Joyce wants to survey a simple random sample of 10 people from members of a gym.
Which of the following sampling methods are not examples of simple random sampling?
Select all that apply.
Select the first 10 people from alist of members
Ask 10 members in the gym on a Monday morning
Use a random number generator to select 10 members from a list
Select 10 members' names from a box without looking.
Select every 20th person from a list of members until she has 10 .
Ask all members of the gym
Answers
The sampling methods here that are not examples of simple random sampling are;
A) Select the first 10 people from a list of members.
B) Ask 10 members in the gym on a Monday morning
E) Select every 20th person from a list of members until she has 10 .
F) Ask all members of the gym
What is the importance of simple random sampling?A simple random sample is defined as a randomly selected subset of a particular population. In this method of sampling, it will be noticed that each member of the population has an exactly equal chance of being selected.
The importance of simple random sampling is that it removes every form of bias as every member has an equal chance of being selected. Thus, it will give a good representation of what we want to research.
A) Select the first 10 people from a list of members; This is not simple random sampling because it is not random but specific.
B) This is not random because it is specific which is just a monday morning and we don't have an idea of the type of people that come on the other days.
C) Use a random number generator to select 10 members from a list; This is simple random sampling because a random number generator is used.
D) Select 10 members' names from a box without looking; This is random because all members have an equal chance of being selected.
E) Select every 20th person from a list of members until she has 10; This is not random as all members don't have an equal chance of being selected.
F) Ask all members of the gym; This is not random selection.
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Related Questions
Write a quadratic function h whose only zero is 2.
h(x) =
Answers
Answer:
h(x) = (x-2)^2
Step-by-step explanation:
While hiking, Kurt ate 1/3 of a cup of nuts. Danielle ate 1/6 of a cup of nuts. How much more did Kurt eat than Danielle?
Answers
Kurt will eat 1/6 cups more than Danielle if Kurt ate 1/3 of a cup of nuts and Danielle ate 1/6 of a cup of nuts by using ratio and proportion concept.
What is ratio and proportion?When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio. Two ratios are set to be equal in an equation called a proportion. For instance, if there is 1 boy and 3 girls, the ratio would be written as 1: 3 (there are 3 girls for every boy), meaning that there are 1 in 4 boys and 3 in 4 girls.
A: b a/b is the ratio formula, which may be used to calculate any two values. A:b::c:da:b::c:da, on the other hand, is how the percentage formula is written. A ratio in mathematics displays the multiplicative relationship between two numbers.
Given,
A cup of nuts ate by Kurt=1/3
A cup of nuts ate by Danielle=1/6
(1/3)-(1/6)
=1/6
Therefore, Kurt will eat 1/6 cups more than Danielle.
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NO LINKS!! Find the specified term of the geometric sequence.
a6: a1 = 3, a2= 18, a3= 108, . . .
a6=
Answers
Answer:
23328
Step-by-step explanation:
since it is a geometrics sequence we will use the formula
[tex] {ar}^{n - 1} [/tex]
The first term(a) = 3
The second term = ar = 18
divide the first term and second term to find the common ratio
[tex] \frac{t2}{t1} = \frac{ar}{a} = \frac{18}{3} [/tex]
r = 6
Now lets find the sixth term
[tex]t6 = {ar}^{6 - 1} [/tex]
[tex]t6 = {ar}^{5} [/tex]
by substituting for the values
[tex]t6 = 3 \times {6}^{5} [/tex]
= 3 × 7776
= 23328
i hope this helped
Answer:
[tex]a_{6} = 23,328[/tex]
Step-by-step explanation:
⭐ Geometric Progression formula: [tex]a_{n} = a_1(b)^{n-1}[/tex]
[tex]a_{1}[/tex] is the first term of the geometric progression[tex]b[/tex] is the common ratio (the number each term gets multiplied by)[tex]a_{n}[/tex] is the notation for which term you are finding, where n is the term numberWe are given that [tex]a_{1}[/tex] = 3. Now, we need to find b.
b is the quotient of [tex]\frac{a__3}{a__2}[/tex].
[tex]\frac{a_3}{a_2}\\ \\\frac{108}{18}\\= 6[/tex][tex]b[/tex] = 6Let's substitute the first term and common ratio into the formula.
[tex]a_n = 3(6)^{n-1}[/tex]
The problem wants us to solve for the 6th term, so we have to substitute 6 for n and solve.
[tex]a_6 = 3(6)^{6-1}\\a_6 = 3(6)^5\\a_6 = 3(7,776)\\a_6 = 23,328[/tex]
Which pairs of rectangles are similar polygons? Select Similar or Not Similar for each pair of rectangles. Similar Not Similar A and B Similar – A and B Not Similar – A and B B and C Similar – B and C Not Similar – B and C A and C Similar – A and C Not Similar – A and C Three rectangles labeled A, B, and C. The length of rectangle A is labeled as 100 centimeters and the width is labeled as 80 centimeters. The length of rectangle B is labeled as 120 centimeters and the width is labeled as 100 centimeters. The length of rectangle C is labeled as 90 centimeters and the width is labeled as 72 centimeters.
Answers
A polygon is a plane shape with a minimum of three straight sides. Thus the appropriate answer are:
i. A and B Not Similar
ii. B and C Not Similar
iii. A and C Not Similar
Polygons are majorly plane shapes which have straight sides. They are named with respect to the number of their sides, and the minimum sides is three. Some common examples are: trigon (3 sides), octagon (8 sides), hexagon (6 sides), pentagon (5 sides) , etc.
Two or more shapes are said to be similar if and only if they have some common properties with respect to their sides or internal angles.
Considering the ratios of the sides of the given polygons, it can be deduced that:
i. A and B Not Similar
ii. B and C Not Similar
iii. A and C Not Similar
Thus none of the polygons are similar.
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Kate and Miley are selling girl scout cookies Kate sold 27 boxes in 45 minutes Miley sold 12 boxes in 30 minutes at the same rates how many total boxes will the girls have sold in one hour?
Answers
Kate and Miley sold 60 boxes of cookies in one hour.
What is ratio?Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.
If a and b are two values, their ratio will be a:b.
Given that,
Cookies sold by Kate in 45 minutes = 27 boxes.
Also,
Cookies sold by Miley in 30 minutes = 12 boxes.
To find the total boxes of cookies sold by girls in one hour,
Use ratio method,
Cookies sold by Kate in 3/4 hours = 27 boxes,
Cookies sold by Kate in 1 hour = 27 x (4/3) = 36
Cookies sold by Miley in 1/2 hours = 12 boxes,
Cookies sold by Miley in 1 hour = 12 x 2 = 24 boxes
Total cookies sold by Kate in Miley in one hour = 36 + 24 = 60
There are 60 boxes of cookies sold by the girls in one hour.
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Luis has 60 m of fencing to build a four-sided fence around a rectangular plot of land. The area of the land is 216 square meters. Solve for the dimensions (length and width) of the field. The dimensions are __ meters by __ meters .
Answers
The dimensions are 12 meter by 18 meter .
what is perimeter of rectangle ?perimeter of rectangle = 2(length + width)
length and width of the Luis plot by L and W, respectively.
We know that the perimeter, is 60 meters. So we can write:
2L + 2W = 60
Simplifying this equation, we can divide both sides by 2:
L + W = 30
now , area of the plot is 216 square meters:
L x W = 216
use substitution to solve for one of the variables. Let's solve for L in the first equation:
L = 30 - W
We can substitute this expression for L into the second equation:
(30 - W) x W = 216
[tex]W^2 - 30W + 216 = 0[/tex]
We can solve this quadratic equation using the quadratic formula:
W = [30 ± [tex]\sqrt{30^2 - 4 * 1 * 216}[/tex] / 2
Simplifying:
W = [30 ± 6] / 2
So W = 18 or W = 12.
If W = 18, then L = 30 - 18 = 12.
If W = 12, then L = 30 - 12 = 18.
Therefore, the dimensions are 18 meters by 12 meters or 12 meters by 18 meters.
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9 more than the quantity of 6 less than a number n is 18
Answers
Answer: n = 15
Step-by-step explanation:
9 + n - 6 = 18
3 + n = 18
n = 15
Test the claim about the difference between two population means
μ1
and
μ2
at the level of significance
α.
Assume the samples are random and independent, and the populations are normally distributed.Claim:
μ1=μ2;
α=0.01
Population statistics:
σ1=3.6,
σ2=1.4
Sample statistics:
x1=18,
n1=27,
x2=20,
n2=26
Determine the alternative hypothesis.
Ha:
μ1
▼
greater than>
greater than or equals≥
less than<
less than or equals≤
not equals≠
μ2
Determine the standardized test statistic.
z=nothing
(Round to two decimal places as needed.)
Determine the P-value.
P-value=nothing
(Round to three decimal places as needed.)
What is the proper decision?
A.Fail to reject
H0.
There is enough evidence at the
1%
level of significance to reject the claim.
B.Reject
H0.
There is enough evidence at the
1%
level of significance to reject the claim.
C.Fail to reject
H0.
There is not enough evidence at the
1%
level of significance to reject the claim.
D.Reject
H0.
There is not enough evidence at the
1%
level of significance to reject the claim
Answers
The correct answer is Option C. The proper decision, in this case, is "Fail to reject H0. There is not enough evidence at the 1% level of significance to reject the claim."
The alternative hypothesis, in this case, is "μ1 ≠ μ2", as the claim being tested is that the two population means are equal.
To calculate the standardized test statistic, we can use the following formula:
z = (x1 - x2) / sqrt(((σ1^2) / n1) + ((σ2^2) / n2))Substituting in the values given in the problem, we get:
z = (18 - 20) / sqrt(((3.6^2) / 27) + ((1.4^2) / 26))
z = (-2) / sqrt((12.96 / 27) + (1.96 / 26))
z = (-2) / sqrt(0.481 + 0.075)
z = (-2) / sqrt(0.556)
z = (-2) / 0.746
z = -2.67
To calculate the P-value, we can use the standard normal table to look up the probability of getting a value of -2.67 or lower if the null hypothesis were true. The P-value in this case would be the probability of getting a value equal to -2.67 or lower, plus the probability of getting a value equal to 2.67 or higher.
Using the standard normal table, we find that the probability of getting a value equal to -2.67 or lower is 0.0039, and the probability of getting a value equal to 2.67 or higher is 0.9961. Therefore, the P-value is 0.0039 + 0.9961 = 1.0000.
Since the P-value is equal to 1.0000, which is greater than the level of significance α = 0.01, we fail to reject the null hypothesis.
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Using three mixed numbers as side lengths draw an equilateral triangle with a perimeter of 8 and 1/4 feet.
Answers
The side of the equilateral triangle is 2 ³/4 feet, having perimeter 8 ¹/₄ feet.
What is an equilateral triangle?If all three of a triangle's sides are the same length, the triangle is said to be equilateral. Congruent sides refer to sides that have the same length, and they characterize an equilateral triangle.
Given that,
The perimeter of equilateral triangle = 8 ¹/₄ feet.
Simplify the rational term.
8 ¹/₄ = (32 + 1) / 4 = 33 /4.
Let each side of an equilateral triangle is a feet.
The perimeter of the equilateral triangle = 3a
Since, 3a = 33/4
a = 11/4
a = 2 ³/4
The required side of the equilateral triangle is 2 ³/4.
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Seventeen less than the product of 3 and a number is -50. what is the answer?
Answers
The number from the expression is 22. 3
What is an algebraic expression?An algebraic expression can be defined as a mathematical expression that consists of variables, terms, constants, coefficients, and factors.
These expressions are also seen to be made up of mathematical or arithmetic operation, such as;
SubtractionAdditionMultiplicationDivisionBracketParentheses, etcSome examples of algebraic expressions;
2x + 6
3x + 8
From the information given;
Let the number be x
Then'
3x - 17 = - 50
collect like terms
3x = 67
Make 'x' the subject
x = 22. 3
Hence, the value is 22. 3
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Can someone answer this for me. I NEED HELPPP
Find the value of y if m∠3 =65° and m∠1 =(15y+5)°
Answers
Answer: 4 i think
Step-by-step explanation:
65=15y+5
65 - 5 = 15y +5 -5
60 = 15y
60/15 = 15y/15
4 = y
65-5=15y+5-5
60=15y
60/15=15y/15=4y
Consider the polynomial g(x) = 4x³ - x² - 24x + 6
a. List all possible rational zeros of the polynomial. (Assume all numbers shown are both + and -).
O 1, 2, 4, 1/2, 1/3, 2/3, 4/3, 1/6
O 1, 2, 3, 4, 6, 1/2, 3/2, 1/3, 2/3, 4/3, 1/4, 3/4, 1/6
O 1, 2, 3, 4, 6, 1/2, 3/2, 1/4, 3/4
1, 2, 3, 6, 1/2, 3/2, 1/4, 3/4
b. List all actual zeros of the polynomial (rational, irrational, real, and complex).
Give exact answers, separated by commas as necessary.
Zeros:
Answers
a. The rational roots of the polynomial g(x) = 4x³ - x² - 24x + 6 is 1/4.
b. The rational and irrational roots of the polynomial g(x) = 4x³ - x² - 24x + 6 are 1/4 and ± √6.
What is a factor of a polynomial?We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given, A cubic polynomial function g(x) = 4x³ - x² - 24x + 6.
Therefore,
g(x) = 4x(x² - 6) - 1(x² - 6).
g(x) = (4x - 1)(x² - 6).
g(x) = (4x - 1)(x + √6)(x - √6).
Hence, x = 1/4, ± √6.
So, The roots of the polynomial are 1/4 and ± √6.
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A tent pole that is 8 feet tall is secured to the ground with a piece of rope that is 17 feet long from the top of the tent pole to the ground. Determine the number of feet from the tent pole to the rope along the ground.
40 feet
30 feet
15 feet
9 feet
Answers
The distance between the tent pole to the rope along the ground is 15 feet.
What is a cone?
A cone is a three-dimensional geometric form with a flat base and a smooth tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that connect the apex—the common point—to every point on a base that is in a plane other than the apex.
Given that length of the tent pole is 8 feet.
The angle between the tent pole and the ground is 90°.
Thus the tent pole, the rope and the ground form a right angle triangle.
According too Pythagorean theorem, the square of the hypotenuse is equal to the sum of the square of the legs.
Here the legs of the right angle triangle is the tent pole and the the distance the tent pole to the rope along the ground.
Assume that the distance the tent pole to the rope along the ground be x.
The length of the rope is 17 feet which is hypotenuse of the right angle triangle.
Therefore,
x² + 8² = 17²
x² + 64 = 289
x² = 225
x = 15
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Answer: 15 feet
Step-by-step explanation:
first we grab 17 feet a square it
17^2 = 289
then we square 8 feet
8^2 = 64
subtract
289-64= 225
what squared equals 225?
15 does
CAN SOMEONE HELP WITH THIS QUESTION?✨
Answers
The time required to grow $5000 to $8300, if the rate of interest is 7.5 %, is 7 years.
What is interest?When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.
Given:
The principal amount, p = $5000,
The amount, A = $8300
The rate of interest, r = 7.5 %,
Calculate the time as shown below,
[tex]A = p(1 + r / 400)^{4n}[/tex]
8300 = 5000 (1 + 7.5 / 400)⁴ⁿ
8300 / 5000 = (1 + 0.01875)⁴ⁿ
1.66 = (1.0188)⁴ⁿ
1.66 = (1.077)ⁿ
(1.077)⁷ = (1.077)ⁿ
n = 7
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PLEASE HELP god bless you /Barak Allah fic A sports team has 65 men and 35 women as members. A new activity has just begun and some new members have joined. Given that the number of men is now 60% of the total members, how many of the 50 new members were women?
Answers
The required number of new boys in a sports team is 62.
As mentioned in the question, A sports team has 65 men and 35 women as members. A new activity has just begun and some new members have joined.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
here,
Given that the number of men is now 60% of the total members, how many of the 50 new members were women is to be determined,
Percentage of women, in the team = 100 - 60 = 40%
40% of total members are women = 35 + 50
Total members = 85 / 40%
Total member = 212
Number of new member that are boys = 212 - 85 - 65 = 62 boys
Thus, the required number of new boys in a sports team is 62.
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Which equations have the same value of X as 5/6x + 2/3=-9? Select three options
Answers
The equations have the same value of x are,
A) 5x + 4 = -54
B) 6(5/6x + 2/3) = -9(6)
C) 5x = -58
What is equation?
The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation
3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."
Consider the given equation
5/6 x + 2/3 = -9
Subtract 2/3 from both sides,
5/6x + 2/3 - 2/3 = -9 - 2/3
5/6x = -29/3
[tex]x = -\frac{29}{3}*\frac{6}{5}\\ x = -11.6[/tex]
The value of x is -11.6.
Hence, the equations have the same value of x are,
A) 5x + 4 = -54
B) 6(5/6x + 2/3) = -9(6)
C) 5x = -58
After solving above these equations we get the same value of x which is -11.6.
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Complete question:
Which equations have the same value of x as 5/6x + 2/3 = -9? Select three options. 6(5/6x + 2/3) = -9
6(5/6x + 2/3) = -9(6)
5 x + 4 = -54 5 x + 4 = -9
5 x = -13
5 x = negative 58
Can someone help me with this? I’m confused
Answers
Answer:
Option 4
Step-by-step explanation:
The domain of this function is the possible values of n that are suitable for this function. Since n represents a number of vehicles, the domain of n should be a whole number (since you cannot have a negative number of vehicles or half of a vehicle).
hope this helps :)
A stage manager is trying to seat important guests in the front row of a theater. The row has seven seats, and she would like a diplomat in the first seat, a singer in the second seat, and a movie director in the third seat. After this, the remaining diplomats, singers, and movie directors will be seated in the last four seats, in no particular order. If there are 3 diplomats, 2 singers, and 2 directors attending the show, how many different front row plans are possible?
Answers
Answer: 12 row plans
The first seat has 2 possible options, the 2 directors. The second seat has another 2 options. With each director comes 2 options for the second seat, so 2 x 2=4 possible options for the 1st and 2nd seats. The third seat has 3 options. That means for each combination of the 1st and 2nd seat, there are 3 possible options. 4x3=12 combinations.
Step-by-step explanation:
Please help me with my question step by step
give brainliest.help
Answers
The required, team 3, tower garden donation shows the proportional relationship between weeks and donation,
What is proportionality?Proportionality is described as the relationship between two or more sets of values, and whether these values are directly proportional or inversely proportionate to one other.
here,
From the table,
The ratio of a week to the donation of the individual team must be the same as the ratio of the preceding week and the donation of the respective team,
So,
Team 1,
1 / 1 = 2 / 3[1/4], false
Similarly, team 2 and team 4's relationship is also not proportional,
Now, team 3
1 / [2 1 / 3] = 2 / [4 2/3 ]
3 / 7 = 3/7
Thus, The necessary, team 3, tower garden gift illustrates the proportional relationship between weeks and donation.
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brett needs 2/3 cups of yogurt for one smoothie. He wants to know how many smoothies he can make with 2 4/6 cups of yogurt. which division expression can be used to represent the situation
Answers
Answer:
4
Step-by-step explanation:
2 4/6 = 16/6Based on the given conditions, formulate:
16/6 ÷ 2/3
Divide a fraction by multiplying its reciprocal:
16/6 × 3/2
(16 × 3) ÷ (6 × 2)
48/12 = 4
Thus, Brett can make 4 smoothies with 2 4/6 cups of yogurt.
Solve for <1. (Will mark as brainiest!)
Answers
Answer:
< 1 = 64°
Step-by-step explanation:
First at all the sum of 2 angles should be 180°
< 3 + 116° = 180°
< 3 = 180 - 116
< 3 = 64°
Then, the sum of intern angles of a triangle must sum 180°, so:
< 1 + 52° + < 3 = 180°
< 1 +52 + 64 = 180
< 1 = 180 - 64 -52
< 1 = 64°
30 POINTS. The county rummage sale arranges 250 tables in three groups. The group on the left has 75 tables. The group on the right has 80 tables. Write an equation to find the number of tables in the middle group. Then sovle your equation.
Answers
Answer: There are 95 tables in the middle group
Step-by-step explanation:
There are a total number of 250 tables.
There are three groups.
We know how many tables the left and right groups have
let x be the number of tables in the middle
75+80+x=250
155+x=250
x=95
A simple random sample of n subjects is selected in such a way that every possible sample of the same size n has the same chance of being chosen. (A simple random sample is often called a random sample, but strictly speaking, a random sample has the weaker requirement that all members of the population have the same chance of being selected.) Determine whether each of the following is a simple random sample and a random sample. Complete parts a through c. .. a. In Major League Baseball, there are 30 teams, each with an active roster of 25 players. The names of the teams are printed on 30 separate index cards, the cards are shuffled, and one card is drawn. The sample consists of the 25 players on the active roster of the selected team. This sample a simple random sample. It v a random sample. b. For the same Major League Baseball population described in part (a), the 750 names of the players are printed on 750 separate index cards, and the cards are shuffled. Twenty-five different cards are selected from the top. The sample consists of the 25 selected players. This sample V a simple random sample. It v a random sample c. For the same Major League Baseball population described in part (a), a sample is constructed by selecting the 25 youngest players. This sample a simple random sample. It a random sample.
Answers
This sample a simple random sample. It v a random sample.
What is simple random sample?A selection of participants from a population is randomly chosen by the researcher using simple random sampling, a sort of probability sampling. The probability of getting chosen is the same for every person in the population.A simple random sample is a subset of people picked at random from a larger group, all with the same probability. It is the process of choosing a sample at random.Simple random sampling, systematic sampling, stratified sampling, and cluster sampling are the four main types of random (probability) sampling.This sample a simple random sample. It v a random sample.To learn more about simple random sample refer to:
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G(x) = 4x - 5, find g(3)
Answers
Step-by-step explanation:
this is a college question ? and you don't know how to do that ?
think back to elementary and middle school. and you had to use that all the way through high school as a very, VERY basic skill.
Focus !
g(3) just means that x = 3, and we need to replace every occurrence of x by 3. and then we calculate the result.
g(3) = 4×3 - 5 = 12 - 5 = 7
that's all to it.
piecewise function.
Express the function graphed on the axes below as a
Please help me
Answers
The piecewise function is:
f(x) = x + 1 if x < 2
f(x) = -7x + 42 if x > 5
How to express the function graphed?On the graph we can see a piecewise function (piecewise means that it has different equations defined for different intervals in the domain).
On the left side, we can see a linear equation that comes from negative infinity and ends at x = 2 with an open circle (so the domain does not contain that value).
That line passes through (-1, 0) and (0, 1), then the slope is:
a = (1 - 0)/(0 -(-1)) = 1
And the y-intercept is y = 1, then the equation of the line is:
y = x + 1
The other line starts at x = 5 (again, open circle) and keeps going, it passes through the points (5, 7) and (6, 0)
The slope is:
a = (0 - 7)/(6 -5) = -7
Then the line is something like:
y = -7*x + b
To find b, we use the point (6, 0)
0 = -7*6 + b
7*6 = 42 = b
Then this line is:
y = -7x + 42
Concluding, the piecewise function is:
f(x) = x + 1 if x < 2
f(x) = -7x + 42 if x > 5
The complete question is : Help please!! Express the function graphed on the axes below as a piecewise function.
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Two angles are complementary. The measure of one angle is 17 degrees. What is the measure of the other angle?
Answers
The measure of the other angle is 73°.
What are complementary angles?
Complementary angles are those whose combined angle is exactly 90 degrees. 30 degrees and 60 degrees, for instance, are complimentary angles.
How do you find a complementary angle?
Two angles are said to be complimentary if their sum is 90 degrees. So, to find the complement of an angle, subtract it from 90.
Here, we have
Given
Two angles are complementary. If one measures 17 degrees.
Complementary angles are two angles that add up to exactly 90 °.
∠A + ∠B = 90°
17 + ∠B = 90°
∠B = 90 - 17
∠B = 73°
Hence, the measure of the other angle is 73°.
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3/4x + 2/3y - 3/8x + 1/2y
Answers
[tex]\frac{3}{8} x+\frac{7}{6} y[/tex].
Step-by-step explanation:1. Write the expression.[tex]3/4x + 2/3y - 3/8x + 1/2y[/tex]
2. Operate with like terms.a) First, start by operating with the terms that contain the "x" variable.
[tex]3/4x- 3/8x\\ \\\frac{3}{4}x-\frac{3}{8}x\\ \\ \frac{3*2}{4*2}x-\frac{3}{8}x\\ \\\frac{6}{8}x-\frac{3}{8}x\\ \\x(\frac{6}{8} -\frac{3}{8} )\\ \\x(\frac{6-3}{8} )\\ \\x(\frac{3}{8} )\\ \\\frac{3}{8}x[/tex]
b) Start with terms containing "y".
[tex]2/3y+1/2y\\ \\\frac{2}{3}y +\frac{1}{2} y\\ \\\frac{2*2}{3*2}y +\frac{1*3}{2*3} y\\ \\\frac{4}{6}y +\frac{3}{6} y\\ \\y(\frac{4+3}{6})\\ \\y(\frac{7}{6})\\ \\\frac{7}{6} y[/tex]
3. Put the terms together.[tex]\frac{3}{8} x+\frac{7}{6} y[/tex].
27/22 as a decimal rounded to the nearest hundreth
Answers
The expression as a rounded decimal is 1.23
How to evaluate the expression as a rounded decimalFrom the question, we have the following parameters that can be used in our computation:
27/22
To start with, we evaluate the expression using a calculator
So, we have the following representation
27/22 = 1.22727272727
Next, we approximate to the nearest hundredth
So, we have the following representation
27/22 = 1.23
Hence, the approximated expression is 1.23
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Enter the x,y value in the text box below for the following table of values where the x value is -2
y = 3x + 4
Answers
Answer:
x=-2
y = 3× -2 + 4
y= -6 + 4
y = -2
A local manufacturing firm produces four different metal products, each of
which must be machined, polished and assembled. The specific time
requirements (in hours) for each product are as follows:
The firm has available to it on weekly basis, 480 hours of machining time, 400 hours of polishing time and 400 hours of assembling time. The unit profits on the product are Birr 360, Birr 240, Birr 360 and Birr 480, respectively.The firm has a contract with a distributor to provide 50 units of product I, and 100 units of any combination of products II and III each week. Through other customers the firm can sell each week as many units of products I, II and III as it can produce, but only a maximum of 25 units of product IV. How many units of each product should the firm manufacture each week to meet all contractual obligations and maximize its total profit? Make a mathematical model for the given problem. Assume that any unfinished pieces can be finished the following week.
Answers
Step-by-step explanation:
The firm should manufacture 50 units of product I, 100 units of product II, and 100 units of product III each week to meet all contractual obligations and maximize its total profit.
To set up the mathematical model for this problem, we can use variables to represent the number of units of each product that the firm manufactures each week. Let x1 be the number of units of product I, x2 be the number of units of product II, x3 be the number of units of product III, and x4 be the number of units of product IV.
The first constraint is that the firm has a contract to provide 50 units of product I and 100 units of any combination of products II and III each week. This can be represented as:
x1 = 50
x2 + x3 = 100
The second constraint is that the firm has a maximum of 480 hours of machining time, 400 hours of polishing time, and 400 hours of assembling time each week. The time required for each product can be represented as:
x16 + x28 + x34 + x410 <= 480 (machining time)
x14 + x26 + x32 + x48 <= 400 (polishing time)
x14 + x24 + x34 + x46 <= 400 (assembling time)
The third constraint is that the firm can sell as many units of products I, II, and III as it can produce, but only a maximum of 25 units of product IV. This can be represented as:
x1 >= 0
x2 >= 0
x3 >= 0
x4 <= 25
The objective is to maximize the firm's total profit, which is the sum of the profits for each product. The unit profits for each product are Birr 360, Birr 240, Birr 360, and Birr 480, respectively. The total profit can be represented as:
360x1 + 240x2 + 360x3 + 480x4
The complete mathematical model for this problem is:
Maximize: 360x1 + 240x2 + 360x3 + 480x4
Subject to:
x1 = 50
x2 + x3 = 100
x16 + x28 + x34 + x410 <= 480
x14 + x26 + x32 + x48 <= 400
x14 + x24 + x34 + x46 <= 400
x1 >= 0
x2 >= 0
x3 >= 0
x4 <= 25
This model can be solved using linear programming techniques to find the values of x1, x2, x3, and x4 that maximize the total profit while satisfying all of the constraints. In this case, the optimal solution is x1 = 50, x2 = 100, x3 = 100, and x4 = 0, which corresponds to manufacturing 50 units of product I, 100 units of product II, and 100 units of product III each week. This meets all of the contractual obligations and maximizes the total profit.
The objective is to maximize total profit, which is given as
P = 360 [tex]x_1[/tex]+ 240[tex]x_2[/tex]+ 360[tex]x_3[/tex] + 480[tex]x_4[/tex]
What is Linear Programming Problem?The goal of the Linear Programming Problems (LPP) is to determine the best value for a given linear function. The ideal value may be either the highest or lowest value. The specified linear function is regarded as an objective function in this situation.
Let[tex]x_1[/tex] , [tex]x_2[/tex], [tex]x_3[/tex] and [tex]x_4[/tex] be the number of units of product I, II, III and IV to be produced, respectively.
The constraints are that the time requirements for each product should not exceed the available time, the firm is contractually obligated to produce 50 units of product I and 100 units of products II and III, and the firm can sell at most 25 units of product IV.
These constraints can be written mathematically as:
3[tex]x_1[/tex] + 2 [tex]x_2[/tex]+ 2 [tex]x_3[/tex] + 4[tex]x_4[/tex] ≤ 480 (Machining)
[tex]x_1[/tex] + [tex]x_2[/tex] + [tex]x_3[/tex] + 3[tex]x_4[/tex] ≤ 400 (Polishing)
2[tex]x_1[/tex] + [tex]x_2[/tex]+ 2 [tex]x_3[/tex] + [tex]x_4[/tex] ≤ 400 (Assembling)
and, [tex]x_1[/tex] ≥ 50 (Product I)
[tex]x_2[/tex] + [tex]x_3[/tex] ≥ 100 (Products II and III)
[tex]x_4[/tex] ≤ 25 (Product IV)
[tex]x_1[/tex] , [tex]x_2[/tex], [tex]x_3[/tex] , [tex]x_4[/tex] ≥ 0
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