Volume of solid generated by revolving the region bounded by the graph is 3817.53 unit
What do you mean by volume of revolution?A volume is created while a plane figure rotating about an axis or around any straight line situated on the same plane.
How to calculate volume of solid generated by revolving the region?We apply definite integration to calculate the required volume.
we are given the equation y = 5x² and y =0, x= 3
volume is calculated by using the formula, V = ∫π y² dx
V = ∫₀³π (5x²) ² dx
On the y-axis x = 0 so upper limit x = 3 and lower limit x= 0
V= π × 25/5 [x⁵] ³₀
V = 15.71 [3⁵- 0]
hence, the volume of solid = 3817.53 unit
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What is the answer to this question?
A. Domain: All Real Numbers; Range: All Real Numbers
B. Domain: −10 ≤x≤10 Range: −4≤y≤8
If you tossed two coins simultaneously 400 times, would you expect the deviation to be greater or less than it was in tossing them 40 times? Explain.
Yes, the deviation is greater than it was in tossing them 40 times.
What is Standard Deviation?A standard deviation (or σ) is a measure of how widely distributed the data is in reference to the mean. A low standard deviation suggests that data is grouped around the mean, whereas a large standard deviation shows that data is more spread out.
Given:
n= 400 trials
Tossing 2 coins 400 times gives 800 trials
so, [tex]\sigma_1[/tex]² = np(1- p)
= 800 x 1/2 x 1/2
[tex]\sigma_1[/tex] = √200
[tex]\sigma_1[/tex] = 10√2
Now, n=40
and, [tex]\sigma_2[/tex]² = np(1- p)
= 80 x 1/2 x 1/2
[tex]\sigma_2[/tex] = √20
[tex]\sigma_2[/tex] = 2√5
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4 adults took their 5 children to a movie. The price for the 9 people was $160. The 5 children recieved a 20% discount on their tickets. The cost for a child ticket is how much less than the cost of an adult ticket?
Answer:
The answer is $14.224.
Step-by-step explanation:
A cube with an edge of 20 cm is filled with water. Would this amount of water fit in a sphere with a 20 cm radius?
The volume of a sphere is 33409.6 cm³ and the volume of a cube is 8000 cm³. Therefore, the volume of water 8000 cm³ can fit in the sphere.
Given that, a cube with an edge of 20 cm is filled with water.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
We know that, the volume of cube =a³, where a=edge
Here, volume of cube =20³
= 8000 cm³
Radius of sphere is 20 cm
As we know, the volume of sphere = 4/3πr³
= 4/3 ×3.14×20³
= 1.33×3.14×8000
= 33409.6 cm³
The volume of a sphere is 33409.6 cm³ and the volume of a cube is 8000 cm³. Therefore, the volume of water 8000 cm³ can fit in the sphere.
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What is the slope?????????
Answer:
AB - [tex]\frac{2}{1}[/tex]
BC - [tex]\frac{4}{2}[/tex]
AC - [tex]\frac{6}{3}[/tex]
Slope = 2
Step-by-step explanation:
For AB the rise (counting upwards) is 2 and the run (counting to the right) is 1. If you simplify it, it would be 2. The reason why it's not a negative is that the slope is going upwards not downwards.
As part of a probability experiment for math class, Reid flipped a coin a hundred times. He
predicted it would land on heads 50 times, but it actually landed on heads 40 times. What is
the percent error for Reid's prediction?
►
If necessary, round your answer to the nearest tenth of a percent.
Answer:
25%
Step-by-step explanation:
we know that you have to do amount of error/ correct amount
so the amount of error is 10 and the correct amount is 40, so its 10/40.
10 divided by 40 is 0.25. They want the answer as a percent, so in order to turn 0.25 to a percent, you have to move the decimal 2 times over. It then turns into 25%
In ΔQRS, m∠Q = 11° and m∠R = 40°. Which list has the sides of ΔQRS in order from shortest to longest?
PLEASE HELP!!
Answer:
RS, SQ, QR
Step-by-step explanation:
The three angles in a triangle add up to 180° Two angles are given, so we can find the third angle.
11 + 40 + S = 180
51 + S = 180
subtract 51
S = 129°
S is the biggest angle, so the biggest side will be opposite from S. QR is the biggest side.
AngleQ is 11°, the smallest angle. The smallest side will be opposite from the smallest angle. The smallest side is RS.
The 40° angle, AngleR is in the middle. The medium length side is opposite from the medium size angle. SQ is the medium length side.
From small to big:
RS, SQ, QR
Answer:
The 4th answer down
RS, SQ, RQ
Step-by-step explanation:
There is a relationship between the angle measurement and the length of the side opposite of the angle. The side opposite of the largest angle measurement has the longest side opposite to that angle, the same is true for the middle angle and the smallest angle.
65. Which of the following could represent the side
lengths of a triangle? Check all that apply.
A. 6, 10, 14
B. 12, 15, 29
C. 8, 8, 11
D. 19, 24, 40
E. 9, 17, 26
Answer: The following that could represent the side lengths of a triangle are A, C, D.
Step-by-step explanation:
The sum of the first two numbers of the triangle must be greater than the third.
A. 6+10= 16>14 -----------a triangle
B. 12+15= 27<29 -----------not a triangle
C. 8+8= 16>11 -----------a triangle
D. 19+24= 43>40 ------------a triangle
E. 9+17= 26=26 -------------not a triangle
Hope this helps! :)
We find a 95% confidence interval for the mean weight of apples in an orchard at a specific given time is between 147 grams to 151 grams. Which of the following is a correct interpretation of this interval?
(a) I am 95% confident that the confidence interval for mean weight of apples in the orchard will be between 147 grams to 151 grams
(b) I am 95% confident that the mean weight for all the apples in the orchard will be between 147 grams to 151 grams
(c) I am 95% confident that the mean weight of apples for this sample will be between 147 grams to 151 grams
(d) 1 am 95% confident that the weight of all the apples in the orchard is between 147 grams to 151 grams
The correct interpretation is (a) I am 95% confident that the confidence interval for mean weight of apples in the orchard will be between 147 grams to 151 grams
What Is a Confidence Interval?A confidence interval, refers to the probability that a population parameter will fall between a set of values for a certain proportion of times.
What is a 95% confidence interval?A 95% confidence interval is a range of values that you can be 95% certain contains the true mean of the population.
How to find the correct interpretation of this interval?Since the 95% confidence interval for the mean weight of apples in an orchard at a specific given time is between 147 grams to 151 grams.
This follows that from our definition of confidence interval and 95 % confidence interval, that there is a 95 % confidence that the mean weight of the apples in the orchard lies between 147 grams to 151 grams.
So, the correct interpretation is (a) I am 95% confident that the confidence interval for mean weight of apples in the orchard will be between 147 grams to 151 grams
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solve each of the following quadratic inequalities using any Convenient
method :
A)
[tex]x(10x + 19) \leqslant 15[/tex]
[tex](x + 2)^{2} > (3x + 1)^{2} [/tex]
Answer:
-2.5 ≤ x ≤ 0.6-0.75 < x < 0.5Step-by-step explanation:
You want the solutions to the following inequalities by any convenient method:
x(10x +19) ≤ 15(x +2)² > (3x +1)²ComparisonWe choose to rewrite these inequalities to be comparisons to zero. This is because our graphing calculator easily identifies the x-intercepts of a graph. We can look a the graph to tell where the function is above or below the x-axis.
f(x) = x(10x +19) -15; f(x) ≤ 0g(x) = (x +2)² -(3x +1)²; g(x) > 0GraphThe attached graph shows the solutions to be ...
f(x) ≤ 0 for -2.5 ≤ x ≤ 0.6g(x) > 0 for -0.75 < x < 0.5The values obtained for the first equation will be x ≤ 3/5 and x ≤ -5/2 and the values obtained for the second equation will be x < 1/2 and x < -3/4.
What is inequality?Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare the two values. Less than (or less than and equal to), larger than (or greater or equal to), or not similar to signs are used in place of the equal sign in between.
As per the given inequalities in the question,
1.
x(10x + 19) ≤ 15
Firstly, simplify it to the simpler form,
10x² + 19x - 15 ≤ 0
Solve the quadratic equation,
D = b² - 4ac
= 19² - 4(10)(-15).
D = 961
Now, use the formula,
(-b±√D)/2a
√D = √961 = 31
(-19 ± 31)/2(10)
So, the roots are:
1.
(-19 + 31)/20 = 12/20 = 3/5
Or, x ≤ 3/5
2.
(-19 - 31)/20 = -50/20 = -5/2
Or, x ≤ -5/2
2.
(x + 2)² > (3x + 1)²
Simplify the equation first.
x² + 4x + 4 > 9x² + 6x + 1
x² - 9x² + 4x - 6x + 4 - 1 > 0
-8x² - 2x + 3 >
8x² + 2x - 3 < 0
Now, find the roots for the equation,
D = b² - 4ac
D = 4 + 96
D = 100
Now, use the formula,
(-b ± √D)/2a
(-2 ± 10)/16
So, the roots are:
1. (-2 + 10)/16 = 1/2
Or, x < 1/2
2. (-2 - 10)/16 = -12/16 = -3/4
Or, x < -3/4
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Solve for x in the equation x2-14x+31-63-
Ox=-16 or x = 2
O x=-7±3-√√7
Ox=-2 or x = 16
Ox=7±3√√√7
Answer:Value of x are 16 and -2
Step-by-step explanation:
Solve for x in the equation:
Subtract 63 from both sides we have;
To factor this equation as:
⇒
Take (x-16) common we have;
⇒
By zero product property we have;
x-16 = 0 or x+2 = 0
⇒x = 16 or x = -2
Therefore, the value of x are: 16 and -2
The value of x in the equation are x = -2 or x = 16.
What are Quadratic Equations?Quadratic equations are polynomial equations of second degree.
The general form of a quadratic equation is ax² + b x + c = 0.
Given is a quadratic equation,
x² - 14x + 31 = 63
We have to find the value of x.
x² - 14x + 31 - 63 = 0
x² - 14x - 32 = 0
Using the quadratic formula,
x = [14 ± [tex]\sqrt{(-14)^2-(4*1*-32)}[/tex]] / 2
= (14 ± √324) / 2
= (14 ± 18) / 2
x = 14 + 18 / 2 or x = 14 - 18 / 2
x = 16 or x = -2
Hence the value of x are x = 16 or x = -2.
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A student paid 13% value added tax (VAT) after receiving 8% discount from the seller while purchasing a mobile set to participate in online class. If the student paid Rs. 10396 to purchase the mobile set, by how much the price paid by the student or the price marked by the seller is more? Find.
Answer: 113% = 9153
100% = ?
100/113 X 9153 = 915300/113 = Rs 8100 = sale price
90 % = 8100
100% = ?
100/90 X 8100 = Rs 9000 = marked price
108% = 8100
100% = ?
100/108 X 8100 = Rs7500 = cost
Difference = 9000 -7500 = Rs 1500
1500/7500 X 100 = 20%
ANSWER Marked price is 20% above cost price
Step-by-step explanation:
how would i match these together
{5x + 2(x - 1) = 6(x + 1) +x}------------------------No solution
{5x + 2(x - 1) = 6(x - 1) - x}------------------------- x = -2
{5x + 2(x - 3) = 6(x - 1) - x}-------------------------x = 0
{5x + 2(x - 3) = 6(x - 1) + x}-------------------------All real numbers
What is linear equation?
A linear equation is an algebraic equation of the shape y= mx + b. regarding simplest a consistent and a first-order (linear) term, wherein m is the slope and b is the y-intercept.
Solution:
Simplifying First equation,
5x + 2x - 2 = 6x + 6 + x
⇒7x - 2 = 7x + 6
⇒ -2 = 6, which is not possible
Similarly second equation,
5x + 2x - 2 = 6x - 6 -x
⇒ 7x - 2 = 5x - 6
⇒ 2x = -4
⇒ x = -2
Similarly third equation,
5x + 2x - 6 = 6x - 6 - x
⇒7x - 6 = 5x -6
⇒ 2x = 0
⇒ x = 0
Similarly fourth equation,
5x + 2x - 6 = 6x - 6 + x
⇒ 7x - 6 = 7x - 6
⇒ 0 = 0
It means all real numbers are the solutions.
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A 60kg student in a rowboat on a still lake decides to dive off the front of the boat. The student's horizontal acceleration is 2.0 m/s/s while in contact with the boat. What horizontal force does the student exert on the boat?
120 N toward the back of the boat
30 N toward the back of the boat
30 N toward the front of the boat
120 N toward the front of the boat
The horizontal force that the student exert on the boat is 120 N toward the front of the boat.
What is third law of Newton ?
As per the third law of Newton, the force exerted by the boat over the student is equal in magnitude to the force that the student exerted on the boat.
So, calculate the force on the student using the second law of Newton, Force = mass * acceleration.
Force on the student = 60 kg * 2.0 m/s^2 = 120 N.
=> horizontal force exerted by the student on the boat = 120 N
Answer: option d. 120 N. toward the back of the boat.
Of course it is toward the back because that is where the student jumped from..
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Use the falling object model,h = -16t2 + s. If h is ground level ands is the initial height of 140 feet above the ground, determine the time (t) in seconds it will take an object to fall to the ground. a.1.71 secondsb.2.96 secondsc.3.06 secondsd.8.75 seconds
Answer:
b
Step-by-step explanation:
when the object is on the ground then h = 0 , then
- 16t² + 140 = 0 ( subtract 140 from both sides )
- 16t² = - 140 ( divide both sides by - 16 )
t² = [tex]\frac{-140}{-16}[/tex] = 8.75 ( take square root of both sides )
t = [tex]\sqrt{8.75}[/tex] ≈ 2.96 seconds ( to the nearest tenth )
i will make you brainiest ok
Answer:
11/20
Step-by-step explanation:
4/5 - 1/4
find greatets common denominator aka 20 cuz 5 and 4 can go into 20
multiply that many tiems it goes into 20 for the numerator
you now have 16/20 - 5/20
the answer is 11/20
A triangle is shown in the image.
What is the area of the triangle represented?
A: 204 in2
B: 216 in2
C: 408 in2
D: 432 in2
Answer:
B. 216 in²
Step-by-step explanation:
You want to know the area of a triangle with a base of 36 inches and a height of 12 inches.
Area formulaThe area of a triangle is given by ...
A = 1/2bh
where b is the base of the triangle (one side), and h is the height to the opposite vertex, measured perpendicular to the base.
ApplicationThe figure shows a base of 36 inches and a height of 12 inches. Using these values in the formula, we have ...
A = 1/2(36 in)(12 in) = 216 in²
The area of the triangle is 216 in².
Answer: 216
Step-by-step explanation: I got it right sorry for the late comment
calculate the volume, in milliliters, of hbrhbr solution required to neutralize 28.0 mlml of a 0.210 mm liohlioh solution . express your answer using three significant figures.
The volume, in milliliters, of hbrhbr solution required to neutralize 28.0 mlml of a 0.210 mm liohlioh solution is 1.176 ml.
Volume is a degree of the quantity of area that be counted occupies. Matter is described as a bodily substance that occupies area and has a mass. In bodily sciences like chemistry, the usual unit of extent is cubic metres (m3). From this, different gadgets are derived inclusive of litre (L) and millilitre (mL).
A correct region to begin is the balanced chemical equation for this neutralization: 2 H Br + Ba (OH)2 → Ba Br2 + 2 H2O The crucial aspect right here is that it takes moles of H Br to neutralize one mole of Ba(OH)2 . The variety of moles of Ba(OH)2 is 0.28x 0.210 =0.0588 moles. Thus 2 x .0.0588 = 1.176 moles of H Br are wished. The extent, V, of H Br answer wished may be computed from V) = 1.176 L.
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The numerator of a fraction is 5 less than its denominator. If 1 is added to the numerator and to the denominator, the new fraction is [tex]\frac{2}{3\\}[/tex] Find the fraction.
The fraction in the question is 9 / 14
FractionsFractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
To solve this problem, we have to write an algebraic equation and solve for the unknown.
Assuming x represents the unknown value
Original fraction = x - 5 / x
When 1 is added to both numerator and denominator;
x - 5 + 1 / x + 1 = 2/3
x - 4 / x + 1 = 2/3
Cross multiplying both sides
2(x + 1) = 3(x - 4)
2x + 2 = 3x - 12
Collect like terms and solve for x
2 + 12 = 3x - 2x
x = 14
The fraction is 14 - 5 / 14 = 9 /14
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what is 32.7 + 21.63
Answer:
54.33
Step-by-step explanation:
Answer:
54.33
Step-by-step explanation:
Addition or a calculwtor can be used
1. Suppose there
are 4 people and 9 different assignments. Each person should receive one
assignment. Assignments for different people should be different. How many ways
are there to do it?
The ways to assign for different people is 126 ways
How to determine the ways of selection?From the question, we have
Total number of questions, n = 9
Numbers to people, r = 4
The number of ways of selection could be drawn is calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 9 and r = 4
Substitute the known values in the above equation
Total = 9C4
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have
Total = 9!/5!4!
Evaluate
Total = 126
Hence, the number of ways is 126
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Evaluate y = ex + 1 for the following values of x. Round to the nearest thousandth.
x = −2, y ≈ x = 1, y ≈ x = 2, y ≈
Answer:
1.135,
3.718,
and 8.389
Step-by-step explanation:
Answer:
[tex]x=-2,\;y\approx\boxed{1.135}[/tex]
[tex]x=1,\;y\approx\boxed{3.178}[/tex]
[tex]x=2,\;y\approx\boxed{8.389}[/tex]
Step-by-step explanation:
Euler's number, denoted as the letter "e", is a mathematical constant approximately equal to 2.7182818 ( 7 d.p.).
To evaluate [tex]y=e^x+1[/tex] for the given values of x, substitute the value of x into the equation and evaluate using a calculator, rounding the final answer to 3 decimal places (nearest thousandth).
[tex]\begin{aligned}x = -2\implies y&=e^{-2}+1\\y&=0.135335...+1\\y&=1.135335...\\y&=1.135\end{aligned}[/tex]
[tex]\begin{aligned}x =1\implies y&=e^1+1\\y&=2.7182818...+1\\y&=3.7182818...\\y&=3.718\end{aligned}[/tex]
[tex]\begin{aligned}x = 2\implies y&=e^{2}+1\\y&=7.389056...+1\\y&=8.389056...\\y&=8.389\end{aligned}[/tex]
Nikola likes to play horseshoes, where players try to score a ringer by throwing a horseshoe so it lands around a post. A player gets 2 attempts each round. Let R represent the number of ringers that Nikola scores in a round. Here's the probability distribution of R along with summary statistics. R=# of ringers 0 1 2 P(R) 0.75 0.20 0.05 Mean: HR=0.3 Standard deviation: OR 0.56 Nikola gets 3 points for each ringer that he scores. Let X represent the number of points that Nikola gets from ringers in a round. What are the mean and standard deviation of X?
The mean and standard deviation of X are 0.9 and 1.68 points.
Since Nikola gets 3 points for each ringer which he scores, then total points he gets from ringers could be determined by multiplying the number of ringers by 3.
So, X = R * 3 = 3R
Where:
R = numbers of ringers
X = total points Nikola gets from ringers
Given:
Mean : μR = 0.3
Standard deviation : σR = 0.56
Thus, multiplying by 3 will effects the mean as follows:
μX = 3 (μR)
= 3 (0.3)
= 0.9
And, multiplying by 3 also will effects the standard deviation as follows:
σX = 3 (σR)
≈ 3 (0.56)
≈ 1.68
Hence, the mean of X is 0.9 and and the standard deviation of X is 1.68.
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 patrick takes a textbook to a pawnshop to borrow some money and is given $30.00. Patrick must pay back the $30.00 in addition to a $12.50 fee in 6 months.
What simple interest rate is he being charged?
Answer:
here,
simple interest (S)=12.50$
Principal(p)=30.00$
time(t)=0.5 year
Now,
S=PTR/100
or,12.50=30×0.5×R/100
or,1250=15R
or,1250/15=R
:.R=83.33% per annum
G(X)=-3x+2 find g(2)
Answer:
-4
Step-by-step explanation:
[tex]-3*2 + 2=-4[/tex]
Tammy and Luke take part in a game in which they earn the same number of points for each catch and lose the same number of points for each miss. Tammy makes 5 catches and misses 1, ending the game with 23 points. Luke earns 8 catches and has 5 misses. Luke ends the game with 30 points.
Write a system of equations that describes Tammy and Luke's outcomes. Use x to represent the number of points for a catch and y to represent the number of points for a miss.
The system of equation to describe Tammy and Luke's outcome is as follows:
5x + y = 23
8x + 5y = 30
How to use system of equation to represent the outcome?Tammy and Luke take part in a game in which they earn the same number of points for each catch and lose the same number of points for each miss.
let
x = number of points for a catch
y = the number of points for a miss.
Tammy makes 5 catches and misses 1, ending the game with 23 points.
Therefore,
5x + y = 23
Luke earns 8 catches and has 5 misses. Luke ends the game with 30 points. Therefore,
8x + 5y = 30
Hence, the combine equation to describe the outcome is as follows:
5x + y = 23
8x + 5y = 30
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Construct a geometric mean between a and c.
Geometric mean will be a line segment with length x such that x² = a × c.
What is Geometric Mean?Geometric mean of two line segments p and q is a line x such that it satisfies the formula x² = a × b or x/a = b/x.
To construct geometric mean, first simply draw a line segment and mark a point P anywhere on this line.
Mark the length of the line segment 'a' from the point P and mark the endpoint of 'a' as A. Now, in the same line, from the point P, mark the length of the given line 'c' and mark its endpoint as C.
Now, draw a perpendicular bisector of the resulting line PC. Then we get the midpoint of PC. Let this point be O.
Draw a semicircle with center O and the endpoints P and C.
Now draw a vertical perpendicular line from the point A until it cuts the semicircle. Let N be the point where this line touches the semicircle.
Now join P with N.
The line PN will be the geometric mean x such that a × c = x².
Hence the line segment PN is the geometric mean with length x.
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a planes average speed was 340 miles per hour how long did it take the plane to travel 1190 miles
Given average speed=340 miles per hour
speed= distance/time (formula)
speed= 340/60
speed=5.6 miles/min
now,we have to calculate time,
time=distance/speed
time=1190/5.6
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Time to think about your New Year's Resolution for the new year. Nora decided she needed more
exercise. She decided that starting with the first full week in 2023, she will do a 45-minute workout
four times a week ( four days during every seven-day week.) This means she will exercise four of the
days during the week of Jan, 1 through Jan. 7 and will do the same during the week from Jan. 8
through Jan. 14, etc. If Nora sticks to her resolution, what is the first possible date on which she will
complete 25 hours of exercise for the year?
The first possible date on which she will complete 25 hours of exercise for the year is on March 1.
How to calculate date?In general, dates can refer to a specific day on the calendar, such as January 1 or December 31. Dates can also refer to a specific point in time, such as a specific hour, minute, or second. In some cases, dates can also refer to a specific period of time, such as a year, month, or week.
Since Nora plans to do a 45-minute workout four times a week,
she will exercise for a total of 4 * 45 minutes = 180 minutes per week.
This means that each week, she will exercise for a total of 180 / 60 = 3 hours.
To complete 25 hours of exercise for the year,
Nora will need to exercise for a total of 25 / 3 = 8.3 weeks.
The first possible date on which she will complete 25 hours of exercise is therefore 8.3 weeks after Jan 1,
Which is approximately 8.3 * 7 = 58 days after Jan 1.
Therefore, the first possible date on which Nora will complete 25 hours of exercise is 58 days after Jan 1, which is on March 1.
Overall, if Nora sticks to her New Year's resolution to exercise four times a week, the first possible date on which she will complete 25 hours of exercise for the year is on March 1.
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classify the following random variable according to whether it is discrete or continuous. the number of goals scored in a hockey game
The number of goals scored in a hockey game is a discrete random variable.
A discrete random variable has a countable number of different possible values, such as 0,1,2,3,4, etc. Usually, but not always, discrete random variables are counted. If a random variable has a limited range of possible values, it is discrete.
The number of children in a household, the Friday night movie attendance, the number of patients at a doctor's office, and the number of faulty light bulbs in a box of ten are a few examples of discrete random variables. A discrete random variable's probability distribution is a table of the probabilities connected to each of its potential values.
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