I know is blurry just pls help

I Know Is Blurry Just Pls Help

Answers

Answer 1

12 - 2^2 x 2

---Remember: PEMDAS

---In this case exponents are first, then multiplication, then subtraction

12 - 4 x 2

12 - 8

4

Answer: 4

Hope this helps!


Related Questions

Please HELPP!!!!! Angles !! Marking brainliest whoever awnsers

Answers

Answer: IN ORDER FROM TOP LEFT OVER

Step-by-step explanation:

1. Example

2. Already correct

3. 43

4. 82

5. Supplementary

6. 68

7. 33

8. Adjacent (could be wrong)

9. 51

10. 128

11. 54

12. Complimentary

13. Parallel

14. 29

15. 117

HOPE THIS HELPS. I MAY HAVE GOTTEN 1 OR 2 WRONG.

Alexia is cutting construction paper into rectangles for a projects. She needs to cut one rectangle that is a 9 inches x 14 1/3 inches. she needs to cut another that is 10 1/4 inches by 10 1/3 inches. How many total square inches of construction paper does Alexia need for her project?

Answers

Answer:

234.8525 square inches

Step-by-step explanation:

To find the total area of construction paper needed for the project, we need to find the area of each rectangle and add them together.

For the first rectangle, the dimensions are:

Length = 9 inches

Width = 14 1/3 inches

Area of the first rectangle = Length x Width

Area of the first rectangle = 9 inches x (43/3) inches

Area of the first rectangle = 9 inches x 14.33 inches

Area of the first rectangle = 128.97 square inches (rounded to two decimal places)

For the second rectangle, the dimensions are:

Length = 10 1/4 inches

Width = 10 1/3 inches

Area of the second rectangle = Length x Width

Area of the second rectangle = (41/4) inches x (31/3) inches

Area of the second rectangle = 10.25 inches x 10.33 inches

Area of the second rectangle = 105.8825 square inches (rounded to four decimal places)

Therefore, the total area of construction paper needed for the project is:

Total area = Area of first rectangle + Area of second rectangle

Total area = 128.97 square inches + 105.8825 square inches

Total area = 234.8525 square inches (rounded to four decimal places)

Therefore, Alexia needs a total of approximately 234.8525 square inches of construction paper for her project.

To find the total square inches of construction paper Alexia needs, we need to find the area of each rectangle and add them together.

For the first rectangle, the area is:

9 inches x 14 1/3 inches = (9 x 14) + (9 x 1/3) = 126 + 3 = 129 square inches

For the second rectangle, the area is:

10 1/4 inches x 10 1/3 inches = (10 x 10) + (10 x 1/4) + (10 x 1/3) + (10 x 1/12) = 100 + 2.5 + 3 1/3 + 5/6 = 105 5/6 square inches

To find the total area, we add the two areas together:

129 square inches + 105 5/6 square inches = 234 5/6 square inches

Therefore, Alexia needs 234 5/6 square inches of construction paper for her project.

Select the correct answer.
Which set of coordinates satisfies the equations x − 2y = -1 and 2x + 3y = 12?

A.
(1, 2)
B.
(3, 1)
C.
(3, 2)
D.
(-3, -2)
E.
(3, -2)

Answers

The set of coordinates that satisfy the equation are as follows:

(2, 3)

How to solve equation?

The equation given is as follows:

x - 2y = -1

2x + 3y = 12

Therefore, let's find the set of coordinates that satisfies the equation. Hence,

x - 2y = -1

2x + 3y = 12

multiply equation(i) by 2

Hence,

2x - 4y = -2

2x + 3y = 12

Therefore, subtract the equations

7y = 14

divide both sides of the equation by 7

y = 14 / 7

y = 2

Let's find x as follows

x - 2y = -1

x = -1 + 2(2)

x = -1 + 4

x = 3

Therefore, the solution is (2, 3)

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PLEASE HELP ME QUICK!!!

Answers

Answer:

Option D.   [tex]g(x)=5(0.8)^{x}+2[/tex]

Step-by-step explanation:

Main concepts

Concept 1: identifying horizontal asymptote

Concept 2: assuring decreasing exponential function

Concept 1. identifying horizontal asymptote

Any exponential function of the form [tex]y=a*b^x[/tex] has a horizontal asymptote on the x-axis.  A constant (positive or negative) added to the end of the exponential expression will shift the graph of the exponential function up (if positive) or down (if negative) the number of units equal to the magnitude of the number.  Since the original function f(x) has a "+2" at the end, it has been shifted up 2 units.  Thus, we can eliminate answers A and C from feasible answers since they each shift the exponential function up 3 units, not 2.

Concept 2. assuring decreasing exponential function

Exponential functions of the form [tex]y=a*b^x[/tex] increase or decrease based on the value of "b".

If "b" is between 0 and 1 (a "small" number), the function will decrease.If "b" is larger than 1 (a "big" number), the function will increase.

Observe that the graph of the function f(x) is decreasing, and the value of b=0.5.

To ensure that g(x) also decreases, the b-value must be between 0 and 1, which eliminates option B.

Option D is the correct answer because the value of "b" is between 0 and 1 (making the graph of the function a decreasing exponential), and the number added at the end is "+2", causing the horizontal asymptote to be at a height of positive 2.

You’re planning to buy a car and you want to have $25,000 to purchase a car in cash in 5 years. If you’re able to receive 10% interest rate for investing the money, how much money should you invest today in order to have $25,000 in 5 years?

Answers

You have to invest $15,506.08

How to solve for the investment

PV = FV / (1 + r)^n

where:

PV = present value (amount of money you need to invest today)

FV = future value (amount of money you want to have in 5 years, which is $25,000)

r = interest rate (10% or 0.1)

n = number of periods (5 years)

Plugging in the values into the formula:

PV = $25,000 / (1 + 0.1)^5

PV = $25,000 / 1.61051

PV = $15,506.08

Therefore, you need to invest approximately $15,506.08 today at a 10% interest rate in order to have $25,000 in 5 years to purchase a car in cash.

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Solve the system of equations.

y=4x2+3x−5y=2x2+x+7

What is the sum of the y-coordinates of the solutions to the system?

Enter your answer in the box.

Answers

Answer:

37

Step-by-step explanation:

We are given the system of equations:

y = 4x^2 + 3x - 5

y = 2x^2 + x + 7

We can set the two equations equal to each other to get:

4x^2 + 3x - 5 = 2x^2 + x + 7

Simplifying, we get:

2x^2 + 2x - 12 = 0

Dividing both sides by 2, we get:

x^2 + x - 6 = 0

Factoring the left-hand side, we get:

(x + 3)(x - 2) = 0

Therefore, the solutions are x = -3 and x = 2.

To find the corresponding y-coordinates, we can plug these values of x into either of the original equations. Using the first equation, we get:

y = 4(-3)^2 + 3(-3) - 5 = 16

and

y = 4(2)^2 + 3(2) - 5 = 21

Therefore, the sum of the y-coordinates of the solutions is:

16 + 21 = 37

Answer: 37.

I need help please


I need to answer the white box i don't know the answer

Answers

The expression of the matrix row operation is 1/4 Row 1 ⇒ Row 1

Determing the matrix row operation and expression

From the question, we have the following parameters that can be used in our computation:

[tex]\left[\begin{array}{cccc}-24&-24&12&20\\-2&3&7&5\\-7&-3&3&-5\end{array}\right][/tex] into [tex]\left[\begin{array}{cccc}-6&-6&3&5\\-2&3&7&5\\-7&-3&3&-5\end{array}\right][/tex]

From the above matrices, we understand that

Dividing the first row of the first matrix by 4 gives the first row of the second matrix Other corresponding row elements of the second and third rows remain unchanged

This means that

row 1 = 1/4(row 1)

This in other words means that

row 1 = (row 1)/4

When these values are evaluated, we have

[tex]\left[\begin{array}{cccc}-24&-24&12&20\\-2&3&7&5\\-7&-3&3&-5\end{array}\right][/tex] into [tex]\left[\begin{array}{cccc}-6&-6&3&5\\-2&3&7&5\\-7&-3&3&-5\end{array}\right][/tex]

This means that we replace -24, -24, 12, and 20 in row 1 with -6, -6, 3 and 5

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what is the nearest tenth to 3.5

Answers

The answer: 3.5
The number is already rounded to the nearest tenth

Answer: 3.5

Step-by-step explanation: i got it right on the quiz

9. Which of the following functions represents a vertical shift of the function f(x) = x? a. f(x) = 2x b. f(x) = x + 5
c. f(x) = x2 d. none of the above 9.____________________
10. Which of the following functions represents a horizontal shift of the function f(x) = x2?
a. f(x) = (x+2)2 b.f(x) = 3x2
c. f(x) = x2 + 2 d. none of the above

Answers

b. f(x) = x + 5, which represents a vertical shift of 5 units upwards.  f(x-a) = (x-a)^2, where a is a constant.

How to find the functions that represents a vertical shift

9) The function f(x) = x represents a linear function with a slope of 1 and y-intercept of 0. To shift the graph vertically, we need to add or subtract a constant from the function. Thus, the function that represents a vertical shift of f(x) = x would be of the form f(x) = x + b, where b is a constant.

Out of the given options, the correct answer is b. f(x) = x + 5, which represents a vertical shift of 5 units upwards.

10) To shift the graph of f(x) = x^2 horizontally, we need to add or subtract a constant inside the function, affecting the position of the vertex of the parabola. Thus, the function that represents a horizontal shift of f(x) = x^2 would be of the form f(x-a) = (x-a)^2, where a is a constant.

Out of the given options, the correct answer is a. f(x) = (x+2)^2, which represents a horizontal shift of 2 units to the left.

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Less than 53% of adults would erase all of their personal information online if they could . The hypothesis test results in a p-value of 0.0059

Answers

A conclusion on the null hypothesis is C. Reject H_{0} because the P-value is less than or equal to a.

What should happen to the null hypothesis ?

Stated in the initial description is the null hypothesis, establishing that adults who possess a desire to eliminate all personal information available online would equate to or exceed 53%, while the alternative conjecture rests on this percentage being under 53%.

The statistical significance level at hand designated as alpha equals 0.05 indicates that a P-Value having less than or equal value of 0.05 is necessary for declining the null hypothesis. As provided by the task's question, the computed P-value registers a score of 0.0059 which falls below the established significance level of 0.50 and thus resulting in null hypothesis rejection.

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if you increase your current quality score of 85% by 7%, you will have a score of?

Answers

Answer:

90.95%

Step-by-step explanation:

85 * 0.07 = 5.95 5.95 + 85= 90.95

Answer:

The answer to your problem is, 90.95%

Step-by-step explanation:

Calculation:

In order to find the answer we need to

= Old score + New Score

= 85 + 7% of 85

= 85 + ( [tex]\frac{7}{100}[/tex] x 85 )

= 85 + ( 0.07 x 85 )

= 85 + 5.95

= 90.95

Which 90.95% is our answer.

Thus the answer to your problem is, 90.95%

Can someone help me with dosage calculation problems #46 and #47.
Would greatly appreciate if you explain how it was solved. Thanks!

Answers

46. There are 9 complete doses available from the bottle. 47. There are 8 full doses available in the 120 mL bottle.

What is weight and mass?

Although weight and mass are frequently used interchangeably, they have distinct meanings in the study of physics. Weight is a measurement of the force of gravity acting on an item, whereas mass is a measure of the amount of matter that makes up an object. Weight is typically expressed in newtons (N) or pounds, while mass is typically expressed in kilogrammes (kg) (lb). While an object's mass remains constant, its weight can change depending on how strongly gravity is pulling on it.

46. We know that,

1 fluid ounce = 29.5735 mL

4 fluid ounces = 4 x 29.5735 = 118.294 mL

Each dose is 12.5 mL:

118.294 / 12.5 = 9.46

So there are 9 complete doses available from the bottle.

47. Given, 1 tablespoon is equal to 15 mL.

Thus, doses of 15 mL are in a 120 mL bottle:

120 / 15 = 8

So there are 8 full doses available in the 120 mL bottle.

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What is the average of the two bases in the following trapezoid in feet? 22 ft 14.75 ft 11 ft 18 ft

Answers

Answer: 18 feet.

Step-by-step explanation:

Average of bases = (22 + 14.75) / 2

Average of bases = 18.375

18.375 to the nearest tenth is = 18ft

Therefore, the average of the two bases of the trapezoid is 18 feet.

7 A right rectangular prism is sliced by a plane perpendicular to its bases. A right cylinder is sliced the same way. Which statement about the plane sections that result is correct?
A Both plane sections have two pairs of parallel sides.
B The plane section of the prism has only straight sides, but the plane section of the cylinder does not.
C The plane section of the prism has four right angles, but the plane section of the cylinder does not.
D Both plane sections are the same shape as the bases of the three-dimensional figures from which they resulted.​

Answers

Both B and C are correct...

Solve the inequality then list 5 numbers that fit in the solution set_,_,_,_,_ 4 - 5g > 39

Answers

The values that fit in the solution are -4, -3, -2, -1 , 0

g > - 5

How to solve the inequality

Inequalities are described as expressions that are used to represent an unequal relationship between numbers or variables.

They are represented with the symbols;

< is less than> represents the greater than≥ represents the greater than or equal≤ represents the less than or equal to

From the information given, we have that;

4 - 5g > 39

collect the like terms, we get;

-5g > 39 - 4

subtract the values

-5g > 35

Divide by the coefficient of g, we get;

g > -5

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Michael invests $1,000 in an account that earns a 4.75% annual percentage rate compounded continuously. Peter invests$1,200 in an account that earns a 4.25% annual percentage rate compounded continuously. Which person's account will grow to $1,800 first?

Answers

Answer:

Step-by-step explanation:

We can use the formula for continuous compounding to determine how long it will take each account to reach $1,800.

For Michael's account, the formula is:

A = P*e^(rt)

where:

A is the amount in the account after t years

P is the principal

r is the annual interest rate

t is the time in years

Plugging in the values given, we get:

1,800 = 1,000*e^(0.0475t)

Taking the natural logarithm of both sides, we get:

ln(1,800/1,000) = 0.0475t

t = ln(1,800/1,000)/0.0475

t ≈ 8.55 years

So it will take approximately 8.55 years for Michael's account to reach $1,800.

Similarly, for Peter's account, the formula is:

A = P*e^(rt)

where:

A is the amount in the account after t years

P is the principal

r is the annual interest rate

t is the time in years

Plugging in the values given, we get:

1,800 = 1,200*e^(0.0425t)

Taking the natural logarithm of both sides, we get:

ln(1,800/1,200) = 0.0425t

t = ln(1,800/1,200)/0.0425

t ≈ 9.03 years

So it will take approximately 9.03 years for Peter's account to reach $1,800.

Therefore, Michael's account will grow to $1,800 first as it will take less time (8.55 years) compared to Peter's account (9.03 years).

find two numbers who’s product is -9 and who’s sum is -8

Answers

Answer:

1, -9

Step-by-step explanation:

xy = -9

x + y = -8    solve this for x and substitute into the 1st equation

x = -8 - y

(-8 - y)y = -9

-y² - 8y + 9 = 0

y² + 8y -9 = 0

Solve for y by factoring:

(y - 1)(y + 9) = 0

y = 1, -9

x(1) = -9

x = -9

x(-9) = -9

x = -9/-9 = 1

helppp I need help pleaseeeeeee

Answers

The new matrix from an elementary row operation to get a 1, in row 1 column 1 will have:

R₁ = [1 -10 2] and R₂ = [-12 7 -13]

What is a matrix row operation

Row operations are a set of operations that can be performed on the rows of a matrix in order to transform it into a row equivalent matrix, which has the same solution set as the original matrix.

The row operation R₁ - 6 — R₁ will be carried out as follows:

7 - 6 = 1 {row 1 column 1}

-4 - 6 = 5 {row column 2}

8 - 6 = -8 {row column 3}

Therefore, the resulting matrix from an elementary row operation to get a 1, in row 1 column 1 will have:

R₁ = [1 -10 2] and R₂ = [-12 7 -13]

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What is the circumference of the following circle? What is the answer?

Answers

Answer:31.42

Step-by-step explanation:

C=2πr=2·π·5≈31.41593

Jermaine invested $3,200 in a defined-contribution account. Assuming he is in a 20% marginal tax bracket, how much did he lower his income taxes with the investment

Answers

Jermaine's income tax was lowered by $640 as a result of the investment.

Investment calculation

Assuming that the defined contribution account is a tax-deferred retirement account, Jermaine can lower his income taxes by the amount of his contribution multiplied by his marginal tax rate. The formula for this tax savings is:

Tax savings = Contribution × Marginal tax rate

Using the given values, Jermaine's contribution to the account is $3,200 and his marginal tax rate is 20%. Substituting these values into the formula, we get:

Tax savings = $3,200 × 0.20 = $640

Therefore, Jermaine can lower his income taxes by $640 by contributing $3,200 to the defined contribution account.

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ACTIVITY 1: Solve the following rational equation.

Answers

The solutions to the rational equations are

(1) x = 14/3 (2) x = -2/3 (3) x = 4(4) x = 0 or x = 3(5) x = 0 or x = -2(6) x = 4/5(7) x = √(17/5)(8) x = 11/9(9) x = -1 or x = 2 (10) x = 1 or x = 2

Solving the rational equations

The rational equations can be solved as follows

(1)

(x - 2)/(2x + 4) = 1/5

This gives

5x - 10 = 2x + 4

So, we have

3x = 14

x = 14/3

(2)

For equation (2), we have

(x + 3)/2 - x/4 = 4/3

So, we have

[2(x + 3) - x]/4 = 4/3

[x + 6]/4 = 4/3

So, we have

3x + 18 = 16

x = -2/3

(3)

For equation (3), we have

3/(x + 1) - 2/(x - 1) = 1/(x² - 1)

So, we have

3(x - 1) - 2(x + 1) = 1

This gives

3x - 3 - 2x - 2 = 1

x = 4

(4)

For equation (4), we have

18/(x² - 3x) = 2x/(x - 3) - 6/x

So, we have

18 = 2x² - 6(x - 3)

This gives

x = 0 or x = 3

(5)

For equation (5), we have

3x/(x + 2) + 6/x + 4 = 12/(x² + 2x)

Multiiply through by x² + 2x

3x² + 6(x + 2) + 4(x² + 2x) = 12

Evaluate

x = 0 or x = -2

(6)

For equation (6), we have

1/(x - 2) + 4/(x + 9) = 3/(x² + 7x - 18)

Multiiply through by (x² + 7x - 18)

x - 9 + 4x + 8 = 3

So, we have

5x = 4

Evaluate

x = 4/5

(7)

For equation (7), we have

3/5x² - 1/5 = 2/25x²

Multiiply through by 25x²

15 - 5x² = 2

So, we have

5x² = 17

Evaluate

x = √(17/5)

(8)

For equation (8), we have

9/(x + 1) = 2/(x² - 1)

Multiiply through by 25x²

9x - 9 = 2

So, we have

9x = 11

Evaluate

x = 11/9

(9)

For equation (9), we have

3/(x³ - 8) = 1/(x - 2)

Cross multiiply

(x³ - 8) = 3(x - 2)

Evaluate

x = -1 and x = 2

(10)

For equation (10), we have

x²/2 - 3x/2 + 1 = 0

Multiiply through by 2

x² - 3x + 2 = 0

Factoize

(x - 1)(x - 2) = 0

So, we have

x = 1 and x = 2

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1 Place an X in the table to show the solution that makes each equation true. 6+x=15 244 X 9x = 18 x=9​

Answers

Step-by-step explanation:

| Equation | Solution |

| 6+x=15 | x = 9 |

| 9x = 18 | x = 2 |

The table would look like:

| Equation | Solution |

| 6+x=15 | X |

| 9x = 18 | X |

One positive integer is 2 less than twice another. The sum of their squares is 260 . Find the integers.

Answers

Hence, 8 and 14 are the two positive integers as Y must be 8 because we are seeking for positive integers.

what is integers ?

All entire numbers (optimistic, negative, and zero) as well as their opposites are included in the category of integers. These can be visualised as evenly spaced-apart points with zero in the middle on a number line. The following numbers are part of the set of integers, which is represented by the symbol Z . The numbers of pupils in an educational setting, the weather in degrees Celsius, or the location of an object in relation to a reference point are all examples of quantities that can be represented by integers and are counted or measured in whole units. They adhere to specific arithmetic laws and can be added, deducted, multiplied, and divided.

given

Assume that x and y are the two positive integers, with x being the greater of the two. Finally, we may convert the provided data into equations:

In order to remove x, we can replace the first equation with the second equation as follows:

[tex](2y-2)^2 + y^2 = 260[/tex]

Adding and subtracting:

[tex]4y^2 - 8y + 4 + y^2 = 260[/tex]

combining comparable phrases

[tex]5y^2 - 8y - 256 = 0[/tex]

Using the quadratic formula, we can solve this quadratic equation:

y = [8 ± sqrt(8^2 - 45(-256))] / (2*5)

y = [8 ± sqrt(3368)] / 10

y ≈ 8.6 or y ≈ -9.4

Y must be 8 because we are seeking for positive integers. The first equation can then be used to determine x:

x = 2y - 2 = 2(8) - 2 = 14

Hence, 8 and 14 are the two positive integers as Y must be 8 because we are seeking for positive integers.

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For the following exercises, convert the angle measures to radians.
-236° (the exact answer) b) 601° (round to two decimal places)

Answers

The calculated values of the angle measures when converted to radians are 1.31π rad and 3.34π rad

Converting the angle measures to radians.

To convert angles from degrees to radians, we multiply the number of degrees by π/180.

This means that

Angle = Degree measure * π/180

Using the above as a guide, we have the following:

Angle 236 = 236 * π/180

Evaluate the products

Angle 236 = 1.31π rad

Next, we repeat the same process for the second angle 601 degrees

Angle 601 = 601 * π/180

Evaluate the products

Angle 601 = 3.34π rad

Hence, the angles are 1.31π rad and 3.34π rad

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Lia deposits $100 into a savings account that earns simple interest at a rate
of 5%. If she makes no withdrawals, how much interest has Lia's savings account earned after 5 years?

A. 45
B. 25
C. 75
D. 15
Please explain. I’ll give brainly

Answers

Answer:

[tex]100( {1.05}^{5} ) = 127.63[/tex]

[tex]127.63 - 100 = 27.63[/tex]

The closest answer here is B. $25

Answer:

B is the answer of the given above question

what is x?
a. 100
b. 120
c. 60
d. 50

Answers

It will be D.) 50 possible

Cual es mayor

1 or 1
_ _
4 3

Answers

Answer:

Step-by-step explanation:

1/3 is greater.

People, I need to figure out a question

Is the sun of 7/10 + 1/5 closer to 0, 1/2 or 1?

Answers

Answer:

1

Step-by-step explanation:

7+10+1/5

7/10 = 0.7

1/5 = 0.2

0.7+0.2=0.9

Therefore it would be closest to 1.

Answer: 1

Step-by-step explanation:

To find an estimate, you need to round your fractions. Let's start with 7/10. First let's look at the numerator, 7. 7 is a number greater than 5, so we'll round it to 10 and you keep your denominator. so now we have 10/10, or 1. Then round 1/5. 1/5 is lower than 5, so we'll round it to 0. Now, for the final step add them. 1 + 0 = 1, so 1 is the answer

Help pleasee

here is the picture is about Row Ops

Answers

The result of the carrying out the operation, Add -4(row 1) to row 3, on the given matrix is:

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]

Reducing row matrices

From the question, we are to perform the given row operation on the given matrix

The given matrix is:

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\4&-1&6&-8\end{array}\right][/tex]

Now,

From the given information,

The operation we are to carry out is:

Add -4(row 1) to row 3

This means we are to multiply the first row by -4. Then, we will add the results to the corresponding elements on the third row (row)

Multiplying by -4

-4 × [ 1     2    1   | -5

     -4   -8   -4  | 20

Now, we will add the result from the multiplication to the corresponding elements in row 3

Adding the results to corresponding elements in row 3

   4    -1     6  |  -8

+  -4   -8   -4  | 20

------------------------

   0    -9    2  |  12

Hence,

The resulting matrix becomes

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]

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a sample of what size would be needed to estimate a population mean to within 4 units with 95 percent confidence if the population has a standard deviation of 12?

Answers

A sample of at least 139 individuals would need to be taken to estimate the population mean to within 4 units with 95% confidence.

Understanding the Population Estimate

To estimate the sample size needed to estimate the population mean to within 4 units with 95% confidence, we can use the formula:

n = (z * σ / E)²

where:

n = sample size

z = z-score for the desired level of confidence (95% in this case), which can be found using a standard normal distribution table or calculator. For 95% confidence, the z-score is approximately 1.96.

σ = population standard deviation (12 in this case)

E = margin of error (4 in this case)

Plugging in the values, we get:

n = (1.96 * 12 / 4)²

n = 34.5744

Rounding up to the nearest whole number, we get a sample size of 35. Therefore, a sample of at least 35 individuals would need to be taken to estimate the population mean to within 4 units with 95% confidence.

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