So the probability that at least four of the 24 soup cans in a shipping box are dented is approximately 0.055, or 5.5%.
What is probability?Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. An event with probability 0 is impossible, while an event with probability 1 is certain. In probability theory, an event is any outcome or set of outcomes of a random process or experiment. The probability of an event is determined by calculating the ratio of the number of ways the event can occur to the total number of possible outcomes. Probability is used in a wide variety of fields, including mathematics, statistics, physics, engineering, finance, and economics, to model and analyze random phenomena and make predictions about future events.
Here,
Let X be the number of dented soup cans in a box of 24. Then X follows a binomial distribution with parameters n = 24 and p = 0.13, since each can has a probability of 0.13 of being dented, and the cans are independent.
We want to find the probability that at least four cans are dented, which can be written as P(X ≥ 4). This is equivalent to 1 - P(X < 4), where P(X < 4) is the probability that fewer than four cans are dented. We can use the binomial cumulative distribution function (CDF) to find P(X < 4), and then subtract it from 1 to get P(X ≥ 4).
Using a binomial CDF table, we find that P(X < 4) ≈ 0.945. Therefore, P(X ≥ 4) ≈ 1 - 0.945 = 0.055, or about 5.5%.
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3.
a) What is the relation between area of rectangle and triangle standing on the same base
and between the same parallel lines? Write it.
Answer:
when they both are separated they form a right angled triangle 90°
The Click-O Pen Company produced 1.8×106 pencils each year for 4 years. What was the total number of pencils the Click-O Pen Company produced during those 4 years?
The Click-O Pen Company produced a total of 7.2×106 pencils during those 4 years.
What is the arithmetic operations?
The basic arithmetic operations are the fundamental mathematical operations used in arithmetic, which include:
Addition: combining two or more numbers to find their total or sum.Subtraction: finding the difference between two numbers by subtracting one from the other.Multiplication: finding the product of two or more numbers, which is the result of repeated addition.Division: dividing a number into equal parts or groups.To find the total number of pencils produced by the Click-O Pen Company during the 4 years, we need to multiply the number of pencils produced each year by the number of years.
We are given that the company produced 1.8×106 pencils each year for 4 years. Therefore, the total number of pencils produced is:
1.8×106 pencils/year × 4 years = 7.2×106 pencils
Hence, the Click-O Pen Company produced a total of 7.2×106 pencils during those 4 years.
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Answer:
The Click-O Pen Company produced 1.8 x 10^6 pencils each year for 4 years.
To find the total number of pencils produced during those 4 years, we need to multiply the number of pencils produced per year by the number of years:
Total number of pencils produced = (1.8 x 10^6) x 4
= 7.2 x 10^6
Therefore, the Click-O Pen Company produced a total of 7.2 million pencils during those 4 years.
Step-by-step explanation:
Start by identifying the number of pencils produced each year by the Click-O Pen Company. According to the problem statement, the company produced 1.8 x 106 pencils per year.
Next, determine how many years the company produced pencils for. In this case, we know that the company produced pencils for 4 years.
To calculate the total number of pencils produced during those 4 years, we need to multiply the number of pencils produced per year by the number of years. This gives us:
Total number of pencils = 1.8 x 106 pencils/year x 4 years
We can simplify this expression by multiplying 1.8 x 4 to get:
Total number of pencils = 7.2 x 106 pencils
Therefore, the Click-O Pen Company produced a total of 7.2 x 106 pencils during the 4-year period.
A landowner recently sold a large plot of land. The sale decreased his total acreage by 12%. Let v be the original acreage. A. Write two equivalent expressions that represent the new acreage. B. Use the expressions to describe another way to find the new acreage
A. Two equivalent expressions that represent the new average are x = v - 0.12v and x = 0.88v.
B. Another way to find the new average directly using:
x = 0.88v (using the second expression )
What is expression ?
In mathematics, an expression is a combination of numbers, symbols, and/or operators that represent a value or a relationship between values. Expressions can be as simple as a single number, variable, or symbol, or they can be complex combinations of terms, functions, and operations.
For example, the expression "2x + 3" is a combination of the number 2, the variable x, and the operators + and *. It represents a relationship between x and a value that is 3 more than twice x.
Expressions can be used in a wide range of mathematical contexts, including algebra, calculus, geometry, and statistics, to name a few. They are an essential tool for describing and solving mathematical problems.
A. Let x be the new acreage after the sale. Then we have:
x = v - 0.12v (12% decrease means 0.12v decrease from v)
x = 0.88v (Simplify by factoring out v)
So, two equivalent expressions that represent the new average are x = v - 0.12v and x = 0.88v.
B. Another way to find the new acreage is to multiply the original acreage by the decimal equivalent of the percent decrease. In this case, the percent decrease is 12%, which is equivalent to 0.12 as a decimal. So, we have:
x = v - 0.12v (using the first expression above)
x = 0.88v (simplify)
x = (1 - 0.12)v (factor out v)
x = 0.88v (simplify)
Alternatively, we can calculate the new average directly using:
x = 0.88v (using the second expression above)
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Answer:A.Two equivalent expressions that represent the new average are x = v - 0.12v and x = 0.88v.B.Another way to find the new average directly using:x = 0.88v (using the second expression )What is expression ?In mathematics, an expression is a combination of numbers, symbols, and/or operators that represent a value or a relationship between values. Expressions can be as simple as a single number, variable, or symbol, or they can be complex combinations of terms, functions, and operations.For example, the expression "2x + 3" is a combination of the number 2, the variable x, and the operators + and *. It represents a relationship between x and a value that is 3 more than twice x.Expressions can be used in a wide range of mathematical contexts, including algebra, calculus, geometry, and statistics, to name a few. They are an essential tool for describing and solving mathematical problems.A. Let x be the new acreage after the sale. Then we have:x = v - 0.12v (12% decrease means 0.12v decrease from v)x = 0.88v (Simplify by factoring out v)So, two equivalent expressions that represent the new average are x = v - 0.12v and x = 0.88v.B. Another way to find the new acreage is to multiply the original acreage by the decimal equivalent of the percent decrease. In this case, the percent decrease is 12%, which is equivalent to 0.12 as a decimal. So, we have:x = v - 0.12v (using the first expression above)x = 0.88v (simplify)x = (1 - 0.12)v (factor out v)x = 0.88v (simplify)Alternatively, we can calculate the new average directly using:x = 0.88v (using the second expression above)
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Find the principal argument Arg z when (a) -2/(1 + √3i);
(b) (√3 - i)^6.
The required answer for the expression -2/(1 + √3i) is Arg (z) = 2π/3. The required answer for the expression (√3 - i)⁶ is Arg (z) = π.
The principal argument is the angle created by the line joining the origin, z, and the positive real axis. A complex number with the expression z = x + i y has the argument form [tex]\text{Arg}(z)=\tan^{-1}\frac{y}{x}[/tex] when x > 0.
a) Given z=2/(1 + √3i). First, simplify the given expression,
[tex]\begin{aligned}\frac{-2}{1+i\sqrt{3}}&=\frac{-2}{1+i\sqrt{3}}\times\frac{1-i\sqrt{3}}{1-i\sqrt{3}}\\&=\frac{-2(1-i\sqrt{3})}{1^2-(i\sqrt{3})^2}\\&=\frac{-2-2\sqrt{3}i}{4}\\&=\frac{-1}{2}-\frac{\sqrt{3}}{2}i\end{aligned}[/tex]
Now find, the arg of the above expression. Here, x is -1/2 and y is√3/2. We get,
[tex]\begin{aligned}\mathrm{Arg}(z)&=\tan^{-1}\frac{y}{x}\\&=\frac{\frac{\sqrt{3}}{2}}{\frac{-1}{2}}\\&=\tan^{-1}(-\sqrt{3})\\&=\frac{2\pi}{3}\end{aligned}[/tex]
The required answer is Arg (z) = 2π/3.
b) Given (√3 - i)⁶. We know that,
[tex]\begin{aligned}\sqrt{3}-i&=2\left(\frac{\sqrt{3}}{2}-\frac{1}{2}i\right)\\ &=2\times e^{\left(-\frac{\pi}{6}i\right)\end{aligned}[/tex]
Then,
[tex]\begin{aligned}(\sqrt {3} -i)^6&=2^6\times e^{-\pi i}\\&=-2^6\end{aligned}[/tex]
Here, x is -64 and y is 0. Then, tan⁻¹ (0) = 0 = π.
The required answer is Arg (z) = π.
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Megan increases 600 by 10%.
She then decreases the result by 10%
What is her final number?
Answer:
Her final number is 594.
Step-by-step explanation:
Increase 600 by !0%:
0.1 * 600 = 60
600 + 60 = 660
Decrease result by 10%:
0.1 * 660 = 66
660 - 66 = 594
Last night, the two dinner specials at Kate's favorite restaurant were salmon filet and steak. The restaurant served 25 specials in all, 10 of which were the salmon filet. What percentage of the specials were salmon filets?
Answer:
Step-by-step explanation: 40% you take the 10 salmon plates and divide it by the 25 specials the restaurant had 10/25=.40
Please Help ASAP 10 POINTS
The amount of wrapping paper use to wrap the rectangular gift box is 292 ft².
What is the surface area of the rectangular prism?The surface area of a rectangular prism is expressed as;
S.A = 2( wl + hl + hw )
Given the data in the diagram;
Length l = 8ftWidth w = 6 ftHeight h = 7 ftPlug the values into the above formula and find the surface area.
S.A = 2( wl + hl + hw )
S.A = 2( (6×8) + (7×8) + (7×6) )
S.A = 2( 48 + 56 + 42 )
S.A = 2( 146 )
S.A = 292 ft²
Therefore, the surface area of the right rectangular prism is 292 ft².
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Arunima buys two bouquets for 121. 75 each and candies for2. 25each. If she left with 21. 10,how much money did she have in the beginning
Knowing that two bouquets of flowers and candies are bought, leaving 21.10, the money at the beginning of the purchase is $266.85.
To find out how much money she had in the beginning, we can use the following equation:
Starting money - (bouquets cost + candies cost) = money left
Let's plug in the given values:
Starting money - ((2 x 121.75) + (2.25 x candies)) = 21.10
Simplifying the equation, we get:
Starting money - (243.50 + 2.25 x candies) = 21.10
Now, we can rearrange the equation to solve for the starting money:
Starting money = 21.10 + 243.50 + 2.25 x candies
If we plug in the given values, we get:
Starting money = 21.10 + 243.50 + 2.25 x candies
Starting money = 266.85
Therefore, Arunima had a total of $266.85 in the beginning.
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how to convert 0.06 as a fraction?
The value 0.06 as a fraction is 3/50 .
In mathematics, fractions are defined as part of a whole. A whole can be an object or a group of objects. In real life, if you cut a pie out of the whole pie, that piece becomes part of the pie. Fractions are words of Latin origin. "Fractus" means "broken" in Latin. In ancient times, rest was expressed in words. Later it was introduced in numerical form.
Fractions are also called parts or sections of any quantity. Represented by the symbol '/'. Bachelor/Bachelor For example, 2/4 is the numerator above and the fraction below the denominator. In this article, you will learn the definition of fractions in mathematics, types of fractions, how to convert fractions to decimals, and many solved examples and full explanations
to convert in fraction we will muliply and devide by 100.
0.06 *100/100 =3/50
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A home buyer is debating between two different mortgages for $167,800. The options are: Option A: 20-year fixed rate loan at 7.45% with a total of $323,198.36 paid in principal and interest over the life of the loan Option B: 15-year fixed rate loan at the same rate. How much more total principal and interest will the buyer pay for the 20-year loan versus the 15-year loan? A spreadsheet was used to calculate the correct answer. Your answer may vary slightly depending on the technology used $46,041.05 $44,061.05 $229,893.95 $292,893.95
The difference in total principal and interest payment between the 20-year loan versus the 15-year loan is B. $44,061.05.
How is the difference determined?The difference is obtained by computing the total payments for the Option B loan and comparing these to the total payments for Option A loan.
The total payments for Option B can be computed using an online finance calculator that determines also the monthly payments.
Option A:Mortgage loan = $167,800
Interest rate = 7.45%
Mortgage period = 240 (20 years x 12)
Total payment (Future Value) = $323,198.36
Monthly payment = $1,346.66 ($323,198.36/240)
Option B:N (# of periods) = 180 months (15 years x 12)
I/Y (Interest per year) = 7.45%
PV (Present Value) = $167,800
FV (Future Value) = $0
Results:
Monthly Payment (PMT) = $1,550.76
Sum of all periodic payments = $279,137.31
Total Interest = $111,337.31
Option A total payment = $323,198.36
Option B total payment = $279,137.31
Difference between the two options = $44,061.05 ($323,198.36 - $279,137.31)
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what is 124 lbs to kg?
Answer: 56.2455
Step-by-step explanation:
How do you find a radical expression??
To find a radical expression, simplify the expression under the radical symbol by factoring it into perfect squares or cubes.
An extreme articulation is a logarithmic articulation that contains an extreme image, for example, a square root or a 3D shape root. To find an extreme articulation, you really want to improve on the articulation under the extreme image.
Here are the moves toward work on an extreme articulation:
Factor the number under the extreme image into its excellent variables.
Recognize sets of variables that are amazing squares or wonderful blocks.
Change the extreme articulation utilizing these ideal squares or wonderful 3D shapes.
Improve on the subsequent articulation by duplicating or separating terms as required.
In the event that the articulation actually contains an extreme image, rehash the cycle until the articulation is completely streamlined.
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What is the result of 4000 x 12 ?
Answer:
I'm positive the answer is 56000
The solution of equation 4000 x 12 is,
4000 x 12 = 48,000
We have to given that,
Expression to solve,
⇒ 4000 x 12
We can multiply it,
⇒ 4000 x 12
⇒ 48,000
Therefore, The solution of equation 4000 x 12 is,
4000 x 12 = 48,000
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how to convert 205 lb to kg?
205 lbs is approximately equal to 92.9864 kg ( rounded to four decimal places )
The conversion factor to convert lbs to kilogram is 0.453592
1 lbs = 0.453592 kg
The conversion is the process of changing the unit of one quantity to another units
The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing
The mass in kg = The mass in lbs × conversion factor
Substitute the values in the equation
1 lbs = 0.453592 kg
205 lbs = 0.453592 × 205
Multiply the numbers
= 92.9864 kg ( rounded to four decimal places )
Therefore, 205 lbs is 92.9864 kg
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in a school orchestra, 2/5 o the students are string players of the string players 5/8 are girls what fractin of all the stuentd in the orchestra are girls who play string instrument.
1/4 girl string players.
multiply the fractuon to obtain the answer.
(2/5) x (5/8) = total
10/40 = 1/4
you can check intuitively by confirming this number is less than total string players.
2/5 is 40% of students play string.
1/4 is 25% students are girls that play string.
and 5/8 is slightly larger than half. which confirms the same.
A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 30 times, and the man is asked to predict the outcome in advance. He gets 22 out of 30 correct. What is the probability that he would have done at least this well if he had no ESP?
The probability that he would have done at least this well if he had no ESP is approximately 2.4%. This can be calculated by determining the probability of getting 22 or more of 30 coin flips correct by chance, which is 0.024.
The probability of getting 23 or more of 30 coin flips correct by chance is 0.0048. The probability of getting 24 or more of 30 coin flips correct by chance is 0.0008. The probability of getting 25 or more of 30 coin flips correct by chance is 0.00012. The probability of getting 26 or more of 30 coin flips correct by chance is 0.000016. The probability of getting 27 or more of 30 coin flips correct by chance is 0.000002. The probability of getting 28 or more of 30 coin flips correct by chance is 0.00000003. The probability of getting 29 or more of 30 coin flips correct by chance is 0.000000004. The probability of getting 30 of 30 coin flips correct by chance is 0.00000000003.
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Calculate the amount that will be in the bank after 5 years if R4 700 is invested at 5% simple interest
The amount after 5 years with a simple interest of 5 % is A = $ 875
What is Simple Interest?Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.
Simple Interest = ( Principal Amount x Rate x Time Period ) / 100
Given data ,
Let the amount in the bank after 5 years be A
Let the simple interest be represented as I
Now , the principal amount invested = $ 700
The rate of interest r = 5 %
The number of years n = 5 years
Simple Interest = ( Principal Amount x Rate x Time Period ) / 100
On simplifying , we get
Simple Interest I = ( 700 x 5 x 5 ) / 100
Simple Interest I = 25 x 7
Simple Interest I = $ 175
Now , the amount after 5 years = P + I = 700 + 175
The amount after 5 years = $ 875
Hence , the amount after 5 years in the bank is $ 875
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62 high school students took part in the mathematical olympiad. there were 7 fewer first year students than sophomores, two thirds of the number of third year students, and 5 fourth year students. how many students from each grade took part in the competition?
Answer:a = 17
b = 24
c = 16
d = 5
Step-by-step explanation:
a+b+c+d=62
a = b-7
c = 2/3·b
d = 5
a+b+c+d = 62
a-b = -7
2b-3c = 0
d = 5
Row 2 - Row 1 → Row 2
a+b+c+d = 62
-2b-c-d = -69
2b-3c = 0
d = 5
Row 3 + Row 2 → Row 3
a+b+c+d = 62
-2b-c-d = -69
-4c-d = -69
d = 5
d = 5/1= 5
c = -69+d/-4= -69+5/-4= 16
b = -69+c+d/-2= -69+16+5/-2 = 24
a = 62-b-c-d = 62-24-16-5 = 17
a = 17
b = 24
c = 16
d = 5
If an aqueduct had a distance of 53 miles, what would the drop (in feet) at the end destination if the slope is 0.1%?
As a result, the drop at the aqueduct's final destination is 279.84 feet.
What is percent?Percent is a term used to represent a part or a fraction of a whole expressed as a value out of 100. The word "percent" comes from the Latin phrase "per centum," which means "per hundred." Percentages are commonly used to express ratios or proportions of quantities, and are denoted using the symbol "%". For example, if a student answers 85 out of 100 questions correctly on a test, their score can be expressed as 85%, which represents the proportion of questions they answered correctly out of the total number of questions.
Here,
If an aqueduct has a distance of 53 miles and a slope of 0.1%, we can use the formula:
drop = distance x slope x 5280
where 5280 is the number of feet in one mile.
Substituting the given values, we get:
drop = 53 x 0.1/100 x 5280
= 279.84 feet
Therefore, the drop at the end destination of the aqueduct is 279.84 feet.
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Use the diagram to find the distance WX across the water
Answer:
115m
Step-by-step explanation:
Given
In TriangleXYZ
XZ = 23m
ZY = 19m
In TriangleXVW
WV = 95m
Solution
In Triangles XYZ and XVW
AngleWXV = AngleYXZ as they are Vertically Opposite Angles
AngleXWV = AngleXZY as they are Alternate Angles
Therefore TriangleXYZ and TriangleXVW are Similar Triangles
So,
XY/XV = YZ/VW = XZ/XW as they are Corresponding Sides of Similar Triangles
So,
XZ/XW = YZ/VW
or
23/XW = 19/95
23/XW = 1/5
XW = 23 × 5
XW = 115m
Therefore the distance WX is 115m
what is 24cm in inch?
24 centimeter is approximately equal to 9.4488 inches ( rounded to four decimal places )
To convert 24 cm to inches, we can use the following formula:
1 cm = 0.393701 inches
The conversion is the process of changing the unit of one quantity to another units
The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing
Therefore,
The length in inches = conversion factor × The length in centimeter
Substitute the values in the equation
24 cm = 24 x 0.393701
Multiply the numbers
= 9.4488 inches ( rounded to four decimal places )
Therefore, 24 centimeter is 9.4488 inches
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The side lengths 5, 12, and 13 are called a Pythagorean Triple. What is so special about these three side lengths
The 13 has a "3" in it.
This triple is special because it contains two prime numbers.
The longest side is just one unit longer than the middle side.
They are positive integers that form a right triangle.
Answer:
D
Step-by-step explanation:
Only way you apply Pythagoras is if the triangle is a right triangle. it won't work anyway else
how many grams is in a qp
113.399 grams make up a quarter pound or 0.25 pounds.
The unit of measurement known as a QP, or quarter pound, is frequently used in the sale and distribution of food item measures.
Kilograms equal 2.2046 pounds.
1,000 grams make up one kilogram.
Alternatively, 1,000 grams is 2.2046 pounds.
So, one pound equals x grams.
Divide 1,000 grams by 2.2046 to get 453.597 grams in a pound.
So, one pound is 453.597 grams.
453.597 divided by 0.25 to get 0.25 pounds, or 0.25 pounds, is 113.399 grams.
To achieve precise and consistent outcomes, weight measures are frequently used in cooking and baking. A quarter pound of a culinary item, such as butter or sugar, is also referred to as a QP.
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Can someone help me on where to put the numbers?
The linear function on the graph is:
f(x) = -x/4 + 13
And the domain is 0 ≤x ≤43
How to find the linear function?A general linear function is written as:
f(x) =a*x + b
Where a is the slope and b is the y-intercept.
On the graph we cans ee that the y-intercept is y = 13 (initial amount of gasoline) then:
f(x) = a*x + 13
To find the value of the slope we can use the fact that the line passes through (20, 8), replacing these values we will get:
8 = a*20 + 13
8 - 13 = a*20
-5 = a*20
-5/20 = a
-1/4 = a
So the function is
f(x) = -x/4 + 13
And the domain is the set of possible values of x.
We start at x = 0
And the maximum of the domain is the value such that the fuell is totally consumed, it is:
0 = -x/4 + 13
x/4 = 13
x = 4*13 = 52
The domain is 0 ≤x ≤43
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conversion a) 192 km b) 15500 dam c) 85000 m d) 3360 hm e) 860000 dm
The given length measurements are converted and given below.
What is unit conversion?Unit conversion is a process with multiple steps that involve multiplication or division by a numerical factor or, particularly a conversion factor.
Given is to convert the given measurements as -
a) 192 km
b) 15500 dam
c) 85000 m
d) 3360 hm
e) 860000 dm
We can write the measurements as -
a) 192 km
192 Km = 192000 meters
b) 15500 dam
15500 dam = 15500 x 10 = 155000 meters
c) 85000 m
85000 m = (85000/1000) Km = 85 Kilometers
d) 3360 hm
3360 hm = 3360 x 100 = 336000 meters
e) 860000 dm
860000 dm = 860000 x 0.1 = 860000 x 1/10 = 86000 meter
Therefore, the given length measurements are converted and given above.
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Printer A prints 100 pages for $26.99. Printer B prints 275 sheets for $67.99. Which printer has the better rate of cost per page?
Printer A, because the approximate rate of Printer A, $0.27 per page, is greater than the approximate rate of Printer B, $0.25 per page
Printer B, because the approximate rate of Printer A, $0.27 per page, is greater than the approximate rate of Printer B, $0.25 per page
Printer A, because the approximate rate of Printer A, $3.71 per page, is less than the approximate rate of Printer B, $4.04 per page
Printer B, because the approximate rate of Printer A, $3.71 per page, is less than the approximate rate of Printer B, $4.04 per page
Answer:
Printer B, because the approximate rate of Printer A, $0.27 per page, is greater than the approximate rate of Printer B, $0.25 per page
Step-by-step explanation:
Rate of cost for printer A = $26.99/100 pages
= $ 0.2699 ≈ $0.27 per page
Rate of cost for printer B = $67.99/275 pages
=$ 0.2472 ≈ $0.25 per page
0.25 < 0.27
So Printer B has the better rate of cost
Answer:Printer B, because the approximate rate of Printer A, $0.27 per page, is greater than the approximate rate of Printer B, $0.25 per page
Step-by-step explanation:
you can compare two marginal distributions to see if the corresponding two variables are related. true or false
The given statement that you can compare two marginal distributions to see if the corresponding two variables are related is false.
What can we infer from the marginal distribution?In probability theory and statistics, the probability distribution of the variables included in a subset is the marginal distribution of a subset of a collection of random variables. Without taking into account the values of the other variables, it provides the probabilities of different values for each variable in the subset.
Hence, to determine whether the relevant two variables are connected, you cannot compare two marginal distributions.
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Kirk and martin, two experimental physicists, want to change the diameter of a laser beam while keeping its rays propagating parallel
Kirk and martin, two experimental physicists, want to change the diameter of a laser beam while keeping its rays propagating parallel so the value of distance l is l = fs - fa.
In a partly ionized plasma with several species, we investigate the propagation of electromagnetic waves (or incompressible waves with little thermal pressure) through the magnetic field. Due of variances in mass and density, each species responds to and hence influences electromagnetic field disturbances differently.
For the first lens , ray of light from distant object are parallel , so image will formed at the focal length of first lens.
For second lens,
object distance (u) = fa + l
image distance (v) = ∞
By lens formula,
1/v - 1/u = -1/fs
u = fs
fa + l = fs
l = fs - fa
Collisions between all of the species complicate the process even further. Based on a multi-fluid treatment and Faraday's and Ampere's laws, including the displacement current, a linear analysis is used to derive the dispersion relation of parallel propagation covering a wide range of frequencies, from magnetohydrodynamics (MHD) waves to light waves, with an arbitrary combination of multiple positively charged species, negatively charged species, and neutral species.
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Complete question:
Kirk and martin, two experimental physicists, want to change the diameter of a laser beam while keeping its rays propagating parallel.
For this set up to work, what must be the distance l ?
The following inequalities represent a system. y ≤ −5x + 2 y < 3x − 1.5 Which of the following graphs represents the system?
The following is a graph that illustrates the inequality system: (B) The graph displays a solid line with shading below it that goes through the points 0 commas 2, and 1 comma negative 3.
What are inequalities?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other.
Hence, inequality emerges from a lack of balance.
A mathematical statement that demonstrates the equality of two expressions is known as an equation, whereas a statement that demonstrates the greater or smaller value of one expression is known as an inequality.
For writing and comprehending an inequality plotted on a graph, there are two (2) main rules in mathematics, and these are as follows:
1. When the inequality symbol is (or), the line on a graph should be solid.
2. When the inequality symbol is (> or ), the line on a graph should be dashed (dotted).
The boundary line is dashed (dotted) and shaded above to indicate that the boundary is not part of the solution, and this must be indicated with the larger than (>) inequality sign.
Moreover, the y-value for this inequality graph meets the x-axis at -1.5.
Therefore, the following is a graph that illustrates the inequality system: (B) The graph displays a solid line with shading below it that goes through the points 0 commas 2, and 1 comma negative 3..
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Complete question:
The following inequalities represent a system.
y ≥ −5x + 2
y > 3x − 1.5
Which of the following graphs represents the system?
A. The graph shows a solid line that passes through 0 comma 2 and 1 comma negative 3, with shading above the line. There is also a dashed line that passes through 0 comma negative 1.5 and 1 comma 1.5, with shading above the line.
B. The graph shows a solid line that passes through 0 comma 2 and 1 comma negative 3, with shading below the line. There is also a dashed line that passes through 0 comma negative 1.5 and 1 comma 1.5, with shading above the line.
C. The graph shows a solid line that passes through 0 comma 2 and 1 comma negative 3, with shading above the line. There is also a dashed line that passes through 0 comma negative 1.5 and 1 comma 1.5, with shading below the line.
D> The graph shows a solid line that passes through 0 comma 2 and 1 comma negative 3, with shading below the line. There is also a dashed line that passes through 0 comma negative 1.5 and 1 comma 1.5, with shading below the line.
what is grains to grams ?
Although both grains and grams are weight-measuring units, they are not interchangeable.
The weight of gunshots, arrows, and gunpowder is often measured in the United States using a unit of mass called a grain. A grain weighs around 0.06479891 grams.
In contrast, a gram is a mass unit in the International System of Units (SI) that is often employed in scientific and practical contexts. There are 15.4323584 grains in one gram.
You may multiply the total number of grains by 0.06479891 to convert grains to grams. If you have 500 grains, for instance, you would convert them to grams as follows: 500 grains x 0.06479891 grams per grain = 32.399455 grams.
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