Joe, Keitaro, and Luis play tennis. To decide who will play against each other in the first match, they put their names in a hat and choose two names without looking.
What subset of the sample space, A, represents the complement of the event in which Joe plays in the first match?
A = {KL}
A = {KJ, KL}
A = {KL, LK}
A = {KJ, KL, LJ}
Answer:
A = {KL}
Step-by-step explanation:
The subset of the sample space that represents the complement of the event in which Joe plays in the first match is A = {JL, KL}
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
The sample space of this experiment consists of all possible ways of choosing two names from a group of three.
Since the order in which the names are chosen does not matter, the size of the sample space is given by the number of combinations of 3 things taken 2 at a time, which is 3.
The three possible outcomes are: {JK, JL, KL}.
If we want to find the complement of the event in which Joe plays in the first match, we need to find the outcomes in which Joe does not play in the first match.
There are two such outcomes: JL and KL.
Therefore, the subset of the sample space that represents the complement of the event in which Joe plays in the first match is A = {JL, KL}
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A store is having a sale in which all items
are discounted 20%. Including tax, Colin paid $21 for a picture. If the
sales tax rate is 5%, what was the original price of the picture?
In linear equation, that price of shorts before discount was $25
What in mathematics is a linear equation?
An x-y linear relationship, or two variables in which the value of one of them (often y) relies on the value of the other one, is what is known as a linear equation in two variables (usually x).The dependent variable in this scenario is y since it depends on the independent variable, x.Assume that the price of shorts after the discount is x
Total payment = price of shorts + taxes
We know that:
total payment = $21
taxes = 5% = 0.05 of the price
This means that:
21 = x + 0.05x
21 = 1.05x
x = $20
Therefore, the price of the shorts is $20 after the discount
Now, we will get the price of the shorts before the discount:
Assume that the price of shorts before discount is y
We know that:
The discount was 20%
This means that Jennifer paid:
100% - 20% = 80% of the price of the shorts
Therefore:
80% of the price = $20
0.8y = 20
y = $25
This means that price of shorts before discount was $25.
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Which relation is a function?
Find the value of each variable
The 'x' and 'y' variables are highlighted in the box
Answer:
x = 7
y = 15
Step-by-step explanation:
Disclosure: After I had completed my answer, I found that Answerwell had already posted a solution. It is more straightforward than my approach. While the answers are the same, I'm still adding mine because 1) I worked hard on it, and 2) it illustrates there can be different ways of reaching a solution.
See attached worksheet.
A circle has a radius of 5 units, 3 students tried to calculate the circumference of the circle, put their answers in order from most accurate to least accurate31.4π units 10π units 31.4 units
A circle has a radius of 5 units, 3 students tried to calculate the circumference of the circle, put their answers in order from most accurate to least accurate
31.4π units
10π units
31.4 units
we know that
the circumference of a circle is equal to
[tex]C=2\pi r[/tex]we have
pi=3.14
r=5 units
substitute
[tex]\begin{gathered} C=2\pi(5) \\ C=10\pi\text{ units} \end{gathered}[/tex]the exact value is 10pi units
the approximate value (assume pi=3.14)
C=31.4 units
so
order from most accurate to least accurate is
10π units
31.4 units
31.4π units
order from least accurate to most accurate is31.4π units31.4 units10π unitsA ride-all-day amusement park ticket last season was $35, and this season it is $27
.
What is the percent Markdown?
Answer:
Step-by-step explanation:
35-27=8
Answer:22.85%
Step-by-step explanation:
27 - 35
|35|
× 100% =
-8
35
× 100 = -22.8571428571% (decrease)
Use the following stem and leaf plot to write out the individual numbers and calculate the mean, median and range for the data
Stem and leaf plot
4 1
5 2 7 8
6 5 6
7 0 5 8
8 0 1
9 5
Use the stem and leaf plot to the right to answer the questions below.
A. How many data values are in the set?
B. What is the greatest and least value from the set?
C. What is the median and range?
D. Is the value 85 in the data set? Explain.
Part A
Answer: 12Explanation: Count the number of leaves.
======================================================
Part B
Answers: Greatest = 95 , least = 41Reason:
Look at the largest stem (9) and the largest leaf of this largest stem (5).
This forms the largest value of 95.
The smallest value is 41 since it corresponds to the smallest stem and smallest leaf.
The term "min" and "max" are often used here.
======================================================
Part C
Answers: Median = 68, range = 54Explanation:
The data set is
41, 52, 57, 58, 65, 66, 70, 75, 78, 80, 81, 95
There are n = 12 items in this set.
Splitting in half gets us n/2 = 12/2 = 6.
The item in slot 6 is 66, and the next item over is 70.
The midpoint of these values is the median. (66+70)/2 = 68.
This midpoint rule only applies if n is even.
To find the range, we subtract the largest and smallest items.
range = max - min = 95 - 41 = 54
======================================================
Part D
Answer: No, 85 is not in the data setReason:
The stem 8 doesn't have a leaf of 5 attached to it.
It only has the leaves 0 and 1 to form the numbers 80 and 81.
50 points if this is correct i need this asap please
Which is the best definition of a two-step equation?
In a two-step equation, you must always start by using the division property of equality.
In a two-step equation, you need to use one inverse operation to solve.
A two-step equation is one that you need to use two properties of equality to solve.
A two-step equation is one that you need to use only a single property of equality to solve.
Answer:
c
Step-by-step explanation:
A two-step equation is one that you need to use two properties of equality to solve.
Write the equation in slope intercept form: -6x+4y=20
Answer:
[tex]y=\frac{3}{2}x+5[/tex]
Step-by-step explanation:
[tex]-6x+4y=20 \\ \\ 4y=6x+20 \\ \\ y=\frac{3}{2}x+5[/tex]
if a 5-card poker hand is dealt from a well-shuffled deck of 52 cards, what is the probability of being dealt the given hand? (round your answer to five decimal places.) two pairs
=========================================================
Explanation:
A hand of two pairs is when we have 2 cards of the same value, and another 2 of the same value, then the fifth card is something else entirely.
An example hand is:
king of hearts, king of clubs ...... 1st pairqueen of spades, queen of clubs ..... 2nd pair7 of diamonds-------------
We use the nCr formula since order doesn't matter.
C(n,r) = (n!)/(r!*(n-r)!)
For any suit, there are n = 13 cards. We make r = 2 selections for each of the two pair.
C(n,r) = (n!)/(r!(n-r)!)
C(13,2) = (13!)/(2!*(13-2)!)
C(13,2) = (13!)/(2!*11!)
C(13,2) = (13*12*11!)/(2!*11!)
C(13,2) = (13*12)/(2!)
C(13,2) = (13*12)/(2*1)
C(13,2) = (156)/(2)
C(13,2) = 78
There are 78 ways to select which two ranks will be chosen to represent each of the two pair.
Let's say one of the ranks of the two pair is a king. There are n = 4 kings and we select r = 2 of them. That gives C(4,2) = 6 ways to select those two kings. We'll also have 6 ways to select the other two cards in the other pair.
Therefore, we have 78*6*6 = 2808 ways to pick the first four cards that consist of the two pair (eg: 2 kings and 2 queens).
-----------------
So far we've considered just the two pairs. We have one card left to select. There are 13-2 = 11 cards of any particular suit that weren't part of the two pair. There are 4 suits to pick from, which means we have 11*4 = 44 cards to pick from for that fifth and final slot.
-----------------
Summary so far:
2808 ways to pick the two pair (eg: 2 kings and 2 queens)44 ways to pick the fifth card that differs from the first four cards (anything other than what was chosen for the two pair).That gives 2808*44 = 123,552 different two pair hands possible.
This is out of C(52,5) = 2,598,960 hands
Divide those two values to get the final answer
(123,552)/(2,598,960) = 0.04753901560624
This then rounds to 0.04754 as the final answer.
y=600(0.75)^x
growth or decay by what precent?
The function f(x) = 600(0.75)^x. is a decay function by 25%
How to graph the function?The equation of the function is given as
f(x) = 600(0.75)^x.
The above function is an exponential function
An exponential function is represented as
y = ab^x
When f(x) = 600(0.75)^x. and y = ab^x are compared, we have
b = 0.75
The value of b in this case is the factor
Also if b is less than 1, then the function is a decay function
0.75 is less than 1
So, the function represents a decay function
The decal percentage is then calculated as
Decay = 1 - b
So, we have
Decay = 1 - 0.75
Evaluate
Decay = 25%
Hence, the function is a decay function
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What is the relationship between the two highlighted angles?
The parallel between 2 highlights is called eduidistand
If h = {(1,5), (-2,6), (4, -3), (6,9)} and
m = {(3,4), (2,-2), (-2,6), (5,8)}, what is (hm) (2)? (See image below)
Answer: [tex](h\circ m)(2) = 6[/tex]
=======================================================
Explanation:
The notation [tex](h \circ m)(2)[/tex] refers to function composition
It's the same as writing [tex]h(m(2))[/tex]
According to
m = {(3,4), (2,-2), (-2,6), (5,8)}
We have m(2) = -2 since x = 2 leads to m(x) = -2
Then the output -2 is treated as the input of the outer function h(x)
Looking through
h = {(1,5), (-2,6), (4, -3), (6,9)}
shows that h(-2) = 6
Therefore, [tex]h(m(2)) = h(-2) = 6, \ \text{ and } \ (h\circ m)(2) = 6[/tex]
Optionally we can write out a table like shown below.
The row highlighted shows the input x = 2 leading to m(x) = -2, which is then plugged into h(x) to get 6 as the final output. Think of it like a chain of dominoes.
If QP bisects ZDQL, m/DQP = 5x - 7, and m/PQL = 11 + 2x, determine
the measure of ZDQL.
m₂DQL =
When QP bisects DQL, then the angles DQP and angle PQL is 23°.
Given that,
In the picture we can see the diagram,
The QL line is there and the QD line.
QP line bisect the angles DQL
The angle DQP is 5x-7
The angle PQL is 11+2x
We have to find the x value and the angles DQP and PQL.
We know,
From the bisection we can say the angle are equal to each other
The angle DQP=The angle PQL
5x-7=11+2x
5x-2x=11+7
3x=18
x=18/3
x=6
Substitute x value in angles DQP and angle PQL.
The angle DQP=5x-7=5(6)-7=30-7=23°
The angle PQL=11+2x=11+2(6)=11+12=23°.
Therefore, the angles DQP and angle PQL is 23°.
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In this isosceles triangle,
AB-AC
4 cm is the bottom line
The perimeter of the triangle is 22 cm
Work out the length of AB.
Answer:
the length of AB is 9
Step-by-step explanation:
an isosceles triangle is a type of triangle i which two of its sides are equivalent(equal). let AB=AC=x
perimeter=22
perimeter=AB+AC+BC
22=x+x+4
22-4=2x
18/2=2x/2
9=x
Please help me with this (will give more credit for the best answer)
Answer:
1. 5ft
2. 2ft
3. 2ft
4. 1ft
Step-by-step explanation:
I need help with this practice problem solving the subject is trig I have an additional picture that is the answer options, I will send this to you
Given
[tex]f(x)=\tan x[/tex]To fill the blanks.
Now,
The grpah of f(x)=tanx is given as,
Therefore, from the graph,
[tex]\tan x=\tan (x+\pi)=\tan (x+2\pi)[/tex]Then,
[tex]\pi\text{ is the fundamental period of tanx.}[/tex]Also,
For x=0, tan(0)=0.
Therefore, the y-intercept is (0,0).
The points for the function f(x)=tanx is,
[tex]\begin{gathered} x=\frac{\pi}{3},\text{ y=tan(}\frac{\pi}{3})=\sqrt[]{3} \\ x=\frac{\pi}{4},y=\tan \frac{\pi}{4}=1 \end{gathered}[/tex]Since
[tex]\tan (-A)=-\tan A[/tex]Then, the points of the graph y=tanx is,
[tex](-\frac{\pi}{3},-\sqrt[]{3}),(-\frac{\pi}{4},-1),(0,0),(\frac{\pi}{3},\sqrt[]{3}),(\frac{\pi}{4},1)[/tex]Hence, the answer should be in the order,
i)
[tex]\pi[/tex]ii)
[tex](0,0)[/tex]iii)
[tex](-\frac{\pi}{3},-\sqrt[]{3}),(-\frac{\pi}{4},-1),(0,0),(\frac{\pi}{3},\sqrt[]{3}),(\frac{\pi}{4},1)[/tex]a³ = 125
Each edge of the cube is
feet long.
Answer:
each cube is 5 feet long because 5*5*5 = 125
Step-by-step explanation:
Expand and simplify each polynomial (Answer both problems)
1. (a^2-3a)^2
2. (1/2x^3 +6x)^2
The simplified form of polynomials are:
1. (a² - 3a)² = 3a²
2. (1/2x³ + 6x)² = -12x²
Given,
We have to expand the given polynomials and simplify them.
1. The polynomial: (a² - 3a)²
Here,
The polynomial is in the form of (a - b)²
So,
(a - b)² = a² - 2ab + b²
Then,
(a² - 3a)² = (a²)² - (2 × a² × 3a) + (3a)²
(a² - 3a)² = a⁴ - 6a³ + 9a²
(a² - 3a)² = a²(a² - 6a + 9)
Here,
(a² - 6a + 9) is in quadratic form. Solve using quadratic formula.
a = 1, b = -6 and c = 9
[tex]\frac{-b(+-)\sqrt{b^{2} -4ac} }{2a}[/tex] = [tex]\frac{6(+-)\sqrt{(-6)^{2}-4(1)(9) } }{2(1)}[/tex] = [tex]\frac{6(+-)\sqrt{36 - 36} }{2}[/tex] = [tex]\frac{6(+-)\sqrt{0} }{2}[/tex] = (6±0) / 2
= 6/2 = 3
Then,
(a² - 3a)² = a²(a² - 6a + 9)
Here,
(a² - 6a + 9) = 3
So,
(a² - 3a)² = 3a²
2. The polynomial: (1/2x³ + 6x)²
Here, the polynomial is in the form (a + b)²
(a + b)² = a² + 2ab + b²
Here,
(1/2x³ + 6x)² = (1/2x³)² + (2 × 1/2x³ × 6x) + (6x)²
(1/2x³ + 6x)² = 1/4x⁶ + 6x⁴ + 36x²
(1/2x³ + 6x)² = x²(1/4x⁴ + 6x² + 36)
a = 1/4, b = 6 and c = 36
Quadratic formula: [tex]\frac{-b(+-)\sqrt{b^{2} -4ac} }{2a}[/tex]
= [tex]\frac{-6(+-)\sqrt{(-6)^{2} -4(1/4)(36)} }{2(1/4)}[/tex] = [tex]\frac{-6(+-)\sqrt{36-36} }{1/2}[/tex] = (-6±0) / (1/2) = -6 × 2 = -12
Therefore,
(1/2x³ + 6x)² = x²(1/4x⁴ + 6x² + 36)
Here,
(1/4x⁴ + 6x² + 36) = -12
Then,
(1/2x³ + 6x)² = -12x²
That is,
The simplified form of polynomials are:
1. (a² - 3a)² = 3a²
2. (1/2x³ + 6x)² = -12x²
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what are the roots of the equation ?-3x = -10x^2-4
Given the following Quadratic equation:
[tex]-3x=-10x^2-4[/tex]You can use the Quadratic formula to solve it:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In this case, you need to add "3x" to both sides of the equation:
[tex]\begin{gathered} -3x+(3x)=-10x^2-4+(3x) \\ 0=-10x^2+3x-4 \end{gathered}[/tex]You can identify that:
[tex]\begin{gathered} a=-10 \\ b=3 \\ c=-4 \end{gathered}[/tex]Substituting values into the formula and evaluating, you get:
[tex]\begin{gathered} x=\frac{-3\pm\sqrt[]{3^2^{}-4(-10)(-4)}}{2(-10)} \\ \\ x_1=\frac{3}{20}-\frac{i}{20}\sqrt[]{151} \\ \\ x_2=\frac{3}{20}+\frac{i}{20}\sqrt[]{151} \end{gathered}[/tex]Answer
Complex roots:
[tex]\begin{gathered} x_1=\frac{3}{20}-\frac{i}{20}\sqrt[]{151} \\ \\ x_2=\frac{3}{20}+\frac{i}{20}\sqrt[]{151} \end{gathered}[/tex]If Y Varies inversely as X. If Y=6 and X=10. FIND X when Y=18, correct to 3 significant figures.
Answer:
x ≈ 3.33
Step-by-step explanation:
given y varies inversely as x then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
to find k use the condition y = 6 , x = 10
6 = [tex]\frac{k}{10}[/tex] ( multiply both sides by 10 )
60 = k
y = [tex]\frac{60}{x}[/tex] ← equation of variation
when y = 18 , then
18 = [tex]\frac{60}{k}[/tex] ( multiply both sides by k to clear the fraction )
18k = 60 ( divide both sides by 18 )
k = [tex]\frac{60}{18}[/tex] ≈ 3.33 ( to 3 significant figures )
2. Dexter needs to find each angle in this figure that is adjacent
to LLON. He claims that LMON is adjacent to LLON.
a. List each angle that is adjacent to LLON.
мор
b. Why is Dexter's claim incorrect?
Answer:
It would be MOP is adjacent
Step-by-step explanation:
a bank of 10 movies is chosen from for a movie marathon in which 7 movies will be played in a specific order. in how many different ways can the movies for the movie marathon be chosen?
The movies for the movie marathon can be chosen in 120 different ways .
In the question ,
it is given that
total number of movies = 10 movies
number of movies that need to be played in specific order = 7 movies .
we have to find how many different ways can the movies be selected for the movie marathon .
we can solve this with Combination ,
where n = 10 and r = 7
So C(n,r) = C (10,7)
= 10! / (3! * 7! )
= (10*9*8*7!)/(3! * 7! )
= ( 10*9*8) / (3*2 )
= 10 * 3 * 4
= 120 ways .
Therefore , The movies for the movie marathon can be chosen in 120 different ways .
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Suppose that 12 inches of wire costs 60 cents.
At the same rate, how many inches of wire can be bought for 25 cents?
Answer:
5 inches of wire.
Step-by-step explanation:
60/12 = 5
So at .05 an inch, you can afford 5 inches at 25 cents
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12. Six hundred people will buy tickets at $4 each
for a district championship game. For each 20¢
decrease in price, 50 more people will buy
tickets. Find the best ticket price, the maximum
income, and the corresponding number of
tickets.
Using concept of Quadratic Equation we got that best ticket price is $16, maximum income is $19,200 and the corresponding number of tickets are 1200.
What is Quadratic Equation?A Quadratic Equation is one of the following: f(x) = ax2 + bx + c, where a, b, and c are positive integers and an is not equal to zero. A parabola is basically a curve that represents the graph of a quadratic equation. Parabolas can open up or down, and their "width" or "steepness" can vary, but they all have the same basic "U" shape.
We know that,
No. of people who will buy tickets at $4 = 600
For each 20¢ decrease, additional no. of people buying tickets = 50
Revenue = (No. of tickets sold)(Pricing)
Revenue = (600+50x)(4+x)
= 50[tex]x^{2}[/tex] + 800x + 2400
Solving the quadratic equation we got,
x = -4 or -12
Since we're dealing with real-life entities such as money, we'll take the value of x as positive.
Taking x as 12 (higher value),
No. of tickets sold = 600 + 50x = 1200
Pricing = 4 + x = 16
Revenue = 1200×16 = $19,200
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I need help fast with my math homework.
Answer:15 twice
Step-by-step explanation:
If segment BD is congruent to segment BC, BD=4x-18, BC=x+3, and AC=34, find AB
If segment BD is congruent to segment BC, and BD = 4x - 18, BC = x + 3, and AC = 34, then AB = 31/x.
What is meant by Congruent angles?Congruent angles are two or more angles that are exactly the same. As a result, the lengths of these angles are equal. Angle measurement is the same for congruent angles. A regular pentagon, for example, has five sides and five angles, each of which is 108 degrees. Angles in a regular polygon will always be congruent regardless of size or scale. Congruent angles are another name for equal angles. Angles that are congruent are those that are vertically opposite each other. Congruent angles are those formed by the intersection of two parallel lines and a transversal.Let the equation be AB + BC = AC
substitute the values in the above equation, we get
AB + x + 3 = 34
simplifying the value of x,
Subtract A B from both sides AB + x + 3 - AB = 34 - A B
x + 3 = 34 - AB
Subtract 3 from both sides,
x + 3 - 3 = 34 - AB - 3
x = -AB + 31
Plug in this value of x into the line segments to find BC and AC.
Where, BC = x + 3
substitute the value of x in the above equation, we get
BC = [-AB + 31 ] + 3
BC = -AB + 34
Then, AB + BC = AC
x = -AB + 31
AB = 31/x
Hence, If segment BD is congruent to segment BC, and BD = 4x - 18,
BC = x + 3, and AC = 34, then AB = 31/x.
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Draw the graph of y = 2x-4 where x E {-2; "-1;" 0; 1; 2}:
Graph is attached below.
Given,
y = 2x - 4
We have to draw a graph according to this
Here,
x E {-2; "-1;" 0; 1; 2}:
Image is attached.
How to draw a graph?
First, label and draw your X and Y axes at a straight angle. Axis Y is vertical, whereas axis X is horizontal. Write the scale for each axis down the line and mark the junction as 0, then draw a line. Calculate the values of Y for various values of X after drawing the axes.
So, the graph is given below.
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Is the following process correct? If not, which step is where the error occurs, justify your answer. Then rework the problem to find the correct answer.
We are given the following absolute value equation
[tex]|4x-1|=5x+37[/tex]Let us solve the problem then we will compare it with the given solution.
[tex]\begin{gathered} |4x-1|=5x+37 \\ 4x-1=\pm(5x+37) \end{gathered}[/tex]Now we will solve for the positive and negative sign separately
[tex]\begin{gathered} 4x-1=5x+37 \\ 4x-5x=37+1 \\ -x=38 \\ x=-38 \end{gathered}[/tex][tex]\begin{gathered} 4x-1=-5x-37 \\ 4x+5x=-37+1 \\ 9x=-36 \\ x=\frac{-36}{9} \\ x=-4 \end{gathered}[/tex]Comparing it with the given solution, there is an error on the left-hand side step 2. (the sign of 38 should be positive but in the figure, it is shown negative)
Now let us substitute the obtained x values into the original absolute value equation and check if they satisfy the equation.
For x = -4:
[tex]\begin{gathered} |4(-4)-1|=5(-4)+37 \\ |-16-1|=-20+37 \\ |-17|=17 \\ 17=17 \end{gathered}[/tex]Hence, x = -4 is a valid solution.
For x = -38:
[tex]\begin{gathered} |4(-38)-1|=5(-38)+37 \\ |-152-1|=-190+37 \\ |-153|=-153 \\ 153\ne-153 \end{gathered}[/tex]Hence, x = -38 is not a valid solution.
The above is an example of an extraneous solution.
An extraneous solution is a solution that we get during the process of solving an equation but it is not really the solution meaning that it does not satisfy the equation!
Therefore, x = -4 is the only solution to the given equation.
Scientists are studying the temperature on a distant planet. They find that the surface temperature at one location is 45 ° Celsius. They also find that the temperature decreases by 7 ° Celsius for each kilometer you go up from the surface. Let T represent the temperature (in Celsius), and let H be the height above the surface (in kilometers). Write an equation relating T to H , and then graph your equation using the axes below.
The equation relating T to H is H = 45 - 7T.
What is temperature?Temperature simply means the degree of hotness and coldness in a body.
In this case, they find that the surface temperature at one location is 45 ° Celsius. They also find that the temperature decreases by 7 ° Celsius for each kilometer you go up from the surface.
Let T = the temperature (in Celsius).
Let H = the height above the surface (in kilometers).
The equation will be:
H = 45 - (7 × T)
H = 45 - 7T
The axes aren't given and can't be graphed.
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