Answers
Hello!
\(\large\boxed{\text{B. } k(x) = (-x + 3)^{\frac{1}{2} }}}\)
We can look at each answer choice to verify whether it has a restricted domain or not:
A. \(f(x) = (3x)^{\frac{1}{5}} - 4\)
This is a function similar to a cubic root function. Its domain is (-∞, ∞), so it has no restriction.
B. \(k(x) = (-x + 3)^{\frac{1}{2}}\)
This is a square root function. This graph only consists of x-values in the interval (3, ∞) because you cannot take the square root of a negative number. This function has a restricted domain.
C. \(g(x) = -(x + 8)^{3}\)
This is a cubic function, so it has an interval of (-∞, ∞)
D. \(h(x) = (4x)^{2} - 5\)
This is a quadratic function, which has no domain restriction.
Therefore, the correct answer is B.
Related Questions
Show that polynomials of degree less than or equal to n-1 are isomorphic to Rn.
That is, show that there is a transformation T:Pn−1 →Rn defined as
T(a0 +a1x+⋯+an−1xn−1)=(a0,a1,...,an−1) which is injective and surjective.
Answers
We have shown that the transformation \(\(T: P_{n-1} \rightarrow \mathbb{R}^n\)\) defined as \(\(T(a_0 + a_1x + \ldots + a_{n-1}x^{n-1}) = (a_0, a_1, \ldots, a_{n-1})\)\) is both injective and surjective, establishing the isomorphism between polynomials of degree less than or equal to \(\(n-1\)\) and \(\(\mathbb{R}^n\)\).
To show that polynomials of degree less than or equal to \(n-1\) are isomorphic to \(\(\mathbb{R}^n\),\) we need to demonstrate that the transformation \(\(T: P_{n-1} \rightarrow \mathbb{R}^n\)\) defined as \(\(T(a_0 + a_1x + \ldots + a_{n-1}x^{n-1}) = (a_0, a_1, \ldots, a_{n-1})\)\) is both injective (one-to-one) and surjective (onto).
Injectivity:
To show that \(T\) is injective, we need to prove that distinct polynomials in \(P_{n-1}\) map to distinct vectors in\(\(\mathbb{R}^n\)\). Let's assume we have two polynomials\(\(p(x) = a_0 + a_1x + \ldots + a_{n-1}x^{n-1}\)\) and \\((q(x) = b_0 + b_1x + \ldots + b_{n-1}x^{n-1}\) in \(P_{n-1}\)\) such that \(\(T(p(x)) = T(q(x))\)\). This implies \(\((a_0, a_1, \ldots, a_{n-1}) = (b_0, b_1, \ldots, b_{n-1})\)\). Since the two vectors are equal, their corresponding components must be equal, i.e., \(a_i = b_i\) for all \(i\) from 0 to \(n-1\). Thus,\(\(p(x) = q(x)\),\) demonstrating that \(T\) is injective.
Surjectivity:
To show that \(T\) is surjective, we need to prove that every vector in\(\(\mathbb{R}^n\)\)has a preimage in \(P_{n-1}\). Let's consider an arbitrary vector \(\((a_0, a_1, \ldots, a_{n-1})\) in \(\mathbb{R}^n\)\). We can define a polynomial \(\(p(x) = a_0 + a_1x + \ldots + a_{n-1}x^{n-1}\) in \(P_{n-1}\)\). Applying \(T\) to \(p(x)\) yields \(\((a_0, a_1, \ldots, a_{n-1})\)\), which is the original vector. Hence, every vector in \(\mathbb{R}^n\)\)has a preimage in \(P_{n-1}\), confirming that \(T\) is surjective.
Therefore, we have shown that the transformation \(\(T: P_{n-1} \rightarrow \mathbb{R}^n\)\) defined as \(\(T(a_0 + a_1x + \ldots + a_{n-1}x^{n-1}) = (a_0, a_1, \ldots, a_{n-1})\)\)is both injective and surjective, establishing the isomorphism between polynomials of degree less than or equal to \(n-1\) and \(\(\mathbb{R}^n\).\)
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please put it in expanded form and solve it
Answers
Answer:
1/xyz^3
Step-by-step explanation:
exponents are subtracted when divided
x^0 is 1
negative exponents are positive in the denominator
(4x^0y^-2z^-3) / (4xy-1)
(4xy^-2z^-3) / (4xy^-1)
x-1y^-1z^-3
1/xyz^3
Which function is shown in the graph?
Answers
Answer:
\(f(x)=log_5 x\)
Step-by-step explanation:
The answer is clear once you graph it. You can use a graphical calculator or the online graphing calculator Desmos.
PLEASE ANSWER ASAP
Find the equation of the exponential function represented by the table below:
Answers
Answer:
y = 4 \((2)^{x}\)
Step-by-step explanation:
For an exponential function in standard form
y = a \((b)^{x}\)
To find the values of a and b, use ordered pairs from the table
Using (0, 4 ), then
4 = a\(b^{0}\) ( \(b^{0}\) = 1 ), so
a = 4
y = 4\(b^{x}\)
Using (1, 8 ), then
8 = 4\(b^{1}\) = 4b ( divide both sides by 4 )
2 = b
Thus
y = 4 \((2)^{x}\) ← exponential function
plz help with this problem
Answers
Answer:
x = 2
Step-by-step explanation:
There are 5 pieces of the segment. The segment is equal to 10. 10 ÷ 5 =2
anne can make 4 pizzas or 6 salads in an hour. bob can make 10 pizzas or 8 salads in an hour. which of the following is incorrect
Answers
Answer:I would think bobs thing..
Step-by-step explanation:
no one can make that many pizzas.
A culpture need to lift a piece of marble. It i a cuboid with dimenion 1 m by 0. 6 m by 0. 3 m. Marble ha a denity of 2. 7g/cm cubed
Answers
The mass of the marble is 2.7 x 1 x 0.6 x 0.3 x 1000 = 162.6 kg. The density of the marble is 2.7 g/cm3. To calculate the mass of the marble, multiply its volume by its density and then multiply that result by 1000.
Step 1: Determine the volume of the marble using the given dimensions.
Volume = 1 m x 0.6 m x 0.3 m = 0.18 m3
Step 2: Multiply the volume of the marble by its density to get the mass.
Mass = 0.18 m3 x 2.7 g/cm3 x 1000 = 162.6 kg
The mass of the marble can be determined by first calculating its volume. The given dimensions of the cuboid are 1 m by 0.6 m by 0.3 m. The volume of the marble is therefore 0.18 m3. The density of the marble is 2.7 g/cm3. To calculate the mass of the marble, multiply its volume by its density and then multiply that result by 1000. This gives a result of 162.6 kg. Therefore, the mass of the marble is 162.6 kg.
the complete question is : A culpture need to lift a piece of marble. It is a cuboid with dimenions 1 m by 0. 6 m by 0. 3 m. Marble has a denity of 2. 7g/cm cubed. What is the mass of the marble in kg?
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square root 71 in math
Answers
Answer: 8.4261
Step-by-step explanation:
A statement and diagram are shown below. The diagram provides a counterexample for the statement.
Complete the explanation that shows why.
Points A, B, and C are noncollinear, so therefore they are noncoplanar.
V
a single plane
The diagram shows three points that are (select) Since it (select)
containing all three points, the points (select) v coplanar.
Answers
Answer: Non-collinear, Shows, Are
Solve 2x2 + 3x = 4. Which of the following are the solutions to the nearest hundredth?
A. 2.35 and 0.85
B. 2.35 and –0.85
C. –2.35 and 0.85
D. –2.35 and –0.85
Answers
Answer:
the answer is C. -2.35 and 0.85
Step-by-step explanation:
1. \(2x^{2}\)+3x-4.=0
2. x=\(\frac{-3+\sqrt{9+8x4.} }{4}\), \(\frac{-3-\sqrt{9+8x4.} }{4}\)
3. 0.850781, -2.350781
Find the distance between the two points rounding to the nearest tenth (if necessary).
(4, -4) \text{ and } (9, -2)
(4,−4) and (9,−2)
Answers
The distance between two points having coordinates (4, -4) and (9, -2) plotted on the cartesian plane, and rounded to the nearest tenth, will be 5.40 units.
As per the question statement, two points having coordinates (4, -4) and
(9, -2) plotted on the cartesian plane.
We are required to calculate the distance between the above mentioned two points, rounded to the nearest tenth.
To solve this question, we need to know the Distance-formula which goes as,
"The distance between any two points (x₁, y₁) and (x₂, y₂) can be given by √[(x₂ - x₁)² + (y₂ - y₁)²]"
Assuming that [(x₁, y₁) = (4, -4)] and [(x₂, y₂) = (9, -2)], and substituting these values in the above-mentioned distance formula, we get,
√[(9 - 4)² + {(-2) - (-4)}²]
= √[(9 - 4)² + {(-2) + 4}²]
= √[(9 - 4)² + (4 - 2)²]
=√[(5)² + (2)²]
=√(25 + 4)
=√29
= 5.38 units.
Therefore, rounding (5.38) to the nearest tenth, we get, 5.40.
That is, the distance between two points having coordinates (4, -4) and (9, -2) plotted on the cartesian plane, and rounded to the nearest tenth, will be 5.40 units.
Distance: In Mathematics, physics or daily life, distance is a numerical or occasionally qualitative measurement of how far objects or points are from each other.Coordinates: In geometry, coordinates are a pair of numbers that can uniquely determine the position of points or other geometric elements on a Euclidean or Cartesian Plane.To learn more about Distances and Coordinates, click on the link below.
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Betty has 42 butterfly stickers, as shown below.
She puts an equal number of stickers on each of 6 pages in her sticker book.
How many stickers does Betty put on each page in her sticker book?
Answers
Answer:
7
Step-by-step explanation:
42/6=7
I need help please and thank you
Answers
9514 1404 393
Answer:
C.
Step-by-step explanation:
The transformation ...
g(x) = f(ax)
represents a horizontal compression of the graph by a factor of 'a'. Here, the original function graph is compressed by a factor of 3 horizontally, so the curve will look a lot narrower.
The appropriate choice is C.
Write an equation in standard form of the line that contains the point (-1,4) and is parallel to (has the same slope as) the line y=2x-7
The equation of the line in standard form is
Answers
Answer:
slope of line AB = 5
Let the required line be 'l'.
since AB is parallel to 'l'.
so slope of 'l' = slope of AB = 5.
So, the required equation of line which passes through (4,5) and having slope 5 is given by
y - 5 = 5(x - 4).........[using slope point form]
y = 5x - 20 + 5
y = 5x - 15.
Step-by-step explanation:
The measure of an angle is 47.6°. What is the measure of its complementary angle?
Answers
Answer:
42.4°
Step-by-step explanation:
complementary angles sum to 90° , then
complement of 47.6° = 90° - 47.6° = 42.4°
A submarine is descending to examine the seafloor 2100 feet below the surface. It takes a submarine two hours to make this decision. What’s an equation to represent the relationship between submarines elevation time
Answers
Elevation = 0 - 1050 × Time or Elevation = -1050t, where Elevation is in feet and Time is in hours, is the expression that describes the connection between the submarine's elevation and time.
What is a mathematical measure of time?Seconds, mins max, minutes, days, periods, months, and years are the fundamental elements of time. To determine the time of day, we use secs, minutes, as well as hours; to determine the date, we use times, months, and years. The lesser measures of time are seconds, minutes, and hours, while the larger ones are days, months, and years.
Assuming that the submarine is descending at a constant rate, we can use the equation:
Elevation = Initial Elevation - Rate × Time
where Initial Elevation is the starting elevation (in this case, the surface), Rate is the rate of descent, Time is the time elapsed, and Elevation is the current elevation.
In this case, the Initial Elevation is 0 feet (the surface), the Rate is -1050 feet per hour (since the submarine is descending at a rate of 1050 feet per hour), and Time is the elapsed time in hours.
Therefore, the equation that represents the relationship between the submarine's elevation and time is:
Elevation = 0 - 1050 × Time
or
Elevation = -1050t
where Elevation is in feet and Time is in hours.
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PLEASE ANSWER ASAP TY
In triangle ABC below, BD is the altitude. Find the length of DC. Leave your answer in
simplified radical form.
Answers
Answer:
Step-by-step explanation:
Step 1: Find AB Use Pythagoras Theorem
AB = \(\sqrt{AC^{2} -BC^{2} } = \sqrt{12^{2} -8^{2} } = \sqrt{80}\)
Step 2: Find the Area of the triangle ABC
Area = \(\frac{1}{2}AB.BC = \frac{1}{2}\sqrt{80}.8 = 4\sqrt{80}\) = \(16\sqrt{5}\)
Step 3: Find BD. Use the area of the triangle above
Area = \(\frac{1}{2}BD.AC\)
We already known the Area and AC so, we just plug all the number in
BD = \(\frac{2. Area}{AC}\) = \(\frac{2.16\sqrt{5}}{12}\) = \(\frac{8\sqrt{5}}{3}\)
Step 4: Find DC. Use Pythagoras Theorem of the triangle BDC
DC = \(\sqrt{BC^{2}-BD^{2} }\) = \(\sqrt{8^{2}-(\frac{8\sqrt{5}}{3})^{2}}\) = \(\frac{16}{3}\)
Jay's world ascendants as an equation 56 is 14 more than the number 14 + P = 56 which statement best describes Jason's work
Answers
The statement that best describes Jace's work is D. Jace is correct. The phrase more than suggests addition, so Jace showed that 14 plus a variable equals 56.
How can the the correct sentence be known?The concept that will be used here is word problem solution , then we need to interprete it then perform the neccessary simplification. . We were told that the sentence as an equation is 56 is 14 more than a number.
14+ = 56
then we can represent the number as X
then input into the equation as:
14+X = 56
x=56-14
=42
Therefore, option D is correct.
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complete question:
Jace wrote a sentence as an equation.
56 is 14 more than a number.
14+ = 56
Which statement best describes Jace's work?
Jace is not correct. The phrase more than suggests using the symbol > and Jace did not use that symbol.
Jace is not correct. He was correct to use addition, but the equation should be 56+ p = 14
Jace is not correct. The first number in the sentence is 56, so the equation should start with 56.
Jace is correct. The phrase more than suggests addition, so Jace showed that 14 plus a variable equals 56.
Line a has a slope of -8/7. Line r is perpendicular to q. What is the slope of line r
Answers
Answer:
The slope of line r is 7/8.
Step-by-step explanation:
The slope of perpendicular lines is the opposite reciprocal (flip the fraction and change the sign).
I am assuming that you meant "a" instead of "q".
PLEASE HELP!!!!!!!!!!!!!
A handicapped ramp is being constructed for the front entrance of First National Bank in Springfield. ADA guidelines requires a rise angle from the foot of the ramp (point furthest from the entrance) not to exceed 4.8 degrees. This means the vertical to horizontal ratio cannot exceed 1:12. If the handicapped ramp must start 15 feet away from the front entrance, contractors estimate the rise to be about 3 feet.
Part A: Explain thoroughly whether or not these ramp dimensions meet the ADA guidelines.
Part B: If the rise estimate does not meet ADA requirements, provide a measurement that would meet the guidelines.
Answers
a) These ramp dimensions do not meet the ADA guidelines.
b) A measurement that would meet the guidelines is the ramp starting 39 feet away, with a height of 3 meters.
What is a slope?The slope of a situation is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
For the ramp in this problem, we have that the vertical change and the horizontal change are given as follows:
The vertical change is of: 3 feet.The horizontal change is of: 15 feet.The ratio between the vertical change to the horizontal change is of:
3/15 = 1/5.
Which is greater than 1/12, hence the ramp does not meet the ADA guidelines.
If the horizontal change was 13 times the vertical change, it would meet the ratio, hence a possible measurement is of:
3 feet vertical.39 feet horizontal.As the ratio would be of:
3/39 = 1/13 < 1/12.
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A. g(x) = 2(x3 + 4)
B. g(x) =
(x3 + 4)
C. g(x) = 2x3 + 4
D. g(x) =x3 + 4
Answers
Answer: C. \(g(x)=2x^3+4\)
Step-by-step explanation:
When the coefficient gets larger, the graph will stretch more, getting closer to the y axis.
\(2x^2-20x=x^{2} -19\)
Answers
Answer:
x = 1, x = 19
Step-by-step explanation:
Given
2x² - 20x = x² - 19 ( subtract x² - 19 from both sides )
x² - 20x + 19 = 0 ← in standard form
(x - 1)(x - 19) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
x - 19 = 0 ⇒ x = 19
(Related to Checkpoint 9.4) (Bond valuation) A bond that matures in
13
years has a
$1 comma 000
par value. The annual coupon interest rate is
12
percent and the market's required yield to maturity on acomparable-risk bond is
14
percent. What would be the value of this bond if it paid interest annually? What would be the value of this bond if it paid interest semiannually?
Question content area bottom
Part 1
a. The value of this bond if it paid interest annually would be
$.
(Round to the nearest cent.)
Answers
The value of this bond, if it paid interest annually, would be $850.78.
What is the value of the bond when interest is paid annually?In order to calculate the value of the bond, we need to use the present value formula for a bond. The present value of a bond is the sum of the present values of its future cash flows, which include both the periodic coupon payments and the final principal payment at maturity.
To calculate the present value of the annual coupon payments, we can use the formula:
PV = C × (1 - (1 + r)⁻ⁿ) / r,
where PV is the present value, C is the coupon payment, r is the required yield to maturity, and n is the number of periods.
In this case, the coupon payment is $120 ($1,000 par value × 12% coupon rate), the required yield to maturity is 14% (0.14), and the number of periods is 13. Plugging these values into the formula, we get:
PV = $120 × (1 - (1 + 0.14)⁻¹³) / 0.14
≈ $850.78.
Therefore, the value of this bond, if it paid interest annually, would be approximately $850.78.
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Point of intersection Question:
Mike has $9.85 in dimes and quarters. If there are 58 coins altogether,
how many dimes and how many quarters does Mike have? Use the point of intersection to find the answer. Explain how you used a formula to calculate the # of quarters and dimes
Answers
Answers:
He has 27 quarters and 31 dimes
=========================================================
Work Shown:
d = number of dimes
q = number of quarters
d+q = 58 since there are 58 coins of only these two types
d = 58-q
10d+25q = 985 .... note that 985 cents is $9.85
10(58-q)+25q = 985 .... replace d with 58-q
580-10q+25q = 985
15q+580 = 985
15q = 985-580
15q = 405
q = 405/15
q = 27 ..... Mike has 27 quarters
d = 58-q
d = 58-27
d = 31 .... Mike also has 31 dimes
-----------
As a way to check:
d+q = 31+27 = 58 so that works out
and
10d+25q = 10*31+25*27 = 310+675 = 985
so that works out as well. The answer is confirmed.
Write the rational numbers rounded to three decimal palaces.
19/6=
And
7/18=
Answers
0.389 ( 3 dp )
There are 6 squares in a chocolate bar. How many squares are there in twelve chocolate bars?
Answers
Answer: 72
Step-by-step explanation:
12*6
The circle graph shows how Jane's family budgets a total of $45,000 for the year.
Insurance.
$3600
Utilities
$3150
Clothing.
$2700
Transportation
$1350
Entertainment-
$5400
Savings
$4050
Taxes
$7200
Food
$7650
Housing
$9900
Find the percentage of the total budgeted for each category listed below.
Answers
The percentage that each expense has out of the total budgeted amount of $45,000 have been computed, where insurance has 8.00%, Utilities 7.00% and so on.
What is a percentage?
In this case, percentage refers to proportion of each expense from the total budgeted expense of $45,000, which means that in order to total budgeted expense of $45,000, which means that in order to compute the percentage of total budgeted for each expense category, we divide the expense by the total budgeted expense
Insurance=$3600/$45,000=8.00%
Utilities=$3150/$45,000=7.00%
Clothing=$2700/$45000=6.00%
Transportation=$1350/$45000=3.00%
Entertainment=$5400/$45000=12.00%
Savings=$4050/$45000=9.00%
Taxes=$7200/$45000=16.00%
Food=$7650/$45000=17.00%
Housing=$9900/$45000=22.00%
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A Closer Look at the Euler Method Question 2, 2.5.5 Part 1 of 2 Apply the improved Euler method to approximate the solution on the interval [0, 0.5] with step size h = 0.1. Construct table showing values of the approximate solution and the actual solution at the points x = 0.1, 0.2, 0.3, 0.4, 0.5. y'=y-3x-1, y(0) = 1; y(x) = 4+ 3x-3 ex Complete the table below. (Round to four decimal places as needed.) Xn 0.1 0.2 0.3 0.4 0.5 Actual, y (xn) HW Score: 0%, 0 of 2 points Points: 0 of 1 O
Answers
The improved Euler method is used to approximate the solution of the given differential equation y' = y - 3x - 1 on the interval [0, 0.5] with a step size of h = 0.1. A table is constructed to display the values of the approximate solution and the actual solution at specific points: x = 0.1, 0.2, 0.3, 0.4, and 0.5.
The improved Euler method is applied to approximate the solution of the given differential equation y' = y - 3x - 1 on the interval [0, 0.5] with a step size of h = 0.1. The table below shows the values of the approximate solution and the actual solution at specific points: x = 0.1, 0.2, 0.3, 0.4, and 0.5.
Xn: 0.1 0.2 0.3 0.4 0.5
Actual: y(0.1) y(0.2) y(0.3) y(0.4) y(0.5)
To calculate the approximate solution using the improved Euler method, we can follow these steps:
1. Set the initial condition y(0) = 1.
2. Iterate through the given points using the step size h = 0.1.
3. Use the formula:
y(n+1) = y(n) + (h/2) * [f(x(n), y(n)) + f(x(n+1), y(n) + h * f(x(n), y(n)))],
where f(x, y) = y - 3x - 1.
4. Calculate the values of the approximate solution at each point.
By applying these steps, you can complete the table by finding the values of the approximate solution using the improved Euler method at x = 0.1, 0.2, 0.3, 0.4, and 0.5. Finally, compare these approximate values with the actual solution values to evaluate the accuracy of the method.
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HURRY!! (52 POINTS!!)
The ages of people visiting a senior center one afternoon are recorded in the line plot.
A line plot titled Ages At Senior Center. The horizontal line is numbered in units of 5 from 60 to 115. There is one dot above 80 and 110. There are two dots above 70 and 85. There are three dots above 75.
Does the data contain an outlier? If so, explain its meaning in this situation.
A. No, there is no outlier. This means that the people were all the same age.
B. No, there is no outlier. This means that the people are all around the mean age.
C. Yes, there is an outlier at 110. This means that one person's age was 110, which is 25 years older than the next closest age.
D. Yes, there is an outlier of 110. This means that the average person at the center is 110 years old.
Answers
Answer:
C. Yes, there is an outlier at 110. This means that one person's age was 110, which is 25 years older than the next closest age.
Step-by-step explanation:
An outlier is a data point that sticks out like a sore thumb. It's so different from the rest of the data that it makes you wonder if it's a mistake or a miracle. One way to spot an outlier is to use the 1.5IQR rule, where IQR stands for interquartile range. The interquartile range is the gap between the third quartile (Q3) and the first quartile (Q1) of the data. The 1.5IQR rule says that any data point that is more than 1.5*IQR above Q3 or below Q1 is an outlier.
In this case, the first quartile (Q1) is 75, the third quartile (Q3) is 85, and the interquartile range (IQR) is 10. So, any data point that is more than 1.5*10 = 15 above 85 or below 75 is an outlier. The only data point that does this is 110, which is 25 above 85. That means 110 is an outlier.
What does this outlier mean in this situation? It means that one person who came to the senior center that afternoon was way older than the rest of the folks. The average age of the visitors was not changed by this outlier, since it was just one out of 12 data points. But, the outlier does mess up the range and the standard deviation of the data, making them bigger than they would be without the outlier.
Answer:The answer is C
Step-by-step explanation:I did the test.
a subset of outcomes of the sample space is called a(n)
a. event
b. solution set
c. sample set d. probability experiment
Answers
The correct answer is (a) event. An event is a subset of outcomes from the sample space. It represents a specific outcome or set of outcomes that we are interested in. Events can be simple, consisting of a single outcome, or they can be compound, consisting of multiple outcomes.
For example, consider rolling a fair six-sided die. The sample space is {1, 2, 3, 4, 5, 6}. Let's say we are interested in the event of rolling an even number. The event in this case would be {2, 4, 6}, which is a subset of the sample space.
Events can also be mutually exclusive, meaning they cannot occur at the same time, or they can be independent, meaning the occurrence of one event does not affect the probability of the other event occurring.
In summary, an event is a subset of outcomes from the sample space and represents a specific outcome or set of outcomes that we are interested in. It is an important concept in probability theory.
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