find the area enclosed by the curve x = t2 − 3t, y = t and the y-axis.
Answers
The area under the curve is [tex]\frac{6 \sqrt{3}}{5}[/tex].
Consider the following parametric equations:[tex]$$x=t^2-3 t \text { and } y=\sqrt{t} \text { and the } y \text {-axis. }$$[/tex]
The objective is to find area enclosed by the curve using the formula.
The area under the curve is given by parametric equations x=f(t), y=g(t), and is traversed once as t increases from α to β, then the formula for calculating the area under the curve:
[tex]$$A=\int_\alpha^\beta g(t) f^{\prime}(t) d t$$[/tex]
The curve has intersects with y-axis. so x=0
[tex]$$\begin{aligned}t^2-3 t & =0 \\t(t-3) & =0 \\t & =0 \text { or } t=3\end{aligned}$$[/tex]
Now we have to draw the graph,
Let f(t)=[tex]t^2-3 t, g(t)=\sqrt{t}$[/tex]
Differentiate the curve f(t) with respect to t.
[tex]f^{\prime}(t)=2 t-3[/tex]
Now, find the area under the curve use the above formula.
[tex]\begin{aligned}A & =\int_0^3(\sqrt{t})(2 t-3) d t \\& =\int_0^3(2 t \sqrt{t}-3 \sqrt{t}) d t \\& =\int_0^3\left(2 t^{\frac{3}{2}}-3 t^{\frac{1}{2}}\right) d t \\& =\left[2 \frac{t^{\frac{5}{2}}}{\frac{5}{2}}-3 \frac{t^{\frac{3}{2}}}{\frac{3}{2}}\right]_0^3 \\& \left.\left.=\left[\frac{4 t^{\frac{5}{2}}}{5}-2 t^{\frac{3}{2}}\right]_0^3\right]^{\frac{5}{2}}\right] \\\\\end{aligned}$$[/tex]
[tex]& =\left[\frac{4(3)^{\frac{5}{2}}}{5}-2(3)^{\frac{3}{2}}\right]-\left[\frac{4(0)^{\frac{5}{2}}}{5}-2(0)^{\frac{3}{2}}\right][/tex]
[tex]$\begin{aligned}& =\left[\frac{4(3)^{\frac{5}{2}}}{5}-2(3)^{\frac{3}{2}}\right]-\left[\frac{4(0)^{\frac{5}{2}}}{5}-2(0)^{\frac{3}{2}}\right] \\& =\frac{4(3)^{\frac{5}{2}}}{5}-2(3)^{\frac{3}{2}}-0 \\& =\frac{6 \sqrt{3}}{5}\end{aligned}[/tex]
Therefore, the area of the curve is [tex]\frac{6 \sqrt{3}}{5}[/tex].
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Related Questions
The library ha enough DVD’ to diplay equal number of them in group of 3, 5, or 9. What i the leat number of DVD the library can have?
Answers
The library ha enough DVD’ to diplay equal number of them in group of 3, 5, or 9. then the least number of DVD the library can have is 45
What is the function of DVD?
Short for digital versatile disc or digital video disc, a DVD or DVD-ROM is a disc capable of storing a significant amount more data than a standard compact disc. DVDs are widely used for storing and viewing movies and other data.
45 is the least common multiple of 3, 5, and 9.
45 can be equally divided by 3, 5, and 9:
45 ÷ 3 = 15
45 ÷ 5 = 9
45 ÷ 9 = 5
the least number of DVD the library can have is 45
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If ST =
2v 59, RU= -v + 83, and PQ = v, what is the value of v?
Answers
Answer:
El valor de la variable b se corresponde con:
a) b = 0,25
b) b = 9
c) b = 125
6(x - 3)2(4x - 3) = 6
0x = 3
0x = -9
0x = 4
0x = 9
Answers
The two possible solutions for the given equation are -
[x] = 0.696 and [x] = 3.054.
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is the equation as follows -
6(x - 3).2(4x - 3) = 6
We have the equation as -
6(x - 3).2(4x - 3) = 6
12(x - 3)(4x - 3) = 6
(x - 3)(4x - 3) = 6/12
(x - 3)(4x - 3) = 1/2
x(4x - 3) - 3(4x - 3) = 1/2
4x² - 3x - 12x + 9 = 1/2
4x² - 15x + 9 = 1/2
2(4x² - 15x + 9) = 1
8x² - 30x + 18 = 1
8x² - 30x + 17 = 0
(x - 0.696)(x - 3.054) = 0
(x - 0.696) = 0 and (x - 3.054) = 0
x = 0.696 and x = 3.054
Therefore, the two possible solutions for the given equation are -
[x] = 0.696 and [x] = 3.054.
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Sam tested every 50th candy bar from the assembly line to make sure there were enough peanuts in each bar. He found 15% did not have enough peanuts. How many candy bars do not have enough peanuts if the factory produces 20,000 candy bars?.
Answers
Here every 50th candy bar is tested . It is a sampling interval .
What does "systematic sampling" mean?
Systematic sampling is a probability sampling technique where researchers choose individuals from the population at regular intervals, such as every 15th person on a population list.
The advantages of simple random sampling can be imitated if the population is arranged randomly.
Systematic sampling is a type of probability sampling method in which sample members from a larger population are selected according to a random starting point but with a fixed, periodic interval. This interval, called the sampling interval.
Here every 50th candy bar is tested . It is a sampling interval .
Therefore he use systematic sampling plan.
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In the figure above, is AB || CD?
1. If m 2 5 = 30 and m 2 3 = 150?
A. Yes because angles 5 and 3 are same-side interior angles.
B. Yes because angles 5 and 3 are alternate interior angles.
C. Yes because angles 5 and 3 are vertical angles.
OD. No because angles 5 and 3 are vertical angles.
O E. No because angles 5 and 3 are corresponding angles.
F. No because angles 5 and 3 are alternate interior angles.
Answers
Answer:
the answer is yes because angles 5 and 2 are same side interior angles and same side interior angles add up to 180*.
Step-by-step explanation:
Make sure not to be fooled by the "it looks like it" theorem. Teachers will try to trick you by making the lines look not parallel. All you need to look at are if the angles are congruent or supplementary based on the theorems you hopefully were taught in class. Wow what has brainly done I sound like a teacher lol.
Ramon is graphing the function f(x) = 3(4)x. He begins by plotting the initial value. Which graph represents his initial step?
On a coordinate plane, the point (0, 3) is graphed.
On a coordinate plane, the point (0, 4) is graphed.
On a coordinate plane, the point (3, 0) is graphed.
On a coordinate plane, the point (4, 0) is graphed.
Answers
The graph that represents Ramon's initial step is, On a coordinate plane, the point (0, 3) is graphed.
What is an ordered pair?The ordinate and abscissa of the x coordinate, along with two values specified in parentheses in a specific order, make up an ordered pair.
Pair in Order = (x, y) where x represents the abscissa, the measure of a point's separation from the main axis, and y represents the ordinate, the measure of a point's separation from the secondary axis.
Given, Ramon is graphing the function f(x) = 3 + (4)x.
We know the initial value of a function is determined when the independent variable is set to zero.
Here the independent variable is 'x'.
Now, at x = 0,
f(0) = 3 + (4)(0).
f(0) = 3.
So, The ordered pair is (0, 3).
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Answer:
a
Step-by-step explanation:
a party store has 54 packs of plates in stock. the packs are either sets of 8 or sets of 12. if the store has 496 total plates in stock, how many plates would a customer but if he or she buys all of the packs of 12 that the store has in stock?
Answers
If the customer purchases every pack of 12 which the shop has 192 plates in stock.
Explain the method of substitution?Three steps make up the substitution technique: For each of the variables, solve one equation. Put this expression (or plug it in) into the other equation, then solve it. To identify the matching variable, rewrite the value's original equation.Total number of packs of plates = 54.
The set are either sets of 8 or sets of 12.
Let x represent the overall number of 12-plate packets.
There will therefore be in total packs of 8 plates: 54 - x.
Thus,
8(54−x) + 12x = 496
432 − 8x + 12x = 496
4x = 64
x = 16
Thus, there are 16 packs of 12 plates in the store.
So, if a consumer purchases all of the 12-packs of plates, he will ultimately purchase 1216 = 192 plates.
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The ratio of the same side interior angles of two parallel lines is 1:14. find the measures of all eight angles formed by the parallel lines and transversals.
Answers
Answer:
x degrees, 14x degrees, x degrees, 14x degrees, x degrees, 14x degrees, 2x degrees, and 28x degrees.
Step-by-step explanation:
The ratio of the same side interior angles of two parallel lines is 1:14, which means that for every one degree of the first angle, the second angle measures 14 degrees. If the first angle is x degrees, then the second angle is 14x degrees.
Since the lines are parallel and the angles are on the same side of the transversal, the alternate interior angles are congruent, so the measure of the third angle is also x degrees, and the measure of the fourth angle is also 14x degrees.
Since the lines are parallel, the alternate exterior angles are also congruent, so the measure of the fifth angle is also x degrees, and the measure of the sixth angle is also 14x degrees.
Finally, the measures of the seventh and eighth angles can be found by adding the measures of the adjacent angles. The seventh angle is adjacent to the third and fifth angles, so its measure is x + x = 2x degrees. The eighth angle is adjacent to the fourth and sixth angles, so its measure is 14x + 14x = 28x degrees.
In summary, the measures of the eight angles formed by the parallel lines and transversal are x degrees, 14x degrees, x degrees, 14x degrees, x degrees, 14x degrees, 2x degrees, and 28x degrees. The value of x can be determined by knowing the measure of one of the angles, or by using other information about the angles or the parallel lines.
7.6u-(30 divided by 6) + 12
Answers
Answer:
7.6u+7
Step-by-step explanation:
7.6u-(30/6)+12
30/6=5
7.6u-5+12
7.6u+7
please help me solve this linear expression
Answers
Answer:
substitute a=-5 and c=5 into a=-3c
Step-by-step explanation:
a= -3c
(-5)= -3(5)
-5= -15
a cylindrical water tank 5 meters high with a radius of 2 meters is buried so that the top of the tank is 1 meter below ground level. how much work is done in pumping a full tank of water up to ground level? (the water weighs 9800 newtons per cubic meter.)
Answers
The work is done in pumping a full tank of water up to ground level is 470400πNm.
Tank sizes variety from 6 ft. to one hundred twenty ft. in diameter with a roof, and as much as two hundred toes in diameter as an open pinnacle tank. Tanks with a roof have capacities starting from seven-hundred gallons to 500,000 gallons at the same time as the open pinnacle tanks may be constructed with even large capacities
The radius of the layer = 2m
V= pi (2)^2 (Delta y) m^3 = four pi Delta y m^3V=π(2) 2 (Δy)m 3 =4πΔym 3
Weight of the layer =9800 (four pi Delta y)=9800(4πΔy)
Weight of the water = 9800 frac=9800 m 3 N
So, weight of the layer = 39200 pi Delta y=39200πΔy
distance layer is moved =5-y=5−y
W=int_^{four} (5-y)(39200 pi dyW=∫ 04 (5−y)(39200πdy
=39200 pi int_^{four} (5-y) dy=39200π∫ 04 (5−y)dy
=39200 pi left[ 5y - frac y^2 right]_^{four}=39200π[5y− 21 y 2 ] 04
=-39200 pi (12) = 470400 pi Nm=−39200π(12)= 470400πNm.
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Can someone help me this is hard
Answers
Answer:
m ≥ 28.5
Step-by-step explanation:
He wants to bike at least 28.5 miles, like he did last year
also whats up with the anime tab TT no judgement tho
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
Answers
Answer:
-3/4
Step-by-step explanation:
equation of a line : y=mx+c
m= slope= 4/3
perpendicular slope is the inverse of m
this is because m1 * m2 = -1
thus perpendicular slope = -3/4
under what circumstances is a discretized b state matrix equivalent to a continuous time b state matrix
Answers
A continuous time system can behave roughly throughout a variety of periods using a discretized state matrix. A continuous time condition matrix should be used in its place if these requirements are not satisfied since a discretized state matrix might not adequately depict the performance of a continuous time system.
A continuous time condition matrix is a matrix that is used to indicate the state of a system at any moment, as opposed to a discretized state matrix, which is used to describe the status of a system at discrete time intervals. Under the following conditions, a discrete-time state matrix is identical to a time series state matrix:
The system may be regarded as being in stable equilibrium at each time point since the time gaps between every discretization are short enough. This indicates that the behavior of the system does not drastically vary from one-time point to the next.
Over the time frames between each discretization, a linear model accurately predicts the behavior of the system. This means that the behavior of the system can be precisely predicted by a linear equation of the type "Ax = Bu," where A as well as B are matrices and x as well as u are vectors that, respectively, represent the system's state and input.
Over the intervals between each discretization, the system's input remains constant. This indicates that the system's input does not drastically vary from one-time point to the next.
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21. Calculate the future value of a $7,000 after 9
years, when there is an interest rate of 2.05%
with quarterly simple interest payments.
[A] $7,322.88
[D] $8,419.30
[B] $8,414.35
[E] $7,527.31
[C] $6,148.05
Answers
The solution is Option A.
The amount after 9 years with an investment of $ 7000 at a simple interest calculated quarterly at rate 2.05 is $ 7,322.88
What is Simple Interest?
Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.
Simple Interest = ( Principal Amount x Rate x Time Period ) / 100
Given data ,
Let the simple interest be represented as I
Now , the amount invested P = $ 7,000
The rate of interest R = 2.05 %
The time period t = 9 years
Since the interest is calculated quarterly , t= T/4
Now , the simple interest is calculated by the formula
Simple Interest = ( Principal Amount x Rate x Time Period ) 100
Substituting the values in the equation , we get
Simple Interest I = [ ( 7000 x 2.05 x 9 ) / 4 ] / 100
On simplifying the equation , we get
Simple Interest I = ( 129150 ) / 400
Simple Interest I = $ 322.875
I = $ 322.88
Now , the amount after 9 years = initial amount P + Interest I
Amount after 9 years = 7,000 + 322.88
Amount after 9 years = $ 7,322.88
Hence , the amount after 9 years is $ 7,322.88
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All the gummy machines at a candy factory work at the same rate: Six machines working simultaneously can complete big order in 22 hours. How many hours would it take t0 fill the order if the number of working machines decreased by a factor of 2? er: hours
Answers
The numbers of hours taken to fill the order if the number of working machines decreased by a factor of 2 is; 44 hours
How to find the rate of work?We are given;
Numbers of hours a work is complete by 6 machines = 22 hours
Now, we know that the number of hours required to complete a work is inversely proportional to the number of machines used.
Therefore, If the number of working machines decreased by a factor of 2, then the number of hours will be increased twice.
Therefore, we can say that;
The numbers of hours taken to fill the order = (22 * 6)/3
= 44 hours
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Which of the following statements is true for all real symmetric matrices Mcq?All the eigenvalues are realAll the eigenvalues are positiveAll the eigenvalues are distinctSum of all the eigenvalues is zero
Answers
Option A is the correct answer. All the eigenvalues of a real symmetric matrix are always real.
Symmetrix matrix: A matrix is said to be a Symmetrix matrix if A=A^T the matrix should be equal to the transpose of A.
All the eigenvalues of the Symmetric matrix are real. Eigenvectors corresponding to distinct eigenvalues are orthogonal.
Skew-Symmetrix matrix: A matrix 'A' is said to be a Skew-Symmetrix matrix if A=-A^T
Eigenvalues of the skew-symmetric matrix are zero or purely imaginary.
Skew-Hermitian matrix: A square matrix is said to be a Skew-Hermitian matrix if it is equal to the negotiation of its complex conjugate transpose.
A=-(A)^T
Eigenvalues of the Skew-Hermitian matrices are zero or imaginary.
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The vector field F = [tex](3x^2y + z^3, x^3 + 2yz, y^2 + 3xz^2)[/tex] has a nonzero divergence and a nonzero curl, indicating that it is not a conservative vector field. F cannot be expressed as the curl of another vector field.
To compute the divergence of F, we take the partial derivatives of each component with respect to their corresponding variables and sum them up. The divergence of F is given by div(F) = ∇·F = (∂/∂x)[tex](3x^2y + z^3)[/tex] + (∂/∂y)[tex](x^3 + 2yz)[/tex] + (∂/∂z)[tex](y^2 + 3xz^2)[/tex]. Evaluating these partial derivatives, we find div(F) = 6xy + 3z^2 + 2yz + 6xz.
To compute the curl of F, we take the curl operator (cross product of the del operator with F) and expand the determinant. The curl of F is given by curl(F) = ∇×F = (∂/∂y)[tex](y^2 + 3xz^2)[/tex] - (∂/∂z)[tex](x^3 + 2yz)[/tex], (∂/∂z)[tex](3x^2y + z^3)[/tex] - (∂/∂x)[tex](y^2 + 3xz^2)[/tex], (∂/∂x)[tex](x^3 + 2yz)[/tex] - (∂/∂y)[tex](3x^2y + z^3)[/tex]. Simplifying these expressions, we obtain curl(F) = [tex](-2xz, -3z^2, -6xy)[/tex].
The divergence of F is nonzero, indicating that F does not satisfy the divergence theorem, which states that a vector field with zero divergence is conservative. Additionally, the curl of F is nonzero, indicating that F does not satisfy the curl theorem, which states that a vector field with zero curl is conservative. Therefore, F is not conservative and cannot be expressed as the curl of another vector field.
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bonjour
voici un programe de calcul
.choisir un nombre relatif
.multiplier par-3
.ajouter -5
1quel nombre obtient-on avec ce programme lorsqu'on choisit au départ:
a.7 ? b.-4 ?
2. Léa a obtenu 1avec ce programme de calcul.
quel nombre avait-elle choisi au départ
Answers
Answer:
1a. -26
1b. -17
2. -2
Step-by-step explanation:
1.
a.
7
7 × (-3) = -21
-21 + (-5) = -26
b.
-4
-4 × 3 = -12
-12 + (-5) = -17
Formule:
r = -3n - 5
2.
r = -3n - 5
1 = -3n - 5
-3n = 6
n = -2
Multiply. 4x(y + x + 2)
Answers
Step-by-step explanation:
4xy + 4x² + 8x
Can also be rearranged as
4x²+8x+4xy
Mark’ mother i planning to borrow $25,000 to remodel the retaurant he own. He contacted everal loan companie, and he i comparing two different option. Company 1 offer an interet rate of 5. 25%. Company 2 offer an interet rate of 8. 5%. Both loan option involve imple interet and mut be repaid in exactly 3 year. How much more will mark’ mother pay in interet if he chooe to borrow the money from company 2?
Answers
If Mark’s mother borrows the money of $25,000 from company 2 which offers a rate of 8.5% for 3 years, she needs to pay the charge of $6375.
How to calculate the simple interest?Interest is the cost of borrowing or saving money. Simple interest is an easy method to calculate the interest charge on a loan.
As its name, calculating the simple interest is simple and quick. We only multiply the money we borrow or deposit, by the period, then multiply them by the interest rate applied by the bank or any financial institution chosen.
The formula for calculating the simple interest is
P x R x T
P means principal or how much money we borrow or save
R means rate or how many percentages of interest applied
T means time or how long we borrow or save the money
By using the formula mentioned before, the simple interest would be
$25,000 x 8.5% x 3 = $6375
Thus, the amount of simple interest paid is $6375 and the total amount paid is $25000 + $6375 = $31,375
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I need help ive been trying to figure them out for an hour and i also want to know if some are correct
Answers
The correct answer for question 1 is C) CA=XY
what is congruence in triangles?Two triangles are said to be congruent if all three corresponding sides are equal and all three corresponding angles are equal in measure.
Given here ΔABC≅XYZ
Therefore AB=XY , BC=YZ , AC=XZ & ∠A=∠X , ∠B=∠Y , ∠C=∠Z but clearly CA≠XY
The full diagram is attached please refer to the diagram for clarity
Hence, option c is the correct answer.
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in need some help. i cant figure this out.
Answers
Answer:
x = 1.28
Step-by-step explanation:
Given equation:
[tex]3 \frac{1}{2}x-6=2-2\frac{3}{4}x[/tex]
Add 2³/₄x to both sides of the equation:
[tex]\implies 3 \frac{1}{2}x+2\frac{3}{4}x-6=2-2\frac{3}{4}x+2\frac{3}{4}x[/tex]
[tex]\implies 3 \frac{1}{2}x+2\frac{3}{4}x-6=2[/tex]
Add 6 to both sides of the equation:
[tex]\implies 3 \frac{1}{2}x+2\frac{3}{4}x-6+6=2+6[/tex]
[tex]\implies 3 \frac{1}{2}x+2\frac{3}{4}x=8[/tex]
Rewrite the mixed numbers as improper fractions:
[tex]\implies \dfrac{3 \cdot 2+1}{2}x+\dfrac{2 \cdot 4+3}{4}x=8[/tex]
[tex]\implies \dfrac{7}{2}x+\dfrac{11}{4}x=8[/tex]
Make the denominators of the fractions the same:
[tex]\implies \dfrac{7 \cdot 2}{2 \cdot 2}x+\dfrac{11}{4}x=8[/tex]
[tex]\implies \dfrac{14}{4}x+\dfrac{11}{4}x=8[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]
[tex]\implies \dfrac{14+11}{4}x=8[/tex]
[tex]\implies \dfrac{25}{4}x=8[/tex]
Multiply both sides by 4:
[tex]\implies 4 \cdot \dfrac{25}{4}x=4 \cdot8[/tex]
[tex]\implies 25x=32[/tex]
Divide both sides by 25:
[tex]\implies \dfrac{25x}{25}=\dfrac{32}{25}[/tex]
[tex]\implies x=\dfrac{32}{25}[/tex]
Convert the improper fraction to a mixed number:
[tex]\implies x=1 \frac{7}{25}[/tex]
The value of x as a decimal:
[tex]\implies x=1.28[/tex]
What is the perimeter, in units, of ΔABC
Δ
A
B
C
with A(−1,−6)
A
(
−
1
,
−
6
)
, B(7,−6)
B
(
7
,
−
6
)
, and C(3,−3)
C
(
3
,
−
3
)
?
Answers
Answer:
To find the perimeter of triangle ABC, we need to find the lengths of all three sides of the triangle. To do this, we can use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by the square root of ((x2 - x1)^2 + (y2 - y1)^2).
Applying this formula, we can find the lengths of the sides of the triangle as follows:
AB = sqrt((7 - (-1))^2 + (-6 - (-6))^2) = sqrt(8^2 + 0^2) = sqrt(64) = 8
BC = sqrt((3 - 7)^2 + (-3 - (-6))^2) = sqrt(-4^2 + 3^2) = sqrt(16 + 9) = sqrt(25) = 5
AC = sqrt((-1 - 3)^2 + (-6 - (-3))^2) = sqrt(-4^2 + 3^2) = sqrt(16 + 9) = sqrt(25) = 5
Thus, the perimeter of triangle ABC is 8 + 5 + 5 = 18 units.
Find g(x), where g(x) is the reflection across the x-axis of f(x)=4x+10
Answers
Answer:
To find the reflection of a function across the x-axis, we simply need to change the sign of the y-coordinates of the function's points. Therefore, the reflection of f(x) = 4x + 10 across the x-axis is g(x) = -(4x + 10) = -4x - 10.
Step-by-step explanation:
To find the reflection of a function across the x-axis, we can follow these steps:
Start with the equation of the original function, which in this case is f(x) = 4x + 10.Change the sign of the y-coordinates of the function's points. This means that we need to multiply the entire equation by -1.Substitute the result from step 2 into the original equation to find the reflected function. In this case, we get g(x) = (-1)(4x + 10) = -4x - 10.Here is an example of how this works in practice. Let's say that the original function f(x) has the points (1,14) and (2,18).
The reflection of these points across the x-axis would be (1,-14) and (2,-18), respectively.
To find the equation of the reflected function g(x), we would simply substitute these points into the equation from step 3 to get g(x) = -4x - 10.
Consider a game in which each play costs one nickel (1¢). During each play, the game dispenses a coin to the player to keep. The game machine contains equal numbers of pennies (1¢), nickels, dimes (10¢), and quarters (25¢). The nickels that the player inserts do not go into the same pool of "reward" coins. What is the expected profit, in cents, for a player who plays five games in a row?
Answers
The expected profit, in cents, for a player who plays 1 game is 5.25 cents.
How to obtain the expected profit?The distribution that models the profit of a player for a single game is given as follows:
P(X = -4 cents) = 0.25. -> pays 5 cents, wins 1 cent, loses 4 cents.
P(X = 0 cents) = 0.25. -> pays 5 cents, wins 5 cents.
P(X = 5 cents) = 0.25. -> pays 5 cents, wins 10 cents.
P(X = 20 cents) = 0.25. -> pays 5 cents, wins 25 cents.
The expected value of a discrete distribution is computed by adding the total of each outcome and multiplying it by its probability, as follows:
E(X) = -4 x 0.25 + 0 x 0.25 + 5 x 0.25 + 20 x 0.25
E(X) = 5.25 cents.
Hence, the expected profit is 5.25 cents
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Super Express Couriers charges a postage fee of Rs 2 for each gram of the weight of a parcel and an additional flat rate of Rs 30.
If Kevin's postage fee was 150 less than 5 times the weight of his parcel, how much did his parcel weigh?
Answers
Answer:
Step-by-step explanation:
я хз
The weight of Kevin's parcel is 60 g.
What is an equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, a postage fee of Rs 2 for each gram of the weight of a parcel and an additional flat rate of Rs 30. and Kevin's postage fee was 150 less than 5 times the weight of his parcel,
Let the weight of the parcel be x
Establishing the equations,
5x - 150 = 30 + 2x
5x - 2x = 30 + 150
3x = 180
x = 180/3
x = 60
Hence, the weight of Kevin's parcel was 60g
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The universal set, &, and sets F and G
are defined below.
{integers from 1 to 14 inclusive}
F = {x: 1≤ x <5}
G = {x:3 < x≤ 9}
A value is chosen at random from §.
Work out P(FG).
Give your answer as a fraction in its
simplest form.
-
Answers
Answer:7/8
Step-by-step explanation:your mom
Which division problem can be described using this model?
A. 2÷1/10
B. 2÷1/5
C. 1÷1/10
D. 2÷5
Answers
Answer:
I believe that the answer is 2/5 because all of the other answers equal 10 (for b and c) or 20 (for a)
Step-by-step explanation:
A cylindrical container has radius 1 m.
The cylinder contains 628 litres of water.
Calculate depth of water in the cylinder giving your answer in cm
take pi to be 3.14
Answers
The depth of water in the cylinder is 20 cm
How to calculate depth of water in the cylinderFrom the question, we have the following parameters that can be used in our computation:
Volume = 628 litres
Radius = 1 m
Convert litres and meters to cm cube and cm
So, we have the following representation
Volume = 628000 cm cubed
Radius = 100 cm
The volume is the calculated as
V = πr²h
So, we have
628000 = 3.14 * 100² * h
Evaluate
628000 = 31400 * h
Divide by 31400
h = 20
Hence, the height is 20 cm
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if a and b are independent events with p(a) = 0.35 and p(b) = 0.20, then, p(a è b) =
Answers
The probability of a intersection b, represented by P(a ∩ b) is equal to 0.07.
What is independent probabilityOne of the axioms of probability states that is two events say A and B are independent that is the probability of occurrence of one of them is not affected by the occurrence of the other, then P(A ∩ B) = P(A) × P(B)
We have from the question two events a and b which are said to be independent events,
P(a) = 0.35
P(b) = 0.20
then;
P(a ∩ b) = 0.35 × 0.20
P(a ∩ b) = 0.07
Therefore, the value 0.07 is the probability of the intersection of the two independent events a and b.
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