To find the average value of a function, we need to calculate the integral of the function over the interval and divide it by the length of the interval. In this case, the average value of the function v(x) = 3x on the interval [1,c] is equal to 5. We can find c by setting up an equation using the formula for the average value and then solving for c.
Explanation:To find the average value of a function on an interval, we need to calculate the integral of the function over that interval and then divide it by the length of the interval. In this case, we have the function v(x) = 3x and the interval [1, c].
So, the average value of the function on this interval is given by: average = 1/(c-1) * ∫(3x dx) from 1 to c. We are given that the average value is equal to 5. Setting this equal to 5, we have: 5 = 1/(c-1) * [3x^2/2] from 1 to c.
Simplifying further, we get: 5 = 1/(c-1) * (3c^2/2 - 3/2). Multiplying both sides by (c-1), we have: 5(c-1) = (3c^2/2 - 3/2).
From here, we can solve for c using algebraic methods. Once we find the value of c, we can verify that it is greater than 1, as stated in the question.
Learn more about Average value of a function here:https://brainly.com/question/32589988
#SPJ2
Based on the density graph below, what is the probability of a value in the sample space being anywhere from 60 to 80?
A.50%
B.75%
C.100%
D.25%
Answer:
75%
Step-by-step explanation:
Solve the system using substitution or elimination and describe your steps. Be sure to verify your solution. • x = y - 3 2x + y = 12
HELP ASAP
What are the coordinates of the vertices of the triangle after a dilation by a scale factor of
1
4
, centered at the origin?
U → U'
V → V'
W → W'
The coordinates of a triangle's vertices after a dilation by a scale factor of 1/4, centered at the origin, are found by multiplying each of the original vertex coordinates by 1/4.
The coordinates of the vertices of the triangle after a dilation by a scale factor of 1/4, centered at the origin, can be found by multiplying the original coordinates of each vertex by 1/4. If the original coordinates are (x, y), then the coordinates after the dilation will be (x/4, y/4).
This applies to all vertices of the triangle, so the transformed triangle, denoted by U', V', and W', will have vertices with coordinates calculated by taking the original vertex coordinates of U, V, and W and scaling them down by a factor of 1/4.
A circus acrobat is shot out of a cannon. The equation for the acrobat's pathway can be modeled by h= -16t^2+25. How long will it take him to reach the ground?
What is the percent chance a coin lands on heads with 3 tosses?
A jet plane is descending at a rate of 200 feet per second from an altitude of 36000 feet let x represent the number of seconds of descent and y represent the jet plane’s altitude in feet.
Which expression represents this situation?
A. y = 200x - 36000
B. y = 200x + 36000
C. y = -200x - 36000
D. y = -200x + 36000
Find two number whose sum is 60 such that the sum of the square of one number plus 12 times the other number is a minimum
The local weather person has been accurate in her predictions within 2 degrees temperature forecast 80% of the time. Find the probability that she is accurate...
a) exactly 3 out of the next 5 days
b) at least 4 of the next 5 days
please help type the integer that represents the correct answer the absolute value of 7
HURRY PLZ
Determine whether each set of side lengths could be the sides of a right triangle. Drag and drop each set of side lengths to the correct box. Right Triangle Not a Right Triangle.
Determine whether each set of side lengths could be the sides of a right triangle.
Drag and drop each set of side lengths to the correct box.
Right Triangle Not a Right Triangle.
6cm, 22.9cm, 20.1cm.
10.5cm, 20.8cm, 23.3cm
Answer:
Second option is the correct answer.
Step-by-step explanation:
To know if the given set of numbers can be possible lengths for a right triangle, we will use the Pythagorean theorem that states:
[tex]a^{2}+b^{2} =c^{2}[/tex]
a and b are smaller lengths.
Option first:
6cm, 22.9cm, 20.1cm.
[tex]6^{2}+20.1^{2} =22.9^{2}[/tex]
=> [tex]36+404.01=524.41[/tex]
=> [tex]440.01\neq 524.41[/tex]
This is not a right triangle.
Option second:
10.5cm, 20.8cm, 23.3cm
[tex]10.5^{2}+20.8^{2} =23.3^{2}[/tex]
=> [tex]110.25+432.64=542.89[/tex]
=> [tex]542.89=542.89[/tex]
This is a right triangle.
What is the smallest natural number that 2, 10, 14, and 36 will divide evenly?
What is the vertex form, f(x) = a(x − h)2 + k, for a parabola that passes through the point (4, −3) and has (5, 2) as its vertex. What is the standard form of the equation?
Answer:
y = x² - 10x + 27
Step-by-step explanation:
Circle P is tangent to the x-axis and the y-axis. If the coordinates of the center are (r, r), find the slope of the line through the origin and the center.
The value of slope of the line through the origin and the center is,
⇒ Slope = 1
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Circle P is tangent to the x-axis and the y-axis.
And, the coordinates of the center are (r, r),
Now, The value of slope of the line through the (0, 0) and the center (r, r) is,
⇒ Slope = (r - 0) / (r - 0)
⇒ Slope = r/r
⇒ Slope = 1
Thus, The value of slope of the line through the origin and the center is,
⇒ Slope = 1
Learn more about the equation of line visit:
https://brainly.com/question/18831322
#SPJ3
The art museum will hang 3 famous paintings in a row. How many different ways could the paintings be hung?
There are six different ways to hang three unique paintings.
The question on how many different ways the paintings could be hung pertains to a mathematical concept known as permutations. Since there are three paintings and each one must occupy a unique position in the row, we need to calculate the number of permutations of three items. In permutations, the order matters, so the sequence ABC is different from ACB even though they contain the same paintings.
To solve this, we use the formula for permutations without repetition, which is n! (n factorial), where n is the number of items to arrange. For three paintings, this gives us:
3! = 3 × 2 × 1 = 6 different ways
Therefore, there are six different ways to hang the three paintings.
Range for the equation 2y=8-4x if the domain is (-2,-1,0,2,5)
FACTORIZE PLEASE, A LOT OF POINTS
64x^(3)-48x^(2)+12xy^(2)-y^(3)
or you can just put it in a smaller form by saying (4x - y)³
Find the value of the lesser root of x 2-8x+7=0
Find the approximate circumference of a circle with a radius of 2.6 millimeters. Use = 3.14.
The fourth term of a sequence is 14. Each term of the sequence is 8 less than the previous term. Which recursive formula represents the situation?
A group consists of five men and seven women. four people are selected to attend a conference.
a. in how many ways can four people be selected from this group of twelve?
b. in how many ways can four women be selected from the seven women?
c. find the probability that the selected group will consist of all women.0
grant is rolling a standard six sided number die eight times. how many outcomes are possible
We have been given that Grant is rolling a standard six sided number die eight times and we have to find the total number of outcomes.
Grant is rolling six sided number die. Hence, we can say that
Number of outcomes if rolled once = 6
Number of outcomes if rolled twice = [tex]6\times 6= 6^2[/tex]
Number of outcomes if rolled thrice= [tex]6\times 6 \times 6= 6^3[/tex]
We can see that if rolled twice then we have exponent 2, when rolled trice then we have an exponent 3.
Hence, if rolled 8 times then we have an exponent 8 on 6.
Therefore, the possible number of outcomes should be [tex]6^8= 1679616[/tex]
Hence, the number of possible outcomes is 1679616
1. What is the median of the following set of numbers?
48.4, 47, 43, 47, 43.6, 41.6, 45, 51.4, 38.6
Hint: Order the numbers from least to greatest first!
A. 48.4 B. 43.6 C. 45
2. Each of the five math teachers are comparing the number of students in their homeroom classes. The number of boys and girls in each teachers’ classes are recorded in the table below.
Hint: Mean is the average.
Which statement best describes the means of the two sets of data?
A. The mean number of girls in 7 times greater than the mean numbers of boys in the homeroom classes.
B. The mean number of girls is the same as the mean number of bboys in the homeroom classes.
C. The mean number of girls is 7 more than the mean number of boys in the homeroom classes.
Answer:b
Step-by-step explanation:divided look around the chart
Tim bought 5 pencils for .25 cents each. he also bought 2 packs of paper for $1.25 each. he paid with a $10.00 bill. how much change could tim receive
PLEASE HELP 20 POINTS
Answer:
Step-by-step explanation:
i put a awnser and that person hacked me lol
There are 158 fourth grade studnets and 139 fifth grade students going on a field trip. There needs to be one caperone for every 8 kids. Explain how to find the number of caperones needed for the trip.
Identify the type of sequence AND provide the next 3 terms:
5 , 9, 13, 17…
-1, 2, -4, 8…
8, 1, -6, -13…
For which of the inequalities below is v = 4 a solution? A v + 5 ≥ 9 B v + 5 > 9 C v + 5 < 8 D v + 5 ≤ 8
The table shows the calories burned during exercise.
(picture of the table attached)
Which statement is true?
A)The y-intercept of the function is (15, 75).
B)The rate of change is 15 calories burned per minute.
C)A linear function to model the calories burned, y, as a function of time in minutes, x, is y = 5x.
D)An exponential function to model the calories burned, y, as a function of time in minutes, x, is y = 5x.
Answer: C. A linear function to model the calories burned, y, as a function of time in minutes, x, is y = 5x.
Step-by-step explanation:
Which expression is equivalent to square root 55x^7 y^6/11x^11 y^8? Assume x > 0 and y > 0.
Answer:
Basically the answer is C.
Which point best represents the square root of 15?
A. Point A
B. Point B
C. Point C
D. Point D