A probability is a number between 0 and 1 that reflects the likelihood of some outcome. According to the classical approach to assigning probability, the probability that an outcome occurs is interpreted as:
Answers
Answer:
Probability of an event \(=\frac{\textrm{Number of favorable outcomes}}{\textrm{Total number of outcomes}}\)
Step-by-step explanation:
According to the classical approach to assigning probability, if an experiment has \(n\) simple outcomes, this method would assign a probability of \(\frac{1}{n}\) to each outcome. In other words, each outcome is assumed to have an equal probability of occurrence.
So, probability of an event \(=\frac{\textrm{Number of favorable outcomes}}{\textrm{Total number of outcomes}}\)
Related Questions
the square of a number is equal to 6 minus the number find all such numbers
Answers
The solutions to the equation \($x^2 = 6 - x$\) are \($x = -3$\) and \(x = 2$.\)
What is square of a number?
The square of a number is the result of multiplying the number by itself. In mathematical notation, the square of a number "\(x\)" is written as "\(x^2\)".
Let's call the number we are looking for "x".
According to the problem statement, we have:
\($$x^2 = 6 - x$$\)
We can rearrange this equation to get:
\($$x^2 + x - 6 = 0$$\)
Now, we can factor the left-hand side of this equation:
\($$(x + 3)(x - 2) = 0$$\)
So, either \($x + 3 = 0$\) or \(x - 2 = 0$.\) Solving for x in each case gives us:
\($$x = -3 \text{ or } x = 2$$\)
Therefore, the solutions to the equation \($x^2 = 6 - x$\) are \($x = -3$\) and \(x = 2$.\)
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King of Diamonds Industries has bonds on the market making annual payments, with 14 years to maturity, and selling for R1 482,01. At this price, the bonds yield 7%. What is the coupon rate?
Answers
The coupon rate of the bonds by King of Diamonds Industries would be 7 %.
How to find the coupon rate ?The formula for the bond price shows the coupon payment and so can be used to find the coupon rate:
= (Coupon payment x ( 1 - ( 1 + r ) ^ ( - number of years till maturity ) ) ) / r + Face value / (1 + rate )^ number of years
1,482.01 = (C x (1 - (1 + 0.07 )^ (- 14) ) ) / 0.07 + F / (1 + 0.07 ) ^ 14
103.7407 - 0.07 x (F / (1 + 0.07) ^14 ) = C x (1 - ( 1 + 0.07) ^ ( - 14) )
Using a calculator, C is $ 70.
This means that the coupon rate is:
= 70 / 1, 000
= 7 %
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suppose 10 percent of households earn over 80,000 dollars a year,and 0.25 percent of households earn over 450,000. a random sample of 400 house-holds has been chosen. in this sample, letxbe the number of households thatearn over 80,000, and letybe the number of households that earn over 450,000.use either the normal or the poisson approximation, whichever is appropriate ineither case, to nd the simplest estimates you can for the probabilitiesp(x48)andp(y2)
Answers
The probability of P(X = 48) and P(Y =2) is 0.1056 and 0.2642 respectively.
Suppose 10 percent of households earn over 80,000 dollars a year,and 0.25 percent of households earn over 450,000.
a random sample of 400 house-holds has been chosen
N = 400
P = 25%
n*p = 400*0.25 = 100
n(1-p) = 400 * 0.75 = 300
100 and 300 are greater than 5 so we use the normal distribution here to estimate further.
mean = n*p = 100
sd = √(np(1 - p))
sd = √(100(1 - 0.25))
sd = √(100 x 0.75)
sd = √75
sd = 8.66
p(X≥48)
= p(X≥47.5)
P(z < (47.5 - 40)/6)
P(z < 1.25)
= 0.8944
1 - 0.8944
= 0.1056
FOR Y
N = 400 p = 0.25% = 0.0025
400 * 0.0025 = 1
1 is less than 5 so we use poisson distribution.
using the excel function,
1 - BINOMDIST(1, 400, 0.0025, TRUE)
= 1 - 0.735759074
= 0.2642
Therefore, the probability of P(X = 48) is 0.1056 and P(Y =2) is 0.2642
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For each of these intervals, list all its elements or explain 2.1 Sets 131 why it is empty. a) [a,a] c) (a, a] e) (a,b), where a > b b) [a,a) d) (a, a) f) [a,b],wherea>b
Answers
Answer: b
Step-by-step explanation:
Consider the function f(x) = (x − 3)2(x + 2)2(x − 1). The zero has a multiplicity of 1. The zero −2 has a multiplicity of .
Answers
Answer:
The zero 1 has a multiplicity of 1.
The zero -2 has a multiplicity of 2.
Hope this clears up any confusion :)
Step-by-step explanation:
Answer:
The zero 1 has a multiplicity of 1.
The zero −2 has a multiplicity of 2 .
Step-by-step explanation:
9 - (-4)=?
What does that equal to?
Answers
Answer:
= 13
Step-by-step explanation:
When you are subtracting a negative both the subtraction sign and the negative cancel out. This makes it so that you are adding them together.
Answer:
the answer is 13
Step-by-step explanation:
This is because when you subtract a positive by a negative if the positive is larger it will be considered the same as addition
if fx and gx are inverse functions of each other
Answers
The functions f(x) = (x + 3)/2 and g(x) = 2x - 3 are inverse functions of each other.
The function is the mathematical statement that shows the relationship between one variable and other variable. If one variable is independent variable then other variable is dependent variable.
The functions are
f(x) = (x + 3)/2
g(x) = 2x - 3
The value of f(g(x)) = ((2x-3) + 3) / 2
= (2x - 3 + 3) / 2
= 2x / 2
= x
The value of g(f(x)) = 2( (x+3)/2) - 3
= (2x + 6)/2 - 3
= x + 3 -3
= x
Therefore, f(x) and g(x) are inverse function of each other
I have answered the question in general, as the given question is incomplete
The complete question is:
How do you prove that f(x) and g(x) are inverses of each other?
f(x) = (x + 3)/2
g(x) = 2x - 3
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No links please and make sure it's correct.
Answers
Answer:
2 acute angles,1 obtuse angle,and also 1 right angle
Step-by-step explanation:
as u can see at the top left corner,it's acute,and at the right down corner. At at the left down corner is obtuse,and at the top right corner is right angle ÔwÔ
x+3/4= -3/16
I need to find the value of x
Answers
Answer:
x=-0.9375
Step-by-step explanation:
x= - \(\frac{3}{4}\)-\(\frac{3}{16}\)
x=-0.9375
An insurance provider states that their customers save at least, on average, 300 dollars per year by switching to them, with a standard deviation of 150 dollars. Before we decide to switch to the new company and go through all of the hassle, we want to test the claim. So, we go out and sample 64 individuals who switched to the new insurance company and found them to have saved an average of 255 dollars per year. Do we have enough evidence at the α = 0.05 level to state that the insurance provider is false in their claim? Discussion Prompts Answer the following questions in your initial post: What are the hypotheses based on the words given in the problem? Should we use a Z or T distribution in this case? What is our Z or T statistic? What is the P-value? Based on your p-value and alpha, what conclusion will we make? Based on your results, would you switch to this company? Explain why or why not (Note: this can go beyond the use of statistics, but statistical analysis can help our decisions)
Answers
The solution to the question is mathematically given as
1)
H0: M \(\geqslant\) 300
H0: M \(\geqslant\) 300
2)
Z distribution.
3)
z=-2.4
4)
P=0.0082
5)
"H0" is rejected as a hypothesis with a level of significance of 0.05.
What is the hypothesis ?Generally, the equation for is mathematically given as
Solutions
we have, \($u=300$$$\begin{aligned}& \sigma=150 \text { dollars } \\N &=64 \text { individuals } \\\bar{x} &=255 \text { dollare. } \\a=& 0.05 .\end{aligned}\)
(1):
H0: M \(\geqslant\) 300 dollars; customers save at least 300 dollars per year by switching to them.
H0: M \(\geqslant\) 300 dollars:
(This is a left-tailed test)
(2):
when \(\sigma\) is known, we use the Z test. we use Z distribution.
(3):
\(\begin{gathered}z=\frac{\bar{x}-\mu}{6 / \sqrt{n}}=\frac{255-300}{150 / \sqrt{64}}=\frac{-45}{18.75}=-2.4 \\z=-2.4\end{gathered}\)
(4):
\(Pvalue $=P(z < -2 \cdot 4)$ $=0.0082 \quad\{$ wing $z$ tables $\}$ \\\\\text { Pvalue }=0.0082\)
(5):
In conclusion, Since p-value = 0·0082 <0.05
This is statistically significant at the 0.05 level.
We thus "Refect H0" using a threshold of significance of 0.05.
"H0" is rejected as a hypothesis with a level of significance of 0.05.
There is not enough data to support the assertion that consumers may save at least $300 annually by switching insurance providers.
Therefore, we would not consider making the transition to this firm.
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The answer for
2(c) = 2c
Answers
2
c
2c from both sides of the equation
—
2
c
=
2
c
2c=2c
2
c
−
2
c
=
2
c
−
2
c
2c−2c=2c−2c
2
Simplify
—
Combine like terms
2
c
−
2
c
=
2
c
−
2
c
2c−2c=2c−2c
0
=
2
c
−
2
c
0=2c−2c
Combine like terms
0
=
0
0=0
Answer:
Any real number could be true for this equation.
A comedy club hosts an amateur comedy night, a good opportunity for aspiring comedians to
perform. Of the 8 amateur comedians who signed up for tonight's show, 6 perform satirical
comedy,
If the host randomly selects 4 comedians from the sign-up list, what is the probability that all
of them practice satirical?
Write your answer as a decimal rounded to four decimal places.
Answers
Answer:
0.2143 probability that all of them practice satirical.
Step-by-step explanation:
The comedians are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
In this question:
8 comedians means that \(N = 8\)
6 practice satirical means that \(k = 6\)
Sample of 4 means that \(n = 4\)
What is the probability that all of them practice satirical?
This is P(X = 4). So
\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)
\(P(X = 4) = h(4,8,4,6) = \frac{C_{6,4}*C_{2,0}}{C_{8,4}} = 0.2143\)
0.2143 probability that all of them practice satirical.
A customer buys a different book that has an original selling price of $38. The book is discounted 25%. The customer must pay a 6% sales tax on the discounted price of the book.
What is the total amount, in dollars, the customer pays for the discounted book? Explain and SHOW how you arrived at your answer.
Answers
Answer:
$30.21
Step-by-step explanation:
100% -25%= 75%
Discounted price of the book
= 75% ×$38
= $28.50
Since the customer must pay an additional 6% of the discounted price,
percentage of discounted price paid
= 100% +6%
= 106%
Total amount paid
= 106% × $28.50
= $30.21
_________________________________
Alternative working:
Original selling price= $38
Since the book is discounted 25%,
100% ----- $38
1% ----- $0.38
75% ----- 75 ×$0.38= $28.50
Since the sales tax is based on the discounted price, we let the discounted price be 100%.
100% ----- $28.50
1% ----- $0.285
106% ----- 106 ×$0.285= $30.21
∴ The total amount the customer pays for the discounted book is $30.21.
Find the quotient of 90 over -10
Answers
90/-10
= 9/-1
= -9
So, -9 is the quotient.
I hope this helps you, Goodluck! :)
1. Solve 9a = 27. The solution is a =
Answers
Answer: 3
Step-by-step explanation: To solve for A we need to get it by itself by doing the inverse of mulitplication, which is, division. 27/9=3, so a=3.
Answer:
3
Step-by-step explanation:
Because 9 x 3 = 27, the variable "a" would be equal to 3. When a variable is next to a number, you multiply it with the coefficient (in this situation, it would be the 9).
Hope this helps.
HELP PLEASE M BEGGNG
Answers
Answer:
Min: 1
Q1: 2
Median: 7
Q3: 9
Max: 11.5
Step-by-step explanation:
The five bars of the box plot correspond (from left-to-right) to the numbers in the five-number summary.
The first bar represents the minimum, which in this case is 1.
The second bar represents the first quartile (Q1), which in this case is 2.
The third bar represents the median, which in this case is 7.
The fourth bar represents the third quartile (Q3), which in this case is 9.
And the fifth bar represents the maximum, which in this case is 11.5.
Answer:
Min: 1
Q1: 2
Median: 7
Q3: 9
Max: 11.5
Step-by-step explanation:
I hope it helps:)
HELPPP PLEASE!!!!!!!!!
Answers
B) 340.34cm3
Which equation has the solution x = 3?
Select each correct answer.
2x + 4 = 10
9−3x=0
3x + 1 = 9
9x−1=4
x3+5=6
5x−7=1 giving 50 pointss so hurry
Answers
Answer:
A and B
Step-by-step explanation:
A: 2x3=6 6+4=10 so correct
B: 9-9=0 so correct
Answer:
2x+4=10
Step-by-step explanation:
2x=10-4=
2x=6
x=6÷2=
3
Juan buys candy that costs $8 per pound. He will spend at least $48 on candy. What are the possible numbers of pounds he will buy?
Use p for the number of pounds Juan will buy.
Write your answer as an inequality solved for p.
Answers
In a case whereby Juan buys candy that costs $8 per pound and will spend at least $48 on candy the possible numbers of pounds he will buy written in inequality is is p>5 (at least 5 pounds).
How can these number be determined?Inequality in math refers to a statement that one quantity is either greater than, less than, or not equal to another quantity. Inequalities are often represented using symbols such as "<" (less than), ">" (greater than), or "≤" (less than or equal to) and "≥" (greater than or equal to). For example, the inequality "x > 3" states that the variable "x" is greater than the value of 3. The inequality "y ≤ 5" means that the variable "y" is less than or equal to 5.
From the question, p = number of pounds Juan will buy.
candy=costs $8 per pound
$20/$4 = 5 pounds
p>5
at least 5 pounds
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Solve the following inequality: 20t + 9, 200 ≤ 16,000
Answer in interval notation.
Answers
Answer:
[0, 799.95]
Step-by-step explanation:
First, we need to isolate the variable by subtracting 9 from both sides of the inequality:
20t + 9 - 9 ≤ 16,000 - 9
This gives us:
20t ≤ 16,000 - 9
Next, we can divide both sides of the inequality by 20 to isolate the variable:
20t / 20 ≤ (16,000 - 9) / 20
This simplifies to:
t ≤ 799.95
Finally, we need to express the solution in interval notation. Since the value of t cannot be negative, the solution is:
[0, 799.95]
Therefore, the solution to the inequality in interval notation is [0, 799.95].
Question content area top
Part 1
In your class, you have scores of 82, 75, 72, 83 and on the first four of five tests. To get a grade of C, the average of the first five tests scores must be greater than or equal to 70 and less than 80.
a.
Solve an inequality to find the least score you can get on the last test and still earn a C.
b.
What score do you need if the fifth test counts as two tests?
Answers
Answer:
..jkl
...............................
The domain of a function is always equal to which one of the following options?
A. all possible output values of the function
B. the range of the function
C. all possible input values of the function
D. all real numbers
Answers
Answer:
C. all possible input values of the function
Step-by-step explanation:
Answer:
C is right
Step-by-step explanation:
domain is f(x)=x^2 is all real numbers but domain g(x)=1/x is all real numbers except for 0 which is x but domains and the rang can be the same also
The total amount of time University students in the United States spend sleeping,grooming,eating and drinking and traveling is about?
Answers
Answer:
11.7 hours
Step-by-step explanation:
According to data gathered between the years of 2015-2020 from full-time University Students at various Universities throughout the US, it was discovered that they spend roughly 11.7 hours completing these tasks (sleeping, grooming, eating/drinking, and traveling) per day. This applies strictly to full-time University Students that have the responsibilities associated with that life such as studying, attending class, group projects, etc. and does not include extra activities such as cooking.
to multiply a decimal number by a 1,000 , move the decimal point four places to the right
Answers
Answer:
that is the answer
Step-by-step explanation:
Answer:
Step-by-step explanation:
whoop
Find the measurement of m
Answers
The measure of the inscribed angle G in the circle is 85 degree.
What is the measure of angle G?An inscribed angle is simply an angle with its vertex on the circle and whose sides are chords.
The relationhip between an an inscribed angle and intercepted arc is expressed as:
Inscribed angle = 1/2 × intercepted arc.
Since the circle equals 360 degrees, we can determine the intercepted arc DF.
Hence:
Arc DF = 360 - ( 70 + 120 )
Arc DF = 360 - 190
Arc DF = 170°
Now, plug the value into the above formula:
Inscribed angle = 1/2 × intercepted arc.
Inscribed angle G = 1/2 × 170°
Inscribed angle G = 85°
Therefore, angle G has a measure of 85 degree.
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Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line.(The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent for a test and their scores on that test are shown below.
(a) x=3 hours
(b) x=4.5 hours
(c) x=13 hours
(d) x=1.5 hours
Answers
ŷ= 6.45x + 31.5 is the equation of the regression line for the given data
How to find the equation of the regression line for a given data?Construct the table of the data as follows:
x >>>> y >>>> x² >>>> y² >>>> xy
1 39 1 1521 39
2 45 4 2025 90
3 52 9 2704 156
4 49 16 2401 196
5 61 25 4096 305
5 72 25 5184 360
................................................................................................
20 318 80 17931 1146
.................................................................................................
∑x = 20, ∑y = 318, ∑x²= 80, ∑xy = 1146, n = 6 (number data points)
The linear regression equation is of the form:
ŷ = ax + b
where a and b are the slope and y-intercept respectively
a = ( n∑xy -(∑x)(∑y) ) / ( n∑x² - (∑x)² )
a = (6×1146 - 20×318) / ( 6×80-20² )
a = 6876-6360 / 480-400
a = 516 / 80
a = 6.45
x' = ∑x/n
x' = 20/6 = 10/3
y' = ∑y/n
y' = 318/6 = 53
b = y' - ax'
b = 53 - 6.45×(10/3)
b = 53 - 21.5
b = 31.5
ŷ = ax + b
ŷ= 6.45x + 31.5
Thus, the equation of the regression line for the given data is ŷ= 6.45x + 31.5. (The scatter plot of the data is shown in the attached image)
(a) x=3 hours
ŷ= 6.45(3) + 31.5 = 50.85
(b) x=4.5 hours
ŷ= 6.45(4.5) + 31.5 = 60.525
(c) x=13 hours
ŷ= 6.45(13) + 31.5 = 115.35
(d) x=1.5 hours
ŷ= 6.45(1.5) + 31.5 = 41.175
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to make his special drink, jerome uses 8 cups of water and 3 cups of drink mix. what is the ratio of water to drink mix?
Answers
Answer:
8:3
Step-by-step explanation:
read the question carefully
Answer:
8/3 or 8:3
Step-by-step explanation:
It says WATER to DRINK MIX. Therefore, It can't be 3:8 or 3/8. The only thing to make sense is 8/3 or 8:3
awnser this for 5 points do you use this app.bc ur lazy and don't want to think
Answers
Answer:
No but when I don't understand something it helps
Step-by-step explanation:
and I'm not lazy either
QUESTION IS DOWN BELOW 30 points for answer
Answers
Answer: a) 25:16 and b) 125:64
Step-by-step explanation:
For simplicity, assume that two spheres have diameters of 5 and 4.
a) 4pi(5^2) and 4pi(4^2)
= 100pi:64pi
= 100:64
= 25:16
b. 4/3 pi(5^3) and 4/3 pi(4^3)
= 166.67pi and 85.33pi
= 500:256
= 125:64
-3x^2+33=48x complete the square
Answers
The complete square form of - 3x² + 33 = 48x is [x + 8]² = 75
Completing the square:
To do this, we add and subtract a constant term to the quadratic expression to make it a perfect square.
In this case, we use the formula x² + 2bx + b² = (x + b)² to rewrite the quadratic expression as a perfect square trinomial, and then we solved for the variable by isolating the squared term and taking the square root.
Here we have
- 3x² + 33 = 48x
Keep 'x' terms on one side and constant terms sides on another side
=> - 3x² - 48x = - 33
Divide by - 3 on both sides
=> -3(x² + 4x)/3 = - 33/3
=> x² + 16x = 11
Take half of the 'x' term and square it and add on both sides
=> x² + 2(8x) (x) + (8)² = 11 + (8)²
Which is in the form of x² + 2bx + b² = (x + b)²
=> [x + 8]² = 75
Therefore,
The complete square form of - 3x² + 33 = 48x is [x + 8]² = 75
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