GIVEN: The given function is f(x)=[tex]x^7[/tex] on the interval [0,7]
To FIND: Here we need to find the value of c by the help of Mean value theorem.
SOLUTION: The mean value theorem is,
[tex]f'(c)=\frac{f(b)-f(a)}{b-a}[/tex]
where, f(x) is defined on a closed interval [0,7] and continuous on the closed [0,7] and derivable on (0,7) and a<c<b,
So, [tex]f'(x)=7x^6[/tex]
By the mean value theorem we have,
[tex]7c^6=\frac{7^7-0}{7-0} \\7c^6=7^6\\c^6=7^5\\c=\sqrt[6]{7^5} \\c=5.077[/tex]
Therefore, the required value of c is 5.077
The height, width and length of a small box are consecutive integers with the height being the smallest
of the three dimensions. If the length and width are increased by 2 cm each and the height is tripled,
then the volume of the box is increased by 552 cm3
. Use algebraic techniques to find the dimensions of
the original small box.
9514 1404 393
Answer:
4 cm, 5 cm, 6 cm
Step-by-step explanation:
If x represents the height of the original box, the other two dimensions are ...
width = x+1
length = x+2
and the volume is ...
V = HWL = x(x +1)(x +2) = x³ +3x² +2x
__
After the change in dimensions, the height is 3x, the width is x+3, and the length is x+4. The new volume is ...
V = HWL = 3x(x+3)(x+4) = 3x³ +21x² +36x
The difference in volumes is ...
(3x³ +21x² +36x) -(x³ +3x² +2x) = 552
In standard form, this equation is ...
2x³ +18x² +34x -552 = 0
Factoring out 2 gives ...
x³ +9x² +17x -276 = 0
Possible rational roots are 1, 2, 3, 4, 6, and other divisors of 276. The largest possibility worth considering is less than ∛276 ≈ 6.5. Trial and error, or a graphing calculator can show us that x=4 is the only real solution to this equation.
The dimensions of the original small box are 4 cm × 5 cm × 6 cm.
what is the value of q?
Answer:20 square-root 5
Step-by-step explanation:
Which of the following is the point-slope form of the equation with slope 3 that goes through the point (4,2)?
Answer:
y–y1 =m (X–X1)
y–2=3(x–4)
y=3x–10
Need the answer to number 4
Answer:
[tex]\sqrt{85}[/tex] /2
Step-by-step explanation:
lets find hypotenuse( longest side) first
let other two samller sides be a and b and hypotenuse be c
pythagorsd theorem
a^2 + b^2 =c^2
9^2 + 2^2 =c^2
81 + 4=c^2
85 =c^2
[tex]\sqrt{85}[/tex] =c
take theta as reference angle
cosec theta=hypotenuse/opposite
=[tex]\sqrt{85}[/tex] / 2
Answer:
Answer is B. CSC ∅ = √85 /2
Step-by-step explanation:
CSC = 1 / Sin ∅
So first find Sin ∅ = 2 / √ 85 and then substitute in the formula
And oh, in case you're wondering, √ 85 is the hypotenuse side which you find like this:
√ 9² + 2²
√ 81 + 4
√ 85
The graph makes it appear that there are how many times as many students per teacher at North HS as there are at
West HS?
Student Teacher Ratios at Area High Schools
North RS
East HS
13
West HS
12
14
18
22
a.
b.
10
2 times
3 times
4 times
5 times
C.
d.
Answer:
5 times
Step-by-step explanation:
Using visual inspection, the bar of North HS is 5 times longer Than the bar of West HS.
The gtids are of equal size, West HS occupies one portion of the grid, while North HS occupies 5 portions of the grid
5 portions / 1 portion = 5
Hence, North HS according to the graph is 5 times West HS
What is the measure of angle x? Round to the
nearest tenth. .
28
21
xº
What is the perimeter of the trapezoid? In unit
Answer:
20 units
Step-by-step explanation:
the perimeter = 7+4+4+5 = 20 units
PLEASE HELP ASAP!!! WILL MARK BRAINLIEST !!
Answer:
CA = LJ
Step-by-step explanation:
The third side
CA = LJ
Answer:
CA=LG is correct answer
A jar contains 6 red marbles numbered 1 to 6 and 8 blue marbles numbered 1 to 8. A marble is drawn at random from the jar. Find the probability that the marble is blue or even-numbered.
Answer:
11/14
Step-by-step explanation:
(P of blue marble) + (P of even numbered) - (P blue and even) =
8/14 + 7/14 - 4/14 = 11/14
Standard Error from a Formula and a Bootstrap Distribution Sample A has a count of 30 successes with and Sample B has a count of 50 successes with . Use StatKey or other technology to generate a bootstrap distribution of sample differences in proportions and find the standard error for that distribution. Compare the result to the value obtained using the formula for the standard error of a difference in proportions from this section.
Answer:
Using a formula, the standard error is: 0.052
Using bootstrap, the standard error is: 0.050
Comparison:
The calculated standard error using the formula is greater than the standard error using bootstrap
Step-by-step explanation:
Given
Sample A Sample B
[tex]x_A = 30[/tex] [tex]x_B = 50[/tex]
[tex]n_A = 100[/tex] [tex]n_B =250[/tex]
Solving (a): Standard error using formula
First, calculate the proportion of A
[tex]p_A = \frac{x_A}{n_A}[/tex]
[tex]p_A = \frac{30}{100}[/tex]
[tex]p_A = 0.30[/tex]
The proportion of B
[tex]p_B = \frac{x_B}{n_B}[/tex]
[tex]p_B = \frac{50}{250}[/tex]
[tex]p_B = 0.20[/tex]
The standard error is:
[tex]SE_{p_A-p_B} = \sqrt{\frac{p_A * (1 - p_A)}{n_A} + \frac{p_A * (1 - p_B)}{n_B}}[/tex]
[tex]SE_{p_A-p_B} = \sqrt{\frac{0.30 * (1 - 0.30)}{100} + \frac{0.20* (1 - 0.20)}{250}}[/tex]
[tex]SE_{p_A-p_B} = \sqrt{\frac{0.30 * 0.70}{100} + \frac{0.20* 0.80}{250}}[/tex]
[tex]SE_{p_A-p_B} = \sqrt{\frac{0.21}{100} + \frac{0.16}{250}}[/tex]
[tex]SE_{p_A-p_B} = \sqrt{0.0021+ 0.00064}[/tex]
[tex]SE_{p_A-p_B} = \sqrt{0.00274}[/tex]
[tex]SE_{p_A-p_B} = 0.052[/tex]
Solving (a): Standard error using bootstrapping.
Following the below steps.
Open StatkeyUnder Randomization Hypothesis Tests, select Test for Difference in ProportionsClick on Edit data, enter the appropriate data Click on ok to generate samplesClick on Generate 1000 samples ---- see attachment for the generated dataFrom the randomization sample, we have:
Sample A Sample B
[tex]x_A = 23[/tex] [tex]x_B = 57[/tex]
[tex]n_A = 100[/tex] [tex]n_B =250[/tex]
[tex]p_A = 0.230[/tex] [tex]p_A = 0.228[/tex]
So, we have:
[tex]SE_{p_A-p_B} = \sqrt{\frac{p_A * (1 - p_A)}{n_A} + \frac{p_A * (1 - p_B)}{n_B}}[/tex]
[tex]SE_{p_A-p_B} = \sqrt{\frac{0.23 * (1 - 0.23)}{100} + \frac{0.228* (1 - 0.228)}{250}}[/tex]
[tex]SE_{p_A-p_B} = \sqrt{\frac{0.1771}{100} + \frac{0.176016}{250}}[/tex]
[tex]SE_{p_A-p_B} = \sqrt{0.001771 + 0.000704064}[/tex]
[tex]SE_{p_A-p_B} = \sqrt{0.002475064}[/tex]
[tex]SE_{p_A-p_B} = 0.050[/tex]
Identify the parent function of g(x)= x^2-2
Answer:
Identify the parent function
g(x)=−x+2−−−−−−√
1-Identify the parent function
2-Identify the transformations being applied, in appropriate order
3-sketch a graph of the transformed function
my work for first one
from parent function
Step-by-step explanation:
Answer:
g(x) =x^2 is the answer
Step-by-step explanation:
I hope this will help you
use quadratic formula to solve these equation (a).3x²+6x+2=0
Answer:
Step-by-step explanation:
3x² + 6x + 2 = 0
Quadratic Formula is:
x = -b ± √b²- 4ac/2a
So...
Δ = b² - 4ac = 6² - 4.3.2 = 12
x = -6 ± √Δ/2.3 = -6 ± √12/6
x' = -6 + √12/6 ≈ -0,4227
x'' = -6 - √12/6 ≈ -1,5774
S = { -0,4227 , -1,5774 }
I think this is it.GOOD STUDIES!
if a student is selected at random find the probability the student is a female given that it’s a junior round to the nearest whole percent
Answer: 40%
Step-by-step explanation:
Answer:
75
Step-by-step explanation:
what I did is that I added 6 and 2 (2 males and 6 women) so that's 8, then I put it as a fraction of 6/8, and I just searched what 6/8 as a percentage was :b
I'm really sorry if u don't understand what I'm trying to say, I'm really bad when it comes to write in English x,d
Help (PLATO)
its Algebra
Answer: The answer is D
Step-by-step explanation:
You add z to the other side then it will cancel out which then it would be (w+z) and then you times it by 2 by both sides which would be 2(w+z) and then you would subtract x from both sides which will be 2(w+z)-x
Hopefully this helps
ayuda ÷18=40 que número falta
Answer:
720
Step-by-step explanation:
x÷18=40
x=18•40
x=720
PLS HELP ASAP!!! WILL MARK AS BRAINLIEST
Answer: A
Step-by-step explanation:
Which inequality has -12 in its solution set?
A
B
с
D
X+6 <-8
X+42-6
X-3-10
x+554
СА
С В
oc
D
Answer:
the answer is a. x+6<-8 I hope I'm correct
Plz help me solve this algebra problem
Answer:
Step-by-step explanation:
What is the slope of the line that contains the points (-1,-1) and (3, 15)?
O A.
1
4
B. 4
O C. -
4
D. -4
Answer:
its b
Step-by-step explanation:
In the figure below, which term best describes point R?
A. Orthocenter
B. Centroid
C. Incenter
D. Circumcenter
Orthocenter is the best term to describes point R in the triangle UVW.
What is orthocenter?" Orthocenter is defined as intersecting point of the altitudes of the sides of the acute angle triangle."
According to the given figure,
In triangle UVW,
Ray VR perpendicular to UW
Ray UR perpendicular to VW
Ray WR perpendicular to UV
Altitudes of side ( UV , VW, and WU) of triangle UVW intersect at
point R.
As per the definition of orthocenter , point R represents orthocenter.
Hence, orthocenter is the best term to describes point R in the triangle UVW.
Learn more about orthocenter here
https://brainly.com/question/19763099
#SPJ2
Hermione thinks she has discovered a protection spell that will reduce the pain of the Cruciatus curse. She believes that a sample of people protected by her spell will rate their pain as less severe than the average person who does not have her protection spell. Her null hypothesis for this study would
Answer:
There will be no difference in pain ratings from people protected by her spell and people who aren't protected by her spell.
Step-by-step explanation:
The claim in this scenario is the alternative hypothesis, which is what we wish to test ; the alternative hypothesis is thus ; people who are protected by spell will rate their pain as a result of cruciatus curse as less severe than the average person who does not use her protection spell ;
As we know, the null hypothesis is the opposite of the alternative hypothesis and the initial truth, which is ;
The average pain felt by both the user of the pain protections spell and those who do not feel the same amount of pain.
A cone has a volume of 60 cubic feet. If the radius is 2 feet,'what is the height of the cone?
10ft
15ft
45ft
90ft
Someone please helppp
Sum of all edges of all shape
Answer:
Infinient amount buddy. They are infinent amounts of polygons, as a polygon is a shape with more then 3 sides and closed. This means as long as a number is bigger then 3, there will be a shape for it, so infinent sides
Step-by-step explanation:
What is the solution to -2(8x - 4) < 2x + 5?
Answer:
See image below:)
Step-by-step explanation:
How many once’s are equal to 7 pounds
Please help! Thank you!
Answer:
D: (2, -3)
Step-by-step explanation:
We have;
y = 3x - 9 - - - (1)
y = -2x + 1 - - - (2)
By substitution method, from eq 1, we see that: y = 3x - 9
Thus,let's put 3x - 9 for y in eq 2;
3x - 9 = -2x + 1
Rearranging to get;
3x + 2x = 9 + 1
5x = 10
x = 10/5
x = 2
Thus;
y = 3(2) - 9
y = 6 - 9
y = -3
Thus,the solution (x, y) = (2, - 3)
round it to the underlined digit
pls help
The
Slope
a line that goes
through the points (r, 6 ) and (4,2
is 4 find r
8) Find the midpoint of the equation y = 4x + 6 between the x-intercepts and the y-intercepts.
9514 1404 393
Answer:
(-3/4, 3)
Step-by-step explanation:
I find it easier to determine the intercepts when the equation is in standard form:
4x -y = -6
The x-intercept is found where y=0:
4x = -6 ⇒ x = -6/4 = -3/2
The y-intercept is found where x=0:
-y = -6 ⇒ y = 6
Then the midpoint is ...
M = ((-3/2, 0) +(0, 6))/2 = (-3/4, 3)
A model train is built at a scale of 1 to 60. If the model train is 10 inches long, how many feet long is the actual train?
Answer:
Step-by-step explanation:
um yes..!
