Considering the definition of probability:
the probability that the student owns either a car or laptop is 86%.the probability that the student owns neither a car nor a laptop is 14%.Definition of ProbabitityProbability is the greater or lesser possibility that a certain event will occur.
In other words, the probability is the possibility that a phenomenon or an event will happen, given certain circumstances. It is expressed as a percentage.
The probability of any event A is defined as the quotient between the number of favorable cases (that is, the number of times that event A may or may not occur) and the total number of possible cases:
[tex]Probability=\frac{number of favorable cases}{total number of possible cases}[/tex]
Union of eventsThe union of events, AUB, is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs. AUB is read as "A or B".
The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:
P(A∪B)= P(A) + P(B) -P(A∩B)
Complementary eventA complementary event, also called an opposite event, is made up of the inverse of the results of another event. That is, That is, given an event A, a complementary event is verified as long as the event A is not verified.
The probability of occurrence of the complementary event A' will be 1 minus the probability of occurrence of A:
P(A´)= 1- P(A)
Events and probability in this caseIn first place, let's define the following events:
A: The event that a student owned a laptop.
B: The event that a student owned a car.
Then you know:
P(A)= [tex]\frac{780}{1000}[/tex]= 0.78P(B)= [tex]\frac{460}{1000}[/tex]= 0.46P(F and R)= P(F∩R)= [tex]\frac{380}{1000}[/tex]= 0.38 [The intersection of events, A∩B, is the event formed by all the elements that are, at the same time, from A and B. That is, the event A∩B is verified when A and B occur simultaneously.]In this case, considering the definition of union of events, the probability that the student owns either a car or laptop is calculated as:
P(A∪B)= P(A) + P(B) -P(A∩B)
P(A∪B)= 0.78 + 0.46 -0.38
P(A∪B)= 0.86= 86%
Then, the probability that the student owns either a car or laptop is 86%.
On the other hand, considering the definition of the complementary event and its probability, the probability that the student owns neither a car nor a laptop is calculated as:
P [(A∪B)']= 1- P(A∪B)
P [(A∪B)']= 1 - 0.86
P [(A∪B)']= 0.14= 14%
Finally, the probability that the student owns neither a car nor a laptop is 14%.
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Need answers asap please
The inverse of a function is n(a) = (a+30)/3 option (A) is correct by using the concept of the inverse of a function.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
a(n) = 3n - 30
To find make subject n and solve
a(n) + 30 = 3n
[tex]\rm n = \dfrac{a(n) + 30}{3}[/tex]
Plug n = n(a) and a(n) = a
[tex]\rm n(a) = \dfrac{a + 30}{3}[/tex]
Thus, the inverse of a function is n(a) = (a+30)/3 option (A) is correct by using the concept of the inverse of a function.
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Adriana can ride her bicycle
6 miles in one hour. How long will it
take her to ride 15 miles?
There are 15 players on a volleyball team. Only 6 players can be on the court for a game. How many different groups of players of 6 players can the coach make, if the position does not matter? 720 810 5,005 3,603,600
The no. of different groups of players of 6 players , if the position does not matter is given by 5005 ,Option C is the right answer.
What is Combination ?Combination is a method of selection of items from a set of distinct objects , when the position doesn't matter .
It is given that
Total number of players = 15 = n
No. of players to be selected = 6 = r
The no. of different groups of players of 6 players , if the position does not matter is given by
[tex]\rm ^nC_r = \dfrac{n!}{r! (n-r)!}[/tex]
So
[tex]\rm ^{15}C_6 = \dfrac{15!}{6! (15-6)!}\\\\\rm ^{15}C_6 = \dfrac{15!}{6! (9)!}\\\\\\^{15}C_6 = \dfrac{15 * 14 * 13* 12 * 11 * 10 }{6 *5* 4 * 3 * 2*1}\\\\ ^{15}C_6 = 5005\\[/tex]
Therefore , The no. of different groups of players of 6 players , if the position does not matter is given by 5005
Option C is the right answer.
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find the x and y values of this graph algebra 2
x y
2,0
1,-2
0,-4
-1,-6
-2,-8
Consider the table that includes the input and output values of a function.
Which best describes the constant difference for the function?
a constant second difference of –6
a constant second difference of 8
a constant third difference of –6
a constant third difference of 8
The first option is correct and it best describes the constant difference for the function as a constant second difference of –6.
What is a function?A function f(x) is the relation between a set of inputs resulting and producing the desired output value of y for each input.
From the given information:
x f(x) first difference second difference third difference
-2 0 - - -
-1 -10 (-10-0)/-1--2 = -10 - -
0 -12 (-12 - 10)/0 -- 1= -2 (-2-10)/2 = -6 -
1 -12 (-12--12)/1-0 = 0 (0-2)/2 = -1 (-1+6)/2 = 5/2
2 -16 (-16--12)/2-1 = -2 (-2-0)/2 = -1 (-1+1)/2 = 0
Therefore, we can conclude that the constant difference for the function is a constant second difference of –6.
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Answer:
A
Step-by-step explanation:
Hello,
I need help with this exercise.
A ball is launched upward at a speed of 20 meters per second (m/s) from a 60-meter tall platform. The equation for the ball’s height (h in meters) at time t seconds after launch is h = -4.9t2 + 20t + 60. How long before the ball hits the ground? What is the maximum height of the ball?
Answer:
s = height above ground
s = 60 + 20 t - 4.9 t^2 (standard physics equation on earth)
at t = 0
s = 60 (clearly :)
now when does it hit the bleak earth?
That is when s = 0
4.9 t^2 - 20 t -60 = 0
solve quadratic and use the positive t (the negative t was back before you threw it if you had thrown it from the ground)
t = 6.09 or - 2.01
use t = 6.09
now to do the last part there are two obvious ways to get t at the peak
1. look for vertex of parabola
2. look for halfway between t = -2.01 and t = 6.09
I will do it the hard (11) waay by completing the square
4.9 t^2 - 20 t = -(s-60)
t^2 - 4.08 t = -.204 s + 12.2
t^2 - 4.08 t +2.04^2 = -.204 s +12.2 + 4.16
(t-2.04)^2 = -.204(s-80.2)
so
top at 80.2 meters at t = 2.04 s
===============
quick check on time
should be average of 6.09 and -2.01
=4.08 /2 = 2.04 check
Answer: I HOPE THAT MY ANSWER WILL HELP U
Step-by-step explanation:
s = height above ground
s = 60 + 20 t - 4.9 t^2 (standard physics equation on earth)
at t = 0
s = 60 (clearly :)
now when does it hit the bleak earth?
That is when s = 0
4.9 t^2 - 20 t -60 = 0
solve quadratic and use the positive t (the negative t was back before you threw it if you had thrown it from the ground)
t = 6.09 or - 2.01
use t = 6.09
now to do the last part there are two obvious ways to get t at the peak
1. look for vertex of parabola
2. look for halfway between t = -2.01 and t = 6.09
I will do it the hard (11) waay by completing the square
4.9 t^2 - 20 t = -(s-60)
t^2 - 4.08 t = -.204 s + 12.2
t^2 - 4.08 t +2.04^2 = -.204 s +12.2 + 4.16
(t-2.04)^2 = -.204(s-80.2)
so
top at 80.2 meters at t = 2.04 s
===============
quick check on time
should be average of 6.09 and -2.01
=4.08 /2 = 2.04 check
What are the factors of this quadratic function?
Answer:
(x-1) and (x-5)
what is the constant proportionality in the equation y = 5/4x?
2x + y ≤ 2
a. change the inequality into slope-intercept form, and then change it into an equation.
b. create a table. Use the x-values indicated
c. Graph the points and draw a line.
d. Shade the solution area.
e. Check your solution. Use (0,0) as your test point and see if it satisfies the conditions of the original inequality.
The graph is attached with the answer.
What is an Inequality ?When two algebraic expressions are equated using an inequality operator , The statement formed is called In equality.
The given Inequality is 2x + y ≤ 2
in slope intercept form can be written as
y ≤ -2x +2 , here slope is -2 and intercept is 2
As an equation it will be
y = -2x +2
x y
0 , 2
1 , 0
2 -2
The graph is plotted
The area is shaded and the test for the origin is applied , and it lies in the shaded region.
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The present value of $100 to be received 10 years from today, assuming an opportunity cost of 9 percent, is
An opportunity cost of 9 percent, is $42.
We have given that,
The present value of $100 is to be received 10 years from today,
assuming an opportunity cost of 9 percent,
present value =$100
N=10 years
I/y=9
What is the formula for the present value?PV= FV/(1+r)^n
Where FV is the future value.
Use the given values in the formula we get,
Therefore the correct answer is 42.
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A restaurant offers 7 appetizers and 8 main courses. In how many ways can a person order a two-course meal?
There are ways a person can order a two-course meal.
Answer:
56
Step-by-step explanation:
so 7 appetizers times 8 main courses
I do a easy trick where I multiple so
7×8=56
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: [ - 10,- 8] \cup[ - 2,0] \cup[2,5][/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
The intervals in which a function is decreasing has a negative slope. and for given graph, the required intervals are :
[tex]\qquad \tt \rightarrow \: [ - 10,- 8] \cup[ - 2,0] \cup[2,5][/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
need help with this question
The local maximum of the equation y = x³ - 5x + 2 is y = 6.3 which occurs at x = -1.29
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation:
y = x³ - 5x + 2
The maximum is at dy/dx = 0, hence:
3x² - 5 = 0
x = -1.29 or x = 1.29
y = (-1.29)³ - 5(-1.29) + 2 = 6.3
The local maximum of the equation y = x³ - 5x + 2 is y = 6.3 which occurs at x = -1.29
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Write an expression that can be used to produce vector b from vector a, and explain how you determined that expression.
Answer:
k(magnitude of vector a).vector a
Step-by-step explanation:
Given question is based on vectors so,
vectors :- Vectors in math is a geometric entity that has both magnitude and direction. Vectors have an initial point at the point where they start and a terminal point that tells the final position of the point. Various operations can be applied to vectors such as addition, subtraction, and multiplication.
To produce an another vector form a given vector we increase its magnitude only not its direction as we have to produce another vector from a given vector.
as its clear from the graph given in the question that only the magnitude of vector a is increased to produce another vector b
hence we multiply any constant ('k') with the magnitude of vector a to increase its magnitude.
and finally multiply the increased magnitude with the vector 'a' itself.
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A. 0 m/s
B. -0.17 m/s
C. 12 m/s
D. 0.17 m/s
Answer:
0 m/s
Step-by-step explanation:
What are the zeros of the quadratic function f(x)=6x^2+12x-7
Answer:
[tex]A) \ x=-1 \ ^ +_-\frac{\sqrt{13} }{\sqrt{6}}.[/tex]
Step-by-step explanation:
if to solve the given equation, then
D=6²+42=78;
[tex]\left[\begin{array}{ccc}x=\frac{-6-\sqrt{78}}{6} \\x=\frac{-6+\sqrt{78}}{6} \end{array} \ = > \ \left[\begin{array}{ccc}x=-1-\sqrt{\frac{13}{6} } \\x=-1+\sqrt{\frac{13}{6} } \end{array}[/tex]
Phil Santos owns an independent mobile phone store. He has a wonderful personality, is very knowledge about the products he sells and people flock to his store. Phil would like to start selling online so he can reach more customers.
He's talked with website developers and the firm he decided to go with will charge him $9500 to build the site. Phil wondered why the site was so expensive and explored the idea of building it himself. He found out it's complicated to build a site that can take payments so he decided to be safe rather than sorry and have it built by experts. They also gave him an estimate of $5300 a year to maintain his site. This will allow him to update the site constantly and add new pictures and videos as new products and promotions are introduced over the course of the year.
A marketing research firm found that he should expect about 133 sales a month averaging about $290 profit per sale. Phil was thrilled with this news and decided to spend $15,000 to add a new room to his store to be used as a shipping area.
He also wanted to make his sales literature and in store promotional materials such as banners, and promotional give-a-ways consistent with the look of the website. Phil has worked with a graphic design class at the local community college and knows it will cost $2300 a year to have the materials designed and printed.
What is the cost to acquire each new customer? Show your full calculation.
Does it make sense for Phil to sell his products online?
Answer:
It makes sense for Phil to sell his products online.
Step-by-step explanation:
Identify the common ratio and first term and fill in the recursive formula for each of the following geometric sequences.
The first term will be 4 and the common ratio will be 2. And the nth term will be given as [tex]\rm a_n = a_{n -1} \cdot 2[/tex].
The complete question is attached below.
What is the geometric sequences?Let a be the first term and r be the common ratio. Then the geometric sequences will be
[tex]\rm a_n = a_{n -1} \cdot r[/tex]
The geometric sequence is given below.
4, 8, 16, 32, 64,................
Then the first term will be 4 and the common ratio will be 2.
And the nth term will be given as [tex]\rm a_n = a_{n -1} \cdot 2[/tex].
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What is the product?
(3a²b7)(5a³b³)
O 8a5b15
O 8a6b56
O 15a³b¹5
O 15a5b56
Answer:
15a^5 b^10
Step-by-step explanation:
The product is 15a⁵b¹⁰.
What is an exponent?Exponentiation is one of the mathematics operations.
Let mᵃ, where m and a are the real numbers.
And m is multiplied by a times to itself.
So, a is the exponent of m.
When multiplying two terms with the same base, you add the exponents. Therefore:
(3a²b⁷)(5a³b³) = 3 x 5 x a⁵ x b ¹⁰
= 15a⁵b¹⁰.
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6. 0, 16, 32, 48, 64, ______, ______, ______
what is the next 3 numbers.
Answer:
Step-by-step explanation:
Remark. Since 6 has a decimal after it, I take it that is the question number.
y = 16x is the basic formula. x starts at 0. Then you add 16 to each number to get the next number in the sequence. Or you could do it the way I propose it.
x 0 1 2 3 4 5 6 7
y 0 16 32 48 64 80 96 112
What is the solution to t - 3 < 12
Answer:
[tex]\boxed {t < 15}[/tex]
Step-by-step explanation:
Given :
⇒ t - 3 < 12
Add 3 to each side :
⇒ t - 3 + 3 < 12 + 3
⇒ t < 15
Answer: t < 15
Step-by-step explanation:
rearrange the terms t - 3 < 12
calculate the sum or difference t < 12 + 3
answer t < 15
What are the solutions to the following system of equations?
2x − y = 6
y = x2 − 9
(3, 0) and (−1, −8)
(3, 0) and (4, 2)
(−3, 0) and (−1, −8)
(−3, 0) and (4, 2)
Answer:
(3, 0) and (−1, −8)
Equation's:
2x − y = 6y = x² − 9Substitute equation 2 into 12x − (x² − 9) = 6
2x - x² + 9 = 6
-x² + 2x + 9 - 6 = 0
-x² + 2x + 3 = 0
x² - 2x - 3 = 0
x² - 3x + x - 3 = 0
x(x - 3) + 1(x - 3) = 0
(x + 1)(x - 3) = 0
x = -1, x = 3
Find values for yIf x = -1, then y = (-1)² - 9 = -8
If x = 3, then y = (3)² - 9 = 0
Solution Set:(x, y) = (-1, -8), (3, 0)
The Mountain States Office of State Farm Insurance Company reports that approximately 84% of all automobile damage liability claims were made by people under 25 years of age. A random sample of ten automobile insurance liability claims is under study.
The mean will be 10.08 and the standard deviation will be 1.27.
The complete question is given below:-
The Mountain States Office of State Farm Insurance Company reports that approximately 84% of all automobile damage liability claims were made by people under 25 years of age. A random sample of twelve automobile insurance liability claims is under study.
Find the mean and standard deviation of this probability distribution.
For samples of size 12, what is the expected number of claims made by people under 25 years of age?
What is mean?Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.
Standard deviation is defined as the amount of variation or the deviation of the numbers from each other.
Given that:-
The Mountain States Office of State Farm Insurance Company reports that approximately 84% of all automobile damage liability claims were made by people under 25 years of age.We need to find For samples of size 12, what is the expected number of claims made by people under 25 years of age?The mean will be calculated by the formula below:-
Mean = [tex]\mu[/tex] = np = 12 x 0.84 = 10.08
The standard deviation will be calculated as:-
Standard deviation = [tex]\sqrt{npq}[/tex] = [tex]\sqrt{12\times 0.84\times 0.16}[/tex] = 1.27
Therefore the mean will be 10.08 and the standard deviation will be 1.27.
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Find the perimeter of this
Tringle
8 cm
7 cm
5 cm
answer is
A. 35 cm
B. 40 cm
C. 20 cm
D. 12.5 cm
Answer:
C) 20cm
Step-by-step explanation:
Perimeter is the distance around the edge of the shape.
8 + 7 + 5 = 20
Answer:
20 is answer
Step-by-step explanation:
as perimeter= sum of all side
= 8 +7+5=2ocm
julie ran a race 2 minutes faster than teri did. if teri ran the race in 28 minutes, what equation would be used to find the number of minutes teri took to run the race
Th equation that can be used to find the umber of minutes Teri ran is m + 2 = 28 minutes.
How many minutes did it take Teri to run the race?Addition is a mathematical operation that is used to determine the sum of two or more numbers.
The total minutes run by Julie = minutes ran by Teri + 2
28 = m + 2
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Use the graph of the function provided to find the indicated values.
a) When x = -2, g(x) = 5.
b) When x = -4, g(x) = 7.
c) When g(x) = 6, x = -3
d) When g(x) = -1, x = 4
If f(x)= 3x +2 and g(x)=x^2+1, which expression is expression is equivalent to (fog) (x)
Composite functions occur when we take two functions and input one into the other as x.
Example:
[tex]f(x) = 2x[/tex]
[tex]g(x) = 3x^2[/tex]
[tex](f\circ g)(x)=f(g(x))[/tex]
[tex](f\circ g)(x) = 2(3x^2)[/tex]
Solving the QuestionWe're given:
[tex]f(x)= 3x +2[/tex][tex]g(x)=x^2+1[/tex]To find [tex](f\circ g)(x)[/tex], input g into f as x:
[tex]f(x)= 3x +2[/tex]
[tex](f\circ g)(x)=3(x^2+1) +2\\(f\circ g)(x)=3x^2+3 +2\\(f\circ g)(x)=3x^2+5[/tex]
Answer[tex](f\circ g)(x)=3x^2+5[/tex]
The statement “a > 2 and a < 5” is true when a is equal to
A. 5
B. 3
C. 10
D. 2
Answer:
B
Step-by-step explanation:
because > means greater than or more than
and < means less than
the answer is B because 3 is more than 2 and the same time less than 5
What is the initial value of the sequence? Please help
The initial value of the sequence is 1
How to determine the initial value?From the graph, we have the following ordered pairs
(x, y) = (1, 1), (2, 4) and (3, 8)
Remove the x values
y = 1, 4, 8
The first value in the above sequence is 1
Hence, the initial value of the sequence is 1
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Which graph represents y= sqrt x-4
Based on the characteristics of the function and the image generated by the graphing tool, we conclude that the first choice represents the function [tex]y = \sqrt{x} - 4[/tex].
How to find the right graph of a given function
In this question we have a radical function ([tex]f(x) = \sqrt{x}[/tex]) translated vertically 4 units in the -y direction. The domain of the function is [0, + ∞). A quick and efficient approach consists in graphing the function and comparing with each image to determine the right choice.
We present the graph description in the image attached below and we conclude that the first choice represents the graph of the function.
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