suppose the following random variables for adult men variable description y1 percent body fat from siri’s (1956) equation y2 age (years) y3 weight (lbs) y4 height (inches) y5 abdomen circumference (cm) follow multivariate normal with mean vector and variance covariance matrix as follows: mean vector: 19 y1 y2 y3 y4 y5 45 y1 70 31 151 -3 74 179 and variance-covariance matrix: y2 31 154 -2 -8 31 70 y3 151 -2 866 33 283 93 y4 -3 -8 33 13 3 y5 74 31 283 3 117 find the conditional distribution of the percent body fat y1 given y2, y3, y
Answers
The conditional distribution of y1 given y2, y3, y4, and y5 is then a univariate normal distribution with the calculated conditional mean and conditional variance.
To find the conditional distribution of the percent body fat (y1) given y2, y3, and y5, we can use the properties of multivariate normal distributions. The conditional distribution is also a multivariate normal distribution.
Given:
Mean vector: μ = [19, 45, y2, y3, y4, y5]
Variance-covariance matrix:
Σ = |31 154 -2 -8 31 70|
|154 866 33 283 93|
|-2 33 13 3|
|-8 283 3 117|
We can partition the mean vector and the variance-covariance matrix into conditional and observed variables as follows:
Mean vector:
μ = [μ1, μ2]
where μ1 = [19, 45] and μ2 = [y2, y3, y4, y5]
Variance-covariance matrix:
Σ = |Σ11 Σ12|
|Σ21 Σ22|
where Σ11 is a 2x2 submatrix corresponding to the observed variables, Σ12 is a 2x4 submatrix corresponding to the observed and conditional variables, Σ21 is the transpose of Σ12, and Σ22 is a 4x4 submatrix corresponding to the conditional variables.
To calculate the conditional distribution, we use the formula:
Conditional mean:
μ1|2 = μ1 + Σ12 * Σ22⁽⁻¹⁾ * (x2 - μ2)
Conditional variance-covariance matrix:
Σ1|2 = Σ11 - Σ12 * Σ22⁽⁻¹⁾ * Σ21
where x2 is the vector of observed variables [y2, y3, y5].
Now let's substitute the given values and calculate the conditional distribution:
μ1 = [19, 45]
μ2 = [y2, y3, y4, y5] = [y2, y3, 31, y5]
x2 = [y2, y3, y5]
Σ11 = |31 154|
|154 866|
Σ12 = |-2 -8 31 70|
Σ21 = transpose(Σ12)
Σ22 = |13 3|
|3 117|
First, calculate the conditional mean:
μ1|2 = μ1 + Σ12 * Σ22⁽⁻¹⁾ * (x2 - μ2)
μ1|2 = [19, 45] + |-2 -8 31 70| * |13 3|⁽⁻¹⁾ * ([y2, y3, y5] - [y2, y3, 31, y5])
μ1|2 = [19, 45] + |-2 -8 31 70| * |13 3|⁽⁻¹⁾ * [0, 0, 0, 0]
Note that the last term becomes zero because we are conditioning on the observed variables. Hence,
μ1|2 = [19, 45]
Next, calculate the conditional variance-covariance matrix:
Σ1|2 = Σ11 - Σ12 * Σ22⁽⁻¹⁾ * Σ21
Σ1|2 = |31 154| - |-2 -8 31 70| * |13 3|⁽⁻¹⁾ * | -2 154|
Σ1|2 = |31 154| - |-2 -8 31 70| * |13 3|⁽⁻¹⁾ * | -2 154|
|
-8 866| | -8 866|
Perform the matrix operations to calculate the resulting matrix.
After obtaining the values for Σ1|2, you will have the conditional variance-covariance matrix for y1 given y2, y3, and y5.
Please note that the calculations involve matrix operations and inversions, which can be computationally intensive.
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Related Questions
Please help, i’ll give brainliest.
Answers
\(\sqrt{4x-5}\)Answer:
f(g(x))= \(\sqrt {(2/x-1)+5}\); g(f(x))= 1/[(\(\sqrt{4x-5}\))-1]
Step-by-step explanation:
- plugin g(x) whenever you see an x in f(x); \(\sqrt{4*(1/2x-2)+5}\)
then simplify into \(\sqrt{(2/x-1)+5}\)
- plugin f(x) whenever you see an x in g(x); 1/[2(\(\sqrt{4x-5}\))-2]; t5ake the GCM or 2 out of the denominator and you are left with 1/[(\(\sqrt{4x-5}\))-1]
for safety reasons, 5 different alarm systems were installed in the vault containing the safety deposit boxes at a beverly hills bank. each of the 5 systems detects theft with a probability of 0.82 independently of the others. the bank, obviously, is interested in the probability that when a theft occurs, at least one of the 5 systems will detect it. what is the probability that when a theft occurs, at least one of the 5 systems will detect it?
Answers
The probability that when a theft occurs, at least one of the 5 systems will detect it is approximately 0.9997.
How likely something is to occur is known as its probability. We can discuss the probabilities of different outcomes, or how likely they are, whenever we are unsure of how an event will turn out.
We can solve this problem using the complement rule. The probability that none of the 5 systems detect the theft is given by:
(1 - 0.82)^5 = 0.00033124
So the probability that at least one system detects the theft is:
1 - 0.00033124 = 0.99966876
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Betty has between 40 and 50 pennies that she wants to arrange in a rectangular array. She
notices she can arrange the pennies in three different ways without any gaps or spaces.
However, if Betty adds two more pennies to her collection, she can only arrange the pennies
in one way without any gaps or spaces: a straight line. How many pennies did Betty
originally have?
Note: An a × b rectangle is considered the same as a b x a rectangle?
Answers
Number of pennies that Betty can have 45
Prime numbers:Prime numbers are natural numbers with only the number itself and the number one as their factors. We are aware that a factor is any integer that evenly divides the provided number.
The prime number from 1 to 100 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
Here given that
Betty has between 40 and 50 pennies
The set of numbers of pennies that Betty may have is
41, 42, 43, 44, 45, 46, 47, 48, 49.
Given that
Betty arranged all pennies in a rectangular array in 3 different ways
Here,
Number of pennies = Area of the rectangle (in No. of pennies)
As we know Area of the rectangle = Lenght × Breadth
This means whatever the number of pennies, the number should be a Non-Prime number
=> The numbers that are non-prime numbers in the given numbers is
42, 44, 45, 46, 48, 49
It is also given that, after adding 2 pennies she can only arrange the pennies in one way without any gaps or spaces i.e a straight line.
This means after adding 2 pennies the number became a prime number so that she has only one way that she arranged them in a straight line.
Now find which number will be a prime number after adding 2
=> 42 + 2 = 44 - Non-Prime number
=> 44 + 2 = 46 - Non-Prime number
=> 45 + 2 = 47 - Prime number
=> 46 + 2 = 48 - Non-Prime number
=> 48 + 2 = 50 - Non-Prime number
=> 49 + 2 = 52 - Non-Prime number
Therefore,
Number of pennies that Betty can have 45
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Use the simplex algorithm to find the optimal solution to the following LP (solve manually): maxz= 36x1+30x2−3x3−4x4
s.t. x1+x2−x3≤5
6x1+5x2−x4≤10
∀xi≥0
Answers
The maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.
maximize: z = c1x1 + c2x2 + ... + cnxn
subject to
a11x1 + a12x2 + ... + a1nxn ≤ b1
a21x1 + a22x2 + ... + a2nxn ≤ b2
am1x1 + am2x2 + ... + amnxn ≤ bmxi ≥ 0 for all i
In our case,
the given LP is:maximize: z = 36x1 + 30x2 - 3x3 - 4x
subject to:
x1 + x2 - x3 ≤ 5
6x1 + 5x2 - x4 ≤ 10
xi ≥ 0 for all i
We can rewrite the constraints as follows:
x1 + x2 - x3 + x5 = 5 (adding slack variable x5)
6x1 + 5x2 - x4 + x6 = 10 (adding slack variable x6)
Now, we introduce the non-negative variables x7, x8, x9, and x10 for the four decision variables:
x1 = x7
x2 = x8
x3 = x9
x4 = x10
The objective function becomes:
z = 36x7 + 30x8 - 3x9 - 4x10
Now we have the problem in standard form as:
maximize: z = 36x7 + 30x8 - 3x9 - 4x10
subject to:
x7 + x8 - x9 + x5 = 5
6x7 + 5x8 - x10 + x6 = 10
xi ≥ 0 for all i
To apply the simplex algorithm, we initialize the simplex tableau as follows:
| Cj | x5 | x6 | x7 | x8 | x9 | x10 | RHS |
---------------------------------------------------------------------------
z | 0 | 0 | 0 | 36 | 30 | -3 | -4 | 0 |
---------------------------------------------------------------------------
x5| 0 | 1 | 0 | 1 | 1 | -1 | 0 | 5 |
---------------------------------------------------------------------------
x6| 0 | 0 | 1 | 6 | 5 | 0 | -1 | 10 |
---------------------------------------------------------------------------
Now, we can proceed with the simplex algorithm to find the optimal solution. I'll perform the iterations step by step:
Iteration 1:
1. Choose the most negative coefficient in the 'z' row, which is -4.
2. Choose the pivot column as 'x10' (corresponding to the most negative coefficient).
3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.
Ratios: 5/0 = undefined, 10/(-4) = -2.5
4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.
5. Perform row operations to
make all other elements in the pivot column zero.
After performing these steps, we get the updated simplex tableau:
| Cj | x5 | x6 | x7 | x8 | x9 | x10 | RHS |
---------------------------------------------------------------------------
z | 0 | 0 | 0.4 | 36 | 30 | -3 | 0 | 12 |
---------------------------------------------------------------------------
x5| 0 | 1 | -0.2 | 1 | 1 | -1 | 0 | 5 |
---------------------------------------------------------------------------
x10| 0 | 0 | 0.2 | 1.2 | 1 | 0 | 1 | 2.5 |
---------------------------------------------------------------------------
Iteration 2:
1. Choose the most negative coefficient in the 'z' row, which is -3.
2. Choose the pivot column as 'x9' (corresponding to the most negative coefficient).
3. Calculate the ratios (RHS / pivot column coefficient) to find the pivot row. We select the row with the smallest non-negative ratio.
Ratios: 12/(-3) = -4, 5/(-0.2) = -25, 2.5/0.2 = 12.5
4. Pivot at the intersection of the pivot row and column. Divide the pivot row by the pivot element to make the pivot element 1.
5. Perform row operations to make all other elements in the pivot column zero.
After performing these steps, we get the updated simplex tableau:
| Cj | x5 | x6 | x7 | x8 | x9 | x10 | RHS |
---------------------------------------------------------------------------
z | 0 | 0 | 0.8 | 34 | 30 | 0 | 4 | 0 |
---------------------------------------------------------------------------
x5| 0 | 1 | -0.4 | 0.6 | 1 | 5 | -2 | 10 |
---------------------------------------------------------------------------
x9| 0 | 0 | 1 | 6 | 5 | 0 | -5 | 12.5 |
---------------------------------------------------------------------------
Iteration 3:
No negative coefficients in the 'z' row, so the optimal solution has been reached.The optimal solution is:
z = 0
x1 = x7 = 0
x2 = x8 = 10
x3 = x9 = 0
x4 = x10 = 0
x5 = 10
x6 = 0
Therefore, the maximum value of z is 0, and the values of the decision variables are x1 = 0, x2 = 10, x3 = 0, x4 = 0.
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is the relationship represented by the table proportional or not? show how do you know on the sketchpad (Table is shown on the sketchpad.)
if it is proportional, what is the constant of proportionality (COP)?
Answers
Answer:
No, the table is not proportional. I know this because when you divide x by y the answer is not the same.
y/x = Unit rate or constant rate
Work : (The numbers that are bold are the quotient of y/x)
85 = 17 79 = 7.9 73 = 3.65 67 = 1.67
5 10 20 40
what is 4x-6x
(simply the expression by combining like terms)
Answers
Answer:
-2x
Step-by-step explanation:
hope it helps!!!!!
What is the binomial probability formula used for?
Answers
The binomial probability formula is used to calculate the probability of a specific number of successes in a fixed number of independent trials, where each trial can only result in success or failure. It is used to model situations where there are only two possible outcomes for each trial, and where the trials are independent and identically distributed.
The formula for binomial probability is:
\(P(x) = (n choose x) * p^x * (1 - p)^{n-x}\\\)
where P(x) is the probability of x successes in n trials, p is the probability of success on each trial, (n choose x) is the binomial coefficient which gives the number of ways to choose x successes from n trials, and (1 - p) is the probability of failure on each trial.
The binomial probability formula can be used in a variety of applications, such as:
Predicting the probability of a certain number of defective products in a production runEstimating the likelihood of a certain number of people out of a sample having a particular characteristicAnalyzing the probability of winning a certain number of games in a sports seasonFor more questions on Binomial Probability
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I need help solving this
Answers
Answer:
the correct answer is 302cm²
Answer:
\(232 ~cm^2\)
Step-by-step explanation:
\(2(8*10)+2(2*10)+2(8*2)=\)
\(2*80+2*20+2*16=\)
\(160+40+32=\)
\(232\)
-----------------------
hope it helps...
have a great day!!
Is 9.45 bigger than 0.945
Answers
Step-by-step explanation:
Yes it is
20 Characters needed but thank me later. Wouldnt mind if you marked me as brainliest
Is it possible to slow light to almost zero miles/second? What machine would benefit from slowing light's
speed?
Answers
Answer:
light, which normally travels the 240,000 miles from the Moon to Earth in less than two seconds, has been slowed to the speed of a minivan in rush-hour traffic — 38 miles an hour.
An entirely new state of matter, first observed four years ago, has made this possible. When atoms become packed super-closely together at super-low temperatures and super-high vacuum, they lose their identity as individual particles and act like a single super-
atom with characteristics similar to a laser.
Step-by-step explanation:
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.
investors buy a studio apartment for $240,000 . Of this amount, they have a down payment of 60,000. Their down payment is what percent of the purchase price? What percent of the purchase price would a $108,000 down payment be?
Answers
Answer:
25%
bc its 1/4 = 0.25 of the purchase price.
the other percentage is 45
108/240 = 54/120 = 18/40 = 4.5/10 = 45/100
pls help in question no 10. a)
Answers
He should sell it at the cost of 11,115.7895 Rs
Explanation:
Find original price:
100% - 5% = 95% = 9600
Let x be the original price.
Thus (95/100)x = 9600
x = (9600 x 100)/95
x = 960000/95
x = 10105.2632
Find the price in order to gain 10%.
x • 110% = 10105.2632 x 110/100 = 11,115.7895
please help answer my questions
Answers
Step-by-step explanation:
OK but what are your questions I will try my best to help you
Answer:
I do not understand :3
Step-by-step explanation:
but sure!!!!
I-Ready
Describe Angle Relationships in Triangles - Quiz - Level H
The figure shoys a triangle with unknown angles.
Which equation shows the relationship between the angles in the triangle?
mL1 + mL2 + mL3 = 360°
mL1 + mL2 + mL3 = 180°
mL1 + mL2 = 360° + mL3
mL1 + mL2 = 180° + mL3
Answers
The equation that shows the relationship between the angles in the triangle is m∠1 + m∠2 + m∠3 = 180.
What is the relationship between the angles of the triangle?The equation that shows the relationship between the angles in the triangle is determined as follows;
The sum of angles in a triangle is equal to 180 degrees.
So based on this information, the equation that shows the relationship between the angles in the triangle is formulated as;
angle 1 + angle 2 + angle 3 = 180
We can re-write the equation as follows;
m∠1 + m∠2 + m∠3 = 180
Thus, the equation that shows the relationship between the angles in the triangle is the sum of angle 1 plus angle 2 plus angle 3.
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Ramil and Carly decided to make more baked goods for the bake sale. They used 1/8 less flour to make bread
Answers
Using fraction formula ,
The flour used by ramil and Carly for making bread is 33/40lb
Fraction: fraction is a number represented as a quotient, in which a numerator is divided by a denominator.
We have given that,
Ramil and Carly used 1/2 lb flour to make the bread.
They used 1/8lb less flour to make bread than to make cookies.
So, they used flour to make the cookies = 1/2+1/8
= 5/8lb
Therefore they used 5/8lb flour to make the cookies.
they used 1/5 lb more breads to make cookies than to make brownies. Mathematically, they used cookies for making the brownies is
= 1/5 + 5/8
=(8 + 25)/40 = 33/40lb
Therefore , they used 33/40lb flour to make the brownies.
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Complete question:
Ramil amd carly decided to make more baked goods for the bake sale. They used 1/8 lb less flour to make bread than to make cookies. She used 1/5 lb more to make cookies than to make brownies. If she used 1/2 lb of flour to make the bread, how much flour did she use to make the brownies
3. Evaluate the expression
-8 + 5 - (-4) - 7
do u know this can u help me its for my math IA
Answers
Step-by-step explanation:
-8+5-(-4)-7
-6 Hope this helos you
Please help guys!!!!! I forgot who you do this?
Answers
Answer:
16 m
You need to get the complete area then get the unknown side to get the small rectangle, least subtract.
Find the complete factored form of thepolynomial:35a³b6 - 45a5 b6
Answers
find the value of x
(words to meet the word thingy)
Answers
The required measure of angle x is given as 60°, for the given quadrilateral.
A quadrilateral is a four-sided enclosed shape, whose sum of the internal angle is equal to 360°,
Examples of the quadrilateral, square, rectangle, etc.
Here,
The sum of the angle of the quadrilateral is equal to 360,
So,
x + 100 + 130 + 66 = 360
x = 360 - 296
x = 64°
Thus, the required measure of angle x is given as 60°, for the given quadrilateral.
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you are making sandwiches for a mountain hike.each sandwich uses 3 slices of bread,and you want to prepare 2 sandwiches for each person going on the hike. how many slices of bread will you need if if 6 people are going on the hike
Answers
Answer:
36
Step-by-step explanation:
3*2*6
To prepare for swim team tryouts, Leann swam in the pool. On Monday, she swam for 24 minutes. On Tuesday, she swam for 18 minutes. On Wednesday, Thursday, and Friday, she swam for 30 minutes each day. How many minutes did Leann swim this week? *
Answers
In order to find how many minutes Leann swan this week, we just need to sum the time from each day:
Monday: 24 minutes
Tuesday: 18 minutes
Wednesday: 30 minutes
Thursday: 30 minutes
Friday: 30 minutes
\(24+18+30+30+30=132\)So in total Leann swan 132 minutes this week.
Table 1.3 shows the hypothetical trade-off between different combinations of brushes and combs that might be produced in a year with the limited capacity for country X, ceteris paribus.
In the production range of 2 to 3 combs opportunity cost producing one more comb is
a)0.67
b)3.33
c)7.0
d)0.14
Answers
In the production range of 2 to 3 combs, the opportunity cost of producing one more comb is d) 0.14 brushes.
Explain about production range refer to:Opportunity cost is the cost of one choice in terms of the best alternative foregone. In this case, the opportunity cost of producing one more comb is the number of brushes that have to be given up in order to produce that additional comb.For example, if the country X is currently producing 2 combs, in order to produce one more comb, 0.14 brushes would have to be given up. This means that for every additional comb produced, 0.14 brushes would have to be sacrificed. This trade-off is reflected in Table 1.3 and is the opportunity cost of producing one more comb in the production range of 2 to 3 combs.In other words, the opportunity cost of producing one more comb is the number of brushes that would have to be sacrificed in order to produce that comb. The opportunity cost is 0.14 brushes per comb, which means that for every additional comb produced, 0.14 brushes would have to be given up.To learn more about production range refer to:
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HELP PLS I DONT WANT TO FAIL
Answers
Answer:
11.9a − 3
Step-by-step explanation:
Faults in an electrical cable are known to occur on average once per 2 km of cable. b) Calculate the probability that in a 800 m drum of cable (i) there is no fault (ii) there are exactly three faults (iii) There are fewer than two faults.
Answers
(i) The probability of no faults in 800 m of cable is approximately 0.4493 or 44.93%.
(ii) The probability of exactly three faults in 800 m of cable is approximately 0.2143 or 21.43%.
(iii) The probability of fewer than two faults in 800 m of cable is approximately 0.7182 or 71.82%.
To calculate the probabilities, we can use the Poisson distribution since the occurrence of faults follows a Poisson process with an average rate of once per 2 km of cable.
The Poisson probability mass function is given by:
P(X = k) = (e^(-λ) * λ^k) / k!
Where X is the random variable representing the number of faults, λ is the average rate of faults per unit length (2 faults per 2 km = 1 fault per km), and k is the number of faults we are interested in.
(i) Probability of no faults in 800 m of cable:
In this case, we need to calculate P(X = 0) for λ = 0.8 (since 800 m is 0.8 km).
P(X = 0) = (e^(-0.8) * 0.8^0) / 0! = e^(-0.8) ≈ 0.4493
(ii) Probability of exactly three faults in 800 m of cable:
In this case, we need to calculate P(X = 3) for λ = 0.8.
P(X = 3) = (e^(-0.8) * 0.8^3) / 3! ≈ 0.2143
(iii) Probability of fewer than two faults in 800 m of cable:
To calculate this probability, we need to sum the probabilities of 0 and 1 fault.
P(X < 2) = P(X = 0) + P(X = 1)
P(X = 1) = (e^(-0.8) * 0.8^1) / 1! ≈ 0.2689
P(X < 2) = P(X = 0) + P(X = 1) ≈ 0.4493 + 0.2689 ≈ 0.7182
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The Lone Star Shipping Company charges $14 plus $2 per pound to ship an overnight package. Discount Shipping Company charges $20 plus $1.50 per pound to ship an overnight package. What is the point where these two companies will be the same amount and what does it mean?
Answers
Answer:
each company will earn $38 when they ship a 12-pound package
Step-by-step explanation:
you can solve this algebraically by setting up two equations:
let 'c' = charges per pound
Lone Star: y = 2c + 14
Discount: y = 1.5c + 20
now set each equation equal to the other to solve for 'c':
2c + 14 = 1.5c + 20
subtract 14 from each side to get:
2c = 1.5c + 6
subtract 1.5c from each side to get:
0.5c = 6
c = 6/0.5
c = 12
if you plug 12 in for 'c' in each equation you will get y = 38
(12,38) is the point where these two companies would each earn $38 for shipping a 12-pound package
Find the slope of the line.
Help pleasee!!
Answers
Answer:
4/4
Step-by-step explanation:
y=4 x+1
4 hope that helps!!
don´t forget to thank and Brainliest.
what is a 5a − 8 = 8 + a
Answers
Answer:
a=4
Step-by-step explanation:
5a-8=8+a
4a-8=8
4a=16
a=4
Felipe calculated that he uses about 545 gallons of fuel each year. His car's owner's manual says that it is approved to use regular fuel. How much money can he save each year by switching from premium fuel, at $4.59 per gallon, to regular fuel at $4.18 per gallon?
$0.41
$2,501.55
$223.45
$2,278.10
$4,779.65
Answers
Answer:
$223.45
Step-by-step explanation:
premium fuel: 4.59 x 545
= 2501.55
regular fuel: 4.18 x 545
=2278.1
2501.55-2278.1 = 223.45
Cups are sold in packages of 8. Napkins are sold in packages of 12.
What is the fewest number of packages of cups and the fewest number of packages of napkins that can be purchased so there will be the same number of cups as napkins?
Answers
Answer:
2 Packages of Napkins, 3 Packages of Cups
Step-by-step explanation:
12 * 2 = 24
8 * 3 = 24
Answer:
3 packages of cups and 2 packages of napkins