The solution is Option C.
The total amount of earnings of Sondra after 5 years is $ 169,113
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the annual salary of Sandra be A = $ 30,000
Now , the percentage increase in salary = 6 %
So , the equation will be
First year :
The increase in first year = annual salary of Sandra + percentage increase in salary x annual salary of Sandra
The increase in first year = 30000 + ( 6/100 ) x 30000
= 30000 + 1800
= $ 31,800
Second year :
The increase in second year = increase in first year + percentage increase in salary x increase in first year
The increase in second year = 31800 + ( 6/100 ) x 31800
= 31800 + 1908
= $ 33,708
Third year :
The increase in third year = increase in second year + percentage increase in salary x increase in second year
The increase in third year = 33708 + ( 6/100 ) x 33708
= 33708 + 2022.48
= $ 35,730.48
Fourth year :
The increase in fourth year = increase in third year + percentage increase in salary x increase in third year
The increase in fourth year = 35730.48 + ( 6/100 ) x 35730.48
= 35730.48 + 2143.8288
= $ 37,874.3088
Now , the equation is
The total earnings of Sondra is = First year salary + second year salary + third year salary + fourth year salary
The total earnings of Sondra is = 30000 + 31,800 + 33,708 + 35,730.48 + 37,874.3088
The total amount earnings of Sondra is = $ 169,112.7888
Therefore , the total amount earnings = $ 169,113
Hence , The total amount of earnings of Sondra after 5 years is $ 169,113
Answer:
C) $199,797
Step-by-step explanation:
Adding 7% of a number to the number is the same as multiplying the number by 1.07
First year: $45,000
Second year: $45,000 × 1.07 = $48,150
Third year: $48,150 × 1.07 = $51,520.50
Fourth year: $51,520.50 × 1.07 = $55,126.94
Total = $199,797.43
Answer: C) $199,797
nitially 100 milligrams of a radioactive substance was present. after 6 hours the mass had decreased by 5%. if the rate of decay is proportional to the amount of the substance present at time t, find the amount remaining after 24 hours. (round your answer to one decimal place.)
If the rate of decay is proportional to the amount of the substance present at time t, then the amount remaining after 24 hours is 57.7 milligrams
Now we need to find the value of k. We know that the mass decreased by 5% after 6 hours, which means that the amount remaining is 95% of the initial amount. We can substitute these values into our formula and solve for k:
0.95 initial amount = initial amount x (1 - k x initial amount)⁶
Simplifying this equation, we get:
1 - [tex](0.95)^{(1/6)})[/tex] = k x initial amount
Solving for k, we get:
k = (1 - [tex](0.95)^{(1/6)})[/tex]) / initial amount
Now we can use this value of k to find the amount remaining after 24 hours:
Amount remaining = 100 x (1 - k x 100)²⁴
Plugging in the value of k, we get:
Amount remaining = 100 x (1 - (1 - [tex](0.95)^{(1/6)})[/tex] * 100)²⁴
Evaluating this expression, we get:
Amount remaining = 57.7 milligrams
Therefore, after 24 hours, there will be approximately 57.7 milligrams of the radioactive substance remaining.
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What makes up an html element
An HTML (Hypertext Markup Language) element consists of several parts that work together to define its behavior and appearance on a webpage. The basic structure of an HTML element includes:
Opening tag: The first part of an HTML element is the opening tag, which is enclosed in angle brackets ("<" and ">") and indicates the beginning of the element. It includes the name of the element, such as "p" for a paragraph or "img" for an image.
Attributes: After the name of the element, you can specify one or more attributes that modify the element's behavior or appearance. Attributes consist of a name and a value, separated by an equal sign. For example, the "src" attribute specifies the source URL of an image element.
Content: The content of an HTML element is the information that appears between the opening and closing tags. For example, the content of a paragraph element would be the text that appears within it.
Closing tag: The closing tag is similar to the opening tag but includes a forward slash ("/") before the element name to indicate the end of the element. For example, the closing tag for a paragraph element would be "</p>".
Here's an example of a complete HTML element:
<p class="intro">This is a paragraph element with a class attribute.</p>
In this example, "p" is the name of the element, "class" is an attribute that specifies the CSS class of the element, and "This is a paragraph element with a class attribute." is the content of the element.
what number does not appear in the first 30 digits of pi? a) 1 b) 2 c) 3 d) 4 e) 0
Answer:
0
Step-by-step explanation:
The point T(-4, -1) is rotated 90° counterclockwise around the origin. What are the coordinates of the resulting point, T?
Answer:
(1, -4)
Step-by-step explanation:
if you rotate from quadrant 3 to 4, x=-y and y=x
After the rotation of 90° clockwise about the origin, the coordinates become P'(- 1, - 4).
What is image rotation?A rotation is a type of transformation which is a turn.A figure can be turned clockwise or counterclockwise on the coordinate plane.In both transformations the size and shape of the figure stays exactly the same.Given is the coordinate of point as (-4, - 1). It is rotated by 90° clockwise about the origin.
When we rotate a figure 90 degrees clockwise about the origin, then the new coordinates will be -
A(x, y) → A(y, - x)
Then, we can write the new coordinates according to the rule as -
P(-4, - 1) → P'(- 1, - 4)
Therefore, after the rotation of 90° clockwise about the origin, the coordinates become P'(- 1, - 4).
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FOR EACH SEQUENCE find he firsst four terms and tenth term n+5
The first four terms of the sequence defined by n+5 are 6, 7, 8, and 9, and the tenth term of the sequence is 15.
To find the first four terms of the sequence defined by n + 5, we simply substitute n = 1, 2, 3, and 4, respectively
When n = 1: 1 + 5 = 6
When n = 2: 2 + 5 = 7
When n = 3: 3 + 5 = 8
When n = 4: 4 + 5 = 9
Therefore, the first four terms of the sequence are 6, 7, 8, and 9.
To find the tenth term of the sequence, we substitute n = 10
When n = 10: 10 + 5 = 15
Therefore, the tenth term of the sequence is 15.
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The area of 1 rectangle is 36 square feet. The area of the 2nd rectangle is 21 square feet. What is the width of both rectangles
The width is 3………..
………..
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The center of the circle lies on the y-axis.
The standard form of the equation is (x – 1)² + y² = 3.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answer:
Step-by-step explanation:
Statements 1, 2, 5 are all true
Suppose that y varies directly with and y=25 and x=5 and x= -3
If y varies directly as x then the value of y is (-15) when x = (-3).
It is given that y varies directly as x. It means y is proportional to x.
y ∝ x
y = kx
{Where k is constant of proportionality.}
It is given that y=25 when x=5. Put x=5 and y=25 in the above equation to find the value of k.
25 = k(5)
Divide both sides by 5.
The value of k is 5.
The relation between x and y is defined by the equation: y = 5x.
Put x = (-3) in the above equation.
Thus, y = 5(-3)
y = (-15)
Therefore the value of y is (-15) when x = (-3).
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—-------- Correct question format is given below —--------
(Q). If y varies directly as x, and y=25 when x=5, find y when x=(-3).
Write an equation that represents each circle. (Include + or - in the first two blanks, as appropriate. No spaces.)
The equation of the first circle is (x + 2)² + (y - 4)² = 16, and the equation of the second circle is x² + y² = 64.
What is equation of circle?
The equation of a circle is a mathematical representation of the geometric shape of a circle. It defines the relationship between the coordinates of the points on the circle and the center of the circle. There are different forms of the equation of a circle, but the most commonly used form is the standard form, which is:
(x - a)² + (y - b)² = r²
Where (a, b) are the coordinates of the center of the circle, and r is the radius of the circle.
The equation can be written in different forms depending on the information given. For example, if the center of the circle is at the origin (0,0), then the equation becomes x² + y² = r²
Here,
Centre of first circle is (-2,4) and radius is 4 unit and centre of second circle is (0,0) and radius is 8 unit.
We can write the equations of the two circles as follows:
First Circle:
Center: (-2, 4)
Radius: 4 units
So, required equation of first circle is (x + 2)² + (y - 4)² = 16
Second Circle:
Center: (0, 0)
Radius: 8 units
So, required equation of second circle is x² + y² = 64
Thus, the equation of the first circle is (x + 2)² + (y - 4)² = 16, and the equation of the second circle is x² + y² = 64.
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I need help with this step-by-step please!
The number of days that the race lasted is five days and the correct formula is 1/16(4^5 - 1)/4 - 1. Option B
What is the sum of a geometric progression?Geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed non-zero number called the common ratio. In other words, each term is a constant multiple of the term that precedes it. The first term in the sequence is denoted by "a" and the common ratio is denoted by "r".
The common difference of the progression is;
1/4/1/16 = 1/4 * 16/1 = 4
Using the formula
a(r^n -1)/r - 1
1/16(4^5 - 1)/4 - 1
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A new cylindrical can with a diameter of 4 cm is being designed by a local company The surface area of the can is 130 square centimeters What is the height of the can? Estimate using 3 14 for x and
round to the nearest hundredth Apply the formula for surface area of a cylinder SA-28+ Ph
The height of the can is approximately 9.74 centimeter.
Define surface area of cylinderThe surface area of a cylinder is the total area of the curved and flat surfaces that make up the cylinder. It can be calculated using the formula:
SA = 2πr² + 2πrh
where r is the radius of the cylinder and h is its height.
In this case, we are given that the diameter of the can is 4 cm, which means the radius is 2 cm.
We are also given that the surface area is 130 square centimeters. Substituting these values into the formula, we get:
130 = 2π(2)² + 2π(2)h
Simplifying this equation, we get:
130 = 8π + 4πh
Subtracting 8π from both sides, we get:
122 = 4πh
Dividing both sides by 4π, we get:
h = 122/(4π) ≈ 9.74 cm (rounded to the nearest hundredth using 3.14 for π)
Therefore, the height of the can is approximately 9.74 cm.
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lynne has \$8.00$8.00dollar sign, 8, point, 00 to spend on apples and oranges. apples cost \$0.65$0.65dollar sign, 0, point, 65 each, and oranges cost \$0.75$0.75dollar sign, 0, point, 75 each. if there is no tax on this purchase and she buys 555 apples, what is the maximum number of whole oranges she can buy?
Lynne can buy 5 apples and 6 oranges with her $8.00.
The first thing to do is determine how much money Lynne spends on the apples. Since she is buying 5 apples,
we can multiply the price of each apple ($0.65) by 5: $5 * 0.65 = $3.25
Therefore, Lynne has $8 - $3.25 = $4.75 to spend on oranges.
Now we need to determine the maximum number of whole oranges that she can buy with $4.75. We can do this by dividing $4.75 by the price of each orange ($0.75): $4.75 ÷ $0.75 = 6.33.
Since we can't buy a fraction of an orange, the maximum number of whole oranges Lynne can buy is 6. Therefore, Lynne can buy 5 apples and 6 oranges with her $8.00.
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find an example of a matrix and a matrix such that, letting and , the composition is a reflection over the line .
The required matrices are:
[tex]A= \begin{bmatrix}1 & 1 & 0\\1 & -1 & 0\end{bmatrix}[/tex] and [tex]B= \begin{bmatrix}1 & 1\\1 & -1\\0 & 1\end{bmatrix}[/tex]
letting T(x)=Ax and U(x)=Bx, the composition T∘U is a reflection over the line y=x.
A matrix is a rectangular array of numbers or other mathematical objects (such as complex numbers, polynomials, or functions) arranged in rows and columns. The size or dimensions of a matrix are given by the number of rows and columns it has, and a matrix with m rows and n columns is said to be an m × n matrix.
Let A be the 2×3 matrix:
[tex]A= \begin{bmatrix}1 & 1 & 0\\1 & -1 & 0\end{bmatrix}[/tex]
and let B be the 3×2 matrix:
[tex]B= \begin{bmatrix}1 & 1\\1 & -1\\0 & 1\end{bmatrix}[/tex]
Then, for any vector x in [tex]R^2[/tex], we have:
[tex]T(U(x)) = A(Bx) = A(x_1 + x_2, x_1 - x_2, x_3)[/tex]
[tex]= (x_1 + x_2 + x_1 - x_2, x_1 - x_2 - x_1 - x_2, 0)[/tex]
[tex]= (2x_1, -2x_2, 0)[/tex]
To show that this is a reflection over the line y=x, we can verify that T(U(x)) is equal to its own inverse. That is, we want to show that:
[tex]T(U(T(U(x)))) = x[/tex]
Substituting T(U(x)) for y, we have:
[tex]T(U(T(U(x)))) = T(U(y)) = A(By) = A(2y_1, -2y_2, 0)[/tex]
[tex]= (2y_1 + (-2y_2), 2y_1 - (-2y_2), 0)[/tex]
[tex]= (4y_1, 4y_2, 0)[/tex]
To see that this is equal to x, we note that the first and second components have been swapped, which corresponds to a reflection over the line y=x. Thus, T(U) is indeed a reflection over the line y=x.
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The complete question is:
Find an example of a 2×3 matrix A and a 3×2 matrix B such that, letting T(x)=Ax and U(x)=Bx, the composition T∘U is a reflection over the line y=x.
Write an equation for the line that passes through the point (3,6) and is parallel to x = 8. A. x = 3 B. x=6 OC. y = 8 OD. y = 6
Answer: A. x = 3
Step-by-step explanation:
I have graphed x = 8 and the point (3, 6). See attached.
We know that options C and D are incorrect because they are y = equations and not x = equations like the one given, so they will not be parallel to x = 8.
Lastly, our point is (3, 6) with a value of x = 3. This gives us a parallel equation that goes through that point (I have added x = 3 to the graph attached as well);
x = 3
Molly is filling bags of marbles. She makes each bag so that 3 out of every 8 marbles are blue. Which equation correctly compares the number of marbles she uses, x, to the number of blue marbles, y?
The equation that correctly compares the number of marbles used, x, to the number of blue marbles, y, is y = 3/8x.
To calculate the number of marbles used, x, and the number of blue marbles, y, Molly is making, the following equation can be used: y = 3/8x. This equation states that for every 8 marbles used, 3 of them will be blue. For example, if Molly uses 24 marbles, then 3/8x = 3/8(24) = 9. Therefore, 9 of the 24 marbles will be blue. To calculate the number of blue marbles for a different number of marbles used, x, the equation can be rearranged to solve for y. For example, if Molly uses 48 marbles, then the equation can be rearranged to y = 8/3x, and then 8/3(48) = 16. Therefore, 16 of the 48 marbles will be blue.
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which of the following values of alpha would cause exponential smoothing to respond the most slowly to forecast errors? question 38 options: 0.80 cannot be determined 0.20 0.40 0.10
Alpha value of 0.80 would cause exponential smoothing to respond the most slowly to forecast errors.
What is exponential smoothing?
Exponential smoothing is a method for estimating time series data in statistics. This method of forecasting is widely used in the estimation of the business cycle and other data with a linear trend. Exponential smoothing predicts the next time period by combining the most recent value of the series with a fraction of the prior forecast. The quantity of smoothing is determined by the alpha parameter.
Exponential smoothing can be described as follows:
[tex]$$S_t=\alpha y_t + (1-\alpha)S_{t-1}$$[/tex]
Where
S_t is the predicted value for time t,
α is the smoothing constanty is the actual value for time t−1
(1−α)S_{t−1} is the forecasted value for time t−1
Based on the equation, it is evident that the larger the value of α, the greater the contribution of the current period to the forecast. In the same way, the lower the value of α, the less significant the role of the current period in the forecast. As a result, it can be concluded that the smaller the value of α, the more slowly exponential smoothing reacts to forecast errors.
Therefore, the answer to this question is alpha value of 0.80 would cause exponential smoothing to respond the most slowly to forecast errors.
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What are two other ways to name <1?
Answer: <PFY and <YFP
Step-by-step explanation:
Answer:
<PFY and <YFP
Step-by-step explanation:
The expression 0. 15c-0. 072 factored is
By factoring out this common factor, we obtain the simplified expression 0.006(25c - 12).
We can start by determining the common factor between the two terms in order to factor the phrase 0.15c - 0.072. The common factor in this situation is 0.006, which we may factor out to obtain:
0.15c - 0.072 = 0.006(25c - 12) (25c - 12)
As a result, factoring the expression 0.15c - 0.072 gives 0.006 (25c - 12).
It is possible to utilise this factored form to further simplify calculations or to resolve equations that contain this statement. If we needed to find c in the equation 0.15c - 0.072 = 0, for instance, we could use the factored form to obtain:
0.006(25c - 12) = 0
25c - 12 = 0
c = 12/25
In conclusion, factoring the expression 0.15c - 0.072 involves finding the common factor between the two terms, which is 0.006. By factoring out this common factor, we obtain the simplified expression 0.006(25c - 12).
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The diagram shows a circle inside a square.
D
C
28
ABCD is a square of side 10 cm.
Each side of the square is a tangent to the circle.
10 cm
Work out the total area of the shaded regions in terms of TT.
Give your answer in its simplest form.
B
Diagram NOT
accurately drawn
er) & siprislostjo
Answer:
100 - 25π cm²
Step-by-step explanation:
Area of Square = 10 × 10 = 100 cm²
Area of Circle = πr² = r² × π = 25π cm²
Area of Shaded Regions = 100 - 25π cm²
you will find information about the statistics used and the findings of statistical tests in which section of the research report?
The section of the research report that may have the information about the statistical parameter used and the findings of statistical tests is the "Results" and ''Reference" section.
The results section usually comes after the introduction and literature review sections of the research report.
A research report is a document that outlines the results of a study conducted by an individual or a group. The research report is a written record of the study and includes information about the research design, data collection, data analysis, and findings. A research report can be written in different formats, depending on the discipline and audience.
Statistics refers to the collection, analysis, interpretation, presentation, and organization of data. Statistics help researchers to draw conclusions from data and make informed decisions. Statistical tests are used to determine whether the results of a study are statistically significant, which means that the results are unlikely to have occurred by chance. Statistical tests are an essential part of the research process, and the findings of these tests are reported in the results section of a research report.
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The box office at a theater is selling tickets for a series of rock concerts. So far, they have sold 27 balcony tickets and 82 general admission floor tickets for Fridays show, for a total of 3,453 in receipts period for Saturday's show comma 90 balcony tickets and 93 general admission floor tickets have been sold comma equaling 7,182 in receipts. How much does each ticket cost?
Thus, the cost of each balcony tickets and general admission floor tickets are 24 and 55.
Define about 2 variable linear equation?Equations linear in two variables: It is a mathematical formula with the notation ax+by+c=0. X and Y are variables, whereas a, b, and c are real numbers. It is possible to state that a and b do not equal zero. When the same integer is added towards both sides, multiplied by the same number, or divided by the same number, a linear equation can be solved. X and Y stand for two-variable linear equations.
For the given query:
Let 'x' be the price of each balcony tickets.
Let 'y' be the price of each floor tickets.
Then, system of linear equation are:
27x + 82y = 3453 ...eq1
90x + 93y = 7182 ..eq2
Using substitution method:
27x + 82y = 3453
x = (3453 - 82y)/27 ...Put in eq 2
90( (3453 - 82y)/27 ) + 93y = 7182
10/3 *(3453 - 82y)) + 93y = 7182
10 *(3453 - 82y)) + 279y = 21546
34530 - 820y + 279y = 21546
541y = 12984
y = 24
Now,
x = (3453 - 82y)/27
x = (3453 - 82(24))/27
x = 55
Thus, the cost of each balcony tickets and general admission floor tickets are 24 and 55.
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Write 39.76% as a decimal
Decimal form of number 39.76% is,
= 0.3976
We have to write,
A number 39.76% into a decimal form.
Now, We can write the number in decimal form as,
= 39.76%
= 39.76 / 100
= 0.3976
Therefore, Decimal form of number 39.76% is,
= 0.3976
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Select all the equations that match the tape diagram.
Tape diagram, 1 part labeled 8, 6 parts labeled x, total 35.
A. 35=8+x+x+x+x+x+x
A. 35 is equal to 8 plus x plus x plus x plus x plus x plus x
B. 35=8+6x
B. 35 is equal to 8 plus 6 x
C. 6+8x=35
C. 6 plus 8 x is equal to 35
D. 6x+8=35
D. 6 x plus 8 is equal to 35
E. 6x+8x=35x
E. 6 x plus 8 x is equal to 35 x
F. 35−8=6x
F. 35 minus 8 is equal to 6 x
Equations B and C match the tape diagram.
What is an equation?An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equals sign (=). The expressions on both sides of the equation can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
The tape diagram shows 1 part of 8 and 6 parts of x, with a total of 35.
Equation B, 35 = 8 + 6x, represents the total of 35 as the sum of the 1 part of 8 and 6 parts of x.
Equation C, 6 + 8x = 35, represents the total of 35 as the sum of the 1 part of 6 and 8 times x, which also matches the tape diagram.
Equations A, D, E, and F do not match the tape diagram because they do not accurately represent the given parts and total.
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When you add -17 to me the result is -22 what intger am I
Answer:
-5
Step-by-step explanation:
Solve the inequality for u.
5u≤45
Simplify your answer as much as possible.
Answer:
u ≤ 9
Step-by-step explanation:
5u ≤ 45 ( divide both sides by 5 )
u ≤ 9
An event where two or more things happen at the same time is called ______
A. Dependent event
B. Compound event
C. Independent event
D. Organized list
Answer:
B. Compound event
Step-by-step explanation:
An event where two or more things happen at the same time is called a compound event.
12. A fence is being built around a
small park. How many feet of
fence will be needed to surround
the park?
21 ft
18 ft
17.6 ft
29 ft
18 ft
Answer:
103.6ft
Step-by-step explanation:
21ft + 18ft + 17.6ft + 29ft + 18
boardwalk electronics manufactures 200,000 circuit boards per month. a random sample of 4,000 boards is inspected every week for seven characteristics. during a recent week, seven defects were found for one characteristic, and two defects each were found for the other six characteristics. if these inspections produced defect counts that were representative of the population, what are the dpmo's for the individual characteristics and what is the overall dpmo for the boards? do not round intermediate calculations. round your answers to the nearest whole number.
The overall DPMO for the boards would be 4750.
Boardwalk Electronics manufactures 200,000 circuit boards per month. A random sample of 4,000 boards is inspected every week for seven characteristics. During a recent week, seven defects were found for one characteristic, and two defects each were found for the other six characteristics. If these inspections produced defect counts that were representative of the population, the dpmo's for the individual characteristics and what is the overall dpmo for the boards would be as follows:To calculate the DPMO, the formula used is:DPMO = (Number of defects / Number of Opportunities) × 1,000,000For Characteristic
1:Number of defects = 7Number of opportunities = 4000DPMO = (7/4000) × 1,000,000= 1750For Characteristic 2:Number of defects = 2Number of opportunities = 4000DPMO = (2/4000) × 1,000,000= 500For Characteristic 3:Number of defects = 2Number of opportunities = 4000DPMO = (2/4000) × 1,000,000= 500For Characteristic 4:Number of defects = 2Number of opportunities = 4000DPMO = (2/4000) × 1,000,000= 500For Characteristic 5:Number of defects = 2Number of opportunities = 4000DPMO = (2/4000) × 1,000,000= 500For Characteristic 6:Number of defects = 2Number of opportunities = 4000DPMO = (2/4000) × 1,000,000= 500For Characteristic 7:Number of defects = 2Number of opportunities = 4000DPMO = (2/4000) × 1,000,000= 500The overall DPMO for the boards would be the sum of the DPMO of all characteristics which would be 1750 + 500 + 500 + 500 + 500 + 500 + 500 = 4750.
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Solve the equation.
4π=w−6π
Answer: W=10pi
Step-by-step explanation:
the percentage of people who prefer dogs to cats is 78% for a given population. what is the standard error of the sampling distribution of sample proportions for samples of size n
The standard error of the sampling distribution of sample proportions for samples size
1) n = 35 ⇒ SE = 0.07
2) n = 100 ⇒ SE = 0.04
3) n = 250 ⇒ SE = 0.03
We know that the formula for thr standard error(SE) of the sample Proportion is:
SE = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
as the sample size increases, the standard error decreases.
Here, the percentage of people who prefer dogs to cats is 78%
so, p = 0.78
For samples of size n = 35,
SE = [tex]\sqrt{\frac{0.78\times (1-0.78)}{35} }[/tex]
SE = [tex]\sqrt{\frac{0.1716}{35} }[/tex]
SE = 0.07
For sample size n = 100,
SE = [tex]\sqrt{\frac{0.78\times (1-0.78)}{100} }[/tex]
SE = [tex]\sqrt{\frac{0.1716}{100} }[/tex]
SE = 0.041
For samples of size n = 250,
SE = [tex]\sqrt{\frac{0.78\times (1-0.78)}{250} }[/tex]
SE = [tex]\sqrt{\frac{0.1716}{250} }[/tex]
SE = 0.03
Learn more about the sample size here:
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The complete question is:
The percentage of people who prefer dogs to cats is 78% for a given population. What is the standard error of the sampling distribution of sample proportions for samples of size n=35, n=100, and n=250?