Answer:
[tex]Area=7\,\pi\,\sqrt{\frac{53}{4}}\,\,\frac{25}{2}[/tex]
Step-by-step explanation:
Let's use the integral formula for the surface area of revolution of the function y(x) around the x-axis, which is:
[tex]Area=\int\limits^b_a {2\,\pi\,y\,\sqrt{1+(\frac{dy}{dx} )^2} } \, dx[/tex]
and which in our case, we can obtain the following:
[tex]y=\frac{7}{2} \,x\\\frac{dy}{dx} =\frac{7}{2} \\(\frac{dy}{dx})^2=\frac{49}{4} \\\sqrt{1+(\frac{dy}{dx})^2} =\sqrt{1+\frac{49}{4} } =\sqrt{\frac{53}{4} }[/tex]
Recall as well that [tex]0\leq x\leq 5[/tex], which gives us the limits of integration:
[tex]Area=\int\limits^b_a {2\,\pi\,y\,\sqrt{1+(\frac{dy}{dx} )^2} } \, dx\\Area=\int\limits^5_0 {2\,\pi\,(\frac{7}{2}\,x) \,\sqrt{\frac{53}{4} } } \, dx\\Area=7\,\pi\,\sqrt{\frac{53}{4}}\,\, \int\limits^5_0 {x} \, dx \\Area=7\,\pi\,\sqrt{\frac{53}{4}}\,\,\frac{x^2}{2} |\limits^5_0\\Area=7\,\pi\,\sqrt{\frac{53}{4}}\,\,\frac{25}{2}[/tex]
If we compare it with the geometry formula:
Lateral surface of cone = [tex]\frac{1}{2} \,\,(Base_{circ})\,\,(slant\,height)= \frac{1}{2} (2\,\pi\,\frac{7}{2} 5)\.(\sqrt{5^2+(\frac{35}{2})^2 } =\frac{7}{2} \,\pi\,25\.\,\sqrt{\frac{53}{4} }[/tex]
which is exactly the expression we calculated with the integral.
If y= -3x7+2x3+ x, the derivative of y with respect to x is
Answer:
[tex]\frac{dy}{dx}[/tex] = - 21[tex]x^{6}[/tex] + 6x² + 1
Step-by-step explanation:
Differentiate each term using the power rule
[tex]\frac{d}{dx}[/tex] (a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex]
Given
y = - 3[tex]x^{7}[/tex] + 2x³ + x , then
[tex]\frac{dy}{dx}[/tex] = (7 × - 3 )[tex]x^{6}[/tex] + (3 × 2)x² + (1 × 1 )[tex]x^{0}[/tex]
= - 21[tex]x^{6}[/tex] + 6x² + 1
HELP ME NOWWWWWW PLZZZZZZ EXPLAIN UR ANSWER FOR BRAINLIEST
Answer:
The answer's A 1/52
Step-by-step explanation:
That's because there's only one ace of hearts in a deck of 52 cards.
Answer: A) 1/52
Step-by-step explanation:
There is 52 cards in a whole deck, and the probability of getting that ace card is 1/52 because there is only 1 ace card in an entire deck of cards.
Hence, the answer is 1/52
On a unit circle, the vertical distance from the x-axis to a point on the perimeter of the circle is twice the horizontal
distance from the y-axis to the same point. What is sine?
Answer:
(2/5)√5 ≈ 0.894427
Step-by-step explanation:
You require the y-coordinate of the point that satisfies two equations:
x^2 +y^2 = 1
y = 2x
Substituting for x, we have ...
(y/2)^2 +y^2 = 1
y^2(5/4) = 1
y^2 = 4/5
y = (2/5)√5 ≈ 0.894427
The sine of the angle is (2/5)√5 ≈ 0.894427.
Answer:
The answer would be C.
Step-by-step explanation:
Members of a gymnastics team are traveling to a tournament. They must pay $250 for a bus plus $40 per athlete to register for the tournament. What is the average total cost per athlete if 20 gymnasts attend? Do not include the dollar sign ($) in your answer.
Answer:
1050 in total, 52.50 for each athlete
Step-by-step explanation:
We can start by writing an equation with x as the number of athletes
250+40x= Total cost
Now we can substitute 20 for x
250+40(20)
250+800
1050
The total cost is 1050
If you need the amount that each athlete is paying individually, just divide it by 20
1050/20=52.50
52.50 for each athlete
Both the P-value method and the critical value method use the same standard deviation based on the claimed proportion p, so they are equivalent to each other. Is this also true about the confidence interval method?
Answer:
Yes, it's also true about the confidence interval method.
Step-by-step explanation:
The confidence interval includes all the null hypothesis values for the population mean that would be accepted by the hypothesis test at the significance level of 5%. Now, it means this assumes a two-sided alternative.
Now, when testing claims about
population proportions, the critical method and the P-value method are equivalent due to the fact that they always produce the same result. Similarly, a conclusion based on a confidence interval estimate will be the same as a conclusion based on a hypothesis test.
So, Yes the confidence interval method and the P-value or critical methods will always lead to the same conclusion when the tested parameter is the standard deviation.
What is the measure of cuz
Answer:
D. 65°
Step-by-step explanation:
The measure of the angle at crossed chords is the average of the measures of the intercepted arcs:
m∠XYZ = (1/2)(arc XZ +arc WV)
m∠XYZ = (1/2)(86° +44°) = 130°/2
m∠XYZ = 65°
EACH PAIR OF FIGURES IS SIMILAR. FIND THE MISSING SIDE!!!!
Answer:
58.1 and 17
Step-by-step explanation:
For the first triangles the similarity ratio is 1:7 so x is 8.3 × 7 = 58.1
For the second triangles the similarity ratio is 1:5 so x is 3.4 × 5 = 17
The first two steps in determining the solution set of the system of equations, y = -x2 + 4x + 12 and y=-3x + 24,
algebraically are shown in the table.
Answer:
C
Step-by-step explanation:
(3,15) and (4,12)
Answer:
C or (3, 15) and (4, 12)
Step-by-step explanation:
I just took the test on Edge 2020
Please help me find the sign of f
Answer: B. f is always negative on the interval
========================================================
Explanation:
-1/5 = -0.2
Pick any number for x that will make the interval -0.2 < x < 2 to be true. I find x = 0 to be easiest.
Plug it into f(x)
f(x) = (5x+1)(4x-8)(x+6)
f(0) = (5(0)+1)(4(0)-8)(0+6)
f(0) = (1)(-8)(6)
f(0) = -48
We get a negative result.
So we can rule out choice A which says that f is always positive. Either f is always negative on this interval, or it's a mix of being positive and negative.
-------------
Note that the roots of f(x) are -1/5, 2 and -6. This is from solving f(x) = 0
Use the zero product property to solve (5x+1)(4x-8)(x+6) to find the three roots mentioned.
The roots of -1/5 and 2 form the boundary of the interval mentioned at the top of the problem. There are no roots in between -1/5 and 2, so this means that f(x) stays entirely negative on this interval. There is no way f(x) becomes positive on this interval because it would have to cross over the x axis, thus forming another root. But again there are no roots between -1/5 and 2.
A graph confirms we have the correct answer. Check out the image attached below. Note the portion from x = -0.2 to x = 2 is entirely below the x axis.
Not sure how I would solve this
The first ordered pair is ( -4 , -3 )
The second ordered pair is ( 8, 3 )
=================================================
Explanation:
The first point is (x,-3) where x is unknown. It pairs up with y = -3 so we can use algebra to find x
x-2y = 2
x-2(-3) = 2 ... replace every y with -3; isolate x
x+6 = 2
x = 2-6
x = -4
The first point is (-4, -3)
---------------------------
We'll do something similar for the other point. This time we know x but don't know y. Plug x = 8 into the equation and solve for y
x-2y = 2
8-2y = 2
-2y = 2-8
-2y = -6
y = -6/(-2)
y = 3
The second point is (8, 3)
Robert wants to arrange the books for statistics, calculus, geometry, algebra, and trigonometry on a shelf. In how many arrangements can he keep them on the shelf such that the algebra and trigonometry books are not together?
Answer: 72 arrangements
Step-by-step explanation:
The books are:
Statistics, calculus, geometry, algebra, and trigonometry.
So we have 5 books.
We want that algebra and trigonometry are not together.
Suppose that we have 5 positions:
Now, we can start with algebra in the first position.
Now, we have 3 positions for trigonometry (3rd, 4th and 5th).
Now, once those two books are in position, we have 3 other positions and 3 other books, so for the first selection we have 3 options, for the second position we have 2 options, and for the last option we have 1 option.
The number of combinations is equal to the number of options in each selection:
3*(3*2*1) = 18
Now, if Algebra is in the second place, then for trigonometry we have only 2 possible options (4th and 5th)
and for the other 3 books again we have 3*2*1 combinations:
the total number of combinations is:
2*(3*2*1) = 12
If algebra is in the 3rd position, trigonometry has 2 options (1st and 5th)
For the other 3 books, we have 3*2*1 combinations.
The total number of combinations is:
(3*2*1)*2 = 12
in the fourth position is the same as the second position, so here we have again 12 combinations.
For the fifth position is the same as for the first position, so we have 18 combinations.
The total number of combinations is:
C = 18 + 12 +12 +12 +18 = 72
if he allows 40 people to choose a treat from the bag about how many lizard lollis can he expect to give away
Answer:
20 Lizard lollies.
Step-by-step explanation:
There are 10 lizard lollis. This is out of 10+4+6 = 20 total treats. This makes the probability of drawing a lizard lollis 10/20 = 1/2.
This means out of 40 treats handed out, we can expect him to give out 1/2(40) = 20 lizard lollis.
add the following - 4/9,7/12and - 3/8
Answer:
[tex] - \frac{17}{72} [/tex]Step-by-step explanation:
[tex] - \frac{4}{9} + \frac{7}{12} + ( - \frac{ 3}{8} )[/tex]
When there is a (+) in front of an expression in parentheses, the expression remains the same:
[tex] - \frac{4}{9} + \frac{7}{12} - \frac{3}{8} [/tex]
[tex] \frac{ - 4 \times 8 + 7 \times 6 - 3 \times 9}{72} [/tex]
Calculate the sum of difference
[tex] \frac{ - 32 + 42 - 27}{72} [/tex]
[tex] \frac{10 - 27}{72} [/tex]
[tex] - \frac{17}{72} [/tex]
Hope this helps..
Good luck on your assignment...
Which equation represents the total cost (c) of purchasing cans of vegetables(v) at a price of $1.18 per can? What is the total cost to purchase 98 cans of vegetables? Question 10 options: A) c = 1.18v; $83.05 B) v = 1.18c; $83.05 C) c = 1.18v; $115.64 D) v = 1.18c; $115.64
Answer:
C
Step-by-step explanation:
The equation must be equal to c since that is the total cost.
c = 1.18v
Plug in 98 for v to find the answer.
c = 1.18(98)
c = $115.64
which of these 3 curves drawn matches the graph of y=2x^2+x
Answer:
Slope: 1
y-intercept: 8
Step-by-step explanation:
x, y
-8,0
0,8
For a segment of a radio show a disc jockey can play 10 records. If there are 12 records to select from in how many ways can the program for this segment be arranged
Answer:
66 different waysStep-by-step explanation:
This is a combination question. Combination has to do with selection. For example if r objects are to be selected from n pool of oblects, this can be done in nCr number of ways.
nCr = n!/(n-r)r!
According to the question, if a radio show can only play 10 records out of 12 records available, this can be done in 12C10 number of ways.
12C10 = 12!/(12-10)!10!
= 12!/2!10!
= 12*11*10!/2*10!
= 12*11/2
= 6*11
= 66 different ways
Please help with this. Thanks!
Answer:
1/5k-2/3j and -2/3j+1/5k
Step-by-step explanation:
This is because the sign of both of the terms stay the same and the fractions and variables stay the same for each term as well.
g Consider writing onto a computer disk and then sending it through a certifier that counts the number of missing pulses. Suppose this number X has a Poisson distribution with lamda = .2. a) What is the probability that a disk has exactly one missing pulse? b) What is the probability that a disk has at least two missing pulses? c) What is EX
Answer:
a) P(1) = 0.1637
b) [tex]P(x\geq 2) = 0.0176[/tex]
c) E(x) = 0.2
Step-by-step explanation:
If X follows a poisson distribution, the probability that a disk has exactly x missing pulses is:
[tex]P(x)=\frac{e^{-m}*m^x}{x!}[/tex]
Where m is the mean and it is equal to the value of lambda. So, replacing the value of m by 0.2, we get that the probability that a disk has exactly one missing pulse is equal to:
[tex]P(1)=\frac{e^{-0.2}*0.2^1}{1!}=0.1637[/tex]
Additionally, the probability that a disk has at least two missing pulses can be calculated as:
[tex]P(x\geq 2)=1-P(x<2)[/tex]
Where [tex]P(x<2)=P(0)+P(1)[/tex].
Then, [tex]P(0)[/tex] and [tex]P(x\geq 2)[/tex] are calculated as:
[tex]P(0)=\frac{e^{-0.2}*0.2^0}{0!}=0.8187\\P(x\geq 2) = 1 - (0.8187 + 0.1637)\\P(x\geq 2) = 0.0176[/tex]
Finally, In the poisson distribution, E(x) is equal to lambda. So E(x) = 0.2
To determine if a particular predictor in a regression analysis is statistically significant, which statistic should one interpret
Answer:
The test statistic used to determine whether a particular predictor in a regression analysis is statistically significant is:
[tex]t=\frac{\beta_{i}}{S.E._{\beta_{i}}}[/tex]
Step-by-step explanation:
The general form of a regression equation is:
[tex]y=\alpha +\beta_{1}x_{1}+\beta_{2}x_{2}+...+\beta_{n}x_{n}[/tex]
Here,
α = y-intercept
βi = regression coefficients, (i = 1, 2, ..., n)
A regression analysis is performed to determine whether the predictor variables are statistically significant or not.
The output of the regression analysis consists of two tables.
One is the regression output and the other is the ANOVA table.
The regression output table is used to display which predictor variables are statistically significant and which are not.
The test statistic used to determine whether a particular predictor in a regression analysis is statistically significant is:
[tex]t=\frac{\beta_{i}}{S.E._{\beta_{i}}}[/tex]
And the ANOVA table displays overall regression analysis.
The F-test statistic is used to for the overall regression analysis.
Thus, the test statistic used to determine whether a particular predictor in a regression analysis is statistically significant is:
[tex]t=\frac{\beta_{i}}{S.E._{\beta_{i}}}[/tex]
Ronnie goes to the racetrack with his buddies on a weekly basis. One week he tripled his money, but then lost $12. He took his money back the next week, doubled it, but then lost $40. The following week he tried again, taking his money back with him. He quadrupled it, and then played well enough to take that much home, a total of $224. How much did he start with the first week?
Answer:
20
Step-by-step explanation:
224÷4 = 56+40 = 96÷2 = 48+12 = 60÷3 = 20
If Ronnie goes to the racetrack with his buddies on a weekly basis. How much did he start with the first week is $20.
How much did he start with?Hence:
4 [2 (3x - 12) -40] = 224
4 [6x - 24 - 40] = 224
Collect like term
24x - 256= 224
24x/24 = 480/24
Divide both side by 24
x=480/24
x=$20
Therefore How much did he start with the first week is $20.
Learn more about How much did he start with here:https://brainly.com/question/25870256
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I NEED HELP PLEASE, THANKS! :)
Hey there! :)
Answer:
[tex]({\frac{-9\sqrt{3} }{2}, 9/2) }[/tex]
Step-by-step explanation:
In rectangular coordinates, the form is:
(r·cosθ, r·sinθ)
In this instance:
Polar coordinates: (9, 150°). Use the coordinates above to solve for the rectangular coordinates.
(r · cos 150°, r· sin 150°)
(9 · cos 150°, 9· sin 150°)
cos 150° = -√3/2
sin 150° = 1/2
Plug these values into the equation:
(9 · (-√3/2), 9 · 1/2)
Multiply and simplify:
(-9√3/2, 9/2)
Therefore, the coordinates in rectangular form are:
[tex]({\frac{-9\sqrt{3} }{2}, 9/2) }[/tex]
Rafael is saving money to buy a game. So far he has saved $30, which is five-sixths of the total cost of the game. How much does the game cost?
Answer:
$36
Step-by-step explanation:
30 is 5/6 of the game, so we can think that 1/6 is equal to 6, since 5(6) is 30.
If we add another sixth, we get 36, which will be the total cost of the game.
plz answer question in screen shot
Answer:
200√3
Step-by-step explanation:
The triangle given here is a special right triangle, one with angles measuring 30-60-90 degrees. The rule for triangles like these are that the side opposite the 30° angle can be considered x, and the side opposite the 60° angle is x√3, while the hypotenuse, or side opposite the right angle, is 2x. All we need to know here are the two legs to find the area.
Since b is opposite the 30° angle, it is x, while side RS is opposite the 60° angle, meaning it is equal to x√3, meaning that the area of the triangle is 1/2*x*x√3. We can substitute in 20 for x, making our area 1/2*20*20√3. Multiplying we get 10*20√3, or 200√3.
Suppose that a population is known to be normally distributed with £ = 2400 and € = 210. Of a random sample of size n = 8 is selected, calculate the probability that the sample mean will exceed 2,500.
Answer:
0.0885 = 8.85% probability that the sample mean will exceed 2,500.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
[tex]\mu = 2400, \sigma = 210, n = 8, s = \frac{210}{\sqrt{8}} = 74.25[/tex]
Calculate the probability that the sample mean will exceed 2,500.
This is 1 subtracted by the pvalue of Z when X = 2500. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2500 - 2400}{74.25}[/tex]
[tex]Z = 1.35[/tex]
[tex]Z = 1.35[/tex] has a pvalue of 0.9115
1 - 0.9115 = 0.0885
0.0885 = 8.85% probability that the sample mean will exceed 2,500.
What would be the angle of elevation of a tree from the ground, if the height of the
tree and its shadow are equal in length?
Answer:
45°
Step-by-step explanation:
The diagram for this question has been attached to this response. Please check.
The angle of elevation is the angle between a horizontal line from a viewer and the line of sight to an object being viewed which is above the horizontal line.
From the diagram;
θ is the angle of elevation
x = height of the tree
y = length of the shadow of the tree = x
Therefore,
tanθ = [tex]\frac{x}{y}[/tex] [Remember that y = x? Then substitute into the equation]
tanθ = [tex]\frac{x}{x}[/tex]
tanθ = 1
θ = tan⁻¹(1)
θ = 45°
Therefore, the angle of elevation is 45°
A political candidate has asked you to conduct a poll to determine what percentage of people support him. If the candidate only wants a 5% margin of error at a 97.5% confidence level, what size of sample is needed? When finding the z-value, round it to four decimal places.
Answer:
The sample size required is, n = 502.
Step-by-step explanation:
The (1 - α)% confidence interval for population proportion is:
[tex]CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p\cdot (1-\hat p)}{n}}[/tex]
The margin of error is:
[tex]MOE=z_{\alpha/2}\sqrt{\frac{\hat p\ \cdot (1-\hat p)}{n}}[/tex]
Assume that 50% of the people would support this political candidate.
The margin of error is, MOE = 0.05.
The critical value of z for 97.5% confidence level is:
z = 2.24
Compute the sample size as follows:
[tex]MOE=z_{\alpha/2}\sqrt{\frac{\hat p\ \cdot (1-\hat p)}{n}}[/tex]
[tex]n=[\frac{z_{\alpha/2}\times \sqrt{\hat p(1-\hat p)}}{MOE}]^{2}[/tex]
[tex]=[\frac{2.24\times \sqrt{0.50(1-0.50)}}{0.05}]^{2}\\\\=501.76\\\\\approx 502[/tex]
Thus, the sample size required is, n = 502.
Ross needs to buy a countertop for a laundry room. He calculated the area to be 12 square feet. The actual area is 11.8 square feet. What is Ross's percentage error? a.1.02% b.1.69% c.20% d.98%
Answer:
b. 1.69
Step-by-step explanation:
So to solve this problem we need to simply find the percentage increase from 11.8 to 12 =>
to solve this we would do 12 - 11.8 = 0.2 --> 0.2 is our "difference in the increase" -->
now we divide this by our amt. which is 11.8 --> 0.2/11.8 = approx. 0.0169
--> finally multiply that by 100 which is simply moving the decimal places 2 places right giving us the final answer of 1.69
Hope this helps!
Answer:
B. 1.69%
Step-by-step explanation:
If Ross calculated the countertop for a laundry room to be 12 square feet but turns out to be actually 11.8 square feet, we need to find out how much percentage error Ross has made!
In order to solve this question,
1) We need to create proportions:
Ross' calculations x
______________ = _________
actual area 100
x represents the percentage error.
100 is the total percentage.
2) Now we plug in the numbers:
We plug in 12 for Ross' calculations. We plug in 11.8 for the actual area. So, it will look like this:
12 x
______ = _______
11.8 100
3) Time for cross multiplication:
12 times 100 is 1,200
11.8 times x is 11.8x
So,
1,200 = 11.8x
4) Now we divide:
1,200 divided by 11.8 equals to 101.69 %
5) We are not done! We still have to subtract:
101.69
-100.00
_______
1.69
Finished!!
Our answer is 1.69%, which is B.
Hope this was helpful !!!
If s=1/2 unit and A=12s^2, what is the value of A, in square unit?
Answer:
3 square units
Step-by-step explanation:
Put the numbers in the formula and do the arithmetic.
A = 12(1/2)² = 12(1/4) = 3 . . . square units
__
Comment on the working
It might be helpful to you to see how this works when the units of the number are attached to the number.
A = 12(1/2 unit)² = 12(1/2 unit)(1/2 unit) = 12(1/2)(1/2)(unit)(unit) = 3 unit²
I often choose to keep the units with the numbers, just to make sure that the numbers and units are correct. For example, you can multiply inches by feet, but you get in·ft, which is not square inches and not square feet. You have to do a conversion to get the result in square units.
Find the first, fourth, and eighth terms of the sequence.
A(n) = -2x2^n-1
Answer:
first term = -2
fourth term = -16
eighth term = -256
Step-by-step explanation:
Given;
A sequence with function;
A(n) = -2x2^(n-1)
The first, fourth, and eighth terms of the sequence can be calculated by substituting their corresponding values of n;
First term A(1); n = 1
A(1) = -2x2^(1-1) = -2×1 = -2
Fourth term A(4); n = 4
A(4) = -2x2^(4-1) = -2×8 = -16
Eighth term A(8); n = 8
A(8) = -2x2^(8-1) = -2×128 = -256
Therefore,
first term = -2
fourth term = -16
eighth term = -256
In a fish tank the number of orange fish is 1 1/4 times the number of blue fish. Drag the blue fish to represent the number of blue fish in the tank dor every 5 orange fish
Answer:
4 blue fish for every 5 orange fish
Step-by-step explanation:
(orange fish) = (1 1/4)·(blue fish) . . . . . the given relation
(orange fish) = (5/4)·(blue fish) . . . . . write as improper fraction
(orange fish)/(blue fish) = 5/4 . . . . . divide by "blue fish"
There are 4 blue fish for every 5 orange fish.