The average value of y=v(x) equals 4 for 1≤x≤6, and equals 5 for 6≤x≤8. what is the average value of v(x) for 1≤x≤8 ?
Answers
Area = 4*(6 -1) +5(8 -6) = 30
Width = 8 - 1 = 7
Average value = 30/7 = 4 2/7
The average value of v(x) for the interval 1≤x≤8 is calculated by summing up the products of the average values each times their respective lengths of interval, and dividing by the total length of the interval, which results in 4.2857 approximately.
Explanation:The average value of v(x) for 1≤x≤8 can be calculated using the formula for the average of a function over an interval, which is the sum of the function values times their respective lengths of interval, divided by the total length of the interval. For the first interval, 1≤x≤6, the average value of y is 4, and the length of the interval is 6-1=5. Hence, the sum of the product of the average value times the length of the interval is 4*5=20.
For the second interval, 6≤x≤8, the average value of y is 5, and the length of the interval is 8-6=2. Hence, the sum of the product of the average value times the length of the interval is 5*2=10.
Summing up these two products, we get 20+10=30. The total length of the overall interval 1≤x≤8 is 8-1=7. Hence, the average value of v(x) for 1≤x≤8 is 30/7=4.2857, approximately.
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Related Questions
the function of (x) varies directly with x^2, and f(x)=96 when x=4 what is the value of f(2)
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[tex]\bf \textit{f(x) varies directly with }x^2\qquad f(x)=kx^2 \\\\\\ \textit{we also know that } \begin{cases} f(x)=96\\ x=4 \end{cases}\implies 96=k(4)^2\implies 96=16k \\\\\\ \cfrac{96}{16}=k\implies 6=k\qquad therefore\qquad \boxed{f(x)=6x^2} \\\\\\ \textit{now, when }\stackrel{f(2)}{x=2}\textit{ what is \underline{f(x)}?}\qquad f(2)=6(2)^2[/tex]
The continuous function f is defined on the interval -4 ≤ x ≤ 3. there is no point c, -4 ≤ c ≤ 3, for which
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help with this question?
Answers
The appropriate choice is ...
c. continuous at every real number except x = 1.
What does same amount means?
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Ramone tossed 1 quarter, 2 dimes, and 13 pennies in the wishing well at the party. What is the total amount of money as a fraction and as a decimal?
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1 quarter:
(1) * (0.25) = 0.25 $
2 dimes:
(2) * (0.1) = 0.2 $
13 pennies:
(13) * (0.01) = 0.13 $
Adding we have:
0.25 + 0.2 + 0.13 = 0.58 $
As a fraction:
58/10 = 29/5 $
Answer:
The total amount of money as a fraction and as a decimal are:
$ 29/5
$ 0.58
How many terms are there in a geometric series if the first terms is 2, the common ratio is 4, and the sum of the series is 2,730 ?
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[tex]S_{n}=a_{1}\dfrac{r^{n}-1}{r-1}[/tex]
Substituting the given numbers, you have
[tex]2730=2\dfrac{4^{n}-1}{4-1}\\\\2730\dfrac{3}{2}=4^{n}-1\\\\4096=4^{n}\\\\\dfrac{\log(4096)}{\log(4)}=n=6[/tex]
There are 6 terms in the series.
Suppose x is a normal random variable with μ = 35 and σ = 10. find p(55.5 < x < 69.7).
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Answer:
[tex]\boxed{\boxed{P(55.5 < X< 69.7)=0.01992}}[/tex]
Step-by-step explanation:
We know that,
[tex]Z=\dfrac{X-\mu}{\sigma}[/tex]
where,
Z = z-score,
X = raw score,
μ = mean,
σ = standard deviation.
So,
[tex]=P(55.5 < X< 69.7)[/tex]
[tex]=P(55.5-35 < X-35< 69.7-35)[/tex]
[tex]=P(\dfrac{55.5-35}{10}< \dfrac{X-35}{10}< \dfrac{69.7-35}{10})[/tex]
[tex]=P(\dfrac{55.5-35}{10}< Z< \dfrac{69.7-35}{10})[/tex]
[tex]=P(2.05< Z<3.47)[/tex]
[tex]=P(Z<3.47)-P(Z<2.05)[/tex]
[tex]=0.99974-0.97982\\\\=0.01992[/tex]
what problem does the model show?
Answers
1/2 is the fraction represents the diagram.
What is Fraction?A fraction represents a part of a whole.
Fractions are of three types.
Proper fraction, improper fraction and mixed fraction.
A proper fraction is a fraction which has its numerator value less than the denominator.
An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
A fraction represented with its quotient and remainder is a mixed fraction
In the diagram there are 8 boxes in whole, the number of boxes shaded are 4 out of 8.
4/8 is the fraction represents the diagram, 1/2 is another way of representing 4/8.
Hence, 1/2 is the fraction represents the diagram.
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Rhombus A has base of 7 inches and an area of 35 square inches. Rhombus B has a Base and Height that are three times the base and height of Rhombus A. Find the area of Rhombus b and compare it to the area of rhombus A Explain
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Rhombus B, which has dimensions three times larger than Rhombus A, has an area that is nine times larger than the area of Rhombus A.
Explanation:This question is based on geometry and compares the areas of two rhombuses. Firstly, remember that the area of a rhombus is obtained by the formula A = base x height. For Rhombus A, with a base of 7 inches and area 35 square inches, this implies that its height is 5 inches (since 7 x 5 = 35). Therefore, the height of Rhombus B which is three times larger than that of Rhombus A would be 15 inches, and its base would be 21 inches (three times that of Rhombus A).
Now applying these values into the formula for the area of a rhombus, for rhombus B we get A = 21 x 15, which equals 315 square inches - this is the area of Rhombus B. Comparing this with the area of Rhombus A (35 square inches), we find that Rhombus B is 9 times larger than Rhombus A (because 315 divided by 35 equals 9).
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By increasing the base and height of Rhombus A by three times, the resulting area of Rhombus B is nine times the area of Rhombus A. The area of Rhombus A is 35 square inches and the area of Rhombus B is 315 square inches.
Explanation:The subject of this question is area of rhombuses. A key concept to remember is that the area of a rhombus is calculated by the formula: Area = base x height.
Rhombus A has base of 7 inches and an area of 35 square inches. This means the height h of Rhombus A is A/base = [tex]35/7 = 5[/tex] inches.
The base and height of Rhombus B are three times the base and height of rhombus A. So, Rhombus B has a base of [tex]7 * 3 = 21[/tex] inches and height of [tex]5 * 3 = 15[/tex] inches.
To find the area of Rhombus B, you apply the same formula, Substituting the values we get, B = base x height = [tex]21 * 15 = 315[/tex] square inches. Therefore, the area of Rhombus B is nine times the area of Rhombus A since 315/35 = 9.
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I need help on this one please
Answers
identify the type of conic section that has the equation 4x^2+25y^2=100 and identify its domain and range.
Answers
4x^2+25y^2=100
The range:
set y=0, and solve for x:
4x^2=100
x^2=25
x=+/-5
thus the domain is:
[-5,5]
Range:
set x=0 and solve for y:
25y^2=100
y^2=4
y=+/-2
thus the range is:
[-2,2]
The equation given represents an ellipse, a type of conic section. The domain of this particular conic section is -5 to 5, and its range is -2 to 2.
Explanation:The equation given represents an ellipse, which is one kind of conic section. The general form of the equation of an ellipse is[tex]x^2/a^2 + y^2/b^2 = 1,[/tex] where a and b are the lengths of the semi major and minor axes respectively. The equation you provided, [tex]4x^2+25y^2=100,[/tex]when arranged to fit into the general form of ellipse becomes [tex]x^2/25 + y^2/4 =1.[/tex] Thus, it is clear that the given equation represents an ellipse.
The domain of the function described by this elliptical equation includes all the x-values that the ellipse covers, and for this particular equation, is -5 to 5. The range includes all the y-values that the ellipse covers, which in this case is -2 to 2.
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Matt has $550 in his savings account. He is eager to know how much interest the bank will pay him for the whole year. He knows that the bank pays a 3 percent interest rate. He sits down with a pen, paper, and calculator to find out the simple interest
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We suppose the question is, "what is the amount of interest Matt will be paid?"
The formula that applies is
I = Prt
I = $550*0.03*1 = $16.50
Matt will be paid $16.50 in interest for the year.
What will be the perimeter and the area of the rectangle below if it is enlarged using a scale factor of 6.5?
Perimeter = 54 cm, area = 181.25 cm2
Perimeter = 54 cm, area = 2,028 cm2
Perimeter = 182 cm, area = 2,028 cm2
Perimeter = 182 cm, area = 181.25 cm2
Answers
2(6 cm + 8 cm) = 28 cm
The area of the given rectangle is
(6 cm)*(8 cm) = 48 cm^2
The larger rectangle will have a perimeter of
6.5*28 cm = 182 cm
The larger rectangle will have an area of
6.5^2*48 cm^2 = 2028 cm^2 . . . . . note the scale factor is squared for area
The appropriate choice is the 3rd one, ...
Perimeter = 182 cm, area = 2,028 cm^2
Answer:
Perimeter = 182 cm, area = 2,028 cm^2
Step-by-step explanation:
Stocks are units of ownership in a company. The stock market is a place where stocks are bought and sold. When you buy a stock, you own a part of the company. If the company’s profits go up, the stock value goes up. If the profits fall, so does the value of the stock. Stock prices rise and fall every day. Last week, Isabelle bought stock in a toy company. Since then, the price of the stock had a change of -3 dollars. What is the absolute value of -3?
Answers
Think of it like this. Whenever the absolute value is there, the number or expression inside, whether negative or positive takes a shower. When they are done showering, they are clean. The clean equals positive, all numbers after absolute value are positive so the answer is three.
Answer:
The absolute value is three!
Step-by-step explanation:
have a nice day/night!
John paid 5% sales tax on his television, which cost $769 before taxes. What did the television cost in total?
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$ 769 ---------> 100%
x --------------> 105%
From here, we clear the value of x.
We have then:
x = (105/100) * (769)
x = 807.45 $
Answer:
the television did cost 807.45 $ in total
In what form is the following linear equation written?
A. standard
B. Point Slope
C. Slope intercept
D. Rise Run
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y - y1 = m(x-x1)
The slope is m, which in this case is m = 2/3
The point this line goes through is (x1,y1) = (1,3)
As the name "point slope form" suggests, this form quickly lets us know the slope and one point that is on the line.
F(x, y, z) = yz i + xz j + (xy + 18z) k c is the line segment from (1, 0, −1) to (5, 6, 1) (a) find a function f such that f = ∇f. f(x, y, z) = (b) use part (a) to evaluate c ∇f · dr along the given curve
c.
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[tex]\displaystyle\int\frac{\partial f}{\partial x}\,\mathrm dx=\int yz\,\mathrm dx[/tex]
[tex]\implies f(x,y,z)=xyz+g(y,z)[/tex]
[tex]\dfrac{\partial f}{\partial y}=xz+\dfrac{\partial g}{\partial z}=xz[/tex]
[tex]\implies\dfrac{\partial g}{\partial z}=0[/tex]
[tex]\implies g(y,z)=h(z)[/tex]
[tex]\dfrac{\partial f}{\partial z}=xy+\dfrac{\mathrm dh}{\mathrm dz}=xy+18z[/tex]
[tex]\implies\dfrac{\mathrm dh}{\mathrm dz}=18z[/tex]
[tex]\implies h(z)=9z^2+C[/tex]
[tex]\implies f(x,y,z)=xyz+9z^2+C[/tex]
[tex]\implies\displaystyle\int_{\mathcal C}\mathbf f\cdot\mathrm d\mathbf r=f(5,6,1)-f(1,0,-1)=30[/tex]
Through anti-derivatives, we find a function f(x, y, z) in part (a) of the problem. We then use the fundamental theorem of line integrals in part (b) to evaluate the line integral of ∇f ∙ dr along a curve c, using the function f we found.
Explanation:This problem lies within the field of vector calculus, specifically dealing with gradient fields and line integrals. Part (a) requires us to find a function f(x, y, z) such that the gradient of f (∇f) is equal to the field F. Since ∇f yields the vector field (Fx, Fy, Fz), we find the anti-derivatives of each component of F to solve for f. For this particular function f, the anti-derivatives are 1/2 * yz^2 + C1 for Fx = yz, 1/2 * xz^2 + C2 for Fy = xz, and 1/2 * xy^2 + 9z^2 + C3 for Fz = xy + 18z. Therefore, the function that satisfies the requirement is 1/2 * yz^2 + 1/2 * xz^2 + 1/2 * xy^2 + 9z^2 + C, where C is a constant.
Part (b) then requires the evaluation of the line integral of ∇f ∙ dr along a curve c, from point (1,0,-1) to (5,6,1). According to the fundamental theorem of line integrals, if a vector field is conservative (as it is in this case because we found a function f such that F = ∇f), the line integral of a vector field F along a curve c from a to b is simply f(b) - f(a). Therefore, using the function f found in part a, you can substitute the coordinates of points a and b to find the solution to the line integral equation.
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hey can some one look at this?
Answers
1 foot = 12 inches.
x feet = 60 inches.
1 foot * 60 inches = 12 * x divide by 12
60 / 12 = 5
So the person is at least 5 feet tall. The height you want is 5 feet 4 inches.
So add 4 inches to 5 feet.
or
Add 4 inches to 60 inches.
you get 64 inches.
There are 20 entries all together. 2 people are 64 inches tall.
P(64) = 2/20 = 1/10 = 0.1
Answer P(64) = 0.1
I would check all of this if I were you. I'm not sure I counted either one correctly.
expand (x^2-3/2)^9 using binomial process
Answers
[tex] x^{18} - \frac{ 27x^{6} }{2}+ 81x^{14}- \frac{ 567x^{12} }{2}+ \frac{ 5103x^{10} }{16}- \frac{ 15309x^{8} }{16}+ \frac{ 15309x^{6} }{16} - \frac{ 59049x^{2} }{256}- [/tex][tex] \frac{19683}{512} [/tex]
Man that was a lot to type out, hopefully i helped, and Gosh I hope I get a brainly for all that freaking typing. hehe~ ^.^
Of the 5th grade boys, 2/3 play sports. Of the boys who play sports, 1/4 play baseball. what fraction of the 5th grade boys play baseball?
Answers
2/3 * 1/4
2/12
Simplify:
1/6 of the 5th grade boys play baseball
How does an earthquake of magnitude 7.9 compare in intensity with an earthquake of magnitude of 3.7 on the Richter scale? The larger earthquake's intensity was nothing times as great as the smaller earthquake's intensity. (Round to the nearest whole number as needed.)
Answers
Answer:
15,849
Step-by-step explanation:
A magnitude 7.9 earthquake releases approximately 2.7 million times more energy than a 3.7 magnitude earthquake, as the Richter scale is logarithmic and represents a 32-fold increase in energy release for each unit increase in magnitude.
Explanation:The Richter scale is logarithmic, which means that each whole number increase represents a tenfold increase in amplitude and roughly a 32-fold increase in the energy released by an earthquake.
Therefore, when comparing a magnitude 7.9 earthquake to a magnitude 3.7 earthquake, there is a difference of 4.2 on the Richter scale.
This corresponds to a tenfold increase in amplitude 4.2 times, which would be 10 to the power of 4.2 in terms of amplitude.
However, if we consider the energy, which increases by a factor of 32 for each whole number increase, we're looking at 32 to the power of 4.2, which is approximately 2,704,156 times greater in terms of energy release.
To determine the intensity difference in a more simplified manner, taking the base-10 logarithm of the energy ratio is effective.
The simplified comparison tells us that the larger quake's intensity is about 2.7 million times greater than the smaller quake's intensity.
After rounding to the nearest whole number, we find that the intensity is 2,704,156 times as great.
NEED HELP WILL GIVE OUT BRAINLIEST AND POINTS
11. Find the area. The figure is not drawn to scale.
12. Find the area of the kite. The figure is not drawn to scale.
Answers
we know that
the area of the triangle is
A=b*h/2
in this problem
b=9
h=12
so
A=9*12/2-----> A=54 units²
the answer part 1) is
Area=54 units²
Part 2) Find the area of the kite
see the picture attached with letters to better understand the problem
we know that
The area of a Kite is half the product of the diagonals
step 1
find CB
applying Pythagoras Theorem
AB²=AC²+BC²------> BC²=AB²-AC²-----> BC²=5²-3²----> BC²=16
BC=4
so
the diagonals are
(10+4) and (3+3)---------> 14 and 6
Area=(1/2)*[14*6]----> Area=42 units²
the answer Part 2) is
the area of a kite is 42 units²
If the typos are randomly distributed over the 10 pages, find the probability of having a single typo on each page
Answers
Lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. a bank conducts interviews of job applicants with the use of the lie detector. there are 15 applicants who are interviewed.
a.assuming all 15 applicants tell the truth, what is the probability that the lie detector will conclude that all 15 are telling the truth?
b.assuming all 15 applicants tell the truth, what is the probability that the lie detector will conclude that at least one is lying?
c.what are the mean and standard deviation of the 15 applicants the lie detector concludes are lying?
d.what is the probability that the number of truthful applicants classified as liars is greater than the mean?
Answers
Given that lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. Thus, lie detectors have a 85% chance of concluding that a person is telling the truth when they are indeed telling the truth.
The case that the lie detector correctly determined that a selected person is saying the truth has a probability of 0.85
Thus p = 0.85
Thus, the probability that the lie detector will conclude that all 15 are telling the truth if all 15 applicants tell the truth is given by:
[tex]P(X)={ ^nC_xp^xq^{n-x}} \\ \\ \Rightarrow P(15)={ ^{15}C_{15}(0.85)^{15}(0.15)^0} \\ \\ =1\times0.0874\times1=0.0874[/tex]
Part B:
Given that lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. Thus, lie detectors have a 85% chance of concluding that a person is telling the truth when they are indeed telling the truth.
The case that the lie detector wrongly determined that a selected person is lying when the person is actually saying the truth has a probability of 0.25
Thus p = 0.15
Thus, the probability that the lie detector will conclude that at least 1 is lying if all 15 applicants tell the truth is given by:
[tex]P(X)={ ^nC_xp^xq^{n-x}} \\ \\ \Rightarrow P(X\geq1)=1-P(0) \\ \\ =1-{ ^{15}C_0(0.15)^0(0.85)^{15}} \\ \\ =1-1\times1\times0.0874=1-0.0874 \\ \\ =0.9126[/tex]
Part C:
Given that lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. Thus, lie detectors have a 85% chance of concluding that a person is telling the truth when they are indeed telling the truth.
The case that the lie detector wrongly determined that a selected person is lying when the person is actually saying the truth has a probability of 0.15
Thus p = 0.15
The mean is given by:
[tex]\mu=npq \\ \\ =15\times0.15\times0.85 \\ \\ =1.9125[/tex]
Part D:
Given that lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. Thus, lie detectors have a 85% chance of concluding that a person is telling the truth when they are indeed telling the truth.
The case that the lie detector wrongly determined that a selected person is lying when the person is actually saying the truth has a probability of 0.15
Thus p = 0.15
The probability that the number of truthful applicants classified as liars is greater than the mean is given by:
[tex]P(X\ \textgreater \ \mu)=P(X\ \textgreater \ 1.9125) \\ \\ 1-[P(0)+P(1)][/tex]
[tex]P(1)={ ^{15}C_1(0.15)^1(0.85)^{14}} \\ \\ =15\times0.15\times0.1028=0.2312[/tex]
Let μ = 160 and σ = 16. find the z-score for the score, x = 150.
Answers
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
and evaluate.
z = (150 -160)/16 = -10/16
z = -5/8
The z-score for the score x=150 is -5/8 = -0.625.
does anyone know the answer???
Answers
slope = (change in y)/(change in x)
slope = (14 -(-3))/(7 -(-10)) = 17/17 = 1
The slope of line CD is the negative reciprocal of that, -1/1 = -1.
The point-slope form of the equation for line CD can be written as
y = -1(x -5) +12
y = -x +17
The x-intercept is the value of x when y = 0.
0 = -x +17
x = 17
The x-intercept is ...
(17, 0)
Another way to write the equation for line CD is "standard form." For this, we add x to the slope-intercept form to get ...
x + y = 17
For the second part of your question, we can find the answer by adding the x- and y-coordinates to see which sum is 17.
-5 +24 = 19
-2 +19 = 17 . . . . . . . . . the point (-2, 19) is the correct choice
7 +(-10) = -3
8 +11 = 19
The domain of u(x) is the set of all real values except 0 and the domain of v(x) is the set of all real values except 2. What are the restrictions on the domain of (u-v)(x)?
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So then domain of (u-v)(x) would be the set of all real values except 0 and 2.
Hope this helps.
Answer: x = 2 and x cannot be any value for which v(x) = 0
Step-by-step explanation:
Is 28 cups greater or less than 14 Pints
Answers
28 cups is exactly equal to 14 pints. (There are 2 cups per pint.)
400,000 + 80,000 + 4,000 + 50 + 9 Write the standard form of the number shown above.
Answers
400,000
80,000
4,000
59
--------------
484,059 (answer)
Short answer: 484,059
Why?
This equation shown is an expanded form of a number. 400k is the largest number, so that'd go first. 80k is the second largest, so that would go next to the largest number, 4. (400k) 4k is the third largest, so that'd go next to the first and second largest numbers, 48. (480k) Now, we have 484,000. Since there is no hundred, we put a zero there. Now, add a 59 at the end of the zero. Which gives us the number 484,059.
Hope this helped you! ♥
19 hundred thousandths in scientific
notation
Answers
The scientific notation of 19 hundred thousandths which is 0.000019 is 1.9 x 10^-5.
Explanation:The number 19 hundred thousandths would mean 19 divided by 1,000,000 which equals 0.000019. When we convert this decimal to scientific notation, it becomes 1.9 x 10^-5. In scientific notation, we want to express a number as a value between 1 and 10 multiplied by a power of 10. So, to convert 0.000019 to scientific notation, we need to move the decimal point five places to the right, which gives us 1.9. The '10^-5' shows that the decimal point has moved five places to the right from the original number.
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