Answers
Step-by-step explanation:
<QTS<BCD<QPO and <ORS<EFG<ACF and <CFE<BED<TUY<ABC+<BCD=180° (being co-interior angles)1. ∠STQ
2. ∠BCD
3. ∠ORS and ∠QPO both are alternate angles of ∠POR
4. ∠EFG
5. ∠DCF and ∠CFH
6. ∠DEB
7. ∠YUT
8. 180° (because they are co-interior angles)
Related Questions
Let A={46,51,55,70,80,87,98,108,122} and R be an equivalence relation defined on A where aRb if and only if a≡b mod 4. Show the partition of A defined by the equivalence classes of R.
Answers
The partition of A defined by the equivalence classes of R is {[51, 55, 87, 91, 122], [46, 70, 98, 108], [80, 84, 116], [87, 91]}.
The equivalence relation R defined on the set A={46, 51, 55, 70, 80, 87, 98, 108, 122} is given by aRb if and only if a ≡ b (mod 4), where ≡ denotes congruence modulo 4.
To determine the partition of A defined by the equivalence classes of R, we need to identify sets that contain elements related to each other under the equivalence relation.
After examining the elements of A and their congruence modulo 4, we can form the following partition:
Equivalence class 1: [51, 55, 87, 91, 122]
Equivalence class 2: [46, 70, 98, 108]
Equivalence class 3: [80, 84, 116]
Equivalence class 4: [87, 91]
These equivalence classes represent subsets of A where elements within each subset are congruent to each other modulo 4. Each element in A belongs to one and only one equivalence class.
Thus, the partition of A defined by the equivalence classes of R is {[51, 55, 87, 91, 122], [46, 70, 98, 108], [80, 84, 116], [87, 91]}.
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What is an equation example?
Answers
The definition and explanation of an equation are given below with an example.
in mathematics, an equation is defined as an expression that expresses equality between 2 quantities or expressions. We use equations quite a lot in our daily lives whenever we have to equate two quantities and find out how they are equal. These are used in all branches of science because of the huge purpose they serve.
in simple words it tells what we have on the Left-Hand Side of the "=" sign is the same as what we have on the right-hand side of the statement. Some examples of equations are-
E²=m²c⁴+p²c²
x²+3x-1=0
70 oranges= 7 oranges × 10 oranges
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If the elasticity of labor is 0.60, a 15 percent increase in the wage rate will induce a a. 4.0 percent decrease in the quantity of labor supplied. b. 9.0 percent increase in the quantity of labor supplied. c. 9.0 percent decrease in the quantity of labor supplied. 4. 4.0 percent increase in the quantity of labor supplied.
Answers
The elasticity of labor refers to the responsiveness of the quantity of labor supplied to changes in the wage rate. If the elasticity of labor is 0.60, a 15 percent increase in the wage rate will induce a decrease in the quantity of labor supplied, but the extent of this decrease will depend on the magnitude of the elasticity. The correct option is c.
In this case, a 0.60 elasticity implies that a 15 percent increase in the wage rate will result in a 9.0 percent decrease in the quantity of labor supplied. This can be calculated using the formula for elasticity, which is the percentage change in quantity divided by the percentage change in price (or wage rate, in this case):
Elasticity of labor = percentage change in quantity / percentage change in wage rate
0.60 = percentage change in quantity / 15 percent
Percentage change in quantity = 0.60 x 15 percent = 9.0 percent
Therefore, the correct answer is (c) a 9.0 percent decrease in the quantity of labor supplied. This means that as the wage rate increases, workers may be less willing to supply labor, resulting in a decrease in the number of workers willing to work at that wage rate.
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La raíz cuadrada de un número más la raíz cuadrada de ese número incrementado 600 unidades es igual a 30. ¿Cuál es el número?
Answers
The required Number is 81,225.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let the number be x
So, the equation can be written as
√x + √(x + 600)= 30
2√x = -570
√x = -285
Taking Square on both side we get
x = 81225
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The Question attached here is in other language whose translation is
The square root of a number plus the square root of that number increased by 600 units equals 30. What is the number?
Which number is equal to four and one-sixth?
four and sixteen hundredths with the six repeating
six twenty-fifths
4.2
416%
Answers
Answer:
4.2
Step-by-step explanation:
Four and one-sixth is equal to 4.2. One-sixth is the same as 1/6, which is equal to 0.16666666666666666. When you add this fraction to 4, you get 4.166666666666667, which can be rounded to 4.2. Four and sixteen hundredths is equal to 4.16, which is close to 4.2 but not exactly the same. Six twenty-fifths is equal to 0.24, which is also not equal to 4.2. 416% is equal to 4.16, which is also not equal to 4.2.
(1 point) a card is drawn from a standard deck of 52 cards, the value noted, and the card replaced. this is repeated 8 times. what is the probability that: a) exactly 5 of the cards are diamonds? b) at least two of the cards are diamonds? c) at most 5 of the cards are diamonds?
Answers
a) The probability of drawing exactly 5 diamonds from a standard deck of 52 cards is 0.1425
The probability of drawing exactly 5 diamonds from a standard deck of 52 cards is
P(exactly 5 diamonds) =\((13/52) * (12/51) * (11/50) * (10/49) * (9/48) * (38/47) * (37/46) * (36/45)\)
= 0.1425
b) The probability of drawing at least two diamonds from a standard deck of 52 cards is:
P(at least 2 diamonds) = 1 - P(0 diamonds) - P(1 diamond)
=\(1 - (39/52) * (38/51) - (13/52) * (39/51)\)
= 0.9133
c) The probability of drawing at most 5 diamonds from a standard deck of 52 cards is:
P(at most 5 diamonds) = P(0 diamonds) + P(1 diamond) + P(2 diamonds) + P(3 diamonds) + P(4 diamonds) + P(5 diamonds)
=\((39/52) * (38/51) + (13/52) * (39/51) + (13/52) * (12/51) * (38/50) + (13/52) * (12/51) * (11/50) * (37/49) + (13/52) * (12/51) * (11/50) * (10/49) * (36/48) + (13/52) * (12/51) * (11/50) * (10/49) * (9/48) * (35/47)\)
= 0.8692
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9x + 3y = 477 work out x and y
Answers
Answer: x=53 - y/3
y=159-3x
Step-by-step explanation:
9x + 3y = 477
(9x + 3y)/3=477/3
3x+y=159
3x-3x+y=159-3x
y=159-3x
3x+y=159
3x=159-y
x=(159-y)/3
x=53 - y/3
A certain brand of coffee comes in two sizes. A 10.5 -ounce package costs $2.99. A 29.9-ounce package costs 7.98. Find the unit price for each size. Then state which size is the better buy based on the unit price. Round your answer to the nearest cent.
Answers
The 29.9-ounce package has a lower unit price of $0.2669 per ounce, making it the better buy.
To determine the unit price for the 10.5-ounce package, you would divide the cost of the package ($2.99) by the weight of the package (10.5 ounces). So:
$2.99 ÷ 10.5 ounces = $0.2847 per ounce
To find the unit price for the 29.9-ounce package, you would divide the cost of the package ($7.98) by the weight of the package (29.9 ounces). So:
$7.98 ÷ 29.9 ounces = $0.2669 per ounce
So, the 29.9-ounce package has a lower unit price of $0.2669 per ounce, making it the better buy.
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find the circulation and flux of the field f = -2xi - 2yj around and across the closed semicircular path that consists of the semicircular arch ij, , followed by the line segment , .
Answers
For the semicircular arch, we can use the equation of the circle to parameterize the path:
r(t) = a(cos(t)i + sin(t)j), 0 <= t <= pi
where a is the radius of the circle. The unit tangent vector along the path is:
T(t) = (-sin(t)i + cos(t)j)
The circulation along the semicircular arch is:
C1 = int_C1 F . dr = int_0^pi (-2a cos(t)i - 2a sin(t)j) . (-a sin(t)i + a cos(t)j) dt
= int_0^pi 2a^2 dt = 2a^2 pi
For the line segment, we can use the endpoints of the path to parameterize the path:
r(t) = (1-t)(a)i + tj, 0 <= t <= 1
The unit tangent vector along the path is:
T(t) = -a i + j
The circulation along the line segment is:
C2 = int_C2 F . dr = int_0^1 (-2a i - 2t j) . (-a i + j) dt
= int_0^1 (2at - 2t) dt = a - 1
The total circulation along the closed semicircular path is:
C = C1 + C2 = 2a^2 pi + a - 1
The flux of the field F = -2xi - 2yj across the closed semicircular path can be calculated using the divergence theorem. Since the path encloses a region in the xy-plane, we can use the 2D form of the divergence theorem:
int_S F . n dA = int_V div(F) dV
where S is the boundary of the region enclosed by the path, n is the unit outward normal vector to S, and V is the region enclosed by S.
The divergence of F is:
div(F) = -2
Since F is a constant vector field, the flux across the closed semicircular path is:
Phi = int_S F . n dA = int_V
Kalila Winston worked for a software company for 26 years. She became permanently disabled and could no longer keep her job. She was 52 years old and had planned to work until she was 62. Her final salary was $43,000. Her rate of benefits was 2%. What is Kalila's monthly disability benefit?
Answers
Answer:
The monthly disability benefit is $2580
Step-by-step explanation:
Given
\(Final\ Salary\ (P) = \$43000\)
\(Age = 52\)
\(Benefit\ Rate (R) = 2\%\)
Worked = 26 years
Expected = 62 years
Required
Determine the monthly disability benefit
First, we need to determine the years (T) left for her to work;
\(T = Expected - Worked\)
\(T = 62 - 26\)
\(T = 36\)
Next, is to calculate the yearly disability benefit as follows;
\(Benefit = PRT\)
Substitute 36 for T, 2% for R and 43,000 for P
\(Benefit = 43000 * 2\% * 36\)
Convert percentage to decimal
\(Benefit = 43000 * 0.02 * 36\)
\(Benefit = 30960\)
There are 12 months in a year;
So; Monthly Benefit is as follows;
\(Monthly = \frac{30960}{12}\)
\(Monthly = \$2580\)
Hence, the monthly disability benefit is $2580
The following table shows the amount of water in a tank after a plug is pulled.How much water is leaking out the tank each second?-7 gallons per second-4 gallons per second-5 gallons per second-9 gallons per second
Answers
This problem is asking for the ratio of change.
To find the ratio, we have to use two pairs: (3, 223) and (9, 193).
Then, we use the following formula.
\(r=\frac{y_2-y_1}{x_2-x_1}\)Where,
\(\begin{gathered} x_1=3 \\ x_2=9 \\ y_1=223 \\ y_2=193 \end{gathered}\)We replace these coordinates.
\(r=\frac{193-223}{9-3}=\frac{-30}{6}=-5\)Therefore, the water is leaking out 5 gallons per second.
The right answer is C.Demi was given a riddle to solve: the sum of two consecutive positive integers is 71. find the two positive integers.
Answers
The required number of two positive consecutive integers are 35 and 36.
Consecutive integers are the whole numbers that follow each other without gaps. consecutive integers are even, and odd integers.
consecutive even integers that differ from previous integer by difference of 2 and each integer is divisible by 2.
consecutive odd integers that differ from previous integer by difference of 2 and each integer is an odd number.
let the first positive integer be x
Therefore the second positive integer be (x+1)
Given that the sum of two consecutive positive integer is 71:
x+(x+1)=71
open the bracket
x+x+1=71
Add the similar terms
2x+1=71
2x=71-1
2x=70
x=35
Finding the second integer Substituate the value of x=35 in (x+1):
x+1=35+1
x+1=36
The required number of two positive consecutive integers are 35 and 36.
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Nat says that a square is a rectangle because it has four right angles. Amy says that a square is a rhombus because it has 4 equal sides. Who is correct? Explain *
Answers
Answer:
They are both correct in special cases of a rectangle and rhombuses
Step-by-step explanation:
A square is quadrilateral, with four equal sides and four equal interior angles of 90°
A rectangle is a quadrilateral, with four equal angles which are all 90°. Therefore, a square is a special case of a rectangle with all the sides equal
A rhombus is also a equilateral quadrilateral with having equal opposite angle.
Therefore, when any of the interior angles is equal to 90°, the rhombus becomes known as a square, hence, a square is a special form of rhombus.
If 1/2 of a gallon of paint covers 1/8 of a wall, how much paint is need to cover the entire wall?
Answers
Answer:
4 gallons
Step-by-step explanation:
multiply 1/2 by 8 to find the number
Answer:
One gallon of paint can cover \(\frac{1}{4}\) of a wall.
Step-by-step explanation:
start by writing the ratio:
\(\frac{1}{2\\}\) : \(\frac{1}{8}\)
There are two halfs in one gallon so you multiply the \(\frac{1}{2\\}\) by 2. And whatever you do to one side must be done to the other so:
\(\frac{1}{2\\}\)×2 : \(\frac{1}{8}\)×2
Evaluate.
1: \(\frac{2}{8}\)
this can be further simplified to
1: \(\frac{1}{4}\)
a linear programming problem with decision variable(s) can be solved by a graphical solution method. a. three b. four c. two d. five
Answers
A linear programming problem with two decision variables can be solved by a graphical solution method. In this method, the constraints and the objective function of the linear programming problem are graphed on a two-dimensional coordinate plane, and the optimal solution is found at the intersection of the feasible region (the area defined by the constraints) and the level curve of the objective function.
The graphical solution method is a simple and intuitive way to solve linear programming problems with few decision variables, but it becomes impractical as the number of decision variables and constraints increase. In such cases, more complex algorithms, such as the simplex method or interior point methods, are used to find the optimal solution.
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A news podcast has 77,000 subscribers. Write an estimate for the number of subscribers as a single digit times an integer power of 10. Show your work.
Answers
To estimate the number of subscribers as a single digit times an integer power of 10, we can round the given number to the nearest power of 10.
The given number of subscribers is 77,000.
Rounding 77,000 to the nearest power of 10 (which is 10^4 or 10,000), we get:
77,000 ≈ 8 × 10,000
So, an estimate for the number of subscribers as a single digit times an integer power of 10 would be 80,000.
Acellus
Choose SSS, SAS, or neither to compare
these two triangles.
Help Resources
А
SAS
neither
SSS
Answers
Answer:
SSS
Step-by-step explanation:
The data shows the total number of employee medical leave days taken for on the job accidents in the first six months of the year 14, 6, 18, 10,22, 14. Find the mean number of days taken for medical leave each month.The mean number of days taken for medical leave each month is
Answers
ANSWER
14 days
EXPLANATION
The mean of a data set is the sum of all data, divided by the number of data,
\(\bar{x}=\frac{1}{n}\sum_{i\mathop{=}1}^nx_i\)In this case, the number of data is 6, so the mean is,
\(\bar{x}=\frac{14+6+18+10+22+14}{6}=\frac{84}{6}=14\)Hence, the mean number of days taken for medical leave each month is 14.
Two planes л₁ and л₂ have vector equations r.(5i-3j+k)=2 and r.(-i-9j+3k)=6 respectively. (a) Find the unit vector which is parallel to both planes. Hence, find a Cartesian equation for the line of intersection, I, of the two planes. (b) Find the angle between these two planes. (c) The planes л, has equation r.(-i+aj+bk)=6, where a and b are real numbers. Find the values of a and b given that the 3 planes л₁, л₂ and л, intersect in the common line l.
Answers
The values of a and b are a = 3, b = 0
How to determine the unit vector?a) The unit vector which is parallel to both planes is the cross product of the normal vectors of the two planes. The normal vector of a plane with a vector equation of r.(a_1i + a_2j + a_3k) = d is (a_1i + a_2j + a_3k). So the normal vectors of planes л₁ and л₂ are (5i - 3j + k) and (-i - 9j + 3k) respectively. The cross product of these two vectors is (15i + 27j - 15k). This is a unit vector if we divide by the magnitude of vector. So the unit vector which is parallel to both planes is (15i + 27j - 15k)/sqrt(15^2+27^2+(-15)^2)= (i+3j-k)/sqrt(19)
The vector equation of the line of intersection is r = r0 + t(i+3j-k)/sqrt(19) where r0 is a position vector of a point on the line of intersection and t is a scalar parameter.
How to determine the angle?b) The angle between two planes is given by the formula:
cos(theta) = (n1.n2) / (|n1| * |n2|)
where n1 and n2 are the normal vectors of the planes and |n1| and |n2| are the magnitudes of the normal vectors.
So, the angle between the two planes is arccos( (5i - 3j + k).(-i - 9j + 3k) / (|5i - 3j + k| * |-i - 9j + 3k|) ) = arccos( (-5 - 27 + 3) / (sqrt(35) * sqrt(91)) ) = arccos(-19/sqrt(35*91))
How to determine the vector of plane?c) The normal vector of plane l is (-i + aj + bk) the direction vector of the common line of intersection should be parallel to both normal vector of plane l and the unit vector found in a) that is parallel to both plane 1 and plane 2.
so, (-i + aj + bk) . (i+3j-k)/sqrt(19) = 0
so, a-3 = 0 and b = 0
so the values of a and b are a = 3, b = 0
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5+6a>-1 solve each inequality.
Answers
Answer:
\(a>-1\)
Explanation:
\(5+6a>-1\)
group variables
\(6a>-1-5\)
simplify
\(6a> -6\)
divide both sides by 6
\(a>-1\)
Answer:
a > -1
Step-by-step explanation:
5 + 6a > -1
-5 -5
6a > -6
/6 /6
a > -1
Hope this helps!
Answer for brainliest.
Answers
Answer:
t > 28
Step-by-step explanation:
Given
\(\frac{t}{4}\) > 7 ( multiply both sides by 4 to clear the fraction )
t > 28
Answer:
\(t>28\)
Step-by-step explanation:
\(\frac{t}{4} >7\\\)
Times both sides by 4
\(t>28\)
Hope this helps and pls do mark me brainliest:)
The probability that Mary will win a game is 0.03, so the probability that she will not win is 0.97. If Mary wins, she will be given $60; if she loses, she must pay $3. If X = amount of money Mary wins (or loses), what is the expected value of X? (Round your answer to the nearest cent.)
Answers
The expected value of X is -$1.11. This means that on average, Mary can expect to lose $1.11 per game.
The probability that Mary will not win is 0.97; hence, the probability that she will win is 0.03.
Probability:Probability is the likelihood of an event happening. It is a way of measuring the chance or the likelihood of an event occurring. Probability is measured on a scale from 0 to 1, where 0 is impossible and 1 is certain.
Probability = (number of favorable outcomes) / (total number of outcomes)
Expected value:The expected value is the sum of the products of each outcome and its probability. It represents the average value that one can expect to win from a game by placing a bet on that game.
In a game where the probability of winning is 0.03 and the probability of losing is 0.97,
Mary will win $60 if she wins and lose $3 if she loses.
Then, the expected value of X (the amount of money Mary wins or loses) can be calculated as:
E(X) = (0.03)($60) + (0.97)($-3)
E(X) = $1.80 - $2.91E(X) ⇒ $-1.11
The expected value of X is -$1.11 (a negative value).
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Read the statements below about the following algebraic expression:
3m +5n +4
Select ALL of the statements that are true.
5n is a term
m and n are coefficients
3m and 5n are not like terms
4 is a variable
Please help
Answers
Your answer is a because if you look at the expression none of the other are true thank me later
Step-by-step explanation:
Question attached as screenshot below: Please help me with my homeworkI am paying attention
Answers
The limit is 1/5
Explanation:Given the function:
\(\frac{\sqrt[]{x^2+24}-5}{x-1}\)Taking this limit as x approaches 1, we have:
\(\begin{gathered} \frac{\sqrt[]{1^2+24}-5}{1-1}=\frac{\sqrt[]{25}-5}{1-1} \\ \\ \frac{5-5}{1-1}=\frac{0}{0} \end{gathered}\)This result means we need to apply a different method.
We apply L'hopital's rule, by taking the derivatives of the numerator and denominator as follows:
\(\begin{gathered} \frac{2x\times\frac{1}{2}(x^2+24)^{-\frac{1}{2}}}{1} \\ \\ =x(x^2+24)^{-\frac{1}{2}} \end{gathered}\)Now, taking the limit as x approaches 1, we have:
\(\begin{gathered} 1(1^2+24)^{-\frac{1}{2}} \\ \\ =\frac{1}{\sqrt[]{25}}=\frac{1}{5} \end{gathered}\)For each of the following situations, decide what sampling method you would use. Provide an explanation of why you selected a particular method of sampling.
a. The major state university in the state is attempting to lobby the state legislature for a bill that would allow the university to charge a higher tuition rate than the other universities in the state. To provide a justification, the university plans to conduct a mail survey of its alumni to collect information concerning their current employment status. The university grants a wide variety of different degrees and wants to make sure that information is obtained about graduates from each of the degree types. A 5% sample of alumni is considered sufficient.
b. The Environmental Protection Agency (EPA) is required to inspect landfills in the United States for the presence of certain types of toxic material. The materials were sealed in containers and placed in the landfills. The exact location of the containers is no longer known. The EPA wants to inspect a sample of 1000 containers from the 40,000 containers know to be in the landfills to determine if leakage from the containers has occurred.
Answers
a. The sampling method that I would use for the given scenario is stratified random sampling.
b. The sampling method that I would use for the given scenario is systematic sampling.
Stratified random sampling is the most effective way to get accurate results in this situation. The university wants to conduct a mail survey of its alumni to collect information about their current employment status to justify charging a higher tuition rate than other universities. Stratified random sampling divides the population into strata based on certain characteristics.
In this case, strata would be the alumni that have different degrees from the university. The information collected through this method will be more representative of the population than simple random sampling. It ensures that each stratum is represented accurately in the sample. It also minimizes the variability within each stratum. It is an effective way of ensuring that each stratum is properly represented.
Systematic sampling involves selecting every kth element from a list of the population. In this situation, the Environmental Protection Agency (EPA) wants to inspect a sample of 1000 containers from the 40,000 containers known to be in landfills to determine if leakage from the containers has occurred. As the exact location of the containers is no longer known, systematic sampling can be used.
EPA can select every 40th container from the list of the population, as 40,000/1000 = 40. In this way, they will have a random sample of 1000 containers from the 40,000 containers. This sampling method is less time-consuming and more cost-effective than other sampling methods. It also ensures the sample is representative of the entire population.
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John had a stock of 1200 books in his bookshop. He sold 75 on Monday, 50 on Tuesday, 64 on Wednesday, 78 on Thursday and 135 on Friday. What percentages of the books were not sold?
Answers
Answer:
Books in inventory= 66.5%
Step-by-step explanation:
First, we determine the number of books sold:
Books sold= 75 + 50 + 64 + 78 + 135= 402 books
Now, using the following formula, the percentage of books in inventory:
Books in inventory= [(books sold/total books) -1]*100
Books in inventory= [1 - (402/1,200)]*100
Books in inventory= 66.5%
Which box plot represents the data above?
W.
X.
Y.
Z.
Answers
Answer:
where's the data
Step-by-step explanation:
WHATS THE ANSEER FAST PLS
Answers
Answer:
Volume is approximately 150.8 (rounded).
Answer:
151 \(cm^3\)
Step-by-step explanation:
\(V = (1/3)\pi r^2h\\V = (1/3)\pi * 4^2 * 9 = 150.796 = 151 cm^3\)
Edward works as a waiter, where his monthly tip income is normally distributed with a mean of $2,000 and a standard deviation of $350. Use this information to answer the following questions. Record yo
Answers
The probability that Edward’s monthly tip income exceeds $2,350 is 0.8413.
Given that Edward works as a waiter, where his monthly tip income is normally distributed with a mean of $2,000 and a standard deviation of $350.
The z score formula is given by;`z = (x - μ) / σ`
Where; x is the raw scoreμ the mean of the populationσ is the standard deviation of the population.
The probability that Edward’s monthly tip income exceeds $2,350 is to be found.`z = (x - μ) / σ``z = (2350 - 2000) / 350``z = 1`
The value of z is 1.
To find the area in the right tail, use the standard normal distribution table.
The table value for z = 1.0 is 0.8413.
Therefore, the probability that Edward’s monthly tip income exceeds $2,350 is 0.8413.
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What are the opposites of 9, −2.7, 3.35, and 6
1
5
? Enter the answers in respective order, each separated by a comma.
Answers
Answer:
Step-by-step explanation: -9,2,-7,-3,-35, and -6