if f is the antiderivative of x^2/1 x^5 such that f(1)=0 then f(4)=
Answers
If f(x) is an antiderivative of x^2/1 x^5, such that f(1)=0 then :
f(4) = 15/32
We can use the fundamental theorem of calculus to solve this problem. According to the theorem, if f(x) is an antiderivative of x^n, then ∫[a,b] x^n dx = f(b) - f(a).
In this case, f(x) is an antiderivative of x^2/1 x^5. We can simplify this expression to x^-3 and apply the theorem.
∫[1,4] x^-3 dx = f(4) - f(1)
Using the power rule of integration, we have:
∫[1,4] x^-3 dx = [-x^-2/2] from 1 to 4
= [-1/32] - [-1/2]
= 15/32
Therefore, f(4) - f(1) = 15/32. We know that f(1) = 0, so we can simplify:
f(4) - 0 = 15/32
f(4) = 15/32
Therefore, f(4) = 15/32.
To learn more about antiderivatives visit : https://brainly.com/question/12956882
#SPJ11
Related Questions
factorise the quadratic equation x^2 + 14 + 48 hence solve the quadratic equation x^2 + 14 + 48 = 0
Answers
Step-by-step explanation:
\( {x }^{2} + 14 + 48 = 0 \\\)
(x+6)=0(or)(x+8)=0
x+6=0 ( or) x+8=0
x=-6 (or)x=-8
You pick a card at random. 5 6 7 What is P(less than 7)? Write your answer as a fraction or whole number.
Answers
The probability of picking a card less than 7 from a standard deck of cards is 2/13.
To find the probability (P) of picking a card less than 7, we need to determine the number of favorable outcomes (cards less than 7) and divide it by the total number of possible outcomes.
In this case, the favorable outcomes are the cards with values less than 7, which are 5 and 6. The total number of possible outcomes is the total number of cards in the deck, which depends on the specific deck being used.
Assuming a standard deck of 52 cards, there are four 5s and four 6s, making a total of eight favorable outcomes.
Therefore, P(less than 7) = favorable outcomes / total outcomes = 8 / 52.
Simplifying the fraction, we find that P(less than 7) = 2 / 13.
For more such questions on probability
https://brainly.com/question/251701
#SPJ8
Jack and Beth are selling blueberry pies and apple pies for a school fundraiser. There is one price for blueberry and one price for apple.
Jack sold 5 blueberry pies and 3 apple pies for a total of $38. Beth sold 5 blueberry pies and 10 apple pies for a total of $80. What is the
cost each of one blueberry pie?
0 A $5.00
OB. $4.00
OC. $6.00
OD. $7.00
Answers
Answer:
5$ i hope this helped if it did not sorry.
Step-by-step explanation:
In a certain tournament bracket, a player must be defeated three times to be eliminated. If 512 contestants enter the tournament, what is the greatest number of games that could be played?
Answers
Here is a rectangle with length 5 units and width 2 units.
1. What is the area of the rectangle?
2. Dilate rectangle ABCD from point A by a scale factor of 2. Calculate the area of the image.
3. Dilate rectangle ABCD from point A by a scale factor of 3. Calculate the area of the image.
Answers
This refers to the ratio between the scale of a given original object and a new object. It is its representation but of a different size (bigger or smaller). For example, if we have a rectangle of sides 2 cm and 4 cm, we can enlarge it by multiplying each side by a number, say 2.
Solving for the area and scale factor we have:
L= 5 units
W = 2 units
The area of the rectangle =L * WA = (5 x 2)
A = 10 square units.
If the rectangle is dilated from point A by a scale factor of 2, the area of the image:A= (Scale factor of L * W)* L * W
= (2 x 2 x 5 x 2)
A = 40 square units.
If the rectangle is dilated from point A by a scale factor of 3, the area of the image is:A= (Scale factor of L * W)* L * W
= (3 x 3 x 5 x 2)
A= 90 square units
Learn more about area on
https://brainly.com/question/29082330
#SPJ1
A school chair has 36 members. This year, there are three times as many returning members as new members. How many
new members are in the choit this year?
12 new members
24 new members
27 new members
Answers
calculate the mean and median number of hours rashawn listened to music for the 6 days. round your answers to the nearest tenth.
Answers
The mean and median number of hours Rashawn spend in listening to music is 5.7 hours and 6 hours, under the condition that there were 6 days in which Rashawn listened to music.
Now to evaluate the mean number of hours Rashawn listened to music for the 6 days, we have to sum up all the hours and divide by the number of days.
Then, total number of hours Rashawn heard music for 6 days is
= 6 + 5 + 5 + 6 + 5 + 7
= 34 hours
Mean = Total number of hours / Number of days
= 34 / 6
= 5.7 hours
Now,
For evaluating the median number of hours Rashawn heard music in the interval of 6 days
We have to set the number in the order of smallest to largest
The numbers in order are 5, 5, 5, 6, 6, 7
The median is the middle value which is 6
The mean and median number of hours Rashawn spend in listening to music is 5.7 hours and 6 hours, under the condition that there were 6 days in which Rashawn listened to music.
To learn more about mean
https://brainly.com/question/1136789
#SPJ4
The complete question is
Rashawn kept a record of how many hours he spent listening to music for 6 days during school vacation and displayed his results in the table
Day -
Monday
Number of hours - 6
Tuesday
Number of hours - 5
Wednesday
Number of hours - 5
Thursday
Number of hours - 6
Friday
Number of hours - 5
Saturday
Number of hours - 7
calculate the mean and median number of hours Rashawn listened to music for the 6 days. Round your answers to the nearest tenth.
Which of the following is equal to the ratio of the circumference of a circle to its diameter?
Answers
Answer:
Im pretty sure its the 1st one
Step-by-step explanation:
Answer:
option 3 π
Step-by-step explanation:
Circumference = πd
Circumference : diameter = πd : d
= π : 1 = π
CAN SOMEBODY HELP ME FACTOR AS THE PRODUCT OF TWO BINOMIALS
x²- x- 42
Answers
Answer:
(x-7)(x+6)
factor and see what works
Williams Corporation is investigating the effects of educational background on employee performance. A potential relevant variable in this case is the self-rated social status of the employee. The company has recorded the annual sales volumes (in $000) achieved by sales employees in each of the categories below. Self-Rated Social Status/School Type { Ivy League { State-Supported{ Small Private Low (64,61) (70,72) (50,52)Medium (66,64) (74,78) (52,55)High (60,61) (77,80) (57,56)Draw an interaction plot of the information. What does it reveal?
Answers
Based on the given data, an interaction plot can be created to visualize the relationship between self-rated social status, school type, and annual sales volumes.
The plot will show three lines, one for each school type (Ivy League, State-Supported, and Small Private), with the x-axis representing social status (Low, Medium, High) and the y-axis representing sales volumes (in $000).
The interaction plot reveals how different combinations of self-rated social status and educational background may affect employee performance in terms of sales volumes.
By analyzing the slopes and intersections of the lines, you can identify potential interactions and trends among these variables. This can help Williams Corporation in understanding the potential influence of educational background and self-rated social status on employee performance.
To learn more about interaction plot visit:
brainly.com/question/29949487
#SPJ11
#ihategeometry geometry makes me want to cry and cry and cry.
Answers
Answer:
RV = 19
Step-by-step explanation:
You have a rectangle, therefore you need to know the following facts:
1. The diagonals are =
2. The diagonals bisect each other.
3. Opposite angles are =
RT = SU Diagonals are = in a rectangle
5x - 12 = 4x - 2 Solve for x
x - 12 = -2
x = -2 + 12
x = 10 Now you know RT = 5x - 12
RT = 5(10) -12
RT = 50 -12 = 38
Now diagonals of a rectangle bisects each other meaning this RT= RV + VT and RV = VT RT =38 so RV =19 and VT =19.
Next m ∠SVT = 70°. m ∠SVT = m ∠VUR are vertical angles are =
RV = VT and SV = VU. so ΔSVT = ΔVUR are congruent by SAS. Thus
m ∠SVT = m ∠VUR Corresponding parts of congruent triangles are ≅ (CPCTC)
These triangles are isosceles (two angles are = to each other.
70°+ x° + x° = 180°; 70° + 2x = 180° ; 2x = 110°; x = 55°. I hope this help.
Answer:
RV = 19
Step-by-step explanation:
Which two of the following are continuous data?
A) concert attendance
B) age of a student
C) number of pens in a box
D) time taken to run 1 mile
Answers
Answer:
Age of a student (B) and Time taken you run 1 mile (D)
Step-by-step explanation:
Only the age of a student and the time taken to run 1 mile are continuous data.
What are the types of data?
The data is classified into majorly four categories:
Nominal data: Nominal Data is used to label variables without any order or quantitative value.Ordinal data: Ordinal data have natural ordering where a number is present in some kind of order by their position on the scale. Discrete data: The term discrete means distinct or separate. The discrete data contain the values that fall under integers or whole numbers.Continuous data: Continuous data are in the form of fractional numbers. It can be the version of an android phone, the height of a person, the length of an object, etc. Continuous data represents information that can be divided into smaller levels. The continuous variable can take any value within a range.As per the given definitions above we can state that Continuous data is (B) the Age of the students (D) the Time taken to run 1 mile
Therefore, the Answer is (B) and (D)
Learn more about data here:
https://brainly.com/question/10980404
#SPJ1
The difference of a number and 13 is two less than the number doubled,
Three time
wal
quot
Answers
Answer:
The number is 5
Step-by-step explanation:
Let the number be x,
13 - x = 2x - 2
or, 13 + 2 = 2x + x
or, 3x = 15
so, x = 5
i need help with this...
Answers
the answer is 60 :) good luckStep-by-step explanation:
Aimee says Bella is lying. Bella says Marc is lying. Marc says Bella is lying. Terry says Aimee is lying. How
many of the four children are lying?
a) 0 b)1 c)2 d)3 e)4
Answers
Kayla has a goal of saving $350 to buy a laptop computer. Label the bar to show how much Kayla has saved when she has 10% of her goal 20% of her goal and so on
Answers
Answer:
10% - 35
20% - 70
30% - 105
40% - 140
50% - 175
60% - 210
70% - 245
80% - 280
90% - 315
100% - 350
Step-by-step explanation:
you sell small candles for 14$ and large candles for 16$ at the warehouse. At the warehouse, you pay x dollars for small candles and y dollars for large candles after one month you sold 45 small candles and 68 large candles at a store. A write and simplify and expression. B if you buy the candles at the warehouse for 5$ for small candles and 7$ for large candles what is the profit after your month of selling at the store?. Thank you so much
Answers
Therefore, the expression for the profit after selling the candles at the store for one month is:
Profit = (Revenue from small candles + Revenue from large candles) - Cost of buying the candles
Profit = (14 * 45 + 16 * 68) - (45x + 68y)
Profit = 630 + 1088 - 45x - 68y
Profit = 1718 - 45x - 68y
B) If the cost of buying small candles is 5 dollars and the cost of buying large candles is 7 dollars, then we can substitute x = 5 and y = 7 into the expression for profit to find the actual profit:
Profit = 1718 - 45(5) - 68(7)
Profit = 1718 - 225 - 476
Profit = 1017
Therefore, the profit after selling the candles at the store for one month would be 1017 dollars if the cost of buying small candles is 5 dollars and the cost of buying large candles is 7 dollars.
5. Suppose X 1and X 2are random variables with mean 10,20 respectively, and SDs 2, 3 respectively.
Let T=11X 1−2X2
Find the mean and SD of T when X 1and X 2are independent.
Find the mean and SD of T when X1and X 2 have correlation of
−0.76
In the case that X1and X 2 are independent, normally distributed
variables, find P(T>30)
Answers
The mean of T is -10 and the standard deviation of T is √425 when X1 and X2 are independent.
To find the mean of T, we can use the properties of expected values. Since T = 11X1 - 2X2, the mean of T can be calculated as follows: E(T) = E(11X1) - E(2X2) = 11E(X1) - 2E(X2) = 11(10) - 2(20) = -10. To find the standard deviation of T, we need to consider the variances and covariance of X1 and X2. Since X1 and X2 are independent, the covariance between them is zero. Therefore, Var(T) = Var(11X1) + Var(-2X2) = 11^2Var(X1) + (-2)^2Var(X2) = 121(2^2) + 4(3^2) = 484 + 36 = 520. Thus, the standard deviation of T is √520, which simplifies to approximately √425. When X1 and X2 have a correlation of -0.76, the mean and standard deviation of T remain the same as in the case of independent variables. To calculate the probability P(T > 30) when X1 and X2 are independent, normally distributed variables, we need to convert T into a standard normal distribution. We can do this by subtracting the mean of T from 30 and dividing by the standard deviation of T. This gives us (30 - (-10))/√425, which simplifies to approximately 6.16. We can then look up the corresponding probability from the standard normal distribution table or use statistical software to find P(T > 30). The probability will be the area under the standard normal curve to the right of 6.16.
Learn more about standard normal distribution here: brainly.com/question/32506784
#SPJ11
Over Thanksgiving Break Joshua drove from Connecticut to Ohio which is 422 miles. This trip took Joshua and his family six hours. How fast was Joshua driving? Be sure to round your answer to the nearest whole number.
Answers
Answer:
70 miles per hour
Step-by-step explanation:
422 divided by 6
Answer:
70 mph :)
Step-by-step explanation:
Do the side lengths 4 5 and 10 form a triangle select the correct answer and reasoning?
Answers
The one of the inequalities is false, then the sides do not form a triangle.
Now, According to the question:
Side 1 of the triangle is = 4
Side 2 of the triangle is = 5
Side 3 of the triangle is = 10
Form a triangle :
To check if they form a triangle or not, we make use of triangle inequality theorem which states that; for sides a, b and c
a + b > c
a + c > b
b + c > a
So for sides 4, 5 and 10, we have:
4 + 5 > 10
4 + 10 > 5
5 + 10 > 4
Since the one of the inequalities is false, then the sides do not form a triangle.
Learn more about Inequalities at:
https://brainly.com/question/20383699
#SPJ4
HELP HELP HELP HELP HEPL HELP
Answers
Answer:
The answer would be Y= 1/4X -3
Step-by-step explanation:
Hope it was helpful .
Good luck ^.^
A certain club has 10 members, including Harry. One of the 10 members is to be chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that Harry will be either the member chosen to be the secretary or the member chosen to be the treasurer
Answers
Answer:
The probability that Harry will be chosen as either as Secretary or as treasurer but not as president out of those 10 members will be \(\frac{1}{5}\).
Step-by-step explanation:
We have 10 members out of which one is Harry, we need to choose one of the 10 members as President, one to be as secretary out of the remaining 9, one as the treasurer of the remaining 8 members.
We want harry to be as either as secretary or as treasurer. so we will consider both the cases
Probability is given by = No of favorable outcomes/ Total no of outcomes
(1) Harry as secretary : If harry is to be chosen as secretary then he can't be a president or he cant be a Treasurer
As president = \(\frac{1}{10}\)
Not as president = \(1 - \frac{1}{10}\) = \(\frac{9}{10}\)
Now he is selected for the secretary so he can't be selected as treasurer.
Not as treasurer = 1
Probability for chosen as secretary = \(\frac{9}{10}*\frac{1}{9}*1\) = \(\frac{1}{10}\)
(2) Harry as treasurer : If harry is to be chosen as the treasurer so he can't be chosen as a President or as a Secretary.
Probability for not chosen as president = \(\frac{9}{10}\)
Probability for not chosen as secretary = \(1-\frac{1}{9} = \frac{8}{9}\)
Probability to be chosen as treasurer = \(\frac{1}{8}\)
Probability to be chosen as Treasurer = \(\frac{9}{10}*\frac{8}{9}*\frac{1}{8}\) = \(\frac{1}{10}\)
Total probability for Harry to be chosen as either secretary or as treasurer will be = P(Secretary) +P(Treasurer)
= \(\frac{1}{10} +\frac{1}{10} = \frac{1}{5}\)
Therefore the probability that Harry will be chosen as either as Secretary or as treasurer but not as president out of those 10 members will be \(\frac{1}{5}\).
Which list shows how many equal-sized groups of 18 students Ms.Lee can make?
Answers
Answer:
The answer is1,2,3,6,9,or 18
Step-by-step explanation:
Sorry i was not there sooner hope you have a good night.
Answer:
The answer is 1,2,3,6,9, or 18
when unwrapped, the lateral surface area of cone A is a sector with central angle 6 radians and radius pi. What is the length of the radius of cone A
Answers
The lateral surface area of cone A unwrapped is a sector with central angle 6 radians and radius pi. The length of the radius of cone A is pi/6.
Since the lateral surface area of cone A is a sector with central angle 6 radians and radius pi when unwrapped, we can use the formula for sector area to find the lateral surface area of the cone. Area of sector=θ/2π×π² where θ is the central angle and π is the radius.
Area of cone’s lateral surface area=L=θ/2π×2πr=rθ. So, r=L/θ=π/6 (when L=π and θ=6 radians). The length of the radius of cone A is π/6 which is approximately 0.524. Thus, the length of the radius of cone A is pi/6 when unwrapped, given that the lateral surface area of cone A is a sector with central angle 6 radians and radius pi.
Learn more about cone here:
https://brainly.com/question/23877107
#SPJ11
How many solutions does the equation
2
(
x
+
4
)
=
2
x
+
8
have?
A.
no solutions
B.
one solution
C.
two solutions
D.
infinite solutions
Answers
The equation has infinite solution.
How to find the solution of an equation?The equation is as follows:
2(x + 4) = 2x + 8
Let's open the bracket of the left side of the equation
2x + 8 = 2x + 8
Therefore, the equation has both sides equal to each other.
Hence, the solution of the equation is infinite.
An infinite solution has both sides equal.
Therefore, the equation has infinite solution.
learn more on equation here: https://brainly.com/question/8429176
#SPJ1
which of the following equations, when written in (x-p)^2=q, have a value of q which is a perfect square?
\(2x^2+12x-126=0\\5x^2-20x+20=0\\x^2-2x-8=0\\3x^2+36x+84=0\\x^2+8x+4=0\)
Answers
Answer:
\(2x^2+12x-126=0\\5x^2-20x+20=0\\x^2-2x-8=0\\3x^2+36x+84=0\\x
Step-by-step explanation:
which of the following equations, when written in (x-p)^2=q, have a value of q which is a perfect square?
\(2x^2+12x-126=0\\5x^2-20x+20=0\\
a newsletter publisher believes that over 54% of their readers own a personal computer. is there sufficient evidence at the 0.05 level to substantiate the publisher's claim?
Answers
Null hypothesis \(H_{0}\): u = 0.54 and Alternative hypothesis \(H_{a}\): u > 0.54 is the publisher's claim supported by enough evidence at the 0.05 level.
Null hypothesis \(H_{0}\) : u = 0.54
Alternative hypothesis \(H_{a}\): u > 0.54
The percentage of their readers who own a computer.
The null hypothesis ( \(H_{0}\)) attempts to demonstrate that there is no substantial variation amongst variables or that a variable is no different from its mean.
While an alternative Hypothesis ( \(H_{a}\)) seeks to demonstrate that a new hypothesis, rather than the old one, is correct. That a variable deviates significantly from the mean.
As a result, in the preceding example;
Null hypothesis \(H_{0}\) : u = 0.54
Alternative hypothesis \(H_{a}\): u > 0.54
Read more about the Null hypothesis and Alternative hypothesis at
https://brainly.com/question/17227951?referrer=searchResults
#SPJ4
In rectangle $ABCD$ below, we have $DP = PC$ and $\angle BAC = 28^\circ$. If $Q$ is the point on $\overline{AC}$ such that $\overline{DQ}\perp \overline{AC}$, what is $\angle QDP$ in degrees?
Answers
Answer:
∠QDP = 34°
Step-by-step explanation:
The complete question is shown in the image attached.
In triangle ABC, ∠ABC = 90° and ∠BCA = 28°. Hence:
∠CAB + ∠ABC + ∠BCA = 180° (sum of angles in a triangle)
∠BCA + 28+ 90 = 180
∠BCA + 118 = 180
∠BCA = 180 - 118
∠BCA = 62°
Also ∠DCA + ∠BCA = 90° (Each angle in a rectangle is 90°)
∠DCA + 62 = 90
∠DCA = 90 - 62 = 28°
∠DAC + ∠BAC = 90 (angle in a rectangle)
∠DAC + 28 = 90
∠DAC = 90 - 28 = 62°
In triangle ADQ, ∠DQA = 90° and ∠QAD = 62°. Hence:
∠QAD + ∠ADQ + ∠QAD = 180° (sum of angles in a triangle)
∠ADQ + 62+ 90 = 180
∠ADQ + 152 = 180
∠ADQ = 180 - 152
∠ADQ = 28°
In triangle DPC,DP = PC, hence ∠PDC = ∠DCP= 28°.
∠PDC + ∠ADQ + ∠QDP = 90° (angle in a rectangle)
28 + 28 + ∠QDP = 90
∠QDP + 56 = 90
∠QDP = 90 - 56
∠QDP = 34°
Find the surface area of the cylinder to the nearest whole number.
15 in
19 in.
Not drawn to scale
Select one:
a. 1791 in. 2
b. 11281 in. 2
c. 3204 in. 2
d. 5815 in. 2
Answers
Answer:
the answer you are looking for is C
A fair dice is rolled.
Work out the probability of getting a factor of 2.
Give your answer in its simplest form.
Answers
Answer:
3/6 or 1/2 (simplified)
Step-by-step explanation:
--> 1, 2, 3, 4, 5, 6 are your options, so the total amount of options you can roll is 6 (denominator)
--> 2, 4, 6 are factors of 2, so you have 3 options to roll a factor of 2 (numerator)
So... 3/6 or 1/2