The probability that Alice leaves before Carol is 0.5 according to the given information.
What is meant by probability?Probability is a branch of mathematics that deals with numerical descriptions of how likely an event or statement is to occur.
If X1 and X2 are both exponential distributions with parameters 1 and 2, respectively, then
P(X₁< X₂)= λ₁/(λ₁+λ₂ )
And P(X>s+t/x>s)=P(X>t), if X≈exp(μ)
Here, Let [tex]X_{A}[/tex], [tex]X_{C}[/tex] denote the service times for Alice and Carol
And also given that,
E[ [tex]X_{A}[/tex]]=1/μ
E[ [tex]X_{A}[/tex]]=4
E[ [tex]X_{C}[/tex]]=4
E[ [tex]X_{A}[/tex]]=E[ [tex]X_{C}[/tex]]=4
So, [tex]X_{A}[/tex], [tex]X_{C}[/tex] ≈exp(1/4)
Now, when Betty completes his service, Alice is still being served, and the remaining time required to complete his service is exp(1/4).
Because the exponential distribution has no memory.
So, P( [tex]X_{A}[/tex]< [tex]X_{C}[/tex] )= λ₁/ λ₁+ λ₂
=(1/4)/((1/4)+(1/4))
=(1/4)/(1/2)
=0.5
As a result, the probability that Alice leaves before Carol is 0.5.
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The midpoint of a segment with endpoints (10, a) and (b, 6) is (-1, -1). What are the values of a and b?
A. a=12, b=6
B. a=-8, b=-12
C. a= 12, b=-8
D. a= -12, b=-8
Applying the midpoint formula, the values of a and b are:
B. a = -8, b = -12
How to Apply the Midpoint Formula?The midpoint formula is used to find the coordinates of the midpoint of a segment, which is given as:
M(x, y) = [tex](\frac{x_2 + x_1}{2}, \frac{y_2 + y_1}{2})[/tex].
Given the points below:
(10, a) = [tex](x_1, y_1)[/tex]
(b, 6) = [tex](x_2, y_2)[/tex]
M(-1, -1) = (x, y)
Plug in the values:
(-1, -1) = [(b + 10)/2, (6 + a)/2]
Solve the variables separately
-1 = (b + 10)/2
-2 = b + 10
-2 - 10 = b
b = -12
-1 = (6 + a)/2
-2 = 6 +a
-2 - 6 = a
a = -8
The answer is: B. a = -8, b = -12
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\sum _{n=1}^{9}(7n-17)
n=1
∑ (7n−17)
9
Answer:
162
Step-by-step explanation:
You want the sum of the first 9 terms described by ...
a[n] = 7n -17
Add the termsThere are several ways the sum can be found. Most straightforward is simply adding up the terms:
For n=1, 7n-17 = -10
For n=2, 7n -17 = -3
The remaining 7 terms are 4, 11, 18, 25, 32, 39, 46.
The sum is ...
-10 -3 +4 +11 +18 +25 +32 +39 +46 = 162
Arithmetic sequenceThe terms form an arithmetic sequence with first term -10 and last term 46. The sum will be the average term multiplied by the number of terms:
((-10 +46)/2)(9) = 18(9) = 162
Sum formulasThe sum can be decomposed into the sums whose formulas we know:
[tex]\displaystyle \sum_{n=1}^9(7n-17)=7\sum_{n=1}^9{n}-17\sum_{n=1}^9{1} =7\cdot\left.\dfrac{n(n+1)}{2}-17n\right|_{n=9}\\\\= 7\cdot\dfrac{9\cdot10}{2}-17(9)=315-153=\boxed{162}[/tex]
Find m ∠ A B C if B D is an angle bisector.
Answer:
Step-by-step explanation:
the answer would be 73 since the angle is split in half which means that they are both equal to each other
Solve for x. 3x^3/5 +6=30
x = [tex]\sqrt[3]{40}[/tex] = 3.42 ( approx.) is the value of x by given equation .
What are exponents ?We often read numbers in words like hundred, thousand, hundred thousand, and ten million. Which number has more digits than we can read? For example, the mass of the Earth is 5972190000000000000000000 kg. This cannot be read in simple words. Therefore, exponents are used to pronounce these kinds of numbers.
Exponents can be observed in four different types: positive, negative, zero, and rational/fractional. Numerical values can be interpreted using exponents as the total number of times a base must be multiplied by the same base.
Calculation3x^3/5 = 24
3x^3 = 120
x^3 = 40
x = [tex]\sqrt[3]{40}[/tex] = 3.42 ( approx.)
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CAN SOMEONE DO THESE 4 QUESTIONS RQ??
Solve the equations by using either the square root method or the factoring method.
1. x²-7= 18
2. x² + 2x -24 = 0
3. 4x² + 2 =38
4. 2x² + 5x -3=0
The solutions of the given equations are:
1. x = 5, -5
2. x = -6, 4
3. x = 3, -3
4. x = 1/2, -3
What is factorization?
Writing a number or other mathematical object as the result of numerous factors—typically smaller or simpler objects of the same kind—is known as factorization or factoring in mathematics.
Here, we have
1. x²-7= 18, by applying factorization
x² = 18 + 7
x² = 25
x = 5, -5
2. x² + 2x -24 = 0, by applying factorization
x² + 6x - 4x - 24 = 0
x(x+6)-4(x+6) = 0
(x-4)(x+6) = 0
x = 4,-6
3. 4x² + 2 = 38, by applying factorization
4x² = 36
x² = 9
x = 3, -3
4. 2x² + 5x -3 = 0, by applying factorization
2x² + 6x - x - 3 = 0
2x(x +3) -1(x+3) = 0
(2x-1)(x+3) = 0
x = 1/2, -3
Hence, The solutions of the given equations are:
1. x = 5, -5
2. x = -6, 4
3. x = 3, -3
4. x = 1/2, -3
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There are 7 boxes,which contain a total of 63 sweaters in a store's warehouse if the store needs 36 sweater how many boxes should they take out from the warehouse?
They take out one box from the warehouse because one box is sufficient for the requirement of 36 sweaters.
What is the number system?A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9. Based on the basic value of its digits, different types of number systems exist.
There are 7 boxes, which contain a total of 63 sweaters in a store's warehouse.
The store needs 36 sweaters.
Here one box is sufficient for the requirement of 36 sweaters because it contains 63 sweaters.
Therefore, they take out one box from the warehouse.
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9. Janice was creating goodie bags for her party. She has 24 lollipops and 36
pieces of gum. After she bagged the candy, there was the same amount of
contents in each bag. What is the greatest number of bags she can create
with no pieces of candy left over?
Answer:
6
Step-by-step explanation:
24/6 = 4
36/6 = 6
6 bags, 4 lollipops and 6 pieces of gum in each bag.
Answer:
12 bags
Step-by-step explanation:
You would need to find the GCF of both numbers: 12
24*12 = 2
38*12 = 4
12 bags with 2 lollipops and 4 pieces of gum in each
Question 3 of 5
What is the fractional equivalent of the repeating decimal 0.5?
5
O A.
OB.
O C. 1
O D. 1/2
59
9
please help me this is geometry
Answer:
largest angle is angle L
Step-by-step explanation:
the angle across the largest side of the triangle is the largest angle
what is the image of the point (-7,-6) after a rotation of 270 degrees counterclockwise
The image of the point after the rotation is:
(-6, 7)
What is the image of the point after the rotation?
We have the point (-7, -6) and we want to apply a rotation of 270° counterclockwise.
This is equivalent to a rotation of 90° clockwise, so we will go from the third quadrant to the second quadrant, such that:
The x-component will be equal to the original y-component.The y-component will be equal to the original x-component, but positive.Then the image after the rotation is:
(-6, 7)
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A taxi company charges a flat fee of $5.50 plus an additional $1.50 per mile. Write an equation in slope-intercept form that represents the total cost, c, of a ride that is m miles long.
The price of an item has dropped to 42$ today. Yesterday it was 60$ . Find the percentage decrease.
Andy says that all rectangles with an area of 24cm² have the same perimeter
Show that Andy is wrong.
Answer:
no because area is multiplication, but perimeter is adding.
tina's score on her midterm exam was at the 50th percentile. the grades were normally distributed. the exam average was 78 and the standard deviation was 6. what was tina's score on the exam?
If Tina's score is in the 50th percentile and the grades were normally distributed, Tina's score on the exam is 78.
A percentile refers to the comparison score between a particular score and the scores of the rest of a group. It represents the percentage of scores that a specific score surpassed. For example, if the score of 75 points on a test is ranked in the 85th percentile, it implies that the score 75 is higher than 85% of the scores. The 50th percentile, which is also the median score implies that 50% of the score is below or above the average score in a normally distributed data. In the given situation, if the grades are normally distributed with a mean of 78, that implies that 50% of the scores are above 78 and 50% of the scores are below 78. The standard deviation in this case is irrelevant. As Tina’s score is at the 50th percentile, her score on the exam would be 78.
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Can somebody help me on this
Answer:
Ummm I dont even kno but s1
Step-by-step explanation:
A movie theater charges $9.50 for an adult ticket to an evening showing of a popular
movie. To help the local animal shelter, the theater management has agreed to reduce
the price of each adult ticket by $0.75 for every can of pet food a customer contributes
to a collection barrel in the theater lobby. Which of the following shows both an
equation in which y represents the cost of an adult ticket in dollars for a customer who
contributes x cans of pet food, and the graph of the cost if a customer brings in 2, 5, 8,
or 10 cans of pet food?
The linear function that represents the cost of an adult ticket in dollars for a customer who contributes x cans of pet food is of:
y = 9.5 - 0.75x.
The graph is given by the image shown at the end of the answer.
How to define the linear function?The general format of a linear function is given by the rule shown as follows:
y = mx + b.
The terms of the linear function are listed and explained as follows;
m is the slope, representing the rate of change of the output relative to the input.b is the y-intercept, representing the initial value of the funciton.The values of these terms in this function are given as follows:
m = -0.75, as for each food contributed, the cost decays by 0.75.b = 9.5, as with no food contributed, the cost is of $9.5.The costs for the amounts of cans are given as follows:
2 cans: y = 9.5 - 0.75(2) = 8.5 cans: y = 9.5 - 0.75(5) = 5.75.8 cans: y = 9.5 - 0.75(8) = 3.5.10 cans: y = 9.5 - 0.75(10) = 2.More can be learned about linear functions at https://brainly.com/question/24808124
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Fatuma invests a total of $30,000 in two accounts paying 5% and 13% annual interest, respectively. How much was invested in each account if, after one year, the total interest was $2,460.00.
The amount invested in the account that yields a 5% interest is $18,000.
The amount invested in the account that yields a 5% interest is $12,000.
How much was invested in each account?The system of equations that represent the question is:
a + b = 30,000 equation 1
0.05a + 0.13b = 2460 equation 2
Where:
a = amount invested in the account that yields a 5% interest b= amount invested in the account that yields a 13% interestThe elimination method would be used to solve the system of equations.
Multiply equation 1 by 0.05
0.05a + 0.05b = 1500
Subtract equation 3 from equation 2:
0.08b = 960
Divide both sides of the equation by 0.08:
b = 960 / 0.08
b = $12,000
Substitute for b in equation 1:
a + 12,000 = 30,000
a = 30,000 - 12,000
a = 18,000
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(03.01 LC) The LCM of 8 and 10 is _______. (
Answer:
Step-by-step explanation:
1. Definition of Least common multiple: The least common multiple of two numbers is the smallest number that is a multiple of both of the numbers
2. Find the LCM 8 and 10=
Multiplies of 8= 8,16,24,32,40....
Multiplies of 10= 10,20, 30,40 ,50....
3. We found it!
40 is the least common multiple!
Katie ordered candle that cot $3 each from a webite. She wa charged a flat hipping fee of $6 and no ale tax. If he pent a total of $54, which equation can be ued to find c, the number of candle he ordered?
3c = 54
6c = 54
3c 6 = 54
3c – 6 = 54
Equation can be used to find the number of candles (c) Katie ordered is 54 = 3c + 6. correct option is (C).
given that
3c+6=54 --------------------------------- (1)
reduce the greatest common factor on both side of the equation, we get:
2+ c= 18 ----------------------------------(2)
rearranging the equation (2), we get,
c + 2 = 18
⇒ c = 18 - 2
⇒ c= 16
∴ putting the value of c in option 3, we get,
3 X 16 + 6 = 54
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The question was incomplete. Check below the complete question.
Katie ordered candle that cot $3 each from a webite. She wa charged a flat hipping fee of $6 and no ale tax. If he pent a total of $54, which equation can be ued to find c, the number of candle he ordered?
A. 3c = 54
B. 6c = 54
C. 3c + 6 = 54
D. 3c – 6 = 54
a circular pool is surrounded by a brick walkway 3 m wide. find the ra- dius of the pool if the area of the walk- way is 198 m*.
The radius of the pool is 9.01 m.
Given,
In the question:
A circular pool is surrounded by a brick walkway 3 m wide.
The area of the walk- way is 198 m^2.
To find the Radius of the pool.
Now, According to the question:
"Area of the circle bounded by the outside edge of the walkway" minus "area of the pool" = "area of the walkway".
Let R = Radius of the pool
Area of the circle bounded by the outside edge of the walkway is:
[tex]\pi[/tex](R +3)^2
Area of the pool is:
[tex]\pi R^2[/tex]
Now, Our equation is:;
[tex]\pi[/tex](R +3)^2 - [tex]\pi R^2[/tex] = 198
[tex]\pi[/tex]((R+3)^2 - [tex]R^2[/tex]) = 198
Open the inner bracket :
[tex]\pi[/tex]([tex]R^2+6R+9-R^2[/tex]) = 198
[tex]\pi[/tex](6R +9) = 198
6R+9 = 198/[tex]\pi[/tex]
6R = 198/[tex]\pi[/tex] - 9
R = (198/[tex]\pi[/tex] - 9)/6
R = (198/(3.14) - 9)/6
R = (63.057 - 9)/6
R = 54.057/6
R = 9.01 meters
Hence, The radius of the pool is 9.01 m.
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3. Determine an exact value for the following expression
{sec π/4 cos 2π/3}/{tan π/6 csc 3π/4}
The exact value for the following expression {sec π/4 cos 2π/3}/{tan π/6 csc 3π/4} is - [tex]\sqrt{3} /2[/tex]
The expression is given that
{sec π/4 cos 2π/3}/{tan π/6 csc 3π/4}
Here we have to use the trigonometric functions
Find the each values of the term
sec π/4 = 1 / cos π/4
= 1 / (1 / [tex]\sqrt{2}[/tex] )
= [tex]\sqrt{2}[/tex]
Next term is cos 2π/3
cos 2π/3 = -1 / 2
Next term is tan π/6
tan π/6 = [tex]\sqrt{3}[/tex] / 3
Next term is csc 3π/4
csc 3π/4 = [tex]\sqrt{2}[/tex]
Substitute the values in the expression
{sec π/4 cos 2π/3}/{tan π/6 csc 3π/4}
= ( [tex]\sqrt{2}[/tex] × (-1/2) ) / ( [tex]\sqrt{3}[/tex] / 3 × [tex]\sqrt{2}[/tex])
= - [tex]\sqrt{3} /2[/tex]
Hence, the exact value for the following expression {sec π/4 cos 2π/3}/{tan π/6 csc 3π/4} is - [tex]\sqrt{3} /2[/tex]
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A camera store develop 2100 rolls of film in one month. Customize one that double prints from 1500 of these rolls. What is the ratio of rolls with double prints to rolls develop?
A camera store develops 2100 rolls of film in one month. Customize one that double prints from 1500 of these rolls, then the ratio of rolls with double prints to rolls develop would be 5:7.
What is the ratio in mathematics?
A ratio in mathematics shows how many times one number contains another. For example, if a bowl of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six. Similarly, the lemon-to-orange ratio is 6:8, and the orange-to-total fruit ratio is 8:14.
A camera store develops 2100 rolls of film in one month. Customize one that double prints from 1500 of these rolls.
Then the ratio of rolls with double prints to develop = 1500/2100
Simplifying the above ratio we get
= 5/7
Hence, the ratio of rolls with double prints to rolls develop would be 5:7.
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which ordered pair is a solution of the equation?
y+1=3( x-4)
a.only (4,-1)
b.only (5,2)
c.both (4,-1) and (5,2)
d.neither
Answer:
C. Both
Step-by-step explanation:
You would substitute the coordinates into the equation to find the answer.
(4,-1)
-1 + 1 = 3 (4-4)
0 = 0
(5,2)
2 + 1 = 3(5-4)
3 = 3
Emmanuel started a business selling watches. He sells each watch for 30% more
than he pays for them. Last week, he sold 7 watches for a total of $455. How much
money does Emmanuel pay for each watch?
Emmanuel paid $50 for each watch.
What is profit?Profit describes the financial benefit realized when revenue generated from a business activity exceeds the expenses, costs, and taxes involved in sustaining the activity in question.
Given that, Emmanuel started a business selling watches. He sells each watch for 30% more than he pays for them. Last week, he sold 7 watches for a total of $455.
Let the original price of each watch be x
According to question,
x*130% = 455/7
x = 65*100/130
x = 50
Hence, Emmanuel paid $50 for each watch.
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Ariany run a farm tand that ell grape and apple. Each pound of grape ell for $3. 75 and each pound of apple ell for $4. Ariany made $251. 75 from elling a total of 64 pound of grape and apple. Determine the number of pound of grape old and the number of pound of apple old
Hence, there should be 5 pounds of apples and 7 pounds of grapes in 12 pounds.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
pound apple cost = 0.60 dollar1 pound of grapes cost = 1 dollarTotal fruits bought = 12 poundsTotal money paid = 10 dollarsTotal grapes that can be bought with 10$ = 10/1Pounds = 10Total apple that can be bought with 10$ = 10/0.6Pounds = 16.66To buy 12 pounds of fruit in 10 dollars each pound cost = 12/10= 1.2$ per poundRatio of grapes and apple in 12 pound fruits = 1/0.6= 1 : 1.6Apples in 12 pounds = 0.6×5Cost = 3$Grapes in 12 pounds = 1×7Cost = 7$Hence, there should be 5 pounds of apples and 7 pounds of grapes in 12 pounds.
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A manufacturing machine has a 7% defect rate. If 4 items are chosen at random, what is the probability that at least one will have a defect?.
A manufacturing machine has a 7% defect rate. If 4 items are chosen at random,
The probability of randomly choosing atleast one defective item would be 0.3043
Given the Parameters :
Defect rate = P(defect) = 0.07
Probability = required outcome / Total possible outcomes
P(atleast 1 is defective) = 1 - P(none is defective)
P(not defective) = 1 - P(defective) = 1 - 0.07 = 0.93
P(none is defective) = P(non defective)^4
P(none defective) = 0.93 × 0.93 × 0.93 × 0.93 = 0.7480
P(atleast one is defective) = 1 - 0.7480 = 0.252
Therefore, probability of atleast one defective item is 0.252.
Hence the answer is, the probability of randomly choosing atleast one defective item would be 0.3043
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solve each system by substitution 5x+4y=-16 y= 2x+9 what is the anwser
x=-20/13 and y=77/13 are solutions of 5x+4y=-16 and y= 2x+9
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The two equations are
5x+4y=-16 ...(1)
Five x plus 4 y equal to minus sixteen.
y= 2x+9 ...(2)
y equal to two times of x plus nine.
Substitute 2 in 1.
5x+4y=-16
5x+4(2x+9)=-16
5x+8x+36=16
13x+36-16=0
13x+20=0
13x=-20
x=-20/13=-1.53
substitute the value of x in y.
y=2(-20/13)+9
y=(-40+117)/13
y=77/13
Hence the value of x is -20/13 and y value is 77/13.
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The picture shows 2 questions (separated with the long straight line)
X = - 4
Pleade help me
Answer:
4[tex]x^{4}[/tex]
6[tex]x^{5}[/tex]
Step-by-step explanation:
For the first problem. I am not sure what is going on with the -4. Is it being added or multiplied by 2[tex]x^{2}[/tex]? I left it out.
[tex](2x^{2}) ^{^{2} }[/tex] means 2[tex]x^{2}[/tex] (2[tex]x^{2}[/tex]) Which is 4[tex]x^{4}[/tex]
(2[tex]x^{2})\\[/tex]([tex]3x^{3)}[/tex] multiple the 2 and the 3 and add the exonents
6[tex]x^{5}[/tex]
A security lighting system spreads its illumination over an angle of 40° to a distance of 48 m. Convert the angle to radians and use the result to find the sector area that is lit, correct to 3 significant decimal places.
The angle in radians and the sector area are 2/9 π and 804.248 m² respectively
How to calculate the sector area lit by the system?
A sector of a circle is the part of a circle made of the arc along with its two radii
Given: angle = 40° and distance(r) = 48m
To convert the angle to radians, multiply the angle by π/180:
Angle in radian(α) = 40 x π/180 = 2/9 π radian (Note: π = 180°)
The formula for sector area = (α×r²)/2
Thus, sector area = (2/9π × 48²)/2 = 804.248 m²
Therefore, the angle in radians is 2/9 π and the sector area is 804.248 m²
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A parabola has a vertex at (-3,2) and is opening left. Where is the axis of symmetry?.
A parabola has a vertex at (-3,2) and is opening left.
A symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity follows a curve of this shape.
So, a parabola has a vertex at (-3,2).
Now where is the axis of symmetry?
• Parabola opens downward or upward. The concept of the axis of symmetry is that, it is a line that when you fold the graph it will be one.
• in y=a(x-h)2+k where vertex is at (h,k), the axis of symmetry is x=h
Hence the answer is X=-3
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