Answer:
1.
a. 2
b. 0.1353 probability that exactly 0 customers will arrive during a five-minute period, 0.2707 that exactly 1 customer will arrive, 0.2707 that exactly 2 customers will arrive and 0.1805 that exactly 3 customers will arrive.
c. 0.1428 = 14.28% probability that delays will occur.
2.
a. 0.4512 = 45.12% probability that the service time is one minute or less.
b. 0.6988 = 69.88% probability that the service time is two minutes or less.
c. 0.3012 = 30.12% probability that the service time is more than two minutes.
Step-by-step explanation:
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
Question 1:
a. What is the mean or expected number of customers that will arrive in a five-minute period?
0.4 customers per minute, so for 5 minutes:
[tex]\mu = 0.4*5 = 2[/tex]
So 2 is the answer.
Question b:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-2}*2^{0}}{(0)!} = 0.1353[/tex]
[tex]P(X = 1) = \frac{e^{-2}*2^{1}}{(1)!} = 0.2707[/tex]
[tex]P(X = 2) = \frac{e^{-2}*2^{2}}{(2)!} = 0.2707[/tex]
[tex]P(X = 3) = \frac{e^{-2}*2^{3}}{(3)!} = 0.1805[/tex]
0.1353 probability that exactly 0 customers will arrive during a five-minute period, 0.2707 that exactly 1 customer will arrive, 0.2707 that exactly 2 customers will arrive and 0.1805 that exactly 3 customers will arrive.
Question c:
This is:
[tex]P(X > 3) = 1 - P(X \leq 3)[/tex]
In which:
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
The values we have in item b, so:
[tex]P(X \leq 3) = 0.1353 + 0.2707 + 0.2707 + 0.1805 = 0.8572[/tex]
[tex]P(X > 3) = 1 - P(X \leq 3) = 1 - 0.8572 = 0.1428[/tex]
0.1428 = 14.28% probability that delays will occur.
Question 2:
[tex]\mu = 0.6[/tex]
a. What is the probability that the service time is one minute or less?
[tex]P(X \leq 1) = 1 - e^{-0.6} = 0.4512[/tex]
0.4512 = 45.12% probability that the service time is one minute or less.
b. What is the probability that the service time is two minutes or less?
[tex]P(X \leq 2) = 1 - e^{-0.6(2)} = 1 - e^{-1.2} = 0.6988[/tex]
0.6988 = 69.88% probability that the service time is two minutes or less.
c. What is the probability that the service time is more than two minutes?
[tex]P(X > 2) = e^{-1.2} = 0.3012[/tex]
0.3012 = 30.12% probability that the service time is more than two minutes.
Which expression is equivalent to -9x-1y-9/-15x5y-3?
Answer: -9x-1y-9/
Step-by-step explanation:
Answer: b
Step-by-step explanation:
I really dont like edge
If A = {x, y, z} then the number of non-empty subsets of A is ________.
a) 8 b) 5 c) 6 d) 7
Answer:
(d) 7
Step-by-step explanation:
The total number of subsets that can be derived from a set with n elements is given by;
2ⁿ
Out of these subsets, there is one empty set. Therefore, the total number of non-empty subsets is given by;
2ⁿ - 1
Given:
A = {x, y, z}
Set A has 3 elements. This means that n = 3
Therefore, the total number of subsets that can be derived from set A is
2ⁿ = 2³ = 8
One of these 8 subsets is an empty set, therefore, the total number of non-empty subsets of A is;
2ⁿ - 1 = 2³ - 1
8 - 1 = 7
This can be checked by writing all the possible subsets of A as follows;
∅
{x}
{y}
{z}
{x, y}
{y, z}
{x, z}
{x, y, z}
Removing the empty set ∅, the non-empty subsets of A are;
{x}
{y}
{z}
{x, y}
{y, z}
{x, z}
{x, y, z}
A box contains 5 white balls, 3 black balls, and 2 red balls.A-What is the probability of drawing a white ball?B- How many white balls must be added to the box so that the probability of drawing a white ball is 3/4?C-How many black balls must be added to the original assortment so that the probability of drawing a white ball is 1/4?
Answer:
[tex](a)\ P(White) = \frac{1}{2}[/tex]
(b) 10 additional white balls
(c) 10 additional black balls
Step-by-step explanation:
Given
[tex]White = 5[/tex]
[tex]Black =3[/tex]
[tex]Red = 2[/tex]
Solving (a): P(White)
This is calculated as:
[tex]P(White) = \frac{White}{Total}[/tex]
[tex]P(White) = \frac{5}{5+3+2}[/tex]
[tex]P(White) = \frac{5}{10}[/tex]
[tex]P(White) = \frac{1}{2}[/tex]
Solving (b): Additional white balls, if [tex]P(White) = \frac{3}{4}[/tex]
Let the additional white balls be x
So:
[tex]P(White) = \frac{White+x}{Total+x}[/tex]
This gives:
[tex]\frac{3}{4} = \frac{5+x}{10+x}[/tex]
Cross multiply
[tex]30+3x = 20 + 4x[/tex]
Collect like terms
[tex]4x - 3x = 30 - 20[/tex]
[tex]x = 10[/tex]
Hence, 10 additional white balls must be added
Solving (c): Additional black balls, if [tex]P(White) = \frac{1}{4}[/tex]
Let the additional black balls be x
So:
[tex]P(White) = \frac{White}{Total+x}[/tex]
So, we have:
[tex]\frac{1}{4} = \frac{5}{10+x}[/tex]
Cross multiply
[tex]10+x = 5 * 4[/tex]
[tex]10+x = 20[/tex]
Collect like terms
[tex]x = 20 -10[/tex]
[tex]x = 10[/tex]
Hence, 10 additional black balls must be added
Couch johnson needs to buy shirts for his soccer players. He finds a package of 2:shirts for 16.00. How much will it cost to buy 18 shirts?
Answer:
144
Step-by-step explanation:
We can write this as 2 shirts = 16.00 . Then, we can write this as a ratio, where
2 shirts / 16.00 = 18 shirts/ cost of 18 shirts as the cost for a pair of shirts remains the same, so the ratio will as well.
Therefore, writing the cost of 18 shirts as c, we have
2 shirts/16.00 = 18 shirts/c
multiply both sides by c to remove a denominator
2 shirts * c/16.00 = 18 shirts
multiply both sides by 16 to remove the other denominator
2 shirts * c = 18 shirts * 16
divide both sides by 2 shirts to isolate the c, as we want to figure that out
c = 18 shirts * 16/2 shirts
c=144
can you help please I have no clue
Answer:
6, 15, 24, 33
Step-by-step explanation:
Basically, the number on top of the sigma represents the number of terms total in that sequence, and on the right you have the equation in which you can plug in whichever value that falls into what the top number says to find the output. In other words, just plug in 1 for k to find a1, 2 for k to find a2, etc.
Hope that helps!
Help please!!
The triangles are similar by:
the SAS similarity theorem.
the ASA similarity theorem.
the AA similarity postulate.
None of the choices are correct.
the SSS similarity theorem.
Find the slope of the line that passes through the two points. -3,6 & -7,3
HELP!!!!
A wheelchair ramp with a length of 61 inches has a horizontal distance of 60 inches. What is the ramp’s vertical distance
Answer:
Step-by-step explanation:
The solution triangle attached below :
Since we have a right angled triangle, we can make use of Pythagoras rule to obtain the vertical distance, x
Recall :
Hypotenus² = opposite² + adjacent²
Hence,
x² = 61² - 60²
x² = 3721 - 3600
x² = 121
x = √121
x = 11
Vertical distance equals 11 inches
A population has mean j = 18 and standard deviation o = 20. Find I, and oz for samples of size n = 100, Round your answers to
one decimal place if needed,
Answer:
))
Step-by-step explanation:
just place your decimal once to the left I think
consider this equation sin(theta) = -4 square root of 29/29 if theta is an angle in quadrant IV what is the value of cos (theta)
Answer:
[tex]\cos(\theta)= \frac{\sqrt{377}}{29}[/tex]
Step-by-step explanation:
Given
[tex]\sin(\theta) = -\frac{4}{\sqrt{29}}[/tex] -- the correct expression
Required
[tex]\cos(\theta)[/tex]
We know that:
[tex]\sin^2(\theta) + \cos^2(\theta)= 1[/tex]
Make [tex]\cos^2(\theta)[/tex] the subject
[tex]\cos^2(\theta)= 1 - \sin^2(\theta)[/tex]
Substitute: [tex]\sin(\theta) = -\frac{4}{\sqrt{29}}[/tex]
[tex]\cos^2(\theta)= 1 - (-\frac{4}{\sqrt{29}})^2[/tex]
Evaluate all squares
[tex]\cos^2(\theta)= 1 - (\frac{16}{29})[/tex]
Take LCM
[tex]\cos^2(\theta)= \frac{29 - 16}{29}[/tex]
[tex]\cos^2(\theta)= \frac{13}{29}[/tex]
Take square roots of both sides
[tex]\cos(\theta)= \±\sqrt{\frac{13}{29}}[/tex]
cosine is positive in the 4th quadrant;
So:
[tex]\cos(\theta)= \sqrt{\frac{13}{29}}[/tex]
Split
[tex]\cos(\theta)= \frac{\sqrt{13}}{\sqrt{29}}[/tex]
Rationalize
[tex]\cos(\theta)= \frac{\sqrt{13}}{\sqrt{29}} * \frac{\sqrt{29}}{\sqrt{29}}[/tex]
[tex]\cos(\theta)= \frac{\sqrt{13*29}}{29}[/tex]
[tex]\cos(\theta)= \frac{\sqrt{377}}{29}[/tex]
At one point in history, the NBA finals required that one of the two teams win at least three of five games in order to win the Championship. If one team wins the first two games, what is the probability that the same team wins the Championship, assuming that the two teams are well matched and each team is equally likely to win each game
Answer:
50% i believe
Step-by-step explanation:
because in every scenario theres 2 teams and if they are well matched it be half and half on every game assuming they're the same level of comp
List the angles in order from the smallest to the largest.
Answer:
D. <S, <R, <T
Step-by-step explanation:
Recall: On a triangle, the bigger an angle measure the longer the side opposite it and vice versa.
In ∆RST,
The longest side, SR = 22, is opposite to <T
Therefore, <T is the biggest angle.
Medium side, ST = 21, is opposite to <R, therefore,
<R is the medium angle measure
The smallest angle measure <S is opposite to the shortest side, RT.
Angels I'm order form the smallest to largest will be:
<S, <R, <T
I need help with this question
9514 1404 393
Answer:
x = 22, y = 123
Step-by-step explanation:
The sum of angles in a triangle is 180°.
(2x +13)° +57° +3x° = 180°
5x +70 = 180 . . . . . . . . . . . . . collect terms, divde by °
5x = 110 . . . . . . . . . . . subtract 70
x = 22 . . . . . . . . divide by 5
__
Angles in a linear pair are supplementary.
y° + 57° = 180°
y = 123 . . . . . . . . divide by °, subtract 57
Can anyone help me please? I've been trying for so long, but I can't figure out the answer to this problem. Picture attached. Thank you so much.
Answer:
C
Step-by-step explanation:
Start by simplifying what you can in each radicalfor example, the
∛(xy⁵)= y∛(xy²)
and
∛(x⁷y¹⁷)=x²y⁵∛(xy²)
So know our equation looks like
y∛(xy²)*x²y⁵∛(xy²)
Now because what's inside the radical is the same we can combine them
y⁶x²∛(xy²)²
distribute the square
so
∛(xy²)²= ∛(x²y⁴)= y∛(x²y)
and finally,
y⁶x²*y∛(x²y)= y⁷x²∛(x²y)
this is equal to option C
5. What is the value of x if the quadrilateral is a kite? B X+2 C С 13 A Xth12 D
Answer: just had this problem! X = 11
AXYZ is reflected across the line x = 3. What is the reflection image of X
Answer:
The answer should be (7, 5)
What is the solution to the following inequality X/-2 > 5
Answer:
x < -10
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
x/-2 > 5
Step 2: Solve for x
[Multiplication Property of Equality] Multiply -2 on both sides: x < -10[tex]\large {\mathsf {\red{\underbrace {\overbrace{\blue{ {\pink}{Answєr}}}}}}} \: [/tex]
x > - 10
[tex] \large \mathtt \green{Step-by-step \: explanation : }[/tex]
[tex] \small \sf \frac{x}{ - 2} > 5 \\ [/tex]
Solve for x
[tex] \small \sf \frac{x}{ - 2} > 5 \\ [/tex]
common denominator is 2
[tex]\small \sf ➪ \frac{2x}{ - 2} >2 \times 5 \\ [/tex]
[tex]\small \sf ➪ \frac{ \cancel{2}x}{ - \cancel{ 2}} >2 \times 5 \\ [/tex]
➪ - x > 2 × 5
➪ - x > 10
multiply by - 1
➪ - x × - 1 > 10 × - 1
x > - 10
had
n=2
n²-n-2
n² – 5n+6
Answer:
0，0
Step-by-step explanation:
n=2，
[tex] {2}^{2} - 2 - 2 = 0 [/tex]
[tex] {2}^{2} - 5 \times 2 + 6 = 0[/tex]
What is the gradient of the graph shown? Give your answer in simplest form
Answer:
gradient = 2
line: y = 2x - 4
Step-by-step explanation:
Find the slope from the slope intercept formula
y = mx + b
b is the y intercept
b = -4 and the point is (0,-4)
So far the equation looks like this.
y = mx - 4
Use the other intercept (x intercept) to find m
x = 2
y = 0
0 = m*2 - 4 Add 4 to both sides
4 = 2m Divide by 2
4/2 = m
m = 2
So the gradient or slope is 2
help help HELP!! will give brainliest
If f(x) = x², g(x) = 5x, and h(x) = x + 4, find each value.
Find h[f(4)].
Answer:
[tex]h(f(4))=20[/tex]
Step-by-step explanation:
We are given the functions:
[tex]f(x)=x^2,\, g(x)=5x\text{, and } h(x)=x+4[/tex]
And we want to find
[tex]h(f(4))[/tex]
Find f(4) first:
[tex]f(4)=(4)^2=16[/tex]
Thus:
[tex]h(f(4))=h(16)[/tex]
Now, evaluate h(16):
[tex]h(16)=(16)+4=20[/tex]
Hence:
[tex]h(f(4))=20[/tex]
What is the smallest 6-digit- palindrome (a number that reads the same forward and backward) divisible by 99
Answer:
108801
Step-by-step explanation:
Palindrome as defined in the given question as a number which reads the same forward and backward. Examples are: 1001, 20202, 1331 etc.
Thus, to determine the smallest 6-digit palindrome divisible by 99 without a remainder, the digits should be in the form of abccba.
Therefore, the smallest 6-digit palindrome that can be divided by 99 is 108801.
So that,
108801 ÷ 99 = 1099
Item 16
What is the area of the triangle in the coordinate plane?
36 units²
38 units²
66 units²
72 units²
The circumference of a circle is 14 inches. Find the circle's radius and diameter.
Please help :)
Mathematics I need help
Answer:
B
Step-by-step explanation:
Exclude C:
[tex] |x| [/tex]
is not curved
To shift right, minus inside the
[tex] |?| [/tex]
Thus
[tex] |x - 4| [/tex]
To shift up, add outside the
[tex] |?| [/tex]
Thus:
[tex] |x +4| + 2[/tex]
B
Brainliest please~
what is the value of x?
what is the value of y?
type in an integer or decimal
9514 1404 393
Answer:
x = 5.6y = 65Step-by-step explanation:
There are a couple of relations that are applicable to these questions.
the product of segment lengths of crossed chords is the same for both chordsthe angle formed at crossed chords is the average of the intercepted arc measures__
The segment lengths relation tells us ...
10x = 8×7 . . . . . . products of segment lengths are equal
x = 56/10 = 5.6 . . . . divide by 10
__
The value of y° is the average of the intercepted arcs:
y° = (85° +45°)/2 = 65°
_____
Additional comment
This diagram does not have enough information to allow computation of z. We would need to know the intercepted arc, or the length of the secant that meets tangent z.
What complex number is represented by the expression 7i^5+9i^8
Answer:
[tex]9 + 7i[/tex]
Step-by-step explanation:
[tex]7i^5+9i^8[/tex]
[tex]i^5 = i\\ i^8 = 1[/tex]
he parent function f(x) = x3 is represented by graph A. Graph A is transformed to get graph B and graph C. Write the functions represented by graph B and graph C.
Graph B represents the function g(x) =
.
Graph C represents the function h(x) =
.
what is the y-intercept of the line shown below?
A:3/4
B:2
C:3
D:4
The y-intercept is the y value where the blue line crosses the Y axis which is the vertical black line.
The line crosses at the number 4, so the y-intercept is 4
Answer: D. 4
You paid $6.99 for a shirt that was 70% of what was the original price of the shirt?
Answer:
$23.3
Step-by-step explanation:
you can use ratios to solve this:
$6.99/x=0.30/0.100 then cross multiply to get 0.3x=6.99
So, 6.99 divided by 0.3 = 23.3
so the original price is $23.3
Find the value of x.
Answer:
x = 3
Step-by-step explanation:
A midsegment in a trapezoid is formed when one connects the midpoints of the two legs (non-parallel sides) in a trapezoid. The midsegment theorem states that the length of the midsegment is equal to the average of the two bases (that is the parallel sides).
One can apply the midsegment theorem here by stating the following;
[tex]\frac{(YZ)+(TM)}{2}=PW[/tex]
Substitute,
[tex]\frac{23+11x+2}{2}=29[/tex]
Simplify,
[tex]\frac{25+11x}{2}=29[/tex]
Inverse operations,
[tex]\frac{25+11x}{2}=29[/tex]
[tex]25+11x=58\\\\11x = 33\\\\x = 3[/tex]