Sequence having rule f(n) = n² - 5, the first four terms will be -4, -1, 4, and 11.
What is a sequence?A sequence in mathematics is a group of integers that adhere to a specific pattern or rule. A sequence of numbers might be infinite or finite, and they are arranged in a certain order.
Every number in the sequence is referred to as a term, and its location within the sequence is referred to as its index. As an illustration, the first term in the series 1, 3, 5, 7, 9, is 1, the second term is 3, the third term is 5, and so on.
Now,
The explicit rule for the sequence is given by f(n) = n² - 5, which means that to find the nth term of the sequence, we need to plug in the value of n into this formula.
To find the first four terms of the sequence, we can simply substitute n = 1, 2, 3, and 4, respectively, into the formula and evaluate the expression.
The first term is f(1) = 1² - 5 = -4.
The second term is f(2) = 2² - 5 = -1.
The third term is f(3) = 3² - 5 = 4.
The fourth term is f(4) = 4² - 5 = 11.
Therefore,
the first four terms of the sequence defined by the explicit rule f(n) = n² - 5 are -4, -1, 4, and 11.
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Find the centroid of the region bounded by the given curves y=2-x^2 , y=x
The location of the region's centroid is (0, 2/5).
What does the region border by the curves' centroid look like?
We must first determine the limits of integration and the formulas for the x-coordinate and y-coordinate of the centroid in order to determine the centroid of the area enclosed by the curves y=2-x2 and y=x.
We shall integrate across the range [-1,1] since the curves intersect at (1,1) and (-1,1).
We must assess the following integral in order to determine the centroid's x-coordinate:
x' = (1/A) ∫[a,b] xf(x) dx
Where: A is the region's area (which we can find by integrating the difference between the two curves).
A = ∫[a,b] (f(x) - g(x)) dx
In this case, f(x) = 2 - x² and g(x) = x, so
A = ∫ [-1,1] (2 - x² - x) dx
= [2x - (1/3)x³ - (1/2) x²] | from -1 to 1
= (4/3)
Now we can evaluate the x-coordinate of the centroid:
x' = (1/A) ∫ [-1,1] x*(2-x²-x) dx
= (1/ (4/3)) ∫ [-1,1] (2x - x³ - x²) dx
= (3/4) [(x²/2) - (1/4) x⁴ - (1/3) x³] | from -1 to 1
= 0
Hence, the x-coordinate of the centroid is 0.
To find the y-coordinate of the centroid, we need to evaluate the following integral:
y' = (1/A) ∫[a,b] (1/2) [f(x)² - g(x)²] dx
y' = (1/ (4/3)) ∫ [-1,1] (1/2) [(2-x²) ² - x²] dx
= (3/4) [(8/15) x⁵ - (2/3) x³ + (1/2) x] | from -1 to 1
= (2/5)
Hence, the y-coordinate of the centroid is 2/5.
Therefore, the centroid is (0,2/5).
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Jimmy cuts grass in the summertime to save money for college. This week, he was paid $50
on Monday, $70 on Tuesday, $25 on Wednesday, $45 on Thursday, and $50 on Friday. What
is the average amount that Jimmy was paid for each work day this week?
$45
A.
B. $48
C. $50
D. $70
Answer:
B. $48
Step-by-step explanation:
Average=sum of the numbers÷number of numbers you added
Average will now be $50+$70+$25+$45+$50= $240÷5= $48
Please help me with this question
The graph of the function is added as an attachment
How to determine the graph of the functionFrom the question, we have the following parameters that can be used in our computation:
g(x) = 6, -7 < x ≤ -2
2, -2 < x ≤ 3
-2, 3 < x ≤ 8
The above is a piecewise function that has three linear functions, and three domains
Using the above as a guide, we have the following:
We plot each function in each domain
See attachment for the graph of the function
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Suppose the same amount of snow fell the following winter, but the same amount of snow fell each week. How much snow fell each week if there were the same number of weeks?
(Type a whole number, fraction, or mixed number.)
The amount of snow that fell each week was 2 units (assuming the units are consistent with the original scenario.
Describe Snowfall measurement?Snowfall measurement is the process of determining the amount of snow that falls at a particular location during a specific period of time. Accurate snowfall measurement is important for a variety of reasons, including transportation safety, weather forecasting, and water resource management.
If the same amount of snow fell the following winter, but the same amount of snow fell each week, and there were the same number of weeks, then we need to divide the total amount of snow by the number of weeks to find the amount of snow that fell each week.
Looking at the diagram, we can estimate the total amount of snow that fell by counting the number of asterisks (*) in the diagram. There are 8 asterisks, which represent the total amount of snow that fell over the winter.
Since there are 4 weeks (the same number of weeks as the original scenario), we can divide the total amount of snow by 4 to find the amount of snow that fell each week:
Total amount of snow = 8 asterisks
Amount of snow that fell each week = Total amount of snow / Number of weeks
= 8 / 4
= 2
Therefore, the amount of snow that fell each week was 2 units (assuming the units are consistent with the original scenario).
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alex runs 5 miles in 40 minutes. if alex runs at the same rate how many miles can ge run in 120 minutes
Answer:
15 miles in 120 minutes
Step-by-step explanation:
We can start by using the unit rate of Alex's running speed:
5 miles / 40 minutes = 0.125 miles per minute
This means that Alex runs at a speed of 0.125 miles per minute.
To find out how many miles he can run in 120 minutes, we can multiply his speed by the number of minutes:
0.125 miles/minute × 120 minutes = 15 miles
Therefore, if Alex runs at the same rate, he can run 15 miles in 120 minutes.
A doctor was interested in the heights of all 14-year-olds in the state of Texas. He gathered data from a random sample of 1,000 pediatricians in the state and wanted to create an appropriate graphical representation for the data.
Which graphical representation would be best for his data?
Circle graph
Bar graph
Line plot
Box plot
The graphical representation that would be best for the doctor's data is a box plot. The correct option is the last option Box plot
Determining the graphical representation that would be best for the dataFrom the question, we are to determine the graphical representation that would be best for the doctor's data
In this case, the doctor is interested in the heights of 14-year-olds in the state of Texas, and has gathered data from a random sample of 1,000 pediatricians in the state. A box plot would allow the doctor to see the range of heights observed in the sample, as well as any potential outliers or unusual observations. It would also allow for easy comparison of the heights of different groups or regions within the state, if desired.
A box plot is a graphical representation of a data set that displays the minimum, maximum, median, and quartiles of the data.
Hence, a box plot would be the best graphical representation for the doctor's data. It can help visualize the spread and distribution of the data and identify any outliers.
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Wireless phone company A charges $20 per
month plus $0.12 per minute. Wireless phone
company B charges $50 per month plus $0.06
per minute. For how many minutes of calls will
the monthly bills be the same?
(A) 80 minutes
(B) 100 minutes
(C) 160 minutes
(D) 250 minutes
(E) 500 minutes
Answer:
E
Step-by-step explanation:
For Company A, the monthly cost y in dollars can be represented by:
y = 0.12x + 20
where x is the number of minutes used.
For Company B, the monthly cost y in dollars can be represented by:
y = 0.06x + 50
where x is the number of minutes used.
To find the number of minutes of calls where the monthly bills will be the same, we need to set the two equations equal to each other and solve for x:
0.12x + 20 = 0.06x + 50
0.06x = 30
x = 500
Therefore, the monthly bills will be the same for both companies when the number of minutes used is 500.
Answer: (E) 500 minutes
The class must seat 40 students along with the teacher's table and shelves, which occupy 350m2. How much space will each student occupy? (Show how you drive at your answer)
The amount of space each student will occupy is 0.25 square meters of space in the classroom.
How to calculate the space each student will occupyTo find the amount of space each student will occupy,
We need to first subtract the area taken up by the teacher's table and shelves from the total area of the classroom.
Then we can divide the remaining area by the number of students.
Let's say the total area of the classroom is A.
Then we have:
A - 350 ( the area available for students)
If each student occupies an area of x, then we have:
40x = A - 350
Substituting the first equation into the second equation, we get:
40x = (A - 350)
We can solve for x by dividing both sides by 40:
x = (A - 350) / 40
We know that there are 40 students, so we can substitute that into the equation:
x = (A - 350) / 40 = (360 - 350) / 40 = 0.25
Therefore, each student will occupy 0.25 square meters of space in the classroom.
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calculate 7 x 3 1/4 pleaseeee help
Answer:
7 x 3 1/4 = 91/4 or 22 3/4
Step-by-step explanation:
To calculate 7 x 3 1/4, we can first convert the mixed number 3 1/4 to an improper fraction:
3 1/4 = (3 x 4 + 1) / 4 = 13/4
Then, we can multiply 7 by 13/4 as follows:
7 x 13/4 = (7 x 13) / 4 = 91/4
Therefore, 7 x 3 1/4 = 91/4 or 22 3/4 (if we want to express the answer as a mixed number).
Answer:
22 3/4
Step-by-step explanation:
There are plenty of ways of solving this question. The improper fraction of 3 1/4 is 13/4.
7 · 3 1/4
[tex]\frac{7}{1}[/tex] x [tex]\frac{13}{4}[/tex] = [tex]\frac{91}{4}[/tex]
[tex]\frac{91}{4}[/tex] = 22.75 = 22 3/4
Carlos evaluated 20-(2x6)+8 divided by 4 and got 29. Is his answer correct? if not, explain what Carlos did wrong and find the correct answer.
10 is the appropriate response to the expression.
Carlos gave the erroneous response of 29.
Carlos made the error of doing addition and subtraction operations prior to multiplication and division operations, as is evident.
What is an expression?Every mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Everything with a variable value is anything whose value changes over time. Typically, alphabetical letters like a, b, c, m, n, p, x, y, and z are used to denote expression variables. A combination of several variables and integers can be used to create a variety of expressions.
From the question:
We must assess the expression utilizing the PEMDAS order of operations and contrast the results:
20 - (2x6) + 8 ÷ 4
= 20 - 12 + 2
= 10
Carlos gave the erroneous response of 29. It seems that Carlos determined the expression to be: 20 - (2x6) + 8 ÷ 4 = 29
Carlos made the error of doing addition and subtraction operations prior to multiplication and division operations, as is evident. Multiplication and division must be done before addition and subtraction, per the PEMDAS order of operations.
Carlos ought to have determined the expression to be:
20 - (2x6) + 8 ÷ 4 = 20 - 12 + 2 = 10
Hence, 10 rather than 29 is the appropriate response to the expression.
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Find the derivative of y=x^4sec(x^9)
Using the product rule and chain rule, we can find the derivative of y with respect to x as follows:
y = x^4sec(x^9)
y' = (4x^3)(sec(x^9)) + (x^4)(sec(x^9))(d/dx(tan(x^9)))
We can simplify the derivative using the identity d/dx(tan(u)) = sec^2(u)(du/dx), where u = x^9:
y' = (4x^3)(sec(x^9)) + (x^4)(sec(x^9))(sec^2(x^9))(9x^8)
Simplifying further, we get:
y' = 4x^3sec(x^9) + 9x^12sec(x^9)
Therefore, the derivative of y with respect to x is 4x^3sec(x^9) + 9x^12sec(x^9).
Helpppp I need somthing quick question #4 pls or any of them
Answer:
4) No, It is not a right triangle
Step-by-step explanation:
12 is the hypotenuse which is the longest side of the triangle
6² + 8² = 12² （Pythagoras Theorem）
36 + 64 ≠ 144
Hence it is not a right triangle
Find the equivalent expression using the
same bases.
1080
Clear all
(21.15)⁹
Enter the correct answer.
000
DONE
(21)⁹ . (15)⁹ is the equivalent expression using the same bases.
What are power and exponent?
One can represent extremely big or extremely small numbers in a more straightforward fashion by using exponents and powers. For instance, we can write 3 x 3 x 3 x 3 as 34, where 4 is the exponent and 3 is the base, to demonstrate 3 x 3 x 3 x 3 in a straightforward manner.
It is claimed that the entire statement 34 possesses power. How many times you should multiply a number depends on its power. Other names for powers include exponents and indices.
using (a.b )ⁿ = (a)ⁿ . (b)ⁿ
( 21.15)⁹ = (21)⁹ . (15)⁹
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The state of Colorado is 4 centimeters long and 3 centimeters wide on a map. A cartographer wants to use a scale factor of 2.5 to enlarge the map. What is the area of the enlarged map?
12 cm2
30 cm2
35 cm2
75 cm2
The area of the enlarged map is 75 cm². Answer: (D) 75 cm².
What is scale ?
Scale refers to the ratio of distances or sizes on a map or drawing to the actual distances or sizes of the objects they represent in the real world. It is often expressed as a ratio, such as 1:10,000 or 1/4 inch = 1 foot, and is used to create maps and drawings that accurately represent real-world objects and distances. Scales can be used to enlarge or reduce the size of a map or drawing, making it easier to view and work with.
The original area of Colorado on the map is:
Area = length x width = 4 cm x 3 cm = 12 cm²
To enlarge the map with a scale factor of 2.5, we need to multiply the length and width by 2.5:
New length = 4 cm x 2.5 = 10 cm
New width = 3 cm x 2.5 = 7.5 cm
The area of the enlarged map is:
New area = new length x new width = 10 cm x 7.5 cm = 75 cm²
Therefore, the area of the enlarged map is 75 cm². Answer: (D) 75 cm².
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Select the expression that represents this real-world situation.
Vesi snowboards 4 hours before lunch and 3 hours after lunch each day. How many hours did she snowboard in 2 days?
4 + 3 + 2
(4 + 3) x 2
4 x 3 ÷ 2
(4 x 3) − 2
Answer:(4 + 3) x 2
Step-by-step explanation:
Vesi snowboards 4 hours before lunch and 3 hours after lunch each day, so the total time she spends snowboarding each day is:
4 + 3 = 7 hours
The question is asking how many hours Vesi snowboarded in 2 days, so we need to multiply the daily total by 2:
7 x 2 = 14
Therefore, the expression that represents this real-world situation is:
B. (4 + 3) x 2 = 14.
Option A adds 2 hours which is not correct as Vesi snowboards 7 hours each day, not 2 hours. Option C multiplies and divides, which is not necessary in this case. Option D multiplies and subtracts, which is also not correct.
if a/5=60/4 what is the value of a
Answer:
a = 75
Step-by-step explanation:
URGENTE PORFAVOR .
If the point (6, -7) is on the graph of the function f(x), which point is on the graph of the inverse function ƒ˜¹(x)?
(-7,6)
(-7,-7)
(6,-7)
(6,6)
Answer:
A) (-7, 6)
Step-by-step explanation:
The graph of the inverse function is a reflection in the line y = x.
The mapping rule for a reflection in the line y = x is:
(x, y) → (y, x)Therefore, if point (6, -7) is on the graph of the function f(x), the point that is on the graph of the inverse function f⁻¹(x) is:
(6, -7) → (-7, 6)If f(x) = 2x(1-x)^2, then f(1) =
(A) 0
(B) 2
(c) 4
(D) 6
(E) 8
Answer:
0
Step-by-step explanation:
2(1)*(1-(1))²=0
plug in 0 for everywhere you see x
how many ounces are there in 4 1
_
2 pounds show your work
Answer:
64 Ounces
Step-by-step explanation:
There are 64 ounces in 4 1/2.
4 1/2 = 4.5
4.5 x 16 = 72
72 ounces - 8 ounces = 64 ounces
Answer:64
Step-by-step explanation:
If you were to reflect the coordinates (4,6), (12,2), and (-1,0) about the y-axis, what would
then be your new coordinates?
Answer:
Step-by-step explanation:
When reflecting coordinates about the y-axis, we change the sign of the x-coordinate while keeping the y-coordinate the same.
So, for the point (4, 6), the new coordinates after reflection about the y-axis would be (-4, 6).
For the point (12, 2), the new coordinates would be (-12, 2).
For the point (-1, 0), the new coordinates would be (1, 0).
Therefore, the new coordinates after reflecting these points about the y-axis are (-4, 6), (-12, 2), and (1, 0).
simplify:(-8+35)+|-16+4| a.15 b.31 c.39d.55
c. 39
Step-by-step explanation:
the answer is 39
suppose A and B are dependent events. If P(A)= 0.4 and P(B)= 0.9, what is P(AnB)
The value of the probability P(A n B) is 0.36
How to determine the value of the probabilityFrom the question, we have the following parameters that can be used in our computation:
A and B are dependent events.
P(A)= 0.4 and P(B)= 0.9
Using the above as a guide, we have the following:
P(A n B) = P(A) * P(B)
Substitute the known values in the above equation, so, we have the following representation
P(A n B) = 0.4 * 0.9
Evaluate
P(A n B) = 0.36
Hence, the solution is 0.36
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three equivalent ratios for 1.5 to 3.5
Answer:
0.3:0.7 3:7
Step-by-step explanation:
A marine biologist was interested in seeing the relationship between a manatee's weight and height. She gathered data and wanted to construct a graph to display the data in order to observe this relationship.
Is a scatter plot or a line graph more appropriate to construct for the data, given the context of the problem? Explain.
A scatter plot, because it would show the association or relationship between two variables
A scatter plot, because it would show how a variable changes over time between each data point given
A line graph, because it would show the association or relationship between two variables
A line graph, because it would show how a variable changes over time between each data point given
The correct answer is a scatter plot, because it would show the association or relationship between two variables.
What is a scatter plot?A scatter plot is a graph that displays values of two variables on two axes. It is used to show the relationship between the two variables and how one variable affects the other. It is also known as a scatter graph, scatter chart, scattergram, or scatter diagram. The points are plotted on a graph and can be used to identify patterns and trends in the data.
A scatter plot can be used to display the relationship between two variables, such as the weight and height of a manatee. The points on the scatter plot would represent each manatee's weight and height, and the pattern of the points can be used to see the overall relationship between the two variables. A line graph, on the other hand, is used to show how a variable changes over time between each data point given, and would not be suitable for this context as the data collected is not related to time.
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A fish and wildlife conservation release three bald eagles that have been rehabilitated. Before release, they measure the wingspan (in feet) and weight (in pounds) of each eagle.
The mean of the wingspans is 6 1/4 feet, the median is 6 feet, and the range is 1 3/4 feet.
The mean of the weights is 12.75 pounds, the media. is 12.75 pounds and the range is 5 pounds
a. What are the wingspan of the 3 bald eagles?
b. What are the weights of the 3 bald eagles?
Answer:
a. Since we know the mean and median of the wingspans, we can assume that the data is approximately normally distributed. We also know the range, which is the difference between the maximum and minimum values. From this information, we can set up two equations:
Mean = (Wingspan1 + Wingspan2 + Wingspan3)/3 = 6 1/4
Median = 6
We can use the second equation to eliminate one of the variables. If the median is 6, then the middle value must be 6 as well. Let's assume that Wingspan2 = 6. Then we have:
(Wingspan1 + 6 + Wingspan3)/3 = 6 1/4
Multiplying both sides by 3 and simplifying:
Wingspan1 + Wingspan3 = 18 3/4
We also know that the range is 1 3/4, so:
Wingspan3 - Wingspan1 = 1 3/4
Solving for Wingspan3 in terms of Wingspan1:
Wingspan3 = Wingspan1 + 1 3/4
Substituting this into the previous equation:
Wingspan1 + (Wingspan1 + 1 3/4) = 18 3/4
2Wingspan1 + 1 3/4 = 18 3/4
2Wingspan1 = 17
Wingspan1 = 8 1/2
Therefore, Wingspan3 = 10 1/4. So the three bald eagles have wingspans of 8 1/2 feet, 6 feet, and 10 1/4 feet.
b. Since the mean and median of the weights are the same, we can assume that the data is exactly normally distributed. We also know the range, which is the difference between the maximum and minimum values. From this information, we can set up two equations:
Mean = (Weight1 + Weight2 + Weight3)/3 = 12.75
Median = 12.75
We can use the second equation to eliminate one of the variables. If the median is 12.75, then the middle value must be 12.75 as well. Let's assume that Weight2 = 12.75. Then we have:
(Weight1 + 12.75 + Weight3)/3 = 12.75
Multiplying both sides by 3 and simplifying:
Weight1 + Weight3 = 38.25
We also know that the range is 5 pounds, so:
Weight3 - Weight1 = 5
Solving for Weight3 in terms of Weight1:
Weight3 = Weight1 + 5
Substituting this into the previous equation:
Weight1 + (Weight1 + 5) = 38.25
2Weight1 + 5 = 38.25
2Weight1 = 33.25
Weight1 = 16.625
Therefore, Weight3 = 21.625. So the three bald eagles have weights of 16.625 pounds, 12.75 pounds, and 21.625 pounds.
A savings account of $2500 earned $225 simple interest in 3 years. Find the
interest rate.
Answer:
Results
Interest Rate -61.911%
Total of 36 Monthly Payment of $8,100.00
Total Interest Paid $-16,900.00
Step-by-step explanation:
Answer:R= 3%/year
Step-by-step explanation:
r = 225 / (2500 x 3) = 0.03
r= 0.03
converting r decimal to a percentage
R = 0.03 * 100 = 3%/year
The interest rate required to accumulate simple interest of $225.00 from a principle of $2,500.00 over 3 years is 3% per year.
kim and courtney share a 20 ounce box of cereal. By the end of the week kim has eat 2/5 of the box and courtney has eaten 1/10 of the box of cereal what fraction of the box is left
Answer: 1/2
Step-by-step explanation:
Kim ate 2/5 which is also equal to 4/10 and Courtney has eaten 1/10
4/10 + 1/10 = 5/10 = 1/2
J
14
20
K
22.4
AKLS-
T
32
L
Similar By:
S
Determine if the triangles are similar. If similar.state how and complete the similarity statement
Answer:
triangles, we can determine if these triangles can be proven similar by using the SSS Similarity ... use AA Similarity to prove the triangles are similar.
Find the value of the sphare
Answer:
[tex]2304[/tex][tex]\pi[/tex]
Step-by-step explanation:
V = [tex]\frac{4}{3} \pi r^{3}[/tex]
V = [tex]\frac{4}{3} *\pi * 12*12*12[/tex]
Use 3 to divide one of the 12 which will be equal to 4
V = [tex]4 *\pi *4*12*12[/tex]
V = [tex]2304\pi[/tex]
f(x)=−5x3−4x2+8x and g(x)=−4x2+8, find (f−g)(x) and (f−g)(−2).
Answer:
(f-g)(x) = -5x^3 + 8x - 8.
(f-g)(-2) = 16.
Step-by-step explanation:
To find (f-g)(x), we need to subtract g(x) from f(x) and simplify:
(f-g)(x) = f(x) - g(x)
= (-5x^3 - 4x^2 + 8x) - (-4x^2 + 8)
= -5x^3 - 4x^2 + 8x + 4x^2 - 8
= -5x^3 + 8x - 8
Therefore, (f-g)(x) = -5x^3 + 8x - 8.
To find (f-g)(-2), we substitute x = -2 into the expression we just found:
(f-g)(-2) = -5(-2)^3 + 8(-2) - 8
= -5(-8) - 16 - 8
= 40 - 24
= 16
Therefore, (f-g)(-2) = 16.