please help ! which of the following is equal to the rational expression when x ≠ 2 or -3?
Answers
Answer:
A
(x+1)(x-2) / (x-2)(x+3) = (x+1)/(x+3)
The simplification of the given rational expression when x is not equal to 2 or negative 3 is determined as (x + 1)/(x + 3).
Simplification of the expressionThe simplification of the given expression when x is not equal to 2 or negative 3 is determined as follows;
[tex]= \frac{(x + 1)(x -2)}{(x-2)(x + 3)}[/tex]
cancel "x-2" since it is common to numerator and denominator
[tex]= \frac{(x + 1)}{(x + 3)}[/tex]
Thus, the simplification of the given rational expression when x is not equal to 2 or negative 3 is determined as (x + 1)/(x + 3).
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Related Questions
Question 8, 1.2.35-PS
Part 1 of 5
iew an example
HW Score: 44.44%, 4
O Points: 0 of 1
- Scatterplots and Graphs
K
If a ball is thrown into the air at 96 feet per second from the top of a 109-foot-tall building, its height can be modeled by the function S=109+961-162, where S is in feet and t is in seconds.
Complete parts a through e below.
a. Graph this function for t representing 0 to 8 seconds and S representing 0 to 300 feet. Choose the correct graph below.
Answers
The quadratic function in this problem is represented by Graph C.
What is the quadratic function for this problem?The quadratic function for the projectile height after t seconds is given by:
S(t) = 109 + 96t - 16t²
From this, we have that:
Due to the negative coefficient of t², it is a concave down parabola, which remoces option d.The initial height is of 109 feet, which removes option b.The initial velocity is positive, which means that the parabola has increasing height for a while before decaying, which removes option A.Thus, the quadratic function in this problem is represented by Graph C.
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Evaluate the expression 3.8 +0+ y for the given values of y value value of expression -4.3 -1.6 0 5.2 -0.5
Answers
The answers are -0.5, 2.2, 3.8, and 9.0
We need to evaluate the expression 3.8 + 0 + y for the given values of y.
Let x = 3.8 + 0 + y
The values of y are -4.3, -1.6, 0, and 5.2
Let's substitute the value of y in the expression and calculate the values of x.
When y = -4.3, x = 3.8 + 0 + (-4.3) = 3.8 - 4.3 = -0.5When y = -1.6, x = 3.8 + 0 + (-1.6) = 3.8 - 1.6 = 2.2When y = 0, x = 3.8 + 0 + 0 = 3.8When y = 5.2, x = 3.8 + 0 + 5.2 = 3.8 + 5.2 = 9.0Refer to the attached image for the values of the expression corresponding to the values of y.
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Answer:
-0.5, 2.2, 3.8, and 9.0
Step-by-step explanation:
I didn’t understand this question please help and thank u
Answers
Just put the coordinates in the equation and see if it’s correct.
Check out the attached photo
R6000 is deposited into a savings account. Four years later, R7000 is added to the savings. The interest rate for the first three years is 8% per annum compounded annually. Thereafter, the interest rate changes to 9% per annum compounded annually. Calculate the value of the savings at the end of the seventh year.
Answers
Answer:
R 19734.32
Step-by-step explanation:
If an amount P is deposited at R% interest compounded annually for n years, the amount at the end of n years is given by the formula
[tex]P = P(1 + r)^t[/tex]
r = R/100
Note
Interest rate 8% = 8/100 =0.08 for computation
Interest rate 9% = 8/100 =0.09 for computation
Since the interest rate changes after 3 years, the first thing to do is to find out how much the value is after 3 years
[tex]V(3 years) = 6000(1 + 0.08)^3[/tex] = 6000 x1.08³ = 6000 x 1.259712 = 7558.27
After 3rd year interest changes to 9%(0..09) but an additional amount is deposited
Let's find the value after the 4th year at 9% compounded annually using the general formula with r = 0.09 and t =1
V (after 4th year) = 7558.27(1.09)¹ = 7558.27 x 1.09 = 8238.51
We are depositing 7000 at the end of the 4th year so the principal becomes 8238.51 + 7000 = 15,238.51
This new amount accrues interest at 9% for 3 more years (7-4)
So value of savings at end of 7th year is
V = 15238.51(1+0.09)³ = 15238.51 x 1.259712 = 19734.32
Answer:
R19734.32
Step-by-step explanation:
Annual Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+r\right)^{t} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)t = time (in years)Years 1-3Given:
P = R6000r = 8% = 0.08t = 3Substitute the given values into the formula and solve for A:
[tex]\implies \sf A=6000(1+0.08)^3[/tex]
[tex]\implies \sf A=6000(1.08)^3[/tex]
[tex]\implies \sf A=6000(1.259712)[/tex]
[tex]\implies \sf A=7558.272[/tex]
Therefore, the amount in the account after 3 years was R7558.272.
Year 4The interest rate changed to 9%.
Given:
P = R7558.272r = 9% = 0.09t = 1Substitute the given values into the formula and solve for A:
[tex]\implies \sf A=7558.272(1+0.09)^1[/tex]
[tex]\implies \sf A=7558.272(1.09)[/tex]
[tex]\implies \sf A=8238.51648[/tex]
Therefore, the value of savings at the end of the 4th year was R8238.51648.
Years 5-7After four years, R7000 was added to the account.
Given:
P = R8238.21648 + R7000 = R15238.21648r = 9% = 0.09t = 3Substitute the given values into the formula and solve for A:
[tex]\implies \sf A=15238.21648(1+0.09)^3[/tex]
[tex]\implies \sf A=15238.21648(1.09)^3[/tex]
[tex]\implies \sf A=15238.21648(1.295029)[/tex]
[tex]\implies \sf A=19734.3207...[/tex]
Therefore, the value of the savings at the end of the seventh year is R19734.32.
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1)
**
16 yd
A
8 yd
12 yd What is the area of the shape
Answers
Answer:
35 yd
Step-by-step explanation:
1. The table represents a quadratic function. Write an equation of the function in standard form. X f(x) -4 -3 -2 0 0 1 2 0
Answers
An equation of the function in standard form is equal to -x²/4 + 1 = 0.
What is a quadratic function?A quadratic function can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph.
In Mathematics, the standard form of a quadratic equation is given by;
ax² + bx + c = 0
y = f(x) = ax² + bx + c
Next, we would formulate a system of equations from the data contained in the table above:
-3 = a(-4)² + b(-4) + c ⇒ -3 = 16a - 4b + c .......equation 1.
0 = a(-2)² + b(-2) + c ⇒ 0 = 4a - 2b + c .......equation 2.
1 = a(0)² + b(0) + c ⇒ 1 = c .......equation 3.
Substituting the value of c into eqn. 1 and eqn. 2, we have:
-4 = 16a - 4b .......equation 4.
-1 = 4a - 2b .......equation 5.
Multiplying eqn. 5 by 2 and solving simultaneously, we have:
-4 = 16a - 4b
-2 = 8a - 4b
-2 = 8a
a = -2/8
a = -1/4
For the value of b, we have:
-1 = 4a - 2b
-1 = 4(-1/4) - 2b
-1 = -1 - 2b
2b = 0
b = 0
Substituting the values of a, b and c into the standard form of a quadratic equation:
ax² + bx + c = 0
-1/4x² + (0)x + 1 = 0
-x²/4 + 1 = 0
Check:
When x = 2, we have:
-x²/4 + 1 = 0
-2²/4 + 1 = 0
-4/4 + 1 = 0
-1 + 1 = 0
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If f(x)=3x-2 determine the value of y for each x value -4, 2, 3
Answers
Answer:
Step-by-step explanation:
y = f(x) = 3x -2
When x = -4,
y = 3(-4) -2 = -12-2 = -14
When x = 2,
y = 3(2) -2 = 6-2 = 4
When x = 3,
y = 3(3) -2 = 9-2 = 7
The ratio of the number of miles run to the number of miles biked is equivalent for each row in the table. What is the relationship between distances biked and distances run?
Answers
The relationship between distances biked and distances run is
D(bike) = 2 × D(run)
Here, we have been shown that when distance run is, lets say x then distance run is 2x
When distance run is 2 then distance biked is 4, twice as distance run.
Again in distance run 3[tex]\frac{1}{2}[/tex], distance biked is 7, so this proves that
D(bike) = 2 × D(run)
What is the importance of distance?The measurement of distance between two objects or points can be quantitative or occasionally qualitative. Distance in physics or common language can refer to a physical length or an assumption based on other factors (e.g. "two counties over").
Since spatial thinking is a rich source of conceptual metaphors in human thought, the term is also frequently used metaphorically to denote a measure of the degree of separation or the statistical distance between two similar objects (such as edit distance between strings of text or statistical distance between probability distributions) (as exemplified by distance between people in a social network).
A metric space is a mathematical concept that is used to define the majority of these conceptions of distance, both literal and figurative.
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Ahmed wants to divide BD 5500 in the ratio 2:4:5 for 3 charity organizations. Can you help him to divide the money?
Answers
We need to know about ratio for solving the problem. Ahmed has to divide the money as 1000, 2000 and 2500.
In simple words ratio indicates how many times one number contains other. With the help of this division we need to assume a number x which is held 2 times in first part, 4 times in second part and 5 times in third part of the total money that Ahmed wants to divide. We can find the ratio of a quantity to another by dividing one quantity by the other and cancelling the common factors. For this question we have a total amount of money 5500 which we need to divide in ratio 2:4:5 in other words we can say that the three parts are 2x,4x and 5x, these three parts will add up to be 5500. So we can write
2x+4x+5x=5500
11x=5500
x=500
The three parts of the money will be 2x500=1000, 4x500=2000 and 5x500=2500
Therefore we found using the concept of ratio that Ahmed needs to divide his money as 1000,2000 and 2500.
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Manuel made $20,000 in taxable income last year.
Suppose the income tax rate is 10% for the first $7000 plus 16% for the amount over $7000.
How much must Manuel pay in income tax for last year?
$0
Check
X
S
Answers
Answer:
$2780
Step-by-step explanation:
Given an income tax of 10% of the first $7000 and 16% of all after that, you want the tax on $20,000.
Piece-wise functionManuel's income is more than $7000, so the tax is computed in two parts.
First $7000
The tax on the first $7000 of income is 10%:
tax = $7000 × 0.10 = $700
Amount Over $7000
The amount over $7000 is ...
$20,000 -7,000 = $13,000
The tax on that amount is 16%:
tax = $13,000 × 0.16 = $2080
Total tax due
The tax Manuel must pay is the total of these two amounts:
$700 +2080 = $2780
Manuel must pay $2780 in income tax for last year.
Find all values of $x$ that solves this system.
\begin{align*}
x^2 - 9y^2 &= 72\\
x + 3y &= 9
\end{align*}
Answers
All the values of x that solve the given system of equations are as follows:
x = 17/2.
What is a system of equations?A system of equations is when multiple variables are related by equations, which are solved to find the values of each variable. Usually, these relations are linear, but they may also be quadratic, as is the case in this problem.
For this problem, we are given two equations, as follows:
x² - 9y² = 72.x + 3y = 9.From the second equation, we have that:
x = 9 - 3y.
Replacing in the first, we have that:
(9 - 3y)² - 9y² = 72.
9y² - 54y + 81 = 72.
54y = 9.
y = 9/54
y = 1/6, as 9/9 = 1, 54/9 = 6.
Hence the solution for x of the system of equations is found by replacement, as follows:
x = 9 - 3y = 9 - 3/6 = 9 - 1/2 = 18/2 - 1/2 = 17/2.
The solution is x = 17/2.
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The mean monthly rent of students at Oxnard University is $910 with a standard deviation of $216. (a) John’s rent is $1,355. What is his standardized z-score? (Round your answer to 3 decimal places.)
Answers
Answer:
maybe if you learn you will know
Step-by-step explanation:
rewrite this expression using a positive exponent
[tex]\frac{1}{2^{-6} }[/tex]
Answers
Answer:
1/5 needs to be 20 words long
Heinrich must buy at least 100 shares of stock for his portfolio. The shares he buys will be from Stock X, which costs $22 per share and Stock Y, which costs $35 per share. His budget for buying stock is no more than $4,500. He must buy at least 20 shares of Stock X and 15 shares of Stock Y. Which of the following represents the situation described if a is the number of shares of Stock X purchased and b is the number of shares of Stock Y purchased?
Answers
The option which represents the situation described if a is the number of shares of Stock X purchased and b is the number of shares of Stock Y purchased is:
D. 22a + 35b ≤ 4,500
a + b ≥ 100
a ≥ 20
b ≥ 15
What does at least and no more than mean in this instance?
At least is interpreted in inequalities as greater than or equals to whereas "no more than" implies that it cannot be greater, hence, can be less than or equals to, as a result, the following relationships are determined:
a≥20(the least number of X shares is a, which is 20)
b≥ 15(the least number of Y shares is a, which is 15)
total amount spent on X=22*a=22a
total amount spent on Y=35*b=35b
maximum amount to invest=4500(less than or equals to)
22a+35b≤ 4500
sum of X and Y shares altogether(least)=100
a+b≥100
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Full question:
Heinrich must buy at least 100 shares of stock for his portfolio. The shares he buys will be from Stock X, which costs $22 per share and Stock Y, which costs $35 per share. His budget for buying stock is no more than $4,500. He must buy at least 20 shares of Stock X and 15 shares of Stock Y. Which of the following represents the situation described if a is the number of shares of Stock X purchased and b is the number of shares of Stock Y purchased?
A. 22a + 35b ≤ 4,500
a + b ≥ 100
a ≤ 20
b ≤ 15
B. 22a + 35b ≤ 4,500
a + b ≤ 100
a ≤ 20
b ≤ 15
C. 22a + 35b ≤ 4,500
a + b ≤ 100
a ≥ 20
b ≥ 15
D. 22a + 35b ≤ 4,500
a + b ≥ 100
a ≥ 20
b ≥ 15
The population of a small town was 12,500 in 1995. Since then, the population has
increased at a rate of 4.5% each year.
Write an exponential function to model the situation
Answers
Answer:
Step-by-step explanation:
the answer is 6847 if anyone solves it
5 people can claim joint ownership of an item and intend to divide it by the Method of Sealed Bids. The winner offers a bid of $72,000 how much will that bidder need to put into a kitty for the other bidders to be compensated?
Answers
The amount that the bidder needs to put into a kitty for the other bidders to be compensated will be $57600.
How to calculate the value?It should be noted that 5 people can claim joint ownership of an item and intend to divide it by the Method of Sealed Bids and the winner offers a bid of $72,000.
Therefore, the fair share will be:
= Bids / Number of people
= 72000 / 5
= 14400
Therefore, the amount that the bidder needs to put into a kitty for the other bidders to be compensated will be:
= $72000 - $14400
= $57600
Therefore, the amount that the bidder needs to put into a kitty for the other bidders to be compensated will be $57600.
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One employee have a computer store is Peter base salary of $2000 a month plus a 2% commission on all sales over $6000 during the month how much Muslim please tell in one month on a total of $5000 for the month
Answers
The employee must make a sale of $ 1,56,000 to get a total salary of $ 5000 with the commission rate as 2 %.
The basic salary of the employee = $ 2000
Now he wants to earn $ 5000.
That means he has to earn 4 500 - $ 2000 = $ 3000 from the sales commission that he gets.
Sales commission is 2 %.
Let the sales above $ 6000 be x
2 % x = 3000
2 / 100 x = 3000
2 x = 3,00,000
x = 1,50,000
Total sales = $ 6000 + $ 1,50,000 = $ 1,56,000
Therefore, the employee must make a sale of $ 1,56,000 to get a total salary of $ 5000 with the commission rate as 2 %.
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What is the y-intercept of f(x) =
700- (2)* ?
A. (0, 1)
B. (1,0)
C. (0,0)
(14)
D.
Answers
Answer:
its A
Step-by-step explanation:
-87.55% rounded to one decimal place
Answers
Answer:
-8756 %
Step-by-step explanation:
Because 5 is a strong number
How tall is the flag pole (please give explanation too)
Answers
Answer:
22 3/4 ft
Step-by-step explanation:
The diagram seems to show a 6 1/2 ft person casting a 9 ft shadow at the same time a flagpole is casting a 31 1/2 ft shadow. You want the height of the flagpole.
ProportionShadow lengths are presumed proportional to the height of the object making them. This means ...
h/(31 1/2) = (6 1/2)/9 . . . . . all lengths in feet
Multiplying by 31 1/2, we get ...
h = (31 1/2)(6 1/2)/9 = (819/4)/9 = 91/4
h = 22 3/4 . . . . ft
The flagpole is 22 3/4 feet tall.
A solid lies between planes perpendicular to the y-axis at [tex]y=0[/tex] and [tex]y=4[/tex]. The cross-sections perpendicular to the y-axis are circular disks with diameters running from the y-axis to the parabola [tex]x=\sqrt{10} y^2[/tex]. Find the volume of the solid.
Answers
For any given [tex]0\le y\le4[/tex], a cross section in that plane is a circle whose diameter is [tex]x=\sqrt{10}\,y^2[/tex] with thickness [tex]\Delta y[/tex]. Such a cross section contributes a volume of [tex]\pi \left(\frac x2\right)^2 \, \Delta y = \frac{5\pi}2 y^4 \, \Delta y[/tex].
As [tex]\Delta y\to0[/tex] and the number of cross sectional cylindrical disks increases without bound, the infinite sum of their volumes converge to the volume of the solid, given by the definite integral
[tex]\displaystyle \frac{5\pi}2 \int_0^4 y^4 \, dy = \frac{5\pi}2 \cdot \frac{4^5}5 = \boxed{512\pi}[/tex]
Use properties of operations to add (−3) and (−17) IF RIGHT I WILL GIVE BRAINIEST
a b c or d
A: −20
B: 20
C: −14
D: 14
Answers
Answer:
14
Step-by-step explanation:
because if you subract -17 it will become a postive 17 and 17-3 is 14
y=(-3)-(-17)y=(-3)+17y=14Hope this helps!
If you have anyother questions feel free to ask!
Right angle ABC is taken by a dilation with center P and scale factor 1/2 to angle A'B'C'. What is the measure of angle A'B'C'?
Answers
Answer: 90 degrees
Step-by-step explanation:
Dilations preserve angle measure.
Find the weighted average of the points on the line.
Answers
The weighted average of the points on the line is 3/5 after applying the concept of the weighted average.
What is average?It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.
It is given that:
The number line is shown in the picture:
The number line can be defined as the representation of the numbers on a straight line that goes infinitely on both sides.
From the number line:
The weighted average = [2(-5) + 8(2)]/(2 + 8)
The weighted average = [-10 + 16]/(10)
The weighted average = [6]/(10)
The weighted average = 3/5
Thus, the weighted average of the points on the line is 3/5 after applying the concept of the weighted average.
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I need help asap please!
Answers
Answer:
5x+10
Step-by-step explanation:
[tex](f \circ g)(x)=f(g(x)) \\ \\ =f(-5x-6) \\ \\ =-(-5x-6)+4 \\ \\ =5x+6+4 \\ \\ =5x+10[/tex]
Find the midpoint of points A(-1,-7) and B (3,-4) graphically
Answers
(0,0) because that is the center
Simon measures the length of an insect that is 2.5 inches long for a science
project. He needs to record his data in centimeters. How long is the insect
in centimeters?
Answers
If the length of the insect is 2.5 inches long, then the length of the insect in centimeter is 6.35 centimeter
Given,
The length of the insect = 2.5 inches
Convert inches to centimeter
We know,
1 inches = 2.54 centimeter
2.5 inches = 2.54× 2.5
=6.35 centimeter
Hence, if the length of the insect is 2.5 inches long, then the length of the insect in centimeter is 6.35 centimeter
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Annenbaum Corporation uses the weighted-average method in its process costing system. This month, the beginning inventory in the first processing department consisted of 400 units. The costs and percentage completion of these units in beginning inventory were:
Answers
1. The cost per equivalent unit for materials for the month in the first processing department of Annenbaum Corporation is $20.50.
2. The cost per equivalent unit for conversion costs for the month in the first processing department of Annenbaum Corporation is $34.208.
How is the cost per equivalent unit determined?The cost per equivalent unit is the quotient of the total costs to be accounted for divided by total equivalent units of production.
The equivalent units of production are a mathematical equivalent of completed units based on their degrees of completion.
Data and Calculations:Beginning work in process:
Materials costs = $5,700 65%
Conversion costs = $6,800 45%
Started units = 6,500 units
Transferred out units = 5,900 units
Ending inventory:
Material costs = 50%
Conversion costs = 35%
Costs incurred during the period:
Materials costs......... $125,500
Conversion costs...... $207,000
Physical units to be accounted for:Beginning inventory = 400 units
Started during period = 6,500 units
Total units processed = 6,900 units
Units transferred out = 5,900 units
Ending inventory = 1,000 units
Equivalent Units (Weighted Average):Physical Units Material Conversion
Transferred out 5,900 5,900 (100%) 5,900 (100%)
Ending inventory 1,000 500 (50%) 350 (35%)
Total equivalent units 6,400 units 6,250 units
Total Production Costs:Material Conversion
Beginning WIP $5,700 $6,800
Costs for the period 125,500 207,000
Total production costs $131,200 $213,800
Total equivalent units 6,400 units 6,250 units
Cost per equivalent unit $20.50 $34.208 ($213,800/6,250)
Thus, the cost per equivalent unit of materials is $20.50, while it is $34.208 for conversion costs.
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Question Completion:Cost Percent Complete Materials costs......... $5,700 65% Conversion costs...... $6,800 45% A total of 6,500 units were started and 5,900 units were transferred to the second processing department during the month. The following costs were incurred in the first processing department during the month: Materials costs......... $125,500 Conversion costs...... $207,000 The ending inventory was 50% complete with respect to materials and 35% complete with respect to conversion costs. Required: 1. What's the cost per equivalent unit for materials for the month in the first processing department? 2. What's the cost per equivalent unit for conversion costs for the month in the first processing department?
Solve the system by back substitution.
-4x - 8y - 2z - 6w = 5
3y + 18z + 6w = 24
z + w =2
-2w = -6
Solution should be set like {( _ , _ , _ , _ )}
Answers
The values of all the variables are:
w = -3z = 5y = -16x = 33 approxWhat are equations?A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.Given equations:
-4x - 8y - 2z - 6w = 53y + 18z + 6w = 24z + w =2-2w = -6To find the values of x, y, w, and z:
-2w = -6w = -6/2w = -3Substitute (w = -3) in z + w = 2:
z + w = 2z -3 = 2z = 2 + 3z = 5Substitute (w = -3) and (z = 5) in 3y + 18z + 6w = 24:
3y + 18z + 6w = 243y + 18(5) + 6(-3) = 243y + 90 - 18 = 243y + 72 = 243y = 24 - 723y = - 48y = - 16Substitute (y = - 16), (w = -3) and (z = 5) in -4x - 8y - 2z - 6w = 5
-4x - 8y - 2z - 6w = 5-4x - 8(-16) - 2(5) - 6(-3) = 5-4x + 128 - 10 + 18 = 5-4x + 118 + 18 = 5-4x + 136 = 5-4x = 5 - 136-4x = - 131x = 131/4x = 32.75Rounding off: x = 33Therefore, the values of all the variables are:
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Amy has a box containing 6 white, 4 red, and 8 black marbles. She picks a marble randomly. It is red. The second time, she picks à white marble. In the third attempt, Amy picks a white marble again. Arny has not replaced the marbles she picked.
Answers
When Amy picks a black marble in the fourth attempt, the probability that in the fifth attempt she will pick a red or a black marble is 0.7143.
How to calculate the probability?It should be noted that after the 3rd pick we have: 4 white, 3 red and 8 black marbles.
The probability that the 4th marble is black is:
P ( Black ) = 8 / 15 = 0.5333
After the 4th pick we have: 4 white, 3 red and 7 black marbles.
P ( Red or Black ) = 10 / 14 = 5 / 7 = 0.7143.
Therefore, the probability is 0.7143.
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Amy has a box containing 6 white, 4 red, and 8 black marbles. She picks a marble randomly. It is red. The second time, she picks a white marble. In the third attempt, Amy picks a white marble again. Amy has not replaced the marbles she picked. The probability that the fourth marble Amy picks is black is . If Amy picks a black marble in the fourth attempt, the probability that in the fifth attempt she will pick a red or a black marble is____.