The answer to f(-1) is (-8) . Given f'(x) = 8x³ + 12x + 2, we can find f(x) by integrating f'(x) with respect to x. Integrating the given function, we get:
f(x) = 2x⁴ + 6x² + 2x + C, where C is the constant of integration. To find C, we can use the given initial condition f(1) = -4:
-4 = 2(1)⁴ + 6(1)² + 2(1) + C
-4 = 2 + 6 + 2 + C
C = -14
So, the complete expression for f(x) is:
f(x) = 2x⁴ + 6x² + 2x - 14
To find f(-1), we substitute x = -1 in the above expression:
f(-1) = 2(-1)⁴ + 6(-1)²+ 2(-1) - 14
f(-1) = 2 + 6 - 2 - 14
f(-1) = -8. Therefore, f(-1) equals -8.
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domain and range: identify the domain and range of the function.
Answer:
domain = 0,1,2,3
range= 5,7,15,44
an umbrella has 12 evenly spaced ribs. If viewed as a flat circle of radius 11 units,
then what would be the area between two consecutive ribs of the umbrella
Answer:
Area = 121pi/12
~= 31.66 sq units
Step-by-step explanation:
They are talking about looking at an umbrella like its a circle. The radius is 11 units. That is from the center to the edge.
Consecutive means "in a row" or "next to each other" The 12 "ribs" are the like skeleton structure in the umbrella. But they cut the umbrella into 12 areas. They are asking for the area of one "slice". It is 1/12 of the area of the whole circle.
Area of a circle is
A = pi × r^2
Area of one slice is 1/12 of the whole.
A(1 slice)
= 1/12× pi × r^2
See image.
NEED HELP ASAP PLEASE AND THANK YOU!!!
In an online feedback comment section, the probability that a comment is positive is 10% (independent of any other comments already present). If there are 10 comments, what is the probability that at least 2 of the comments are positive?
To find the probability that at least 2 of the comments are positive, we can use the concept of complementary probability. We'll find the probability that fewer than 2 comments are positive and then subtract it from 1 to get the desired probability.
Let's consider the following scenarios:
1. No comments are positive (all 10 comments are negative).
2. Exactly 1 comment is positive.
Let's calculate the probability of each scenario:
1. Probability of no comments being positive:
P(No positive comments) = (0.9)^10 = 0.3487 (rounded to four decimal places)
2. Probability of exactly 1 comment being positive:
P(Exactly 1 positive comment) = 10 * (0.1)^1 * (0.9)^9 ≈ 0.3874 (rounded to four decimal places)
To find the probability that at least 2 comments are positive, we subtract the sum of the above probabilities from 1:
P(At least 2 positive comments) = 1 - P(No positive comments) - P(Exactly 1 positive comment)
= 1 - 0.3487 - 0.3874
≈ 0.2639 (rounded to four decimal places)
Therefore, the probability that at least 2 of the comments are positive is approximately 0.2639 or 26.39%
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(Multiple choice/ brainiest will be given)
Can I please get some help with this answer?
Answer: d
Step-by-step explanation:
A pizza parlor charges $8 per pizza plus $0.65 per topping. Which equation can be used to find the cost of a pizza that costs $11.25?
Group of answer choices
8x+0.65=11.25
8+0.65x=11.25
8-0.65x=11.25
8x-0.65=11.25
3x + (-9x) + 12 + 8
Answer:
Stop being lazy
Do write the complete question.
The Ques is 3x-9x+12+8=0. Then find x
It's x=20/6=10/3
please solve and explain fir 15 poitns
They look yo be all functions due to them not intersecting one another
How do you find the angles of a 5/12/13 triangle?
The angles of a triangle with side lengths 5 , 12 and 13 are 90°, 22.63°, 67.38°.
What is Law of cosines formula?In trigonometry, the law of cosines, also known as the law of cosines or cosine formula, basically relates the length of a triangle to one cosine of its angle. It states that if we know the lengths of two sides of a triangle and the angle between them, we can determine the length of the third side. c² = a²+ b² – 2ab cosγ
where a, b, c are the sides of the triangle and γ is the angle between a and b, see image above.
To find the length of a side of a triangle, take △ABC according to the cosine formula, which can be written as follows.
a² = b²+ c²– 2bc cos αb²= a² + c²– 2ac cos βc²= b² + a² – 2ba cos γWe have , a = 5 , b = 12 , c= 13
cos α =( 12² + 13² - 5² )/2×12×13= 288/312
=> α = cos⁻¹(0.923 ) = 22.63°
cos β = (5² + 13² - 12² )/2×13×5 = 50/130
=> β = cos⁻¹(5/13) = 67.38°
cos γ = (12² + 5² - 13² )/2×12×5= 0
=> γ = cos⁻¹(0) = 90°
Hence, the required angles are 90°, 22.63°, 67.38°.
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Work out m and c for the line: y=3x
Answer:
m = 3, c = 0
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x , or y = 3x + 0 ← is in slope- intercept form
with m = 3 and c = 0
what is 8/3y=5/6x-2 in standard form?
Answer:
Y=5/16x -3/4
Step-by-step explanation:
3/8 * 8/3y=(5/6x -2) *3/8
y=5/16x - 3/4
The standard form of the equation is 5x -16y = 2.
It is required to find the standard form.
What is arithmetic?Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
According to given question we have,
The least common multiple of the fraction denominators is 6. Multiplying by that gives
16y = 5x -2
We can put this in standard form by adding 2-16y to both sides.
5x -16y = 2
Therefore, the standard form of the equation is 5x -16y = 2.
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Your grades on three exams are 80, 93, and 91. What grade do you need on the next exam to have an average of 90 on the four exams?
Answer: You would need a score of 96 on your last exam.
Step-by-step explanation:
If you take the 90 average and multiply it by 4, you get 360. If you add your first 3 exam grades and subtract them from 360, then you get 96 as your final score. To check your work, add the 4 exam scores and find the average. The average is 90.
(Pls mark me brainliest) Thanks!
Have a great day!
Answer:
96
Step-by-step explanation:
The average of a set of data can be found by taking the sum of the values in the data divided by the number of values.
\(\boxed{\text{Average of 4 exams}= \frac{\text{Total score of 4 exams}}{4}}}\)
Let the score of the next exam be x.
\(90=\frac{x+80+93+91}{4}\)
Multiply both sides by 4:
360= x +264
Subtract both sides by 264:
x= 360 -264
x= 96
Thus, a grade of 96 is needed on the next exam.
Supplementary:
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https://brainly.com/question/159026111/3 bigger than 5/9?
Answer:
No 1/3 is not greater than 5/9.
Step-by-step explanation:
(09.06)
For two functions, f(x) and g(x), a statement is made that f(x) = g(x) at
x = 5. What is definitely true about x = 5? (2 points)
Both f(x) and g(x) cross the x-axis at 5.
O Both f(x) and g(x) cross the y-axis at 5.
Both f(x) and g(x) have a maximum or minimum value at x = 5.
Both f(x) and g(x) have the same output value at x = 5.
Answer:
Both f(x) and g(x) have the same output value at x = 5
Step-by-step explanation:
When we are writing a function, while x gives the input value, writings like f(x), g(x) or h(x) will represent the output values of the input value of x
Now, looking at the relation, we are told that the value of f(x) = g(x) at x = 5
What this mean is that at x = 5; the output value of g(x) is the same as the output value of f(x)
Hence, we can conclude that both functions have the same output value at the given input value of x = 5
Answer:
D) Both f(x) and g(x) have the same output value at x = 5.
Step-by-step explanation:
I got it right on the test.
I have no idea how to do this, pls help. Question in the picture. Please show your work. Thanks!
Answer:
C
Step-by-step explanation:
This is a stem and leaf plot. If you don't know what a stem and leaf plot is, try searching it before coming back and viewing the solution. I also see an "example" button. It might help to hit that too.
First, we sort the list of numbers. Here is what we get:
64, 66, 67, 68, 69, 74, 75, 76, 78, 79
Here, the stems are the tens digits and the leaves are the ones digits.
Therefore, for the stem 6, the leaves are:
4, 6, 7, 8, 9
For the stem 7, the leaves are:
4, 5, 6, 8, 9
The answer, I believe, is C
What is the largest factor that all even numbers have in common?
Ann traveled 47.8 miles each day for the past 7 days. How many miles did she travel in all?
Answer:
334.6 miles
Step-by-step explanation:
Do either
47.8 x 7 = 334.6
or
47.8 + 47.8 + 47.8 + 47.8 + 47.8 + 47.8 + 47.8 + 47.8 = 334.6
A certain animated movie earned 81. 1 x 10^9 in revenue at the box office the movie lasts 9. 1 x 10^1 minutes. How much revenue was earned per minute of the movie?
The revenue earned per minute of the movie is approximately $8.9 x 10^7.
To calculate the revenue earned per minute of the movie, we need to divide the total revenue by the duration of the movie in minutes.
Revenue earned per minute = Total revenue / Duration of the movie
Total revenue = $81.1 x 10^9
Duration of the movie = 9.1 x 10^1 minutes
Revenue earned per minute = ($81.1 x 10^9) / (9.1 x 10^1)
To divide numbers in scientific notation, we subtract the exponents and divide the coefficients:
Revenue earned per minute = $81.1 x 10^(9-1) / 9.1
Simplifying the exponent:
Revenue earned per minute = $81.1 x 10^8 / 9.1
Dividing the coefficients:
Revenue earned per minute ≈ $8.9 x 10^7
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What kind of polynomial is 3x²?
3x² is a second-degree polynomial, also known as a quadratic equation.
A polynomial is a mathematical expression that consists of constants, variables, and exponents. This polynomial can be represented as an equation in the form of ax^2 + bx + c, where a, b, and c are constants, and x is an unknown. In this case, a = 3, b = 0, and c = 0. In this case, the polynomial is 3x², which contains one constant (3) and one variable (x) with an exponent of 2. To calculate the value of this polynomial, we can substitute a value for x and then solve. For example, if x=2, then 3x² = 3x2 = 3(2)2 = 3(4) = 12.
Therefore, when x=2, 3x² = 12.
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If it costs $300 to tile a 420 square foot room, how much will it cost to tile a
room with 1,050 square feet?
Answer:
750$
Step-by-step explanation:
\(Amount= 300*\frac{1050}{420} =750\)
It will cost approximately $750.01 to tile a room with an area of 1,050 square feet.
To find out how much it will cost to tile a room with 1,050 square feet, we can set up a proportion using the given information.
Cost₁: The cost to tile the first room with an area of 420 square feet, which is $300.
Area₁: The area of the first room, which is 420 square feet.
Cost₂: The cost to tile the second room with an unknown area, which we want to find.
Area₂: The area of the second room, which is 1,050 square feet.
We can set up the proportion:
Cost₁ / Area₁ = Cost₂ / Area₂
Substituting the known values:
$300 / 420 sq ft = Cost₂ / 1,050 sq ft
Now we can solve for Cost₂:
Cost₂ = ($300 / 420 sq ft) * 1,050 sq ft
Calculating:
Cost₂ = $0.7143 * 1,050 sq ft
Cost₂ ≈ $750.01
Therefore, it will cost approximately $750.01 to tile a room with an area of 1,050 square feet.
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6 cm
6 cm
18 cm
9.5 cm
3cm
11cm
9cm
6cm
Answer: 68.5
Step-by-step explanation:
6 cm + 6 cm + 18 cm+ 9.5cm + 3cm + 11cm+ 9cm+ 6cm= 68.5
~Hope this helps ;0~
Write the expression c · d · c · c · d · b · c · d · d · b · d · d · d · d using exponents. Write the variables in alphabetical order.
Answer:
b^2 * c^4 * d^6
Step-by-step explanation:
i think this is right
Paul wants to visit his aunt who lives 300 miles away from his house. He drives his car at about 50 miles an hour. If X represents the time spent driving and why represents the distance from his aunts house which scatterplot could represent the situation
Answer:
It would take 6 hours.
An equation for that could be: 50x = 300 (X is how long it would take)
So 50 mph• X (time spent) = 300 miles
You didn't give me any scatterplots to look at so I can't help you with that sorry
A die is rolled and a coin is flipped simultaneously. the number rolled on the die and whether the coin lands heads or tails is recorded. how many outcomes are in the sample space? 8 6 10 12
Answer: 12
Step-by-step explanation:
how much must be deposited at the beginning of every six months in an account that pays 6% compounded semi-annually so that the account will contain 35,000 at the end of five years the semi-annual payments are___?round to 2 decimal places
In order to determine the initial investment, use the following formula for the composed interest:
\(I=P(1+\frac{r}{n})^{nt}\)where:
P: initial investment = ?
r: interest rate = 6% = 0.06
n: number of times per time period = 6
t: time period = 5 x 2 = 10
I: final account = 35,000
replace the previous values of the parameters and solve for P, as follow:
\(\begin{gathered} 35000=P(1+0.06/6)^{6\cdot10}=P\cdot1.816 \\ P=35000/1.816 \\ P=19273.13 \end{gathered}\)Hence, the initial investment was 19,273.13
Answer the following 6 questions in full on paper. Then upload them for grading by your teacher. Note that you will be graded not only on the accuracy of your final answer, but also on the methods you use to reach the answer, so be sure to show all of your work and explain your reasoning carefully. (Don't just copy the answer from a calculator or a computer algebra system!) 1. List the first 9 terms of the sequence defined recursively by Sn = $n-2 (Sn-1-1), with s₁ = 2 and $₂=3 2. Compute the value of 1 $. where s, is the same sequence as in the previous question. I 3. Is the sequence from question 1 arithmetic, geometric, or neither? Explain how you reach your conclusion. 4. Find the sum of the first 200 terms of the arithmetic sequence that begins: 12, 18, 24... 5. Find the sum of the first 8 terms of the geometric sequence that begins: 12, 18, 27....
1. The first 9 terms of the sequence are: 2, 3, -1, 8, -9, 26, -43, 96, -181.
3. Based on the differences between consecutive terms, we observe that they are not constant, indicating that the sequence is neither arithmetic nor geometric.
4. The sum of the first 200 terms of the arithmetic sequence is 121,800.
5. The sum of the first 8 terms of the geometric sequence is 18.
1. To find the terms of the sequence, we can use the given recursive formula and initial values:
s₁ = 2
s₂ = 3
sₙ = n - 2(sₙ₋₁ - 1)
Using these values and the recursive formula, we can calculate the first 9 terms:
s₃ = 3 - 2(s₂ - 1) = 3 - 2(3 - 1) = 3 - 2(2) = 3 - 4 = -1
s₄ = 4 - 2(s₃ - 1) = 4 - 2(-1 - 1) = 4 - 2(-2) = 4 + 4 = 8
s₅ = 5 - 2(s₄ - 1) = 5 - 2(8 - 1) = 5 - 2(7) = 5 - 14 = -9
s₆ = 6 - 2(s₅ - 1) = 6 - 2(-9 - 1) = 6 - 2(-10) = 6 + 20 = 26
s₇ = 7 - 2(s₆ - 1) = 7 - 2(26 - 1) = 7 - 2(25) = 7 - 50 = -43
s₈ = 8 - 2(s₇ - 1) = 8 - 2(-43 - 1) = 8 - 2(-44) = 8 + 88 = 96
s₉ = 9 - 2(s₈ - 1) = 9 - 2(96 - 1) = 9 - 2(95) = 9 - 190 = -181
Therefore, the first 9 terms of the sequence are: 2, 3, -1, 8, -9, 26, -43, 96, -181.
2. To compute the value of 1 $, we need to substitute n = 1 into the recursive formula:
s₁ = 1 - 2(s₀ - 1)
Since s₀ is not given in the question, we need additional information or assumptions about its value to proceed with the calculation. Please provide the value or any additional information about s₀ for a more accurate calculation.
3. To determine whether the sequence from question 1 is arithmetic, geometric, or neither, we need to examine the differences between consecutive terms.
The given recursive formula does not explicitly indicate an arithmetic or geometric relationship. However, we can calculate the differences between consecutive terms to identify any patterns:
Difference between s₂ and s₁: 3 - 2 = 1
Difference between s₃ and s₂: (-1) - 3 = -4
Difference between s₄ and s₃: 8 - (-1) = 9
Difference between s₅ and s₄: (-9) - 8 = -17
Difference between s₆ and s₅: 26 - (-9) = 35
Difference between s₇ and s₆: (-43) - 26 = -69
Difference between s₈ and s₇: 96 - (-43) = 139
Difference between s₉ and s₈: (-181) - 96 = -277
Based on the differences between consecutive terms, we observe that they are not constant, indicating that the sequence is neither arithmetic nor geometric.
4. To find the sum of an arithmetic sequence, we can use the formula: Sn = (n/2)(2a + (n - 1)d), where Sn is the sum of the first n terms, a is the first term, and d is the common difference.
First term (a) = 12
Common difference (d) = 6 (obtained by subtracting the first term from the second term)
We need to find the sum of the first 200 terms (n = 200). Substituting these values into the formula, we get:
S200 = (200/2)(2(12) + (200 - 1)(6))
= 100(24 + 199(6))
= 100(24 + 1194)
= 100(1218)
= 121,800
Therefore, the sum of the first 200 terms of the arithmetic sequence is 121,800.
5. To find the sum of a geometric sequence, we can use the formula: Sn = a(1 - rⁿ) / (1 - r), where Sn is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.
First term (a) = 12
Common ratio (r) = 18/12 = 3/2 (obtained by dividing the second term by the first term)
We need to find the sum of the first 8 terms (n = 8). Substituting these values into the formula, we get:
S8 = 12(1 - (3/2)⁸) / (1 - (3/2))
= 12(1 - (6561/256)) / (1/2)
= 12(1 - 6561/256) / (1/2)
= 12(1 - 81/4) / (1/2)
= 12(1 - 20.25) / (1/2)
= 12(0.75) / (1/2)
= 9 / (1/2)
= 9 * 2
= 18
Therefore, the sum of the first 8 terms of the geometric sequence is 18.
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an international calling plan charges 45 cent per minute or a fraction of a minute for each call. which graph models the cost, y, in cents of making x minutes of international calls?
The correct graph would be a straight line with a slope of 45 and passing through the origin (0, 0).
We have,
The graph that models the cost, y, in cents of making x minutes of international calls would be a linear graph, as the cost is directly proportional to the number of minutes.
The equation of the linear graph would be:
y = 45x
Here, y represents the cost in cents, and x represents the number of minutes.
Therefore,
The correct graph would be a straight line with a slope of 45 and passing through the origin (0, 0).
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A lifeguard recorded the daily average temperature in degrees Fahrenheit and the number of swimmers at the pool each day for 29 days. The scatterplot displays the data.
Complete the correct answers from each drop down menu to complete the statements.
As the x-values increase, the y-values decrease or increase?
This represents a negative or positive? linear or nonlinear? association between the daily average temperature and the number of swimmers at the pool.
For the given graph, As the x-values increase, the y-values also increase. This represent a positive graph. It is nonlinear function graph.
What is graph?In elementary mathematics, the term "graph" designates a plot or a function graph. A graph is, in the language of mathematicians, a set of points and the connections between some subset of those points (which may be empty). In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.
Here,
For the given graph, As the x-values increase, the y-values also increase.
This represent a positive graph.
It is nonlinear function graph.
As the x-values rise for the presented graph, the y-values rise as well. This graph shows a favorable trend. It is a graph of a nonlinear function.
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Solve for the value of s.
Answer:
6s+2=4s-2
-4s -4s
2s+2=-2
-2 -2
2s=0
/2 /2
s=undefined or x=0
the sample space contains 5 as and 7 bs. what is the probability that a randomly selected set of 2 will in- clude 1 a and 1 b?
the probability that a randomly selected set of 2 will include 1 a and 1 b is 35/66
What is probability?The probability is equal to the variety of possible outcomes. the total number of outcomes that could occur. For instance, there is only one way to get a head and there are a total of two possible outcomes, so the probability of flipping a coin and getting heads is 1 in 2. Writing P(heads) = 12
What are the 4 types of probability?Classical
Empirical
Subjective.
Axiomatic
There are 66 equally likely outcomes, or C(5+7,2) =C(12,2)=66 possible outcomes. Only C(5,1)*C(7,1)=35 of these contain 1A and 1B. thus, the likelihood is 35/66.
The value of the solution is 35/66
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