Answers
Using simplex method to maximize the given function is (x, y, z) = (17.33, 1.33, 0) and f = 35.67.
How to solve linear programming?To solve the given linear programming problem using the simplex method, follow these steps:
Step 1: Convert the problem into standard form.
Step 2: Set up the initial simplex tableau.
Step 3: Perform iterations of the simplex method.
Step 4: Determine the solution and the maximum value of the objective function.
Step 1: Convert the problem into standard form:
Introduce slack variables to convert the inequality constraints into equations:
Maximize f = 7x + 11y + 4z
Subject to:
3x + 5y + 4z + s1 = 30
3x + 2y + s2 = 4
x + 2y + s3 = 8
All variables are nonnegative: x ≥ 0, y ≥ 0, z ≥ 0, s1 ≥ 0, s2 ≥ 0, s3 ≥ 0.
Step 2: Set up the initial simplex tableau:
Construct the initial simplex tableau using the coefficients of the variables and the right-hand side values of the equations is attached (tableau 1).
Step 3: Perform iterations of the simplex method:
Apply the simplex method by selecting the most negative value in the bottom row (the objective row) as the pivot column and the minimum ratio test to determine the pivot row.
Iteration 1:
Pivot column: y (since it has the most negative coefficient in the bottom row)
Pivot row: s2 (minimum ratio: 4/2 = 2)
Perform row operations to make the pivot element 1 and other elements in the pivot column zero:
Divide the pivot row by the pivot element (2/2 = 1/1 = 1).
Subtract appropriate multiples of the pivot row from other rows to make the elements in the pivot column zero.
Updated tableau after iteration 1 attached (tableau 2).
Iteration 2:
Perform row operations to make the pivot element 1 and other elements in the pivot column zero:
Divide the pivot row by the pivot element (3/2).
Subtract appropriate multiples of the pivot row from other rows to make the elements in the pivot column zero.
Updated tableau after iteration 2 also attached (tableau 3).
Iteration 3:
Since all coefficients in the bottom row are non-negative, the optimal solution has been reached. We can read the values of variables x, y, z, and the objective function f directly from the tableau.
The optimal solution is:
x = 17.33
y = 1.33
z = 0
f = 35.67
Therefore, (x, y, z) = (17.33, 1.33, 0) and f = 35.67.
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Related Questions
if 12 people get a collective number of 775 questions in a 7 day period how man questions are being asked in a day
Answers
The number of questions asked in a day is A = 110
Given data ,
To determine the number of questions being asked in a day, we need to divide the total number of questions by the number of days.
Now , 12 people are collectively asking 775 questions in a 7-day period.
So , the number of questions being asked in a day, we divide 775 by 7
A = 775 / 7
On simplifying the equation , we get
A ≈ 110.71
Hence , 110.71 questions are being asked in a day
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On a coordinate plane, point A is at (2, 3), point B is at (4.5, negative 6), point C is at (negative 0.5, negative 3), and point D is at (negative 6, 2).
Look at the graph to help you complete the statements.
Point D is located in quadrant
.
The coordinates of point A are
.
The coordinates of point
are both negative.
Answers
1. Point D is located in quadrant 2.
2. The coordinates of point A are (2, 3).
3. The coordinates of point C are both negative. It is located in quadrant
1. Point D is located in quadrant 2, which is the quadrant where the x-coordinates are negative and the y-coordinates are positive. This means that the x-coordinate of point D, which is -6, is negative and the y-coordinate, which is 2, is positive.
2. The coordinates of point A are (2, 3). This means that the x-coordinate of point A is 2, and the y-coordinate is 3. Point A is located in the first quadrant, which is the quadrant where both the x-coordinate and y-coordinate are positive.
3. The coordinates of point C are both negative. It is located in quadrant 3, which is the quadrant where the x-coordinates are negative and the y-coordinates are also negative. This means that the x-coordinate of point C, which is -0.5, is negative and the y-coordinate, which is -3, is also negative.
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State all possible conditions that must be true for j and k so that the product of the expression is negative -2jk
Answers
The product -2jk is negative if and only if either j or k is negative (but not both). Therefore, the possible conditions for j and k are:
j < 0 and k > 0
j > 0 and k < 0
For the expression -2jk to be negative, at least one of the factors j or k must be negative, since the product of two positive numbers is always positive, and the product of two negative numbers is positive as well. Therefore, the possible conditions for j and k are:
j is negative and k is positive.
j is positive and k is negative.
In other words, if j and k have opposite signs, their product will be negative. However, if both j and k are positive or both are negative, their product will be positive. It's important to note that there are infinite possibilities for j and k that satisfy these conditions, since j and k can take on any real value as long as one is negative and one is positive.
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Find the slope of each line.
Answers
Answer:
Step-by-step explanation:
slope is rise over run or y over x
Let m be the slope
On this case, simply count the units for both x and y from tip to tip of the line segment
m = y/x
direction of the line is up and right so the sign is both positive
m = 4/1
m = 4
m = y/x
direction of the line is down and right so y is negative and x is positive
m = -3/4
Please answer quick I will mark BRAINLIEST . Simplify the expression (-1/7r - 9 -2/3r) - (-5/7r + 10)
A. -32/21r - 1
B. -2/21r + (-19)
C. -2/21r - 1
D. 4/11r + (-19)
Answers
Answer:
Answer is -2/21r + (-19)
Step-by-step explanation:
(-1/7r - 9 -2/3r) - (-5/7r + 10)
= -1/7r - 9 - 2/3r + 5/7r - 10 (distributing the negative sign)
= (-1/7r + 5/7r) + (-2/3r) - 9 - 10 (grouping the like terms)
= 4/7r - 2/3r - 19 (combining the like terms)
= (12r - 14r)/21r - 38r/21r (getting a common denominator)
= -2r/21r - 38r/21r
= (-2r - 38r)/21r
= -40r/21r
= -40/21
Therefore, the simplified expression is B. -2/21r + (-19).
Find the probability of randomly choosing an ace or a club from a standard deck of cards. Remember that a standard deck consists of
52 cards, where each card is made up of a number or letter from {2, 3,4, 5, 6, 7, 8, 9, 10, J, Q, K, A} and a suit from {clubs, diamonds, hearts, spades
Answers
Answer: The probability of choosing an ace or a club is 16.
Step-by-step explanation:
Probability
See picture attached
Answers
Answer:
The answer is down below
Step-by-step explanation:
G={2,3,4}
W={1,5}
Total cards=1,2,3,4,5
let P(x) be G
Probability of X=G/Total
P(x)=3/5
P(not x)=2/5
X={2,3,4}
not X={1,5}
Simplify Square root of x^2-8x+16 if x<4
Answers
If x = 4, then the expression becomes:
sqrt(4^2 - 8(4) + 16) = sqrt(16 - 32 + 16) = sqrt(0) = 0
If x > 4, then we can simplify the expression as follows:
sqrt(x^2 - 8x + 16) = sqrt((x - 4)^2) = |x - 4|
Therefore, the simplified expression is |x - 4| for x > 4, and it is undefined for x < 4.
The expression πr2h represents the volume of a right circular cylinder with radius r and height h. Why is this expression a monomial? What is its degree?
I NEED ASAP
Answers
Answer:
The expression πr2h is a monomial because it is a single term that is the product of three variables: π, r2, and h. The term "mono" means "one," and "monomial" refers to a single term in algebraic expressions.
The degree of a monomial is the sum of the exponents of its variables. In this case, the degree of the monomial is 3, because the variables π, r, and h have exponents of 1, 2, and 1 respectively. Therefore, the degree of the monomial is 1 + 2 + 1 = 3.
Alice is cutting pieces of cloth to sew into a quilt. She cut one piece of cloth into a parallelogram with a base of 7 inches and a height of 4 inches. What is the area of this piece of cloth?
Answers
Answer:
28 in²
Step-by-step explanation:
Area of parallelogram = base X vertical height
= 7 X 4
= 28 in²
P(Pink, Blue)
Enter your answer as a fraction in simplest terms in the box.
Answers
The probability that the selection will be P(pink, blue) is: 9/64
What is the probability of the spinner?The total number of sections on the spinner are 8 sections.
Now, out of the 8 sections, the divisions are as follows:
Yellow sections = 2
Blue sections = 3
Pink sections = 3
Thus:
P(first is pink) = 3/8
P(second is blue) = 3/8
Thus:
P(pink, blue) = (3/8) * (3/8)
= 9/64
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Solve part A and B on the picture (statistics)
Answers
The distribution of the weight of one dozen eggs is approximately normally distributed with a mean of 68 grams and a standard deviation of 4.2 grams.
How to calculate the valueThe distribution of the weight of one dozen eggs is also approximately Normally distributed. The mean of the distribution is the same as the mean of the individual eggs, which is 68 grams.
The standard deviation of the distribution is the square root of the sum of the variances of the individual eggs and the sample size, which is:
= 2.2 * ✓12
= 4.2 grams.
Therefore, the distribution of the weight of one dozen eggs is approximately normally distributed with a mean of 68 grams and a standard deviation of 4.2 grams.
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1.4 "The teaching and learning of Mathematics aims to develop a critical awareness of how mathematical relationships are used in social, environmental, cultural and economic relations" (DBE 2011, p.8). Design an activity that could help learners recognise that percentages can be applied across social situations (relating to activities in real life) and fully explain how you would use it in teaching and learning.
Answers
Activity: "Percentage Analysis in Real-Life Situations"
Objective: The objective of this activity is to help learners recognize the practical application of percentages in various social situations. It aims to develop their critical awareness of how percentages are used in real-life contexts and their significance in social, environmental, cultural, and economic relations.
Procedure:
1. Provide learners with a set of real-life scenarios, such as a discount sale, population growth, or budget allocations.
2. Ask them to identify the relevant information and calculate percentages based on the given data.
3. In small groups, learners discuss and analyze the implications of these percentages in the given social situations.
4. Encourage learners to think critically about how percentages impact decision-making, resource allocation, and understanding social phenomena.
5. Have groups present their findings and engage in a class discussion about the significance of percentages in these scenarios.
Teaching and Learning Approach:
This activity promotes an active learning approach by engaging learners in real-life problem-solving. It helps them recognize the practical relevance of percentages and fosters critical thinking skills.
By connecting mathematical concepts to social situations, learners develop a deeper understanding of how percentages are utilized in various aspects of their lives.
The teacher's role is to facilitate discussions, provide guidance, and encourage learners to articulate their understanding of the connections between mathematics and real-world contexts.
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Which of the following sets of ordered pairs represents a function? {(−5, −4), (−3, −2), (−1, 0), (0, −1), (0, 3)} {(−4, −4), (−4, −3), (−4, −2), (−4, −1), (−4, 0)} {(−3, −4), (−3, 0), (−2, −3), (0, −2), (2, −1)} {(−5, −2), (−3, −2), (−2, −2), (−1, −2), (0, 0)}
Answers
The required set of ordered pairs that represent a function is {(−5, −4), (−3, −2), (−1, 0), (0, −1), (0, 3)}. Option A is correct.
Given functions,
A= {(−5, −4), (−3, −2), (−1, 0), (0, −1), (0, 3)}
B= {(−4, −4), (−4, −3), (−4, −2), (−4, −1), (−4, 0)}
C = {(−3, −4), (−3, 0), (−2, −3), (0, −2), (2, −1)}
D = {(−5, −2), (−3, −2), (−2, −2), (−1, −2), (0, 0)}
The other sets have repeated x-values with different y-values, which violates the definition of a function where each x-value can only have one corresponding y-value.
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Answer: The awnser is D
Step-by-step explanation: Hope this helps
how do i find x from the equation x(x+6)=108
Answers
Answer:
x = -3 + √117
x = -3 - √117
Step-by-step explanation:
So the equation is x(x+6)=108
first you gotta simplify
x*x + x*6 = 108
x^2 + 6x = 108
x^2 + 6x - 108 = 0
using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a) with a=1, b=6 and c=-108
Convert 2553 base 10 to base 16
Step by step explanation
Answers
Step 1: Divide 2553 by 16 and write down the quotient and remainder:
2553 ÷ 16 = 159 remainder 9
Step 2: Write down the remainder (9) as the least significant digit (rightmost digit) in the base 16 number.
Step 3: Divide the quotient (159) by 16 and write down the new quotient and remainder:
159 ÷ 16 = 9 remainder 15
Step 4: Write down the remainder (15) as the next digit to the left in the base 16 number. Since 15 represents the value of the decimal number 15, we represent it as the letter F in base 16.
Step 5: Repeat steps 3 and 4, dividing the quotient by 16 until the quotient is zero:
9 ÷ 16 = 0 remainder 9
0 ÷ 16 = 0 remainder 0
Step 6: Write down the final remainder (9) as the most significant digit (leftmost digit) in the base 16 number.
Step 7: Combine all the digits in reverse order to obtain the final answer:
2553 base 10 = 9F9 base 16
Therefore, 2553 in base 10 is equal to 9F9 in base 16.
Can someone please help me out with this?
Answers
Answer: center: (5,-5) radius: 8
Step-by-step explanation:
found it online:)
Mark was suspicious that his wife was unfaithful to him. He obtained blood samples from all family members. When the results came back, it turned out that Mark has blood type AB. His wife has blood type O. They have three children. One child has blood type A. One child has blood type B. One child has blood type O. “You cheated!” Mark yells accusingly. Is he right to make such a statement or does he owe his wife an apology? Show your work with Punnett Squares or with a written explanation
Answers
Mark's accusation is incorrect. Based on the blood type combinations, it is possible for the children to have the observed blood types without any infidelity. Mark owes his wife an apology for the false accusation.
Mark has blood type AB, which means he has one A allele and one B allele.
Mark's wife has blood type O, which means she has two O alleles.
One child has blood type A, indicating they have inherited one A allele.
One child has blood type B, indicating they have inherited one B allele.
One child has blood type O, indicating they have inherited two O alleles.
Child 1:
Mark's allele: A
Wife's allele: O
Possible combinations: AO
Child 2:
Mark's allele: B
Wife's allele: O
Possible combinations: BO
Child 3:
Mark's allele: A or B (since Mark has AB blood type)
Wife's allele: O
Possible combinations: AO or BO
From the possible combinations, we can see that it is possible for the children to have blood types A, B, and O without any issues.
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Post Test: Connecting Algebra Classes
A circle is defined by the equation given below.
2² +²2-2y
= 0
What are the coordinates for the center of the circle and the length of the radius?
12.app.edmentum.com/assessments-delivery/ua/la/launch/49003916/45317916/aHR0cHM6Ly9mMiShcHAUZWRtZW5odWouY29tL2xlYXJuZXItdw
Next O Post Test: Connecting Algebra and Geometry through Coordinates
OA. (-1,-1), 4 units
B.
(,1), 2 units
OC. (-, -1), 2 units
OD. (,1), 4 units
Answers
The coordinates for the center of the circle are (1/2, 1), and the length of the radius is 2 units. Option C is a correct choice.
To find the coordinates of the center of the circle and the length of the radius, we need to rewrite the equation of the circle in standard form, which is (x - h)² + (y - k)² = r². Here, (h, k) represents the coordinates of the center of the circle, and r represents the radius.
Given equation: x² + y² - x - 2y - 1 = 0
To convert it into standard form, we complete the square for the x and y terms separately.
Rearranging the equation:
x² - x + y² - 2y = 1
Completing the square for x:
(x² - x + 1/4) + (y² - 2y) = 1 + 1/4
Completing the square for y:
(x² - x + 1/4) + (y² - 2y + 1) = 1 + 1/4 + 1
Simplifying:
(x - 1/2)² + (y - 1)² = 9/4
Comparing it with the standard form, we can see that:
Center coordinates: (1/2, 1)
Radius: √(9/4) = 3/2 = 1.5 units
Therefore, the correct answer is C. The coordinates for the center of the circle are (1/2, 1), and the length of the radius is 2 units.
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Question -
A circle is defined by the equation given below. x² + y² - x - 2y - 1 = 0 What are the coordinates for the center of the circle and the length of the radius?
A. (-1,-1), 2 units −1),
B. (- 1/2 ,1), 4 units
C. (1/2 , 1), 2 units
D. (-1/2 ,-1), 4 units
are the answers highlighted in yellow
correct?
Answers
1. In the short run, the firms in the competitive industry will earn positive profits because the market price is higher than the minimum of the average cost curve. The Option A.
2. If the market price is P4, the individual firm in a competitive industry will earn zero profit. The Option B
3. Firm would be encouraged to enter this market for all price that exceeds P4. The Option D,
Why do firms earn positive profits in the short run?When the market price is between P4 and P6, firms in a competitive industry are able to earn positive profits in the short run because the price is above their average variable cost (AVC) but below their average total cost (ATC).
This means that firms are covering their variable costs and also making a contribution towards their fixed costs. As a result, they are earning positive profits. But, in the long run the firms will enter the industry and increase supply causing market price to decrease towards P4 where firms earn zero economic profits in the long run.
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Fill in the blank using the scaling factor that makes the number sentence true. 5.3 × > 5.3 0.886 or 1.00 or 1.003
Answers
The given options, the only value greater than 1 is 1.003. Therefore 0.886, which is less than 1 and makes the inequality true.
The given number sentence is 5.3 × > 5.3, where we need to find the scaling factor that makes the inequality true. To do this, we can divide both sides of the inequality by 5.3. This gives us:
5.3 × x > 5.3 ÷ 5.3 × k
We need to find the value of k that makes the inequality true. Simplifying the right-hand side of the equation, we get:
5.3 ÷ 5.3 × k = k × 1 = k
Substituting this into our equation, we get:
5.3 × x > k
We know that 5.3 × 1 = 5.3, which means that k must be greater than 1 to satisfy the inequality. Among the given options, the only value greater than 1 is 1.003. However, this value would make the inequality too large, so it is not the correct answer.
The correct answer is therefore 0.886, which is less than 1 and makes the inequality true.
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100 POINTS!!
Select the correct answer.
The function g(x)=x² is transformed to obtain function :
h(x) = g(x) + 1.
Which statement describes how the graph of his different from the graph of g?
A. The graph of h is the graph of g horizontally shifted left 1 unit.
B. The graph of h is the graph of g vertically shifted down 1 unit.
C. The graph of h is the graph of g horizontally shifted right 1 unit.
D. The graph of h is the graph of g vertically shifted up 1 unit.
Answers
A statement that describes how the graph of his different from the graph of g include the following: D. The graph of h is the graph of g vertically shifted up 1 unit.
What is a translation?In Mathematics and Geometry, the translation of a graph to the left simply means subtracting a digit from the numerical value on the x-coordinate of the pre-image;
g(x) = f(x + N)
Conversely, the translation a geometric figure or graph upward simply means adding a digit to the numerical value on the positive y-coordinate (y-axis) of the pre-image; g(x) = f(x) + N.
Based on the information provided, we have:
(x, y) → (x, y + 1)
g(x) = x²
h(x) = g(x) + 1 → h(x) = x² + 1
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what is the meaning of sequence in mathematic and
Answers
Answer:
A list of numbers or objects in a special order. Example: 3, 5, 7, 9, ... is a sequence starting at 3 and increasing by 2 each time.
Step-by-step explanation:
Write an equation to solve for X.
Answers
Step-by-step explanation:
The sum of the interior angles of a n-gon is equal to ( n-2)(180) degrees
for this 6-gon the sum is (6-2) * 180 = 720 degrees
(145 + 165 + 58 + 130 + 125 + x ) degrees = 720 degrees
x = 97 degrees
The sine of an angle 0 in the third quadrant is -0.5. What is the value of cos(0)?
Answers
The measure of angle θ is 210°. Therefore, the value of the cos θ will be -√3 / 2.
Given that:
sin θ = -0.5
The angle θ lies in the third quadrant.
Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
The angle θ is calculated as,
sin θ = -0.5
θ = 210°
The value of the cosine of anlge θ is calculated as,
cos θ = cos 210°
cos θ = -√3 / 2
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NEED HELP W QUESTIONS 4-6
Answers
The volume of the figures are;
4. 27. 18 in³
5. 3. 024 m³
6. 23 6/18 yd³
How to determine the volumeThe formula for calculating the volume of a triangular prism is expressed with the equation;
V = Bl
Given that the parameters are;
V is the volume of the triangular prisml is the length of the triangular prismB is the base area of the triangular prism4. We have that;
Base area = 1/2 × 2.6 × 4.1
Multiply the values
Base area = 5. 33in²
Then,
Volume = 5.33 × 5.1
Volume = 27. 18 in³
5. Base area = 1/2 × 2. 4 × 1.4
Multiply the values
Base area = 1. 68 m²
Volume = 1.8 ×1.68
Multiply the values
Volume= 3. 024 m³
6. Base area = 1/2 × 10/3 × 14/3
Multiply the values
Base area = 7 14/18yd²
Volume = 140/18 × 3
Multiply the values
Volume = 23 6/18 yd³
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2 ( a + 4b) +5 + 7b +6
Answers
Answer:
2a+15b+11
Step-by-step explanation:
2*a + 2*4b + 5 + 7b + 6
2a + 8b + 5 + 7b + 6
2a + 8b + 7b + 5 + 6
2a + 15b + 11
Answer this question
Answers
Using the Pythagorean theorem and trig identities, it is proved sinθ + cosθ = 1.
The Pythagorean theorem states that for a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we can use the Pythagorean theorem to prove that sinθ+cosθ=1.
Let's take a right triangle with an angle θ and sides a, b and c, as shown in the diagram below:
By the Pythagorean theorem, we have:
a² + b² = c²
Now, we can substitute a and b with the trigonometric functions for the sides of our triangle:
sin²θ + cos²θ = 1
We can simplify this expression by using the trigonometric identity:
sin²θ + cos²θ = 1
sin²θ + cos²θ = (sinθ + cosθ)²
Substituting (sinθ + cosθ)² back into the equation, we get:
(sinθ + cosθ)² = 1
Hence, using the Pythagorean theorem and trig identities, it is proved sinθ + cosθ = 1.
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Find the area of the parallelogram with vertices L(–5, –2, –4), M(–12, –2, –4), N(–12, –8, –10), and O(–5, –8, –10).
Answers
From the vertices provided, the area of the parallelogram is 42cm².
How do we calculate the area of a parallelogram with the vertices provided?The area of a parallelogram remain
Area = base×height
we need to start by creating two vectors using the given vertices. We can use LM and LN.
Vector LM = M - L = (-12, -2, -4) - (-5, -2, -4) = (-7, 0, 0)
Vector LN = N - L = (-12, -8, -10) - (-5, -2, -4) = (-7, -6, -6)
LM x LN = (0×(-6) - 0×(-6), 0×(-7) - (-7)×0, -7×(-6) - 0×0)
= (0, 0, 42)
Area = ||LM x LN|| =√(0² + 0² + 42²) = √(0 + 0 + 1764)
= √(1764) = 42 cm²
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10. Mr. Brown bought a car for commuting to
work and completing errands. He found
that he traveled an average 1,100 miles per
month, with a standard of 100 miles. About 95% of the data lies in which interval
Answers
To determine the interval in which about 95% of the data lies, we can use the concept of standard deviation and the properties of the normal distribution.
Given that the average monthly mileage is 1,100 miles and the standard deviation is 100 miles, we can apply the empirical rule (also known as the 68-95-99.7 rule) for normally distributed data. According to this rule:
- Approximately 68% of the data lies within one standard deviation of the mean.
- Approximately 95% of the data lies within two standard deviations of the mean.
- Approximately 99.7% of the data lies within three standard deviations of the mean.
Since the standard deviation is 100 miles, we can conclude that about 95% of the data lies within two standard deviations of the mean.
Therefore, the interval within which about 95% of the data lies is:
1,100 miles ± (2 * 100 miles) = 1,100 miles ± 200 miles
So, the interval is from 900 miles (1,100 miles - 200 miles) to 1,300 miles (1,100 miles + 200 miles).
d = 5t + 20
your answer is there so i'll be on my way, Have a nice day!!
