(a) The probability of each possible number of sets that are acceptable without any adjustment can be found using the binomial distribution formula:
P(x) = (n choose x) * p^x * (1-p)^(n-x)
Where:
P(x) is the probability of x successes in n trials
n is the number of trials (in this case, the number of sets produced in a week)
x is the number of successes (in this case, the number of sets that are acceptable without any adjustment)
p is the probability of success (in this case, the probability that a set is acceptable without any adjustment, which is 0.70)
Plugging in the values, we get:
P(0) = (3 choose 0) * 0.70^0 * (1-0.70)^(3-0) = 0.028
P(1) = (3 choose 1) * 0.70^1 * (1-0.70)^(3-1) = 0.081
P(2) = (3 choose 2) * 0.70^2 * (1-0.70)^(3-2) = 0.162
P(3) = (3 choose 3) * 0.70^3 * (1-0.70)^(3-3) = 0.126
(b) To find the expected number of sets that are tested and found to be acceptable without adjustment, we can use the formula:
E(x) = n * p
Plugging in the values, we get:
E(x) = 3 * 0.70 = 2.1
The expected number of sets that are tested and found to be acceptable without adjustment is 2.1.
(c) The cumulative probability distribution for the number of sets that are tested and found to be acceptable without adjustment is the sum of the probabilities of each possible number of successes. For example, the probability of 0 or 1 successes is the sum of the probabilities of 0 and 1 successes: P(0 or 1) = P(0) + P(1) = 0.028 + 0.081 = 0.109. The probability of 0, 1, or 2 successes is the sum of the probabilities of 0, 1, and 2 successes: P(0 or 1 or 2) = P(0) + P(1) + P(2) = 0.028 + 0.081 + 0.162 = 0.271.
The cumulative probability distribution for the number of sets that are tested and found to be acceptable without adjustment is:
P(0) = 0.028
P(0 or 1) = P(0) + P(1) = 0.028 + 0.081 = 0.109
P(0 or 1 or 2) = P(0) + P(1) + P(2) = 0.028 + 0.081 + 0.162 = 0.271
P(0 or 1 or 2 or 3) = P(0) + P(1) + P(2) + P(3) = 0.028 + 0.081 + 0.162 + 0.126 = 0.397
The corresponding graph would be a step function with a step at each possible value of x (in this case, 0, 1, 2, and 3) and the corresponding probability at each step.
hi can you please help me complete this work.
The two column proof is written as follows
Statement Reason
line UT ≅ line GH given
line UV ≅ line GH given
< U ≅ < G given
Δ TUV ≅ Δ BEC Congruent triangles by SAS
< F ≅ < V CPCTC theorem
What is congruency of triangle?Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules
Some of the rules include
Side - Side - Side = SSS
Side - Angle - Side = SAS
Angle - Side - Angle = ASA
Angle - Angle - Side = AAS
Hypotenuse and one leg = HL
The problem requires the prove by Side - Angle - Side = SAS to ensure that the the triangles are congruent
The SAS have it that the two sides of the triangles being compared should be equal and the included angles are equal
The given sides and the included angle are
line UT ≅ line GH Side
< U ≅ < G included angel
line UV ≅ line GH Side
< F ≅ < V CPCTC theorem
According to the CPCTC theorem, whenever two triangles are congruent, then each of their corresponding parts are also congruent. In other words, if two or more triangles are congruent, then their corresponding sides and angles are also congruent or equivalent in size.
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b. [4 pts] Factor f(x). Show all your work. (Hint: You can use the fact that if f(a)=0, then the f(x) must have (x-a) as a factor.
a. [5 pts] How much would he have to invest initially to have the necessary money in 4 years? Round your answer to the nearest whole dollar
1(a) The value of f(2) in the fuction f(x) = x³+7x²-36 0, 1 (b) The factors of the function f(x) = (x-2)(x+3)(x+6) 2 The initial amount that must be invested is $53263.
What is a function?function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
(a) To calculate the f(2), we substitute 2 into the function below.
f(x) = x³+7x²-36f(2) = (2³)+(7×2²)-36f(2) = 8+28-36f(2) = 36-36f(2) = 0(b) To factor f(x), we need to look for the zeros of f(x). The zeros of f(x) are
2, -3, -6Putting them in polynomial form
Facctorizing f(x) = (x-2)(x+3)(x+6)(2) To calculate the amount he would invest initially to have the neccessary amount in 4 years, we use the formula below.
Formula:
A = P(1+R/n)ⁿˣ........................... Equation 1Where:
A = Amount after four years price of the carP = Initial investmentR = Raten = Number of time the rate is compounded per yearx = Number of yearsMake P the subject of the equation
P = A/(1+R/n)ⁿˣ..................Equation 2From the question,
Given:
A = $60000R = 3% = 0.03n = 2x = 4Substitute these values into equation 2
P = 60000/(1+0.03/2)²ˣ⁴P = 60000/(1.015)⁸P = $53263Hence, 1(a) The value of f(2) = 0, 1 (b) The factors of f(x) = (x-2)(x+3)(x+6) 2 The initial amount that must be invested is $53263.
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Begin a rhythm: clap, whistle, click (your fingers), snap, stomp, clap, whistle, click, snap, stomp, clap, whistle, click, snap, stomp, clap, whistle, click … What will you be doing on the 51st beat? Explain
Answer:
clap
Step-by-step explanation:
since the rhythm repeats every 5, then you will be clapping on the fifty first beat. on the 6th beat in the rhythm, its a clap, so since 50/5 is 10 then the next will be clap
Andy, Bobby, and Cindy each went for a walk yesterday afternoon. Andy walked 2 3/4 at a constant speed of 2 1/2 mi/h. Beth walked 1 3/4 mi at a constant speed of 1 1/4 mi/h. Cathy walked for 1 h and 16 min at a constant speed of 1 1/4 mi/h. List the three people in order of the times they spent walking from least time to greatest time.
In linear equation ,The correct order from least time to greatest time is: Andy, Beth, Cindy.
Describe a linear equation using an example.
An equation with only one variable is referred to as a linear equation in one variable.
It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value. One such linear equation in one variable is 9x + 78 = 18.
Consider the provided information,
Andy walked [tex]2\frac{3}{4}[/tex] mi at a constant speed of [tex]2\frac{1}{2}[/tex] mi/h.
As we know
Time = distance/speed
= [tex]\frac{2\frac{3}{4} }{2\frac{1}{2} }[/tex]
= [tex]\frac{11/4}{5/2}[/tex]
= 11/40
Therefore, Andy takes 1.1 hours.
Beth walked 1 1/2 mi at a constant speed of 1 1/8 mi/h .
time = [tex]\frac{1 1/2}{ 1 1/8}[/tex]
= 3/2/ 9/8
= 4/3
Therefore, Beth takes 1.33 hours.
Cindy walked for 1 h and 24 min at a constant speed of 1[tex]\frac{1}{4}[/tex] mi/h.
1 hour 24 min = 1 + 24/60 = 1.4 hours
Therefore Cindy takes 1.4 hours.
Andy spent least time i.e 1.1 hours and Cindy spent greatest time i.e 1.4 hours.
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WILL GIVE BRAINLIEST*
A plane slices a double-napped cone parallel to the base of the cone. Which conic section is formed?
Answer:
A circle is formed.
Step-by-step explanation:
When a plane, parallel to the base of a cone, slices a cone, a circle is formed
and for proof:
What are the values of x and y that simultaneously satisfy the two linear equations graphed below? HELP PLEASE
Answer:
D
Step-by-step explanation:
x=9 and y=4 is given in the graph, this makes the answer between B and D
Since y=-⅔x+10 and y=x-5, 4=-⅔(9)+10 and 4=9-5
So the answer is D
Can someone help me solve this inequality 5x = 7x +4
Grasshopper is 5cm and can jump 10 times its length. How many jumps will it take to get to 9m?
Answer:
18 jumps
Step-by-step explanation:
5*10 = 50cm
50/100 = 0.5m (metre conversion)
9/0.5 = 18
somebody please help!!
Step-by-step explanation:
since AD is an altitude (height) of ABC, the angle at D must be 90° (that is the definition of an altitude or height).
so,
90 = x² + 6x + 18
72 = x² + 6x
0 = x² + 6x - 72
the general solution to such a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = (-6 ± sqrt(6² - 4×1×-72))/(2×1) =
= (-6 ± sqrt(36 + 288))/2 = (-6 ± sqrt(324))/2 =
= (-6 ± 18)/2 = -3 ± 9
x1 = -3 + 9 = 6
x2 = -3 - 9 = -12
so, the 2 solutions are
x = 6
x = -12
Please help me in this grade 7 percentage question
The number 490 is 72% of the number 680.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that 490 is some percentage of the number 680.
The percentage of 490 to the number 680 will be calculated as,
680 x (x / 100) = 490
x = (490 x 100)/680
x = 72%
Therefore, the number 490 is 72% of the number 680.
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please help!!!! need help asap!!!!!
Answer:
third option
Step-by-step explanation:
sinX = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{YZ}{XY}[/tex] = [tex]\frac{3}{\sqrt{34} }[/tex]
tanY = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{XZ}{YZ}[/tex] = [tex]\frac{5}{3}[/tex]
8 . How can we prove these triangles congruent?
F ASA
G AAS
H SAS
J SSS.
A triangle with } 3congruent angles is called a ______
1. We can prove these triangles are congruent through J. SSS.
2. A triangle with 3 congruent angles is called an equilateral triangle.
What is congruence?If all three corresponding sides are equal and all three corresponding angles are equal in measure, two triangles are said to be congruent. These triangles can be moved, rotated, flipped, and turned to look exactly the same. They coincide if they are repositioned.
SSS rule states that two triangles are congruent if all three sides of one triangle are equivalent to the corresponding three sides of the other triangle.
An equilateral triangle has all three sides and angles equal.
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I solved my question
Good now whats the question?
The table summarizes results from 975 pedestrian deaths that were caused by automobile accidents.
Driver
Intoxicated? Pedestrian Intoxicated?
Yes No
Yes 48 78
No 241 608
If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was not intoxicated or the driver was intoxicated.
Report the answer as a percent rounded to one decimal place accuracy. You need not enter the "%" symbol.
Therefore, the probability of the first case : 94.5% and second case:9.7%
Define probability.the likelihood that an event will take place. The proportion of feasible outcomes to outcomes in an exhaustive set of equally likely outcomes that result in a particular event. a field of mathematics that focuses on the investigation of probability.
Here,
Thus, the probabilities of following cases comes out to be:
1) The odds that either the pedestrian or the driver weren't are
=>(246+603+83)*100/986
=>(932/986)*100 =94.5%
2) The likelihood that both incidents involved inebriated pedestrians is equal to
=>(305/978)*(304/977)*100 = 9.7%
Therefore, the probability of the first case : 94.5% and second case:9.7%
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Find x and y in the figure below
One of the interior angles of the triangle, angle y is equal to 67° and the exterior angle x is equal to 113°.
Sum of interior angles of a triangle.The interior angles of a triangle have a total sum of 180°.
Considering the triangle with interior angles: y, 51°, and 62° we have that;
y + 51° + 62° = 180°
y + 113° = 180°
y + 113° - 113° = 180° - 113° {subtract 113° from both sides}
y = 67°
the exterior angle x and the angle y lie on a straight line, so they sum up to 180°.
x + 67° = 180°
x + 67° - 67° = 180° - 67° {subtract 67° from both sides}
x = 113°
Therefore, the interior angle y = 67° and the exterior angle x = 113°.
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The minimum amount required by a bank to open a new checking account is $75. Write an inequality that represents the amounts in dollars a that could be used to open a new account.
The Inequality expression that shows the above situation is x ≥ 75.
What is inequality:The word "inequality" describes the state of being unequal, In Inequalities like in equations, we compare two values but not with the equal signs here we use signs like Not equal, less than, less than or equal to; greater than or greater than or equal to, etc.
Here we have,
The minimum amount required to open a new checking account is $ 75
Let us assume that we used $ x dollars to open a bank account
By the given data,
The amount is a minimum of $ 75
=> x ≥ 75 [ x is less than or equal to $ 75 ]
Therefore,
The Inequality expression that shows the above situation is x ≥ 75.
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convert 34 in base 5 into base 2
Answer:
34 in base 2 = 10011
Step-by-step explanation:
34 written in base 2 or in binary form is 10011 . 34 written in base 10 or decimal form is 19 .
Given, Convert 34 in base 5 to base 2
Firstly convert base 5 to base 10 .
34(base 5) = [tex]3\times 5 ^1 + 4\times 5^0[/tex]
34(base 5) = 19(base 10)
Convert base 10 to base 2 .
To convert 19 to binary, divide it by 2 repeatedly and note the remainders:
19 ÷ 2 = 9, remainder 1
9 ÷ 2 = 4, remainder 1
4 ÷ 2 = 2, remainder 0
2 ÷ 2 = 1, remainder 0
Reading the remainders from bottom to top including the last 1.
10011.
So, 19 in binary is 10011.
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Melody made a brownie for a potluck. She cut the pan of brownies into equal size pieces. At the end of the potluck, there were 6 brownies left over. Explain how you can find the number of pieces in the whole pan of brownies if Melody told you that 2⁄5 of the
pan was left. Use a drawing to show your work.
We are told that 6 is two-fifths of the brownies. So we can figure it out as such:
[tex]\frac{6}{x} = \frac{2}{5}[/tex]
Cross multiply
6 * 5 = x * 2
30 = 2x
Divide both sides of the equal sign by 2 to get x by itself
[tex]\frac{30}{2} =\frac{2x}{2}[/tex]
15 = x
15/5 = 3. Every third piece is 1/5 of the pan.
The graph above shows the distance a tow truck is away from the company's base.
What is the rate of change of change from hour 4 to hour 7 ?
Answer:
50
Step-by-step
What is the approximate volume of this cylinder? 3,140 cm³ 7,850 cm³ 10,000 cm³ 31,400 cm -20 cm 25 cm
Answer: 28055
Step-by-step explanation:
You are dealt one card from a 52-card deck. Find the probability that you are not dealt a card with number from 3 to 8.
Answer: There is a 54% chance that you will not choose one of those cards.
Step-by-step explanation: There are 4 of ever card in a deck.
3, 4, 5, 6, 7, and 8 are 6 different types of cards
6 x 4 = 24
24 divided by 52 ( the total cards ) = .46
So there is a 54% chance that you will not choose one of those cards.
A street light is mounted at the top of a 6-meter-tall pole. A man 2 m tall walks away from the pole with a speed of 1.4 m/s along a straight path. How fast (in m/s) is the tip of his shadow moving when he is 15 m from the pole?
2.1m/s is the tip of his shadow moving when he is 15 m from the pole
What are Similar Triangles?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
x is the distance from the man to the pole, and y is the distance from the tip of the man's shadow to the pole. i assume the man and pole are standing straight up, which means the 2 triangles are similar.
(y-x)/y=2/6
(y-x)/y=1/3
Apply cross multiplication
3(y-x)=y
3y-3x=y
2y=3x
y=3/2x
differentiate both sides with respect to t or time.
dy/dt=3/2dx/dt
By given dx/dt=1.4m/s
dy/dt=3/2×1.4
dy/dt=2.1m/s
Hence, 2.1m/s is the tip of his shadow moving when he is 15 m from the pole
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do parenthaseses change the result in an expression involving only addtion?
Answer:Yes
Step-by-step explanation:It changes the answer,
Answer:
Step-by-step explanation:
nope
Example:
5+(6+3) (+) (+) = +
5+9= 14
A truck cost 60,000 it depreciate in value 4000 per year write a linear model in the form VT equals MT plus b
When the truck cost 60,000 it depreciate in value 4000 per year, the model is 60000 - 4000x
How to calculate the equation?Equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario
In this case, the truck cost 60,000 it depreciate in value 4000 per year.
Let the number of years be x.
The linear model in the representation will be:
60000 - 4000(x)
= 60000 - 4000x
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"constant of proportionality" between to cost and number of classes is 16. what is the unit rate for dollers per class?
The required unit rate for the dollars per class is 16 dollars per class,
Given that,
The "constant of proportionality" between to cost and the number of classes is 16. The unit rate for dollars per class is to be determined.
proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
Here,
Let, y be the dollars is directly proportional to the x classes,
According to the question,
y = kx
k = 16
y = 16x
Now,
y/x = 16 dollars per class
Thus, the required unit rate for the dollars per class is 16 dollars per class,
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Critical Thinking Consider a family with three children . Assume the prob- ability that one child is a boy is 0.5 and the probability that one child is a girl is also 0.5 and that the events "boy" and "girl" are independent . ( a ) List the equally likely events for the gender of the three children , from oldest to youngest (b) What is the probability that all three children are male ? Notice that the complement of the event " all three children are male " is "at least one of the children is female ." Use this information to compute the probability that at least one child is female .
The equally likely events are
Boy, Boy, BoyBoy, Boy, GirlBoy, Girl, BoyBoy, Girl, GirlGirl, Boy, BoyGirl, Boy, GirlGirl, Girl, BoyGirl, Girl, GirlThe probability that all three children are male
0.875.
the probability that at least one child is female.
0.875.
What are the probabilities?(a) The equally likely events for the gender of the three children, from oldest to youngest, are:
Boy, Boy, BoyBoy, Boy, GirlBoy, Girl, BoyBoy, Girl, GirlGirl, Boy, BoyGirl, Boy, GirlGirl, Girl, BoyGirl, Girl, Girl(b) The probability that all three children are male is (0.5)^3 = 0.125.
The probability that at least one child is female is the complement of the event "all three children are male," which means it is 1 - 0.125 = 0.875.
In conclusion, The probability that at least one child is female is 1 - (0.5)^3 = 0.875.
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You want to have a $70,000 college fund in 13 years. How much will you have to deposit now under the scenario below. Assume that you make no deposits into the account after the initial deposit.
An APR of 7.4% compounded daily
You will able to deposit X=7000.182500⁴⁷⁴⁵/182537⁴⁷⁴⁵now under the scenario Below.
What is initial deposit?A minimum deposit or initial deposit is the lowest minimum amount of the money required to open an object account with all the financial institution, such as the bank or the brokerage firm.
Based on the given scenario the formulate is-
X×(1+7.4%÷ 365)¹³×365 = 70000
Now we have to solve the equation -
X×(1+0.074/365)¹³×365=70000
Convert the number
X× 1+ (74/365000)¹³×365=70000
Now reduce
X×(1+37/182500)¹³×365=70000
Now we have to calculate=
X× (1+ 37/182500)⁴⁷⁴⁵=70000
We have to transfer the edition
X× (1+ 37/182500)⁴⁷⁴⁵=70000
Devide both side
X= 70000/ ( 182537/182500)⁴⁷⁴⁵
By Calculation we can get
X= 70000×182500^4745/182537⁴⁷⁴⁵
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Given that ABCD is a rectangle, where EC=7 x-3 and AE=4 x+8 . Find DE.
The length of side DE of the rectangle ABCD is 11/5 units .
What is rectangle?
In euclidean plane geometry, a rectangle may be a quadrilateral with four right angles. It also can be outlined as: an angular quadrilateral, since angular means all of its angles square measure equal; or a tetragon containing a right angle.
Main body:
given:
AE = 4x+8 -----------(1)
CE = 7x - 3 -----------(2)
as we know diagonal of rectangle bisect each other , which means AE = CE
using the property , we get
4x+ 8 = 7x -3
taking like terms to one side,
7x - 4x = 8+3
3x = 11
x = 11/3
put the value of x in any equation,
AE = 4(11/3) +8
AE = 44/3 +24/3
AE = 68/3
as AE = DE
Hence the value of DE is 68/3 units.
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Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t increases.
The curve for the vector equation r(t) = <t, -t, 2t>, is |r(t)| = (√6)t.
Find the curve in the attachment
What is a vector?A vector is a physical quantity that has both magnitude and direction
What is a vector equation?A vector equation is a linear combination of vector quantities
What is a curve?A curve is a path which an object follows.
How to sketch the curve of the given vector?Since we are given the vector equation r(t) = <t, -t, 2t>, to sketch the curve of the vector equation, we need to know the magnitude of the vector.
What is the magnitude of a vector?The magnitude of a vector r = <a, b, c> is |r| = √(a² + b² + c²)
So, to sketch the vector equation, since r(t) = <t, -t, 2t>, comapring bothnequations,
a = t, b = -t and c = 2tSo, the magnitude of r(t) = √(a² + b² + c²)
= √(t² + (-t)² + (2t)²)
= √(t² + t² + 4t²)
= √(6t²)
= (√6)t
Since |r(t)| = (√6)t, we sketch the curve for this equation
Find the curve in the attachment
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The bill at dinner was $58.24 before tax and tip.
There is a 6% sales tax. After the tax, an 18% tip is
added.
What is the total including tax and tip? show answer
Total amount payable including sales tax and tip = $68.12
What is sales tax?A sales tax is a tax levied by a government on the sale of certain goods and services. Generally, laws allow the seller to collect tax funds from the consumer at the point of sale. A use tax is a tax on goods or services paid directly to a governing body by a consumer.
Given:
Bill at dinner was before tax and tip = $58.24
Sales tax = 6%
Tip = 18%
As per the question:
first, we will calculate the amount payable after adding tax.
The amount payable after adding sales tax = bill + 6% sales tax of the bill
The amount payable after adding sales tax = 58.24 + [tex]\frac{6}{100} 58.24[/tex]
Amount payable after adding sales tax = A = $57.73
Now we will calculate the total amount payable after adding the tip.
Total amount payable = A + 18% of A
Total amount payable = $57.73 + 18% of $57.73
Total amount payable = 57.73 + 10.40
Total amount payable including sales tax and tip = $68.12
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Total amount payable including sales tax and tip = $68.12
What is sales tax?A sales tax is a tax levied by a government on the sale of certain goods and services. Generally, laws allow the seller to collect tax funds from the consumer at the point of sale. A use tax is a tax on goods or services paid directly to a governing body by a consumer.
Given:
Bill at dinner was before tax and tip = $58.24
Sales tax = 6%
Tip = 18%
As per the question:
first, we will calculate the amount payable after adding tax.
The amount payable after adding sales tax = bill + 6% sales tax of the bill
The amount payable after adding sales tax = 58.24 +
Amount payable after adding sales tax = A = $57.73
Now we will calculate the total amount payable after adding the tip.
Total amount payable = A + 18% of A
Total amount payable = $57.73 + 18% of $57.73
Total amount payable = 57.73 + 10.40
Total amount payable including sales tax and tip = $68.12
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