Answer:
[tex]P(A) = 0.45[/tex]
[tex]P(B) = 0.32[/tex]
Step-by-step explanation:
Given
[tex]P(A) > P(B)[/tex]
[tex]P(A\ u\ B) = 0.626[/tex]
[tex]P(A\ n\ B) = 0.144[/tex]
Required
Find P(A) and P(B)
We have that:
[tex]P(A\ u\ B) = P(A) + P(B) - P(A\ n\ B)[/tex] --- (1)
and
[tex]P(A\ n\ B) = P(A) * P(B)[/tex] --- (2)
The equations become:
[tex]P(A\ u\ B) = P(A) + P(B) - P(A\ n\ B)[/tex] --- (1)
[tex]0.626 = P(A) + P(B) - 0.144[/tex]
Collect like terms
[tex]P(A) + P(B) = 0.626 + 0.144[/tex]
[tex]P(A) + P(B) = 0.770[/tex]
Make P(A) the subject
[tex]P(A) = 0.770 - P(B)[/tex]
[tex]P(A\ n\ B) = P(A) * P(B)[/tex] --- (2)
[tex]0.144 = P(A) * P(B)[/tex]
[tex]P(A) * P(B) = 0.144[/tex]
Substitute: [tex]P(A) = 0.770 - P(B)[/tex]
[tex][0.770 - P(B)] * P(B) = 0.144[/tex]
Open bracket
[tex]0.770P(B) - P(B)^2 = 0.144[/tex]
Represent P(B) with x
[tex]0.770x - x^2 = 0.144[/tex]
Rewrite as:
[tex]x^2 - 0.770x + 0.144 = 0[/tex]
Expand
[tex]x^2 - 0.45x - 0.32x + 0.144 = 0[/tex]
Factorize:
[tex]x[x - 0.45] - 0.32[x - 0.45]= 0[/tex]
Factor out x - 0.45
[tex][x - 0.32][x - 0.45]= 0[/tex]
Split
[tex]x - 0.32= 0 \ or\ x - 0.45= 0[/tex]
Solve for x
[tex]x = 0.32\ or\ x = 0.45[/tex]
Recall that:
[tex]P(B) = x[/tex]
So, we have:
[tex]P(B) = 0.32 \ or \ P(B) = 0.45[/tex]
Recall that:
[tex]P(A) = 0.770 - P(B)[/tex]
So, we have:
[tex]P(A) = 0.770 - 0.32 \ or\ P(A) =0.770 - 0.45[/tex]
[tex]P(A) = 0.45 \ or\ P(A) =0.32[/tex]
Since:
[tex]P(A) > P(B)[/tex]
Then:
[tex]P(A) = 0.45[/tex]
[tex]P(B) = 0.32[/tex]
Find the midrange for the group of data items.
2, 2, 5, 5, 8, 8, 10
Answer:
5
Step-by-step explanation:
Answer:5
Start striking off the numbers one from the left and then from the right continuously until you're left with a number in the middle
Henry wants to get a job this summer. He can either mow lawns or work in the local library. What is the opportunity cost if he decides to mow lawns? A. the librarian employing another person B. the chance to earn by working in a library C. the chance to earn by mowing lawns
Answer:
b
Step-by-step explanation:
plato
If Henry decides to mow lawns then the opportunity cost would be - the chance to earn by working in a library
The correct answer is an option (B)
What is opportunity cost?"It is the value of what you lose when choosing between two or more options.""It is the value of the next best option."We know that,
the opportunity cost is the cost of the alternative that we waive when we make a certain decision, including the benefits that we could have obtained from having chosen the alternative option.It is referred to as "the value of the best option not selected".The opportunity cost is the values that are lost while choosing one alternative in place of others.This value may or may not be measured in money.It is the value of what you have to give up in order to choose something else.Henry wants to get a job this summer.
He can either mow lawns or work in the local library.
if he decides to mow lawns, he would lost the chance to earn by working in a library.
This means, the opportunity cost is - the chance to earn by working in a library
Therefore, if Henry decides to mow lawns then the opportunity cost would be - the chance to earn by working in a library
The correct answer is an option (B)
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Identify the functions that exhibit a removable discontinuity.
Answer:
h(x) and k(x)
Step-by-step explanation:
The functions that exhibit a removable discontinuity are function i(x) and function k(x)
What is a quadratic equation?"An equation of the form ax² + bx + c = 0 is a quadratic equation."
What is a function?"It defines a relation between input and output values."
What is discontinuous function?"This function has a discontinuity at one or more values mainly because of the denominator of a function is being zero at that."
What is removable discontinuity?"If adjusting the function's value at the point of discontinuity will render the function continuous, then such discontinuity is called removable discontinuity."
What is non-removable discontinuity?"If adjusting the function's value at the point of discontinuity will not render the function continuous, then such discontinuity is called non-removable discontinuity."
For given question,
1) Consider a function [tex]f(x)=\frac{x^{2} +4x-21}{x^{2} -13x+42}[/tex]
If we factorize the quadratic equation at numerator and denominator then the given function would be,
[tex]f(x)=\frac{(x-3)(x+7)}{(x-7)(x-6)}[/tex]
We can observe that the function f(x) is discontinuous at x = 7 and x= 6.
So, the function f(x) has non-removable discontinuity.
2) Consider a function [tex]g(x)=\frac{2x^{2} -5x+12}{2x+3}[/tex]
We can observe that the function g(x) is discontinuous at x -3/2.
We cannot factorize the quadratic equation at numerator.
So, the function g(x) has non-removable discontinuity.
3) Consider a function [tex]h(x)=\frac{x-3}{x^{2} -9}[/tex]
If we factorize the quadratic equation at denominator then the given function h(x) would be,
[tex]\Rightarrow h(x)=\frac{(x-3)}{(x-3)(x+3)}\\\\\Rightarrow h(x)=\frac{1}{x+3}[/tex]
We can observe that the function h(x) is discontinuous at x = -3
So, the function h(x) has non-removable discontinuity.
4) Consider a function [tex]i(x)=\frac{x^{2} -8x+15}{x-5}[/tex]
If we factorize the quadratic equation at numerator then the given function would be,
[tex]\Rightarrow i(x)=\frac{(x-5)(x-3)}{x-5}\\\\ \Rightarrow i(x)=x-3[/tex]
We can observe that the function i(x) is a continuous function.
So, the function i(x) has removable discontinuity.
5) Consider a function [tex]j(x)=\frac{x+4}{-2x+8}[/tex]
We can observe that the function j(x) is discontinuous at x = 4
And the function j(x) has non-removable discontinuity.
6) Consider a function [tex]k(x)=\frac{2x^{2} +x-15}{2x-5}[/tex]
If we factorize the quadratic equation at numerator then the given function would be,
[tex]\Rightarrow k(x)=\frac{(x+3)(2x-5)}{(2x-5)}\\\\ \Rightarrow k(x)=x+3x^{2}[/tex]
We can observe that the function k(x) is a continuous function.
So, the function k(x) has removable discontinuity.
Therefore, the functions that exhibit a removable discontinuity are function i(x) and function k(x)
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Convert:
2 tons 15,000 ounces =
ounces
James used 30% of his savings to buy video games. If he had $60 dollars saved. How much does he have left
Answer: $42 left
Step-by-step explanation:
30% of 60 = 18 60-18 leaves $42
sora
-
[tex](secx - 1 \secx + 1) [/tex]
Answer:
[tex] \frac{ \frac{1}{ \cos(x) } - 1 }{1 + \frac{1}{ \cos(x) } } = \frac{ \frac{1 - \cos(x) }{ \cos(x) } }{ \frac{1 + \cos(x) }{ \cos(x) }} = (1 - \cos(x)) \times (1 + \cos(x)) = 1 - { \cos(x) }^{2} = { \sin(x) }^{2} [/tex]
Solve the equation
2x - 1/ 4
+ x/3 = 2
Answer:
= 2 7 /2 8
Step-by-step explanation:
Answer:
x = 1 1/8
Step-by-step explanation:
2x - 1/4 + x/3 = 2
2x + x/3 = 2 1/4 (added 1/4 to both sides)
6x = 6.75 (multiplied both sides by 3)
x = 1 1/8, or 1.125
:-)
Write the equation for a parabola with a focus at (7, 2) and a directrix at y = -2.
y =
Answer:
(x-7) squared over 8
Step-by-step explanation:
[tex]y=\frac{(x-7)^{2} }{8}[/tex]
find the number of terms in the series for the series given below.
The makers of a certain diet cola claim that its taste is identical to the full-calorie version. To test this claim, a
researcher recruits 175 volunteers, has them drink samples of both colas from identical cups in a randomized order,
and then asks them to identify which sample is the diet cola. If we assume that the volunteers truly cannot tell the
difference, then the probability that they correctly identify the diet cola is 0.5.
X = the number of volunteers who correctly identify the diet cola and is a binomial random variable.
Calculate the mean and standard deviation of X. Round to 4 decimal places, when necessary.
Hx=
x =
Answer: ux: 87.5
ox= 6.6144
Step-by-step explanation:
Answer:
Calculate the mean and standard deviation of X. Round to 4 decimal places, when necessary.
μx = 87.5
σx = 6.6144
Step-by-step explanation:
9(6k + 3r)=
A) 15k+12r
B) 54k+27r
C) 6(3k+0r
D) 3(18k+9r
Answer:
B
Step-by-step explanation:
9*6k+9*3r
54k+27r so the answer is B
Determine the independent and dependent variable from the following equations:
1. y = 3x - 5
2. 9 = -16s + 6
3. p= 7+39
4. m = 2 - 4n
Answer:123 because 1 is before 2
Answer:
I don't know what I have already asked for record
It takes Gloria 3 hours to rake the leaves in her yard. If Gloria rakes the leaves 4 times each
fall for 5 years, how many hours will she rake leaves over the five year period?
A 60 hours
CB 75 hours
C 120 hours
D 160 hours
simplify the expression cosxcotx+sinx
Answer:
I might be wrong but I think it is c²o²stx²+nsxi
Which statement is true about the graph y = - 3x + 2
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]y = -3x + 2[/tex]
Required
The true statement
The question is incomplete, as no option is given.
I will solve generally, as follows;
A linear equation is represented as:
[tex]y =mx+b[/tex]
Where
[tex]m \to[/tex] slope
[tex]b \to[/tex] y intercept
So, by comparison:
[tex]m = -3[/tex]
[tex]b = 2[/tex]
Hence, the graph has a slope of -3 (a negative slope)
And the y intercept of 2
The graph shown matches which quadratic equation?
A
y2.1
yox-1
D)
yox + 1)
Step-by-step explanation:
Am sorry but i cannot click on it am so sorry but wishing you the best i hope simeone can help
Yall i need help with this
Answer:
7
Step-by-step explanation:
Count all of the dots that are above 2. (3,4,5)
Mika is a local farmer who is interested in how often residents in her town go to a farmer's market each month. She surveys 124 families and finds that, on average, those families visit a farmers' market 4.2 times per month with a sample standard deviation of 1.3. If Mika wants to be 99% confident (z=2.58) using this sample, what should her margin of error be and what does it mean?
Answer:
The margin of error is of 0.3012, and it means that we should be 99% confident that the population mean would be within 0.3012 of the sample mean.
Step-by-step explanation:
Margin of error
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
Standard deviation of 1.3
This means that [tex]\sigma = 1.3[/tex]
She surveys 124 families
This means that [tex]n = 124[/tex]
Margin of error and meaning:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]M = 2.58\frac{1.3}{\sqrt{124}}[/tex]
[tex]M = 0.3012[/tex]
The margin of error is of 0.3012, and it means that we should be 99% confident that the population mean would be within 0.3012 of the sample mean.
Simplify: [3(2a)3/2]2
Answer:
the correct answer would be the first one, 72a^3
Answer:
the first one
Step-by-step explanation:
HELP ME PLEASEEEEEEEEEEE
Answer:
The correct answer is 6
Step-by-step explanation:
42 = 7r
R = 42/7 = 6
Answer:
r=6
Step-by-step explanation:
Divide both sides of the equation by the same term
simplify
What steps would I take to solve this question?
9514 1404 393
Answer:
arc FG = 115°
arc EG = 165°
Step-by-step explanation:
The first step is to understand how these arcs are arranged on a circle. The next step is to realize the whole is the sum of the parts. Arcs have the same measure as their central angle. A circle totals 360°.
arc EF + arc FG = arc EFG . . . . parts of an arc add to give the whole arc
80° + arc FG = 195°
arc FG = 115° . . . . . . . . . subtract 80°
__
Similarly, parts of a circle add to give the whole circle.
arc EFG + arc EG = 360°
195° + arc EG = 360°
arc EG = 165° . . . . . . . . . subtract 195°
3,9,15 find the 45th term
Answer:
d
Step-by-step explanation:
i took the test
Answer: 267
Step-by-step explanation:
What is the perimeter of this shape? Use numbers only.
Answer:
30 m
Step-by-step explanation:
You simply add the lengths of all the sides. 3 m is not needed for this.
Answer:
10+5+4+6+5 = 30m
Step-by-step explanation:
What is the total of the surface are of this figure
Answer:
answer: 200
Step-by-step explanation:
Finding surface area for triangles is base × height ÷ 2 So 10 x 10 = 100 100 ÷ 2 = 50 sense all of these triangles are identical we just have to multiply 50 with the number of triangles so
50 × 4 = 200 So 200 is our answer. Hope this helps!
Elizabeth has a loyalty card good for a 20% discount at her local hardware store.
What would her total In dollars and cents be, after the discount and before tax, if the
total cost of all the items she wants to buy is $19.20? Round to the nearest cent.
Answer:15.36
Step-by-step explanation:
Took the test
Pls help me,
Answer choices are :
A. 7
B. 30
C. 28
D. 49
Just wanted to make sure I got the right answer
Answer:
D
Step-by-step explanation:
Helpppp please prettty please this is timed. NO LINKS OR I WILL REPORT YOU. I WILL MARK brainliest. PLEASE I WILL GIVE 30 POINTS please give explanation. The question is asking “Vocabulary How is a rhombus related to a parrallelogram? How does finding the area of a rhombus compare to finding area of parallelogram? Select all the statements that are true.
A: A rhombus is a parallelogram with equal sides
B:The area of a rhombus is found using the formula A=B*H.
C:The area of a rhombus is less than the area of a parallelogram with equal dimensions.
D: A parrelogram is always a rhombus
E: The area is found the same way for both a rhombus and a parallelogram
Answer:
A, B, and E
Step-by-step explanation:
Those are all true the ones I picked.
Which form allows you to identify the y-intercept?
A.) vertex
B.factored
C.Standard
Help it’s important!!
Answer:
The answer is going to be letter B.