The lowest amount in pounds that Noah can pay to purchase pencils is ≥ 16.8 pounds.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, Noah wants to buy exactly 84 pencils.
Pack of 10 pencils for 2 pounds.
So, the cost of each pencil is 2/10 =0.2 pounds
Then the cost of 84 pencils is
8 packs + 4 pencils
= 8×2+4×0.2
= 16+0.8
= 16.8 pounds
So, the cost of 84 pencils ≥ 16.8 pounds
Therefore, the lowest amount in pounds that Noah can pay to purchase pencils is ≥ 16.8 pounds.
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If U And V Are Orthogonal, What Is The Magnitude Of U Times V?
If U and V are orthogonal then the magnitude of U times V will be U.V = 0 or |UxV| = uv.
U and V are two orthogonal vectors.
since the angle between them is θ = 90⁰
let u and v be the magnitudes of the vectors U and V respectively.
so first dot-product: If two non-zero vectors are orthogonal than the dot product of these vectors will be zero. Dot product of two vectors is expressed by:
U.V = uv cosθ
since these vectors are orthogonal so,
U.V = uv cos90⁰ = 0
And Cross-product: Magnitude Cross product of two orthogonal vectors will be equal to product of magnitude of these vectors.
|UxV| = uv sin θ
|UxV| = uv sin 90⁰ = uv
Therefore, U.V = 0, |UxV| = uv.
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A polynomial function is represented by the data in the table.
Choose the function represented by the data.
f(x) = −14x − 11
f(x) = −12x + 1
f(x) = 2x2 + 1
f(x) = x2 − 6x + 1
a survey was conducted on 218 undergraduates from duke university who took an introductory statistics course in spring 2012. among many other questions, this survey asked them about their gpa and the number of hours they spent and studying per week. based on this study, can we conclude that studying longer hours leads to higher gpas?
No, we cannot conclude that studying longer hours leads to higher GPAs based on this survey.
This survey only provides us with the average GPAs and average hours per week spent studying for a sample of 218 undergraduates from Duke University who took an introductory statistics course in spring 2012. This is not enough information to draw a conclusion about the correlation between hours of study and GPA. To do this, we would need to look at the correlation between the two variables. To calculate the correlation, we would need the individual data points of the GPAs and hours of study for each respondent. We could then calculate the Pearson correlation coefficient and the significance of the correlation. This would provide us with a more definitive answer to our question.
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The bug has friends in nearby trees.
For each description, write equations similar to Problem 2.
Assume each bug starts at the same position as the bug in Problem 2.
1. The equation when Buggo crawls did 28 minutes at a rate of -2 centimeters per minute will be x = -2 × 28
2. The equation when Buggy slides for 3.2 seconds at -8.1 millimeters per second will be: y = -8.1 × 3.2
3. The equation when Buggum creeps for 3.5 seconds and finishes at -28.5 centimeters will be 3.5x = -28.5
How to solve the equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
The equation when Buggo crawls did 28 minutes at a rate of -2 centimeters per minute will be:
Let x = total centimeters
x = -2 × 28
The equation when Buggy slides for 3.2 seconds at -8.1 millimeters per second will be:
Let y = ital millimeters
y = -8.1 × 3.2
The equation when Buggum creeps for 3.5 seconds and finishes at -28.5 centimeters will be 3.5x = -28.5
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Let S(t) be the number of students enrolled in a school district in terms of the number of years, t, after 2000.
Which statements regarding function S are true? Select TWO that apply.
Answer:
S(t) is a function, because there is a unique output value (number of students) for each input value (number of years after 2000)
S(t) can be represented by a graph, where the horizontal axis represents the number of years after 2000, and the vertical axis represents the number of students
Step-by-step explanation:
The statements regarding function S are true are:
S(5) = 2024 means there were 2024 students in 2005.
S(10)= S(5) there same number of students in 2005 and 2010.
We have function,
S(t)= 2000t
First, S(0) in 2000 means that there were 2000 students in starting.
Second, S(5) = 2024 means there were 2024 students in 2005.
Third, S(10)= S(5) there same number of students in 2005 and 2010.
Fourth, S(15)- S(10)= -40 means that there were 40 less students in 2015 than in 2010.
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I need help with the x and y intercepts I’m to exhausted to comprehend anything please help me
The solutions to the x and y intercepts are;
1) The slope will be positive.
2) The student is incorrect because (0, 5) is not the x-intercept.
3) The point at which the graph crosses the x axis is; x = 2
4) The point at which the graph crosses the y axis is; y = 6
5) x-intercept is x = 4 and the y-intercept is; y = 2
6) The x-intercept is x = 6 and the y-intercept is; y = 2
7) The x-intercept is x = 2 and the y-intercept is; y = 10
How to find the x and y-intercepts?1) The formula for the slope of a graph is;
Slope = Change in y value/change in x value
Thus, if both x and y intercepts are negative, then the slope will be positive.
2) The equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
The equation can be rewritten as;
y = -¹/₂x + 5
At y =0,
0 = -¹/₂(x) + 5
x = 8
Thus, (0, 5) is not the x-intercept.
3) The point at which the graph crosses the x axis is the x-intercept which is when y = 0. Thus;
2x + 0 = 4
2x = 4
x = 2
4) The point at which the graph crosses the y axis is the y-intercept which is when x = 0. Thus;
3(0) + y = 6
y = 6
5) 2x + 4y = 8
x-intercept; 2x + 4(0) = 8
x = 4
y-intercept; 2(0) + 4y = 8
y = 2
6) x + 3y = 6
x-intercept; x + 3(0) = 6
x = 6
y-intercept; 0 + 3y = 6
y = 2
7) 5x + y = 10
x-intercept; 5x + 0 = 10
x = 2
y-intercept; 5(0) + y = 10
y = 10
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Jaxson bought a pair of sunglasses online for $66. He used a coupon code to
get a 30% discount. The website also applied a 15% processing fee to the price
after the discount. How much was the discount, in dollars and cents?
The discount was 17 dollars and 87 cents.
What is a discount?
A discount is a reduction in the price of a product or service. It can be offered for a variety of reasons, such as to encourage sales or to reward loyal customers.
We have,
price of pair of sunglasses for $66,
coupon code discount of 30%,
15% processing fee to the price.
The final price is:
$66 * (1 - 30%) * (1 + 15%)
$66 * 0.7 * 1.15
$53.13
So, the actual discount is,
$(71 - 53.13)
= $17.87
Hence, the discount was 17 dollars and 87 cents.
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I buy 4 gallons of milk at the grocery store. Each gallon sells for $3. 50. Is this relationship a function? Justify your claim
Yes, this relationship is a Funtion.
The relationship between the no of gallons of milk purchased and the total cost can be represented by this equation:
y = 3.5x
where y is the total cost and x represents the number of gallons of milk purchased. A function is a collection of ordered pairs (x, y) with exactly one value of y for each value of x. for each input (x), just one output (y) is created.
In this situation, there is only one equivalent value of y for each value of x .We may see this by putting different value of x into the equation and get ing a different result for y.
For example, when x = 1, y = 3.5 ×1 = 3.5
when x = 2, y = 3.5 × 2 = 7
when x = 3, y = 3.5 × 3 = 10.5
and so on.
So, the relationship between the number of gallons of milk purchased and the total cost is a Funtion.
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Solve 35 / 2 using an area model. Use long division and the distributive property to record your work
Answer by solving the expression 35 /2 using different methods are:
a. Area model : 35 /2 can be expressed as 17. 5 + 17.5 .(attached figure)
b. Long division method : 35 /2 = 17 + 1/2
c. Distributive property expressed as 35/2 = ( 34 + 1 ) × 1/ 2.
a. Area model.
Expression 35 /2 solved by area model is attached in the figure.
One part of 35 is divided into two parts each of 17.5 .
17.5 + 17.5 = 35
b. Long division.
How many 2's are there in 3
Answer is 1.
3−1⋅2=3−2=1
Write down the next digit of the dividend.
How many 2's are there in 15
Answer is 7
15−7⋅2=15−14=1.
( 35 /2 ) = 17 + ( 1/2)
c. Distributive property
35 /2
= ( 34 + 1 ) × 1/ 2
= 34 /2 + 1 /2
= 17 + 1 /2
= 17 + 0.5
= 17.5
Therefore, the solution of 35/2 using different methods are:
a. Using area model : 17.5 + 17.5 represent 35/2.
b. long division : 35 /2 = 17 + 1/2
c. Distributive property: 35/2 = ( 34 + 1 ) / 2
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answer choices:
x=22
x=68
x=90
x=112
Answer: I think x=22.
Step-by-step explanation:
If you look at half of the circle you can see a line in it right? This line measures to 180 degrees. This is a right triangle. Usually triangles have a little box in the corner to tell you that is it indeed a right triangle. I don't know why this one doesn't. anyways, if you add 90+68, you get 158. Now you need to get to 180 by simply adding 22. Thats why i think the answer is 22. Sorry if im wrong.
John is making apple pies and apple cobblers to sell at his stand at the Farmer's Market.
A pie uses 4 cups of apples and 3 cups of flour.
A cobbler uses 2 cups of apples and 3 cups of flour.
John has 16 cups of apples and 15 cups of flour.
When John sells the pies and cobblers at the Farmer's Market, he will make $3.00 profit per pie and $2.00 profit per cobbler.
Let x = the number of pies John makes.
Let y = the number of cobblers John makes.
Since John cannot make a negative number of pies or cobblers, what additional constraints exist on the variables?
Since John cannot make a negative number of pies or cobblers, the additional constraints that exist on the variables include the following:
B. x ≥ 0.
y ≥ 0.
How to write an equation to model this situation?In order to write an equation that model this situation, we would assign a variable to the number of pies John makes and the total number of cobblers John makes respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of pies John makes.Let the variable y represent the total number of cobblers John makes.However, it should be noted that John cannot make a negative number of pies or cobblers and as such, the number of pies he makes must be greater than or equal to zero (0) such as 0 pies, 1 pies, 2 pies, 3 pies, 4 pies, etc. Similarly, the aforementioned constrain applies to the number of cobblers John makes.
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Convert 4 liters into gallons. Round your answer to the nearest hundredth.
*Note: you must use these exact conversion factors to get this question right.
1 cup (cup) = 8 fluid ounces (fl oz)
1 liter (L) 1000 milliliters (mL)
1 pint (pt) = 2 cups (cups)
1 cubic meter (m³) = 1000 liters (L)
1 quart (qt) = 2 pints (pt)
1 gallon (gal) = 3.785 liters (L)
1 gallon (gal) = 4 quarts (qt)
1 fluid ounce (fl oz) = 29.574 milliliters (ml)
1 cubic foot (ft³) = 7.481 gallons (gal)
Answer:
= (blank) gallons
During a single day at radio station WMZH, the probability that a particular song is
played is 23%. What is the probability that this song will be played on at least 2 days
out of 4 days? Round your answer to the nearest thousandth.
The probability that this song will be played on at least 2 days out of 4 days is 40.71%.
How to calculate the probability?To calculate the probability that a song will be played on at least two days, you would need to find the probability that it is not played on any of the days (the complement) and then subtract that from 1.
The probability that a song is not played on a given day is 1 - 0.23 = 0.77. To find the probability that it is not played on at least two days, you would raise that probability to the power of the number of days, in this case 2.
So, 0.77^2 = 0.5929. To find the probability that it is played on at least two days, you would subtract that from 1: = 1 - 0.5929
= 0.4071
=40.71%.
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Target is having a sale, Every item in the store is 20% off the orignal price . if a tvs oringal price is 250$ , what was the sale price
The final sales price is equal to $200.
What is a percentage?In Mathematics, a percentage simply refers to any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.
In order to decrease 250 dollars by 20 percent (20%), we would have to multiply the given amount of money by 80 percent (80%) because it denotes a percentage decrease:
Percentage decrease = 250 × 80/100
Percentage decrease = 250 × 0.8
Percentage decrease = $200.
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Help w math homework pls
Part A - The area of the deck is approximately equal to 691.150 square feet.
Part B - The deck requires 3.379 gallons of weather treatment.
Part C - The weather treatment have a cost of $ 121.48.
How to determine the deck area around the poolIn this problem we must find the area of the deck around the pool, how many gallons of weather treatment are required and how much is needed to.
Part A - The area of the deck is a circular corona, whose formula is:
A = π · (R² - r²)
Where:
A - Area of the circular corona, in square feet.r - Inner radius, in feet.R - Outer radius, in feet.If we know that r = 6 ft and R = 16 ft, then the area of the deck is:
A = π · [(16 ft)² - (6 ft)²]
A = 220π ft²
A ≈ 691.150 ft²
Part B - If we know that a gallon is effective for an area of 204.5 square feet, the number of gallons can be determined by cross multiplication:
x = (691.150 ft² / 204.5 ft²) × 1
x = 3.379
A number of 3.379 gallons are required for weather treatment.
Part C - The cost of the number of gallons (C), in monetary units, is equal to the product of the number of gallons (n), in gallons, and unit cost (c), in monetary units per gallon:
C = n · c
If we know that n = 3.379 gal and c = $ 35.95 / gal, then the cost of the number of gallons is:
C = (3.379 gal) · ($ 35.95 / gal)
C = $ 121.48
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the average weekly work hours of full-time u.s. workers have approximately a normal distribution with mean 37 hours and standard deviation hours. suppose 200 u.s. citizens are randomly chosen. find an approximate probability that less than 10 of them are working more than 50 hours a week on average (round off to third decimal place).
The approximate probability that less than 10 out of 200 U.S. citizens are working more than 50 hours a week on average is 0.019
We can use the normal distribution to approximate the probability that less than 10 out of 200 U.S. citizens are working more than 50 hours a week on average.
To do this, we have to standardize the variable by subtracting the mean and dividing by the standard deviation.
In this case, X = (50 - 37) / hours = 1.83
We know that for a standard normal distribution, the probability of X being less than a certain value can be found using a standard normal table or a calculator with a built-in standard normal cumulative distribution function (CDF).
Now, we will use the cumulative distribution function to find the probability of less than 10 out of 200 working more than 50 hours a week on average. Using a standard normal table or calculator, we can find the probability of having X < -2.04.
P(X < -2.04) = 0.0188
So the approximate probability that less than 10 out of 200 U.S. citizens are working more than 50 hours a week on average is 0.0188 which rounding it off to the third decimal place we get 0.019.
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define partial products. what partial products can you use to find how many 6 bags of cat food will cost?
Partial products can be used to multiply two or more numbers.
In Mathematics, partial products mean multiplying each digit of a number with each digit of another number where each digit maintains its place value6 bags × cat food cost
Nick is splitting 3 quarts of ice cream with 15 members of thw team. If the ice cream is split evenly how many cups will each person get 1 quart equals=
whixh equals = _cups
so 3 quarts equaks _cups divibg thw ice cream among _ people means each gets _ cups
1 quart equals 2 pints, which equals 4 cups, so 3 quarts equals 12 cups. Dividing the ice cream among 15 people means each gets 1 3/12 cup(s).
Nick has 3 quarts of ice and he wants to split it with 15 members of the team.
To solve this, we have to convert quarts to cups. We have that:
1 quart = 2 pints
and 1 pint = 2 cups
This means that:
1 quart = 2 × 2 cups
1 quart = 4 cups
So, 3 quarts will be:
3 quarts=3 × 4
3 quarts =12
Therefore, dividing the ice cream among 15 people would mean that we have to divide 12 cups by 15 people.
That is:
= 15/12
= [tex]1\frac{3}{12}[/tex]
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The complete question is:
Nick is splitting 3 quarts of ice cream with 15 members of the team. If the ice cream is split evenly, how many cups will each person get?
Explain 1 quart equals _ pints, which equals _ cups, so 3 quarts equals _ cups. Dividing the ice cream among _ people means each gets _ cup(s).
Consider absolute value function f
f(x) = -2/3|x + 4|
The vertex of the function is a (minimum/maximum) at (0,4)(0,-4)(4,0)(-4,0)
For the absolute value function, the vertex is at its maximum at (-4,0).
What is function?A function is an expression, rule, or law in mathematics that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are common in mathematics and are required for the formulation of physical relationships in the sciences. A function is defined as a relationship between a set of inputs that each have one output. A function is a relationship between inputs in which each input is related to exactly one output.
Here,
The vertex for the absolute value function is at its maximum at (-4,0).
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find the length x. round to the nearest tenth
The numerical value of to the nearest tenth is 14.3.
What is the value of x ?From the diagram, we have a right angle triangle.
Angle Ф = 40 degreeOpposite to angle 40 degree = 12Adjacent to angle 40 degree = xUsing trig ratio, Tangent = Opposite / Adjacent.
Hence;
tan( Ф ) = Opposite / Adjacent
Plug in the given values and solve for x
tan( 40° ) = 12/ x
tan( 40° ) × x = 12
x = 12 / tan( 40° )
x = 12 / 0.8390996
x = 14.3
Therefore, the value of x is approximately 14.3.
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Give your answer in point notation with the x and y coordinates. If there are
multiple solutions, separate the answers with commas and no spaces. For example,
if your answers are (0,2) and (-3,1), you would type it as: (0,2),(-3,1). Order does not
matter.
V
N
AV
The points (2,2) and (-2,2) are both solutions to the equation y=2.
A coordinate pair(2,2),(3,1)When solving a system of equations, one way to find the solution is by graphing.To graph the given system of equations, start by plotting the two equations on the coordinate plane.The first equation, x + y = 4, can be written in the form y = -x + 4.Plot this line on the coordinate plane, with any two points that satisfy the equation. In this case, the two points could be (0,4) and (4,0).Plot the second equation, x - y = 2, in the same way.This line can be written in the form y = x - 2.Plot two points that satisfy this equation, such as (0,-2) and (2,0).After plotting the two lines, look for the point of intersection, which is the solution to the system.In this case, the point of intersection is (2,2) and (3,1).Therefore, the solution to the system is (2,2),(3,1).This equation is a line that has a y-intercept of 2, meaning that the line crosses the y-axis at the point (0,2). The slope of the line is 0, meaning that the line is vertical and does not cross the x-axis.Therefore, any point along this line will have the same y-coordinate, which in this case is 2. In other words, for any given x-coordinate, the y-coordinate will always be 2. This means that both (2,2) and (-2,2) are valid solutions for the equation y=2.To learn more about a coordinate pair refer to:
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Can you give me great examples of buildup, unit ratio, and cross multiplication for proportional relationships? I am trying to get an A on this test and dont want to mess up.
Cross multiplying will help us identify the variable if it is the same variable that is present on both sides of the equation. Let's explain with the use of examples. Solve X/5 = 5/X, for instance.
What is cross multiplication in ratio and proportion?When you multiply the denominator of one ratio by the numerator of another, you get a cross product. In the event when the cross products are equal, the ratios are proportionate. In the case of ratios and, and are proportional and can be expressed as a b = c d.So 4×32=128. Moreover, we obtain the result 726=182 when we cross-multiply these two. The fact that 182 is greater than 128 enables us to conclude that 732 is greater than 426. The number we multiplied by our numerator symbolises the matching fraction, and we must always keep this in mind.For comparison of fractions, cross multiply. The most typical application of cross multiplication is the comparison of fractions. multiplying the numerator while paying closer attention to the procedure.To learn more about Cross multiplying refer to:
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how to graph y=2x+1
-2x=y=-2
Answer:
For y=2x+1
The line y=2x+1 has a y-intercept of +1, so begin with a point at (0,1)
and its slope is 2/1, which means from there you go Up 2 and Right 1.
Follow that pattern until you can draw a straight line through all the points.
For -2x=y=-2
In this point it only passes (0,2) and (1.0)
Have a wonderful day! :-)
Determine whether each set of side lengths could be the sides of a right triangle.
The side length that could be a right triangle are
6 8 105 12 13How to find out side lengths of right triangleApplying Pythagoras theorem, for each side length we solve for the longest side in each case assuming the longest side is x
Using Pythagoras theorem given by the the formula
hypotenuse² = opposite² + adjacent²
checking for 4 7 8
let x be the required distance
x² = 4² + 7²
x² = 16 + 49
x² = 65
x = √65
this is not a right triangle
checking for 6 8 10
let x be the required distance
x² = 6² + 8²
x² = 36 + 64
x² = 100
x = √100
x = 10
this is a right triangle
checking for 5 12 13
let x be the required distance
x² = 5² + 12²
x² = 25 + 144
x² = 169
x = √169
x = 13
this is a right triangle
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Use the graph of the parabola to fill in the table.
PLEASE HURRY
a) Upwards
b) x = -1
c) (-1,-9) (-1,-9)
d) Intercepts of x; and (2, 0) (-4,0)
is y intercept (0,-8)
What is intercept calculation?a) The parabola, as seen, faces upward.
b) To identify the point through the parabola's vertex that precisely divides the parabola into two equal sections, we look at the plot of the graph.
The place where the line has an x-value of -1 is where the axis of symmetry's equation is located.
d) In this case, the vertex marks the circle's lowest point.
As we can see, this is the location where the axis of symmetry passes to divide the parabola symmetrically.
The location's coordinates are as follows:
(-1,-9)
The intercepts (d)
The parabola crosses the x-axis at two places, which are known as the x-intercept.
We have 2 and -4 for this point.
the coordinates of the x-intercepts are (2,0) and
In terms of the y-intercept, it is the y-coordinate of the location where the parabola crosses the y-axis.
The Complete Question.
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URGENT!! HOMEWORK DUE SOON!!
The difference between two positive numbers is 50. One number is four times the other number. What are the two numbers?
The two missing positive numbers are; 50/3 and 200/3
How to solve algebra word problems?The difference between two positive numbers is 50. Let the two numbers be x and y and as such we have;
x - y = 50 -----(1)
One number is four times the other number. Thus;
x = 4y -----(2)
Put 4y for x in eq 1 to get;
4y - y = 50
3y = 50
y = 50/3
Thus;
x = 4(50/3)
x = 200/3
We conclude that x and y above are the two positive numbers.
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8112 equals 2 ^ 4 times 3 times 13 ^ 2 find the value of the smallest square number that is a mutiple of 8112
The factor 3 does not occur in pair. Thus, ‘3’ is the smallest number by which 8112 should be divided to get a perfect square.
What is the lowest square number?The LCM of 8, 15, and 20 is 120. Prime factors 2, 3, and 5 do not have a pair in this case. To construct a perfect square, 120 must be multiplied by 2 x 3 x 5. As a result, the least square number divisible by 8, 15, and 20 is 3600.
The smallest square matrix is 2 2 2 2 ; there is no theoretical limit to the highest size square matrix, however anything larger than 10 10 10 10 becomes impossible to manage numerically.4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, and 961
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Xander is making soup for his youth group's annual dinner party for the elderly people in their community. His group
leader told him to mix the number of cans of soup concentrate and the number of cans of water in the ratio
1:5. Construct a ratio table for all possible combinations of cans of soup concentrate and cans of water that will giv
Xander up to 24 total cans of heated soup to serve. Let s represent the number of cans of soup concentrate and let
w represent the number of cans of water.
The ratio table is presented below and a total of 4 cases of possible.
Given that,
s: the number of cans of soup concentrate
w: the number of cans of water
Ratio: 1:5
so w = 5s
Therefore,
s w Total cans of heated soup to serve
1 5 6
2 10 12
3 15 18
4 20 24
Therefore, a total of four cases are possible to make up to 24 total cans of heated soup to serve at the party.
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in a sample of 2000 people, 430 people have their ears pierced. two unrelated people are selected at random without replacement, find the probability that neither of the people have their ears pierced.
The probability that neither of the people have their ears pierced is 0.6157
What is the probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.
The probability of A happening is the number of people who do not have their ears pierced divided by the total number of people in the sample, which is:
P(A) = (2000 - 430) / 2000 = 1570 / 2000 = 0.785
The conditional probability of B given A is the number of people who do not have their ears pierced and are still available to be selected as the second person divided by the total number of people available to be selected as the second person, which is:
P(B|A) = (2000 - 430 - 1) / (2000 - 1) = 1569 / 1999 = 0.7845
Therefore, the probability that neither of the people have their ears pierced is:
P(A) * P(B|A) = 0.785 * 0.7845 = 0.6157
Hence, the probability that neither of the people have their ears pierced is 0.6157
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The post office’s human resources manager wants to determine an optimal hiring plan. Day Number of full-time employees required 1 = Monday 17 2 = Tuesday 13 3 = Wednesday 15 4 = Thursday 19 5 = Friday 14 6 = Saturday 16 7 = Sunday 11 Union rules state that each full-time employee must work 5 consecutive days and then receive 2 days off. Formulate an IP to minimize the number of fulltime employees who must be hired, and solve it using Excel Solver to find the optimal solution
Here is a simple framework to model the problem as an Integer Programming (IP) problem and solve it using Excel Solver:
Define decision variables:Let x(i,j) be the number of full-time employees assigned to work on day i (1 <= i <= 7) and given day off on day j (1 <= j <= 7).
Set constraints:a. Work days constraint: For each day i, the number of employees working must meet the demand:
∑(j=1 to 7) x(i,j) = demand(i) (1 <= i <= 7)
b. Availability constraint: Each employee can work only 5 consecutive days, so for each day j (1 <= j <= 7), the number of employees given day off on day j must be less than or equal to the number of employees working on day j-5:
∑(i=1 to 7) x(i,j) <= ∑(i=j-5 to j-1) x(i,j-5) (1 <= j <= 7)
Set objective:The objective is to minimize the total number of full-time employees hired, so the objective function is:
minimize: ∑(i=1 to 7) ∑(j=1 to 7) x(i,j)
Solve using Excel Solver:Excel Solver can be used to find the optimal solution to the IP problem. The constraints and objective function should be set up in the spreadsheet, and Solver should be configured to use the integer constraint option. The solution will give the optimal number of full-time employees hired and their assignment on each day.
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