As per the information provided, the answer to all the parts in the question will be as follows:
a. To solve the LP problem by ignoring the integer constraints in Excel using Solver, we can follow the steps below:
Enter the objective function and the constraints in a new Excel worksheet: Objective function: Maximize 15x1 + 2x2 Constraints: 7x1 + x2 <= 23 3x1 - x2 <= 5
Open the Solver add-in by clicking on Data -> Solver in the Excel menu.
Set the objective function to maximize and set the variable cells to x1 and x2. Set the constraints by clicking on Add in the Solver Parameters dialog box.
Set the Solver options to "Assume Linear Model" and "Make Unconstrained Variables Non-Negative". Click Solve. The solution to the LP problem is x1=3, x2=2.714, with an optimal objective function value of 51.714.
b. If we round up fractions greater than or equal to 1/2, the solution becomes x1=3, x2=3, with an objective function value of 51. This is not the optimal integer solution, as we will see in part d.
c. If we round down all fractions, the solution becomes x1=2, x2=2, with an objective function value of 34. This is not the optimal integer solution either, as we will see in part d.
d. To solve the ILP problem in Excel using Solver, we can follow the steps below:
Open the Solver add-in by clicking on Data -> Solver in the Excel menu. Set the objective function to maximize and set the variable cells to x1 and x2. Set the constraints by clicking on Add in the Solver Parameters dialog box. Set the Solver options to "Assume Linear Model" and "Make Unconstrained Variables Non-Negative". Add integer constraints by clicking on Add in the Solver Parameters dialog box, and setting the integer constraints for x1 and x2. Click Solve.
The solution to the LP problem is x1=2, x2=3, with an optimal objective function value of 48.
As we can see, the optimal objective function value for the LP problem (48) is lower than that for the LP problem (51.714), regardless of rounding up or down.
e. The optimal objective function value for the ILP problem is always less than or equal to the corresponding LP's optimal objective function value because the LP problem allows fractional solutions, while the ILP problem only allows integer solutions. Introducing additional constraints that restrict the variables to integers can only reduce the feasible solution space, and thus lead to a lower optimal objective function value. The LP and ILP problems would be equal if the optimal solution for the LP problem happens to be an integer solution.
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Note that the full question is:
Given the following all-integer linear program: (COMPLETE YOUR SOLUTION IN EXCEL USING SOLVER AND UPLOAD YOUR FILE. BE SURE THAT EACH WORKSHEET IN THE EXCEL FILE CORRESPONDS TO EACH QUESTION BELOW ) Max 15x1 + 2x2 s. t. 7x1 + x2 < 23 3x1 - x2 < 5 x1, x2 > 0 and integer a. Solve the problem (using SOLVER) as an LP, ignoring the integer constraints.
b. What solution is obtained by rounding up fractions greater than or equal to 1/2? Is this the optimal integer solution? c. What solution is obtained by rounding down all fractions? Is this the optimal integer solution? Explain. d. Show that the optimal objective function value for the ILP is lower than that for the optimal LP (Eg. Resolve original problem using SOLVER with the Integer requirement). e. Why is the optimal objective function value for the ILP problem always less than or equal to the corresponding LP's optimal objective function value? When would they be equal?
45degree , 30degree , 105degree are what triangle?
The angles 45 degrees, 30 degrees, and 105 degrees do not form a valid triangle.
In a triangle, the sum of the angles must be 180 degrees. However, in this case, the sum of the three angles is:
45 + 30 + 105 = 180
This tells us that these three angles can be arranged in a straight line, but they cannot form a triangle.
In a valid triangle, the sum of the two smaller angles must be greater than the measure of the largest angle. However, in this case, the sum of the two smaller angles (30 degrees and 45 degrees) is only 75 degrees, which is less than the measure of the largest angle (105 degrees).
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The perimeter of a rectangle is 72, and the width is 4 less
than 3 times the length. What is the length?
O 12
O 10
O 16
O 14
Answer is 10
Explaination:
10x3=30
30-4=26
Perimeter = length times 2 + width times 2
26 x 2= 52
10 x 2= 20
52+20=72
Please mark brainliest
how to substitute for a equation
Answer:
Simplify the given equation by expanding the parenthesisSolve one of the equations for either x or ySubstitute the step 2 solution in the other equationNow solve the new equation obtained using elementary arithmetic operationsFinally, solve the equation to find the value of the second variablewhat is the range of standard irq numbers? question 2 options: a) 0-7 b) 0-15 c) 0-32 d) 8-15
The range of standard IQR (Interquartile Range) numbers is option b) 0-15. The correct option is B).
The interquartile range (IQR) is a measure of variability used in statistical analysis. The IQR is often used as a measure of spread because it is less sensitive to outliers than the range. Standard IQR numbers are values that have been standardized to fit within a specific range of 0-15.
Standardizing the IQR allows for easier comparison of data across different datasets, as it ensures that the IQR values fall within a consistent range. The range of standard IQR numbers is often used in educational assessments and other standardized tests to report the variability of student performance or other metrics. So, the correct answer is option B).
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1. 2x^2+2x-4
2. 6x^2-7x-20
3. 2x^2-5x-3
factor the polynomial
A soccer coach bought eight soccer balls. This line plot shows the weight of each ball the coach bought?
180 represents the price of the goal, 15x represents the total price of the soccer balls
The expression consists of ONE CONSTANT 180 and another VARIABLE EXPRESSION 15x.
Since the coach purchased ONE GOAL, this corresponds to the CONSTANT, which is 180. 180 is the price of the goal.
Since the coach purchased several soccer balls, but doesn't say how many, it is the variable part, 15x, where
either 15 is the price of the ball and x is the number of balls, OR
15 is the number of balls and x is the price of each
180 represents the price of the goal
15x represents the total price of the soccer balls
The complete question is -
A soccer coach purchased one goal and some soccer balls for the team. The expression 180 + 15x represents the cost before tax. What do the different parts of the expression model? Drag the parts of the expression into the boxes to match each description.
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Help me with this question?
The system of equations that represent the question are:
6a + 8p = 6.54
7a + 5p = 5.68
(option D)
What are the system of equations that represent the question?A linear equation is an equation that has a single variable that is raised to the power of one. The general form of a linear equation is y = mx + c
Where:
m = slope c = interceptThe form of the equations in this question are:
(number of apples bought x price of one apple) + (price of one pear x number of pears bought) = total cost of the apples and pears
6a + 8p = 6.54
7a + 5p = 5.68
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The system of equations that represent the question are: 6a + 8p = 6.54 and 7a + 5p = 5.68. Option D
The system of equations that represent the questionA linear equation is an equation with one variable raised to the power of one. It can be written in the form y = mx + c, where m represents the slope and c represents the y-intercept.
The given equations are in the form of:
6a + 8p = 6.54
7a + 5p = 5.68
These equations represent the total cost of buying apples and pears based on their respective prices per unit. 'a' represents the number of apples bought, 'p' represents the number of pears bought.
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Briana found a $45 sweater that is on sale for 30% off the regular price. The sales tax rate is 6%. What is the total price Briana will pay for the sweater?
The total price Briana will pay for the sweater after discount is $34.2.
What is discount?
Discount is the state of having a bond's price lower than its face value. The difference between the purchase price and the item's par value is the discount.
Discounts are different types of price reductions or deductions from a product's cost. It is frequently employed in consumer transactions when consumers receive discounts on a range of goods. The % discount rate is provided.
Here the Sale price of sweater on sale = $45
Discount = 30%
Sale tax rate = 6%
If cost is 100% , after 30% discount and 6% sale tax rate then ,
cost price = 100%- 30%+6% = 70%+6%=76%
Now cost price = 76% of 45
=> 76%×45
=> 76/100 ×45
=>$34.2
Hence the total price Briana will pay for the sweater is $34.2.
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The thermostat in an office is set to turn the heat on any time the temperature drops below 15C. What are all the temperatures at which the heat is on.
The heat in the office is on whenever the temperature drops below 15C. Therefore, all temperatures less than 15C will turn the heat on.
The set of all temperatures that will turn the heat on can be represented mathematically using inequalities.
Let T be the temperature in Celsius.
The inequality T < 15 represents all temperatures that are less than 15C. Therefore, the set of all temperatures that will turn the heat on is given by:
{ T | T < 15 }
This set can be read as "the set of all T such that T is less than 15." This means that any temperature below 15C will turn the heat on.
For example, if the temperature is 14C, then the heat will be on because 14C is less than 15C. If the temperature is 10C, then the heat will also be on because 10C is less than 15C. However, if the temperature is 15C or higher, then the heat will not be on because 15C is not less than 15C.
In summary, the heat in the office will be on whenever the temperature drops below 15C. The set of all temperatures that will turn the heat on is { T | T < 15 }, which represents all temperatures less than 15C.
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a study is designed to examine the effect of exercise (against no exercise) on knee pain, with measurements taken at 1 week, 3 weeks, and 6 weeks. participants are randomly assigned to one of the exercise conditions. the appropriate design would be:
A study is designed to examine effect of exercise on knee pain, with measurements taken at 1, 3 and 6 weeks. The appropriate design would be C. two-way analysis of variance with one repeated measure.
A two-way mixed-design ANOVA with one repeated measure would be the best choice. This is so because exercise and time are the two variables being investigated. Exercise becomes a between-subjects factor when individuals are randomly assigned to circumstances that involve exercise or no exercise. The repetitive measure is due to the fact that each participant's measurements are collected after 1, 3, and 6 weeks, respectively.
The two-way ANOVA examines the primary impacts of time and exercise as well as their interactions. When there are both within-subjects and between-subjects variables, the mixed-design ANOVA is used. Because it combines autonomous and repetitive measures, it is known as a "mixed" measure. In this situation, leisure is the within-subjects component and exercise is the between-subjects factor.
Complete Question:
A study is designed to examine the effect of exercise (against no exercise) on knee pain, with measurements taken at 1 week, 3 weeks, and 6 weeks. Participants are randomly assigned to one of the exercise conditions. The appropriate design would be?
A. one-way repeated measures analysis of variance.
B. two-way analysis of variance.
C. two-way analysis of variance with one repeated measure.
D. one-way analysis of variance.
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Stuart created a piece of decorative wall art that has the dimensions shown. Fine the area of the wall art
The calculated area of the wall art is 474 square inches
from the question, we have the following parameters that can be used in our computation:
The composite figure
The area of the figure is the sum of the individual areas
So, we have
Area = 21 * 9 + 9 * 19 + 6 * 19
So, we have
Area = 474
Hence, the area is 474 square inches
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Mr. Sonny's science class is calculating the average number of blinks per minute. Jan blinks 75 times in 5 minutes. What is her blinking rate, in blinks per minute?
Answer:
18 blinks per min since 126 divided by 7 equals 18.
A bike wheel has a radius of 13 inches. About how far does thhe bike wheel travel in 5 rotations? Explain.
Step-by-step explanation & Answer
C = 2pir = 2pi(13) = 26pi = 81.68"
Which we can easily find.
But that is for 1 rotation in the question it says 5!
So multiply it by 5
81.68 x 5 = 408.4
Thus the answer to your problem is, 408.4
Answer:408.4
Step-by-step explanation:
Use the fact that√7 is a solution to the equation x*2=7 to find a decimal approximately of√7 whose square is between 6.9 and 7.1
Given that √7 is a solution to the equation x² = 7, we can use this equation to find a decimal approximation of √7 that satisfies the given condition.
First, we can estimate that √7 is between 2.5 and 3, since 2² = 4 < 7 and 3² = 9 > 7.
Next, we can try using a decimal approximation of √7, such as 2.6 or 2.7, and square it to see if the result is between 6.9 and 7.1.
If we try 2.6, we get:
(2.6)² = 6.76
Since this is less than 6.9, we can try a larger value, such as 2.7:
(2.7)² = 7.29
Since this is greater than 7.1, we can try a value between 2.6 and 2.7, such as 2.65:
(2.65)² = 7.0225
This result is between 6.9 and 7.1, so a decimal approximation of √7 that satisfies the given condition is approximately 2.65.
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help asap assignment closes soon!
Answer:
48 ft^3
Step-by-step explanation:
Volume = (length x width x height)/3
V = (b times b times h)/3
V = (4 x 4 x 9)/3
V = 144/3
V = 48
(units: cubic feet --> 48 ft^3)
Write each of the following expressions without using absolute value
|6m-4| if m<9
Answer:
If m < 9, then 6m - 4 is negative. Therefore, |6m - 4| is equal to -(6m - 4) or -6m + 4. Thus, the expression without absolute value is -6m + 4.
show that the numbers 0 to 7 can be written using 3 binary digits (bits). how many bits are required to write the numbers 0 to 6? 0 to 20?
Six can be represented using 3 bits, but 2⁴ = 16 unique numbers can be represented using four bits. However, 20 can be represented using 5 bits since 2⁵ = 32 unique numbers can be represented using five bits.
How many bits are required to write the numbers 0 to 6? 0 to 20?The question "show that the numbers 0 to 7 can be written using 3 binary digits (bits).Binary numbers are constructed by concatenating bits (binary digits).
Each bit can take on one of two values: 0 or 1. Binary notation is frequently utilized in computer engineering to represent data, instructions, and addresses. Three bits can represent 2³ = 8 unique numbers since each bit has two options (0 or 1).
Thus, the numbers 0 to 7 can be represented using 3 bits since 2³ = 8. We can also figure out how many bits are required to represent the numbers 0 to 6 or 0 to 20.
Six can be represented using 3 bits, but 2⁴ = 16 unique numbers can be represented using four bits. However, 20 can be represented using 5 bits since 2⁵ = 32 unique numbers can be represented using five bits.
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a bowl of kashi cereal has 25 grams of total carbohydrates of which 4g is fiber, and 1 gram of fat, how many total calories does it have?
The bowl of Kashi cereal has a total of 93 calories
Each gram of carbohydrates provides 4 calories, and each gram of fat provides 9 calories. To calculate the total calories in the bowl of Kashi cereal, we need to determine the calories from carbohydrates and fat separately and then add them together.
Calories from carbohydrates
Total carbohydrates = 25g
Fiber = 4g
Net carbohydrates = Total carbohydrates - Fiber = 25g - 4g = 21g
Calories from carbohydrates = Net carbohydrates x 4 calories/gram
Calories from carbohydrates = 21g x 4 calories/gram
Calories from carbohydrates = 84 calories
Calories from fat
Fat = 1g
Calories from fat = Fat x 9 calories/gram
Calories from fat = 1g x 9 calories/gram
Calories from fat = 9 calories
Total calories = Calories from carbohydrates + Calories from fat
Total calories = 84 calories + 9 calories
Total calories = 93 calories
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How do I divide -5 by 1,000? and is not 200
Answer:To divide -5 by 1,000, we can use a calculator or perform long division.
Using a calculator, we get -0.005 as the result.
To perform long division, we can follow these steps:
1. Write -5 as the dividend and 1,000 as the divisor.
2. Place the divisor outside the long division bracket and the dividend inside the bracket.
3. Divide the first digit of the dividend by the divisor. In this case, 1,000 does not go into -5, so we write 0 as the first digit of the quotient.
4. Bring down the next digit of the dividend (which is 0) and place it next to the 0 in the quotient.
5. Divide 1,000 into 0, which gives 0 as the next digit of the quotient.
6. Continue bringing down digits from the dividend and dividing until you have enough decimal places in the quotient. In this case, we can stop after two decimal places because we know the answer is not 200.
7. The final result is -0.005.
Therefore, -5 divided by 1,000 is equal to -0.005.
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The graph shows the supply and demand curves for a Cajun spice mix that Leroy manufactures in a home business. What will happen if Leroy sets the price at $3.99?
Group of answer choices
The demand will exceed the supply.
The market will be in equilibrium.
Five hundred spice mixes will be demanded.
The supply will exceed the demand.
If the demand curve indeed shows that 500 units are demanded at the $3.99 price point, then that is the quantity of Cajun spice mix buyers are willing to purchase at that price.
Hi! Based on the information provided and the terms mentioned, I'll try to address your question:
When analyzing a graph with supply and demand curves for a product like Leroy's Cajun spice mix, the interaction between these curves can help determine the market outcome at a specific price point. If Leroy sets the price at $3.99, we can look at how supply and demand react at that price level.
If the demand curve is above the supply curve at the $3.99 price point, this means that the quantity demanded is higher than the quantity supplied. In this case, the demand will exceed the supply, leading to a shortage of Cajun spice mix in the market. Buyers may be willing to purchase more than what Leroy can supply at this price.
On the other hand, if the supply curve is above the demand curve at the $3.99 price point, this indicates that the quantity supplied is greater than the quantity demanded. In this scenario, the supply will exceed the demand, resulting in a surplus of Cajun spice mix.
Leroy might have to lower the price to encourage more buyers to purchase his product and clear the excess inventory.
Regarding the term "Five hundred spice mixes will be demanded," this specific number can't be confirmed without more details about the graph. However,
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select all of the equations that are equivalent to 3x+5=20-x
Based on the above, the equivalent equations are 4x = 15 and 4x - 15 = 0.Hence options A and C are correct.
What is the equations about?To determine which equations are equivalent to 3x + 5 = 20 - x, we need to simplify and manipulate the original equation until it has the same form as the other equations. Here's how we can do it:
3x + 5 = 20 - x
Add x to both sides:
4x + 5 = 20
Subtract 5 from both sides:
4x = 15
So the equation 4x = 15 is equivalent to 3x + 5 = 20 - x.
Therefore, the other equations are not equivalent:
4x = 15 can be obtained by adding x to both sides of 3x + 5 = 20 - x, then adding x to both sides again to obtain 4x = 15.4x - 15 = 0 can be obtained by adding x to both sides of 3x + 5 = 20 - x, then adding 15 to both sides to obtain 4x = 15, then subtracting 15 from both sides to obtain 4x - 15 = 0.2x = 25 can be simplified to x = 12.5, which is not the same as the solution to 3x + 5 = 20 - x.-4x + 20 = -5 can be simplified to 4x = 25, which is not the same as the solution to 3x + 5 = 20 - x.x - 20 = 5 + 3x can be simplified to x = 25, which is not the same as the solution to 3x + 5 = 20 - x.Learn more about equations from
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Select all of the equations that are equivalent to 3x + 5 = 20 - x.
4x = 15
2x = 25
4x - 15 = 0
-4x+20 = -5
x - 20 = 5 + 3x
Kelvin has $1842. He wants to save 1/2 of the money and use the rest to buy a new bike. How much money will Kelvin save
Answer:
Kelvin will save (1/2) × $1,842 = $921.
Travis wants to buy a new bed that cost 45 for this dog Rusty Travis also wants to buy several packages of dog treats for six each but he doesn’t want to pay more than 15 shipping fee.
Answer:
Travis can buy a new bed for Rusty and 5 packages of dog treats for a total cost of $75 with a shipping fee of $15.
Step-by-step explanation:
Let x be the number of packages of dog treats Travis wants to buy.
The cost of the dog bed is $45.
The cost of the dog treats is $6 per package.
The shipping fee is $15 for orders less than $90.
To find out how many packages of dog treats Travis can buy without exceeding the $15 shipping fee, we can set up an inequality:
6x + 45 + 15 ≤ 90
Simplifying and solving for x, we get:
6x ≤ 30
x ≤ 5
Therefore, Travis can buy up to 5 packages of dog treats without exceeding the $15 shipping fee. If he buys 5 packages of dog treats, the total cost of his order will be:
Total cost = Cost of dog bed + Cost of 5 packages of dog treats + Shipping fee
Total cost = $45 + ($6 * 5) + $15
Total cost = $75
So, Travis can buy a new bed for Rusty and 5 packages of dog treats for a total cost of $75 with a shipping fee of $15.
YALL PLSS PLS PLS I NEED HELP
Answer:
8218.406
Go through the process yourself to make sure my answer is correct
Step-by-step explanation:
The best way to solve these problems is by breaking them up into the difference shapes you see
A. Semi-sphere
The volume of a sphere is [tex]\frac{4}{3} \pi r^3[/tex]. Since we have a semi-sphere, we divide this by 2 and get:
[tex]V=\frac{4}{6} \pi r^3\\\\V= \frac{4}{6} \pi (12)^3\\\\V=3619.115[/tex]
B. Cone
The volume of a cone is [tex]\pi r^2\frac{h}{3}[/tex]
[tex]V = \pi (12)^2\frac{30.5}{3}\\V = 4599.292[/tex]
C. Add
Add these two values:
3619.115 + 4599.292 = 8218.406
10x5+4to the power of 2+(5+30 divided by 10 how to solve
The value of the expression is 74.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
To solve this expression, we need to follow the order of operations, which is a set of rules that dictate the order in which mathematical operations should be performed. The order of operations is: Parentheses
Exponents and Multiplication and Division (performed left to right)
Addition and Subtraction (performed left to right)
Using this order, we can evaluate the expression as follows:
10 × 5 + 16+ (5 + 30 ÷ 10)
= 50 + 16 + (5 + 3)
= 50 + 16 + 8
= 74
Therefore, the value of the expression is 74.
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y=3.5x+5 and y=4x+2 when will they be the same
The park manager wants to make a timetable for busses and minibusses leavi
(a) The departure timetable is from 00:00 hrs. to 8:00am, 8:40 am 8:50 am , 9 a.m. 9:20 am , 9 a.m. 9:40 am , 11 a.m. 11:20 a.m. , 12:50 pm 2:40 pm , 3:30 pm- 15:20pm ,15:20m- 16:10pm,16:00 pm 16:50pm 17:00pm
(b) both vehicles leave the park at the same time at 10:00 a.m., 12:40 p.m. and 3:20 p.m. respectively.
(c) Traffic congestion can be controlled by properly scheduling buses and minibuses to ensure reasonable time intervals between departures.
Factorization:
Factoring is the process of finding factors of numbers or algebraic expressions.
(a) The departure time table for the 2 vehicles from 8:00am to 5:00pm
00h00 8:00 am
8:40 am 8:50 am
9 a.m. 9:20 am
9 a.m. 9:40 am
11 a.m. 11:20 a.m.
12:50 pm 2:40 am
3:30 pm 15:20
15:20 16:10
16:00 16:00
16:50 17:00
(b) Finding the time Two cars at the same time Out of the park, we need to find the least common multiple of 40 and 50. The prime factor of 40 is 2³ × 5 and the prime factorization of 50 is 2 × 5². The least common multiple is 2³ × 5² = 200.
Therefore, both vehicles leave the park at the same time at 10:00 a.m., 12:40 p.m. and 3:20 p.m. respectively.
(c) Traffic congestion can be controlled by:
Arranging buses and minibuses to ensure reasonable intervals between departures. The provides clearly visible signs and signals directing drivers and passengers to loading and unloading areas.
Assign qualified personnel to monitor the loading and unloading process and manage the flow of traffic into and out of the park. Regularly maintain and repair roads and parking lots to ensure they are in good condition and can handle traffic.
Complete Question:
The park manager wants to make a time table for buses and mini buses leaving the park at different time of the day, from 8:00am to 5:00pm . Buses and mini buses leave the park at intervals of 40minutes and 50minutes respectively after loading . Both vehicles start loading at the same time TASK: Help the park manager to
(a)Draw a departure time table for the 2vehicles from 8:00am to 5:00pm (b)Identify any time of the day when the two vehicles will leave the park at the same time.
(c)How can traffic jam be controlled?
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a sample is obtained from a population by grouping people according to age and then randomly selecting 5 people from each group. what type of sampling technique is this?
The type of sampling technique described is stratified random sampling.
In stratified random sampling, the population is first divided into homogeneous subgroups or strata based on some criteria, such as age, gender, income, or education level. In this case, the population was grouped according to age. Then, a random sample is selected from each stratum.
By doing so, the sample represents the entire population better than simple random sampling, as each subgroup is represented proportionally to its size in the population. This technique ensures that there is less variation within each subgroup, which can result in more precise estimates of the population parameters.
In summary, stratified random sampling is a type of probability sampling technique where the population is divided into subgroups, and a random sample is selected from each subgroup.
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which is indicative of an inverse relationship between x and y? multiple choice a negative p-value for the correlation coefficient a negative f statistic either a negative f statistic or a negative p-value a negative correlation coefficient group ends
The indicative of an inverse relationship between x and y is a negative correlation coefficient. When the correlation coefficient between two variables is negative, it means that as one variable (x) increases, the other variable (y) decreases. This is also known as an inverse relationship or a negative association.
A negative p-value for the correlation coefficient or a negative f statistic does not necessarily indicate an inverse relationship between x and y. A negative p-value for the correlation coefficient simply means that the observed correlation is unlikely to be due to chance, while a negative f statistic indicates that the model is not a good fit for the data.
If the correlation coefficient is negative, then it provides clear evidence of an inverse relationship between x and y.
A negative correlation coefficient is the best indicator of an inverse relationship between x and y, and it is important to interpret statistical measures carefully to determine the nature of the relationship between variables.
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manuel can paint 5 pictures in 12.5 hours. at this rate, which proportion can be used to find p , the number of pictures manuel can paint in 8 hours?
Manuel can paint 3.2 pictures in 8 hours if he can paint 5 pictures in 12.5 hours.
The proportion that can be used to find the number of pictures Manuel can paint in 8 hours is:
5 pictures / 12.5 hours = p pictures / 8 hours
To solve for p, we can cross-multiply and simplify:
5 pictures * 8 hours = 12.5 hours * p pictures40 = 12.5pp = 40 / 12.5p = 3.2We can use the formula of proportion to find the unknown value of p. The formula of proportion states that two ratios are equal to each other. Here, the ratio of the number of pictures painted to the hours taken to paint them is constant. We can use this constant ratio to find the unknown value of p. By cross-multiplying the ratio, we get the equation
5 pictures * 8 hours = 12.5 hours * p pictures.We can then solve for p by dividing both sides of the equation by 12.5 hours. The answer we get is 3.2, which means that Manuel can paint 3.2 pictures in 8 hours.
Learn more about proportion
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