The income plainness of demand for eatery reflections is Income plainness = 200/ 20 = 10
What's chance?Chance is a way of expressing a volume as a bit of 100. It's frequently denoted using the percent symbol(), which represents" per hundred". For illustration, 25 is original to25/100 or0.25 as a numeric.
By question-
The income plainness of demand measures the responsiveness of the volume demanded of a good or service to a change in income, all other effects being equal .However, it means that the good is a normal good, and the volume demanded increases as income increases, If the income plainness is positive. However, it means that the good is an inferior good, and the volume demanded diminishments as income increases, If the income plainness is negative.
In this case, John's pay increased by 20 percent, and the average number of eatery reflections he consumed increased from one a week to three a week. We can calculate the income plainness of demand for eatery reflections as follows
Income plainness = chance change in volume demanded/ chance change in income
The chance change in volume demanded is
( 3 reflections per week- 1 mess per week)/ 1 mess per week) x 100 = 200
The chance change in income is 20
thus, the income plainness of demand for eatery reflections is
Income plainness = 200/ 20 = 10
Since the income plainness is positive and lesser than 1, we can conclude that eatery reflections are a luxury good for John. Option( b) is the correct answer.
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DUE TODAY HELP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
4. Suppose you lengthen the rope, then lay the hula hoop and the rope on the floor, with the rope arranged in a circle with the same center as the hula hoop. How much rope would you have to add in order to allow a person to lie down on the floor with their toes pointing towards the hula hoop and their head towards the rope, but toughing neither?
We need to add (t - 2πr) units of rope.
We have,
Let's call the radius of the hula hoop "r" and the distance from the center of the hula hoop to the rope "d".
We want to find the length of the rope we need to add in order to create a circle with radius "d" that is tangent to the hula hoop.
The distance between the center of the hula hoop and the center of the tangent circle is (r + d), so the diameter of the tangent circle is
2(r + d), and the length of the circle is 2π(r + d).
We want to find the value of d that will make the circle just touch the person's toes, so the radius of the tangent circle is equal to the length of the person's toes, which we'll call t.
So we have the equation:
2π(r + d) = t
Solving for d.
d = (t/2π) - r
The amount of rope we need to add is:
2πd = 2π((t/2π) - r) = t - 2πr
Thus,
We need to add (t - 2πr) units of rope.
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25 points. I need assistance, please show working out.
Answer:
81°
Step-by-step explanation:
the sum of the interior angles of a triangle is 180°.
The base of the 10 triangles make a straight line. 180/10 = 18°
The small angle along the base is 18°
180-18 = 162
The other two angles of the triangle must add up to 162. Since this is a isosceles triangle. The other 2 angles have the same measurements.
162/2 = 81. The measurement of the angle we are looking for is 81°
What is 51/16 as a Decimal?
For converting fractions to decimals, we need to divide numerator with denominator,
So, the value of 51/16 as a decimal is equal to 3.1875.
In mathematics, the ratio of two integers is how a fraction is defined in mathematics.
The fraction indicates that it is the numerator value to denominator value ratio.
A decimal number is one in which the decimal point separates the whole number component from the decimal component.
From the question,
As we need to convert the given fractional value to decimal.
So, for determining the equivalent decimal value, we will simply divide the value given in the numerator to the value given in the denominator.
So, dividing 51 by 16
We will get it as:
51/16: 51 16 = 3.1875
As a result, 51/16 is equivalent to 3.1875 in decimal form.
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At a NASCAR race, the lead car has 7 1/2 laps to go. Suddenly there is a caution flag, so all the racers must hold position while continuing at a reduced speed for 5/6 of a lap. When racing resumes, how many laps does the lead car have to go?
After reduced speed when race resumes the number of laps left are 6 2/3 laps.
What is the definition of speed?
The following is the definition of speed:
The rate with which the position of an item changes .
The ratio of distance travelled to time taken in travelling is known as speed. Speed is a scalar number because it has only one direction and no magnitude.
Formula for Speed
The speed formula is as follows:
s=d/t
Where,
s= speed in metres per second, d = distance travelled in metres, and t = time in seconds.
Now,
Total laps left for the lead car= 7 1/2
After race is paused or reduced speed for race until 5/6 of a lap
so only 1/6 of a lap had normal racing
so total lap left is 15/2-1+1/6
=45-6+1/6
=40/6
=20/3
=6 2/3
Hence,
when race resumes the number of laps left are 6 2/3 laps.
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what is the correct way to measure the zone of inhibition?
The correct way to measure the zone of inhibition is to place a known amount of an antimicrobial agent on a solid medium.
What is Area?Area is a quantity that measures the size of a two-dimensional surface or shape. It is expressed in square units such as square centimetres (cm2), square metres (m2) or square kilometres (km2). Area is used to describe the size of a garden, a house, a room, a city and much more. It can also be used to calculate the amount of material required for a project, such as paint, carpet or tiles. Knowing the area of a shape can help to calculate costs, and to make sure that enough materials are ordered.
The zone of inhibition is then measured as the area surrounding the antimicrobial agent where microbial growth has been inhibited. This area is typically measured in millimeters. To accurately measure the zone of inhibition, it is important to ensure that the size of the inoculum and the amount of antimicrobial agent used remain constant. Additionally, it is important to consider the type of organism being studied, as different organisms can have different levels of susceptibility to the antimicrobial agent. Finally, the medium used should be appropriate for the organism being studied, as different media can produce different results.
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What are the solutions to the equation cosine of the quantity x plus 3 times pi over 2 end quantity equals radical 2 over 2 on the interval [0, 2π]?
Answer:
The solutions to the equation cos(x + 3π/2) = √2/2 on the interval [0, 2π] are x = π/4 + 2kπ, k ∈ {0, 1, 2, 3}.
what is the best fit line
The best fit line is a straight line that reflects the best feasible estimate of the connection between two variables in a dataset in statistics and data analysis. The line is deemed to have the "best fit" since it minimises the difference between the observed data points and the line's anticipated values.
The method of least squares is the most often used approach for identifying the best fit line, which entails finding the line that minimises the sum of the squared differences between the observed data points and the corresponding predicted values on the line. This approach yields a linear equation of the form y = mx + b, where "m" represents the line's slope and "b" represents the y-intercept.
The best fit line may be used to anticipate the relationship between the variables in the dataset, as well as to detect any outliers or atypical data points that may be influencing the overall relationship. It is often used to evaluate data and create predictions in domains including as economics, engineering, and social sciences.
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how to calculate optimum replacement interval
The economic life cycle analysis does not take into account factors such as technological advancements or changes in regulatory requirements, which can affect the optimal replacement interval.
Yet, it is important to review and update the analysis periodically to ensure that the replacement interval remains optimal.
There are the normal steps for calculating the optimum replacement interval using the economic life cycle analysis:
1. Estimate the annual maintenance and repair costs for the item, based on historical data or industry standards.
2. Estimate the annual operating costs for the item, such as energy or fuel costs.
3. Compare the total cost of ownership for the item over its expected useful life to the cost of replacing the item with a newer or more efficient model.
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Suppose that E and F are two events and that P(E and F)=0.1 and P(E)=0.2. What is P(F/E)
From the given information provided, the probability of event F given that event E has occurred is 0.5.
Conditional probability is probability of an event A occurring with given that event B has occurred. It is denoted as P(A|B) and is calculated as follows:
P(A|B) = P(A and B) / P(B)
To find P(F/E), we use the conditional probability formula:
P(F/E) = P(E and F) / P(E)
We are given that P(E and F) = 0.1 and P(E) = 0.2. Substituting the given values in the formula, we get:
P(F/E) = 0.1 / 0.2
Simplifying this expression, we get:
P(F/E) = 0.5
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what will be the value of x after the following code is executed? int x = 10; for (int y=5; y<20; y = 5) x = y;
The value of x after the following code 'int x = 10; for (int y=5; y<20; y = 5) x = y' is executed will be 5.
The given for loop initializes the variable y to 5, then checks if y is less than 20, and then sets y to 5 again in each iteration. This means that the loop will execute only once with the value of y being 5, and after that, the loop condition will always be false because y is never incremented or changed in any way.
During the execution of the loop, the value of y is assigned to the variable x. Therefore, after the loop, the value of x will be 5.
So, the final value of x will be 5.
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find the volume of the solid generated when the region bounded by y 9x and y =27x/x is revolved about the​ x-axis.
The volume of the solid generated when the region bounded by y = 9x and y = 27x/x is revolved around the x-axis is given by V = 27lnx - 9x + c
To calculate this volume, we need to calculate the area of the cross-section of a shell at x.
The cross-section is found by taking the difference of the two curves, y = 9x and y = 27x/x, at that particular x in the form of a rectangle.
The height of the rectangle is y₂ - y₁ and the width is the interval dx. Therefore, the area of the cross-section is given by
A(x) = (y₂ - y₁)dx = [(27x/x - 9x)dx].
The volume of the solid is then given by the formula
=> V = ∫A(x)dx.
Substituting in the expression for A(x), we have
=> V = ∫(27x/x - 9x)dx.
Integrating this expression, we get V = 27lnx - 9x + c, where c is an arbitrary constant.
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Linda plans to sign up for three field events. She wants to run a total of more than a kilometer but less than 1.5 kilometers which three events should she sign up for?
Linda can choose any combination of three events that adds up to more than a kilometer but less than 1.5 kilometers
In order to find the best combination of events for Linda to sign up for to run a total of more than a kilometer but less than 1.5 kilometers, we must first determine the total distances of the individual events.
Depending on the events offered, Linda can choose three events that add up to more than a kilometer but less than 1.5 kilometers.
If Linda has the option of running the 100m, 200m, and 800m, she can satisfy her requirement of running more than a kilometer but less than 1.5 kilometers by choosing the 100m, 200m, and 800m.
This would add up to 1100m, which is slightly over a kilometer but below 1.5 kilometers.
Another option for Linda is to run the 100m, 400m, and 600m, which would add up to 1100m, once again satisfying her requirement.
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in one school, each class has 23 students and 1 teacher. how many total people are there in 10 classes
Answer: 240 people
Step-by-step explanation:
If each class has 23 students and 1 teacher then there are a total of 24 people in each class. Multiply that by 10 classes, you should get 240 people.
Write one sentence summarizing something different that the second article said about the topic. Begin your sentence with these words: According to the EPA, . . . . . or, In the article “Climate Change and Ecosystems,” the EPA says, . . . . . )
In reference to the article “Climate Change and Ecosystems,” the EPA explains how the Earth's ecosystems are being impacted by climate change, resulting in negative consequences for both natural resources and human well-being.
What is the main role of the Environmental Protection Agency?In response to widespread public environmental concerns that grew in strength in the 1950s and 1960s, the Environmental Protection Agency was established. By examining the effects of pollutants and setting usage restrictions, the EPA has worked to preserve and protect the environment while also enhancing human health.
The EPA controls the production, transformation, use, and disposal of chemicals and other pollutants. The EPA is also tasked with figuring out the acceptable levels of chemicals and other pollutants in water, animal feed, and food.
In general, the Environmental Protection Agency develops and implements environmental regulations, sponsors and conducts research, and guards against serious health risks to people and the environment and also maintain a favorable climate for all.
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Offering 50 points!!
Answer: Here is the answers to your previous question that was deleted. As for this question, I believe the answer is the first one.
1) [tex]200\pi[/tex]
2) [tex]3\sqrt{3}[/tex]
3) [tex]-1[/tex]
4) 9
5) 0.151
Step-by-step explanation:
#1
[tex]=\frac{dV}{dt} =\frac{4}{3} \pi .3r^3\frac{dr}{dt}[/tex]
[tex]=\frac{dV}{dt} =4\pi r^2\frac{dr}{dt}[/tex]
[tex]=\frac{dV}{dt} =4\pi r^2*2...[\frac{dr}{dt} =2][/tex]
[tex]=\frac{dV}{dt} = 8\pi r^2~~~ in^3/min[/tex]
[tex]r=5[/tex]
[tex]=\frac{dV}{dt} =8\pi (5)^2[/tex]
[tex]=200\pi ~~~in^3/min[/tex]
#2
[tex]\frac{d}{dt} (x^2+y^2)=\frac{d}{dt} (16)[/tex]
[tex]2x(\frac{dx}{dt} )+2y(\frac{dy}{dt})=0[/tex]
[tex]2x(\frac{dx}{dt} )+-2y(\frac{dy}{dt})=0[/tex]
Divide both sides by 2.
[tex]x(\frac{dx}{dt})=-y(\frac{dy}{dt})[/tex]
[tex]\frac{dx}{dt}=\frac{-y(\frac{dy}{dt}) }{x}[/tex]
As the particle is passing through the point [tex](2,2\sqrt{3})[/tex] , So, the point will satisfy the equation. Substituting the value of [tex]x=2[/tex] , [tex]y=2\sqrt{3}[/tex] and [tex]\frac{dy}{dt} -3[/tex],
we get ,
[tex]\frac{dx}{dt} =\frac{((-2\sqrt{3})*(-3))}{2}[/tex]
[tex]=\frac{6\sqrt{3} }{2}[/tex]
[tex]=3\sqrt{3}[/tex]
#3
Go on to Desmos and put in [tex]x+3y=6[/tex] and look at x=0 and x=1 and use those two as your points.
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]=\frac{1-3}{2-0}[/tex]
[tex]=\frac{-2}{2}[/tex]
[tex]=-1[/tex]
#4
[tex]y=3x^2-4x-6[/tex]
[tex]\frac{dy}{dt} =5x-6[/tex]
[tex]\frac{dy}{dt}=5(3)-6[/tex]
[tex]\frac{dy}{dt} =9[/tex]
#5
[tex]V=s^3[/tex]
[tex]\frac{dV}{dt} =3*s^2(\frac{ds}{dt})[/tex]
[tex]-2=3*s^2(\frac{ds}{dt} )~~~~~~~~~~~~~Equation 1[/tex]
[tex]\frac{ds}{dt} =\frac{1.33}{s^2}[/tex]
[tex]V=s^3[/tex]
[tex](27)^0^.^3^3=(s^3)^0^.^3^3[/tex]
[tex]s[/tex] ≈ [tex]2.97 ~~~~~~~~~~~~~~~~~~~~~~Equation2[/tex]
Substitute equation2 to equation1, we get
[tex]\frac{ds}{dt} =\frac{1.33}{(2.97)^2} =0.151[/tex]
I hope this helps you! Cheers! ^^
y is directly proportional to the square of x. find the percentage increase when x is increased by 5%
The change in percentage of y when x increases by 5% will be 25%
What is direct proportion?Direct proportion is a mathematical comparison between two numbers where the ratio of the two numbers is equal to a constant value.
Given that, y is directly proportional to the square of x. we need to find the percentage increase when x is increased by 5%
Since, Y varies directly as the square of x.
Therefore, the general equation to show the direct variation :-
Y = kx²
Let the value of x be 25
25 will be x as 100%. therefore when x is 100% the value of y will be
Y = 25²k
= 625k
Increasing the value of x by 5%,
(105x25)/100 = 26.25
Therefore, 105% of 25 = 26.25.
Applying the variation equation, we obtain
Y = (26.25)²k
= 689.0625k
We will find the percentage change in y caused by an increase of x by 5%
(689.0625x100)/625 = 110.25%
Therefore, to find the percentage change in y when x increases by 5% will be,
(110.25-100)% =10.25%
Hence, the change in percentage of y when x increases by 5% will be 25%
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danielle construct a scale model of byilding with a rectangule base. her model is 2 inchs in length and 1 inch in width. the scale on the model is 1 inch = 47 feet. what is the actual area, in ssquare feet of the base o the buidlding
Answer:
Step-by-step explanation:
If 1in is equal to 47 feet irl, then that means that the actual width is 47ft and the actual length is 94ft.
Multiply those two together and you get 4,418 sq ft as your answer.
h(t)=−20+11th, left parenthesis, t, right parenthesis, equals, minus, 20, plus, 11, t
ℎ
(
11
)
=
h(11)
The required value of h(t)=-20+11t at t=11 is , h(11)=101.
What is PEDMAS Rule ?The word PEMDAS is primarily used in the US, although we refer to it as BODMAS in India and the UK. Yet, there is no distinction between them. For both the rule and brackets, addition, subtraction, multiplication, and division are performed in the same order.
The following is the full form of PEMDAS:
P – Parentheses [{()}]
E – Exponents (Powers and Roots)
MD- Multiplication and Division (left to right) (× and ÷)
AS –A= Addition and S= Subtraction (left to right) (+ and -)
whereas the full form of BODMAS is – Brackets Order Division Multiplication Addition and Subtraction.
If h(t)=-20+11t and you wish to evaluate h(11):
h(11)=-20+11(11)
h(11)=-20+121
h(11)=101
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What is the coefficient
Answer:
A coefficient is a number that is multiplied by a variable or term in an algebraic expression.
Examples:
[tex]3x[/tex]
[tex]60x[/tex]
-6-4-2
Intro
8
6
ty ↑
2
-2
2
4
X
6
Which functions could represent a reflection over the y-
axis of the given function? Check all that apply.
g(x)=-(4)
Og(x)=0.5(4)*
□ g(x) = 2(4)
□ g(x)=1/(²
□ g(x)=1/(2*
4
Dons
the reflection of the given function will be f(-x) = 0.5 4⁻ˣ and the graph of this function is attached below.
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
Given, a function as shown in the graph:
To reflect a function over the y-axis we use the rule:
f(-x) reflects the graph of f(x) over the y-axis. In other words, to reflect f(x) over the y-axis, we just need to replace x with -x.
Let's find f(x) first using the standard exponential growth function:
f(x) = a( 1 + b )ˣ
From our graph, we can infer that f(x) = 1/2 when x =0, so let's replace those values in our function:
f(x) = a( 1 + b )ˣ
1/2 = a(1 +b)⁰
a = 1/2
We can also infer that f(x) = 8 when x =2. Since we already know that a = 1/2, let's replace the values to find and complete our function:
f(x) = a( 1 + b )ˣ
8 = 1/2(1 +b)²
4 = 1+b
b = 3
So putting it all together:
f(x) = 1/2( 1 + 3 )ˣ
Finally, we can apply the reflection rule to find the reflection over the y-axis:
f(-x) = 1/2(4)⁻ˣ
f(-x) = 0.5 4⁻ˣ
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Marie went golfing and tracked her golf cart's distance from the first hole over time. She stayed at the first hole for the first 30 minutes. Then she drove away from the first hole for the next 2 hours. She then took 2 hours to drive back to the first hole.
Which of the following graphs could represent Marie's situation?
first quadrant of coordinate plane titled Marie's round of golf with the x axis labeled time in hours and the y axis labeled distance in miles, with a line segment from the point 0 comma 0 to one half comma 0, a line segment from one half comma 0 to 2 and a half comma 5, a line segment from 2 and a half comma 5 to 3 and a half comma 5, and a line segment from 3 and a half comma 5 to 5 and a half comma 0
first quadrant of coordinate plane titled Marie's round of golf with the x axis labeled time in hours and the y axis labeled distance in miles, with a line segment from 0 comma 0 to one half comma 0, a line segment from one half comma 0 to 2 and a half comma 5, and a line segment from 2 and a half comma 5 to 4 and a half comma 0
first quadrant of coordinate plane titled Marie's round of golf with the x axis labeled time in hours and the y axis labeled distance in miles, with a segment from the point 0 comma 0 to 2 comma 5, a line segment from 2 comma 5 to 3 comma 5, and a line segment from 3 comma 5 to 5 comma 0
first quadrant of coordinate plane titled Marie's round of golf with the x axis labeled time in hours and the y axis labeled distance in miles, with a line segment from 0 comma 0 to 2 comma 5, and a line segment from 2 comma 5 to 4 comma 0
The second graph, first quadrant of coordinate plane titled Marie's round of golf could represent Marie's situation.
What is a coordinate plane?A coordinate plane is a two-dimensional plane made up of the x-axis and y-axis, two perpendicular number lines. Using the coordinates (x, y), which stand for the horizontal and vertical distances from the origin (the point where the x- and y-axes cross), it is possible to find locations in a two-dimensional space. The first quadrant, second quadrant, third quadrant, and fourth quadrant of the coordinate plane are designated in order anticlockwise.
Given that, she stayed at the first hole for the first 30 minutes. Then she drove away from the first hole for the next 2 hours.
The situation is best described by the graph 2, first quadrant of coordinate plane titled Marie's round of golf with the x axis labeled time in hours and the y axis labeled distance in miles, with a line segment from 0 comma 0 to one half comma 0, a line segment from one half comma 0 to 2 and a half comma 5, and a line segment from 2 and a half comma 5 to 4 and a half comma 0.
Hence, the second graph could represent Marie's situation.
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Answer:
the answer is the graph shone below
i took the test and IT WAS RIGHT
Step-by-step explanation:
have a good day!
Theden went on three day hike up a 40 mile trail he decided to hike 12.8 miles the first day and 16.9 miles the second day how many miles does he need to hike on the third day to finish the trail
To determine how many miles Theden needs to hike on the third day to finish the trail, we can subtract the distance he hiked on the first two days from the total trail distance:
Total trail distance = 40 miles
Distance hiked on first day = 12.8 miles
Distance hiked on second day = 16.9 miles
Total distance hiked on first two days = 12.8 + 16.9 = 29.7 miles
Distance left to hike on the third day = 40 - 29.7 = 10.3 miles
Therefore, Theden needs to hike 10.3 miles on the third day to finish the trail.
Please Answer in ( a + bi ) form
Answer:
-10 - 4i
Step-by-step explanation:
We can rewrite the equation as (by getting rid of parentheses):
-8 + 3i - 2 - 7i
Now, we can add/subtract the values:
(-8-2) + (-7i+3i)
= -10 - 4i
HELP ME math DIVIDE 28 BY 25,704 USING LONG DIVISION
Answer:
918
Step-by-step explanation:
The graph below represents the prices, in dollars, of different numbers of pounds of regular bananas. The table below represents the prices, in dollars, of different numbers of pounds of organic bananas.
Which statement correctly compares the prices of regular bananas and organic bananas?
A. Organic bananas cost $0.50 more per pound.
B. Organic bananas cost $0.05 more per pound.
C. Regular bananas cost $0.08 more per pound.
D. Regular bananas cost $0.53 more per pound.
Please help me immediately
The exponent is 81.m⁴.n²⁰
Here we have to determine the sign for exponential or radical expression
[tex](-3mn^5)^4[/tex]
Now using the exponent power rule (aˣ)ⁿ = aˣⁿ =. We get
= 81.m⁴.n²⁰
Therefore the exponent as a product of power is 81.
What is an exponent?The number of times a number has been multiplied by itself is referred to as an exponent. For instance, the phrase "2 to the 3rd" (written as 23) means:
2 x 2 x 2 = 8.
23 and 2 x 3 = 6 are not equivalent.
Keep in mind that any number is itself when raised to the power of 1.
The outcome is always a fraction when the exponent is negative. A numerator and a denominator make up fractions. The numerator in this case is always 1. Assuming the negative exponent is positive, raise the number to that power to determine the denominator
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To win at LOTTO in one state, one must correctly select 7 numbers from a collection of 50 numbers (1 through 46). The order in which the selection is made does not matter. How many different selections are possible?
The total number of possible selections is 18,643,560. This is calculated using the combination formula nCr.
In nCr, n is the total number of objects (50) and r is the number of objects to be selected (7). This is equal to 50C7, which can be written as
50!/(7!*(50-7)!), or 18,643,560.To explain this further, the combination formula is used to find the total number of combinations when selecting a certain number of objects from a larger set. In this case, we are selecting 7 numbers from a set of 50, so the total number of combinations is 18,643,560.
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the measure of 2 angles are (3y+11) and (11 y+15). What is the value of y if the angles are congruent
As a result, if the two angles' measurements are (3y+11) and (11y+15) and they are congruent, then y must equal -1/2.
What is angle?An angle is a geometric figure formed by two rays that have a common endpoint, called the vertex. The rays are also known as the sides or legs of the angle. Angles are typically measured in degrees, with a full circle measuring 360 degrees. Angles can also be measured in radians, which are another unit of angular measurement used in mathematics and physics. One radian is equal to the angle subtended by an arc of a circle that has a length equal to the radius of the circle. The size of an angle is determined by the amount of rotation that occurs between the two rays. This is typically measured relative to the positive x-axis, with counterclockwise rotations being considered positive and clockwise rotations being considered negative. Angles are used in a wide range of mathematical and scientific applications, including geometry, trigonometry, physics, engineering, and architecture. They are also used in many everyday situations, such as measuring the size of an opening or the angle of incidence of sunlight on a surface.
Here,
If the two angles are congruent, then they must have the same measure.
So we can set the expressions for the measures of the two angles equal to each other and solve for y:
3y + 11 = 11y + 15
Subtracting 3y from both sides:
11 = 8y + 15
Subtracting 15 from both sides:
-4 = 8y
Dividing both sides by 8:
y = -1/2
Therefore, if the measure of the two angles is (3y+11) and (11y+15) and they are congruent, then y must equal -1/2.
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Is {(-7, 20), (3, 5), (0, 5), (-2, 0), (6, -4), (-6, -9), (4, 4)} a function? Explain why
The given set of points {(-7, 20), (3, 5), (0, 5), (-2, 0), (6, -4), (-6, -9), (4, 4)} is a function since each x-value has a unique y-value.
To determine whether the given set of points is a function or not, we need to check if each input (x-value) corresponds to exactly one output (y-value).
Let's first list the x-values in the set: -7, 3, 0, -2, 6, and -6.
Now, we need to check if each of these x-values has a unique y-value. We can see that:
The point (-7, 20) has an x-value of -7 and a y-value of 20.
The point (3, 5) has an x-value of 3 and a y-value of 5.
The point (0, 5) has an x-value of 0 and a y-value of 5.
The point (-2, 0) has an x-value of -2 and a y-value of 0.
The point (6, -4) has an x-value of 6 and a y-value of -4.
The point (-6, -9) has an x-value of -6 and a y-value of -9.
The point (4, 4) has an x-value of 4 and a y-value of 4.
We can see that each of the x-values has a unique y-value. Therefore, this set of points is a function.
In fact, we can even represent this function using set-builder notation as:
{ (x, y) | x ∈ {-7, 3, 0, -2, 6, -6, 4}, y is the corresponding y-value for x }
or using a mapping notation as:
f = { (-7, 20), (3, 5), (0, 5), (-2, 0), (6, -4), (-6, -9), (4, 4) }
where f(x) is the corresponding y-value for x.
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Use the trapezoid shown to select all statements that are true. Select 2 correct answer(s) Question 7 options: The length of AB can be found using 3 2 + b 2 = c 2 . The length of AB can be found using 3 2 + 4 2 = c 2 . The perimeter of the trapezoid shown is 22 units. The perimeter of the trapezoid can not be found.
For the given trapezoid,
a) Length of AB is found by
b² = 3² + 4²
b) Perimeter = 30 units.
What is a trapezoid?
A trapezoid is a quadrilateral with at least one pair of parallel sides. A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs. A trapezoid is a closed, four-sided form or figure that has a perimeter and covers a specific area. It is a 2D figure rather than a 3D one.
The trapezoid is given in the figure below.
a) In this trapezoid, we can draw a perpendicular from B to the line AD. Let this point be E.
So the triangle ABE will be a right triangle.
Now the hypotensue will be AB.
Using Pythagoras' theorem, we can write the following relation.
AB² = AE² + BE²
From the graph of the trapezoid, we can get
AE= 4 -1 = 3 units
BE = 7 - 3 = 4 units
So if AB =b
The length of AB can be found using the,
b² = 3² + 4²
b = 5
Therefore the given statement is false.
b) The perimeter of trapezoid = perimeter of triangle ABE + periemeter of rectangle BCDE
= 5+4+3 + 2* (5+4)
= 12 + 18 = 30 units.
Therefore for the given trapezoid, the perimeter is 30 units.
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