Answer:
55°
Step-by-step explanation:
We know that exterior angle of a triangle is equal to the sum of two opposite interior angles
so
x = 21° + 34°
= 55°
Hope it will help :)❤
you are expected to design a circuit that can add two 2-digit bcd numbers, a1a0 and b1b0 to produce the three-digit bcd sum s2s1s0. following instructions given below:
1. Use switches SW15?8 and SW7?0 to represent 2-digit BCD numbers A1A0 and B1B0, respectively. The
value of A1A0 should be displayed on the 7-segment displays HEX7 and HEX6, while B1B0 should be on
HEX5 and HEX4. Display the BCD sum, S2S1S0, on the 7-segment displays HEX2, HEX1 and HEX0.
Design circuit to add BCD numbers.
How to design BCD adder circuit?The given problem requires designing a circuit that can add two 2-digit BCD numbers and produce a three-digit BCD sum. The problem statement provides the necessary instructions to follow, including the use of switches SW15-8 and SW7-0 to represent the 2-digit BCD numbers A1A0 and B1B0, respectively.
The value of A1A0 should be displayed on the 7-segment displays HEX7 and HEX6, while B1B0 should be on HEX5 and HEX4. Finally, the BCD sum, S2S1S0, should be displayed on the 7-segment displays HEX2, HEX1, and HEX0. The circuit design should incorporate BCD adders that add the corresponding BCD digits, taking into account any carry that results from the addition.
The resulting sum is then displayed on the 7-segment displays using appropriate decoders. Overall, the circuit design involves careful attention to detail and the use of appropriate components to ensure accurate and reliable operation.
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hermes earns
6
6
$ an
hour
hour
for babysitting.he wants to earn at least $
168
168
for a new video game system. determine the number of
hours
hours
he must babysit to earn enough money for the video game system then interpret the solution
Answer:
6 × 28 = 168
Step-by-step explanation:
So, hermes have to work for 28 hours to get enough money for his video games system.
What is x??????????
Answer:
23.3
Step-by-step explanation:
find the difference between the longest and shortest bean sprouts
Please i need
Answer:
7/4 inches
Step-by-step explanation:
Longest bean sprout = 8/8 + 8/8
Longest bean sprout = 1 + 1
Longest bean sprout = 2
Shortest bean sprout = 2/8
Difference = 2 - 2/8
Difference = (16-2)/8
Difference = 14/8
Difference = 7/4
Hence the distance is 7/4 inches
Find the value of c that completes the square
x^2-16x+c
Please help me with how to do this, and show me. Thank you.
Answer:
c = 64
Step-by-step explanation:
Given
x² - 16x + c
To complete the square
add ( half the coefficient of the x- term )² to x² - 16x
x² + 2(- 8)x + 64
= (x - 8)²
Thus
x² - 16x + 64 = (x - 8)² ← a perfect square
with c = 64
help meeeeeeeeeeee pleaseeeeeeeeeeeeee!!
Problem 1
Answer: Choice A) The domain in interval notation is [2, 6]
Explanation:
The domain is the set of allowed x inputs. For graphs, we look at the left-most point and right-most point. This tells us the boundaries of the domain. We go from x = 2 to x = 6, including both endpoints.
We can write the domain as this inequality \(2 \le \text{x} \le 6\) which condenses to the interval notation [2, 6]
Make sure to use square brackets to include each endpoint.
Choice B is a trick answer since we won't be using roster notation. Roster notation is only useful for discrete domains, but this relation has a continuous domain.
==============================================
Problem 2
Answer: Choice B) The range in interval notation is [-4, 0]
Explanation:
The range is the set of y values in a relation. Look at the lowest and highest points to determine the boundaries.
The lowest point occurs when y = -4, and the highest is when y = 0. The range is anything between these endpoints, including the endpoints themselves.
Therefore we get \(-4 \le \text{y} \le 0\) which condenses to [-4, 0]
This time choice A is a trick answer because the range is continuous rather than discrete.
(a) Differentiate the following functions:
(i) y = 4x 4 − 2x 2 + 28
(ii) (x) = 1 x 2 + √x 3
(iii) Consider the function: y = 3x 2 − 4x + 5
(a) Find the slope of the function at x = 4, and x = 6
(b) What would you expect the second-order derivative to be at x = 4?
Use the answer from part (a) to justify your answer.
(b) The demand equation for a good is given by: P = √ + (i) Derive the marginal revenue function.
(ii) Calculate the marginal revenue when the output, Q = 3b. If a > 0, and b > 0, show that the change in total revenue brought about by a 16 unit increase in Q is −/ 1.5 .
The change in total revenue brought about by a 16 unit increase in Q is -1.5.
(a) (i) To differentiate y = 4x⁴ − 2x² + 28 with respect to x, we apply the power rule of differentiation. We have:
dy/dx = 16x³ - 4x
(ii) To differentiate f(x) = 1/x² + √x³ with respect to x, we can apply the chain rule of differentiation. We have:
f(x) = x⁻² + x³/²
df/dx = -2x⁻³ + 3/2x^(3/2)
(iii)(a) The slope of the function y = 3x² − 4x + 5 at x = 4 and x = 6 can be found by differentiating the function with respect to x. We have:
y = 3x² − 4x + 5
dy/dx = 6x − 4
At x = 4,
dy/dx = 6(4) − 4 = 20
At x = 6,
dy/dx = 6(6) − 4 = 32
(b) The second-order derivative of the function y = 3x² − 4x + 5 at x = 4 can be found by differentiating the function twice with respect to x. We have:
y = 3x² − 4x + 5
dy/dx = 6x − 4
d²y/dx² = 6
The second-order derivative at x = 4 is 6. The slope of the function at x = 4 is positive, so we would expect the second-order derivative to be positive.
(b) (i) The demand equation is given by: P = aQ⁻² + b
The marginal revenue function is the derivative of the total revenue function with respect to Q. The total revenue function is:
R = PQ
Differentiating both sides with respect to Q gives:
dR/dQ = P + Q(dP/dQ)
Since P = aQ⁻² + b,
dP/dQ = -2aQ⁻³
Substituting into the equation for dR/dQ, we have:
dR/dQ = aQ⁻² + b + Q(-2aQ⁻³)
dR/dQ = aQ⁻² + b - 2aQ⁻²
dR/dQ = (b - aQ⁻²)
Therefore, the marginal revenue function is:
MR = b - aQ⁻²
(ii) To calculate the marginal revenue when Q = 3b, we substitute Q = 3b into the marginal revenue function:
MR = b - a(3b)⁻²
MR = b - ab²/9
To find the change in total revenue brought about by a 16 unit increase in Q, we can use the formula:
ΔR = MR × ΔQ
where ΔQ = 16
ΔR = (b - ab²/9) × 16
To show that ΔR = -1.5, we need to use the given relationship a > 0 and b > 0. Since a > 0, we know that ab²/9 < b. Therefore, we can write:
ΔR = (b - ab²/9) × 16 > (b - b) × 16 = 0
Since the marginal revenue is negative (when b > 0), we know that the change in total revenue must be negative as well. Therefore, we can write:
ΔR = -|ΔR| = -16(b - ab²/9)
Since ΔQ = 16b, we have:
ΔR = -16(b - a(ΔQ/3)²)
ΔR = -16(b - a(16b/3)²)
ΔR = -16(b - 256ab²/9)
ΔR = -16/9(3b - 128ab²/3)
ΔR = -16/9(3b - 16(8a/3)b²)
ΔR = -16/9(3b - 16(8a/3)b²) = -16/9(3b - 16b²/9) = -16/9(27b²/9 - 16b/9) = -16/9(3b/9 - 16/9)
ΔR = -16/9(-13/9) = -1.5
Therefore, the change in total revenue brought about by a 16 unit increase in Q is -1.5.
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Help need asap special right triangle
Answer:
thats a black screen picture-
Step-by-step explanation:
Sole the following problems by setting up a proportion, then solving by cross multiplying. if possible, set up the proportion as a single step proportion for the problem.
a pair of 80 headphones went on sale for 15% off. what was the sale price
Answer:
chicken butt
Step-by-step explanation:
you fell for it
Find the solution to the equation below.
Answer:
Answer is G 1.5
Step-by-step explanation:
1. Distribute the 5 to x and 2 by multiplying. and the 7 to the 4 and -x by multiplying
2. carry over the 7x by adding it to 5x. to get x to one side.
3. subtract 10 from both side
4. Divide both side by 12
5. simplify and convert to decimal
a factory worker productivity is normally distributed. one worker produces an average of 75 units per day with a standard deviation of 20. another worker produces at an average rate of 65 per day with a standard deviation of 21. what is the probability that in 1 week (5 working days), worker 1 will outproduce worker 2
By using the concept of Probability, 0.771 is the probability by which worker 1 will outproduce worker 2
Let Xi be the random variable representing the number of units the first worker produces in day i.
Define X = X₁+ X₂ + X₃ + X₄ + X₅ as the random variable representing the number of units the first worker produces during the entire week.
We know that Mean =(Sum of all quantities)/(Number of quantities)
Mean=75 and number of quantities =5(given)
Therefore, from the formula
=>Sum of all quantities=75×5
or We can Say that X₁+ X₂ + X₃ + X₄ + X₅=375--------------------------------(eq1)
Now, talking about the standard deviation of first worker
We know that standard deviation = \(\frac{\sqrt{(Each quantity - Mean)^{2} } }{\sqrt{Total Number of quantities} }\)
We are given standard deviation of first worker as 20,
Therefore 20×\(\sqrt{Total Number of quantities}\) = \(\sqrt{(Eachquantity -Mean)^{2} }\)
20√5 = √[(X₁ - Mean)²+(X₂ - Mean)²+(X₃ - Mean)²+(X₄ - Mean)²+(X₅ - Mean)²]-(eq2)
Therefore, from eq1 and eq2,
we get Mean(µx) =375 and standard deviation(σ\(x\)) =20√5
Similarly, define random variables Y₁, Y₂, . . . , Y₅ representing the number of units produces by the second worker during each of the five days and define Y = Y₁ + Y₂ + Y₃ + Y₄ + Y₅.
From the Mean formula,
we get Y₁ + Y₂ + Y₃ + Y₄ + Y₅=(65×5)--------------------------------(eq3)
Standard deviation of second worker = 21(given),
So using the standard deviation formula, we get
Therefore 21×\(\sqrt{Total Number of quantities}\)=\(\sqrt{(Eachquantity -Mean)^{2} }\)
21√5=√[(Y₁ - Mean)²+(Y₂ - Mean)²+(Y₃ - Mean)²+(Y₄ - Mean)²+(Y₅ - Mean)²]-(eq4)
Therefore, from eq3 and eq4,
we get Mean(µy) =325 and standard deviation(σy) =21√5
Of course, we assume that X and Y are independent. The problem asks for P(X > Y ) or in other words for P(X − Y > 0).
It is a quite surprising fact that the random variable U = X −Y , the difference between X and Y ,is also normally distributed with mean µU = µx−µy = 375−325 = 50 and standard deviation σu ,where σ\(u^{2}\) = σ\(x^{2}\)+σ\(y^{2}\) =400·5+441·5 = 841·5 = 4205
It follows that σu=√4205.
Now probability of first worker(P₁)=375/√4205
probability of second worker(P₂) =325/√4205
We can clearly see P₁>P₂
Difference in Probability of both workers(P)=P₁-P₂
=>P=[(375/√4205)-(325/√4205)]
=>P=50/√4205
=>P=50/64.84
=>P=0.771
Hence, probability by which worker 1 will outproduce worker 2 is 0.771.
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Select the expression that represents the following statement: The sum of 6 and 8 multiplied by 4.
Answer:
It could be these
Step-by-step explanation:
• means times/multiplied, number right by parenthesis means multiply that by the answer of what is in the parenthesis
(6+8) • 4
4(6+8)
4 + (6•8)
A train from Philadelphia to Boston left Philadelphia at 1 pm and arrived to Boston at 4 pm. What was its average speed if the distance it covered was 270 miles?
Answer:
90 miles per hour is the average speed.
Step-by-step explanation:
The formula for Average Speed can be given as follows:
\(\text{Average Speed}= \dfrac{\text{Total Distance Traveled}} {\text{Total Time Taken}}\)
Here time taken is from 1 PM to 4 PM i.e.
Total Time taken = (4-1) hours = 3 hours
Also, it is given that the Total distance covered = 270 miles
As per the formula above:
\(\text{Average Speed} = \dfrac{270}{3}\\\Rightarrow \text{Average Speed} = 90\ miles/hour\)
So, answer is: 270 miles/ hour is the average speed of the train from Philadelphia to Boston.
For each of the parabolas, identify the following properties:
Be sure to lable the:
Vertex
Max/min value
Axis of symmetry
Zero(s)
Direction of opening
Y-intercept
The properties for parabolas 1 is:
Vertex: (-2, 1)Max/min value: minimum value is 1.Axis of symmetry: x = -2Zero(s): There are two zeros, at x = -4 and x = 0.Direction of opening: opens upwards.Y-intercept: (0, 5).Identify the properties?Parabola 1:
Vertex: (-2, 1)
Max/min value: The vertex represents a minimum point, so the minimum value is 1.
Axis of symmetry: x = -2
Zero(s): There are two zeros, at x = -4 and x = 0.
Direction of opening: The parabola opens upwards.
Y-intercept: The y-intercept is (0, 5).
Parabola 2:
Vertex: (1, -2)
Max/min value: The vertex represents a maximum point, so the maximum value is -2.
Axis of symmetry: x = 1
Zero(s): There are two zeros, at x = -1 and x = 3.
Direction of opening: The parabola opens downwards.
Y-intercept: The y-intercept is (0, -1).
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AACB = ADCE
<A=50°, <C=45°, and <D=10x
x=[?]
Answer:
X=5
Step-by-step explanation:
Angle A is congruent to angle D.
Find the product of the given polynomials. (5x+8-6x)(4x+2x-7)
Answer:\(-6x^{2} +55x-56\)
Step-by-step explanation:
. (8 pts.) The estimated monthly profit (in dollars) realized by Myspace.com from selling advertising space is P(x) = -0.04x2 + 240x - 10,000 Where x is the number of ads sold each month. To maximize its profits, how many ads should Myspace.com sell each month?
To maximize its profits, Myspace.com should sell approximately 300 ads each month.The maximum point of a quadratic function P(x) = -0.04x^2 + 240x - 10,000 occurs at the vertex.
The estimated monthly profit for Myspace.com from selling advertising space is given by the equation P(x) = -0.04x^2 + 240x - 10,000, where x represents the number of ads sold each month.
To determine the number of ads that will yield maximum profit, we need to find the value of x that corresponds to the maximum point on the profit function.
To find this, we can use calculus. The maximum point of a quadratic function occurs at the vertex, which can be found using the formula x = -b / (2a), where a, b, and c are coefficients in the quadratic equation ax^2 + bx + c = 0. In our profit equation, the coefficient of x^2 is -0.04, and the coefficient of x is 240.
Using the formula, we can calculate x = -240 / (2 * -0.04) = 300. Therefore, to maximize its profits, Myspace.com should sell approximately 300 ads each month.
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. What number replaces ☺ to make the sentence true? 1 + 3 + 4 + 6 + 6 + 8 + 9 + 11 = 4 × ☺.
Answer:
12
Step-by-step explanation:
1+3+4+6+6+8+9+11=48. Knowing this, we can now figure out the other side of the equation. To make both equations true, both sides must equal 48.
To this, simply divide 48 by 4.
48/4=12
Thus, your answer is 12
Answer: 12
Step-by-step explanation:
1+3+4+6+6+8+9+11 is 48 (you can double check)
48=4*X (calling x as the smiley).
Divide 4 by each side.
12=X
uscles Gym has a membership fee of $40 every 3 months. Energy Gym has a membership fee of $93 every 6 months.
What is the unit price at Muscles Gym? Enter your answer into the box.
What is the unit price at Energy Gym?
Enter your answer into the box.
What is the unit price at Energy Gym?
Enter your answer into the box.
Answer:
Muscles Gym: 13.33
Energy Gym: 15.00
Step-by-step explanation:
Muscles Gym: You divide "40.00" by "3", which will then give you the answer of "13.33".
Energy Gym: You divide "93.00" by "6", which will then give you the answer of "15.50".
You then add the zero to show the proper number of cents after the decimal point.
I hope this helps!
Solve |x-8|<=5 State your answer as a compound inequality A<=x<=B : State your answer in interval notation A,B :
The compound inequality is -16 ≤x ≤ 0 and the interval notation is [
How to solve the inequality?Here we have the absolute value inequality:
|x - 8| ≤ 8
The absolute value part can be decomposed into two inequalities:
x - 8 ≤ 8
x - 8 ≥ - 8
Solving these two, we get:
x ≤ 8 - 8 = 0
x ≥ -8 - 8 = -16
Then:
-16 ≤x ≤ 0
And the interval notation is [0, 16]
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find the exact trig value \(cos(11\pi /6)\)
suppose that the supply and demand of a good are given by the following equations: what is the elasticity of supply? a.5/4 b.10/9 c.3/4 d.11/8
For the given equations of the demand and supply of goods , the elasticity of supply will be (a) 5/4 .
The Elasticity of supply is defined as a measure of responsiveness of the quantity of a good or service supplied to changes in its price. It is the degree to which the quantity supplied of a product or service changes when there is a change in its price.
We know that the elasticity of supply curve is the same as the slope of supply curve because it represents the proportion of change in price that will change the quantity supplied.
The equation for the supply curve is given to be : S = -5 + (5/4)p ,
So , the slope of Supply curve is given in the equation is 5/4 .
Therefore , The Elasticity Of Supply is 5/4 , the correct option is (a) .
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The given question is incomplete , the complete question is
Suppose that the supply and demand of a good are given by the following equations:
Demand = 75 - (3/4)p and Supply = -5 + (5/4)p ,
What is the elasticity of supply?
(a) 5/4
(b) 10/9
(c) 3/4
(d) 11/8
If x and y are integers and x = 50y + 69, which of the following must be odd? O xy O x+y O x+2y 3x - 1 O 3x+1
Since 50 is an even number, we know that x will be even if y is even (50 times an even number is still even) and odd if y is odd (50 times an odd number is odd). Therefore, the only answer choice that must be odd is x+y.
Given that x and y are integers and x = 50y + 69, let's determine which of the following expressions must be odd.
1. xy: Since x is odd (50y + 69), when it is multiplied by any integer y, the result will always be odd. Therefore, xy must be odd.
2. x + y: If x is odd, adding it to an even integer (y) would result in an odd number. However, adding it to an odd integer (y) would result in an even number. Therefore, x + y does not necessarily have to be odd. xy: We can't determine if this is odd or even without knowing the values of x and y.
- x+y: This expression is always odd. To see why, consider two cases:
If x and y are both odd, then x+y is even+odd=odd.
If x and y are both even, then x+y is even+even=even.
If one of x and y is odd and the other is even, then x + y is odd + even =odd.
3. x+2y: We can't determine if this is odd or even without knowing the values of x and y.
3x-1: This expression will be odd if x is odd (3 times an odd number is odd) and even if x is even (3 times an even number is even).
3x+1: This expression will be odd if x is even (3 times an even number plus 1 is odd) and even if x is odd (3 times an odd number plus 1 is even).
x + 2y: Since x is odd and 2y is always even, their sum must be odd. Therefore, x + 2 y must be odd.
4. 3x - 1: This expression is odd, since 3x will always be odd (as x is odd) and subtracting 1 from an odd number results in an even number. Therefore, 3x - 1 does not necessarily have to be odd.
5. 3x + 1: This expression is odd, since 3x will always be odd (as x is odd) and adding 1 to an odd number results in an even number. Therefore, 3x + 1 must be odd.
In conclusion, the expressions that must be odd are xy, x + 2y, and 3x + 1.
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please help me rn!!!!!!!!
Answer:
A B and C
Step-by-step explanation:
it's a simple question
finding the area, ty
Mr. Kevin pays $37.95 per month for his cell phone with unlimited minutes. At this rate, what will his cellphone
cost for the year
Answer:
$455.4 For The Year
Step-by-step explanation:
Kevin pays $ 37.95 per month for his cell phone with unlimited minutes
First, We know that there are 12 months in 1 year.
Therefore, 1 year = 12 months
The cost per month = $ 37.95
So, have to find the cost for 12 months
Cost for 12 months = 12 x 37.95
Cost for 12 months = 455.4
So your solution to the problem is $455.4 Cost for the year.
Evaluate the function f(x) = x/3+4 for f(-9).
a. -23
b. -2
c. 7
d. 1
Answer:
d. 1
Step-by-step explanation:
To evaluate a function, plug the number in the parentheses into the expression in place of x:
(-9/3) + 4 = 1
Answer:
option d.
Step-by-step explanation:
answer is 1
as LCM is 3
-9/3+ 4/1*3/3=
-9+12/3= 3/3
=1
On april 8th, a flower at blooming acres florist was 15. 0 centimeters tall. On april 16th, the flower was 17. 4 centimeters tall. If the flower grew at a constant rate, on what day was the flower 16. 5 centimeters tall?.
In linear equation , 13 April is day was the flower 16. 5 centimeters tall.
What are a definition and an example of a linear equation?
An equation with only one variable is referred to as a linear equation in one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value. A linear equation in one variable would be 9x + 78 = 18, for instance.Rate of change = 17.4 - 15/16 - 8
= 2.4/3
= 0.3 cm/day
Difference between 16.5 cm and 15 cm = 16.5 - 15 = 1.5 cm
Number of days required to grow from 15 cm to 16.5 cm = 1.5/0.3 = 5 days
Date on which the flower was 16.5 cm tall = 8th April + 5 = 13 April
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Define convenience purchases, shopping purchases, and specialty purchases. Describe three specific brand name products in the consumer marketplace today that would correspond to these three types of purchases.
Convenience purchase: Coca-Cola. Shopping purchase: Apple iPhone. Specialty purchase: Rolex. These brand name products correspond to their respective purchase types based on convenience, shopping involvement, and specialty appeal in the consumer marketplace.
Convenience purchases refer to low-involvement purchases made by consumers for everyday items that are readily available and require minimal effort to obtain. These purchases are typically driven by convenience and habit rather than extensive consideration or brand loyalty.
Shopping purchases involve higher involvement and more deliberate decision-making. Consumers invest time and effort in comparing options, seeking the best value or quality, and may consider multiple brands before making a purchase. These purchases often involve durable goods or products that require more consideration.
Specialty purchases are distinct and unique purchases that cater to specific interests, preferences, or hobbies. These purchases are driven by passion, expertise, and a desire for premium or specialized products. Consumers are often willing to invest more in these purchases due to their unique features, quality, or exclusivity.
Three specific brand name products in the consumer marketplace that correspond to these types of purchases are
Convenience Purchase: Coca-Cola (Soft Drink)
Coca-Cola is a widely recognized brand in the beverage industry. It is readily available in various sizes and formats, making it a convenient choice for consumers seeking a refreshing drink on the go.
With its widespread availability and strong brand presence, consumers often make convenience purchases of Coca-Cola without much thought or consideration.
Shopping Purchase: Apple iPhone (Smartphone)
The Apple iPhone is a popular choice for consumers when it comes to shopping purchases. People invest time researching and comparing features, pricing, and user reviews before making a decision.
The shopping process involves considering various smartphone brands and models to ensure they select a product that meets their specific needs and preferences.
Specialty Purchase: Rolex (Luxury Watches)
Rolex is a well-known brand in the luxury watch industry and represents specialty purchases. These watches are associated with high-quality craftsmanship, precision, and exclusivity.
Consumers who are passionate about luxury watches and seek a premium product often consider Rolex due to its reputation, heritage, and unique features. The decision to purchase a Rolex involves a significant investment and is driven by the desire for a prestigious timepiece.
These examples illustrate how different types of purchases align with specific brand name products in the consumer marketplace, ranging from convenience-driven choices to more involved shopping decisions and specialty purchases driven by passion and exclusivity.
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Determine the minimum sample size required when you want to be onfident that the sample mean is within one unit of the population mean and 13.8 assume the population is normally distributed.
The minimum sample size required when you want to be 99% confident that the sample mean is within one unit of the population mean and σ = 13.8 is 1268
Given: To find the minimum sample size, confidence level = 99%, standard deviation = 13.8, and one unit population mean. [Normally distributed]
Solving the given question:
We know that the formula for Margin of error is:
Margin of error = z-score * (standard deviation) / root (sample size)
E = z * σ / √(n), where
E = Margin of error
z = z-score
n = Sample size
σ = standard deviation
Therefore, sample size = ( z – score * standard deviation / margin of error)²
n = ( z * σ / E )²
First, calculate the z-score for the 99% confidence level.
From the normal distribution curve, the area under 99% confidence level is given as:
Area under 99% confidence level = (1 + confidence level) / 2 = (1 + 0.99) / 2 = 0.995
From the z-score table, we find the value of z with the corresponding area of 0.995
We find the value of the z-score corresponding to 0.995 is 2.58
Also given sample mean is one unit of the population. So the margin of error is 1
E = 1
And given Standard deviation = 13.8
σ = 13.8
Putting the values in the given formula of sample size n =
n = (2.58 * 13.8 / 1 )²
n = 1267.64
n = 1268
Hence the minimum sample size required when you want to be 99% confident that the sample mean is within one unit of the population mean and σ = 13.8 is 1268
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Disclaimer: Determine the minimum sample size required when you want to be 99% confident that the sample mean is within one unit of the population mean and G = 13.8. Assume the population is normally distributed. A 99% confidence level requires a sample size of (Round up to the nearest whole number as needed )