Marta found a website that sells her favorite style of coffee mugs. She writes the function C(m)=4.50 m+7, where C(m) represents the total cost of ordering m mugs, to decide how many mugs to order. Determine whether each statement about the features of the function is true or false in terms of the context.
The range is {y l y ≥ 11.5\}.
The domain is all real numbers.
The y-intercept is 4.5.
There is no x-intercept.
The rate of change is $ 4.5 per mug.
Answers
The true or false values of the statements are:
The range is {y l y ≥ 11.5\}: FalseThe domain is all real numbers: FalseThe y-intercept is 4.5: TrueThere is no x-intercept.: TrueThe rate of change is $4.5 per mug: TrueHow to determine the true statements from the scenario?From the question, we have the following parameters that can be used in our computation:
C(m) = 4.50m + 7
The smallest number of mugs she can sell is 0
So, we have the following equation
C(0) = 4.50 * 0 + 7
Evaluate
C(0) = 0
This means that the range is y ≥ 0
Next, the domain cannot be all real numbers
This is because real numbers include negative and decimal numbers
For the y-intercept, we have
C(m) = 4.50m + 7
Set m to 0
y-intercept = 4.5 * 0 + 7
Evaluate
y-intercept = 7
For the y-intercept, we have
C(m) = 4.50m + 7
Set C(m) to 0
4.5 * x-intercept + 7 = 0
Evaluate
x-intercept = -7/4.5 -- this cannot be taken as the x-intercept because it is a negative number
Also, we have the slope to be 4.5
So, the rate of change is $4.5 per mug
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Related Questions
2 A scale model of a building has a height that is 16 inches tall. The actual height of
the building is 240 feet. Which scale is used to represent the scale drawing of the
building?
F 1 inch : 8 feet
G 1 inch 9 feet
H 1 inch 15 feet
J 1 inch 16 feet
Which proportion can be used to find the length of EP in centimeters?
Answers
Answer:
inverse proportion
Step-by-step explanation:
2=k240/16
50 POINTS
Question 5
The sample space for tossing a coin 3 times is {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}.
Determine P(2 tails).
12.5%
37.5%
50%
75%
Question 6
Which table shows the sample space for spinning the spinner twice?
spinner with 3 equal sections colored yellow, blue, and red
Blue Yellow Red
Red Red Red Red
Blue Blue Blue Blue
Yellow Yellow Yellow Yellow
Blue Yellow Red
Blue Blue, Blue Blue, Yellow Blue, Red
Blue Blue, Blue Blue, Yellow Blue, Red
Red Blue Yellow
Red Red, Red Blue, Red Yellow, Red
Blue Red, Blue Red, Yellow Blue, Yellow
Yellow Yellow, Red Yellow, Blue Yellow, Blue
Red Blue Yellow
Red Red, Red Blue, Red Yellow, Red
Blue Red, Blue Blue, Blue Yellow, Blue
Yellow Red, Yellow Blue, Yellow Yellow, Yellow
Question 7
A set of 3 cards, spelling the word ADD, are placed face down on the table. Determine P(D, D) if two cards are randomly selected with replacement.
one third
two thirds
two sixths
four ninths
Answers
In the fall of 1996, tuition and registration fees for undergraduates at the University of California, Davis was $1411. In the fall of 2018, tuition and fees
were $14,402. Find the percent increase. Round your answer to the nearest tenth percent
% increase
Answers
To find the percent increase, we need to calculate the difference between the new tuition and fees and the old tuition and fees, and then divide this difference by the old tuition and fees and multiply by 100%.
The difference between the new tuition and fees of $14,402 and the old tuition and fees of $1411 is $14,402 - $1411 = $12,991.
The percent increase is: ($12,991/$1411) * 100% = 9.2 * 100% = 920%
Therefore, the percent increase in tuition and fees between the fall of 1996 and the fall of 2018 was 920%, rounded to the nearest tenth percent.
Solving Equations and Inequalities
Answers
The error occur from line 2 to line 3(optionB)
What is a linear equation?An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has an exponent more than 1. The graph of a linear equation forms a straight line.
A linear equation can have one or two variables. For example 5 = y+ 3y is an example of linear equation with one variable and y = 5 +3x is an example of linear equation with two variables.
8x-4= 2(4x+1)-6
8x-4= 8x+2-6
8x-4= 8x-4
Therefore the error is made where the parentheses is been solved, 2 is to multiply both 4x and 1.
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y=3x-34
у = 2x — 5
Help me with this
Answers
Answer:
x=29 and y=53
Step-by-step explanation:
let y=3x-34 be the first equation (1) and y=2x-5 be the second equation (2)
Using the elimation method, (1)-(2): 0=x-29
-x=-29
x=29
Substitute x=29 into (2),
y=2(29)-5
y=58-5
y=53
So, x=29 and y=53
write an equation for the money they collect,y,as a function of the number of t-shirts they sell,x.
Answers
Answer:
Step-by-step explanation:
There are several ways to write an equation for the money collected as a function of the number of t-shirts sold. One possible equation is $y = x \cdot p$, where $p$ is the price of each t-shirt. This equation says that the total amount of money collected is equal to the number of t-shirts sold multiplied by the price of each t-shirt.Another possible equation is $y = p \cdot (x - c)$, where $c$ is the cost of producing each t-shirt. This equation says that the total amount of money collected is equal to the price of each t-shirt multiplied by the number of t-shirts sold minus the cost of producing each t-shirt.These are just two examples of how to write an equation for the money collected as a function of the number of t-shirts sold. The exact equation will depend on the specific details of the situation.
4
BOOKMARK
Simplify each of the following expressions:
-5 - 2 + 8 =
Answers
Answer:
1
Step-by-step explanation:
-5 -2=-7
Keep in mind that negative is below zero. by adding eight we have reach 1 point to the right of zero. Thus, explaining tha answer of positive 1.
-7+8=1
Final Answer: 1
Prepare a manifesto in which you propose alternatives to overcome discrimination in the case of activity 2. Consider the following
the needs and rights of those involved. What do you think are the reasons for not discriminating against these groups?
to seek equality in dignity and rights. What would you do to avoid this discrimination?
Answers
Avoiding discrimination is extremely important because this is an attitude that goes against human dignity and different values.
1. Alternatives to overcome discriminationSome alternatives to overcome discrimination are:
Promote good values, such as respect. Raise awareness about the negative effects of discrimination.2. What do you think are the reasons for not discriminating against these groups?No group should be discriminated against because discrimination promotes negative values and does not allow the correct development of people.
3. What would you do to avoid this discrimination?To avoid discrimination you can:
Seek to raise awareness about why we should not discriminate. Promote good values such as respect.Promote inclusion.¡Hope this helped!
It says my answer is correct over a part of the domain of the integrand, but undefined on another part of the domain. Entered Answer 3*In(\n(7*x))+C
Preview Message 3 ln(ln(7x)) +C
Your answer is correct over part of the domain of the integrand, but is undefined on another part of the domain Evaluate the indefinite integral: 1 x In (18) 3 dx x In(7x) = 3*ln[In(7x)]+C
Answers
Answer:
3 ln(abs ln(7x)) +C
Step-by-step explanation:
Do not forget to add the absolute value!
At the end of a snowstorm, Gabriella had 11 inches of snow on her lawn. The
temperature then increased and the snow began to melt at a constant rate of 0.5
inches per hour. Assuming no more snow was falling, how much snow would
Gabriella have on her lawn 3 hours after the snow began to melt? How much snow
would Gabriella have on her lawn after t hours of snow melting?
Answers
The snow melted in 3 hours would be 1.5 inches, and the expression which represents the amount of snow left after 't' hours of snow melting S(t) = 12.5 - 0.5t
What is a constant rate of change?
A rate of change is a rate that describes how one quantity changes in relation to another quantity.
Constant rate is also called uniform rate which involves something traveling at a fixed and steady pace or else moving at some average speed.
The snow started melting at a rate of 0.5 inches per hour and it is known that 3 hours after the storm ended, the depth of snow was down to 11 inches.
Snow melted in 3 hours = 0.5 * 3 = 1.5 inches
Thus;
The Initial depth of snow = 11 + 1.5 inches = 12.5 inches.
Now, depth of snow on Gabriella's lawn = Initial depth - 0.5(Number of hours)
Let S(t) be the depth of snow on Gabriella's lawn, in inches, t hours after the snow stopped falling.
Hence, the snow melted in 3 hours would be 1.5 inches, and the expression which represents the amount of snow left after 't' hours of snow melting S(t) = 12.5 - 0.5t
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Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. Group of answer choices 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x + 9) = –3 + 9 2(x2 + 6x) = –3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x) = 3
Answers
The following are the actions she could take to solve the quadratic equation: 2(x² + 6x + 9) = 18 + 3.
Define the term quadratic equation?In relation to squares, the square operation, concepts of a second degree, including equations or formulas containing such terms, something is said to as quadratic.Following is the determination of the quadratic equation's solution;
2x² + 12x - 3 = 0
2x² + 12x = 3
Divide equation by 2.
x² + 6x = 3/2
Add both of the equation's sides after squarely multiplying the x-coefficient by half:
(x + 3)² = 3/2 + 3²
x² + 6x + 9 = 9 + 3/2
2(x² + 6x + 9) = 18 + 3
Thus, in order to calculate the quadratic equation, she could follow these steps: 2(x² + 6x + 9) = 18 + 3.
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If sin (0) = -3.29, what is sin ( + 0)?
A.
-2.39
B. -3.29
C. 2.39
D. 3.29
Answers
Answer:
Step-by-step explanation:
B
what does it mean by element c32
Answers
Answer:
2 (the first choice)
Step-by-step explanation:
This is a matrix of size 3 rows and 5 columns (3 x 5)
Any element of the matrix can be reference by row and column number
C₃₂ refers to the element in the 3rd row, 2nd column which is 2
The matrix is of size 3 rows and 5 columns (3*5)
Back to the question
C32 is the same as elements on the third row.
The answer is 2nd column which is 2.
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which of the following assets is not an example of a fixed asset for a manufacturer of road building equipment? group of answer choices employee parking lot production equipment for assembling engines shipping area for finished goods and receiving area for component parts cans of yellow paint for refurbishing equipment warehouse building for storing finished equipment
Answers
The following assets is not an example of a fixed asset for a manufacturer of road building equipment is " cans of yellow paint for refurbishing equipment warehouse building for storing finished equipment " .
Given :
which of the following assets is not an example of a fixed asset for a manufacturer of road building equipment group of answer choices employee parking lot production equipment for assembling engines shipping area for finished goods .
What is fixed asset ?
A fixed asset is a long-term tangible property or piece of equipment that a company owns and uses in its operations to generate income.
It is clear that the paints cans cannot a property so it is not an example of fixed assets .
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helppp me please. i did my points but I need help on the rest
Answers
By using linear equation, it can be calculated that
New Solution #1 : (-6, 1) is a solution because when you plug it into the original equation x + 3y = -3, the equation simplifies to -3 = -3
New Solution #2: (-9, 2) is a solution because when you plug it into the original equation x + 3y = -3, the equation simplifies to -3 = -3
What is linear equation?
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Equation of line : x + 3y = -3
Putting y = 1
x + 3 [tex]\times[/tex] 1 = -3
x = -3 - 3
x = -6
Putting y = 2
x + 3 [tex]\times[/tex] 2 = -3
x + 6 = -3
x = -3 - 6
x = -9
New solutions (-6, 1) and (-9, 2)
New Solution #1 : (-6, 1) is a solution because when you plug it into the original equation x + 3y = -3, the equation simplifies to -3 = -3
New Solution #2: (-9, 2) is a solution because when you plug it into the original equation x + 3y = -3, the equation simplifies to -3 = -3
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Max is thinking of a number, which he calls n. He adds 8 and then doubles the sum.
Write an expression to represent Max's number.
Answers
Answer:
2n + 16
Step-by-step explanation:
he adds 8 then doubles the sum
2(n + 8) which is 2n + 16
What is the degree form for 4/ 9 ?
Answers
Answer:
the expression is constant, which means it can be rewritten with a factor of x⁰.
The degree is the largest exponent on the variable.
0
A hypothesis test is used to test a claim. On a right-tailed hypothesis test with a 1.6257 critical value, the collected sample's test statistic is calculated to be 1.3994. Which of the following is the correct decision statement for the test?
a. Claim the null hypothesis is true
b. Claim the alternative hypothesis is true
c. Reject the null hypothesis
d. Fail to reject the null hypothesis
Answers
The correct part is (d) i.e. Fail to reject the null hypothesis.
What is hypothesis testing?
By evaluating whether or not the observed test statistic is more extreme than would be anticipated if the null hypothesis were true, the critical value approach determines whether something is "likely" or "unlikely." This means that the alternative hypothesis is accepted in place of the null hypothesis when the observed test statistic is more extreme than a cutoff number, known as the "critical value." The null hypothesis is not disproved if the test statistic does not deviate significantly from the crucial value.
Here, The critical value is 1.6257 and the sample's test statistic value is 1.3994.
We can see that the sample's test statistic value is not extreme as the critical value, So the null hypothesis should not be rejected.
Hence, It fails to reject the null hypothesis.
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the equation of the normal to the 2x² + 2y² -4x +4y =12 at the point (-1,1) is
Answers
To find the equation of the normal to the given curve at the point (-1,1), you can use the following steps:
Rewrite the given equation in the form "y = mx + b," where m is the slope of the curve and b is the y-intercept.
Find the slope of the curve at the point (-1,1). This can be done by taking the derivative of the equation and evaluating it at x = -1.
The slope of the normal line at the point (-1,1) is the negative reciprocal of the slope of the curve at that point. Calculate this value.
Use the point-slope formula to write the equation of the normal line in the form "y - y1 = m(x - x1)," where (x1, y1) is the point (-1,1) and m is the slope of the normal line.
Substitute the values for x1, y1, and m into the point-slope formula to obtain the final equation of the normal line.
For example, if the given equation is 2x^2 + 2y^2 - 4x + 4y = 12, you can follow these steps:
Rewriting the equation in slope-intercept form, we get: y = -x + 2
Taking the derivative of the equation, we get: y' = -1
The slope of the normal line is the negative reciprocal of the slope of the curve, which is 1/-1 = -1
Using the point-slope formula, we get: y - 1 = -1(x + 1)
Substituting the values into the point-slope formula, we get: y - 1 = -1x - 1
Thus, the equation of the normal line at the point (-1,1) is y - 1 = -1x - 1.
48.49 ÷ 0.4
Round your answer to the nearest hundredth.
Answers
Answer:
121.23
Step-by-step explanation:
48.49/0.4 = 121.225
121.225 rounding into nearest hundredth = 121.23
a bag contains 56 marbles, some green and some red. The ratio of green marbles to red ones is 3:4. How many green marbles are there?
Answers
15 green marbles are there among 56 marbles.
A bag contains 56 marbles, so Total marbles =56.
In That, There are Green and red marbles contained in a ratio of 3:4.
Now we have to assume that
Let 3x = the number of green marbles and 4x = the number of red marbles
By using the ratios and the total we can know how many green and red marbles are there in a bag. so the formula is:
ax+bx=t-------(1)
a and b are ratios of given marbles
t is the total number of marbles
x is to find the value
substituting the values in the above equation we get
3x + 4x =35
7x = 35
x = 5
substitute the x value in 3x we get:
Green: 3x = 15
Therefore,15 green marbles are present among 56 marbles
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If a polynomial f(x) has a remainder of 4 when divided by x-5, what is f(5)?
Answers
The remainder of 4 when f(x) is divided by x - 5 means that f(5) = 4
How to determine the remainder of the quotientFrom the question, we have the following parameters that can be used in our computation:
The function is given as
Polynomial = f(x)
Remainder = 4
The function is represented as
z(x)
This means that
x = 5 in f(x)
So, we add -5 to both sides of the equation
This gives
x - 5 = 0
Also, we have
A remainder of 4 when divided by x-5
So, when the equation in interpreted, it means
The remainder when f(x) is divided by x - 5 is 4
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The fox population in a certain region has an annual growth
estimated that the population in the year 2000 was 25800.
rate of 4 percent per year. It is
(a) Find a function that models the population t years after 2000 (t = 0 for 2000).
Your answer is P(t) =
(b) Use the function from part (a) to estimate the fox population in the year 2008.
Your answer is (the answer should be an integer)
Answers
The function and the estimated value for the given population of fox are obtained as P(t) = P₀(1 + r)^t and 35346 respectively.
How to model a population growth function?In order to model the population growth first find the value of the growth rate then substitute it into the expression P(t) = P₀(1 + r)^t.
Now, the value of P₀ can be found for t = 0 and thus the function is obtained.
The given problem can be solved as follows,
(a) The population of fox in year 2000 is given as 25800.
And, the growth rate is 4%.
Suppose t = 0 for year 2000.
And for some value of t, the population is P(t).
Now, the following expression for the population can be written as,
P(t) = P₀(1 + r)^t
Where P₀ is the population at the year 2000.
Thus, the expression can be written as,
P(t) = 25800(1 + 4/100)^t
(b) In the year 2008, the value of t is 8.
Substitute t = 8 in the expression of the population to get,
P(t) = 25800(1 + 4/100)^8
⇒ 25800 × 1.37
⇒ 35346
Hence, the function that models the population and the estimated population for year 2008 are given as P(t) = P₀(1 + r)^t and 35346 respectively.
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During a clearance sale at a sporting goods store, skateboards were marked down 30%. On Saturday, an additional 25% was taken off the already reduced prices of the skateboards. If a skateboard originally cost $119.50, what was the final price after all discounts? Round to the nearest cent.
Answers
The final cost of a skateboard after all the discounts and reductions is $53.775.
Given that, during a clearance sale at a sporting goods store, skateboards were marked down 30%. On Saturday, an additional 25% was taken off already reduced prices of skateboards.
We need to find the final price after all discounts had been taken.
What is the discount?
The basic way to calculate a discount is to multiply the original price by the decimal form of the given percentage rate. To calculate the sale price of any item, we need to subtract the discount from the original price.
Given, that the original cost of the skateboard is $119.50.
Now, 30+25=55
So, the total decrease in percentage is 55%.
The final cost of a skateboard=119.50-55% of 119.50
=119.50-0.55 × 119.50
=119.50-65.725
=$53.775
Therefore, the final cost of a skateboard after all the discounts and reductions is $53.775.
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URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Answers
Answer:
False
A sphere is 3 dimensional.
Jimmy began deriving the quadratic formula. ax² + bx + c = 0 x2+bax+ca=0 x2+bax=−ca x2+bax+(b2a)2=−ca+(b2a)2 What step should Jimmy do next? Responses Subtract b2a from each side. Subtract , b over 2a, from each side. Factor the trinomial. Factor the trinomial. Add x² to each side. Add , x, ² to each side. Subtract x² from each side.
Answers
The required step to be taken is to factor the trinomial in the derivation.
What is a quadratic equation?The general form of a quadratic equation is given as ax^2 + bx + c = 0.
Here, a ≠ 0 and b and c are integers.
The degree of a quadratic equation is 2.
It can be factorized by completing square method.
The given problem can be solved as follows,
The derivation made by Jimmy is given as,
ax² + bx + c = 0
=> x² + (b/a)x + c/a = 0
=> x² + (b/a)x = -c/a
=> x² + (b/a)x + (b/2a)² = -c/a + (b/2a)²
Now, in order to solve the equation the trinomial on the LHS can be factored as follows,
(x + b/2a)² = -c/a + (b/2a)²
Hence, the next step taken by jimmy should be to factorize the trinomial on LHS.
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Determine if the expression 7 y-6 y²-y⁵ is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial.
The given expression ______ a polynomial.
Answers
Since the Polynomial has three non zero terms then the type of the polynomial is Trinomial
What are Polynomials?
A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive-integer powers of variables.
Solution:
Yes the mentioned Ploynomial
7y - 6y² - y^5 is a Polynomial
Since the Polynomial has three non zero terms then the type of the polynomial is Trinomial
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Rewrite 1 1/5 using fifths
1 1/5 - 1/3
= __ /__ - 1/3
Answers
The value of mixed fraction 1(1/5) using fifths is 6/5.
How may a number be written as a mixed number?
Divide the numerator by the denominator in step 1.The quotient should be expressed as a whole number in step 2. Input the numerator and denominator as the remainder and the divisor, respectively in step 3.As an illustration, we convert 7/3 into a mixed fraction form by using the instructions provided.
[tex]1\frac{1}{5}[/tex] = [(5 * 1) + 1]/5
= (5 + 1) / 5
= 6/5
Hence, The value of mixed fraction 1(1/5) using fifths is 6/5.
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The height y (in feet) of an arrow t seconds after it is shot from a bow can be modeled by the function y=-16t² + 112t + 2.
a. Write the function in vertex form.
Y
b. Find the maximum height of the arrow.
The maximum height of the arrow is
feet.
c. How long does it take the arrow to hit the ground? Round your answer to the nearest second.
It takes about seconds for the arrow to hit the ground.
Answers
a) The function in vertex form is; y = -16(x - 3.5)² + 198
b) The maximum height if the arrow is; 198 feet
c) The time that it takes the arrow to hit the ground is; 16 seconds
How to write the quadratic equation in vertex form?We are given the function as;
y = -16t² + 112t + 2.
where;
y is the height (in feet) of an arrow
t is the time in seconds after it is shot from a bow
This is the equation of a vertical parabola open downward
The vertex is a maximum
The general form of a quadratic equation in vertex form is;
y = a(x - h)² + k²
where (h, k) is the vertex coordinate
a) y = -16t² + 112t + 2
This is in standard form and using completing the square, we can write in vertex form as;
y = -16(x - 3.5)² + 198
b) The vertex is the point (3.5, 198)
The maximum height of the arrow represents the y-coordinate of the vertex of the function
Thus, the maximum height of the arrow is 198 feet
c) We know that when the arrow hits the ground, the value of y is equal to zero. Thus, at y= 0, we have;
-16(x - 3.5)² + 198 = 0
Rearranging gives;
(x - 3.5)² = (198/16)
(x - 3.5) = ±√(198/16)
(x - 3.5) = ±12.375
x = 12.375 + 3.5
x = 15.875 ≈ 16 seconds which is the time it will take to hit the ground.
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Determine the sample size required to estimate the mean score on a standardized test within 4 points of the true mean with 95% confidence. Assume that s = 13 based on earlier studies.
Answers
The sample size required to estimate the mean score on a standardized test within 4 points of the true mean with 95% confidence. Assume that s = 13 based on earlier studies is 40.58.
How to find the sample size?Making use of the given data to determine the sample size.
Sample size (n) =?
The confidence level = 95% or 0.95
Z-score for 95% confidence interval =1.960
Using this formula
Margin of error = Zα/2 × α/√n
Solving for n
4 = 1.960 × 13/√n
√n = 6.37
n = 40.58
Therefore the sample size is 40.58.
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