By using the Law of Syllogism, a conditional should be used to write this statement "If a baby has a fever, then the baby is sick. If a baby is sick, then the baby must be brought to the hospital" as follows: B. If the baby has a fever, then the baby must be brought to the hospital.
What is the Law of Syllogism?In Mathematics, the Law of Syllogism is sometimes referred to as reasoning by transitivity and it states that if two (2) statements are true, then a third true statement can be logically derived.
Mathematically, the Law of Syllogism follows a specific pattern and can be represented by the following conditional statements:
Conditional statement 1: If P, then Q (P ↔ Q).
Conditional statement 2: If Q, then R (Q ↔ R.
Conditional statement 3: If P, then R ( P ↔ R).
In this context, we can reasonably infer and logically deduce that a sick baby must be taken to hospital based on the given premise in accordance with the Law of Syllogism.
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Complete Question:
Use the Law of Syllogism to write a conditional for the following statement.
If a baby has a fever, then the baby is sick. If a baby is sick, then the baby must be brought to the hospital.
answer choices
If the baby is sick, then the baby must be brought to the hospital.
If the baby has a fever, then the baby must be brought to the hospital.
If the baby has a fever, then the baby is sick.
Three students practiced
converting values into scientific
notation as shown. In 1-3,
describe the mistake each student
made and correct their work.
What's the circumference of a circle with a radius of 8 inches? Use 3.14 for π. C = [?] inches
The circumference of the circle is 50. 24 Inches
How to determine the circumference of the circleIt is important to note that the circumference of a circle is represented with the formula;
C = 2πr or πd
Given that;
C is the circumference of the circleπ takes the value 3.1 4r is the radius of the circled is the diameter of the given circleAlso, the formula for calculating the radius of the circle given the diameter is expressed as;
Radius = diameter /2
Now, let's substitute the values into the formula, we get;
Circumference, C = 2 × 3. 14 × 8
Multiply the values
Circumference, C = 50. 24 Inches
Hence, the value is 50. 24 Inches
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The table below shows the ratio of a bird's brain to body weight.
Brain (part) 0.4 B 1.6 E
Body (part) A 12.1 17.6 44
Total (whole) 4.8 C D 48
Which table shows the correct missing values?
Brain (part) 0.4 1.1 1.6 4
Body (part) 4.4 12.1 17.6 44
Total (whole) 4.8 13.2 19.2 48
Brain (part) 0.4 2.1 1.6 4
Body (part) 4.0 12.1 17.6 44
Total (whole) 4.8 14.2 19.2 48
Brain (part) 0.4 1.1 1.6 4
Body (part) 3.8 12.1 17.6 44
Total (whole) 4.8 14.2 33.6 48
Brain (part) 0.4 2.1 1.6 4
Body (part) 4.4 12.1 17.6 44
Total (whole) 4.8 13.2 33.6 48
The table that shows the correct missing values would be option A = Brain (part) 0.4 1.1 1.6 4
Body (part) 4.4 12.1 17.6 44
Total (whole) 4.8 13.2 19.2 48
What is addition?Addition is the combination of two or more values which leads to the arrival of a common value.
To calculate for A;
Brain = 0.4
body part = A
Total = 4.8
A = 4.8 -0.4 = 4.4
To calculate for B;
Brain = B
Body part = 12.1
Total = 13.2
B = 13.2 - 12.1 = 1.1
To calculate for C;
Brain = 1.6
Body part = 17.6
Total (C ) = 19.2
To calculate E;
Brain= E
Body= 44
Total = 48
E = 48-44 = 4
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Suppose you deposit $2000 in a savings account that pays interest at an annual rate of 6%. If no money is added or withdrawn from the account, answer the following questions.
A. how much will be in the account after 4 years?
B. How much will be in the account after 16 years?
C. How many years will it take for the account to contain $2500?
D. How many years will it take for the account to contain $3000?
Step-by-step explanation:
The account starts at 2000$
2000$×0.06(same as 6%)= 120$
The account gains 120$ yearly
A. After 4yrs that would be 480$ interest
120$×4= 480$
2000$+480$= 2480$ after 4yrs
B. Aftee 16yrs that would be 1920$ interest
120$×16= 1920$
1920$+2000$= 3920$
C. 2500$-2000$= 500$
500$÷120$= 4.16yrs
It will take about 4.2 years for the account to reach 2500$
D. 3000$-2000$= 1000$
1000$÷120$= 8.33yrs
It will take about 8.3yrs for the account to reach 3000$
Find the volume of the solid describe below:
The solid lies between the planes perpendicular to the x-axis at x= 0 and x=8 . The cross-sections perpendicular to the axis on the interval 0≤x≤8 are squares whose diagonals run from the parabola y=−√x to the parabola y=√x
Jana’s cookies sales are represented by the graph. What is the rate at which Jana is selling cookies?
Answer:
Step-by-step explanation:
15 an hour
Evaluate the iterated integral by converting to polar coordinates.20√4 − x20e−x2 − y2 dy dx
Integrating this expression, we obtain: −20√4 cosθe−r2 + C, where C is the constant of integration. Therefore, the integral evaluates to this expression.
Using polar coordinates, we have:
20√4 − r cosθ20e−r2 − r sin2θ dr dθ
This simplifies to:
20√4 − r cosθ20e−r2 dr dθ
Now we can integrate:
∫20√4 − r cosθ20e−r2 dr dθ = −20√4 cosθe−r2 + C
Where C is the constant of integration.
This iterated integral can be evaluated by converting to polar coordinates. We first rewrite the integral as: 20√4 − r cosθ20e−r2 dr dθ. Integrating this expression, we obtain: −20√4 cosθe−r2 + C, where C is the constant of integration. Therefore, the integral evaluates to this expression.
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help everyone help me please
A convex mirror's generated image is always virtual and situated behind the mirror. The picture is erect and situated at the focal point when the item is far from the mirror.
What is the location of the image at the center of the curvature?The radius of curvature is the measurement between the vertex and the center of the curve (represented by R). The sphere from which the mirror was sliced has a radius equal to the radius of curvature. The distance between the vertex of the circle used to create the cylindrical mirror's shape to its center is known as the center of curvature.
In addition, the center of curvature will house the image. The image will be upside-down in this situation. The proportions of the image match those of the object. The image is the same size as the object, actual, and inverted if the object is at the center of the curve. The image is bigger, realer, and inverted if the object lies between the center of curvature and the main focus.
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1. Find the area of the region enclosed by one loop of the curve.
r = sin(8theta)
2.Find the area of the region enclosed by one loop of the curve.
r = 7 cos(3theta)
1. The area of the region enclosed by one loop of the curve r = sin(8theta) is 16π.
2. The area of the region enclosed by one loop of the curve r = 7 cos(3theta) is 28π.
The area of a region enclosed by one loop of a curve is calculated by using a method called the “area under the curve”. This method involves integrating the equation of the curve over one full period (or loop) of the curve. For example, in the case of a curve with equation r = sin(8theta), the area of the region enclosed by one loop of the curve is equal to the integral of r = sin(8theta) from 0 to 2π. This integral evaluates to 16π, which is the area of the region enclosed by one loop of the curve. The same method can be applied to a curve with equation r = 7 cos(3theta) to find the area of the region enclosed by one loop of the curve. In this case, the integral of r = 7 cos(3theta) from 0 to 2π evaluates to 28π, which is the area of the region enclosed by one loop of the curve.
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A senator wants to know what her constituents think of a proposed health bill. Her staff reports that 222 letters have been received on the subject, of which 200 opposed the bill. Define both the population and the sample in this scenario.
A senator wants to know what her constituents think of a proposed health bill. In this scenario, the population would be all of the constituents of the senator. The sample would be the 222 letters that were received on the subject.
What are the population and the sample?Generally, In statistics, a population is the entire group of individuals or items that you want to study.
A sample is a smaller group of individuals or items that is selected from the population to represent the larger group. The sample is used to make inferences about the population.
For example, let's say you want to study the political opinions of all the registered voters in your city. The population in this case would be all the registered voters in your city.
However, it might not be practical or possible to survey every single registered voter, so you might instead select a sample of registered voters to survey. This sample would be used to make inferences about the political opinions of the larger population of registered voters in your city.
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You multiply two numbers. The first number, 21, is 6.25% of the product. What is the second number?
Answer:
12.5
Step-by-step explanation:
The products of two numbers is 6.25 if one of them is 0.5 then find the other Number. - 31133581.
0.5 * x = 6.25
x = 6.25 / 0.5
= 12.5
A group of friends wants to go to the amusement park. They have no more than $160 to spend on parking and admission. Parking is $10. 50, and tickets cost $32. 50 per person, including tax. Write and solve an inequality which can be used to determine xx, the number of people who can go to the amusement park.
Using the idea of inequality and some simple math calculations, the total number of persons who can visit an amusement park is 4.
Given that a group of friends has a maximum of $160 in this question.
$10.50 is the cost of parking.
The price of each ticket is $32.50.
We must address inequality.
So let's attempt to define inequity.
Inequalities in mathematics describe the connection between two non-equal quantities. Equal does not necessarily mean unequal. When two values are not equal, we typically use the "not equal sign (≠)". However, a number of inequalities are used to compare the numbers and determine whether one is greater than the other.
A relation is called an inequality if two real numbers or algebraic expressions are related by the symbols ">" "<" "≥" "≤".
Let's Suppose we have a total of x number of persons.
then the total cost of tickets is 32.5 * x.
cost of parking is $10.50.
So the total cost to visit an amusement park is = 32.5x+ 10.50
Given that the total cost will be no more than $160.
So according to that
32.5x+ 10.50 ≤ 160.
32.5x ≤ 160-10.50
32.5x ≤ 149.5
x ≤ 149.5/32.5
x ≤ 4.6.
The nearest integer will be 4.
So the number of people who can go to an amusement park is 4.
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The group of friends can have no more than 4 people go to the amusement park.
We can use an inequality to determine the number of people who can go to the amusement park. We know that the group has no more than $160 to spend on parking and admission. We also know that parking is $10.50 and tickets cost $32.50 per person, including tax.
The inequality we can use to determine the number of people who can go to the amusement park is: 10.50 + 32.50x ≤ 160
To solve the inequality, we must first subtract 10.50 from both sides of the equation to isolate variable x. This gives us: 32.50x ≤ 149.50
Next, we must divide both sides of the equation by 32.50 to solve for x. This gives us: x ≤ 4.62
Since x is the number of people who can go to the amusement park, we must round down to the nearest whole number. This gives us: x ≤ 4
Therefore, we can conclude that the group of friends can have no more than 4 people go to the amusement park.
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What is fully factored form of 32a3 12a2?
On factorizing , we get that the fully factored form of the expression [tex]32a^{3} + 12a^{2}[/tex] can be written as [tex]4a^{2} (8a+3)[/tex] .
The Factorizing is defined as a process of expressing the given number or the algebraic expression as a product of its factors .
the expression is given as : [tex]32a^{3} + 12a^{2}[/tex] ;
the first term of the expression is ⇒ [tex]32a^{3}[/tex] , it can be expressed as [tex]4\times 8 \times a \times a \times a[/tex] ;
the second term of given expression is ⇒ [tex]12a^{2}[/tex] , it can be expressed as [tex]4\times 3 \times a \times a[/tex] ;
we see that in both terms , the common factor is [tex]4\times a \times a = 4a^{2}[/tex] ;
which means that , it is written as : [tex]4a^{2} (8a+3)[/tex] ;
Therefore , the fully factored form is [tex]4a^{2} (8a+3)[/tex] .
The given question is incomplete , the complete question is
What is fully factored form of the expression [tex]32a^{3} + 12a^{2}[/tex] ?
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Which statement is true?
Answer:
Step-by-step explanation:
first one
Ms. Hall wrote the expression 5 × (2 + 6)2 ÷ 4 on the board. Shyann said the first step is to evaluate 62.
Complete the explanation of Shyann's mistake. Then evaluate the expression.
The value of the expression is _____
The value of the expression is 20.
Shyann made a mistake by saying that the first step is 6 × 2. The first step should be obtaining the value for the expression in the bracket.
How is the expression solved?For an expression as the above, we can arrive at the answer by using the rule of BODMAS. In this rule, the expression in the bracket is first solved. Thus, we can obtain the answer this way:
5 × (2 + 6) 2 ÷ 4
5 × (8) 2 ÷ 4
This is followed by the division of 2 by 4 which gives 0.5
5 × (8) 0.5
Next, we multiply the figures
40 × 0.5
= 20
So, the correct value for the expression is 20.
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gebra 1 > DD.13 Checkpoint: Problem solving with equations and inequalities QZQ
The area of a rectangular porch is 264 square feet. The width of the porch is 1 foot less than
half its length. Which equation can be used to find the width, w, of the porch?
W
-1=264
w² - w = 263
W = 11
Which value of w gives the width of the porch, in feet?
Submit
W = 13
2w² -2=264
2w² + 2w = 264
W = 16
W = 23
NG
9
2W² + 2W = 264 is the equation that an be used to find the width, W, of the porch. The value w = 11 gives the width of the porch, in feet.
What is width and length?The tools that aid in indicating an object's measurements are length, width, and height. We can calculate the volume of geometric shapes using their length, width, and height.
The length of an object or a figure on a planar surface is its longest measurement. The length of the specified object or figure is indicated.
The width of an object or figure on a planar surface is its smallest dimension. It provides the object or figure's width information.
Height is the measurement of an object's vertical distance from a figure or a planar surface.
Given that a rectangular porch has an area of 264 ft²
L × W = 264 ft²
And
W = L/2 - 1
or
L = 2(W + 1)
Substitute the value of L in area Equation
2(W + 1) × W = 264
2W² + 2W = 264
Putting the equation in quadratic formula we get
x = 11
x = -12
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State Income Tax Rates
Taxable Income Tax Rate
Up to $20,000 2%
Next $20,000
4%
Over $40,000
6%
True or False: If you are single and make $18,000 and the state allows a $2,000
exemption for each person in your household, the amount of your annual state
income tax is $320.
O True
O False
Answer: im assuming it is true
Step-by-step explanation:
What is the projection of (4,4) onto (3,1)? A. 1.3(3,1)
B. 1.3(4,4)
C. 1.6(4,4)
D. 1.6(3,1)
Answer: D
Step-by-step explanation:
the lot is 90 feet by 110 feet. the fence is to be 6 feet tall. cost for the fence is $3.00 per linear foot, plus $.40 per square foot for labor. what is the total cost of the fence
the lot is 90 feet by 110 feet. the fence is to be 6 feet tall. cost for the fence is $3.00 per linear foot, plus $.40 per square foot for labor then the total cost of the fence is 8643 dollar
We have to sum the three distances to get the perimeter.
P= 90 ft + 110 ft+ 6 ft
P = 201 ft
And each foot of material cost $3.00
we get the cost with the distance and de cost of the material:
Cost = 201 ft * 3.00 $ per ft = $603
he needs $603.00 to fence her backyard garden
40 per square labor
then 201*40 = 8040
total = 8040+603= 8643
thus the total cost of the fence is 8643 dollar
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Find the minimum sample size n needed to estimate μ for the given values of c, o, and E. c= 0.95, σ = 5.7, and E = 1 Assume that a preliminary sample has at least 30 members. n= (Round up to the nearest whole number.)
The minimum sample size needed to estimate μ for the given values of c, o, and E is 100
The minimum sample size needed to estimate μ for the given values of c, o, and E is 100
We use the formula
n= (zc/E)2σ2
Where,
n = sample size
zc = The minimum sample size needed to estimate μ for the given values of c, o, and E is 100
E = margin of error
σ = standard deviation
Substituting the given values,
n= [(1.96*0.95)/1]2*5.72
n= 95.29
Therefore, the minimum sample size n equals 96 (rounded up to the nearest whole number).
The minimum sample size needed to estimate μ for the given values of c, o, and E is 100
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ST, a vertical pole 2 metres high, is situated at the corner of a rectangular garden, PQRS.
RS is 8 metres long and QR is 12 metres long.
Ł
Q
P
M
12 m
The pole casts a shadow over the garden.
The shadow reaches M, the midpoint of QR.
Calculate the size of the shaded angle TMS.
R
T
S
2 m
Subtract the given supplementary angle (its value in degrees) from 180.
How do you calculate the size angle?In △ABC and △DEF
∠A=∠D=90∘
Since the tower and the stick cast their respective shadows at the same time on the ground,
So, ∠C=∠F
∴△ABC∼△DEF ….(by AA similarity)
AB/DE=AC/DF so 12/x=8/40
X=60m
Calculating the magnitude of an angle necessitates knowledge of complementary, additional, and neighboring angles, as well as geometric form attributes. To compute the magnitude of the angle in question, subtract the specified supplementary angle (its value in degrees) from 180. An angle is measured in degrees from 0° to 180° in geometry. The angle’s size is indicated by the number of degrees.
The Pythagorean theorem Let xyz angle = A So, tan(A) = opposite/next => tan(A) = 15/6 As a result, A = tan-1(15/6) => 68.19863 As a result, angle xyz = 68 degrees. I hope this helps. You can also schedule a class for more clarification. Right angles are 90 degrees in length. Obtuse angles are more than 90 degrees.
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Mikaela purchased a paddleboard originally priced at $899. if all merchandise was on sale for 40% off and the state tax rate is 7.25%, what is the total amount that mikaela spent on the paddleboard? $385.67 $424.78 $578.51 $604.58
The total amount that Mikaela spent on the paddleboard is $578.506. which is the correct answer would be option (D)
What is the percentage?
The percentage is defined as a ratio expressed as a fraction of 100.
We have been given that Mikaela purchased a paddleboard originally priced at $899. If all merchandise was on sale for 40% off and the state tax rate is 7.25%.
Here,
Original cost = $899
Discount = 40% = 0.40
State tax rate = 7.25% = 0.0725
Total amount = Original cost × (1 - Discount) × (1 + State tax)
Total amount = 899×(1 - 40%)×(1 + 7.25%)
Total amount = 899×(1 - 0.40)×(1 + 0.0725)
Total amount = 578.506
Thus, the total amount that Mikaela spent on the paddleboard is $578.506
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The total amount that Mikaela spent on the paddleboard is $578.51. The result is obtained by subtracting the discount from the original price and adding the tax.
How to calculate the total price to pay?When we get a discount of a product, the price will get cheaper. The price is subtracted by the discount. When there is a tax, you have to pay for it.
Mikaela purchased a paddleboard with the original price of $899. She got a discount of 40%. The tax rate is 7.25 %. Find the total amount she paid for the paddleboard!
From the information, we get the discount
= 40% × $899
= 0.4 × $899
= $359.6
The tax would be
= 7.25% × $899
= 0.0725 × $899
= $39.11
The total price is
= original price - discount + tax
= $899 - $359.6 + $39.11
= $578.51
Hence, Mikaela spent $578.51 for the paddleboard.
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Solve the following system of equations by elimination.
3x-2y=1
9x-6y=3
The value of x and y in the equations is 1
What is Simultaneous equation?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 4x − 4y = 4.
Simultaneous equation can be solved by elimination and substitution method, but we are going to use elimination method here.
3x - 2y = 1 equation 1
9x - 6y = 3 equation 2
making the coefficient of x to be thesame in both equations
27x - 18y = 9 equation 3
27x - 18y = 9 equation 4
equation 3 and 4 are equal, this means that the value of x and y are equal.
Therefore for the equation to be true, x = 1 , y= 1
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A scenic train ride has one price for adults and once price for children. One family of two adults and two children pays $62 for the train ride. Another family of one adult and four children pays $70. Which system of linear equations can you use to find the price x for an adult and the price y for a child? please help i will mark you brainliest.
The system of linear equations with our defined variables are 2x + 2y = 62 ...eq(i) and x + 4y = 70 ...eq(ii)
What is System of Linear EquationA system of linear equations is a collection of two or more linear equations that use the same set of variables. The solution of a system of linear equations is the set of values for the variables that make all of the equations in the system true.
In this problem, let's define our variables as;
x = adultsy = childrenThe equations can be written as;
2x + 2y = 62 ...eq(i)
x + 4y = 70 ...eq(ii)
Which is synonymous to option D in the question
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Yu Yan makes a wall hanging from a piece of fabric. For the first part, she cuts off of the length of the original piece of fabric. For the next two parts, she cuts off 10 inches and 5 inches from the length of the remaining fabric. In total, she cuts 35 inches from the length of the original piece of fabric. How long was the original piece of fabric? Write and solve an equation. Check your solution.
Answer: Let x be the length of the original piece of fabric.
We know that:
x - y = length after first cut
(x - y) - 10 = length after second cut
((x - y) - 10) - 5 = length after third cut
Therefore, we can set up the equation:
x - y - 10 - 5 = 35
x - y = 50
To find the original length of the fabric, we can add y to both sides:
x = y + 50
The original length of the fabric is 50 inches + y inches.
We know that the total length cut was 35 inches.
So we can set up the equation:
y + 10 + 5 = 35
y = 20
So the original length of the fabric is 50 + 20 = 70 inches.
We can check the solution by using the equation:
x - y - 10 - 5 = 35
70 - 20 - 10 - 5 = 35
which is true.
Step-by-step explanation:
please give the answer as soon as possible. asap
Answer:
by solution of 4/3 πr^3
volume of sphere= 5.57×10^-3 m^3
hope this would help you!
Graph a line that has a slope of -3
Answer:
See explanation
Step-by-step explanation:
Every time x increases by 1, y decreases by 3.
In statistics, a population consists of:
A. all people living in the area under study
B. all subjects or objects whose characteristics are being studied
C. a selection of a limited number of elements
D. all people living in a country
All subjects or objects whose characteristics are being studied.
What is Statistics?In statistics, a population consists of all subjects or objects whose characteristics are being studied. This means that a population can be defined as a group of individuals, objects, or events that have something in common.
For example, if you are conducting a survey on the opinions of people in a city, the population would be all the people living in the city. If you are studying the behavior of cats, then your population would be all cats. In short, the population is the group of individuals or objects that you are interested in studying.
In addition, the population can be further broken down into subgroups, such as males and females, different age groups, geographical regions, and so on. This is known as stratifying the population and can help researchers to better understand the characteristics of their population and make more accurate conclusions.
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The sides of parallelogram $MNPQ$ are represented by the expressions below. Find the perimeter of $MNPQ$ . $MQ=-2x+37$ $NP=x-5$ $QP=y+14$ $MN=4y+5$. Whar is the perimeter is units?
Answer: P=52
Step-by-step explanation:
sorry if wrong
Answer:p=52
Step-by-step explanation:
A research scientist wants to know how many times per hour a certain strand of bacteria reproduces. He wants to construct the 95% confidence interval with a maximum error of 0.19 reproductions per hour. Assuming that the mean is 12.6 reproductions and the variance is known to be 3.61 what is the minimum sample size required for the estimate? Round your answer up to the next integer.
Answer:
the minimum sample size required is 139
Step-by-step explanation:
To construct a 95% confidence interval with a maximum error of 0.19 reproductions per hour, we need to use the t-distribution. The t-distribution is used when the population variance is unknown and the sample size is small.
To find the minimum sample size required, we need to use the following formula:
n = (t_(α/2,df) * s / E)^2
where:
n is the minimum sample size
t_(α/2,df) is the critical value of the t-distribution for a confidence level of 95% (α = 0.05) and df is the degrees of freedom
s is the standard deviation of the population
E is the maximum error allowed
We are given that the mean is 12.6 reproductions and the variance is 3.61. The standard deviation is the square root of the variance, so the standard deviation is 1.9.
To find the critical value of the t-distribution, we need to know the degrees of freedom. The degrees of freedom is equal to the sample size minus 1. Since we don't know the sample size yet, we will use a symbol (let's use "df") to represent the degrees of freedom in the formula.
Plugging the values into the formula, we get:
n = (t_(0.025,df) * 1.9 / 0.19)^2
To find the critical value of the t-distribution, we need to use a t-table or a computer program. Looking up the critical value in a t-table or using a computer program, we find that the critical value for a 95% confidence level and df = 9 is 2.262.
Plugging this value into the formula, we get:
n = (2.262 * 1.9 / 0.19)^2
Simplifying the expression, we get:
n = (11.868)^2
n = 138.7
The minimum sample size required is 138.7. Since we can't have a fractional number of samples, we need to round up to the next integer, which is 139.
Therefore, the minimum sample size required is 139.
