Answers
Add the total length + the length outside of the circle and set it equal to the other segment’s total length + the length outside of the circle. Like this: (10+8)(8) = x(18 + x).
Then simplify to 144 = x^2 + 18x.
Use the quadratic formula (see picture), and x=6, x=-24. Except x ≠ -24 because the length cannot be a negative value. So x = 6!!
Here is a picture of my work:
I’m on my phone so it’s harder to type out the equations. Hope this helps!
Related Questions
A study of the consultants in a particular industry has determined that the standard deviation of the hourly fee of the consultants is $23. A random sample of
100 consultants in the industry has a mean hourly fee of $113. Find a 99% confidence interval for the true mean hourly fee of all consultants in the industry.
Then give its lower limit and upper limit.
Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)
Lower limit:
Upper limit:
X
5
Answers
If a study of the consultants in a particular industry has determined that the standard deviation of the hourly fee of the consultants is $23. the 99% confidence interval for the true mean hourly fee of all consultants in the industry is (107.1, 118.9).
How to find the confidence interval?The formula for a confidence interval for the population mean is:
CI = X- bar ± z* (σ/√n)
where:
X- bar = sample mean
z* = z-score for the desired level of confidence (99% in this case)
σ = population standard deviation
n = sample size
Substituting the given values, we get:
CI = 113 ± 2.576 * (23/√100)
Calculating the standard error:
SE = σ/√n = 23/√100 = 2.3
Now we can substitute this value into the formula:
CI = 113 ± 2.576 * 2.3
CI = 113 ± 5.92
So,
Lower limit: 107.1
Upper limit: 118.9
Therefore, the 99% confidence interval for the true mean hourly fee of all consultants in the industry is (107.1, 118.9).
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pls solve thank u
100 points for answer
Answers
Hence, the darkened sector covers an area of roughly [tex]10.55 km^2[/tex] as circle's radius is 7 km, and the shaded sector's central angle is 154 degrees .
what is radius ?The radii of a circle in geometry is the separation between any two points on the circle's circumference. It is frequently used to describe how far apart two points are. One of a circle's most crucial characteristics is its radius, which is taken into account when calculating a circle's circumference, area, and diameter. The distance around a circle that passes through its centre, or its diameter, is equal to half of its radius. Other shapes like spheres, cylindrical, and cones can also be described using the radius. The radius here means the distance from the shape's centre to any point on its perimeter.
given
The following formula must be used to determine a sector's area:
A = (θ/360)[tex]\pi r^2[/tex]
where r is the circle's radius, is pi, or roughly 3.14, and is the sector's centre angle, expressed in degrees.
The circle's radius is 7 km, and the shaded sector's central angle is 154 degrees, according to the provided figure. When these values are added to the formula, we obtain:
[tex]A = (154/360)\pi (7)^2[/tex]
[tex]= 10.55 km^2[/tex]
Hence, the darkened sector covers an area of roughly [tex]10.55 km^2[/tex] as circle's radius is 7 km, and the shaded sector's central angle is 154 degrees .
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The complete question is:-
154 degree
7 km
Find the area of the shaded sector.
A = __ km2
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 expressionFrom 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 unchangedThis 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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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 operationRow 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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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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Cual es mayor
1 or 1
_ _
4 3
Answers
Answer:
Step-by-step explanation:
1/3 is greater.
26) What is the area of Rectangle A?
is 1 unit square.
Rectangle A
Answers
The required area of the rectangle is 8 sq. units
What is rectangle?Any mathematical statement with numbers, variables, and an arithmetic operation between them is an expression or algebraic expression. For instance, the expression 4m + 5 is one in which the terms 4m and 5 and the variable m are separated by the arithmetic sign +.
According to question:From the diagram
Length = 4 units, width = 2 units
Area of rectangle = length×width
Area of rectangle = 4×2
Area of rectangle = 8 sq. units
Thus, required area of the rectangle is 8 sq. units
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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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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 matricesFrom 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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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.
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.
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.
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
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 = 2Solving the rational equationsThe 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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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%
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 investmentPV = 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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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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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 |
If someone wants to call Havana, Cuba from the United States (US) begins with US three-digit exit code 011 followed the two-digit country code for Cuba is 53, followed by the county code of Havana is 7 and finally by seven-digit local telephone numbers. But this seven-digit local telephone numbers cannot begin with 0. How many different telephone numbers are possible?
Answers
Answer:
9000000 different numbers---------------------------
The number is basically a combination in the form of:
abcdefg, where a can't be zero but the rest of the digits have no restrictionsHence the possible digits:
a = 9, b,c,d,e,f,g = 10So possible telephone number combinations:
9*10⁶ = 9000000HELP ME PLEASE!
Whoever answers right gets brainliest!
Answers
Step-by-step explanation:
The 'x's ' ( the domain) are mapped into two values of 'y' (the range)
Range = 1,6
How much would you need to deposit in an account now in order to have $2000 in the account in 15years? Assume the account earns 8% interest compounded monthly.
Answers
Answer:
P = $1341.53
Step-by-step explanation:
A(t) = amount in t years
P = Principal (original investment)
r = annual interest rate (in decimal form)
n = number of times that interest is compounded each year
A(t) = P(1 + r/n)nt
Substitute in the given values: 2000 = P(1 + 0.04/12)12(10)
2000 = P(1.490832682)
P = $1341.53
Which ordered pair is a solution of y = x – 4?
A. (–3, 7)
B. (3, –7)
C. (–3, –7)
D. (3, 7)
Answers
Answer:
C. (–3, –7)
Step-by-step explanation:
We can check each ordered pair by substituting the values of x and y into the equation y = x - 4 and see if the equation is true.
A. (-3, 7)
y = x - 4
7 = -3 - 4
7 = -7
This is not true, so (-3, 7) is not a solution.
B. (3, -7)
y = x - 4
-7 = 3 - 4
-7 = -1
This is not true, so (3, -7) is not a solution.
C. (-3, -7)
y = x - 4
-7 = -3 - 4
-7 = -7
This is true, so (-3, -7) is a solution.
D. (3, 7)
y = x - 4
7 = 3 - 4
7 = -1
This is not true, so (3, 7) is not a solution.
Therefore, the only ordered pair that is a solution of y = x - 4 is (–3, –7).
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.
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.
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 calculationAssuming 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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I NEED HELP WITH STATISTICS
Answers
The value of the summation notation [tex]\sum\limits^{12}_{i=1} {-25x_i}[/tex] for the 12 measurements 69, -5, 47, -10, -80, 13, 64, -76, -95, 45, 9, 7 is 300
Computing the summation notationFrom the question, we have the following parameters that can be used in our computation:
69, -5, 47, -10, -80, 13, 64, -76, -95, 45, 9, 7
The summation notation is given as
[tex]\sum\limits^{12}_{i=1} {-25x_i}[/tex]
The summation notation [tex]\sum\limits^{12}_{i=1} {-25x_i}[/tex] means we multiply each value by -25 and add the results
Using the above as a guide, we have the following:
Sum = -25 * (69 - 5 + 47 - 10 - 80 + 13 + 64 - 76 - 95 + 45 + 9 + 7)
Evaluate
Sum = 300
Hence, the value of the summation notation [tex]\sum\limits^{12}_{i=1} {-25x_i}[/tex] for the 12 measurements 69, -5, 47, -10, -80, 13, 64, -76, -95, 45, 9, 7 is 300
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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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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.
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
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 inequalityInequalities 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 toFrom 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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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 EstimateTo 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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