 - 125,000)/10,000 = 1.5. The probability can be found using the Z-score table or by using a calculator, and is equal to 0.9332.
b) The probability that the timing belt fails before the car reaches the manufacturer’s recommended mileage of 90,000 miles can be found using the Z-score formula. The Z-score is calculated as (90,000 - 125,000)/10,000 = -2.5. The probability can be found using the Z-score table or by using a calculator, and is equal to 0.0062.
c) The 1st percentile of a normal distribution is the Z-score corresponding to the cumulative probability of 0.01. The Z-score for the 1st percentile is -2.33. The mileage of the car when the timing belt should be replaced can be found using the Z-score formula. The mileage is equal to 125,000 - (2.33 * 10,000) = 110,700 miles.
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find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 2e−x, y = 2, x = 4; about y = 4
The volume V of the solid obtained by rotating the region bounded by the given curves y = 2[tex]e^{-x}[/tex], y = 2, x = 4; about y = 4 is 256π.
The volume of the solid obtained by rotating the region bounded by the given curves about the line y=4 is given by
V = 2π ∫⁴₀ (4-2[tex]e^{-x}[/tex])² dx
We can calculate the integral using integration by parts.
Let u = 4-2[tex]e^{-x}[/tex]
⇒ du = 2d[tex]e^{-x}[/tex]
and dv = 2dx
⇒ v = x
So,
V = 2π ∫⁴₀ (4-2[tex]e^{-x}[/tex])² dx
= 2π (x (4-2[tex]e^{-x}[/tex])² - 0 (4-2[tex]e^{-x}[/tex]})² - 2∫⁴₀ x d (4-2[tex]e^{-x}[/tex]))
= 2π (2×4³ - 4∫⁴₀ x [tex]e^{-x}[/tex] dx)
Using integration by parts again
Let u = 4-2[tex]e^{-x}[/tex] ⇒ du = -2d[tex]e^{-x}[/tex]
and dv = xdx ⇒ v = x²/2
So,
V = 2π (2×4³ - 4∫⁴₀ x [tex]e^{-x}[/tex] dx)
= 2π (2×4³ - 2×2∫⁴₀ x² [tex]e^{-x}[/tex] dx)
Again we can calculate the integral using integration by parts.
Let u = x² ⇒ du = 2xdx
and dv = [tex]e^{-x}[/tex] dx ⇒ v = -[tex]e^{-x}[/tex]
So,
V = 2π (2×4³ - 2×2∫⁴₀4 x^2 [tex]e^{-x}[/tex]} dx)
= 2π (2 × 4³-2 × 2 × ([tex]-e^{-4}[/tex] + 2∫⁴₀ [tex]e^{-x}[/tex]dx))
= 2π (2×4³ - 2×2 (1+4))
= 2π (2×4³ - 16)
= 2π (128-16)
= 256π
Therefore, the volume V of the solid obtained by rotating the region bounded by the given curves y = 2[tex]e^{-x}[/tex], y = 2, x = 4; about y = 4 is 256π.
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2. Is the following inequality always, sometimes, or never true?
2(3x - 1) +4> 6x + 2
The two sides of an inequality are not the same so inequality can never be true.
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.
Given that the inequality is 2(3x - 1) +4> 6x + 2. The inequality will be solved as below;-
2(3x - 1) +4> 6x + 2
6x - 2 + 4 > 6x + 2
6x + 2 > 6x + 2
The two sides are equal so inequality can never be true.
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If you know Emma Waton peech "HeforShe" what ele could I analye other than her tone in voice , word choice and body language ?
Women Emma Watson spoke intelligently, significantly, and powerfully about gender inequity and how to combat it.
She did this in order to begin the HeForShe campaign, which tries to recruit men and boys to the feminist movement's struggle for gender parity.
The purpose of this campaign is to encourage as many men and boys to support gender equality as they can. The terrible reality that "feminism" is all too frequently associated with "man hate," effectively stopping the progress toward attaining gender equality, was brought to light by Emma Watson in her powerful statement.
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Equation: &-
Solution:
,. © Justify Conclusions Seventy-five percent, or 15, of the students in Emily's homeroom class are going on a field trip. Two thirds, or 12, of the students in Santiago's homeroom class are going on the field trip. Which class has more students? Justify your answer.
The class that has more students, given the percentage of students in both classes is Emily's homeroom tab .
How to find the class with more student ?To find the class with the higher number of students, you need to find the total number of students in these classes.
The number of students in Emily's homeroom class is:
= Number of students / Percentage of students
= 15 / 75 %
= 20 students
Students in Santiago's homeroom class is :
= 12 / ( 2 / 3 )
= 12 x 3 / 2
= 18 students
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How do you recruit people for research?
Recruiting participants for research can be done through various methods such as:
1. Online advertisements
2. Flyer distributions in public places
3. Collaboration with organizations or schools
4. Referral from previous participants
5. Direct mailing to potential participants
6. Social media promotion.
It is important to consider ethical guidelines and informed consent procedures when recruiting participants for research.
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Compare the key feature (slope and y-intercept) of each linear function g with those of the graph of f(x)= 2x + 3. Describe how the value of k affects the key features.
23. g(x)=3(2x+3) has a slope of 6 and y-intercept of 9.
24. g(x)=2(0.5x) +3 has a slope of 1 and y-intercept of 3.
25. g(x)=1(2x+3) has a slope of 2 and y-intercept of 3.
26. g(x)=2(1)x+3 has a slope of 2 and y-intercept of 3.
How did we get the values?23. g(x)=3(2x+3) can be written as g(x)=6x + 9. This shows that the slope of the function is 6 and the y-intercept is 9.
24. g(x)=2(0.5x) +3 can be written as g(x)=x + 3. This shows that the slope of the function is 1 and the y-intercept is 3.
25. g(x)=1(2x+3) can be written as g(x)=2x + 3. This shows that the slope of the function is 2 and the y-intercept is 3.
26. g(x)=2(1)x + 3 can be written as g(x)=2x + 3. This shows that the slope of the function is 2 and the y-intercept is 3.
The value of k in the linear function g(x)=k(mx+b) affects the slope of the function by multiplying the slope of the original function m by k. The y-intercept of the function remains unchanged.
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a one-sample z-test for a population proportion will be conducted using a simple random sample selected without replacement from a population. which of the following is a check for independence? A
npo 10 and n(1-P) 10 for sample size n and population proportion P-
Each sample proportion value is less than or equal to 0.5.
B
c
The sample size is more than 10 times the population size.
D
The population size is more than 10 times the sample size.
E
The population distribution is approximately normal.
The check for independence in a one- sample is
The population size is further than 10 times the sample size.
The Correct option is D.
What is Z- test?
A Z- test is a statistical thesis test used to determine whether a sample mean significantly differs from a given population mean when the population standard divagation is known.
For a one- sample z- test for a population proportion, the sample is named without relief from a finite population.
In order for the test to be valid, it's necessary to insure that the sample is small relative to the population size.
still, it can be considered large enough to satisfy the independence supposition, If the population size is further than 10 times the sample size. This supposition is necessary for the validity of statistical conclusion in this environment.
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Find the centroid of the triangle whose vertices are A(2, 6), B(4, 9), and C(6,15).
As a result, the triangle's centroid at vertices A(2, 6), B(4, 9), and C(6, 15) is (4, 10).
Given the vertices of a triangle, how do you get its centroid? The center of the thing is represented by the centroid.The centroid of a triangle is the location where the triangle's three medians cross.The junction of all three medians is another definition of it.A line connecting a side's midway to the triangle's opposite vertex is called the median.C = [(y1 + y2 + y3)/ 3, (x1 + x2 + x3)/ 3]. The triangle's centroid is indicated with the letter C.The x-coordinates of a triangle's three vertices are x1, x2, and x3.The y-coordinates for a triangle's vertices are y1, y2, and y3. As a result, the triangle's centroid at vertices A(2, 6), B(4, 9), and C(6, 15) is (4, 10).To learn more about triangle's centroid refer
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Evander King is ordering a luxury convertible. The base price is $81,975. Options include satellite radio, $475; keyless entry, $555; navigation system, $1,250; and custom paint, $983. The destination charge is $890. The dealer's costs are 90% of the base price and 88% of the options price. The dealer will sell Evander the car for $200 more than the dealer's cost plus a 6% sales tax. What is the total cost of the convertible, including tax?
Answer: $82,403.28
Step-by-step explanation:
475+555+1250+983 = 3263 (total option price)
81,975 (total base price)
0.9 * 81,975 = 73,777.5 + 200
.88 * 3263 = 2,871.44
1.06 * (73,977.5 + 2871.44 + 890) = 82,403.28 (Rounded to nearest tenth)
elementary statistics, a step-by-step approach, 10th ed., bluman
The subject is taught in a non-theoretical manner in Al Bluman's Elementary Statistics. Today's world speaks statistics, and Bluman's market-leading Step-by-Step Approach makes it simple to learn and comprehend.
Bluman gives your students all the assistance they need to understand the foundations of statistics and draw that link by assisting them in transitioning from the computational to the conceptual.
Elementary Statistical Methods are the collection, analysis, presentation, and interpretation of data, and probability. The analysis includes descriptive statistics, correlation and regression, confidence intervals, and hypothesis testing.
Thus, The subject is taught in a non-theoretical manner in Al Bluman's Elementary Statistics. Today's world speaks statistics, and Bluman's market-leading Step-by-Step Approach makes it simple to learn and comprehend.
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If the scores on an intelligence test form a normal curve with a standard deviation of 15,the mean, median, and mode are 100.68 percent of scores are between 85 and 115.60 percent of test-takers earned at least a 100.the first and second choices only are true.the first three choices are true.
The mean, median, and mode are all equal to 100, and 68% of the scores are between 85 and 115. The third choice is also true, as 60% of test-takers earned at least a 100.
The normal curve is a symmetrical bell-shaped distribution with the mean, median, and mode all equal to 100. If we take 15 as the standard deviation, then 68% of the scores will lie between 85 (100-15) and 115 (100+15). We can calculate this using the z-score formula: z=(x-μ)/σ, where x is the score, μ is the mean, and σ is the standard deviation.
In this case, the z-score for the lower limit (85) is (85-100)/15=-1. The z-score for the upper limit (115) is (115-100)/15=1. We can then use the z-score table to determine that the area between -1 and 1 is 68%. Therefore, 68% of the scores are between 85 and 115.
To determine the percentage of test-takers who earned at least a 100, we can use the same z-score formula. The z-score for x=100 is (100-100)/15=0. We can then use the z-score table to determine that the area above 0 is 60%. Therefore, 60% of test-takers earned at least a 100.
Therefore, the first two choices are true. The mean, median, and mode are all equal to 100, and 68% of the scores are between 85 and 115. The third choice is also true, as 60% of test-takers earned at least a 100.
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reaching into the change drawer, sue notices that she only has nickels (worth 5 cents) and dimes (worth 10 cents). from prior experience, she knows that the variance of the number of nickels is 8, the variance of the number of dimes is 10 and the covariance of the number of nickels to the number of dimes is 5. what is the covariance of the number of coins to the value of the coins (in cents)?
The covariance between the number of coins and the value of the coins is 240.
The covariance between the number of coins (N) and the value of the coins (V) can be calculated as
Cov(N, V) = Cov(n nickels + n dimes, 5n nickels + 10n dimes)
= 5 Cov(n nickels, n nickels) + 10 Cov(n nickels, n dimes) + 5 Cov(n dimes, n nickels) + 10 Cov(n dimes, n dimes)
= 5 * Var(n nickels) + 10 * Cov(n nickels, n dimes) + 5 * Cov(n dimes, n nickels) + 10 * Var(n dimes)
= 5 * 8 + 10 * 5 + 5 * 5 + 10 * 10
= 40 + 50 + 50 + 100
= 240
So the covariance between the number of coins and the value of the coins is 240.
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2x1+48-5x48+96-23= blank please helppppppppp
Answer:
-117
Step-by-step explanation:
2x1+48-5x48+96-23=-117
First multiplication
2×1=2
5×48=240 ->
2+48-240+96-23
2+48=50
50-240=-190
-190+96=-94
-94-23=-117
Hope that helped! Let me know if you have any further questions.
Solve the inequality 4+p<11
Answer:
p<11-4
p<7
Step-by-step explanation:
we have 4+p<11 where we send 4 in another side and we get p<11-4 =p<7
How do pattern in mathematic help individual better undertand the world and predict what come next?
Pattern in mathematic help individual better undertand the world and predict what come next because patterns follow a predictable rule and that rule allows us to predict what will come next.
What is Predictable Rule?
A prediction function is a mathematical function that predicts a future occurrence based on past events. Many other types of functions can be classified as prediction functions, such as those based on likelihood, sufficiency, and plausibility.
Reasons:
Patterns are more than just beautiful designs (though they frequently are), they follow a predictable law, and that rule allows us to forecast what will happen next. Mathematics, according to mathematicians, is the study of patterns—patterns and structure in numbers, as well as patterns and structure in geometry.
Mathematical tools can explain and improve the way the world works. Mathematical modeling has the potential to save lives, aid in policy and decision-making, and optimize economic growth. It can also be used to better understand the Universe and the conditions required for life to thrive.
Scientists, like everyone else, rarely, if ever, make accurate predictions. The future remains unpredictable regardless of the data and mathematical models available. As a result, scientists must account for mistake in our fundamental equation. In other words, Y = f(X) + E, where "E" represents our incapacity to forecast accurately.
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Patterns in mathematic help individual better understand the world and predict what comes next because patterns follow a predictable rule and that rule allows us to predict what will come next.
What is the Predictable Rule?
A prediction function is a mathematical function that predicts a future occurrence based on past events. Many other types of functions can be classified as prediction functions, such as those based on likelihood, sufficiency, and plausibility.
Reasons:
Patterns are more than just beautiful designs (though they frequently are), they follow a predictable law, and that rule allows us to forecast what will happen next. Mathematics, according to mathematicians, is the study of patterns—patterns and structure in numbers, as well as patterns and structure in geometry.
Mathematical tools can explain and improve the way the world works. Mathematical modeling has the potential to save lives, aid in policy and decision-making, and optimize economic growth. It can also be used to better understand the Universe and the conditions required for life to thrive.
Scientists, like everyone else, rarely, if ever, make accurate predictions. The future remains unpredictable regardless of the data and mathematical models available. As a result, scientists must account for mistake in our fundamental equation. In other words, Y = f(X) + E, where "E" represents our incapacity to forecast accurately.
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As shown in the diagram, PQ/QR = 1/3. Find [PAB]/[QAB].
The ratio of [PAB]/[QAB]. is 1/3
How to determine the division of the anglesFrom the question, we have the following parameters that can be used in our computation:
The triangle
Also, we have
PQ/QR = 1/3
This means that;
The line segments divide PAB to 1/3
So, we have
PAB = 1
QAB = 1 - 1/3 = 2/3
When represented as quotient, we have
[PAB]/[QAB] = 3/2
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What is the letter name of the point (-3, 4)?
Answer: R
Step-by-step explanation: you are gonna go left 3 and up 4.
x=-3 and y=4
Liam’s class has 30 students each either 11 or 12 years old the sum of their ages is 352 years how many of each age are in his class 
Answer: There are 8 11-year-old students and 22 12-year-old students in Liam's class.
Step-by-step explanation:
Let's call the number of 11-year-old students in class x. Then, the number of 12-year-old students in the class would be 30 - x.
The total number of years that the 11-year-old students represent is 11 * x.
The total number of years that the 12-year-old students represent is 12 * (30 - x).
The sum of all the years is 352, so we can set up an equation based on the above information:
11x + 12(30 - x) = 352
Expanding the second term on the left-hand side:
11x + 360 - 12x = 352
Combining like terms:
-x + 360 = 352
Subtracting 360 from both sides:
-x = -8
Dividing both sides by -1:
x = 8
So, there are 8 11-year-old students and 30 - 8 = 22 12-year-old students in Liam's class.
Let u and v be vectors in R^2. Which of the following is/are true?(select all that apply)[ ] None of the choices is correct.[ ] The set of all vectors which are scalar multiple of a nonzero vector u is a line through u and 0.[ ] The operation of vector addition is not commutative.[ ] A column vector in R^2 is a 1x2 matrix.[ ] The magnitude of a vector cv is c times the magnitude of v, where c is any scalar.
None of the choices is correct, and a column vector in R^2 is not a 1x2 matrix.
[ ] The set of all vectors which are scalar multiple of a nonzero vector u is a line through u and 0.
[ ] The operation of vector addition is not commutative.
[ ] The magnitude of a vector cv is c times the magnitude of v, where c is any scalar.
None of the choices is correct, and a column vector in R^2 is not a 1x2 matrix.
None of the choices is correct. The set of all vectors which are scalar multiple of a nonzero vector u is a line through u and the origin (not just 0). The operation of vector addition is not commutative, meaning that the order of addition matters. The magnitude of a vector cv is c times the magnitude of v, where c is any scalar and v is a vector. A column vector in R^2 is a matrix with two columns and one row (1x2 matrix).
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True or false: if the truth is x, and y and z are conflicting claims, it must be true that either y≠x or z≠x, or neither?
Tt is also possible neither y nor z is x.
Now, According to the question;
The x and y-axis are two important lines of the coordinate plane. The x-axis is a horizontal number line and the y-axis is a vertical number line. These two axes intersect perpendicularly to form the coordinate plane. The x-axis is also called the abscissa and the y-axis is called the ordinate.
If x is true, a non true statement cannot be the same as it.
Now, In symbolic logic, = doesn't mean two statements have the same value—it means they are the same literal statement.
So, if x is true, and y and z contradict, at least one of y and z is false, and that false statement cannot possibly be x.
Hence, it is also possible neither y nor z is x.
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What is the Slope of (8,6) and (16,11)
Answer:
5/8
Step-by-step explanation:
[tex]\textrm{Slope } = $\dfrac{y_2 - y_1}{x_2 - x_1}$[/tex]
where[tex](x_1, y_1) \;\; (x_2, y_2)[/tex] are two points on the graph
The given points on the graph are (8,6) and (16,11)
Difference in y values, y2 - y1 = 11 - 6 = 5
Difference in x values,: x2 - x1 = 16 - 8 = 8
Slope = 5/8
Two students in Mr. Huber's class, Emmy and Warren, have been assigned a workbook to complete at their own pace. They get together at Emmy's house after school to complete as many pages as they can. Emmy has already completed 27 pages and will continue working at a rate of 13 pages per hour. Warren has completed 33 pages and can work at a rate of 10 pages per hour. Eventually, the two students will be working on the same page. How long will that take? How many pages will each of them have completed?
The time taken by both of them to work on the same page is 2 hours. The number of pages written by Emmy is 53 and the number of pages written by Warren is 53.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Emmy has already completed 27 pages and will continue working at a rate of 13 pages per hour. Warren has completed 33 pages and can work at a rate of 10 pages per hour.
The time taken to reach the same page is,
13t + 27 = 33 + 10t
13t - 10t = 33 - 27
3t = 6
t = 2 hours
The number of pages written by Emmy is,
N = 13t + 27
N = ( 13 x 2) + 27 = 53
The number of pages written by Warren is,
N = 33 + 10t
N = 33 + 20
N = 53
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Use the given function to find the following.
x + 10
5
f (x) =
=
-1
f-¹ (x).
Find
-1
Find f (ƒ-¹ (5)).
(no spaces)
The composite function f (ƒ-¹ (5)) is 5
How to determine the composite functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = (x + 10)/5
Also, we have
f-¹ (x) = 5x - 10
The composite function f (ƒ-¹ (5)) is calculated as
f (ƒ-¹ (x)) = (5x - 10 + 10)/5
Evaluate the difference
f (ƒ-¹ (x)) = 5x/5
So, we have
f (ƒ-¹ (x)) = x
Substitute 5 for x
f (ƒ-¹ (5)) = 5
Hence, the solution is 5
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Complete question
Use the given function to find the following.
f(x) = (x + 10)/5
f-¹ (x) = 5x - 10
Find f (ƒ-¹ (5)). (no spaces)
vector a⃗ =6.0i^−4.0k^. construct a unit vector that is parallel to
The unit vector that is parallel to a⃗ is (6/√74)i^−(4/√74)k^.
1. Calculate magnitude of a⃗:
a⃗ = 6.0i^−4.0k^
|a⃗| = √(6.0^2+4.0^2) = √74
2. Construct unit vector, u⃗= (6/√74)i^−(4/√74)k^
u⃗ = (6/√74)i^−(4/√74)k^
3. The unit vector that is parallel to a⃗ is (6/√74)i^−(4/√74)k^.
The unit vector that is parallel to a⃗ is (6/√74)i^−(4/√74)k^.
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Lupe's family traveled 5 7 of the distance to her aunt’s house on Saturday. They traveled 1 2 of the remaining distance on Sunday. What fraction of the total distance to her aunt’s house was traveled on Sunday?
Answer:
3/14
Step-by-step explanation:
They traveled 5/7 of the distance on Saturday and 1/2 of the remaining
distance, 3/7, on Sunday so..
(1/2)(3/7) = 3/14
Hope this helps :)
Answer:Lupe's family traveled 5/7 of the total distance to her aunt's house on Saturday, so the remaining distance was 1 - (5/7) = 2/7.
On Sunday, they traveled 1/2 of the remaining distance, which was 2/7, so the total distance traveled on Sunday was 1/2 * 2/7 = 2/14 of the total distance.
Step-by-step explanation:
Lupe's family traveled 5/7 of the total distance to her aunt's house on Saturday, so the remaining distance was 1 - (5/7) = 2/7.
On Sunday, they traveled 1/2 of the remaining distance, which was 2/7, so the total distance traveled on Sunday was 1/2 * 2/7 = 2/14 of the total distance. :D
find the rules for the composite functions f ∘ g and g ∘ f.
The composite functions f ∘ g and g ∘ f is defined as follows:
f ∘ g (x) = f(g(x))
g ∘ f (x) = g(f(x))
In other words, f ∘ g is the composition of two functions f and g, such that the output of g is used as the input to f. Similarly, g ∘ f is the composition of two functions g and f, such that the output of f is used as the input to g.
It's important to note that the order in which the functions are composed matters, as f ∘ g is not necessarily equal to g ∘ f. In general, the composite function of two functions is not commutative, meaning that the order in which the functions are composed affects the result.
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In Exercises 17-20, find the volume of the solid generated by revolv- ing ` the shaded region about the given axis. 17. About the x-axis 18. About the J-axis x + 2 = 2 1 19. About the y-axis 20. About the x-axis sin x cOS X Lan'
the volume of the solid generated by revolving the shaded region about the given axis x- axis is: 2π/3
What is shaded region?The difference between the area of the complete polygon and the area of the unshaded portion inside the polygon is the area of the shaded region. There are two methods for the area of the darkened component to appear in polygons. The darkened area can be found either in the polygon's center or on one of its sides.
We first solve for y from the equation:
x+2y=2
or, 2y = 2 - x
or, y = (2 - x) / 2
From the graph we see that the equation is from x=0 to x=2
And it is rotating about the x axis. We can use the Disk method to find the volume of the solid:
= π [tex]\int\limits^2_0 {((2 - x)/2)^2} \, dx[/tex]
= π/4 [4x - 2x² + x³/3]₀²
= 2π/3
so, 2π/3 is the volume of the solid, it is rotating about the x axis.
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The complete question is as follows:
Please answer the question :)
According to the information in the graph, it can be established that the profit for 600 people would be $3,013.96
How to calculate the profit for 600 people?To calculate the profit for 600 people we must take into account the information in the graph. In this case we must establish how many people participated in the survey and how much was the total profit of the store with these customers.
11 + 8 + 9 + 19 + 3 = 5087.98 + 66.45 + 32.50 + 34.50 + 29.95 = 251.08Now we must make a rule of three to establish how much the profit would be in a group of 600 buyers.
50 - $251.08600-x600 * 251.08 / 50 = 3,012.96According to the above, the profit of the store with a group of 600 buyers would be 3,012.96
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Find the values of a and b that make the following piecewise defined function both continuous and differentiable everywhere. f(x) = 3x + 4, X<-3
2x2 + ax + b. X>-3
The values of a and b that make the function both continuous and differentiable everywhere are a = -3 and b = 19.
What do you mean by function?A function is a mathematical concept that assigns a unique output value for each input value. It is a rule that takes in an input or set of inputs and maps it to a specific output. Functions are represented by symbols, usually denoted by a letter, such as "f".
In mathematical notation, a function is usually expressed as "f(x)" where "x" is the input and "f(x)" is the corresponding output. For example, a function could be defined as f(x) = x^2, which means that for any value of x, the function will calculate and return the square of that value.
Functions play a central role in mathematics and are used to model real-world phenomena and to study the relationships between variables. They are also used in computer programming to perform specific tasks, such as converting temperatures from Celsius to Fahrenheit or calculating the square root of a number.
To make the function continuous at x = -3, the value of f(-3) must be equal for both the first and second parts of the definition. That is, 3 * -3 + 4 = -3 * -3 + a * -3 + b. Solving for a and b gives us:
a = -3
b = 19
To make the function differentiable at x = -3, the limits of the first and second parts of the definition must be equal, and their derivatives must also be equal.
The limit from the left of f(-3) is:
[tex]\lim_{x \to \ -3}[/tex]f(x) = 3 * -3 + 4 = 5
The limit from the right of f(-3) is:
[tex]\lim_{x \to \ -3}[/tex] + f(x) = -3 × -3 + a × -3 + b = -3 × -3 + 19 = 19
So the function is continuous at x = -3. To check for differentiability, we find the derivative of the first part:
f'(x) = 3
And the derivative of the second part:
f'(x) = -6x + a
The derivative of the two parts must be equal at x = -3, so we have:
3 = -6 × -3 + a
3 = 18 - a
a = -15
This value of a is different from the value we found in the first step, so the function is not differentiable at x = -3. To make it differentiable, we must choose the value of a that makes the function continuous, which is a = -3.
So the values of a and b that make the function both continuous and differentiable everywhere are a = -3 and b = 19.
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