Which graph shows a function whose inverse is also a function?
If g(x) is the inverse of f(x), what is the value of f(g(2))?
Answers
It is discovered that the (1) graph represents a function whose inverse is also a function using the concept of an inverse function.
What is a graph?The set of ordered pairs is the graph of a function f in mathematics, where these pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.
To develop a graph is to make a diagram that depicts the relationship between two or more objects.
Make a sequence of bars on graph paper as an example of a graph.
Since there is only one value of x in the first graph for any value of y, the inverse is also a function, making this the right answer.
The inverse is not a function in the second graph since, for instance, y = 0 when x = -1 and when x = 1.
For instance, in the third graph, the inverse is not a function because y = -3 when x = 0 and x = 2.
For instance, in the fourth graph, y = 1 for two different values of x, proving that the inverse is not a function.
Therefore, it is discovered that the (1) graph represents a function whose inverse is also a function using the concept of an inverse function.
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Correct question:
Which graph shows a function whose inverse is also a function?
Related Questions
How do you find the minimum and maximum of a quadratic function?
Answers
For a quadratic function f(x) = ax² + bx + c, we can find the minimum and maximum value using the formula -b/2a or by graphing the function.
We know that the general form of quadratic function is f(x) = ax² + bx + c ; a ≠ 0
The graph of quadratic function is a parabola. The graph is parabola that either opens upward or downward.
For a quadratic function is f(x) = ax² + bx + c,
if a is positive (a > 0) then the parabola opens upward.
In this case you will be finding the minimum value of f(x) at the vertex of parabola.
if a is negative (a < 0), then the parabola opens downward.
In this case you will find its maximum value of f(x) at the vertex of parabola.
Also, the value of -b/2a will tell you the minimum or maximum value of f(x) which is the vertex of the parabola.
Therefore, to find the minimum and maximum of a quadratic function f(x) = ax² + bx + c :
1) find vertex of function from the graph
2) use formula -b/2a
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A triangle has two sides measuring 8. 5 cm and 15 cm. What is the greatest whole number length possible for the third side? explain.
Answers
The greatest whole number possible length for the given measures of triangle is 23 cm.
As given in the question,
Measure of two side-length of a given triangle are :
Let 'x' be the side length = 8.5cm
And 'y' be the side length = 15cm
'z' be the side length of the third side of a triangle.
Sum of two sides is greater than third side and difference of two sides is smaller than the third side.
y - x < z < y + x
⇒ 15 - 8.5 < z < 15 + 8.5
⇒ 6.5 cm < z < 23.5cm
Greatest whole number representing length of the third side of a triangle is less than 23.5 .
⇒ z = 23cm
Therefore, the length of the third side of a triangle represented by greatest whole number is equal 23cm.
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find the are of the parallelogram 10in by 9.8 and 5.6
Answers
The area of the parallelogram that has a base of 98 in. and a height of 5.6 in. is calculated as: 54.88 in.².
What is the Area of a Parallelogram?The area of a parallelogram is calculated as the product of its base length and its height. That is:
Area of parallelogram = base × height.
From the image given, we have the given dimensions of the parallelogram that we can use to find its area:
Base = 9.8 in.
Height = 5.6 in
Plug in the values:
Area of parallelogram = 9.8 × 5.6
Area of parallelogram = 54.88 in.²
Therefore, the exact answer is, 54.88 in.².
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The triangular base of a prism is a right triangle of sides a and b = 2a. The height h of the prism is equal to 10 mm and its volume is equal to 40 mm3, find the lengths of the sides a and b of the triangle.
Answers
A prism having a triangular base is a right triangle of sides a and b = 2a.
The lengths of side "a" is 3.464 mm.
The length of side "b" is 6.928 mm.
Volume of the Triangular Prism:
A triangular prism is an object in three dimensional space with a triangular base and three other triangles connected to it. A triangular prism has four corners, and the distance from the base to the diagonal vertex is called the height of the triangular prism.
It is given by the multiplication of the area of the base to the height of the prism.
V = (Area × height of prism)/3
=> V = Ah/3
we have given that,
Base of prism is right angle triangle with sides "a" and "b" such that b = 2a ---(1)
Height of prism (h) = 10mm
Volume (V) = 40mm³
the Area of triangluar base = 1/2 × base× height of triangular base
A = (1/2)a ×b
=> A = (1/2)a × 2a = a²
Volume of prism (V) = a²×h/3 = 40
=> a²×10/3 = 40
=> a² = 120/10 = 12
=> a = √12 = 2√3
=> a = 2(1.732) = 3.464
from equation (1) , b = 2a = 2(3.464)
=> b = 6.928
So, the lengths of sides of triangle are
a= 3.464 and b = 6.928
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Given N(-3,-7), O(-4,-2), P(1, -7), and Q(-2, y). Find y
such that NO|| PQ.
Answers
Answer:
y = 8
Step-by-step explanation:
Given N(-3,-7), O(-4,-2), P(1, -7), and Q(-2, y), you want to find y such that NO ║ PQ.
GraphWhen we plot the points, we see that point O is 1 unit left and 5 units up from point N. Point Q is on a line 3 units left of P, so it will need to be 3×5 = 15 units up from P in order for PQ to have the same slope as NO:
y = -7 +15 = 8
The value of y is 8; the point Q is (-2, 8).
Meteorologists in Texas want to increase the amount of rain delivered by thunderheads by seeding the clouds. Without seeding, thunderheads produce, on average, 300 acrefeet. The meteorologists randomly selected 29 clouds which they seeded with silver iodide to test their theory that average acrefeet is more.
What conclusion can they reach based on the above output when they set the significance level to be 0.10?
a.The data does not provided statistical evidence that the average acrefeet from seeded clouds is more than 300.
b.The data does provide statistical evidence that the average acrefeet from seeded clouds is more than 300.
c.The data does not provided statistical evidence that the sample average acrefeet from seeded clouds is more than 300.
d.Two of the above are correct.
e.We can not draw conclusions based on the above statistical output because the conditions are not met due to the extreme outliers.
Answers
Conclusion can they reach based on the above output when they set the significance level to be 0.10 is that we can not draw conclusions based on the above statistical output because the conditions are not met due to the extreme outliers.
Define meteorologists.A person with specific training in meteorology applies scientific principles to describe, comprehend, observe, or forecast atmospheric occurrences on earth and/or how the atmosphere impacts the planet's surface and life are meteorologists.
Given,
Meteorologists in Texas want to increase the amount of rain delivered by thunderheads by seeding the clouds. Without seeding, thunderheads produce, on average, 300 acrefeet. The meteorologists randomly selected 29 clouds which they seeded with silver iodide to test their theory that average acrefeet is more.
Conclusion can they reach based on the above output when they set the significance level to be 0.10 is,
e. We can not draw conclusions based on the above statistical output because the conditions are not met due to the extreme outliers.
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(03.01 LC)
The leg of a right triangle is 2 units and the hypotenuse is 3 units. What is the length, in units, of the other leg of
the triangle? (5 points)
O√5 units
O√13 units
5 units
O 13 units
Answers
2^2+b^2=3^2
4+b^2=9
b^2=5
b=sqrt(5)
So the other leg is the square root of 5 units
please i need help fast!!!
Answers
Answer:c
Step-by-step explanation:
which list could not be the measures of lengths of the threee sides of a give triangle
Answers
Based on the triangle inequality theorem, the list that could not be the measures of lengths of the three sides of a give triangle is: D. 12 yd, 35 yd, 20 yd.
What is the Triangle Inequality Theorem?The triangle inequality theorem expresses the relationship between the three lengths of sides that can form a triangle. If the sides are are a, b, and c, it states that:
a + b > c
a + c > b
c + b > a.
Considering this set of three sides, 5cm, 12 cm, 15 cm, we have:
5 + 12 > 15
17 > 15 [true]
5 + 15 > 12
20 > 12 [true]
12 + 15 > 5
27 > 5 [true]
Therefore, the measures of lengths 5cm, 12 cm, 15 cm, will form a triangle.
Same applies to 2 ft, 6 ft, 5 ft and 11 mi, 4 mi, 12 mi, except 12 yd, 35 yd, 20 yd.
This is because, 12 + 20 > 35 is not true.
Therefore, the answer is: D. 12 yd, 35 yd, 20 yd
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Complete Question:
Which list could not be the measures of lengths of the three sides of a given triangle?
A. 5cm, 12 cm, 15 cm
В. 2 ft, 6 ft, 5 ft
C. 11 mi, 4 mi, 12 mi
D. 12 yd, 35 yd, 20 yd
there is no such thing as a group of answer choices sound argument that is also valid. valid argument that is also sound. valid argument that is not sound. sound argument that is not valid.
Answers
There is no such thing like Sound argument that is not valid.
What is an argument that is valid?
Any argument whose conclusion is not supported by its premises is invalid (i.e., faulty). That is, the conclusion could still be wrong even though all the premises are true.
Because validity of the argument is a requirement for soundness
A valid argument is one in which we can demonstrate that, if its premises are true, its conclusion will also be true.A good argument is one with just true premises and is valid.A sound argument cannot be given false premises.A sound argument cannot support a valid one.An argument is valid and contains all true premises if it is sound. The argument is sound, so if all of the premises are true, the conclusion must also be true. It follows that the conclusion of a sound argument must be true since all of its premises are true.
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What is surface area of any figure?
Answers
Surface area of any figure is the area that the outer surface of any figure covers.
If we look at the different figures we find that these figures if placed somewhere or if we need to cover the figures with some kind of material then in order to find the the dimensions of the material we will need to find out the area that the overall surface of the figure will cover. This will reduce the time and complication of the calculations of every part of the shape. For example, If there is a need to find the surface area of the cylinder then we use the formula for its curved surface area as
S = 2πrh where r is the radius and h is the height of cylinder
Also, the total surface area will be expressed as
T = 2πr(r + h) where r is the radius and h is the height.
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Given the function h (x) = -10x + 5, find the corresponding range values when the domain is {-1,2,4]
-35
35
000000
15
- 15
25
-25
W
Answers
The range of the function f(x) = 5 -10x for domain {-1, 2, 4} is { 15, -15, -35}
What is Domain and Range of a function ?A function's domain and range are its constituent parts. Range, Domain, and Function. A is the domain and B is the co-domain if a function f: A B exists that maps every element of A to an element in B. 'b', where (a,b) R, provides the representation of an element 'a' under a relation R. The collection of photos is the function's range. In general, a function's domain and range are denoted as follows:
Domain(f) = {x ∈ R} and range(f)={f(x) : x ∈ domain(f)}
"All the values" that are input into a function are referred to as the domain of a function. The collection of all potential inputs for a function is its domain. Think of this box as the f(x) = 2x function. The domain is only the collection of natural numbers when the input values are x = 1,2,3,4,..., and the values that are returned are referred to as the range. However, f(x) = 2x is often defined for all real values of x, and as a result, its domain is the set of all real numbers, which is represented by (-∞, ∞). The general formulae for determining the domain of various types of functions are listed below. The set of all real numbers, or R, is used here.
The collection of all a function's outputs is its range. Example: Let's have a look at the function f: A->B, where f(x) = 2x and A and B each represent a "collection of natural numbers." The domain in this instance is A, and the co-domain is B. The range then appears as the function's output. Set of even natural numbers is the range. The components of the co-domain that are mapped are known as the pictures, while the elements of the domain are known as pre-images. The set of all pictures of the domain's elements in this case serves as the function's range, as does the set of all of its outputs.
Domain of the function x = {-1,2,4}
The function is f(x) = 5 - 10x
range when x = -1
f(x) = 5 - 10*(-1) = 15
when x = 2
f(x) = 5 - 10* 2 = -15
and x= 4
f(x) = 5 - 10*4 = -35
The range of the function for domain {-1, 2, 4} is { 15, -15, -35}.
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The range of the function f(x) = 5 -10x for domain {-1, 2, 4} is { 15, -15, -35}
What is Domain and Range of a function ?
The domain of a function is the set of all possible inputs for the function. It is the set of all x-values which will make the function "work", and will output real y-values. The range of a function is the set of all possible outputs of the function. It is the set of all y-values which can be produced by the function for the given set of x-values. In other words, it is the set of values that result when the function is applied to all the elements of the domain. In order for a function to be defined, both the domain and the range must be specified.
Domain of the function x = {-1,2,4}
The function is f(x) = 5 - 10x
range when x = -1
f(x) = 5 - 10*(-1) = 15
when x = 2
f(x) = 5 - 10* 2 = -15
and x= 4
f(x) = 5 - 10*4 = -35
The range of the function for domain {-1, 2, 4} is { 15, -15, -35}.
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2x-7y=12 slope intercept form please help
Answers
Answer:
[tex]y=\frac{2}{7} x -\frac{12}{7}[/tex]
students who study for 7 hours over the course of a week will perform better than students who cram for 7 hours the night before the exam. the dependent variable in this hypothesis is:
Answers
The dependent variable in this hypothesis is test performance.
What is a dependent variable?
In mathematical modelling, statistical modelling, and experimental sciences, there are dependent and independent variables. Dependent variables get their name because, during an experiment, one‘s values are examined under the assumption as well as demand that they are dependent on the value of another variable due to some law or rule (for example, a mathematical function). In the context of the experiment in question, independent variables are those that are not thought to be depending on other variables. Time, space, specific gravity, mass, fluid flow rate and previous values of certain observed value of interest (such as the size of the human population) are examples of common independent variables that can be used to forecast future value systems (the dependent variable).
The outcome of this hypothesis is the dependent variable.
Hence, the dependent variable in this hypothesis is test performance.
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please help me!!!.....
Answers
Answer: 52 degrees
Step-by-step explanation:
angles stay the same even when the size is decreased. they are similar so the angle is the same. while line ab might be 2 units, and line de might be 1, the angle would stay the same.
The point (2, -3) is the midpoint of segment JK . Point K is located at (-6, -3). What is the length of segment JK ?
Answers
Answer:
16
Step-by-step explanation:
The distance from the midpoint to [tex]K[/tex] is [tex]|-6-2|=8[/tex].
By definition, this is half the length of [tex]\overline{JK}[/tex], meaning [tex]JK=16[/tex].
Last year, Elsa opened an investment account with$5400 . At the end of the year, the amount in the account had increased by 6.5%. How much is this increase in dollars? How much money was in her account at the end of last year? Increase in amount and Year-end amount
Answers
Answer:
Here you go
Step-by-step explanation:
The increase in amount is $351.00 ($5400 x 0.065 = $351). The amount in the account at the end of the year was $5751.00 ($5400 + $351 = $5751).
there are about 10,000 taste buds on a human tongue. write this number in scientific notation
Answers
Answer:
I guess 1*10^4 is the answer. Not sure.
Answer:
1 * 10⁴
Step-by-step explanation:
10,000 = 10 * 10 * 10 * 10 = 1 * 10⁴
coffee is draining from a conical filter into a cylindrical coffeepot at the rate of 10 in3/min. (a) how fast is the level in the pot rising when the coffee in the cone is 5 in deep?
Answers
The level in the pot rising when the coffee in the cone is 5 in deep is 0.35 in/min.
Here the variables are the height of the coffee in the filter hf , the radius of the top of the coffee in the filter rf , and the height of the coffee in the pot hp:
We allowed Vp to represent the volume of coffee in the pot. We are interested in the instant when
hf = 5 in and dVp/dt = 10 in³/min.
The question is dhp/dt =? when dVp/dt = 10 in³/min and hf = 5 in
We need to relate hp to the other variables. In the pot (idealized as a cylinder), we have the volume Vp as Vp = π(3)²hp = 9πhp in³(since the volume of a cylinder of radius r and height h is V = πr²h).
Differentiation of Vp with respect to time gives dVp/dt = 9πhp/dt or
dhp/dt = (1/9π).(dVp/dt)
When dVp/dt = 10 in³/min and hf = 5 in, we have
dhp/ dt = 1/9π(10)
= 10/9π in/min
dhp/ dt ≈ 0.35 in/min (notice that the answer here is independent of hf ).
Hence, the level in the pot rising when the coffee in the cone is 5 in deep is 0.35 in/min.
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Write an inequality for the statement:
negative three eighths is at most the product of a number and negative five sevenths
A negative 3 over 8 ≤ negative 5 over 7w
B negative 5 over 7 ≤ negative 3 over 8w
C negative 5 over 7 ≥ negative 3 over 8w
D negative 3 over 8 ≥ negative 5 over 7w
Answers
The inequality for the statement negative three eighths is at most the product of a number and negative five sevenths is negative 3 over 8 ≤ negative 5 over 7w which is option A.
What is inequality?inequality, In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
negative three eighths = -3/8
negative five sevenths = -5/7
At most for inequality symbol = [tex]\leq[/tex]
mathematically
-3/8 [tex]\leq[/tex] -5/7w
which is negative 3 over 8 ≤ negative 5 over 7w
In conclusion the inequality for the statement is negative 3 over 8 ≤ negative 5 over 7w
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Which tatement are true? Select all that apply. A) The equation |-x - 4| = 8 will have two olution. B) The equation 3. 4|0. 5x - 42. 1| = -20. 6 will have one olution. C) The equation |1/2x - 3/4| = 0 will have no olution. D) The equation |2x - 10| = -20 will have two olution. E) The equation |0. 5x - 0. 75| 4. 6 = 0. 25 will have no olution. F) The equation |1/8x - 1| = 5 will have infinitely many olution
Answers
The true statement is option (A) The equation |-x - 4| = 8 will have two solution
Consider each statement
All the statements are absolute value equation
Part A
|-x-4| = 8
We can write it in two way
-x - 4 = 8
- x = 12
x = -12
Then,
-(-x-4) = 8
x+4 = 8
x = 4
It has two solution
Part B
3. 4|0. 5x - 42. 1| = -20. 6
Divide both side by 3.4
|0.5x - 42.1| = -103/17
Absolute value cannot be negative
The equation has no solution
Part C
|1/2x - 3/4| = 0
1/2x - 3/4 = 0
1/2x = 3/4
x = 3/4 ÷ 1/2
x = 3/2
The equation has one solution
Part D
|2x - 10| = -20
Absolute value cannot be negative
This equation has no solution
Part E
|0. 5x - 0. 75| 4. 6 = 0. 25
Divide both side by 4.6
|0.5x - 0.75| = 5/92
The equation divided into two
0.5x - 0.75 = 5/92
x = 37/23
0.5x - 0.75 = -5/92
x = 32/23
The equation has two solution
Part F
|1/8x - 1| = 5
1/8x - 1 = 5
x = 48
1/8x - 1 = -5
x = -32
The equation has two solution
Therefore, the equation |-x - 4| = 8 will have two solution is true
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write the converse inverse and contrapositive of each conditional statement. Determine the truth of each of the new statements. a. if each side of a triangle has a length of 10, then the triangles perimiter is 30 b. if an angle is acute, then it has a measure greater than 0 and less than 90
Answers
If a triangle does not have one angle greater than 90°, then it is not an obtuse triangle. Remember that you create a contrapositive by inverting and swapping both terms.
What is the triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC.
If a triangle lacks one angle greater than 90°, it is not an obtuse triangle. Remember that a contrapositive is formed by inverting and swapping both terms. If you have if A then B, then the contrapositive is if not B then not-A. Because you've been given "If a triangle is obtuse, then
It has one angle with a measure greater than 90°," the converse would be "If a triangle has no angles with a measure greater than 90°, it is not an obtuse triangle." So, check through the options and see what fits in intent, even if it's not phrased precisely the same.
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Please help me to show your work for this. I know it's 7, but we need to show our work. 5.6 x 1.25
Answers
Answer:
Linked below.
Step-by-step explanation:
To solve, first line up your numbers. Then, multiply the ones place of the digit by the numbers on top individually. Write this below.
Do the same with all other places except add a zero each time there is one more row.
Two dice are rolled. What is the probability that the sum of the numbers rolled is either 2 or 5? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answers
Answer: first lowest: 1/3 second lowest:2/6
Step-by-step explanation:
Geometry HL question. Statements and proofs.
Answers
The proof that shows that ΔPRS ≅ ΔQSR by HL congruence theorem is explained below.
How to Prove that two Triangles are Congruent by HL?The HL congruence theorem can be used to prove that two triangles are congruent to each other if we can show that the two triangles are right triangles that have a pair of corresponding congruent legs, and a pair of congruent hypotenuse.
The proof for stating that triangles PRS and QSR are congruent is given below.
Statement Reasons
1. QS ≅ PR, PS ⊥ RS, QR ⊥ RS 1. Given
2. <RSP and <SRQ are right angles 2. Definition of perpendicular
3. SR ≅ RS 3. Reflexive property of congruency
4. ΔPRS ≅ ΔQSR 4. HL
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29. The school that Lilly goes to is selling tickets to a drama performance. On the first day of ticket sales the
school sold 3 adult tickets and 1 child ticket for a total of $38. The school took in $104 on the second
day by selling 6 adult tickets and 4 child tickets. Find the price of an adult ticket and the price of a child
ticket.
Answers
Answer:
the price of an adult ticket is $8, and the price of a child ticket is $14.
Step-by-step explanation:
To find the price of an adult ticket and the price of a child ticket, we need to set up a system of equations. Let "A" represent the price of an adult ticket and "C" represent the price of a child ticket.
On the first day, the school sold 3 adult tickets and 1 child ticket for a total of $38, so we can set up the following equation to represent this information:
3A + C = 38
On the second day, the school took in $104 by selling 6 adult tickets and 4 child tickets, so we can set up the following equation to represent this information:
6A + 4C = 104
Now that we have our two equations, we can solve for the values of A and C. We can use the elimination method to solve this system of equations. To do this, we need to multiply one of the equations by a constant so that one of the variables has the same coefficient in both equations. We'll multiply the first equation by 2:
6A + 2C = 76
We can then subtract this equation from the second equation to eliminate the C term:
6A + 4C - 6A - 2C = 104 - 76
This simplifies to:
0A + 2C = 28
Dividing both sides by 2, we get:
C = 14
We can now substitute this value for C in one of our original equations and solve for A. We'll use the first equation:
3A + 14 = 38
Subtracting 14 from both sides, we get:
3A = 24
Dividing both sides by 3, we get:
A = 8
Therefore, the price of an adult ticket is $8, and the price of a child ticket is $14.
Marina needs to earn at least each month to cover her living expenses. Her income comes from a commission that she earns on everything she sells. What is the minimum amount she needs to sell in order to earn ?
Answers
Answer:
Step-by-step explanation:
Amount sold = $23000
Percentage rate = 15%
Total salary = Amount sold × Percentage rate = $23000 × (15 / 100) = $3450
Answer is $3450
Solve for x.
-4> 10-7x
Answers
Answer:
x > 2
Step-by-step explanation:
-4 > 10-7x
-4 - 10 > -7x
-14 > -7x
Inequality reverses when dividing or multiplying a negative number.
-14/-7 < x
2 < x
x > 2
0.796 divided by 9.95
Answers
Answer:
0.08
Step-by-step explanation:
bert and ernie each have a well-shuffled standard deck of 52 cards. they each draw one card from their own deck. compute the probability that: bert and ernie both draw a heart.
Answers
The probability that Bert and Ernie both draw a heart = (1/4)²
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
Probability = (Number of possible outcomes)/(Total number of outcomes)
Bert:
Probability of drawing a heart = 1/4
Ernie:
Probability of drawing a heart = 1/4
The probability that Bert and Ernie both draw a heart = 1/4 * 1/4 = (1/4)²
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