Answer:
\(|-3|=3\\-3=-3\)
Step-by-step explanation:
The absolute value represents the distance from the zero on the numberline, so \(|-3|\) represents the distance between number -3 and 0, which is 3 units, and \(-3\) is only the point (value) on the numberline.
So, the value of \(|-3|\) is equal to 3, and the value of -3 is -3.
Figure B is a scaled copy of Figure A.
Figure A
14
Figure B
56
16
7
64
28
What is the scale factor from Figure A to Figure B?
Answer:
4
Step-by-step explanation:
Notice each side was increased by 4 times
You can set up a ratio of
\(\frac{new}{old}\)
then reduce or divide
please help thank you
$85.50 divided by six
if c= 1+px^2+3p and b= 2p+6p^2 find an expression that equals 2c-b in standard form
Answer:
if c= 1+px^2+3p and b= 2p+6p^2 find an expression that equals 2c-b in standard form
2p² + 14p + 2
Step-by-step explanation:
Given that;
C= 1+p²+3p
B=2p+6p
The expression that equals to : 2C - -B will be;
2{1+p²+3p} - {-2p-6p}
2+2p²+6p + 2p + 6p
2p² + 6p +2p +6p +2
2p² + 14p + 2
What is the gradient along the same stretch of the Sacramento River (from this the 115 ft interval at mile marker 195, to the mouth of the river at sea level) _______________ft/mi.
without knowing the distance between mile marker 195 and the mouth of the river, we cannot calculate the gradient along the same stretch of the Sacramento River.
The gradient along the same stretch of the Sacramento River can be calculated by finding the change in elevation divided by the distance.
Given that the interval is 115 ft and the distance is from mile marker 195 to the mouth of the river at sea level, we need to determine the total distance in miles.
To do this, we need to know the distance between mile marker 195 and the mouth of the river. Unfortunately, this information is not provided in the question.
Without knowing the specific distance, we cannot accurately calculate the gradient. Therefore, the answer cannot be determined with the information given.
In conclusion, without knowing the distance between mile marker 195 and the mouth of the river, we cannot calculate the gradient along the same stretch of the Sacramento River.
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suppose there are four people in a room, exactly one of whom is a foreign agent. the other three people have been given pairs corresponding to a shamir secret sharing scheme in which any two people can determine the secret. the foreign agent has randomly chosen a pair.
Three of them possess pairs corresponding to a Shamir secret sharing scheme, enabling any two people to determine the secret.
Can any two people determine the secret using the Shamir secret sharing scheme?In this scenario, there are four people in a room. Three of them possess pairs corresponding to a Shamir secret sharing scheme, enabling any two people to determine the secret.
The remaining person is a foreign agent who has chosen a pair randomly. Thus, if any two of the three people with the valid pairs collaborate, they can successfully uncover the secret, as per the properties of the Shamir secret sharing scheme.
The presence of the foreign agent does not affect the security of the scheme unless they collaborate with another person possessing a valid pair.
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Determine the value of x
Answer:
x=10
Step-by-step explanation:
40= 3x+10 (it equals 40 because of vertical angles)
PLEASE HELP AND EXPLAIN HOW YOU GOT THE ANSWER. I WILL MARK YOU BRAINLIEST
Answer:
D. (4,4), (8,8), (-8,4)
Step-by-step explanation:
We have A (2,2), B(4,4) and C (-4,2)
Dilation by factor of 2: (x,y) => (2x,2y)
A (2,2) => A'(4,4)
B(4,4) => B'(8,4)
C (-4,2) => C'(-8,4)
Needed help with this part of the homework. Am i headed in the right direction? Having trouble finding the range as well
Given -
Where b>1
To Find -
a. Which is the graph of f(x) = -bˣ
b. Which is the graph of f(x) = b-ˣ
c. For which graph(s) is the range (-∞, 0)
Step-by-Step Explanation -
a. Since b > 1
So, bˣ will be positive
f(x) = -bˣ will be negative.
So,
The correct Option is B.
b. f(x) = b-ˣ
So, b-ˣ will be positive
Also, in -x will tends to 1
So,
The correct Option is A
c. Range of (-∞, 0)
So,
we can observe the value of y tending to -∞ in graphs B and D.
Final Answer -
a. Option B
b. Option A
c. Options B and D
What is the recursive formula, if the sequence is 4, 7, 10, 13, ...?
O A(n - 4) + 3
O 4 + 3(n-1)
O A(n-1) + 3
Answer:
Step-by-step explanation:
In the arithmetic sequence \(t_1\), \(t_2\), \(t_3\), ..., \(t_n\), \(t_1=23\) and \(t_n= t_{n-1} - 3\) for each n > 1. What is the value of n when \(t_n = -4\)?
A. -1
B. 7
C. 10
D. 14
E. 20
Hide Answer
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_________________
Best Regards,
E.
MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730
Answer:
4 + 3(n-1)
Step-by-step explanation:
Sequences start from n=1,2,3....
In this case
4 + 3(1-1)= 4
4 + 3(2-1) =7
And continue the pattern
9 oranges cost $3.60. How much are 4 oranges?
Answer:
$1.60
Step-by-step explanation:
Set up an equation where you have the total oranges (o) on top and the cost (c) on the bottom. So you will have two fractions equaling each other. So you will have o/c=o/c. Now you just have to replace the variables with what you know. 9 oranges= $3.60, and you want to know how much 4 oranges cost. Since the cost per orange is the same, no matter how many oranges you buy if you divide the amount of oranges by the price you will always get the same number. So replace the variables with the numbers you know and you get,
9/$3.60=4/c
Now to solve an equal fraction problem, simply cross multiply (multiply the two numbers diagonal so 4 and 3.6), and divide (take the multiplied number and divide by the number remaining which will be the number diagonal from the variable) which gives you $1.60 for four oranges.
a popular sports drink can be made by adding 12 grams of powdered drink mix to 23 ounces of water. however, you can make as much or as little of the sports drink as you'd like by varying the amount of drink mix and water so that they remain proportional. write a formula that expresses the amount of water (in ounces), n , needed to make the sports drink using x grams of powdered drink mix.
The formula that expresses the amount of water (in ounces), n , needed to make the sports drink using x grams of powdered drink mix is n=\(\frac{12x}{3}\)
Let n be the amount of water required and x be the amount of mix required to make the drink.
Given, 12 grams of the drink mix is required in 23 ounces of water.
Therefore, n= 12 and x= 23.
We can make any amount of the drink by using different amounts of mix and water. But to do so, we first need to develop a formula that complies with the perfect ratio of the drink.
Now, the ratio of drink mix to that of water is 12:23.
n/x= 12/ 23
So, 23n=12x
Or, n= 12x/ 23
Therefore we can use this formula to express the amount of water (in ounces), n , needed to make the sports drink using x grams of powdered drink mix.
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The ratio of the quantities of salt to baking soda needed to complete a science experiment is 3:7. What is the quantity of salt in grams needed for this experiment, if 420 grams of baking soda is used to complete the experiment?
The quantity of salt in grams needed to complete the experiment is 180 grams.
What are ratios?Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).
What is the quantity of sat needed?Quantity of salt needed = (grams of baking soda x ratio of salt) / ratio of baking soda
(3 x 420) / 7 = 180 grams
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The reliability factor table provides factors for as many as
three computations when planning and evaluating the results of a
PPS sample. Describe in general terms each of these
computations
The three computations covered by the reliability factor table are sample size, index of reliability, and index of precision. Sample size deals with the size of the sample being used in order to achieve a desirable level of reliability.
Index of reliability is used to measure the consistency of results achieved over multiple trials. It does this by calculating the total number of items that contribute significantly to the final result. Finally, the index of precision measures the effect size of the sample, which is determined by comparing the results from the sample with the expected results.
The sample size computation gives the researcher an idea of the number of items that should be included in a sample in order to get the most reliable results. This is done by taking into account a number of factors including the variability of the population, the type of measurements used, and the desired level of accuracy.
The index of reliability is commonly calculated by finding the ratio of the number of items contributing significantly to the total result to the total number of items in the sample. This ratio is then multiplied by 100 in order to get a final score.
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Kristen's financial advisor has given her a list of 8 potential investments and has asked her to select and rank her favorite four. In how many different ways can she do this?
The number of ways in which Kristen can rank her favorite four from 8 using permutations is 1680.
The permutation is a way of finding the number of ways of selecting a set of articles from a larger set of articles, with the order of selection being significant.
If we want to choose r items from n items, where the order of selection is significant, then we can find the number of ways of doing this using the permutation as follows:
nPr = n!/{(n - r)!}.
In the question, we are asked to find the number of ways Kristen can rank her favorite four investments from the 8 potential investments that her financial advisor has given her.
Thus, using permutations, we need to select 4 items from 8 items, with order of selection being significant.
Substituting n = 8, and r = 4 in the formula, we get:
8P4 = 8!/{(8 - 4)!}
= 8!/4!
= 5 * 6 * 7 * 8
= 1680.
Thus, the number of ways in which Kristen can rank her favorite four from 8 using permutations is 1680.
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The angle measurements in the diagram are represented by the following expressions.
\qquad \blueD{\angle A= 5x - 5^\circ}∠A=5x−5
∘
start color #11accd, angle, A, equals, 5, x, minus, 5, degrees, end color #11accd \qquad \greenD{\angle B= 3x + 13^\circ}∠B=3x+13
∘
start color #1fab54, angle, B, equals, 3, x, plus, 13, degrees, end color #1fab54
Answer:
x = 9, ∠ B = 40°
Step-by-step explanation:
∠ A and ∠ B are corresponding angles and congruent, so
5x - 5 = 3x + 13 ( subtract 3x from both sides )
2x - 5 = 13 ( add 5 to both sides )
2x = 18 ( divide both sides by 2 )
x = 9
Then
∠ B = 3x + 13 = 3(9) + 13 = 27 + 13 = 40°
The value of the x is 9 and the measure of the angle B is 40 degrees because two parallel lines are cut by a transversal line the adjacent angle made will be equal.
What are vertically opposite angles?It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.
We have:
The angle measurements in the diagram are represented by the following expressions:
When the two parallel lines are cut by a transversal line the adjacent angle made will be equal:
Angle A = Angle B
5x - 5 = 3x + 13
Solving the above linear equation:
5x - 3x = 5+13
2x = 18
x = 9
The measure of the angle B = 3x + 13
= 3(9) + 13
= 27 + 13
= 40 degrees
Thus, the value of the x is 9 and the measure of the angle B is 40 degrees because two parallel lines are cut by a transversal line the adjacent angle made will be equal.
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Need help with this review question how would I know if they are congruent?
A chord is a line segment joining two points on a circumference. If two different chords share one of their extremes then they form an angle known as an inscribed angle. The other extremes of these chords form an arc that is known as the intercepted arc of the inscribed angle. For example, in the picture you'll notice that chords AD and DB form the angle ADB and its intercepted arc is arcAB. The measure of an inscribed angle is half the aperture of its intercepted arc so we get:
\(\angle ADB=\frac{1}{2}\measuredangle arcAB\)Angle ACB also has arcAB as its intercepted arc. This means that we also have:
\(\begin{gathered} \angle ACB=\frac{1}{2}\measuredangle arcAB=\angle ADB \\ \angle ACB=\angle ADB \end{gathered}\)So angles ACB and ADB are congruent since they have the same measure. So as you can see, if two inscribed angles have the same intercepted arc they are congruent.
Angles CAD and CBD also share the same intercepted arc, arcCD. This means that this angles are also congruent.
ADB and CAD are not congruent because their intercepted arcs (arcAB and arcDC) are not the same. The same happens with BCA and CBA since their intercepted arcs are arcAB and arcBC.
The last pair of angles that we must analyze is the one composed by DEA and CEB. These two angles are formed at the intersection between two line segments. At this type of intersections four angles are formed with consecutive angles being supplementary and opposite angles being congruent. DEA and CEB are opposite angles since they share their vertex but not their sides. Therefore DEA and CEB are congruent.
AnswerThen the correct options are A, C and D.
A multiple-choice test has 5 questions each with 5 possible answers, the probability of guessing all the questions correctly is
In a multiple-choice test that has 5 questions, each with 5 possible answers, the probability of guessing all the questions correctly can be found using the formula:p = (1/5) × (1/5) × (1/5) × (1/5) × (1/5) = 1/3125.
The probability of guessing one question correctly is 1/5 since there are five possible answers. Since there are five questions, we multiply the probability by itself five times.
Therefore, the probability of guessing all the questions correctly is 1/3125, which is approximately 0.00032. This means that the chance of guessing all the questions correctly by random chance is very low.
This indicates that one should have studied for the test rather than relying solely on guesswork.
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Given 3x+y=1
Write the equation in general form Ax+By+C =0
3* -y+=0
-3x +y-1=0
3x-y=-1
QUESTION:- Given 3x+y=1
Write the equation in general form Ax+By+C =0
3x-y+1=0
-3x +y-1=0
3x-y=-1
\(3x + y - 1 = 0 \: \: ✔\)
ANSWER:-
Equation-->\(3x + y = 1 \)
Form of the given equation->
\(Ax + By = C\)
so we need to change the side of the C !
while changing side of C we need to change the sign of C !
\( \bold{ \red{SO :- }}\)
\(3 x + y = 1 \\ 3x + y - 1 = 0\)
FORM OF THE RESULTED EQUATION:-
\(Ax + By + C = 0 \\
A = 3 \\ B = 1 \\ C = - 1\)
in a recently published sociology article about transportation patterns, a sociologist studied whether families rely on their own transportation instead of public transportation. let the mean number of cars owned by a family be μ. if the sociologist wanted to know if families own, on average, more than 3 cars, what are the null and alternative hypotheses?
The null hypothesis is \(H_0:\mu=3\) and the alternative hypothesis is \(H_1:\mu > 3\)
There are two hypothesis considered in a statistical test. They are:
Null hypothesis (\(H_0\))Alternative hypothesis (\(H_1\))Formulation of null and alternative hypothesis are considered as the first step of a statistical procedure. The whole procedure, then, continues on testing whether to accept or reject these hypotheses.
Null Hypothesis is the actual hypothesis which is tested. Alternative hypothesis, as its name suggests, is the hypothesis accepted when the null hypothesis is rejected in the test carried out.
Here the sociologist is carrying out the test on the mean number of cars, \(\mu\).
So to check whether the families own more than 3 cars in average,
the null hypothesis will be ,\(\bold{H_0:\mu=3}\)
and the alternate hypothesis will be, \(\bold{H_1:\mu > 3}\)
So if the null hypothesis is rejected, then there is the possibility for only more than 3 cars in average.
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Point P is located at (−2, 7), and point R is located at (1, 0). Find the y value for the point Q that is located two thirds the distance from point P to point R. 4.9 4.7 2.5 2.3
Answer:
5.1
Step-by-step explanation:
Before we calculate the y value for the point Q that is located two thirds the distance from point P to point R, we need to get the distance of point p from point R using the formula for calculatingf the distance between two points
D = √(x2-x1)²+(y2-y1)²
Given P(−2, 7), and R(1, 0)
RP = √(1-(-2))²+(0-7)²
RP = √3²+(-7)²
RP = √9+49
RP =√58
To get the y value for point Q that is located two thirds the distance from point P to point R, this will give
PQ = y = 2/3 of √58
= 5.1
Answer: I Believe its 2.3
Step-by-step explanation:
P is located at (-2,7)
R is located at (1,0)
Look at the y coordinates
P(-2,7) R(1,0)
7 to 0= distance of 7
multiply 2/3 by 7 = 4.7 (it was originally 4.666666665 but i couldnt find the answer with just 4.6 so i rounded it to 4.7)
Now plug in the info we know:
.y axis = 7 - 4.7 = 2.3
Hope this helped! Im taking the test and ill be back if this is wrong
What is the equation of the line that passes through the points (–12, –8) and (–17, –16)?
Answer:
firstly find the gradient given by the equation
m=y2-y1/x2-x1
in this case x1 is -12,x2 is -17, y1 is -8 and y2 is-16
m=-16+8/-17+12
=-8/-5 or1.6
then use the equation
y-y1=m(x-x1)
y+8=1.6(x+12)
y+8=1.6x+19.2
y=1.6x+11.2
I hope this helps and sorry if it's wrong
How can you apply it triangle congruence to real life situation?
Congruent triangles are also frequently employed in architectural designs, carpet patterns, stepping stone patterns, and geometric art.
The following are the two most typical instances of this: Equilateral triangles are used to make truss bridges, which are built on both sides.
Congruence :
If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. A term used to describe an object and its mirror counterpart is congruence. If two things or shapes superimpose on one another, they are said to be congruent. They are identical in terms of size and shape. Line segments having the same length and angles with the same measure are congruent in the context of geometric figures.
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evaluate the integral by reversing the order of integration. 4 0 12 11ex2 dx dy 3y
To evaluate the integral by reversing the order of integration, we first need to draw the region of integration. From the given limits of integration, we can see that the region is a rectangle with vertices at (0,4), (0,12), (11,4), and (11,12).
Now, we can reverse the order of integration by integrating with respect to y first, and then x. The new limits of integration will be y = 4 to y = 12 and x = 0 to x = 11e^(2y/3).
So, the new integral will be:
∫(0 to 11) ∫(4 to 12) 3y e^(2x/3) dy dx
We can evaluate this integral using integration by parts. Integrating with respect to y gives us:
∫(0 to 11) [3y^2/2 e^(2x/3)] from y = 4 to y = 12
Simplifying this expression gives us:
∫(0 to 11) [36e^(2x/3) - 6e^(8x/3)]/2 dx
Now, integrating with respect to x gives us:
[27e^(2x/3) - 9e^(8x/3)] from x = 0 to x = 11
Substituting these values and simplifying gives us the final answer:
(27e^22/3 - 9e^88/3) - (27 - 9) = 27e^22/3 - 9e^88/3 - 18
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a 25 kgkg air compressor is dragged up a rough incline from r⃗ 1=(1.3ı^ 1.3ȷ^)mr→1=(1.3ı^ 1.3ȷ^)m to r⃗ 2=(8.3ı^ 4.4ȷ^)mr→2=(8.3ı^ 4.4ȷ^)m, where the yy-axis is vertical.
The work done in dragging the air compressor up the incline is 4,168.24 J.
What method is used to calculate work done?To solve this problem, we need to determine the work done in dragging the air compressor up the incline.
First, we need to determine the change in height of the compressor:
Δy = y2 - y1
Δy = 4.4 m - 1.3 m
Δy = 3.1 m
Next, we need to determine the work done against gravity in lifting the compressor:
W_gravity = mgh
W_gravity = (25 kg)(9.81 m/s^2)(3.1 m)
W_gravity = 765.98 J
Finally, we need to determine the work done against friction in dragging the compressor:
W_friction = μmgd
where μ is the coefficient of kinetic friction, g is the acceleration due to gravity, and d is the distance moved.
We can assume that the compressor is moved at a constant speed, so the work done against friction is equal to the work done by the applied force.
To find the applied force, we can use the fact that the net force in the x-direction is zero:
F_applied,x = F_friction,x
F_applied,x = μmgcosθ
where θ is the angle of the incline (measured from the horizontal) and cosθ = (r2 - r1)/d.
d = |r2 - r1| = √[(8.3 m - 1.3 m)² + (4.4 m - 1.3 m)²]
d = 8.24 m
cosθ = (r2 - r1)/d
cosθ = [(8.3 m - 1.3 m)/8.24 m]
cosθ = 0.888
μ = F_friction,x / (mgcosθ)
μ = F_applied,x / (mgcosθ)
μ = (F_net,x - F_gravity,x) / (mgcosθ)
μ = (0 - mg(sinθ)) / (mgcosθ)
μ = -tanθ
where sinθ = (Δy / d) = (3.1 m / 8.24 m) = 0.376.
μ = -tanθ = -(-0.376) = 0.376
F_applied = F_net = F_gravity + F_friction
F_applied = F_gravity + μmg
F_applied = mg(sinθ + μcosθ)
F_applied = (25 kg)(9.81 m/s^2)(0.376 + 0.376(0.888))
F_applied = 412.58 N
W_friction = F_appliedd
W_friction = (412.58 N)(8.24 m)
W_friction = 3,402.26 J
Therefore, the total work done in dragging the compressor up the incline is:
W_total = W_gravity + W_friction
W_total = 765.98 J + 3,402.26 J
W_total = 4,168.24 J
So the work done in dragging the air compressor up the incline is 4,168.24 J.
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this year Benny is 12 years old and his mom is 48 years old what percent of his mom's age is Benny's age
Answer:
25%
Step-by-step explanation:
Let's set up a percent proportion:
12/x = 48/100
To solve for x, we would do:
x = (12*100)/48 = 1200/48 = 25
x = 25%
In my opinion, the easiest way to do this would be to look at this and notice that 12 * 4 =48 so that means 12 is 1/4 of 48 and 1/4 = 25%.
Let me know if you have any questions.
Can you help me solve this!
Hello!
surface area
= 2(6*2) + 2(4*2) + 4*6
= 2*12 + 2*8 + 24
= 24 + 16 + 24
= 64 square inches
Consider the given pseudo code. Write the function T(n) in terms of the number of operations, and then give the asymptotic (big Oh) complexity of the algorithm, show all the work you do. [ write the summation formula and solve it, or use the "Look for pattern"method. a. Matrix Multiplication
The function T(n) in terms of the number of operations is:
T(n) = 2n^3 + 3n^2 + 2n + 1 and the asymptotic complexity of the matrix multiplication algorithm is O(n^3).
To analyze the provided pseudo code for matrix multiplication and determine the function T(n) in terms of the number of operations, we need to examine the code and count the number of operations performed.
The pseudo code for matrix multiplication may look something like this:
```
MatrixMultiplication(A, B):
n = size of matrix A
C = empty matrix of size n x n
for i = 1 to n do:
for j = 1 to n do:
sum = 0
for k = 1 to n do:
sum = sum + A[i][k] * B[k][j]
C[i][j] = sum
return C
```
Let's break down the number of operations step by step:
1. Assigning the size of matrix A to variable n: 1 operation
2. Initializing an empty matrix C of size n x n: n^2 operations (for creating n x n elements)
3. Outer loop: for i = 1 to n
- Incrementing i: n operations
- Inner loop: for j = 1 to n
- Incrementing j: n^2 operations (since it is nested inside the outer loop)
- Initializing sum to 0: n^2 operations
- Innermost loop: for k = 1 to n
- Incrementing k: n^3 operations (since it is nested inside both the outer and inner loops)
- Performing the multiplication and addition: n^3 operations
- Assigning the result to C[i][j]: n^2 operations
- Assigning the value of sum to C[i][j]: n^2 operations
Total operations:
1 + n^2 + n + n^2 + n^3 + n^3 + n^2 + n^2 = 2n^3 + 3n^2 + 2n + 1
Therefore, the function T(n) in terms of the number of operations is:
T(n) = 2n^3 + 3n^2 + 2n + 1
To determine the asymptotic (big O) complexity of the algorithm, we focus on the dominant term as n approaches infinity.
In this case, the dominant term is 2n^3. Hence, the asymptotic complexity of the matrix multiplication algorithm is O(n^3).
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Need help on the level 10 question. Only comment if you know. Please step by step
2xy^2+xy^2+xy-2x
2x(y^2-1)+xy(y+1)
2x(y-1)(y+1)+xy(y+1)
(y+1)(2xy-2x+xy)
(y+1)(3xy-2x)
I divide 3xy^2 into 2xy^2+xy^23xy² + xy - 2x
Take x common from all the terms.= x (3y² + y - 2)
Now, split the middle term of the bracketed portion.= x (3y² + 3y - 2y - 2)
= x {3y (y + 1) - 2 (y + 1)}
= x (y + 1) (3y - 2)
Answer:
\(x (y + 1) (3y - 2)\)
Hope you could understand.
If you have any query , feel free to ask.
Introduction to Probability
Please show all work
Suppose you are taking an exam that only includes multiple choice questions. Each question has four possible choices and only one of them is correct answer per question. Questions are not related to the material you know, so you guess the answer randomly in the order of questions written and independently. The probability that you will answer at most one correct answer among five questions is
The probability of guessing the correct answer for each question is 1/4, while the probability of guessing incorrectly is 3/4.
To calculate the probability of answering at most one correct answer, we need to consider two cases: answering zero correct answers and answering one correct answer.
For the case of answering zero correct answers, the probability can be calculated as (3/4)^5, as there are five independent attempts to answer incorrectly.
For the case of answering one correct answer, we have to consider the probability of guessing the correct answer on one question and incorrectly guessing the rest. Since there are five questions, the probability for this case is 5 * (1/4) * (3/4)^4.
To obtain the probability of answering at most one correct answer, we sum up the probabilities of the two cases:
Probability = (3/4)^5 + 5 * (1/4) * (3/4)^4.
Therefore, by calculating this expression, you can determine the probability of answering at most one correct answer among five questions when guessing randomly.
Learn more about probability here:
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