Answer:
(x^3+2x-1) * (x^4-x^3+3)
Step-by-step explanation:
To simplify this expression, we can multiply each term in the first expression by each term in the second expression and combine like terms:
(x^3)(x^4) + (x^3)(-x^3) + (x^3)(3) + (2x)(x^4) + (2x)(-x^3) + (2x)(3) + (-1)(x^4) + (-1)(-x^3) + (-1)*(3)
Simplifying further:
x^7 - x^6 + 3x^3 + 2x^5 - 2x^4 + 6x - x^4 + x^3 - 3
Combining like terms:
x^7 - x^6 + 2x^5 - 3x^4 + 4x^3 + 6x - 3
Therefore, the expression representing the product of (x^3+2x-1) and (x^4-x^3+3) is x^7 - x^6 + 2x^5 - 3x^4 + 4x^3 + 6x - 3.
If P= (4,2) Find: RX=3 (P)
Answer: 2,2
Step-by-step explanation:
trust me
Movimiento en linea recta
El movimiento en línea recta se refiere al desplazamiento de un objeto en una trayectoria rectilínea, es decir, sin cambios de dirección.
En este tipo de movimiento, la velocidad y la aceleración del objeto pueden variar, pero su dirección se mantiene constante a lo largo del recorrido.
El movimiento en línea recta puede ser uniforme o no uniforme. En el caso del movimiento uniforme, la velocidad del objeto es constante, lo que implica que el desplazamiento realizado en intervalos iguales de tiempo es también constante.
Por otro lado, en el movimiento no uniforme, la velocidad cambia a lo largo del tiempo, resultando en diferentes desplazamientos en intervalos de tiempo iguales.
La descripción matemática del movimiento en línea recta se basa en conceptos como la posición, la velocidad y la aceleración. La posición se refiere a la ubicación del objeto en relación a un punto de referencia, la velocidad representa la tasa de cambio de la posición y la aceleración indica la tasa de cambio de la velocidad.
El estudio del movimiento en línea recta es fundamental en la física y tiene aplicaciones en diversas áreas, como la mecánica, la cinemática, la dinámica y la física de partículas.
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Given that √x + √y=138 and x-y=1656, find x.
The value of x is 5625 when √x + √y=138 and x-y=1656.
To solve for x using the given equations, we will use the method of substitution. Let's go through the steps:
Start with the equation √x + √y = 138.
We want to express y in terms of x, so solve for y in terms of x by isolating √y:
√y = 138 - √x
Square both sides of the equation to eliminate the square root:
(√y)² = (138 - √x)²
y = (138 - √x)²
Now, substitute the expression for y in the second equation x - y = 1656:
x - (138 - √x)² = 1656
Expand the squared term:
x - (138² - 2 * 138 * √x + (√x)²) = 1656
Simplify the equation further:
x - (19044 - 276 * √x + x) = 1656
Combine like terms and rearrange the equation:
-19044 + 276 * √x = 1656
Move the constant term to the other side:
276 * √x = 20700
Divide both sides of the equation by 276 to solve for √x:
√x = 20700 / 276
√x = 75
Square both sides to solve for x:
x = (√x)²
x = 75²
x = 5625
Therefore, the value of x is 5625.
By substituting this value of x back into the original equations, we can verify that √x + √y = 138 and x - y = 1656 hold true.
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Para tener una sucesión es imprescindible que los números que lo forman :
A: sean infinitos
B: tengan una ley de formación C:estén ordenados
For a collection of numbers to be considered a sequence, it is essential that they have a law of formation, are ordered in a specific manner, and can be either finite or infinite.
B: They have a law of formation:
A sequence is a set of numbers arranged in a specific order according to a rule or pattern. The numbers in a sequence are not random but follow a specific law of formation.
This law can be a mathematical formula, a recursive relationship, or any other systematic pattern that determines the values of the sequence. Without a well-defined law of formation, a collection of numbers cannot be considered a sequence.
C: They are ordered:
In a sequence, the numbers are arranged in a specific order or sequence. The order of the numbers is crucial and defines the pattern and structure of the sequence.
Each number in the sequence has a unique position or index that determines its place in the sequence. The order of the numbers allows us to identify the next number or predict the pattern of the sequence. Without the concept of order, the numbers would simply be a set of unrelated elements and not a sequence.
A: They may or may not be infinite:
Sequences can be finite or infinite. A finite sequence has a specific number of terms, and once the pattern or rule is established, the sequence ends.
On the other hand, an infinite sequence continues indefinitely, and its terms extend infinitely in one direction or both directions. Whether a sequence is finite or infinite depends on the context and the specific rule or pattern that governs its formation.
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Note: the translated question is:
To have a sequence it is essential that the numbers that form it:
A: be infinite
B: they have a law of formation C: they are ordered
The radius of a circle is 3 meters. What is the area of a sector bounded by a 90° arc?
Give the exact answer in simplest form.
Answer:
(90°/360°)π(3^2) = (1/4)(9π) = 9π/4 m²
22. Ms. Hernandez has $150 to spend on parking and admission to the zoo. The parking will cost $3, and
admission tickets will cost $10.40 per person, including tax. Write and solve an equation that can be
used to determine the number of people that she can bring to the zoo, including herself.
SHOW ALL WORK
23.A car travels 50+ miles in of an hour. What is the average speed, in miles per hour, of the car?
SHOW ALL WORK
Answer:
Step-by-step explanation:
Let's represent the number of people that Ms. Hernandez can bring to the zoo as "x". Each person will require an admission ticket, which costs $10.40 per person. Additionally, there is a parking fee of $3.
The total cost of admission tickets and parking is given as $150. We can set up the equation as follows:
10.40x + 3 = 150
To solve for x, we need to isolate the variable:
10.40x = 150 - 3
10.40x = 147
Now, divide both sides of the equation by 10.40 to solve for x:
x = 147 / 10.40
Using a calculator, we find:
x ≈ 14.13
Since we can't have a fractional number of people, we need to round down to the nearest whole number since we can't bring a fraction of a person. Therefore, Ms. Hernandez can bring 14 people to the zoo, including herself.
The average speed of a car is calculated by dividing the total distance traveled by the total time taken. In this case, the car travels 50+ miles in "of an hour".
To calculate the average speed in miles per hour, we need to determine the value of "of an hour". If the value is given as a fraction, we need to convert it to a decimal.
Assuming "of an hour" is 1/2 (0.5), the average speed can be calculated as:
Average speed = Total distance / Total time
Average speed = 50+ miles / (1/2) hour
To divide by a fraction, we can multiply by its reciprocal:
Average speed = 50+ miles * (2/1) hour
Average speed = 100+ miles per hour
Therefore, the average speed of the car is 100+ miles per hour.
Complete the following number sequence. 2, 4, 7, __, 16, __, 29, __
The completed sequence would then be: 2, 4, 7, 9, 16, 19, 29.
To complete the given number sequence, let's analyze the pattern and identify the missing terms.
Looking at the given sequence 2, 4, 7, __, 16, __, 29, __, we can observe the following pattern:
The difference between consecutive terms in the sequence is increasing by 1. In other words, the sequence is formed by adding 2 to the previous term, then adding 3, then adding 4, and so on.
Using this pattern, we can determine the missing terms as follows:
To obtain the third term, we add 2 to the second term:
7 + 2 = 9
To find the fifth term, we add 3 to the fourth term:
16 + 3 = 19
To determine the seventh term, we add 4 to the sixth term:
__ + 4 = 23
Therefore, the missing terms in the sequence are 9, 19, and 23.
By identifying the pattern of increasing differences, we can extend the sequence and fill in the missing terms accordingly.
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Triangle ABC with vertices at A(4, 3), B(3, −2), C(−3, 1) is dilated using a scale factor of 1.5 to create triangle A′B′C′. Determine the vertex of point A′.
The vertex of point A' in the dilated triangle A'B'C' is (6, 4.5).
1. Start by calculating the distance between the vertices of the original triangle ABC:
- Distance between A(4, 3) and B(3, -2):
Δx = 3 - 4 = -1
Δy = -2 - 3 = -5
Distance = √((-[tex]1)^2[/tex] + (-[tex]5)^2[/tex]) = √26
- Distance between B(3, -2) and C(-3, 1):
Δx = -3 - 3 = -6
Δy = 1 - (-2) = 3
Distance = √((-6)² + 3²) = √45 = 3√5
- Distance between C(-3, 1) and A(4, 3):
Δx = 4 - (-3) = 7
Δy = 3 - 1 = 2
Distance = √(7² + 2²) = √53
2. Apply the scale factor of 1.5 to the distances calculated above:
- Distance between A' and B' = 1.5 * √26
- Distance between B' and C' = 1.5 * 3√5
- Distance between C' and A' = 1.5 * √53
3. Determine the coordinates of A' by using the distance formula and the given coordinates of A(4, 3):
- A' is located Δx units horizontally and Δy units vertically from A.
- Δx = 1.5 * (-1) = -1.5
- Δy = 1.5 * (-5) = -7.5
- Coordinates of A':
x-coordinate: 4 + (-1.5) = 2.5
y-coordinate: 3 + (-7.5) = -4.5
4. Thus, the vertex of point A' in the dilated triangle A'B'C' is (2.5, -4.5).
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Evalute 3n² - 8n - 9, given n(n - 3) = 10.
Answer:
19 or 26
Step-by-step explanation:
You want the value of 3n² -8n -9, given that n(n -3) = 10.
Values of nWe recognize that 10 = 5·2 and that these factors differ by 3. This means n(n -3) = 10 is equivalent to saying n ∈ {-2, 5}.
Expression in nThe value of 3n² -8n -9 will be one of ...
(3n -8)n -9 = (3(-2) -8)(-2) -9 = (-14)(-2) -9 = 19 . . . . for n = -2
or
(3(5) -8)(5) -9 = (7)(5) -9 = 26 . . . . . . . for n = 5
The expression 3n² -8n -9 will be either 19 or 26.
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I need help with a question
The function for which f(x) is equal to f⁻¹(x) is: C. [tex]f(x) = \frac{x+1}{x-1}[/tex]
What is an inverse function?In this exercise, you are required to determine the inverse of the function f(x) with an equivalent inverse function f⁻¹(x). This ultimately implies that, we would have to swap (interchange) both the independent value (x-value) and dependent value (y-value) as follows;
[tex]f(x) = y = \frac{x+6}{x-6} \\\\x=\frac{y+6}{y-6}[/tex]
x(y - 6) = y + 6
y = xy - 6x - 6
f⁻¹(x) = (-6x - 6)/(x - 1) ⇒ Not equal.
Option B.
[tex]f(x) = y = \frac{x+2}{x-2} \\\\x=\frac{y+2}{y-2}[/tex]
x(y - 2) = y + 2
y = xy - 2x - 2
f⁻¹(x) = (-2x - 2)/(x - 1) ⇒ Not equal.
Option C.
[tex]f(x) = y = \frac{x+1}{x-1} \\\\x=\frac{y+1}{y-1}[/tex]
x(y - 1) = y + 1
y - xy = x + 1
f⁻¹(x) = (x + 1)/(x - 1) ⇒ equal.
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Given the circle below with tangent NO and
secant QPO. If NO = 18 and Q0 = 27, find
the length of PO. Round to the nearest tenth if necessary.
Answer:
PO = 12
Step-by-step explanation:
given a tangent and a secant from an external point to the circle then
the product of the measures of the secant's external part and the entire secant is equal to the square of the measure of the tangent , that is
OP × OQ = NO²
OP × 27 = 18² = 324 ( divide both sides by 27 )
OP = 12
find the ratio for cos
The value of cos E in the triangle is √2/2
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. Trigonometric ratio is only applied in right triangles.
Some of the trigonometric functions are ;
sinθ = opp/hyp
cosθ = adj/hyp
tanθ = opp/adj
In the triangle taking reference from angle E, 5 is the opposite and 5 is the adjascent and 5√2 is the hypotenuse.
Therefore;
cos E = 5/5√2
cos E = 1/√2
rationalizing the value;
cos E = √2/2
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Question 23 of 41
What is the name of the Platonic solid shown below?
A. Octahedron
B. Dodecahedron
C. Hexahedron
D. Icosahedron
Answer:
That Platonic solid is a dodecahedron.
B is the correct answer.
Percents - Modeling Uncategorized Problems
The Nature of Mathematics: page 312 # 1-5, 29, 31, 35, 47 and 54; page 319-320 # 4, 9, 23
In Problems 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, and 21, change the
given form into the two missing forms.
Textbook-
1. Fraction
3. Fraction
5. Fraction
1/3
Write each ront
Decimal
0.75
Decimal
Decimal
Percent
Percent
40%
Percent
2.
Fraction
4. Fraction
Decimal
Decimal
Percent
0.02
Percent
100%
Answer:
Step-by-step explanation:
Converting between Fraction, Decimal, and Percent:
Fraction to Decimal: Divide the numerator by the denominator. The result is the decimal form.
Example: 1/4 = 1 ÷ 4 = 0.25
Decimal to Fraction: Write the decimal as a fraction by placing the decimal value over the appropriate power of 10.
Example: 0.75 = 75/100 = 3/4
Fraction to Percent: Divide the numerator by the denominator and multiply by 100.
Example: 1/3 = (1 ÷ 3) × 100 = 33.33...%
Percent to Fraction: Write the percent as a fraction with a denominator of 100 and simplify if necessary.
Example: 40% = 40/100 = 2/5
Decimal to Percent: Multiply the decimal by 100 and add the percent symbol (%).
Example: 0.75 = 0.75 × 100 = 75%
Percent to Decimal: Divide the percent by 100.
Example: 40% = 40 ÷ 100 = 0.4
The functions f(x) and g(x) are graphed.
1(x) 5
32
1
-6-5-4-3-2-11-
-2-
-3-
3458
-4
2 3 4
g(x)
Which represents where f(x) = g(x)?
Of(0) = g(0) and f(2)= g(2)
Of(2)= g(0) and f(0) = g(4)
Of(2)= g(0) and f(4) = g(2)
Of(2)= g(4) and f(1) = g(1)
Answer: the answer is -4
Step-by-step explanation: the reason why the answer is -4 becaue all of the option is in correct.
Rotate the triangle 180 counterclockwise around the origin and enter the coordinates. Enter the number that belongs in the green box A (1,-1) B (4,-2) C (2,-4)
Answer:
A''(-1, 1), B''(-4, 2), C''(-2, 4)
Step-by-step explanation:
When rotated 180°, the symbol of the coordinames change
i.e., if x = 2 it becomes x = -2 and if y = -4, it becomes y = 4
so the coordinates A(1, -1), B(4, -2), C(2, -4)
change to A''(-1, 1), B''(-4, 2), C''(-2, 4)
GEOMETRY 80POINTS
ty
Answer:
37.98
Step-by-step explanation:
Find Tan A 6-11, please?
Answer:
5) tan A = 0.42
6) Acute angle is less than 90°
7) Right angle is exactly 90°
8) Obtuse angle is greater than 90° but less than 180°
9) Straight angle is exactly 180°
10) Complementary angles add up to 90°
11) Supplementary angles add up to 180°
Step-by-step explanation:
tan A = opposite / adjacent
= 5/12
= 0.42
Bronson Building Inc. is considering a possible investment project, consisting of constructing an office building and then renting it out for use to various local businesses. The initial cost of acquiring the land and constructing the building (first cost) is $21,000,000. The building is expected to be sold for $2,000,000 in 23 years, at the end of the last year of the project. Annual revenue from collecting rents is expected to be $4,000,000, while annual maintenance and operating expenses are projected to equal $2,000,000. Using MARR of 10%, compute the present worth of the project. Note: if the present worth is negative you must include the negative sign with your answer
Answer:The present worth of the project for Bronson Building Inc is $6,389,137.
In order to calculate the present worth, follow these steps:
1. The given information is:
Initial cost (first cost) = $18,000,000
Annual revenue = $5,000,000
Annual expenses = $2,000,000
Net annual cash flow = Annual revenue - Annual expenses = $5,000,000 - $2,000,000 = $3,000,000
MARR = 11%
Project duration = 18 years
Sale price at the end of the project = $8,000,000
2. To calculate the present worth, we first need to find the present value of the net annual cash flows using the MARR as the discount rate. Then, we will add the present value of the sale price and subtract the initial cost.
Present value of net annual cash flows (PV_ACF) = Net annual cash flow * [(1 - (1 + MARR)^(-duration)) / MARR]
PV_ACF = $3,000,000 * [(1 - (1 + 0.11)^(-18)) / 0.11] = $3,000,000 * 7.696 = $23,088,000
3. Find the present value of the sale price at the end of the project.
Present value of sale price (PV_SP) = Sale price / (1 + MARR)^duration
PV_SP = $8,000,000 / (1 + 0.11)^18 = $8,000,000 / 6.146 = $1,301,137
4. Calculate the present worth of the project.
Present worth = PV_ACF + PV_SP - Initial cost
Present worth = $23,088,000 + $1,301,137 - $18,000,000 = $6,389,137
Step-by-step explanation:
Please look at photo. Thank you. If you get it right I’ll give you a good rating!
a. The absolute maximum of g is 4.
The absolute minimum of g is -4.
b. The absolute maximum of h is 3.
The absolute minimum of h is -4.
What is a vertical asymptote?In Mathematics and Geometry, the vertical asymptote of a function simply refers to the value of x (x-value) which makes its denominator equal to zero (0).
By critically observing the graph of the polynomial function g shown above, we can logically deduce that its vertical asymptote is at x = 3. Furthermore, the absolute maximum of the polynomial function g is 4 while the absolute minimum of g is -4.
In conclusion, the absolute maximum of the polynomial function h is 3 while the absolute minimum of h is -4.
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please answer i am stuck
Answer:
x intercept : -1
y intercept : 3
Step-by-step explanation:
We have 3x - y = -3 ---eq(1)
The x intercept is the value of x when y = 0 in eq(1),
⇒ 3x - 0 = -3
⇒ x = -3/3
⇒ x = -1
The y intercept is the value of y when x = 0 in eq(1),
⇒ 3(0) - y = -3
⇒ -y = -3
⇒ y = 3
Given ABCD, what is the measure of
145
A. 90°
B. 35°
C. 10°
D. 145°
E. 55°
F. 235°
Answer: D. 145°
Step-by-step explanation:
Since it is a parallelogram given by the symbol, then angle B is equal to angle D which is 145°.
help please i need help
The number line inequality that represents x > -7 is: Option D
How to identify the Inequality number line?In number line inequalities we know that:
A closed circle indicates "greater than or equal to" or "less than or equal to" .
Meanwhile an open circle indicates "greater than" or "less than".
A closed circle pointing to the right indicates "greater than or equal to" while a closed circle pointing to the left indicates "less than or equal to,"
Similarly:
An open circle pointing to the right indicates "greater than" while An open circle pointing to the left indicates "less than".
Thus , the correct number line that shows x > -7 is: Option D
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The sum of three numbers $x$ ,$y$, $z$ is 165. When the smallest number $x$ is multiplied by 7, the result is $n$. The value $n$ is obtained by subtracting 9 from the largest number $y$. This number $n$ also results by adding 9 to the third number $z$. What is the product of the three numbers?
Answer:
Step-by-step explanation:
Let's break down the given information step by step to solve the problem:
The sum of three numbers x, y, and z is 165: x + y + z = 165.
When the smallest number x is multiplied by 7, the result is n: 7x = n.
The value n is obtained by subtracting 9 from the largest number y: y - 9 = n.
The value n is also obtained by adding 9 to the third number z: z + 9 = n.
We can use this information to form a system of equations:
Equation 1: x + y + z = 165
Equation 2: 7x = n
Equation 3: y - 9 = n
Equation 4: z + 9 = n
To find the product of the three numbers, we need to determine the values of x, y, z, and n.
First, let's solve for n using Equation 2:
7x = n
Now, let's substitute the value of n into Equations 3 and 4:
Equation 3: y - 9 = 7x
Equation 4: z + 9 = 7x
We can rearrange Equation 3 to express y in terms of x:
y = 7x + 9
Now, we can substitute the value of y in Equation 1:
x + (7x + 9) + z = 165
Simplifying:
8x + z = 156
Now, we have two equations:
Equation 4: z + 9 = 7x
8x + z = 156
We can solve this system of equations to find the values of x and z:
From Equation 4, we have z = 7x - 9.
Substituting z in Equation 8x + z = 156:
8x + (7x - 9) = 156
15x - 9 = 156
15x = 165
x = 11
Substituting x = 11 in Equation 4:
z + 9 = 7(11)
z + 9 = 77
z = 68
Now, we have the values of x = 11, y = 7x + 9 = 7(11) + 9 = 86, and z = 68.
The product of the three numbers x, y, and z is:
Product = x * y * z = 11 * 86 * 68 = 64648.
Therefore, the product of the three numbers is 64648.
The numbers on two consecutively numbered gym lockers have a sum of 129,
What are the locker numbers?
Answer:
64 and 65
Step-by-step explanation:
Let the two lockers be x and (x+1) since they are consecutive
The sum is 129 so,
x + (x+1) = 129
2x + 1 = 129
2x = 128
x = 64
x + 1 = 65
The locker numbers are 64 and 65
I can’t figure this out. Please help
Answer:
Relative maximum at x=0; Relative minimum at x=8/3
Step-by-step explanation:
To find the relative maximums and the relative minimums, you must first find the first derivative of the function. The first derivative of this function is 6x^2-16x. Simply it and you get 2x(3x-8). X would be equal to 0 and 8/3. Next, make a number line where you put 0 and 8/3 have a value of zero.
+ - +
-------------------0----------------------------8/3-----------------------
Plug in a value of x<0 to get the region left of 0. Say we use -1, we get -2(-3-8), which is positive, meaning that it is increasing there. From 0 to 8/3, if we use 1, we get 2(3-8), which is decreasing. If we use 3, we get 6(9-8), which is increasing. From this, we can see that when x=0, the graph has a relative maximum. When x=8/3, the graph has a relative minimum.
at the movie theatre, child admission is $5.20 and adult admission is $9.60 on sunday, 131 tickets were sold for a total sales of $1020.00 how many adult tickets were sold that day
Taking into account the definition of a system of linear equations, on Sunday 77 adult tickets were sold.
Definition of 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 with which when replacing, they must give the solution proposed in both equations.
Amount of adult tickets soldIn this case, a system of linear equations must be proposed taking into account that:
"a" is the amount of adult tickets sold."c" is the amount of children tickets sold.You know:
At the movie theatre, child admission is $5.20 and adult admission is $9.60 On sunday, 131 tickets were sold for a total sales of $1020.00So, the system of equations to be solved is
a + c= 131
9.60a + 5.20c= 1020
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.
In this case, isolating the variable c from the first equation:
c= 131 -a
Substituting the expression in the second equation:
9.60a + 5.20×(131 -a)= 1020
Solving:
9.60a + 5.20×131 -5.20a= 1020
9.60a + 681.2 -5.20a= 1020
9.60a -5.20a= 1020 - 681.2
4.4a= 338.8
a= 338.8÷ 4.4
a= 77
In summary, 77 adult tickets were sold that day.
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if the graph of f(x) =3^x shifted 6 units to the right, what is the equation of the new graph
Use inductive reasoning to predict the most probable next number in the list.
3, 9, -3, 3, -9, -3, -15, -9, -21, ?
Need Help
Answer: -27
Step-by-step explanation: Use inductive reasoning to predict the most probable next number in the list.
3, 9, -3, 3, -9, -3, -15, -9, -21, ?
We can start by looking at the differences between consecutive terms in the list:
9 - 3 = 6 -3 - 9 = -12 3 - (-3) = 6 -9 - 3 = -12 -3 - (-9) = 6 -15 - (-3) = -12 -9 - (-15) = 6 -21 - (-9) = -12
Notice that the differences alternate between positive 6 and negative 12. This suggests that the pattern involves adding 6, then subtracting 12, and then adding 6 again. Applying this pattern to the last term in the list (-21), we get:
-21 + 6 = -15 -15 - 12 = -27 -27 + 6 = -21
Therefore, we predict that the most probable next number in the list is -27.
A student is applying to the University of Florida (UF) and Florida State (FSU).
There is a 40% chance of being accepted at FSU. If the student is accepted at FSU, the probability of being accepted at UF is 60%. If the student is not accepted at FSU there is an 90% chance of non-acceptance at UF.
Of the students not accepted at UF, what is the probability they are accepted at FSU?
Answer:
Let's denote:
- A as the event "student is accepted at FSU"
- B as the event "student is accepted at UF"
We have the following probabilities given:
- P(A) = 0.4 (probability of being accepted at FSU)
- P(B|A) = 0.6 (probability of being accepted at UF given acceptance at FSU)
- P(B'|A') = 0.9 (probability of not being accepted at UF given non-acceptance at FSU), where B' is the complement of B (not being accepted at UF) and A' is the complement of A (not being accepted at FSU).
We want to find P(A|B'), or the probability of being accepted at FSU given non-acceptance at UF.
To calculate this, we can use Bayes' Theorem, which states that:
P(A|B') = P(B'|A) * P(A) / P(B')
We can calculate P(B'|A), the probability of non-acceptance at UF given acceptance at FSU, by using the fact that the sum of probabilities of complementary events equals 1:
P(B'|A) = 1 - P(B|A) = 1 - 0.6 = 0.4
Next, we need to find P(B'), the total probability of non-acceptance at UF. We can use the law of total probability to calculate this:
P(B') = P(B'|A) * P(A) + P(B'|A') * P(A')
P(B') = 0.4 * 0.4 + 0.9 * 0.6 = 0.16 + 0.54 = 0.7
Finally, we can substitute these values into Bayes' theorem:
P(A|B') = P(B'|A) * P(A) / P(B') = 0.4 * 0.4 / 0.7 ≈ 0.229
Therefore, the probability that a student is accepted at FSU given that they are not accepted at UF is approximately 22.9%.