P(A and B) expressed in the simplest form is (B) 2/21.
What is probability?Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.To express P(A and B) in the simplest form:
P(A and B) means that you need to multiply the two probabilities together since both A and B need to happen. The probability of drawing a black tile on the first draw is 4/15 since there are 15 total tiles and 4 of those are black. On the second draw, the bag is already missing a tile, and there are therefore 14 tiles remaining. For the second one, the probability is 5/14, since there are 14 total tiles and 5 of them are white. Multiplying these two together, we get 4/15 × 5/14 = 20 / 210 = 2/21.Therefore, P(A and B) expressed in the simplest form is (B) 2/21.
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The complete question is given below:
A bag contains 4 black tiles, 5 white tiles, and 6 blue tiles. Event A is defined as drawing a black tile from the bag on the first draw, and event B is defined as drawing a white tile on the second draw.
If two tiles are drawn from the bag, one after the other without replacement, what is P(A and B) expressed in the simplest form?
A. 4/45
B. 2/21
C. 4/15
D. 5/14
.
Let’s assume the following statements are true: Historically, 75% of the five-star football recruits in the nation go to universities in the three most competitive athletic conferences. Historically, five-star recruits get full football scholarships 93% of the time, regardless of which conference they go to. If this pattern holds true for this year’s recruiting class, answer the following:
a. Based on these numbers, what is the probability that a randomly selected five-star recruit who chooses one of the best three conferences will be offered a full football scholarship?
b. What are the odds a randomly selected five-star recruit will not select a university from one of the three best conferences? Explain.
c. Explain whether these are independent or dependent events. Are they Inclusive or exclusive? Explain.
The probability that a randomly selected five-star recruit who chooses one of the best three conferences will be offered a full football scholarship is 69.75%.
What is the computation for the above solution?
Note that this is simple probability.
Hence probability of the 75% football starts selected randomly where the chance is 93% =
75% x 93%
= 69.75%
What are the odds a randomly selected five-star recruit will not select a university from one of the three best conferences?The chance that 25% of the five-star recruit will not select a university form one of the three best conferences is explained as follows:
Because only 75% stand the chance of being selected into the three ivy leagues, this means that 25% stand no chance.
Recall that the total population is 100%.
Are these are independent or dependent events. Are they Inclusive or exclusive?From the statement of problem given, it is clear that the events are mutually exclusive. Recall "Historically, five-star recruits get full football scholarships 93% of the time, regardless of which conference they go to.
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what is the Pythagorean theorem
Answer:
a^2+b^2=c^2
Step-by-step explanation:
leg1=a
leg2=b
hypotenuse=c
a^2+b^2=c^2
Answer:
u see this is how the Pythagorean theorem works a^2 + b^2 = c^ i hope this helps have a great day bye please mark as brainliest :D
Step-by-step explanation:
How much money do I need now if I am going to recieve $5000 every 6 months (starting in 6 months) for 10 years if the interest rates are 4%/a compounded semi-annually?
By using the compound interest model, the initial deposit required to receive $ 5 000 every 6 months is $ 125 000.
How many money should be deposited in the beginning to receive a certain amount periodically
In this problem we must apply the compound interest model, which represent a periodic accumulation of interest according to the following formula:
C' = C · (1 + r/100)ˣ (1)
Where:
C - Initial depositr - Interest rateC' - Resulting moneyx - Period indexIf we know that x = 1, r = 4, C = x and C' = x + 5 000, then the initial deposit is:
x + 5 000 = x · (1 + 4/100)
x + 5 000 = 1.04 · x
0.04 · x = 5 000
x = 125 000
By using the compound interest model, the initial deposit required to receive $ 5 000 every 6 months is $ 125 000.
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Pls help me answer this question3 x 2 2/5
Answer:
7 1/5
Step-by-step explanation:
I need help pls and thank you
Answer:
12 in, 7 in
Step-by-step explanation:
The area of a rectangle is the product of length and width. Here, you are given the area, and an additional relation between length and width.
SetupThe two relations between length and width described by this problem are ...
A = LW . . . . . . . dimensions are of a rectangle
L = W +5 . . . . . . length is 5 inches more than width
A = 84 . . . . . . . . area in square inches
SolutionSubstituting for L and A in the area formula, we have ...
84 = (W +5)(W)
We can solve this as a quadratic in any of several ways. One of those ways is by factoring.
Essentially, we're looking for factors of 84 that differ by 5. We can consider different factorizations of 84 to see what we get:
84 = 84×1 = 42×2 = 28×3 = 21×4 = 14×6 = 12×7
The differences between the factors in these pairs are 83, 40, 25, 17, 8, 5.
This means the last pair, with a difference of 5, is the one we're looking for.
W+5 = 12, W = 7
The rectangle is 12 inches long and 7 inches wide.
__
Additional comment
As a quadratic in standard form, we would have ...
W² +5W -84 = 0 ⇒ (W +12)(W -7) = 0 ⇒ W = {7, -12}
If you were to solve this by completing the square, you would have ...
(W +2.5)² = 90.25 ⇒ W = -2.5 ±9.5 = {7, -12}
Given the points (–3,k) and (2,0), for which values of k would the distance between the points be 34‾‾‾√ ?
The distance between the points (–3,k) and (2, 0) exists k = ± 3.
How to estimate the distance between points (–3, k) and (2, 0)?
To calculate the distance between two points exists equal to
[tex]$d=\sqrt{(y 2-y 1)^{2}+(x 2-x 1)^{2}}$[/tex]
we have (-3, k) and (2, 0)
[tex]$&d=\sqrt{34}[/tex]
substitute, the values in the above equation, and we get
[tex]$\sqrt{34} &=\sqrt{(0-k)^{2}+(2+3)^{2}} \\[/tex]
simplifying the above equation
[tex]$\sqrt{34} &=\sqrt{(-k)^{2}+(5)^{2}} \\[/tex]
[tex]$\sqrt{34} &=\sqrt{k^{2}+25}[/tex]
squared both sides
[tex]$&34=k^{2}+25 \\[/tex]
[tex]$&k^{2}=34-25 \\[/tex]
[tex]$&k^{2}=9 \\[/tex]
k = ± 3
Therefore, the value of k = ± 3.
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The average of 15,19,23,41,and Z is 20. What is the value of x
The value of x from the given data is 2
Calculating the average of numbersMean is the ratio of sum of numbers to the total samples. Given the following data
15,19,23,41, and Z
The mean is calculated as
Mean = 15+19+23+41+z/5
Since the mean the of the data is given as 20. Substitute
20 = 15+19+23+41+z/5
Cross multiply
20*5 = 15+19+23+41+z
100 = 15+19+23+41+z
100 = 98 + z
z = 100- 98
z = 2
Hence the value of x from the given data is 2
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How can x² = x² + 2x + 9 be set up as a system of equations? (1 point)
1. y= x²-9
y = x² + 2x + 9
2. y=x²
y = x² + 2x +9
3. y = x² + 2x
y = x² +9
4. y=x²
y = 2x + 9
Answer: 2
Step-by-step explanation:
Each of the two sides of the equation is set equal to y
A newspaper started an online version of its paper 14 years ago. In a recent presentation to stockholders, the lead marketing executive states that the revenues for online ads have more than doubled that of the revenues for printed ads since starting the online version of the paper. Use the graph below to justify the lead executive’s statement and to determine the approximate year that the two ad revenues were equal.
It is to be noted that at the seven and half year, is when the revenue of both ads became equal. This is a graph problem. See the explanation below.
What is the explanation for the above answer?Step 1:
Note that the amount of money earned by routine company activities is known as revenue, which is calculated by dividing the average sales price by the number of units sold.
Step 2:
Note that the graph is to be used to justify the statement by the lead executive.
Step 3
From the graph, we know that the revenue in the 10th year for printed ads was $ 2,000,000 and $ 3,000,000 for online ads. Represented on as coordinates, that would be (0,3); (10, 2).
Thus, we can create an equation that states:
(y-2) = [(3-2)/(0-10)] * (x - 10)
⇒ y - 2
= [-1/10] * [x - 10]
Hence,
10y - 20 = - x + 10
10 y + x = 30 ........Lets call this equation A
We can also state that:
Online revenue coordinates on the graph are (0,0,) (10, 3)
Thus,
(y-0) =
[(3-0)/(10-0)] (x -0)
⇒ y = [3x/10] [10y - 3x] = 0.........Lets make this equation B
For printed Ad Revenue:
Year 12= x
10y + 12 = 30
Y = 18/10
y = 1.8
For online Ad revenue
Year = 12 = x
10y = 36
Y = 36/10
y = 3.6
From the above, it is clear that in year 10, the online ad revenue got doubled as same as that of revenue from printed ads.
In order to get the year in which the revenue were equal, we solve both equations simultaneously:
+ 10y + x = 30
± 10y ≠ 3x = 3
4x = 30
x thus, = 30/4
= 7.5
Thus, it is correct to state that both revenue's became equal by the mid of the 7th year going to the eight year.
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Full Question:
Missing graph is attached.
the point in the graph of the equation 2x+5y=20, where x coordinate is 5/2, is
Answer: (5/2, 3)
Step-by-step explanation:
Substituting in x=5/2,
[tex]2(5/2)+5y=20\\\\5+5y=20\\\\5y=15\\\\y=3[/tex]
So, the point is (5/2, 3)
What value of z* should be used to construct an 88% confidence interval of a population mean?
Z = 1.555 should be used
If we seek an 88% confidence interval, that means we only want a 12% chance that our interval does not contain the true value.
Assuming a two-sided test, that means we want a 6% chance attributed to each tail of the Z-distribution.
the zα/2 value of z0.06.
This z value at α/2=0.06 is the coordinate of the Z-curve that has 6% of the distribution's area to its right, and thus 94% of the area to its left. We find this z-value by reverse-lookup in a z-table.
What is Z-distribution?The standard normal distribution, also called the z-distribution, is a special normal distribution where the mean is 0 and the standard deviation is 1.
Any normal distribution can be standardized by converting its values into z-scores. Z-scores tell you how many standard deviations from the mean each value lies.
Why is z-score used?The standard score (more commonly referred to as a z-score) is a very useful statistic because it
(a) allows us to calculate the probability of a score occurring within our normal distribution and
(b) enables us to compare two scores that are from different normal distributions.
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A parabola opens up and passes through (-4, 2) and (6, -3). How do you know that (-4, 2) is not the vertex
Answer:
Step-by-step explanation:
The minimum is at the vertex of this parabola because it opens up.
Now if (-4, 2) is the minimum then all the y values on the parabola must be > 2,
But we are given that y = -3 is on the graph ( the point (6,-3) - that is y < 2 here,
Therefore (-4, 2) cannot be the vertex .
Complete the equation.
2 x 4 =
X 2
Answer:
4 is correct answer.
Step-by-step explanation:
That because it contains property of communicative. That is a×b=b×a.
S is a geometric sequence.
a) (√x + 1), 1 and (√x-1) are the first three terms of S.
Find the value of x.
You must show all your working.
Which describes the combined variation shown in the equation F = kxy/z?
1) F varies directly with x, and inversely with y
and z.
2)F varies directly with z, and inversely with x
and y.
3)F varies directly with y, and inversely with x and z.
4) F varies directly with x and y, and inversely
with z.
Answer:
option 4
Step-by-step explanation:
F = [tex]\frac{kxy}{z}[/tex]
k is the constant of variation
• if the variables are on the numerator they vary directly
• if the variables are on the denominator they vary inversely
In this case F varies directly with x and y ( variables on numerator ) and inversely with z ( variable on denominator )
In a scale drawing of a painting, 2 centimeters represents 7 inches.
The height of the real painting is 35 inches. What is the height of the painting in the scale drawing?
The height of the painting in the scale drawing is 10 centimeters if the height of the real painting is 35 inches given that in a scale drawing of a painting, 2 centimeters represents 7 inches. This can be obtained by using the ratio of scale drawing to the real drawing.
Find the height of the painting in the scale drawing:Here in the question it is given that,
In a scale drawing of a painting, 2 centimeters represents 7 inchesThe height of the real painting is 35 inchesThus we can say that, scale of the painting is 2 cm : 7 in
Ratio of scale drawing and real painting is 2 : 7
⇒ Similarly here height of the painting in the scale drawing to the height of the painting in the real drawing will be in the ratio 2 : 7.
We can say that,
2 cm/7 in = x cm/35 in
where x is the height of the painting in the scale drawing
2 cm × 35 in /7 in = x cm
x = 2 × 5 cm
x = 10 cm
Hence the height of the painting in the scale drawing is 10 centimeters if the height of the real painting is 35 inches given that in a scale drawing of a painting, 2 centimeters represents 7 inches.
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A 400 L tank is filled with pure water. A copper sulfate solution with a concentration of 20 g/L flows into the tank at a rate of 4 L/min. The thoroughly mixed solution is drained from the tank at a rate of 4 L/min. a. Write a differential equation (initial value problem) for the mass of the copper sulfate. b. Solve the differential equation
(a) Let [tex]C(t)[/tex] denote the amount (in grams) of copper (II) sulfate (CuSO₄) in the tank at time [tex]t[/tex] minutes. The tank contains only pure water at the start, so we have initial value [tex]\boxed{C(0)=0}[/tex].
CuSO₄ flows into the tank at a rate
[tex]\left(20\dfrac{\rm g}{\rm L}\right) \left(4\dfrac{\rm L}{\rm min}\right) = 80 \dfrac{\rm g}{\rm min}[/tex]
and flows out at a rate
[tex]\left(\dfrac{C(t)\,\rm g}{400\,\mathrm L + \left(4\frac{\rm L}{\rm min} - 4\frac{\rm L}{\rm min}\right) t}\right) \left(4\dfrac{\rm L}{\rm min}\right) = \dfrac{C(t)}{100} \dfrac{\rm g}{\rm min}[/tex]
and hence the net rate of change in the amount of CuSO₄ in the tank is governed by the differential equation
[tex]\boxed{\dfrac{dC}{dt} = 80 - \dfrac C{100}}[/tex]
(b) This ODE is linear with constant coefficients and separable, so we have a few choices in how we can solve it. I'll use the typical integrating factor method for solving linear ODEs.
[tex]\dfrac{dC}{dt} + \dfrac C{100} = 80[/tex]
The integrating factor is
[tex]\mu = \exp\left(\displaystyle \int \frac{dt}{100}\right) = e^{t/100}[/tex]
Distributing [tex]\mu[/tex] on both sides gives
[tex]e^{t/100} \dfrac{dC}{dt} + \dfrac1{100} e^{t/100} C = 80 e^{t/100}[/tex]
and the left side is now the derivative of a product,
[tex]\dfrac d{dt} \left[e^{t/100} C\right] = 80 e^{t/100}[/tex]
Integrate both sides. By the fundamental theorem of calculus,
[tex]e^{t/100} C = e^{t/100}C\bigg|_{t=0} + \displaystyle \int_0^t 80 e^{u/100}\, du[/tex]
The first term on the right vanishes since [tex]C(0)=0[/tex]. Then
[tex]e^{t/100} C = 8000 \left(e^{t/100} - 1\right)[/tex]
[tex]\implies \boxed{C(t) = 8000 - 8000 e^{-t/100}}[/tex]
1,615×10 to the 2 power
simplifying 1,615×10 to the 2 power would give 161500
Simplifying the index form
Index notation is known as a way of representing numbers (constants) and variables (e.g. x and y) that have been multiplied by themselves a number of times.
Index notations, or indices are use to simplify expressions or solve equations involving powers.
For instance;
8 × 8 × 8 × 8
8 is multiplied by itself 4 times
In index form , it is written as 8 ^4, that is, 8 to the 4 power
From the information given, we have to simply 1,615×10 to the 2 power
It can be written as;
= 1, 615 × 10 × 10
= 1, 615 × 100
= 161500
Thus, simplifying 1,615×10 to the 2 power would give 161500
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If the top ten nations were randomly selected to march, one after another, into the stadium at the closing ceremonies, in how many ways could the nations have marched in?
Step-by-step explanation:
1. Entrance of Head of State and IOC President
2. Playing of the national anthem
3. The parade of the athletes
4. The symbolic release of doves
5. Olympic Laurel Award
6. Official Speeches
7. Opening of the Games
8. Raising the Olympic flag and playing the Olympic Anthem
9. Athletes, judges and coaches’ oath
10. Lighting of the Olympic flame
11. The artistic programme
Use the distributive property to simplify the expression.
-6(2²+3)-2(1²-2)
A. 4² +22
B. 4:² +14
C. -8²-22
D. -8:²-14
[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]
Given:[tex]\bold{-6(2^2+3)-2(1^2-2)}[/tex][tex]\\[/tex]
The [tex]\mathrm{distributive \: property}[/tex] states that an expression that is given in the form of [tex]\small\sf{ A(B + C)}[/tex] can be solved as [tex]\small\sf{A \times (B + C) = AB + AC}[/tex] . So:
[tex]\small\longrightarrow\sf{-24-18-2+4}[/tex]
[tex]\small\longrightarrow\sf{-42+2}[/tex]
▪ [tex]\large\tt{All \: \: options \: \: are \: \: wrong}[/tex]
[tex]\\[/tex]
[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]
[tex]\small\longrightarrow\sf{−6 (2^2+3) − 2 (1^2 - 2) = \underline{-6(4+3)}}[/tex]
Please help and explain!!!
Answer:
Option A
Step-by-step explanation:
The solution is in the image
What type of construction is illustrated in the figure?
A
The bisection of ∠D
B
A line segment congruent to segment AB
C
An angle congruent to ∠D
D
The bisection of segment BD
Option A is correct. The type of construction that we have here is the bisection of the <D.
What is the bisection of an angle?The bisection of angle can be defined to be the construction of a ray that would help to divide a particular angle into two equal halves.
In this diagram we can see that the angle here is at D. Hence the construction is aimed at dividing this particular angle into 2. Therefore the answer to the question is The bisection of ∠D.
The bisector does the job of creating an equal measure. The given bisector is known to have the midpoint of the segment. It cuts through this angle and creates two different angles that are of the same size.
If we draw the line in that shape, we will be having the division of that angle. From the explanation here, we can see the answer is the first option
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What is the scale factor of the dilation shown ?
Work Shown:
k = scale factor
k = (A'B')/(AB)
k = 8/12
k = (4*2)/(4*3)
k = 2/3
Triangle A'B'C' (image) has side lengths that are 2/3 as long compared to the side lengths of triangle ABC (preimage).
Find the absolute maximum and minimum values of the function, subject to the given constraints. g(x,y)=9x2 6y2; −1≤x≤1 and −1≤y≤7
For function g(x, y) = 9x² + 6y²,
the absolute minimum is 15 and the absolute maximum is 303
For given question,
We have been given a function g(x, y) = 9x² + 6y² subject to the constraint −1≤x≤1 and −1≤y≤7
We need to find the absolute maximum and minimum values of the function.
First we find the partial derivative of function g(x, y) with respect to x.
⇒ [tex]g_x=18x[/tex]
Now, we find the partial derivative of function g(x, y) with respect to x.
⇒ [tex]g_y=12y[/tex]
To find the critical point:
consider [tex]g_x=0[/tex] and [tex]g_y=0[/tex]
⇒ 18x = 0 and 12y = 0
⇒ x = 0 and y = 0
This means, the critical point of function is (0, 0)
We have been given constraints −1 ≤ x ≤ 1 and −1 ≤ y ≤7
Consider g(-1, -1)
⇒ g(-1, -1) = 9(-1)² + 6(-1)²
⇒ g(-1, -1) = 9 + 6
⇒ g(-1, -1) = 15
And g(1, 7)
⇒ g(1, 7) = 9(1)² + 6(7)²
⇒ g(1, 7) = 9 + 294
⇒ g(1, 7) = 303
Therefore, for function g(x, y) = 9x² + 6y²,
the absolute minimum is 15 and the absolute maximum is 303
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Please please please help
In a lottery, the probability of the jackpot being won in any draw is
a What is the probability that the jackpot prize will be won in each of four consecutive draws? 1/60^4
b How many consecutive draws need to be made for there to be a greater than 98% chance that at least
one jackpot prize will have been won?
The probability that the jackpot prize will be won in each of four consecutive draws is (1/60)⁴.
The number of consecutive draws needed will be, n = 233
What is probability?Probability is the likelihood or chance of an event happening or not.
Probability = number of expected outcomes/number of possible outcomes.From the given question, the probability of the jackpot being won in any draw is 1/60.
The probability that the jackpot prize will be won in each of four consecutive draws will be:
1/60 * 1/60 * 1/60 * 1/60 = (1/60)⁴
b. The number of consecutive draws that needs to be made for there to be a greater than 98% chance that at least one jackpot prize will have been won is calculated as follows:
There is a 100% - 98% chance that that none has been won = 2% that none has been won.
Also, the probability of the jackpot not being won in a draw is = 1 1/60 = 59/60
The number of consecutive draws needed will be (59/60)ⁿ ≤ 0.02
Solving for n by taking logarithms of both sides:
n = 233
In conclusion, probability measures chances of an event occurring or not.
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Will has twice as many stamps in his collection as Carlton and Ashley do in their collections combined. If Ashley has 30 stamps and she has a third as many as Carlton has, how many stamps are in Will’s collection?
Taking into account the definition of a system of linear equations, 240 stamps are in Will’s collection.
System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.
Number of stamps that are in Will’s collectionIn this case, a system of linear equations must be proposed taking into account that:
W: Number of stamps that are in Will’s collectionC: Number of stamps that are in Carlton’s collectionA: Number of stamps that are in Ashley’s collectionOn the other hand, you know that:
Ashley has 30 stamps and she has a third as many as Carlton has → A= [tex]\frac{1}{3}[/tex]C → 30= [tex]\frac{1}{3}[/tex]CWill has twice as many stamps in his collection as Carlton and Ashley do in their collections combined. → W= 2(C + A)So, the system of equations to be solved is
[tex]\left \{ {{30=\frac{1}{3}C } \atop {W=2(C+30)}} \right.[/tex]
There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
Solving the first equation:
30= [tex]\frac{1}{3}[/tex]C
30÷[tex]\frac{1}{3}[/tex]= C
90= C
Substituting the value in the second equation:
W= 2(90 + 30)
W= 2×120
W=240
Finally, 240 stamps are in Will’s collection.
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necesito la respuesta, urgente
The value of the function f(x) = ( 8x² - 2x + 4 ) / 2 when x = -3/5 is 101/25.
Hence, f(-3/5) = 101/25.
What is the value of the function at f(-3/5) ?Given the function; f(x) = ( 8x² - 2x + 4 ) / 2
To determine the value of the function when x = -3/5, we simply replace the variable x with -3/5 in the function.
f(x) = ( 8x² - 2x + 4 ) / 2
f(-3/5) = ( 8(-3/5)² - 2(-3/5) + 4 ) / 2
Divide each term by 2
f(-3/5) = 4(-3/5)² - (-3/5) + 2
f(-3/5) = 4(9/25) - (-3/5) + 2
f(-3/5) = 36/25 +3/5 + 2
f(-3/5) = ( 36 + 3×5 + 2×25 ) / 25
f(-3/5) = ( 36 + 15 + 50 ) / 25
f(-3/5) = 101/25
The value of the function f(x) = ( 8x² - 2x + 4 ) / 2 when x = -3/5 is 101/25.
Hence, f(-3/5) = 101/25.
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you spent $14.95 for a new shirt. you now have $12.48. write and solve an equation to find how much money you had before you bought the shirt
Answer:
x - 14.95 = 12.48
x = 27.43
Step-by-step explanation:
Evaluate the integral.
√
S-
5
√x (4+5√x)²
2
dx
Substitute [tex]y=4+5\sqrt x[/tex] and [tex]dy=\frac5{2\sqrt x}\,dx[/tex]. Then the integral is
[tex]\displaystyle \int \frac5{\sqrt x (4+5\sqrt x)^2} \, dx = 2 \int \frac{1}{(4+5\sqrtx)^2} \frac{5}{2\sqrt x} \, dx = 2 \int y^{-2} \, dy[/tex]
By the power rule,
[tex]\displaystyle \int y^{-2} \, dy = -y^{-1} + C[/tex]
so that
[tex]\displaystyle \int \frac5{\sqrt x (4+5\sqrt x)^2} \, dx = \boxed{-\frac2{4+5\sqrt x} + C}[/tex]
The expression x2y - 2xy - 24y can be factored by first factoring out a common factor of y. After the common factor is removed, the remaining factor is a\
The remaining factor of x^2y - 2xy - 24y is (x - 6)(x + 4)
How to determine the remaining factor?The expression is given as:
x^2y - 2xy - 24y
Factor out y from the expression
y(x^2 - 2x - 24)
Expand the equation
y(x^2 + 4x - 6x - 24)
Factorize
y(x - 6)(x + 4)
Hence, the remaining factor of x^2y - 2xy - 24y is (x - 6)(x + 4)
Read more about factored expression at:
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