The statement “Every sample space S is a finite set” is false because some sample spaces can be infinite, such as rolling a continuous random variable.
Explanation:The statement “Every sample space S is a finite set” is false. A sample space is the set of all possible outcomes of a random experiment. While some sample spaces may be finite, not all sample spaces are. There are situations where the sample space can be infinite, such as when rolling a continuous random variable like a dice.
For example, the sample space of rolling a fair six-sided die is finite, consisting of the numbers {1, 2, 3, 4, 5, 6}. However, the sample space of choosing a real number between 0 and 1 is infinite, as there are infinitely many possible outcomes between 0 and 1.
Therefore, it is incorrect to say that every sample space is a finite set.
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Find the domain of the following piece wise function.
[4,8)
(2,8]
[2,8)
(4,8]
The domain is the second option:
(2, 8]
Which is the domain of the piece wise function?For a function y = f(x), we define the domain as the set of the possible inputs for the function.
Here we have a piecewise function that is defined in the 3 regions:
2 < x ≤ 4
4 < x < 8
x ≥ 8
So the domain is the set of any value larger than 2, and we can write that as:
(2, 8]
We end it at "8" becase is the last defined value and that is the only option that makes sense.
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eigen values of A= [1 2 1
0 2 1
0 0 3]
The eigen values of matrix A [tex]\left[\begin{array}{ccc}1&2&1\\0&2&1\\0&0&3\end{array}\right][/tex] are respectively, 1, 2, 3
What are eigen values?In mathematics, the eigen values are characteristic roots of the equation
| A - λI |,
where, A is matrix and λ is eigen value of the matrix
Properties of matrix,
1. Sum of diagonal elements = Sum of eigen values
2. Determinant of matrix = Product of eigen values
Given that,
Matrix A = [tex]\left[\begin{array}{ccc}1&2&1\\0&2&1\\0&0&3\end{array}\right][/tex]
The eigen values of A = ?
It is known that,
For the upper and lower triangular matrix, eigen values of the matrix are diagonal elements,
given matrix is, upper triangular,
Diagonal elements are 1, 2, 3
So, The eigen values will be 1, 2, 3
Thus, the eigen values are 1, 2, 3
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Suppose you plan to buy many blank compact disks. You check price lists and find out that
if you buy 100 CDs or fewer you pay $0.74 each. However, if you buy over 100 CDs the pricedrops to $0.69 for each additional CD up to 300.
(a)Write a function that describes the cost C(n) of n number of CDs purchased.
(b)What is the cost of 53 CDs?
(c)What is the cost for 201 CDs?
Answer:
a) C(n) = 0.74 * min(n, 100) + 0.69 * max(n - 100, 0)
b) 39.22
c) 143.69
Step-by-step explanation:
(a) We can write a piecewise function to describe the cost C(n) of n CDs purchased:
C(n) = 0.74 * min(n, 100) + 0.69 * max(n - 100, 0)
(b) The cost of 53 CDs is:
C(53) = 0.74 * min(53, 100) + 0.69 * max(53 - 100, 0) = 0.74 * 53 = 39.22
(c) The cost for 201 CDs is:
C(201) = 0.74 * min(201, 100) + 0.69 * max(201 - 100, 0) = 0.74 * 100 + 0.69 * 101 = 74 + 69.69 = 143.69
Find the maximum value of the function z=5x+3y subject to the following constraints.
x≥2
y22
6x+7y≤68
The maximum value of the function z = 5x + 3y subjected to the constraints is given as follows:
48.1665.
How to obtain the maximum value of the function?The function for this problem is defined as follows:
z = 5x + 3y.
The constraints are given as follows:
x ≥ 2.y ≥ 3.6x + 7y ≤ 68.x has a higher multiplier than y, hence the value of y should be minimized to obtain the maximum value, hence:
y = 3.
Then the value of x is obtained as follows:
6x + 7(3) = 68
6x = 47
x = 7.8333.
Then the maximum value of the function is given as follows:
z = 5(7.8333) + 3(3)
z = 48.1665.
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MP Model with Mathematics Jonathan uses this
area model to show the product of two mixed
numbers. What equation models the product?
The equation which models the product is, A = 6 x 8
What is multiplication?The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the components that are multiplied are referred to as the factors.
Given that,
A area model,
which has 6 box in column arrangement and 8 box in row arrangement,
Suppose, each box has 1 unit square area
Now, area of a model can be written as,
Area = Number of box in column x Number of box in row
Number of box in column = 6
Number of box in row = 8
Each box has 1 unit square area,
So,
A = 6 x 8
= 48 unit square
Hence, it can be represented as, A = 6 x 8
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Fred decided to use some change to buy some brownies that he wanted for dessert. After
pulling the coins from his pocket, Fred paid with 3 quarters, 4 dimes, 2 nickels, and 1
penny. How much money did Fred spend on brownies?
Answer:
Fred spent $3.18 on brownies.
number 6 only please help
Answer: 1
_
32
Step-by-step explanation: because the are skip count and adding the number every single time .
In a random survey, 9 out of 36 people preferred vanilla ice cream. What percent of people preferred vanilla ice cream? I would appreciate any help :)
Complete the equation for the line perpendicular to g(x) = 4x + 3 and passing
through the point (7,3)
y =
Two lines that are perpendicular to one another have a slope product that is negative one. If m1 and m2 are the slopes of the two lines, then m1.m2 = -1.
What is meant by line perpendicular?Many perpendicular lines can be seen in the actual world. Examples include the edges of a set square, a clock's arms during particular times of day, the corners of a blackboard, a window, and the Red Cross emblem. Right angles are formed when two perpendicular lines cross. Examine the slopes of the equations in order to determine whether they are perpendicular. Perpendicular lines' slopes are their opposite reciprocals.By comparing the equation of the line with y = mx + c, where m is the line's slope and c is its y-intercept, it is now possible to determine the slope of line y = 4x + 3.As a result, we may state that m1 = 4, which is the slope of this line.
As a result, m2 = -1/4 is the slope of the line perpendicular to this line.
Now, the 2nd line's general equation can be expressed as
y = (-1/4)x + c —— 1)
Since point (-12,4) is located on this line, we may solve for c by substituting y = -12 and x = 4 in the equation above.
We may finish the equation for the line perpendicular to the line y = 4x+3 once we know the value of c.
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Solve the following inequality: |2x+5|<2−x
Step-by-step explanation:
To solve the inequality |2x + 5| < 2 - x, we need to split it into two cases:
When 2x + 5 > 0:
In this case, the absolute value is positive, so we can simplify the inequality as follows:
2x + 5 < 2 - x
Expanding the left side:
3x + 5 < 2
Subtracting 5 from both sides:
3x < -3
Dividing both sides by 3:
x < -1
So the solution for this case is x < -1.
When 2x + 5 < 0:
In this case, the absolute value is negative, so we can simplify the inequality as follows:
(2x + 5) < 2 - x
Expanding the left side:
-2x - 5 < 2 - x
Adding x to both sides:
-2x - 5 + x < 2
Combining like terms:
-x - 5 < 2
Adding 5 to both sides:
-x < 7
Dividing both sides by -1:
x > -7
So the solution for this case is x > -7.
Taking the union of the two solutions, we get:
-7 < x < -1.
This means that x is between -7 and -1, excluding -7 and -1.
solve and graph the inequality 3x < 13
The solution of the inequality 3x < 13 is x < 4.33.
None of the given option is correct.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Given:
An inequality,
3x < 13.
Simplifying,
x < 4.33
The graph is given in the attached image.
Therefore, the solution is x < 4.33.
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Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.
The three statements about his solution that are true include the following:
1. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5.
2. He did not multiply the numerator and denominator by the correct number to equal 1,500.
5. He should have multiplied the numerator and denominator by 75, not 30, because 20 × 75 = 1,500.
How to determine the true solutions?Based on the information provided, a mathematical expression which models the number of songs of each genre on Josiah's MP3 player to be 300 songs:
here, we have,
10/20 = x/1500
Multiplying the mathematical expression by 75, we have the following:
75 × (10/20) = x/1,500
750/1500 = x/1500
1,500x = (750 × 1,500)
x = (750 × 1,500)/1,500
x = 750.
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A paper mill cuts posterboards that are 36 inches long a posterboard is acceptable if the percent error of its length is less than one. 5% what is the range of acceptable length show your work
Answer:
The range of acceptable length is between 35.28 inches and 36.72 inches.
To calculate the range of acceptable length:
Lower bound: 36 in. - (36 in. x 0.05) = 35.28 in.
Upper bound: 36 in. + (36 in. x 0.05) = 36.72 in.
certain date, there had been a total
16,756 Performances of two Shows on broadway,
with 3312 more Performances of Show A than
were there of
Show B. How many Performances
each show?
There were _____ performances for Show A
The system of equations are solved and the number of performers for the show A is 10,034
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as T
Now , the value of T is
The total number of performers in the two shows T = 16,756
A + B = 16,756
The number of performers in show A = 3312 + number of performers in show B
Substituting the values in the equation , we get
A = B + 3,312
On simplifying the equation , we get
A + A - 3,312 = 16,756
Subtracting 3,312 on both sides of the equation , we get
2A = 16,756 + 3,312
2A = 20,068
A = 10,034
Hence , the equation is A = 10,034
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What is the equation of the line which has a gradient of -2 and passes through the point (1, 7)
The equation of line is y = -2x + 9 , where the slope is m = -2
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the point be represented as P ( 1 , 7 )
Let the slope of the line be m = -2
And , equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
Substituting the values in the equation , we get
y - 7 = -2 ( x - 1 )
On simplifying the equation , we get
y - 7 = -2x + 2
Adding 7 on both sides of the equation , we get
y = -2x + 9
Hence , the equation of line is y = -2x + 9
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Which set of equivalent fractions can be used when adding 7/8 and 5/12 ? Select three answer’s
The fraction equivalent of 7/8 + 5/12 is 31/24
What is a fraction in math?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
Given here: Two fractions 7/8 and 5/12
Now sum of the two fractions are 7/8+5/12
We know When two or more fractions with different denominators are added together, then we cannot the numerators directly. Thus Make the denominators of the fractions same, by finding the LCM of denominators and rationalising them with LCM(8,12)=24
Thus, 7/8+5/12= 21+10 /24
= 31/24
Hence, The fraction equivalent of 7/8 + 5/12 is 31/24
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-50 + 5/13p. When p = -26
The value of the given expression, -50 + 5/13p, when p = -26 is -60
Evaluating an expressionFrom the question, we are to evaluate the given expression for the given value of p
The given expression is
-50 + 5/13p
and
The given value of p is p = - 26
Substitute the given value of p into the given expression
That is,
-50 + 5/13p
When p = -26, the expression becomes
-50 + 5/13(-26)
Simplify
-50 + 5(-2)
-50 - 10
= - 60
Hence, the value of the expression is -60
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In traveling across flat land, you notice a mountain directly in front of you. Its angle of elevation (to the peak) is 3.5°. After you drive x = 11 miles closer to the mountain, the angle of elevation is 9°. Approximate the height of the mountain. (Round your answer to one decimal place.)
Answer:
Below
Step-by-step explanation:
See diagram
.158384 = height/x <====== x = height/.15838
.061162 = height /(11+x) <====sub in x from above into here
.061162 = height /(11+height/.158384) solve for height
.672789 + .386163 height = height
height = 1.1 mi high
What's the measurement of angle B?
Answer:
121
Step-by-step explanation:
The formula for calculating the sum of interior angles is ( n − 2 ) × 180
so you have 5 sides n=5
so total is 3*180 = 540
there are 3 right angles = 3/90 = 270
so 540-270 = 270 = angle B+ angle C
so 6x+1 +8x-11 =270
14x-10 = 270
14 x =280
x=20
B =6x+1 =121
25) Peter cut a piece of lumber 9 5/6 feet long from a piece that was 15 feet long. How much
of the lumber was left?
31/6 or 5.167 feet of lumber was left.
What are mathematical operations?The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.
Given, Peter cut a piece of lumber 9 5/6 feet long from a piece that was 15 feet long.
Since the total length of wood is 15 feet
Thus,
The remaining wood = 15 - (9 5/6)
The remaining wood = 6 - 5/6
The remaining wood = 31/6
therefore, 31/6 or 5.167 feet of the lumber was left.
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I need to find the domain and range
The domain and range are x >= 3 and y >= 0
How to find the domain and rangeFrom the question, we have the following parameters that can be used in our computation:
The graph
The domain is the set of the input values
On the graph, we have
Input values start from x = 3 and increases
So, the domain is x >= 3
The range is the set of the output values
On the graph, we have
output values start from y = 0 and increases
So, the range is y >= 0
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PLEASE HELP QUICKKKK
Answer:
Step-by-step explanation:
If 3<y<7 then,
0 < 14-2y < 8
14 - 2(3) = 8
14 - 2(7) = 0
FLUENCY AND SKILLS PRACTICE
Lesson 21 Session 2
Solving One-Variable Addition Equations
Solve each equation for the unknown. The answers are mixed up at the bottom.
of the page. Cross out the answers as you complete the problems.
What is d plus 3.2 equals 6.3 minus 2.5 and what’s 25 plus k plus 4(1/4) equals 37
The solution for the One-Variable Addition Equations is,
1: d = 0.6, 2: k = 11, and 3: y = 3.
What is a linear equation?When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."
There are both one-variable and two-variable linear equations.
Given 1: d + 3.2 = 6.3 - 2.5
subtract 3.2 from both sides
d = 6.3 - 2.5 - 3.2
d = 0.6
2: 25 + k + 4(1/4) = 37
divide 4/4 = 1
25 + k + 1 = 37
k = 37 - 26
k = 11
3: 4(1/2) + y = 10(1/2)
so 4/2 = 2 and 10/2 = 5
2 + y = 5
y = 3
Hence d = 0.6, k = 11, and y = 3.
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Canal Industries has provided the following information:
Net income, $260,000
Preferred shares issued, 6,200
Weighted average number of shares of common stock issued, 24,200
Cash dividends declared and paid on common stock, $32,000
Market price per share, $38
Weighted average number of treasury shares of common stock, 4,200
What is Canal's price/earnings ratio?
The Canal's price/earnings ratio is 2.92.
To calculate Canal's price/earnings ratio, we need to find the earnings per share (EPS) first. The EPS can be calculated by dividing the net income by the weighted average number of common shares outstanding.
The weighted average number of common shares outstanding can be calculated as follows:
Weighted average number of common shares outstanding = Total number of common shares - Weighted average number of treasury shares
Weighted average number of common shares outstanding = 24,200 - 4,200 = 20,000
EPS = Net income / Weighted average number of common shares outstanding
EPS = $260,000 / 20,000 = $13
Finally, the price/earnings ratio can be calculated by dividing the market price per share by the EPS:
Price/earnings ratio = Market price per share / EPS
Price/earnings ratio = $38 / $13 = 2.92
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7. Joanna took 35 minutes to and from school. If the journey to school was 5 minutes faster than the return journey, find the time taken: a. to school b. from school
Answer:
Step-by-step explanation: https://flexbooks.ck12.org/cbook/ck-12-middle-school-math-concepts-grade-6/section/6.15/primary/lesson/elapsed-time-msm6/
GIVING BRAINLIEST! CHECK IMAGE. is it possible for this function to have a degree of 5 and a positive leading coefficient? explain please!
What is the area of a 7 by 10 grid?
The area of a 7 by 10 grid would be 70 square units.
This is calculated by multiplying the length (7 units) by the width (10 units), resulting in 7 x 10 = 70.
2.
1.
Naira
280
400
800
2500
Change each of the given amounts in Naira to the following currencies. Use the exchange
rates given in the previous page.
3750
Pound sterling
Amount in
Us dollars
Cedis
Leones
Franc (CFA)
In each of the following are two equivalent amounts of money. Find the exchange rate
terms of N1. Limit your answer to 2 decimal places.
a. N150 = £18
d. N80 = US$20
b. £52 = N400
e. N9.36 = Le 72
h. N25 = 1 178 frs
A book costs £3. If the rate of exchange is £1 = N8.33, find its cost in Naira
Mr Awolowo wants to send £500 to his brother in the United Kingdom How much
pay in Naira at the post office?
The cost of the book in Naira is N 24.99
Mr. Awolowo needs to pay N 4165 at the post office.
Rate of exchange of currency:An exchange rate determines the value of one unit of currency in relation to another type of money. Which means exchanging the price from one currency to another currency.
People use the exchange rates when they want to travel abroad and It is necessary to convert cash into local currency in order to do purchases locally.
Here we have
The book costs £3. If the rate of exchange is £ 1 = N 8.33
Cost of the book in Naira = 3 × N 8.33
= N 24.99
Mr Awolowo wants to send £500 to his brother in the United Kingdom
As we know the rate of exchange, is £ 1 = N 8.33
=> £500 = 500 × 8.33 = N 4165
Therefore,
The cost of the book in Naira is N 24.99
Mr. Awolowo needs to pay N 4165 at the post office.
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I’m not sure how to solve this, really need help, would appreciate if you showed work so i could learn how to solve it too thank you
Answer:
There are two solutions:
[tex]\boxed{v = \dfrac{4}{3} \text { and }v = \dfrac{3}{2}}\\\\or\\\\\boxed{v = 1.3333.... \text{ and }v= 1.5}\\[/tex]
Step-by-step explanation:
The given equation is :
[tex]\dfrac{2}{v-2}=-6\:+\:\dfrac {1}{v-1}\\\\[/tex]
Find the LCM of the denominators:
LCM = [tex]\left(v-2\right)\left(v-1\right)[/tex]
Multiply by LCM:
[tex]\dfrac{2}{v-2}\left(v-2\right)\left(v-1\right)=-6\left(v-2\right)\left(v-1\right)+\dfrac{1}{v-1}\left(v-2\right)\left(v-1\right)[/tex]
Simplify
[tex]\dfrac{2}{v-2}\left(v-2\right)\left(v-1\right):\quad 2\left(v-1\right)[/tex]
[tex]\dfrac{1}{v-1}\left(v-2\right)\left(v-1\right):\quad v-2[/tex]
So the equality becomes
[tex]2\left(v-1\right)=-6\left(v-2\right)\left(v-1\right)+v-2[/tex]
Expand the brackets:
[tex]2\left(v-1\right):\quad 2v-2[/tex]
[tex]\text {Right side becomes: }\\-6\left(v-2\right)\left(v-1\right)+v-2\\Expand \; \left(v-2\right)\left(v-1\right):\quad v^2-3v+2\\\\\text {Right side becomes}\\-6\left(v^2-3v+2\right) + v -2\\= -6v^2+6\cdot \:3v-6\cdot \:2 + v - 2\\\\\\= -6v^2+18v-12+v-2\\\\\text{Simplify}\\= -6v^2+19v-14\\\\\text{Left side}2(v-1= 2v-2\\\\\text{Finally we get}\\2v - 2 = 6v^2+19v-14\\\\[/tex]
Switch sides:
[tex]-6v^2+19v-14=2v-2[/tex]
Move 2 from right to left(sign changes)
[tex]-6v^2+19v-14 + 2 =2v\\\rightarrow -6v^2+19v-12=2v\\\\[/tex]
Move 2v to left side(sign changes)
[tex]-6v^2+19v-12-2v = 0\\\\\rightarrow -6v^2+17v-12=0\\\\[/tex]
This is a quadratic equation which can be solved with a quadratic equation calculator. I used a calculator to solve this:
The solutions are:
[tex]v = \dfrac{4}{3} \text { and }v = \dfrac{3}{2}\\\\\\\text{In decimal these would be}\\\\v = 1.3333.... \text{ and v}= 1.5\\[/tex]
According to the audio, what can be inferred from the fairy’s action?
She was appreciative.
She was a gossiper.
She was dishonest.
She was vengeful.
From the audio, what is inferred from the fairy's action is that she was appreciative. The Option A is correct.
What does the word fairy mean?A fairy tale is a story, typically intended for children, that features fantastic and wondrous characters such as elves, goblins, wizards, and even, but not always, fairies. The term "fairy" tale appears to refer to a story's fantastic and magical setting or magical influences, rather than the presence of a fairy character within that story.
Fairy tales are frequently traditional; many were passed down from storyteller to storyteller before being written down in books. Examples of Fairy Tale includes Snow White, Cinderella, Rip Van Winkle, The Twelve Dancing Princesses, Rumpelstiltskin, Thumbelina
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Answer: She was vengeful
Step-by-step explanation:
The audio states that the other fairies were giving the princess positive spells while a fairy that wasn't invited to the party casted an evil spell on the princess, making her sleep for a 100 years. (It's based on the sleeping beauty story)