So a linear equation in the form p is P(n) = -$0.004*n + $79.
We have two data points:
6000 shirts can be sold for $55 each.
8000 shirts can be sold for $47 each.
Then we can define the relation:P(n).
Where P is the price, and n is the number of shirts.
Now, we know that we can model this as a linear relationship that passes through the points (6000, $55) and (8000, $47)
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
In this case, the slope is:
a = ($47 - $55)/(8000 - 6000) = -$0.004
Then our equation is:
P(n) = -$0.004*n + b
Now let's find the value of b, we know that:
P(6000) = $55= -$0.004*6000 + b
$55 = -$24 + b
b= $79
Our equation is:
P(n) = -$0.004*n + $79.
The linear equation P(n) = -$0.004*n + $79 has the form p.
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Answer ASAP
Point R is at (3, 1.3) and Point T is at (3, 2.4) on a coordinate grid. The distance between the two points is
. (Input numbers and decimal point only, such as 8.2.) (3 points)
Answer:
1.1
Step-by-step explanation:
Find the solution to the system by substitution
y=2x-1
x-2y=-1
Answer:
x = 1
y = 1
Step-by-step explanation:
Substitute y with 2x-1:
x - 2(2x-1) = -1
x - 4x + 2 = -1
-3x + 2 = -1
-3x = -1 - 2
-3x = -3
x = 1
Substitute x with 1
y = 2(1) - 1
y = 2 - 1
y = 1
WILL MARK BRAINLIEST
Your friend Samir very excitedly tells you about opening his new checking account. “I’m so glad they only had a minimum opening amount of $50! I will leave my money in there so it can grow!” What is some advice you might give to Samir? Responses A checking account isn’t very safe, so you should hide your money in your mattress instead A checking account isn’t very safe, so you should hide your money in your mattress instead A checking account is the best place to leave your money because of the high interest rates A checking account is the best place to leave your money because of the high interest rates A checking account won't grow your money much because of low interest rates and fees A checking account won't grow your money much because of low interest rates and fees A checking account won’t be good because it will be difficult to get your money into and out of A checking account won’t be good because it will be difficult to get your money into and out of
Answer:
A checking account is the best place to leave your money because of the high interest rates.
For this philosopher, the existence of human beings is not reduced to the realization of an essence thought by God; man exists to the extent that he is carried out, it is the set of his acts and nothing else.
The philosopher who thought that the existence of human beings is not reduced to the realization of an essence thought by God has been Jean-Paul Sartre.
¿Who was Jean-Paul Sartre?This character was a Frenchman who had several professions and stood out in different branches, Jean-Paul Sartre was:
PhilosopherWriterNovelistPlaywrightPolitical activistBiographerLiterary criticJean-Paul Sartre is recognized for being an exponent of existentialism and humanist Marxism, among his thoughts, he himself thought that man exists to the extent that he is realized.
¡Hope this helped!
PLEASE HELP WILL MARK BARINLIEST
The length of the side AB of the triangle ACB will be equal to 12.72.
What is a triangle?The basic polygonal shape of a triangle has three sides & three interior angles. This is one of the fundamental shapes in geometry and is particularly associated. It has three connected vertices.
Triangles can be divided into a variety of categories according to their sides and angles.
As per the given information in the question,
As we can see, the triangle ACB in the figure,
AC = 9 cm
Angle = 45°
cos θ = B/H
cos 45° = 9/H
1/√2 = 9/H
H = 12.72 cm
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Can someone help please? Picture is already attached
Answer:
-4 C
Step-by-step explanation:
Use the given conditions.
tan(u) = -3/4, 3π/2 < u < 2π
(a) Determine the quadrant in which u/2 lies.
O Quadrant I
O Quadrant II
O Quadrant III
O Quadrant IV
(b) Find the exact values of sin(u/2), cos(u/2), and tan(u/2) using the half-angle formulas.
sin(u/2) =
=
cos(u/2) =
tan(u/2)
Submit Answer
The quadrant in which u/2 lies is II quadrant.
What is Quadrant?
Quadrant is a business intelligence tool that helps companies extract, analyze, and visualize data from multiple sources in real-time. It enables users to create actionable insights to improve decision-making, optimize operations, and increase profitability. Quadrant provides an intuitive platform for teams to uncover hidden trends and correlations in data, develop predictive models, and generate reports. It also allows users to customize dashboards and create interactive visualizations. Quadrant simplifies data analysis and helps teams make more informed decisions.
a) tan(u) = -3/4, 3π/2 < u < 2π
[tex]\frac{3\pi }{2} < u < 2\pi \\\\270^{o} < u < 360^{o}\\\\Dividing\ both\ side\ by\ 2\\\\135^{o} < \frac{u}{2} < 180^{o}[/tex]
u/2 lies in II quadrant.
b) We have half angle formula's,
[tex]sin(\frac{u}{2} )= \sqrt[]{\frac{(1-cos\\ u)}{2} } \\[/tex]
[tex]sin \frac{u}{2} = \frac{3}{5}[/tex]
[tex]cos(\frac{u}{2} )= \sqrt[]{\frac{(1+cos\ u)}{2} } \\[/tex]
[tex]cos\frac{u}{2} =\frac{4}{5}[/tex]
[tex]tan(\frac{u}{2} )= \sqrt[]{\frac{(1-cos\ u)}{sin \ u} } \\[/tex]
[tex]tan(\frac{u}{2} )= \frac{3}{4}[/tex]
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7. suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000. use the 68-95-99.7 rule to find the percentage of buyers who paid: a. between $147,700 and $152,300 if the standard deviation is $2300. b. more than $154,800 if the standard deviation is $2400.
a. 68 % between $147,700 and $152,300 if the standard deviation is $2300
b. 2.5 % more than $154,800 if the standard deviation is $2400
Given that:
Prices of a certain model of a new home are normally distributed with a mean of $150,000.
Using the 68-95-99.7 rule , find the percentage of buyers who paid between $147,700 and $152,300 if the standard deviation is $2300.
Let X = prices of a certain model of a new home
SO, X ~ Normal ( μ = 150,000 , σ = 2,300 )
z score probability distribution for normal distribution
Z = X - μ / σ
where μ population mean price = $150,000
σ standard deviation = $2,300
According to 68-95-99.7 rule;
Around 68% of the values in a normal distribution lies between μ - σ and μ +σ .
Around 95% of the values occur between μ - 2σ and μ + 2σ .
Around 99.7% of the values occur between μ - 3σ and μ + 3σ.
Find the z scores for both given values
Z = X - μ / σ
= [tex]\frac{147,700 - 150,000}{2,300}\\ \\ \\[/tex]
= -1
Z = X - μ / σ
= [tex]\frac{152,300 - 150,000}{2,300}[/tex]
= -1
The z score indicates that the category of between μ - σ and μ +σ .
Therefore , this represents that percentage of buyers who paid between $147,700 and $152,300 is 68%.
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What is the volume of a cube with a side length of 3.75 m?
Round to the nearest hundredth.
O 7.50 m³
O 11.25 m³
O 14.06 m³
O 52.73 m³
The volume of a cube with a side length of 3.75 m is D. 52.73 m³.
What is the volume?Volume is described as the space occupied within the boundaries of an object in three-dimensional space.
Volume is the product of the length, width, and height of a three-dimensional space.
A cube is a three-dimensional space of equal lengths.
The side length of the cube = 3.75 m
The volume of a cube = a³ where a is the side length
= 3.75 m³
= 3.75 x 3.75 x 3.75
= 52.734375 m³
= 52.73 m³
Thus, the volume of the cube cannot be 7.50 m³, 11.25 m³, or 14.06 m³, but 52.73 m³.
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Overtime Hours Worked A random sample of 15 registered nurses in a large hospital showed that they worked on average 44.6
hours per week. The standard deviation of the sample was 2.3. Estimate the mean of the population with 99% confidence.
Assume the variable is normally distributed. Round intermediate answers to at least three decimal places. Round your final
answers to one decimal place.
0
6
Answer:
The mean of the population with 99% confidence is between 43.1 and 46.1
Step-by-step explanation:
The mean of the population with 99% confidence and The standard deviation of the sample was 2.3, which is between 43.07 to 46.13.
What is mean?Mean is a measurement of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."
Given:
A random sample of 15 registered nurses in a large hospital showed that they worked on average 44.6 hours per week, X = 44.6
The standard deviation of the sample was, n = 2.3,
The confidence = 99%,
1 - α = 99%
α = 1 - 0.99
α = 0.01
Calculate the margin of the error as shown below,
[tex]E = Z_{\alpha /2} \ Mean / standard\ deviation[/tex]
E = 2.576 × 2.3 / √15
E = 1.5298
Calculate the mean as shown below,
X - E < Mean < X + E
44.6 - 1.5298 < Mean < 44.6 + 1.5298
43.07 < Mean < 46.13
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The table of values represents a proportional relationship.
What is the constant of proportionality in the relationship, written as an improper fraction (fraction greater than one)?
X Y
2 3
6 9
The constant of proportionality in the relationship is 3/2
How to determine the constant of proportionality in the relationshipFrom the question, we have the following parameters that can be used in our computation:
X Y
2 3
6 9
The above represents the table of values
Since the data on the table of values represents a proportional relationship, then the constant of proportionality is
Constant of proportionality = Y/X
So, we have
Constant of proportionality = 3/2
Hence, the constant of proportionality is 3/2
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find the length and width of a rectangle that has the given area and a minimum perimeter. area: 5a square centimeters cm (smaller value) cm (larger value)
The Length and width of a rectangle that has one(1) and 2√1
for a given area, the minimum perimeter would be a square
A=s^2 = 5 where s= a side of the square
s=√5= 2√1
length=width = 4sqr1 = about 4(1) = about 1 feet
perimeter =4s = 4(2sqr1) = 8sqr1 = about 8(1) = 8
A=LW
5=LW
L=5/W
or using calculus
Perimeter = P = 2L+2W = 2(/W) + 2W = 10/W + 2W
take the derivative and set it equal to zero, then solve for W
P'(W) = 2 -10/W^2 = 0
2W^2 =10
W^2 = 5
W =sqr5 = 2sqr1 = width of the rectangle that minimizes the perimeter
L= 5/sqr5 = sqr5= 2sqr1 = length of the rectangle that minimizes perimeter
L=W means a square with 4 sides each = 2sqr1
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Suppose that one factory inputs its goods from two different plants, A and B, with different costs, 4 and 6 each respective. And suppose the price function in the market is decided as p(x,y)= 100−x−y where x and y are the demand functions and 0≤x,y. Then as
x=
y=
the factory can attains the maximum profit,
The maximum profit that the factory can attain can be calculated by finding the maximum of the price function p(x,y)= 100-x-y.
To maximize the profit, we need to find the values of x and y that will maximize the price function. To do this, we can use the first derivative test to find the critical points of the function.
Differentiate the price function with respect to x and y, we obtain
p'(x) = -1
p'(y) = -1
Setting both derivatives to zero and solving for x and y, we obtain x= y= 100
To check if this is a maximum, we use the second derivative test.
Differentiate the price function again with respect to x and y, we obtain
p''(x) = 0
p''(y) = 0
Since both second derivatives are equal to 0, this is a point of inflection, and not an absolute maximum. Therefore, we need to check the boundary.
Since x and y must be positive, the boundary would be x=0 and y=0.
Substituting these values into the price function, we obtain
p(0,0) = 100
Therefore, the maximum profit the factory can attain is 100, when x=0 and y=0.
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find the nth maclaurin polynomial for the function f (x )space equals space sin space x comma space space n space equals space 5. the coefficient of x to the power of 5 is
The nth maclaurin polynomial for the function sinx= x -[tex]\frac{x^{3} }{3!}[/tex]+[tex]\frac{x^{5} }{5!}[/tex]-[tex]\frac{x^{7} }{7!}[/tex]+[tex]\frac{x^{9} }{9!}[/tex]
we can find this by using maclaurin series.
what is expansion of function?A relation in which involving one or more variables.It represent partial function as sum of power in one variables or by sum of power of other function.
what is maclaurin series used for?It can be used to approximate function ,find the antiderivative of complicated function or compute on otherwise uncomputable sums.It is a type of series expansion in which all terms are non-negative integer power of the variables.
Now given a function is
f(x)=sinx n=5
Using x=0 the given equation becomes
f(0)= sin(0) = 0
Now taking derivative of given function and using x=0
Then we have
[tex]f_{1}[/tex](x)= cosx [tex]f_{1}[/tex](0)=cos(0)=1
[tex]f_{2}[/tex](x)=-sinx [tex]f_{2}[/tex](0)=sin(0)=0
[tex]f_{3}[/tex](x)= - cosx [tex]f_{3}[/tex](0)= - cos(0)= -1
[tex]f_{4}[/tex](x)= sinx [tex]f_{4}[/tex](0)= sin(0) = 0
[tex]f_{5}[/tex](x)=cosx [tex]f_{5}[/tex](0)= cos(0)= 1
and so on.
Now using maclaurin polynomial series
f(x)=f(0)+x[tex]f_{1}[/tex](0)+[tex]\frac{x^{2} }{2!}[/tex][tex]f_{2}[/tex](0)+ [tex]\frac{x^{3} }{3!}[/tex][tex]f_{3}[/tex](0)+[tex]\frac{x^{4} }{4!}[/tex][tex]f_{4}[/tex](0)..............
by putting the value in the above series
sinx=0+x(1)+[tex]\frac{x^{2} }{2!}[/tex](0) +[tex]\frac{x^{3} }{3!}[/tex](-1)+[tex]\frac{x^{4} }{4!}[/tex](0)........
sinx=x -[tex]\frac{x^{3} }{3!}[/tex]+[tex]\frac{x^{5} }{5!}[/tex]-[tex]\frac{x^{7} }{7!}[/tex]...
Hence this is the 5th term maclaurin series.
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PLEASE QUICK I NEED IT NOW URGENT!!
c) For the high jump, each competitor receives multiple opportunities to clear the bar at each height. On average, Shane completes 3 out of 3 jumps on the lowest bar, 5 out of 6 jumps on the middle bar, and 3 out of 4 jumps on the highest bar. What is
Shane’s overall average number of jumps completed? (2 points)
d) If Shane’s average number of jumps completed is greater than one-half, then the eighth graders earn 50 points. Which grade should be awarded 50 points**? (1 point)
Answer:
c) To find Shane's overall average number of jumps completed, we need to add up the total number of jumps he completed at each height and divide by the total number of jumps he attempted.
At the lowest height, Shane completed 3 out of 3 jumps, for a total of 3 completed jumps.
At the middle height, Shane completed 5 out of 6 jumps, for a total of 5 completed jumps.
At the highest height, Shane completed 3 out of 4 jumps, for a total of 3 completed jumps.
In total, Shane completed 3 + 5 + 3 = 11 jumps out of a total of 3 + 6 + 4 = 13 jumps attempted.
His overall average number of jumps completed is 11 / 13, or approximately 0.85 jumps.
d) Since Shane's average number of jumps completed is greater than one-half (0.5), the eighth graders should be awarded 50 points
Step-by-step explanation:
For your other question A and B for A Correct! To find the total distance thrown by Claire and Grace, you first converted the mixed numbers 5/8 and 3/5 to fractions with a common denominator (in this case, 40), then added those fractions together to find the total distance in fraction form. Finally, you converted the fraction 49/40 back to a mixed number and added it to the whole number distances thrown by Claire and Grace to find their total distance.
The total distance thrown by Claire and Grace is 82 feet 9/40 inches, or approximately 82.225 feet. For B also Correct! Since the total distance thrown by Claire and Grace is not greater than 83.7 feet, the eighth graders should be awarded 50 points.
Translate the sentence into an inequality.
Twice the difference of a number and 6 is at least 27
Use the variable c for the unknown number
Answer:
The answer to the inequality is c >= 19.5. This means that the unknown number, represented by the variable c, must be greater than or equal to 19.5 in order for the inequality to hold true.
Step-by-step explanation:
Twice the difference of a number and 6 is at least 27
2 * (c - 6) >= 27
2c - 12 >= 27
2c >= 39
c >= 19.5
Please let me know if you have any questions.
solve -2 + 12/25
thanks
Answer:
-38/25
in decimal form: -1.52
Step-by-step explanation:
Answer: -38/25 or -1 13/25 or -1.52
Step-by-step explanation:
-2 is the same as -50/25 because -50/25 is -2
-50/25+12/25
-50+12 = -38
-50/25+12/25=-38/25
-1 13/25
A satellite flies 37604 miles in 5.53 hours. How many miles has it flown in 7.15
hours?
Answer:
It will fly 48,620 is 7.15 hours.
Step-by-step explanation:
[tex]\frac{37604}{5.53}[/tex] ≈ 6800 miles in 1 hour. This is rounded to the nearest whole number
7.15 x 6800 = 48,620
40. Write an expression to represent the area of the flag as the sum of the areas of each section.
? x+?\(1 {1}/{2}+3(x+7)
The expression to represent the area of the flag as a sum of areas of each section is 2*x + 2([tex]1\frac{1}{2}[/tex] ) + 3*(x + [tex]1\frac{1}{2}[/tex] ) .
In the question ,
a flag is given that have three colors ,
we have to find an expression for the area of the flag .
For the Green Part ;
the length is 2 units ,
and the width is x units .
So ,the area of the green part is = 2*x .
For the Orange Part ;
the length is 2 units ,
and the width of the orange part is = [tex]1\frac{1}{2}[/tex] units ,
So , the area of the orange part is = 2([tex]1\frac{1}{2}[/tex] ) units .
For the Purple part ;
the length is = 3 units ,
and the width is = (x + [tex]1\frac{1}{2}[/tex] ) units .
So , the area of the purple part is = 3*(x + [tex]1\frac{1}{2}[/tex] ) units .
So the area of the flag is = area of ( Green part + Orange Part + Purple Part) .
Substituting the values ,
we get ,
Area = 2*x + 2([tex]1\frac{1}{2}[/tex] ) + 3*(x + [tex]1\frac{1}{2}[/tex] ) .
Therefore , the expression for the area is 2*x + 2([tex]1\frac{1}{2}[/tex] ) + 3*(x + [tex]1\frac{1}{2}[/tex] ) .
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What is the end behavior of the graph of the polynomial function f(x) = 3x6 + 30x5 + 75x4?
As x→-co, Y→- and as x→∞o, y →→∞
As x→-co Y→- and as x→∞ Y→∞
As x→-co, Y→∞ and as x→∞o, y →-co
As x→-co, y →∞and as x→∞o, y →∞
The end behavior of the graph of the polynomial function (x)=3x⁶+ 30x⁵ + 75x⁴ is x→±∞, y→∞.
What is Polynomial?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables
The given polynomial function is f(x)=3x⁶+ 30x⁵ + 75x⁴
y=f(x)=3x⁴(x+5)²≥0
The zeros are 0, 0, 0,0,-5 and -5.
x-intercept ( y = 0 ): x = -5.
Local mini/max turning points ( y' = 0 ): 0 0, 0, -10/3 and -5.-,
As x→±∞, y→∞.
Hence, the end behavior of the graph of the polynomial function (x)=3x⁶+ 30x⁵ + 75x⁴ is x→±∞, y→∞.
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Answer:
the 4th option
Step-by-step explanation:
ed2023
using the following uniform density curve, determine what is the probability that a random variable has a value less than 44?
The probability that a random variable has a value less than 44 is 44.
The probability that a random variable has a value less than 44 can be determined by calculating the area under the curve to the left of 44.
In a uniform density curve, the probability of a random variable falling within a certain range is equal to the length of that range. To find the probability of a random variable having a value less than 44, we need to find the length of the range from 0 to 44.
The length of this range is 44 - 0 = 44.
Therefore, the probability that a random variable has a value less than 44 is 44.
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Read the following prompt and type your response in the space provided.
Sarah has a $30 music gift card. Each day she uses it to buy a $1.99 song download. For how many days will the gift card have still have a balance of more than $18?
Write an inequality to solve the problem and then solve showing your work. Explain what the solution to the inequality means.
.
Answer:
The answer is 6 days
Step-by-step explanation:
$30 - $18 = $12
$12 / $1.99 = 6.03015075377= 6 days
The boxplot below displays the average number of apple pies consumed in eating contests across a particular state. The higher outlier is from a professional, heavyweight contests, and the lower outlier is from a children's eating contest. X TI X 10 20 30 30 30 What effect will removing all outliers have on the mean and median of the data set? O a Neither the mean nor the median we change O b The mean will remain unchanged and the median will increase O c The mean will remain unchanged and the median wit decrease O d The median will remain unchanged and the mean will increase O e The median will remain unchanged and the mean will decat
The effect that will removing all outliers have on the mean and median of the data set is; C. median will remain unchanged and the mean will increase.
What are mean and median?
The mean is the average value which can be calculated by dividing the sum of observations by the number of observations
Mean = Sum of observations/the number of observations
The Median represents the middle value of the given data when arranged in a particular order.
WE have been given boxplot that displays the average number of apple pies consumed in eating contests across a particular state.
The higher outlier is from a professional,the heavyweight contest, and the lower outlier is from a children's eating contest.
The effect that will removing all outliers have on the mean and median of the data set is; C. median will remain unchanged and the mean will increase.
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Bob bought a sofa on sale for $134.40. This price was 68% less than the original price. What was the original price?
Answer:
$420
Step-by-step explanation:
To find the original price, we need to determine how much the sale price was discounted, and then add that amount back to the sale price. Since the sale price was 68% less than the original price, the discount was 100% - 68% = 32% of the original price.
To find the amount of the discount, we multiply the original price by the discount percentage: 32% * original price = $134.40
Dividing both sides of the equation by the discount percentage gives us the original price: original price = $134.40 / (32% * 1) = $134.40 / 32% = $420.
Therefore, the original price of the sofa was $420.
Select the correct answer.
Solve the following.
√50 x 3√2 = ?
6√13
10
30
6
30 is the correct answer.
The square root of 50 is 5x sqrt of 2 and the multiplied by 3 becomes 15 times 2 = 30 because the two square roots of 2 multiplied together become 2.
5 x 3 x 2 = 30
Math, help pls..................................
The measure of ∡ PRQ, if the sum of an interior angle of a triangle is [tex]180^o[/tex] is 75°, so option B is correct.
What is the triangle?One of the fundamental shapes in geometry is represented by the symbol Δ and consists of three connected vertices.
Given:
The lines m and n are parallel,
∡ QPR = 70°
As the lines are parallel, the alternate angles will be equal,
∡PQR = ∡ QPN = 35°
The sum of the interior angles of the triangle is [tex]180^o[/tex]
∡ QPR + ∡ PRQ + ∡ RQP = 180
70 + 35 + ∡ PRQ = 180
∡ PRQ = 180 - 105
∡ PRQ = 75°
Therefore, the measure of ∡ PRQ, if the sum of an interior angle of a triangle is [tex]180^o[/tex] is 75°.
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George decides to put away $200 a month for 20 years.
If he chooses to put it into an annuity paying 6% interest compounded monthly how much would he end up with? - how much interest does he earn?
Answer:
If George puts away $200 a month for 20 years at an interest rate of 6% compounded monthly, he will end up with a total of $200 x 12 x 20 = $<<2001220=48000>>48,000.
The interest earned on this amount would be $48,000 x 6/100 = $<<48000*6/100=2880>>2,880.
Step-by-step explanation:
reduction of variability is part of what is called choose the answer from the menu in accordance to the question statementchoose the answer from the menu in accordance to the question statement quality of control .
Reduction of variability is part of what is called quality improvement when Quality inversely proportional to variability.
Given that,
What reduces variability is a component of —————————-
We have to fill the blank.
We know that,
Quality inversely proportional to variability
That is
Quality α 1/ variability
The reduction of variability means increases quality. Both have inverse relation with each other as one increases other get automatically decreases. Variability in any process leads to us quality of process. If we want to maintain the quality of process / product we have to reduced variation in process / product
Therefore, Reduction of variability is part of what is called quality improvement when Quality inversely proportional to variability.
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The figures below are made out of circles, semicircles, quarter circles, and a square. Find the area and the perimeter of each figure and give your answers as a completely simplified exact value in terms of π (no approximations). 50 points!!!
The value of the area of the shaded region in the circle is 4π - 8.
What is a circle?A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.
The longest line which can be drawn inside the circle will be the diameter.
As per the given circle,
By Pythagoras' theorem,
LN = √(4² + 4²) = √32
Radius r = LN/2 = √32/2
Area of shaded region = area of the semicircle - the area of right angle triangle.
A = π(√32/2)²/2 - (1/2) × 4 × 4
A = (32π)/8 - 8
A = 4π - 8
Hence, "The circle's shaded region's area has a value of 4 to 8".
To learn more about the circle,
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here are two rectangles. The first rectangle with heading Account A and content principal: $16,000; annual interest: 3%, compound quarterly number of years: 10 and the second rectangle with heading Account B and content principal: $16,000; annual interest: 3%, compound monthly number of years: 10. What type of growth do both accounts model?
Answer:
Due to compound interest, the total return on both investments is significantly higher than the original principal.
Step-by-step explanation:
Both accounts model compound interest growth. Compound interest is a type of growth in which the interest earned on an investment is added to the principal, so that the interest earned in the future is based on a higher principal. In both of the accounts you described, the interest is compounded at a specific frequency (quarterly in Account A and monthly in Account B) over a number of years. This means that the interest earned on the investment is added to the principal at regular intervals, and the interest earned in the future is based on the new, higher principal.
To calculate the total return on an investment that compounds interest, you can use the following formula:
Total Return = Principal * (1 + Interest Rate/Number of Compoundings per Year) ^ (Number of Years * Number of Compoundings per Year)
For example, to calculate the total return on Account A after 10 years, you would use the following formula:
Total Return = $16,000 * (1 + 0.03/4) ^ (10 * 4) = $22,217.33
To calculate the total return on Account B after 10 years, you would use the following formula:
Total Return = $16,000 * (1 + 0.03/12) ^ (10 * 12) = $22,303.47
In both cases, the total return on the investment is significantly higher than the initial principal, due to the compounding of the interest.