The solution to the two functions f(x) = 3ˣ and g(x) = -x + 4 is, 1
What are functions?Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).
Vertical line test:-
Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.
If we get more images then it will not be a function.
For example, let us take, y² = 4ax
y = ±√4ax
For single value of x we get two values of y
Hence, it will not be a function.
Given that,
The number of visitors increases exponentially as the temperature increases, and this situation is represented by the function
f(x) = 3ˣ
The number of people who leave the park early depending on the change in temperature, and it is represented by
g(x) = −x + 4
the solution of both the graphs = ?
the intersection of the two curves of graphs of the functions is the solution,
Basically, it represent that,
both function have same value for particular value of x,
So,
when both functions have same value that will be our solution,
f(x) = 3ˣ
g(x) = −x + 4
It can be seen in the graph that both the functions intersects at x = 1,
f(1) = 3
g(1) = −1 + 4 = 3
Hence, the solution is 1
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In a research proposal, which of the following sections discusses the types of scales to be used
for data collection?
a) Definition of the target population
b) Sample design
c) Data collection method
d) Specific research instruments e) Definition of the sample size
The correct answer is option C. In a research proposal, the Data Collection method discusses the types of scales to be used for data collection.
The Data Collection Method section of a research proposal is where the various scales for data collection are discussed. The types of scales (such as Likert scales, qualitative scales, etc.) and specific research instruments (such as surveys, interviews, questionnaires, or focus groups) typically are described in this section. that will be applied to the measurement of the variables. The target population and the definition of the sample size might also be discussed in the sample design section.
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6TH GRADE MATH!!! Please Help me I'm stuck on this (worth 20 points!) Pleasee Help!!!! MARKING BRAINLIST!
A gardener would like to add to their existing garden to make more flowers available for the butterflies that visit the garden. Her current garden is 20 square feet. If she added another rectangular piece with vertices located at (−18, 13), (−14, 13), (−18, 5), and (−14, 5), what is the total area of the garden?
640 ft2
320 ft2
52 ft2
32 ft2
The total area of the garden is given as follows:
52 ft².
How to obtain the area of a rectangle?The area of a rectangle of length l and width w is given by the multiplication of these dimensions, as follows:
A = lw.
For the new rectangle, the dimensions are given as follows:
l = 18 - 14 = 4.w = 13 - 5 = 8.Hence the area of the new part is of:
A = 4 x 8
A = 32 ft².
Considering the previous part of 20 ft², the total area is given as follows:
32 + 20 = 52 ft².
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find diameter of 7 in radius
Answer:
The answer is 7/2
Step-by-step explanation:
d=2r
7=2r
r=7/2
A vehicle's distance d in miles is given by the function d(r,t)=r⋅t, in which r is the rate in miles per hour and t is the time in hours. What happens to the value of d if the rate is tripled and the time increases by 3 hours?
If the rate is tripled and the time increases by 3 hours, the value of d will increase by a factor of 12.
What is Distance?The length along a line or line segment between two points on the line or line segment.
Distance=√(x₂-x₁)²+(y₂-y₁)²
The original distance, d(r,t), can be expressed as d(r,t) = rt.
Value of d if the rate is tripled and the time increases by 3 hours
The new distance, d(3r,t + 3), can be expressed as d(3r,t + 3) = 3r(t + 3).
The new distance d(3r,t + 3) = 3r(t + 3)
= 3rt + 3(3r)
= 3rt +9r
= 3d(r,t) + 9r
Therefore, if the rate is tripled and the time increases by 3 hours, the value of d will increase by a factor of 3 + 9 = 12.
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Auberon swam 52 meters in five minutes at this rate how many meters would he swim in 10 minutes 12 minutes
If Auberon swim 52 meters in five minutes then at this rate the number of meters would he swim in 10 minutes & 12 minutes are respectively,
104 meters & 124.8 meters
What is the relation between time, distance & speed ?The distance covered by the object is equal to the product of the speed at which the object is moving and time taken for covering the distance.
Distance = Time × Speed
Since Auberon swim 52 meters in 5 minutes,
you can find his average rate of swimming by dividing the distance by the time:
Rate = 52 meters / 5 minutes
= 10.4 meters per minute
To find the distance he would swim in 10 minutes, you can multiply his average rate by the time:
Distance in 10 minutes = 10.4 meters per minute x 10 minutes
= 104 meters
To find the distance he would swim in 12 minutes, you can multiply his average rate by the time:
Distance in 12 minutes = 10.4 meters per minute x 12 minutes
= 124.8 meters
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The polynomial of degree 3 , P ( x ) , has a root of multiplicity 2 at x = 3 and a root of multiplicity 1 at x = − 2 . The y -intercept is y = − 1.8 .
Answer:
[tex]\displaystyle P(x)=-\frac{1}{10}(x-3)^2(x+2)[/tex]
Step-by-step explanation:
Multiplicity is basically how much of a factor of a polynomial appears. In this case, if we disregard the y-intercept, we can show a multiplicity of 2 at x = 3 and a multiplicity of 1 at x=-2 with [tex]y=(x-3)^2(x+2)[/tex].
Of course, there will need to be a scale factor for the function so that the y-intercept will be at y = -1.8, so we can solve the following:
[tex]-1.8=a(0-3)^2(0+2)\\-1.8=a(3)^2(2)\\-1.8=a(9)(2)\\-1.8=18a\\-0.1=a[/tex]
Thus, we can write the function as [tex]\displaystyle P(x)=-\frac{1}{10}(x-3)^2(x+2)[/tex]. See below for a visual.
Let u = [0 26 8] and A = [5 -3 1 -3 7 1]. Is u in the plane in R^3 spanned by the columns of A? Why or why not? Select the correct choice below and fill in the answer box to complete your choice. A. Yes, multiplying A by the vector writes u as a linear combination of the columns of A. B. No, the reduced row echelon form of the augmented matrix is which is an inconsistent system.
B. No, the reduced row echelon form of the augmented matrix is which is an inconsistent system. In this case, the vector u is [0 26 8] and the matrix A is [5 -3 1; -3 7 1].
To check if u is in the plane spanned by the columns of A, we can form the augmented matrix by appending u to A, and attempt to reduce it to the reduced row echelon form.
If the resulting augmented matrix is an inconsistent system (i.e. the last row has a non-zero coefficient in the last column and a zero in the right-hand side), then u cannot be written as a linear combination of the columns of A, and thus it is not in the plane spanned by the columns of A.
In this case, the reduced row echelon form of the augmented matrix is an inconsistent system, which means that u cannot be written as a linear combination of the columns of A, and thus it is not in the plane spanned by the columns of A.
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Worth 25 points! Pls show work on both questions inside of the picture.
The area of the composite figure is 54 inches².
The perimeter of the figure is 35 inches.
How to find the area and perimeter of a composite figure?A composite figures is a figure with 2 or more 2 dimensional figures. The composite figure can be divided into three shapes.
Let's find the area of the composite figure as follows:]
area of the composite figure = area of the trapezium + area of the square + area of the rectangle
area of the trapezium = 1 / 2 (a + b)h
area of the trapezium = 1 / 2 (5 + 8)4
area of the trapezium = 1 / 2 × 4 × 13
area of the trapezium = 52 / 2
area of the trapezium = 26 inches²
Therefore,
area of the square = 4² = 16 inches²
area of the rectangle = 4 × 3 = 12 inches²
Therefore,
area of the composite figure = 12 + 16 + 26
area of the composite figure = 54 inches²
Let's find the perimeter of the composite figure as follows:
perimeter of the composite figure = 12 + 7 + 4 + 3 + 5 + 4
perimeter of the composite figure = 35 inches
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Help! I hate algebra
Answer: 77
Step-by-step explanation:
the formula for calculating the ____ of a square is A = Length x Length
Therefore , the solution of the given problem of area comes out to be Formula for Square Area is = length * length.
Describe surface area.Its surface area provides a good estimate of its overall size. When computing a right triangle's squared, the surroundings are taken into consideration. The surface area of everything determines its overall size. The sum of the volumes on each of the six horizontal sides makes up the volume of water inside a cuboid. Utilize the following formula to get the box's dimensions: In 2lh, 2lw, and 2hw, the region is the same (SA). The flexible shape's total area serves as a representation of the area.
Here,
To fill the blank space in the given problem is
Formula for Square Area
We are aware that Side Side equals the area of a square.
7 7 Equals 49 when the side length of 7 cm is substituted.
As a result, the square's area is 49 cm2.
Therefore , the solution of the given problem of area comes out to be Formula for Square Area is = length * length.
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the not the play took in $728 one night. the number of $adult tickets was 14 less than twice the number of $5 child tickets.
Answer:
Let's call the number of $5 child tickets sold "x".
According to the problem, the number of $adult tickets was 14 less than twice the number of child tickets, so the number of $adult tickets sold can be represented as 2x - 14.
The total revenue from ticket sales was $728, so we can set up an equation:
5x + 20(2x - 14) = 728
Expanding the second term on the left side of the equation:
5x + 40x - 280 = 728
Combining like terms:
45x = 1008
Dividing both sides of the equation by 45:
x = 22.4
So the number of child tickets sold was 22 and the number of adult tickets sold was 2 * 22 - 14 = 36.
Ted bought 2 bags of gravel and a potted tree that weighed 7.4 pounds at Marvin's Garden Shoppe. The total weight of his purchases was 16 pounds. How much did each bag of gravel weigh? Write and Solve Use a bar diagram and an equation to represent the situation. Then solve the equation. Each bag weighed 4.3 pounds.
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Which two solid figures have the same volume
suppose you roll two six-sided dice. let the macrostate s of the two dice be the sum of their top faces.
The macrostate s of two six-sided dice can be defined as the sum of the top faces of the dice.
The macrostate of a system refers to a comprehensive description of the system in terms of its properties and variables that are used to characterize it. In the case of two six-sided dice, the macrostate is described by the sum of the numbers on the top faces of the two dice, which determines the total score or outcome. This macrostate, represented by the variable "s", is a measurable quantity that summarizes the state of the system, providing information about the distribution of the outcomes over all possible configurations of the two dice.
It's important to note that a macrostate does not specify the exact configuration of the system, but rather provides a probabilistic description of it. In other words, the macrostate "s" only describes the sum of the two dice and does not specify which number is on each die. In thermodynamics, macrostates are used to characterize the thermodynamic properties of a system, such as its temperature, pressure, and entropy. The study of macrostates and their distributions helps us to understand the behavior of complex systems and make predictions about their future behavior.
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Solve the system by substitution
Y= 8
-3x-y=1
Answer:
x = -3
Step-by-step explanation:
-3x - 8 = 1
-3x = 9
3x = -9
x = -9/3
x = -3
select all the rates that are unit rates 2/4/5 3/4/1 3:4 9/1 10:1
From the given rates, the unit rates are as follows 9/1 and 10:1. That is option D and E.
What is a unit rate?A unit rate of a measurement of the distance of a traveling vehicle or of a moving object is the rate for per one of the value of interest.
A unit rate can only be two figures that shows the relationship that exists between them and a whole value.
Therefore the given rates that shows unit rate are 9/1 and 10:1
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25. An electrician charges an initial fee of $50 and $190 after 4 hours of w
a. Write a linear model that represents the total cost as a function of t
b. How much does the electrician charge per hour?
Answer:
Step-by-step explanation:
A. The total cost after t hours can be represented by the linear equation C(t) = 50 + 190/4 * t, where C(t) is the total cost after t hours.
B. The electrician charges 190/4 = $47.5 per hour.
Answer please (30 points)
I really think it's option A because it's more than 90° and less than 180°
Answer:
A
Step-by-step explanation:
An obtuse triangle is a triangle in which one of the interior angles measures more than 90° degrees
formula for finding obtuse triangle is 1/2 *base*height
In triangle BCD below, H is the circumcenter. Given BD= 80 and HB=50, find the segments below. Round to tenths if necessary.
The length of EH is determined as 10.72.
What is the length EH?The length of EH can be determined if the length of the each side is properly identified as shown below.
In the given figure, H is the circumcenter of triangle BCD,
BD = 80HB = 50BC = 18HD = 14Triangle BHD is isosceles, therefore BH = HD
Point E is midpoint of BC, therefore BE = ¹/₂ of BC
Using Pythagorean, calculated the value of EH as follows;
EH = √ (BH² - BE²)
EH = √ ( 14² - ( 18 /2) ² )
EH = √ ( 196 - 81 )
EH = √115 = 10.72
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The side length of BE is 40 units
How to determine the side length of BEFrom the question, we have the following parameters that can be used in our computation:
H is the circumcenter.
BD= 80 and HB=50
Using the above as a guide, we have the following:
BE = 1/2 * BD
Substitute the known values in the above equation, so, we have the following representation
BE = 1/2 * 80
Evaluate
BE = 40 units
Hence, the side length of BE is 40 units
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Recall that in Problem 3 of the reading questions for Section 2.1, you found that if f(x) = ln(x), then f'(2) = 1/2. Use this to find a formula for the tangent line to f(x) = ln(x) at x = 2.y=__________
The formula for the tangent line to f(x) = ln(x) at x = 2 is 2y = x − 2.
We must first differentiate f(x).
The derivative of ln(x) is 1/x
The slope of the tangent at a point x = a on the function f(x) is given by evaluating f'(a).
Hence, the slope of the tangent is 1/x = 1/2
The function passes through,
(1/2, ln1)=(2, 0).
Now, we can use point slope form to find the equation of the tangent.
y − y1 = m( x− x1)
y − 0 = 1/2( x− 2 )
2y = x - 2
Thus, the equation of the tangent is 2y = x − 2.
The straight line that "just touches" the curve at a given position is known as the tangent line to a plane curve at that location. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.
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Let p, q, r be logical statements. Use truth tables to determine whether the following statements are tautologies.
a. [(p ^ q) -> r] <-> [p -> (q -> r)]
b. [(p Ë… q) ^ (~ q)] -> p
Truth tables are utilized to decide redundancies by assessing reality an incentive for every single imaginable mix. Both [(p ^ q) - > r] <-> [p - > (q - > r)] and [(p ∧ q) ^ (~q)] - > p were viewed as repetitions.
a. We should assemble reality table for [(p ^ q) - > r] <-> [p - > (q - > r)].
p | q | r | (p ^ q) - > r | p - > (q - > r) | [(p ^ q) - > r] <-> [p - > (q - > r)]
T | T | T | T | T | T, T | T | F | F | F | F, T | F | T | T | T | T, T | F | F | T | T | T,
F | T | T | T | T | T, F | T | F | T | T | T, F | F | T | T | T | T, F | F | F | T | T | T
Since every one of the qualities in the last segment are "T", the assertion [(p ^ q) - > r] <-> [p - > (q - > r)] is a redundancy.
b. We should construct reality table for [(p ∧ q) ^ (~q)] - > p.
p | q | ~q | (p ∧ q) ^ (~q) | [(p ∧ q) ^ (~q)] - > p
T | T | F | F | T, T | F | T | T | T, F | T | F | F | T, F | F | T | F | T
Since every one of the qualities in the last section are "T", the assertion [(p ∧ q) ^ (~q)] - > p is a repetition.
A repetition is a coherent explanation that is in every case valid, no matter what reality values doled out to its singular parts. To decide whether an assertion is a repetition, we can utilize a reality table which records generally potential blends of truth values for the parts and assesses reality worth of the whole assertion. In the event that reality worth of the assertion is generally "Valid" for every conceivable mix, then, at that point, the assertion is a redundancy. In the models given, the two explanations [(p ^ q) - > r] <-> [p - > (q - > r)] and [(p ∧ q) ^ (~q)] - > p were viewed as repetitions through truth tables.
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What is the value today of $5,100 per year, at a discount rate of 7.9%, if the first payment is received 6 years from today and the last payment is received 20 years from today?
Answer:
$30,029.78
Step-by-step explanation:
NPV = Cash flow / (1 + i)^t – initial investment (assuming initial investment =$1).
solve NPV
$30,029.78
The regular price of an item at a store is p dollars. The item is on sale for 20% off the regular price. Some of the expressions shown below represent the sale price, in dollars, of the item.
Expression A: 0.2p
Expression B: 0.8p
Expression C: 1 - 0.2p
Expression D: p - 0.2p
Expression E: p - 0.8p
Which two expressions each represent the sale price of the item?
The expressions of the sale price is as follows:
Expression B: 0.8p
Expression D: p - 0.2p
How to find the expression that represent the sale price of the items?The regular price of an item at a store is p dollars. The item is on sale for 20% off the regular price.
Therefore, the expression that represent the sale price in dollars of the items can be calculated as follows:
original price = p
Therefore, let's find the percent off the price.
price off = 20% of p
price off = 20 / 100 p
price off = 0.2p
Therefore,
sale price = p - 0.2p
sale price = 0.8p
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Need Help For Parts B and C, chart is below
For the function f(x) = x, we know f(4) = 2 and f(9)=3.
a. Use linear interpolation to find [tex]\sqrt{5}[/tex].
Answer: [tex]\sqrt{5} = 2.2[/tex]
b. Use the table of square roots in the back of the text to find the error to 3 decimal places
c. What is the percentage error? (Recall that percentage error is 100∗error/(exact answer). )
The error to 3 decimal place is 0.036
The percentage error is solved to be 1.61%
How to find the errorThe error is calculated using the formula
= Approximate value – Exact Value
where
the approximate value = 2.2
Exact value from the table = 2.236
error = 2.2 - 2.236
error= -0.036
The percentage error
=(Approximate value – Exact Value) / Exact value * 100
= 0.036 / 2.236 * 100
= 0.0161 * 100
= 1.61%
The percentage error is 1.61%
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You have three dice: one red (R), one green (G), and one blue (B).? When all three dice are rolled at the same time, calculate the probability of the following outcomes:! a. 1 (R), 1 (G), 1 (B) _________? b. odd (R), even (G), any number (B) _________ c. 6 or 5 (R), 4 or 3 (G), 1, 2 or 3 (B) _________ ? d. No fives at all_________? e. A different number on each dice_________!
The probability of rolling 1 (R), 1 (G), 1 (B) is 1/216, odd (R), even (G), any number (B) is 1/36, 6 or 5 (R), 4 or 3 (G), 1, 2 or 3 (B) is 1/18, no fives at all is 125/216, and a different number on each dice is 1/6.
a. The probability of rolling 1 (R), 1 (G), 1 (B) is 1/216. This is because there are 6 faces on each die, and 6 x 6 x 6 = 216 total possible outcomes. Since there is only one way to roll the dice and get 1 (R), 1 (G), 1 (B), the probability of this outcome is 1/216.
b. The probability of rolling odd (R), even (G), any number (B) is (3/6) x (3/6) x (1/6) = 1/36. This is because there are 3 odd numbers on the red die, 3 even numbers on the green die, and 6 numbers on the blue die, thus making the total number of outcomes (3/6) x (3/6) x (6/6) = 1/36.
c. The probability of rolling 6 or 5 (R), 4 or 3 (G), 1, 2 or 3 (B) is (2/6) x (2/6) x (3/6) = 1/18. This is because there are 2 faces with a 6 or 5 on the red die, 2 faces with a 4 or 3 on the green die, and 3 faces with a 1, 2, or 3 on the blue die, thus making the total number of outcomes (2/6) x (2/6) x (3/6) = 1/18.
d. The probability of rolling no fives at all is (5/6) x (5/6) x (5/6) = 125/216. This is because there are 5 faces on each die that do not have a 5, thus making the total number of outcomes (5/6) x (5/6) x (5/6) = 125/216.
e. The probability of rolling a different number on each dice is (6/6) x (5/6) x (4/6) = 1/6. This is because there are 6 different numbers on the red die, 5 different numbers on the green die, and 4 different numbers on the blue die, thus making the total number of outcomes (6/6) x (5/6) x (4/6) = 1/6.
In conclusion, the probability of rolling 1 (R), 1 (G), 1 (B) is 1/216, odd (R), even (G), any number (B) is 1/36, 6 or 5 (R), 4 or 3 (G), 1, 2 or 3 (B) is 1/18, no fives at all is 125/216, and a different number on each dice is 1/6.
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Danielle is working on practice problems and must translate the verbal expression "4 less than twice a number" in to an algebraic expression. Write the algebraic expression that Danielle should write. Type your expression with no spaces.
The algebraic expression that Danielle should write is 2x - 4
How to determine the algebraic expression that Danielle should writeFrom the question, we have the following parameters that can be used in our computation:
4 less than twice a number
Represent the number with x
So, we have the following representation
4 less than twice x
Twice x means 2x
So, we have
4 less than 2x
Less than here means minut
So, we have the following representation
2x - 4
Hence, the expression is 2x - 4
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If the arc measures of MN=87, what is the measure of
The required measure of the angle ∠MON is given as 87°.
Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
Here,
For the given circle, the measure of arc MN is given in the form of an angle of 87° which consists of an angle MNO, so the measure of the section is equal to MON i.e.
∠MON = 87°
Thus, the required measure of the angle ∠MON is given as 87°.
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At a local store, 2 bagels and 2 cups of coffee cost $4.40. The cost of 3 bagels and 4 cups of coffee is $7.80.
Write a system of equations to represent this situation, where x
is the number of bagels and y
is the number of cups of coffee.
A system of equations to represent this situation include the following:
2x + 2y = 4.40
3x + 4y = 7.80
How to write a system of equations to describe the situation?In order to write a system of equations that model this situation, we would assign variables to the number of bagels and the number of cups of coffee respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of bagels.Let the variable y represent the number of cups of coffee.Next, we would translate the word problem into algebraic equation as follows:
Since 2 bagels and 2 cups of coffee cost $4.40, we would have:
2x + 2y = 4.40 .....equation 1.
Additionally, 3 bagels and 4 cups of coffee cost $7.80:
3x + 4y = 7.80 .....equation 2.
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An editor has a stack of k documents to review. The order in which the doc- uments are reviewed is random with each ordering being equally likely. Of the k documents to review, two are named "Relaxation Through Mathematics" and "The Joy of Calculus." Give an expression for each of the probabilities below as a function of k. Simplify your final expression as much as possible so that your answer does not include any expressions in the form () (a) What is the probability that "Relaxation Through Mathematics" is first to review? (b) What is the probability that "Relaxation Through Mathematics" and "The Joy of Calculus" are next to each other in the stack?
The probability that "Relaxation Through Mathematics" is first to review is 1/k, and the probability that "Relaxation Through Mathematics" and "The Joy of Calculus" are next to each other in the stack is (1/k)*(1/(k-1)).
A) The probability that "Relaxation Through Mathematics" is first to review is 1/k. This is because there are k documents to review, and the order in which they are reviewed is random with each ordering being equally likely. Therefore, the probability that any given document is chosen first is 1/k.
B) The probability that "Relaxation Through Mathematics" and "The Joy of Calculus" are next to each other in the stack is (1/k)*(1/(k-1)). This is because there are k documents to review, and the probability that the first document is "Relaxation Through Mathematics" is 1/k. Then, since there are k-1 documents remaining in the stack, the probability that the second document is "The Joy of Calculus" is 1/(k-1). Therefore, the probability that both documents are next to each other is (1/k)*(1/(k-1)).
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Find the area of the following shape. Make sure to indicate what shapes were used, by sketching on the image, listing
formulas, and show work listed for each shape. (5 total points – 2 for accurate shapes, 2 for accurate work, 1 for total
area answer)
The area of the given figure is 43.3 units².
What is trapezium?A trapezium is a quadrilateral with four sides where two sides are parallel to each other.
We have,
The figure has two shapes:
Trapezium and a semicircle.
Now,
We will consider one box as one unit.
Trapezium:
Height = 6 units
Parallel sides = 8 units and 5 units
Area = 1/2 x height x (sum of the parallel sides)
Area = 1/2 x 6 x (8 + 5)
Area = 3 x 13
Area = 39 units²
Semicircle:
Diamter = 6 units
Radius = 3 units
Area = 1/2 x πr²
Area = 1/2 x 3.14 x 3²
Area = 4.3 units²
Now,
Area of the figure.
= 39 + 4.3
= 43.3 units²
Thus,
The area is 43.3 units².
Learn more about trapezium here:
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