Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis. (Round your answer to three decimal places.)
Answers
Answer:
1.066 (3 d.p.)
Step-by-step explanation:
The volume of the solid formed by revolving a region, R, around a vertical axis, bounded by x = a and x = b, is given by:
[tex]\displaystyle 2\pi \int^b_ar(x)h(x)\;\text{d}x[/tex]
where:
r(x) is the distance from the axis of rotation to x.h(x) is the height of the solid at x (the height of the shell).[tex]\hrulefill[/tex]
We want to find the volume of the solid formed by revolving a region, R, around the y-axis, where R is bounded by:
[tex]y=\dfrac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{3}}[/tex]
[tex]y=0[/tex]
[tex]x=0[/tex]
[tex]x=1[/tex]
As the axis of rotation is the y-axis, r(x) = x.
Therefore, in this case:
[tex]r(x)=x[/tex]
[tex]h(x)=\dfrac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{3}}[/tex]
[tex]a=0[/tex]
[tex]b=1[/tex]
Set up the integral:
[tex]\displaystyle 2\pi \int^{1}_0x \cdot\dfrac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{3}}\;\text{d}x[/tex]
Take out the constant:
[tex]\displaystyle 2\pi \cdot \dfrac{1}{\sqrt{2\pi}}\int^{1}_0x \cdot e^{-\frac{x^2}{3}}\;\text{d}x[/tex]
[tex]\displaystyle \sqrt{2\pi}\int^{1}_0x \cdot e^{-\frac{x^2}{3}}\;\text{d}x[/tex]
Integrate using the method of substitution.
[tex]\textsf{Let}\;u=-\dfrac{x^2}{3}\implies \dfrac{\text{d}u}{\text{d}x}=-\dfrac{2x}{3}\implies \text{d}x=-\dfrac{3}{2x}\;\text{d}u[/tex]
[tex]\textsf{When}\;x=0 \implies u=0[/tex]
[tex]\textsf{When}\;x=1 \implies u=-\dfrac{1}{3}[/tex]
Rewrite the original integral in terms of u and du:
[tex]\displaystyle \sqrt{2\pi}\int^{-\frac{1}{3}}_0x \cdot e^{u}\cdot -\dfrac{3}{2x}\;\text{d}u[/tex]
[tex]\displaystyle \sqrt{2\pi}\int^{-\frac{1}{3}}_0 -\dfrac{3}{2}e^{u}\; \text{d}u[/tex]
[tex]-\dfrac{3\sqrt{2\pi}}{2}\displaystyle \int^{-\frac{1}{3}}_0 e^{u}\; \text{d}u[/tex]
Evaluate:
[tex]\begin{aligned}-\dfrac{3\sqrt{2\pi}}{2}\displaystyle \int^{-\frac{1}{3}}_0 e^{u}\; \text{d}u&=-\dfrac{3\sqrt{2\pi}}{2}\left[ \vphantom{\dfrac12}e^u\right]^{-\frac{1}{3}}_0\\\\&=-\dfrac{3\sqrt{2\pi}}{2}\left[ \vphantom{\dfrac12}e^{-\frac{1}{3}}-e^0\right]\\\\&=-\dfrac{3\sqrt{2\pi}}{2}\left[ \vphantom{\dfrac12}e^{-\frac{1}{3}}-1\right]\\\\&=1.06582594...\\\\&=1.066\; \sf (3\;d.p.)\end{aligned}[/tex]
Therefore, the volume of the solid is approximately 1.066 (3 d.p.).
[tex]\hrulefill[/tex]
[tex]\boxed{\begin{minipage}{3 cm}\underline{Integrating $e^x$}\\\\$\displaystyle \int e^x\:\text{d}x=e^x(+\;\text{C})$\end{minipage}}[/tex]
Related Questions
(b) a dy integral that represents the surface area of the solid formed when c is rotated about the (x or y)-axis
Answers
The surface area of the surface generated by rotating the curve y = x² about the y-axis, and we found that the surface area is approximately 54.33 square units.
In this case, the curve we want to rotate is y = x², and we want to rotate it about the y-axis. To use the formula above, we need to express the equation of the curve in terms of x. Therefore, we need to rewrite y = x² as x = √y.
Next, we need to find the derivative of x = √y with respect to y, which is:
dx/dy = 1/2√y
Substituting this into the formula for the surface area, we get:
Surface Area = 2π ∫[0,4] √y √(1+(1/2√y)²) dy
Simplifying the expression inside the square root, we get:
Surface Area = 2π ∫[0,4] √(y+(1/4)) dy
We can evaluate this integral using the power rule of integration, which gives:
Surface Area = 2π [2/3(y+(1/4))^(3/2)]₀⁴
Simplifying further, we get:
Surface Area = 2π [2/3(17/4)^(3/2)]
Surface Area ≈ 54.33 square units
Therefore, the surface area of the surface generated by rotating the curve y = x² about the y-axis is approximately 54.33 square units.
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Complete Question:
How do you find the area of the surface generated by rotating the curve about the y-axis y = x^2 , 0 ≤ x ≤ 2 ?
find the two numbers whose ratio is 3:7 and their difference is 20
Answers
Answer:
the two numbers are 15 and 35, and their ratio is 3:7, and their difference is 20.
Step-by-step explanation:
A shop is having a 40% sale. A jumper originally costs £50. How much will it be in sale?
Answers
Answer:
30 pounds
Step-by-step explanation:
Since the jumper costs 50 pounds, the decimal for the number will be:
50.
To find ten percent of the number, you move the decimal one time to the LEFT.
Therefore, 10% of 50 pounds will be 5 pounds. To find 40%, we simply will multiply the 10% amount by 4.
40% of 50 will be:
20
Therefore, the jumper will have 20 pounds off.
Since the original cost is 50 pounds, we simply will just subtract 50 - 20:
50 - 20 = 30
The jumper will cost 30 pounds with the sale deal.
6x+16=8x-18 i need x
Answers
Answer:
x = 17
Step-by-step explanation:
Subtract 6x from both sides:
2x - 18 = 16
Add 18 on both sides to isolate the variable:
2x = 18 + 16
2x = 34
Divide by 2: x = 17
A normal distribution is informally described as a probability distribution that is "bell-shaped" when graphed. Draw a rough sketch of a curve having the bell shape that is characteristic of a normal distribution.
Choose the correct answer below.
A.
A symmetric curve is plotted over a horizontal scale. From left to right, the curve starts on the horizontal scale and rises at a decreasing rate to a central peak before falling at an increasing rate to the horizontal scale.
B.
A symmetric curve is plotted over a horizontal scale. From left to right, the curve starts above the horizontal scale, falls from the horizontal at an increasing rate, then falls at a decreasing rate to a central minimum before rising at an increasing rate, then rising at a decreasing rate, and finally becoming nearly horizontal.
C.
A symmetric curve is plotted over a horizontal scale. From left to right, the curve starts on the horizontal scale, rises from horizontal at an increasing rate, then rises at a decreasing rate to a central peak before falling at an increasing rate, then falling at a decreasing rate, and finally approaches the horizontal scale.
Answers
The correct answer is C. A normal distribution is a symmetric probability distribution that is bell-shaped when graphed. When plotted on a horizontal scale, the curve starts on the horizontal axis, rises to a central peak, and then falls back to the horizontal axis.
The curve is symmetric, meaning that the left and right halves of the curve are mirror images of each other. The curve approaches the horizontal axis but never touches it, which indicates that there is a non-zero probability of observing values at any distance from the mean, although the probability decreases as the distance from the mean increases.
Normal distribution is a type of probability distribution that is commonly found in natural and social phenomena, where the majority of the observations tend to cluster around the mean, with fewer observations further away from the mean.
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93. Electricity Usage The graph shows
the daily megawatts of electricity used
on a record-breaking summer day in
Sacramento, California.
(a) Is this the graph of a function?
(b) What is the domain?
(c) Estimate the number of megawatts
used at 8 A.M.
(d) At what time was the most electric-
ity used? the least electricity?
(e) Call this function f. What is f(12)?
Interpret this answer.
(f) During what time intervals is usage
increasing? decreasing?
Answers
Sacramento, California's electricity demand on a scorching summer day is depicted in a function graph. The domain is 24 hours of a day.
The site is available around-the-clock.
One thousand two hundred megawatts are consumed at eight in the morning.
The hours between 4:00 and 6:00 pm saw the highest electricity use, while 4:00 am saw the lowest use.
It would be 1,900 megawatts for f (12).
From 4 am to 5 pm, usage rises, and from 5 pm to 4 am, it falls.
What is displayed by the graph?Because each point on the graph reflects a different megawatt usage, the graph is a function. As this graph of electricity usage illustrates, the domain would be available throughout the entire day.
At 8 a.m., these megawatts are used:
= 1, 300 - ( 200 / 2 )
equal to 1,200 megawatts
As people get ready for work and leave for work, we can observe an increase in power demand from 4 am to 5 pm, but a reduction from 5 pm to 4 am.
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For the graph, find the average rate of change on the intervals given
See attached picture
Answers
The average rate of change on the intervals [0, 3], [3, 5], [5, 7], and [7, 9] are 2, -1.5, 1, and -1.5, respectively.
What is the average rate in math?It expresses how much the function changed per unit on average during that time period. It is computed by taking the slope of the straight line connecting the interval's endpoints on the function's graph.
To calculate the average rate of change for the intervals shown in the graph, we must first determine the slope of the line connecting the endpoints of each interval.
0-3 interval:
Because the interval's endpoints are (0, 1) and (3, 7), the slope of the line connecting them is:
slope = (y change) / (x change) = (7 - 1) / (3 - 0) = 2
pauses [3, 5]:
Because the interval's endpoints are (3, 7) and (5, 4), the slope of the line connecting them is:
slope = (y change) / (x change) = (4 - 7) / (5 - 3) = -1.5
[5–7] Interval:
Because the interval's endpoints are (5, 4) and (7, 6), the slope of the line connecting them is:
slope = (y change) / (x change) = (6 - 4) / (7 - 5) = 1
Interval 7 and 9:
Because the interval's endpoints are (7, 6) and (9, 3), the slope of the line connecting them is:
slope = (y change) / (x change) = (3 - 6) / (9 - 7) = -1.5
As a result, the average rate of change on the intervals [0, 3], [3, 5], [5, 7], and [7, 9] is 2, -1.5, 1, and -1.5.
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According to a poll, about % of adults in a country bet on professional sports. Data indicates that % of the adult population in this country is male. Complete parts (a) through (e).
(b) Assuming that betting is independent of gender, compute the probability that an adult from this country selected at random is a male and bets on professional sports.
P(male and bets on professional sports)
0.0568
(c) Using the result in part (b), compute the probability that an adult from this country selected at random is male or bets on professional sports.
P(male or bets on professional sports)
0.5362
(d) The poll data indicated that 7.3% of adults in this country are males and bet on professional sports. What does this indicate about the assumption in part (b)?
A.
The assumption was incorrect and the events are not independent.
Part 5
(e) How will the information in part (d) affect the probability you computed in part (c)? Select the correct choice below and fill in any answer boxes within your choice.
A.
P(males or bets on professional sports) = ?
Answers
a) D. No. A person can be both male and bet on professional sports at the same time
How to solveb) If the events A and B are independent, P(A&B) = P(A) x P(B)
P(male and also bets on professional sports) = 0.484x0.13 = 0.0629
c) P(male or bets in professional sports) = P(male) + P(bets in professional sports) - P(male and also bets on professional sports)
= 0.484 + 0.13 - 0.0629
= 0.5511
d) A. The assumption was incorrect and the events are not independent
(if the were independent, the percentage would have been 6.29)
e) A. P(male or bets on professional sports = 0.484 + 0.13 - 0.081
= 0.5330
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Find x, if √x +2y^2 = 15 and √4x - 4y^2=6
pls help very soon
Answers
Answer:
We have two equations:
√x +2y^2 = 15 ----(1)
√4x - 4y^2=6 ----(2)
Let's solve for x:
From (1), we have:
√x = 15 - 2y^2
Squaring both sides, we get:
x = (15 - 2y^2)^2
Expanding, we get:
x = 225 - 60y^2 + 4y^4
From (2), we have:
√4x = 6 + 4y^2
Squaring both sides, we get:
4x = (6 + 4y^2)^2
Expanding, we get:
4x = 36 + 48y^2 + 16y^4
Substituting the expression for x from equation (1), we get:
4(225 - 60y^2 + 4y^4) = 36 + 48y^2 + 16y^4
Simplifying, we get:
900 - 240y^2 + 16y^4 = 9 + 12y^2 + 4y^4
Rearranging, we get:
12y^2 - 12y^4 = 891
Dividing both sides by 12y^2, we get:
1 - y^2 = 74.25/(y^2)
Multiplying both sides by y^2, we get:
y^2 - y^4 = 74.25
Let z = y^2. Substituting, we get:
z - z^2 = 74.25
Rearranging, we get:
z^2 - z + 74.25 = 0
Using the quadratic formula, we get:
z = (1 ± √(1 - 4(1)(74.25))) / 2
z = (1 ± √(-295)) / 2
Since the square root of a negative number is not real, there are no real solutions for z, which means there are no real solutions for y and x.
Therefore, the answer is "no solution".
A pond in the shape of a right-angled triangle is shown below. Calculate the perimeter of the pond. Give your answer in metres to 1 d.p. 1.46 m 100 73°
Answers
The perimeter of the pond is 2.92 meters.
What s a right-angle triangle:
A right-angled triangle is a triangle in which one of the angles measures exactly 90 degrees, also known as a right angle.
The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs.
The perimeter of a right-angled triangle is the sum of the lengths of its three sides.
Here we have
The Hypotenuse of the triangle is 1.46 m
The angle between hypotenuse and perpendicular height = 73°
From triagonometric ratios,
=> cos A = Perpendicular height/ Hypotenuse.
=> cos (73) = Perpendicular height/1.46
=> Perpendicular height = 1.46 × 0.29 = 0.42 m
As we know from Pythagoras' theorem,
Hypotenuse² = side² + side²
Side = √Hypotenuse² - side²
= √[(1.46)²- (0.42)²] = 1.04
Therefore, the sides of the pond are 1.46 m, 0.42 m, and 1.04
Hence, perimeter of the pond = 1.46 + 0.42 + 1.04 = 2.92 meters
Therefore,
The perimeter of the pond is 2.92 meters.
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The complete Question is given below
How this app works? Why I can’t find any answers? I need pay for points when I ask questions? I subscribe this app and when I’m lucky to the answers almost the answers are wrong
Answers
Prove the following using a direct proof:
The sum of the squares of 4 consecutive integers is an even integer
Answers
It ahs been proved by mathematical induction that the sum of the squares of 4 consecutive integers is an even integer.
How to solve Mathematical Induction?To prove that the sum of the squares of 4 consecutive integers is an even integer.
Let x, (x + 1), (x + 2), (x + 3) be the four consecutive integers.
The sum of the squares of these integers are:
S = x² + (x + 1)² + (x + 2)² + (x + 3)²
Expanding this gives us:
S = 4x² + 12x + 14
Simplifying this gives:
S = 2(2x² + 6x + 7)
The number 2x² + 6x + 7 is either even number or odd number.
However, since it is multiplied by 2x² + 6x + 7, the sum will always be an even number.
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The figure below displays the SAT scores of three students, but each chart looks different. The two charts have the same data, but the difference seems larger for the graph on the left. Why?
Answers
Answering the presented question, we may conclude that This greater expressions scale makes it easier to see the variations between the ratings of the three college students in a extra correct and informative way.
what is expression ?In mathematics, an expression is a collection of integers, variables, and complex mathematical (such as arithmetic, subtraction, multiplication, division, multiplications, and so on) that describes a quantity or value. Phrases can be simple, such as "3 + 4," or complicated, such as They may also contain functions like "sin(x)" or "log(y)". Expressions can be evaluated by swapping the variables with their values and performing the arithmetic operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.
The difference in look between the two charts is due to the choice of the scales on the x and y-axes. In the left chart, the y-axis starts offevolved at 800 and has a range of only 200 points, whilst the x-axis starts offevolved at 1300 and has a vary of 200 points. This compressed scale makes the variations between the ratings of the three students appear larger than they absolutely are.
On the other hand, the proper chart has a y-axis that starts at zero and has a vary of 800 points, whilst the x-axis begins at 1200 and has a range of 800 points. This greater expanded scale makes it easier to see the variations between the ratings of the three college students in a extra correct and informative way.
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3. Each sample of water from a river has a 10% chance of contamination by a particular heavy metal. Find the probability that in 18 independent samples taken from the same river, only two samples were contaminated. [3 marks]
Answers
The probability that, out of 18 independent samples received from one river, just two were contaminated is 0.8438.
Explain about the independent samples?Randomly chosen samples are known as independent samples since their results are independent of other observations' values. The premise that sampling are independent underlies many statistical analysis.When each trial possesses the same probability of achieving a given value, the number of trials or observations is represented using the binomial distribution.In the following 18 samples to be evaluated,
Let X = the number of samples that now the pollutant is present in.
Thus, with p = 0.10 and n = 18, X is a binomial random variable.
Using the binomial theorem:
[tex](^{n} _{r} ) p^{x} q^{n-x}[/tex]
p = 0.10
q = 1 - 0.10 = 0.9
n = 18
The likelihood that only two samples out of 18 obtained in different ways from the same river were polluted
P(x = 2) = [tex](^{18} _{2} ) (0.1)^{2} (0.9)^{18-2}[/tex]
= [tex](^{18} _{2} ) (0.1)^{2} (0.9)^{16}[/tex]
= 153 x 0.01 x 0.1853
= 0.8438
Thus, the probability that, out of 18 separate samples received from one river, just two were contaminated is 0.8438.
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in a batch of 10,000 clock radios 500 are defective. A sample of 10 clock radios is randomly selected without replacement from the 10,000 and tested. The entire batch will be rejected if at least one of those tested is defective. what is the probability that the entire batch will be rejected?
Answers
Answer:
Step-by-step explanation:
This is an example of a hypergeometric distribution problem, where we have a population of 10,000 clock radios with 500 defective ones, and we want to calculate the probability of getting at least one defective radio in a random sample of 10 without replacement.
The probability of getting no defective radios in the sample is:
(9500/10000) * (9499/9999) * (9498/9998) * ... * (9491/9992)
This is because, for the first radio, there are 9500 good radios out of 10,000, and for the second radio, there are 9499 good radios out of 9,999, and so on.
The probability of getting at least one defective radio in the sample is then:
1 - (9500/10000) * (9499/9999) * (9498/9998) * ... * (9491/9992)
which is approximately equal to 0.401.
Therefore, the probability that the entire batch will be rejected is 0.401.
The roots of a quadratic equation a x +b x +c =0 are (2+i √2)/3 and (2−i √2)/3 . Find the values of b and c if a = −1.
Answers
[tex]\begin{cases} x=\frac{2+i\sqrt{2}}{3}\implies 3x=2+i\sqrt{2}\implies 3x-2-i\sqrt{2}=0\\\\ x=\frac{2-i\sqrt{2}}{3}\implies 3x=2-i\sqrt{2}\implies 3x-2+i\sqrt{2}=0 \end{cases} \\\\\\ \stackrel{ \textit{original polynomial} }{a(3x-2-i\sqrt{2})(3x-2+i\sqrt{2})=\stackrel{ 0 }{y}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{ \textit{difference of squares} }{[(3x-2)-(i\sqrt{2})][(3x-2)+(i\sqrt{2})]}\implies (3x-2)^2-(i\sqrt{2})^2 \\\\\\ (9x^2-12x+4)-(2i^2)\implies 9x^2-12x+4-(2(-1)) \\\\\\ 9x^2-12x+4+2\implies 9x^2-12x+6 \\\\[-0.35em] ~\dotfill\\\\ a(9x^2-12x+6)=y\hspace{5em}\stackrel{\textit{now let's make}}{a=-\frac{1}{9}} \\\\\\ -\cfrac{1}{9}(9x^2-12x+6)=y\implies \boxed{-x^2+\cfrac{4}{3}x-\cfrac{2}{3}=y}[/tex]
Jonathan says that the function represented by the graph is always decreasing. Is he correct? fI not, where is the function decreasing?
Explain your reasoning.
Answers
If the slope of the graph is increasing from positive x-axis to negative x-axis, then the function is not that decreasing. Therefore, Jonathan's statement is incorrect.
What is the graph function about?The function is decreasing on intervals where the slope is negative. In this case, since the slope is increasing from positive x-axis to negative x-axis, the function is decreasing on the interval where x is negative.
To determine this interval more precisely, we would need to find the x-value(s) where the slope changes sign from positive to negative. These x-values correspond to critical points, such as local maximums or minimums. The function is decreasing before a local maximum and after a local minimum.
Therefore, Jonathan's statement is not correct, and the function represented by the graph is decreasing on the interval where x is negative.
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Zoe was comparing the variability of three of her stocks. Over the last month ACE stock had a mean price of $37.03 per share with a standard deviation of $1.5, while FHJ stock had a mean price of $60.55 per share with a standard deviation of $2.62, and LMP stock had a mean price of $124.9 per share with a standard deviation of $3.06. Out of these three stocks, what was the greatest coefficient of variation?
Round your answer to a hundredth of a percent. Input just the number. Do not input the percent sign. Do not use a comma. Example 4.35
Answers
In respοnse tο the questiοn, we may say that As a result, FHJ stοck has equatiοn highest cοefficient οf variatiοn, with a value οf arοund 4.33%.
What exactly is an equation?In mathematics, an equatiοn is a statement that expresses the equality οf twο expressiοns. Equatiοn is made up οf twο sides that are jοined by the algebraic symbοl (=). Fοr example, in this argument, it is asserted that "2x + 3 = 9" denοtes that "2x plus 3" equals the number "9".
Equatiοn sοlving is the prοcess οf determining the value(s) οf the variable(s) required fοr the equatiοn tο be true. There are many different kinds οf equatiοns, such as regular and nοnlinear οnes with οne οr mοre elements. This fοrmula raises the variable x tο the secοnd pοwer: "x² + 2x - 3 = 0." Lines are used in the study οf mathematics in the fields οf algebra, calculus, and geοmetry.
The cοefficient οf variatiοn (CV) represents the standard deviatiοn as a percentage οf the mean and is a relative measure οf variability. It is cοmputed as fοllοws:
CV = (standard deviatiοn / mean) multiplied by 100%
Tο determine which οf the three stοcks has the highest cοefficient οf variatiοn, we must cοmpute the CV fοr each and cοmpare the results.
Fοr ACE inventοry:
CV = (1.5 / 37.03) x 100% ≈ 4.05%
In the case οf FHJ stοck:
CV = (2.62 / 60.55) x 100% ≈ 4.33%
In the case οf LMP stοck:
CV = (3.06 / 124.9) x 100% ≈ 2.45%
As a result, FHJ stοck has the highest cοefficient οf variatiοn, with a value οf arοund 4.33%.
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Which of the following random variables can be approximated to discrete distribution and continuous distribution? a. b. C. d. The wages of academician and non-academician workers in UPSI. The time taken to submit online quiz answer's document. The prices of SAMSUM mobile phones displayed at a phone shop The number of pumps at Shell petrol stations in Perak. [2 marks] 10% chance of contamination by a particular
Answers
10% chance of contamination by a particular: It's not clear what random variable is being referred to here, but if it's the probability of contamination.
What is Distribution?In general terms, a distribution refers to the way something is divided or spread out. In the context of statistics and probability theory, a distribution is a mathematical function that describes the likelihood of different possible outcomes or values that a variable can take.
There are various types of distributions, but some of the most commonly used ones include:
Normal distribution: also known as the Gaussian distribution, it is a continuous probability distribution that is symmetrical around the mean, with most of the data falling within one standard deviation of the mean.
Binomial distribution: this is a discrete probability distribution that describes the likelihood of a certain number of successes in a fixed number of trials.
Poisson distribution: another discrete probability distribution that describes the likelihood of a certain number of events occurring in a fixed interval of time or space.
Exponential distribution: a continuous probability distribution that describes the time between events occurring at a constant rate.
Distributions are essential in statistical analysis as they can help to understand and analyze data, make predictions, and draw conclusions about a population based on a sample of data.
Given by the question.
a. The wages of academician and non-academician workers in UPSI: This random variable can be approximated to a continuous distribution as wages can take on any numerical value within a range. However, it's worth noting that in practice, there may be discrete intervals or categories of wages, in which case a discrete distribution may be more appropriate.
b. The time taken to submit online quiz answer's document: This random variable can also be approximated to a continuous distribution as it can take on any numerical value within a range.
c. The prices of SAMSUNG mobile phones displayed at a phone shop: This random variable can be approximated to a continuous distribution as prices can take on any numerical value within a range.
d. The number of pumps at Shell petrol stations in Perak: This random variable can be approximated to a discrete distribution since the number of pumps can only take on integer values.
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If A = [ 1 2 4 0 5 6 ] and B= [ 7 3 2 5 1 9] find C= A+B and D=A-B
Answers
Step 1: Arrange the arrays so that A and B are in the same order: A = [ 1 2 4 0 5 6 ], B = [ 7 3 2 5 1 9]
Step 2: To find C = A+B, add each element of A and B together.
C = [1+7, 2+3, 4+2, 0+5, 5+1, 6+9]
C = [8, 5, 6, 5, 6, 15]
Step 3: To find D = A-B, subtract each element of B from A.
D = [1-7, 2-3, 4-2, 0-5, 5-1, 6-9]
D = [-6, -1, 2, -5, 4, -3]
Use the equation f=d–5 to find the value of f when d=7.
Answers
Therefore answer is 2
Answer:
2
Step-by-step explanation:
since d=7 and the equation is d-5 in the place of d we'll put 7 therefore 7-5=2
Uri paid a landscaping company to mow his lawn. The company charged $74 for the service plus
5% tax. After tax, Uri also included a 10% tip with his payment. How much did he pay in all?
Answers
Uri paid a total of $85.47 for the landscaping service including tax and tip.
What is tax?Taxes are compulsory payments made by a government organisation, whether local, regional, or federal, to people or businesses. Tax revenues are used to fund a variety of government initiatives, such as Social Security and Medicare as well as public infrastructure and services like roads and schools. Taxes are borne by whoever bears the cost of the tax in economics, whether this is the entity being taxed, such as a business, or the final users of the items produced by the firm. Taxes should be taken into consideration from an accounting standpoint, including payroll taxes, federal and state income taxes, and sales taxes.
Given that company charged $74 for the service plus 5% tax.
The tax is 5%, that is:
Tax = 5% of $74 = 0.05 x $74 = $3.70
Cost after tax = $74 + $3.70 = $77.70
Now, tip is 10%:
Tip = 10% of $77.70 = 0.10 x $77.70 = $7.77
Total cost = $77.70 + $7.77 = $85.47
Hence, Uri paid a total of $85.47 for the landscaping service including tax and tip.
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7. Jada walks up to a tank of water that can hold up to 10 gallons. When it is active, a
drain empties water from the tank at a constant rate. When Jada first sees the tank, it
contains 7 gallons of water. Three minutes later, the tank contains 5 gallons of water.
a. At what rate is the amount of water in the tank changing? Use a signed number, and
include the unit of measurement in your answer.
b. How many more minutes will it take for the tank to drain completely? Explain or
show your reasoning.
c. How many minutes before Jada arrived was the water tank completely full? Explain
or show your reasoning.
Answers
In the word problem,
a)Gallons per minute change is -2/3 gallons per minute
b) 7.5 minutes to drain the other 5 gallons
c)The tank was full 4 1/2 minutes before Jada arrived.
What is word problem?
Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.
a) Gallons per minute change is -2/3 gallons per minute since it decreases by 2 gallons in 3 minutes.
b) we have 5 gallons and lose 2/3 gallons per minute
=> (2/3 gal/minute)(x minutes) = 5 gallons
=> x = 5(3/2) = 15/2 = 7.5 minutes to drain the other 5 gallons
c) There was 10 gallons when the tank is full . That is 3 gallons more than the 7 gals there when Jada arrived.
=> (2/3)(x) = 3
=> x = 3(3/2) = 9/2 = 4 1/2 minutes
The tank was full 4 1/2 minutes before Jada arrived.
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the annual rainfall in 2017 in opuwo was 420mm.
the annual rainfall in 2018 was 12% more than in 2017.
Answers
Answer:
470.4 mm
Step-by-step explanation:
Given: the annual rainfall in 2017 in opuwo was 420 mm, the annual rainfall in 2018 was 12% more than in 2017.
First, find 12% of 420 mm:
12% of 420 mm
[tex]\frac{12}{100}[/tex] x 420 mm
1.2 x 420 mm
= 50.4 mm
Then add 50.4 mm to the previous annual rainfall of 420 mm:
50.4 mm + 420 mm
= 470.4 mm
Therefore, the annual rainfall in opuwo in 2018 is 470.4 mm.
The Ford F-150 is the best selling truck in the United States.
The average gas tank for this vehicle is 23 gallons. On a long
highway trip, gas is used at a rate of about 3.2 gallons per hour.
The gallons of gas g in the vehicle's tank can be modeled by the
equation g(t)=23 -3.2t where t is the time (in hours).
a) Identify the domain and range of the function. Then graph
the function.
b) At the end of the trip there are 6.4 gallons left. How long
was the trip?
Answers
a) The domain and the range of the function are given as follows:
Domain: [0, 7.1875].Range: [0,23].The graph of the function is given by the image presented at the end of the answer.
b) The trip was 5.1875 hours long.
What are the domain and the range of a function?The function for this problem is defined as follows:
g(t) = 23 - 3.2t.
The domain is the set of input values that can be assumed by the function. The time cannot have negative measures, hence the lower bound of the domain is of zero, while the gas cannot be negative, hence the upper bound of the volume is given as follows:
23 - 3.2t = 0
3.2t = 23
t = 23/3.2
t = 7.1875 hours.
The range is given by the set of all output values assumed the function, which are the values of the gas, hence it is [0,23].
The graph is a linear function between points (0, 23) and (7.1875, 0).
At the end of the trip there were 6.4 gallons left, hence the length of the trip is given as follows:
23 - 3.2t = 6.4
t = (23 - 6.4)/3.2
t = 5.1875 hours.
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What is the probability that a 58% free-throw shooter will miss her next free throw?
Answers
21/50
Step by step explanation:
The probability that a 58% free-throw shooter will miss her next free throw is equal to 1 minus the probability that she will make it.
If she has a 58% chance of making a free throw, then she has a 42% chance of missing it.
Therefore, the probability that she will miss her next free throw is 0.42
42/100 = (42 ÷ 2) / (100 ÷ 2) = 21/50
A scuba diver was 30 feet below sea level when he ascended f feet to a depth of 16 feet below sea level to see a school of fish.
Answers
In order to see the school of fish, the scuba diver descended to a depth of 14 feet below sea level.
What dοes "depth" mean?Hοw far sοmething stretches is described by the cοncept οf depth. The pοοl has a six-fοοt depth. Unknοwn is the well's depth. We can use the fοllοwing equatiοn tο determine the scuba diver's initial depth:
Initial depth = Final depth + Depth Change The scuba diver's change in depth is positive because he rose f feet (positive because he went up) and ended up 16 feet below the surface. Therefοre:
initial depth = 16 + f - 30 initial depth.
Simplifying the phrase:
Original depth = -14 + f
The scuba diver reached his initial depth there after descended another 14 feet below sea level to observe the school of fish.
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Questions-
A scuba diver was 30 feet below sea level when he ascended f feet to a depth of 16 feet below sea level to see a school of fish. what is her new elevation now?
If a ll b, find the value of x.
Answers
Answer:
x = 18
Step-by-step explanation:
Alternate exterior angles are congruent. Set the equations equal to each other and solve for x.
7x + 11 = 10x - 43 Subtract 7 x from both sides
7x - 7x + 11 = 10x - 7x - 43
11 = 3x - 43 Add 3 to both sides
11 + 43 = 3x -43 + 43
54 = 3x Divide both sides by 3
[tex]\frac{54}{3}[/tex] = [tex]\frac{3x}{3}[/tex]
18 = x
Helping in the name of Jesus.
-3x=-32
X=32/3
can’t seem to get this any help
A. 27.4
B. 37.3
C. 40.0
D. 42.0
Answers
Answer:
Step-by-step explanation:
In the boys triangle:
[tex]tanx=\frac{56}{48}[/tex]
[tex]x=tan^{-1}(\frac{56}{48} )=49.4\textdegree[/tex]
Because triangles are similar:
[tex]tan 49.8=\frac{h}{32}[/tex]
[tex]h=32tan49.8 = 37.3[/tex]
Bokomo produced 300 Granola megapacks for the Mogoditshane market. Bokomo’s marginal cost equation is as follows: MC=2x-100. Find the cost of producing an additional 200 items due to increased demand.
Answers
The cost of producing an additional 200 items due to increased demand is 180,000 Botswana Pula.
What is marginal cost?Marginal cost is the additional cost incurred by producing one additional unit of a good or service. In other words, it is the cost of producing one more unit of output.
According to question:The marginal cost (MC) equation given is MC = 2x - 100, where x is the number of units produced.
To find the cost of producing an additional 200 items due to increased demand, we need to calculate the marginal cost of producing these 200 items and then multiply that by 200.
The marginal cost of producing 200 additional items is given by:
MC(200) = 2(300 + 200) - 100
MC(200) = 2(500) - 100
MC(200) = 900
So the marginal cost of producing 200 additional items is 900. To find the total cost of producing these 200 items, we can simply multiply the marginal cost by the number of units produced, which in this case is 200:
Total cost = MC(200) × 200
Total cost = 900 × 200
Total cost = 180,000
Therefore, the cost of producing an additional 200 items due to increased demand is 180,000 Botswana Pula.
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