Answer:
48
Step-by-step explanation:
50 (total green apples) - 2 (green apples eaten) = 48 (green apples left)
how many square feet of carpet will we need for this hole
Answer: 44 ft²
Step-by-step explanation:
We will find the area of the large rectangle and subtract the area of the square. The area of a rectangle (and square) can be used with this formula:
A = LW
Large Rectangle:
A = LW
A = (12 ft)(4 ft)
A = 48 ft²
Square:
A = LW
A = (2 ft)(2 ft)
A = 4 ft²
Subtract:
48 ft² - 4 ft² = 44 ft²
summation notation for the series
7+11+15+…+203+207
The series can be represented in summation notation as follows: ∑(n = 7 to 207) (4n - 1)
What is the summation?In this notation, the Greek letter sigma (∑) represents the summation symbol, and n represents the index of summation. The series starts from n = 7 and goes up to n = 207, with each term being (4n - 1). The notation "n = 7 to 207" indicates the range of values that n takes on in the summation. The expression (4n - 1) represents the general term in the series, which changes as n varies from 7 to 207.
Summation notation, denoted by the Greek letter sigma (∑), is a shorthand way to represent the sum of a sequence of numbers. In this case, the series you provided is:
7 + 11 + 15 + … + 203 + 207
The general term of the series, which changes as "n" varies, is (4n - 1). This means that for each value of "n", we substitute it into the expression (4n - 1) to get the corresponding term in the series. For example, when "n" is 7, the corresponding term is (4 * 7 - 1) = 27. When "n" is 11, the corresponding term is (4 * 11 - 1) = 43, and so on, up to "n" = 207.
The summation notation "∑(n = 7 to 207) (4n - 1)" represents the sum of all the terms in the series, where "n" takes on values from 7 to 207, and the term for each "n" is (4n - 1). This notation allows us to compactly represent the entire series in a concise mathematical form.
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answer these questions please
The difference in the two figure's areas is 96 square units.
The height of the horse trough is 4 feet.
How to find the difference in the two figure's areas?No. 11
The area of Figure A is:
A = l * w = 12 * 8 = 96 square units
The area of Figure B is:
B = l * w = 16 * 12 = 192 square units
The difference in the two figure's areas is:
B - A = 192 - 96 = 96 square units
Therefore, the difference in the two figure's areas is 96 square units.
No. 12
We are given that the base area is 24 square feet, and the volume is 96 cubic feet.
Volume = base area * height
96 = 24 * height
height = 96/24
height = 4 feet
Therefore, the height of the horse trough is 4 feet.
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Answer:...............
Step-by-step explanation:
...................
Given a reduced echelon matrix in R3 onto iff for every vector b in R3, Ax = b has a solution iff every row of A has a pivot.
a. true b. false
Every vector b in R3, the equation Ax = b has a solution if every row of A has a pivot.
The statement is true.
True.
If a reduced echelon matrix in R3 is obtained by row operations from a matrix A, then the reduced echelon matrix is in row echelon form and is equivalent to the original matrix A.
If every row of A has a pivot, then every row has a leading non-zero entry in the row echelon form of A.
This means that each row of the row echelon form of A has a pivot, and so the matrix has full row rank.
The number of pivot columns in the reduced echelon matrix equals the row rank of A, which is also the same as the column rank of A.
Vector b in R3, the equation Ax = b has a solution if and only if b is a linear combination of the columns of A.
If A has full column rank, then the columns of A span the column space of A, which means that any vector in the column space can be expressed as a linear combination of the columns of A.
If every row of A has a pivot, then A has full row rank, full column rank, and the columns of A span R3.
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Does y=2(15)^x represent an exponential function? need ASAP
Answer:
Yes it is an exponential function
Step-by-step explanation:
The given equation can be written in the form y = abˣ , and:
a and b are constants (a = 2, b = 15)
a ≠ 0
b > 0
b ≠ 1
I have 45 min 2 attempts help pls!!!
The missing points of the table at x = 5, y = 1 and y = 0 has been completed in the table attached.
How to complete the table of the graph?
In general, to complete a table based on a graph, you need to follow these steps:
Look at the graph carefully and identify the variables represented on each axis.Determine the range of values for each variable.Decide on the intervals or steps you want to use for the table, based on the level of detail required.Create a table with the appropriate number of columns and rows.Label the columns and rows with the variables and their corresponding units.Fill in the table by reading the values of the dependent variable (y-axis) for each value of the independent variable (x-axis) and recording them in the appropriate cell of the table.Learn more about completing graph tables here: https://brainly.com/question/29298329
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What is the domain of the radical function shown below?
What is the domain of the radical function shown below?
The required domain of the given function f(x) = √x+4 is (D) {x|x ≥ -4} respectively.
What is a domain?The domain of a function is the set of values that we are allowed to enter into our function.
This collection includes the x values for functions like f(x).
The set of values that a function can accept as input is known as its range.
The function outputs this list of values once we enter an x value.
Think about the equation y = f(x), where x and y are the independent and dependent variables.
If a value for x successfully enables the creation of a single value y using another value for x, it is said to be in the domain of the function f.
Considering the function's expression:
f(x) = √x+4
We are aware that the set of input values for which the function is real and defined constitutes the function's domain.
We are aware that for the function to continue to be defined, the value included within the radical expression must be larger than or equal to 0.
x+4 ≥ 0
Take 4 off of both sides.
x+4-4 ≥ 0-4
x ≥ 4
Then, the domain is:
{x|x ≥ -4}
Therefore, the required domain of the given function f(x) = √x+4 is (D) {x|x ≥ -4} respectively.
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Correct question:
The graph of the function f(x)=V x+4 is shown below. The domain of the function?
3. (07.05 MC) An equation is shown below: 12x + 3(x - 5) = 6x + 9x - 15
Part A: Solve the equation and write the number of solutions. Show all the steps. (6 points)
Part B: Name one property you used to solve this equation. (4 points)
The equation 12x + 3(x - 5) = 6x + 9x - 15 has infinite many solutions
Solving the equationPart A:
Starting with the given equation:
12x + 3(x - 5) = 6x + 9x - 15
Simplify by distributing the 3:
12x + 3x - 15 = 6x + 9x - 15
Combine like terms on both sides:
15x - 15 = 15x - 15
Add 15 to both sides:
0 = 0
Therefore, the equation has infinite many solutions
Part B:
The property used to solve this equation is the distributive property of multiplication over addition, which states that a(b + c) = ab + ac. In this case, we used the distributive property to simplify 3(x - 5) to 3x - 15.
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Type the correct answer in the box. Use numerals instead of words.
For this item, if the answer is not a whole number, enter it as a fraction in simplest form using / as the fraction bar.
Isolde is stacking books. The stack of books forms a rectangular prism.
Each book is the same size. Isolde knows the area of the base of one book is 22 1/2 square inches and each book is 3/4 inch thick.
The volume of a stack of 9 books is cubic inches.
The volume of a stack of 9 books is 1368.75 cubic inches.
Volume of a book stackTo find the volume of a stack of 9 books, we first need to find the height of the stack. Since each book is 3/4 inch thick, the height of the stack is 9 times 3/4 inch, which is 6 3/4 inches.
Now we need to find the area of the base of the rectangular prism formed by the stack of books. Since each book has an area of 22 1/2 square inches, the total area of the base of the stack is 9 times 22 1/2 square inches, which is 202 1/2 square inches.
Therefore, the volume of the stack of 9 books is:
Volume = Area of base x heightVolume = (202 1/2 square inches) x (6 3/4 inches)Volume = 1368.75 cubic inchesMore on volume of stacked books can be found here: https://brainly.com/question/1058070
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In Problems 55–62 write each function in terms of unit step functions. Find the Laplace transform of the given function. = {0, 0<_t<1 f(t) = {t^(2) t>_ 1
The Laplace transform of the given function f(t) = {0, 0 < t < 1, t², t ≥ 1} is 2s⁻³.
Given the function f(t) = {0, 0 < t < 1, t², t ≥ 1}, we need to find its Laplace transform. The Laplace transform of a function f(t) is denoted by F(s) and is defined as follows:
F(s) = L{f(t)} = ∫[0,∞) f(t)e⁻ᵃˣdt,
where s is a complex variable.
To find the Laplace transform of the given function, we need to split the function into two parts: one for 0 < t < 1 and another for t ≥ 1. For 0 < t < 1, f(t) = 0, so the integral becomes:
L{0} = ∫ 0e⁻ᵃˣdt = 0.
For t ≥ 1, f(t) = t², so the integral becomes:
L{t²} = ∫ t²e⁻ᵃˣdt.
To evaluate this integral, we can use integration by parts. Let u = t² and dv = e⁻ᵃˣdt, then du/dt = 2t and v = (-1/s) e⁻ᵃˣ. Using the integration by parts formula, we get:
L{t²} = ∫ t²e⁻ᵃˣdt = (-t²/s)e⁻ᵃˣ∣∣∣[0,∞) + (2/s)∫[0,∞) te⁻ᵃˣdt.
The first term in the above equation evaluates to zero because e⁻ᵃˣapproaches zero as t approaches infinity. Using integration by parts again for the second term, we get:
L{t²} = (-t²/s)e⁻ᵃˣ∣∣∣[0,∞) + (2/s)(-t/s)e⁻ᵃˣ∣∣∣[0,∞) + (2/s²)∫[0,∞) e⁻ᵃˣdt.
The first two terms in the above equation evaluate to zero for the same reason as before. The integral in the last term evaluates to (1/s²), so we get:
L{t²} = 2/s³.
Therefore, the Laplace transform of the given function f(t) is:
L{f(t)} = L{0} + L{t²} = 0 + 2/s³ = 2s⁻³.
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What is the area, in square inches, of the trapezoid below?
Answer:
Step-by-step explanation:
Split it into 3 shapes.
2 triangles and 1 square.
The squares answer is 53.25 And for the triangles you would get 26 and there are 2 triangles so 52.
52+53.25=105.25.
Calculate the GDP if the consumers of a country spent R220 billion the government spends R50 billion and businesses spend R100 billion exports totaled R25 billion and imports R32 billion (show all calculations)
The GDP of the hypothetical country in this case is R363 billion.
To calculate GDP, we use the following formula:
GDP = C + G + I + NX
where:
C = consumer spending
G = government spending
I = business investment
NX = net exports (exports - imports)
Now, let's plug in the given values into the formula and calculate the GDP:
GDP = R220 billion (C) + R50 billion (G) + R100 billion (I) + (R25 billion - R32 billion) (NX)
GDP = R220 billion + R50 billion + R100 billion - R7 billion
GDP = R363 billion
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“Write a proof to show that the triangles are congruent.”
The given triangles ABD and CBD are congruent because their corresponding sides and angles are equal.
What are congruent triangles?Congruent triangles are two triangles that have exactly the same size and shape. In other words, all corresponding sides and angles of the two triangles are equal.
There are several ways to show that two triangles are congruent, including:
Side-Side-Side (SSS) Congruence: If the three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.
Side-Angle-Side (SAS) Congruence: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.
Angle-Side-Angle (ASA) Congruence: If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent.
In the given triangles ABD and CBD, each of their angles is 60⁰, since the triangles are equilateral, so the triangles are congruent.
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Violet rents a bike in a city she is visiting. She pays an initial fee of $2.50 plus $3.75 per hour she rents the bike. Which equation can be used to find y, the total cost of renting a bike, if x represents the number of hours Violet rents the bike?
Answer: y = 3.75x + 2.50
Step-by-step explanation:
The equation that can be used to find y, the total cost of renting a bike, if x represents the number of hours Violet rents the bike is:
y = 3.75x + 2.50
Explanation:
Violet pays an initial fee of $2.50, which is a fixed cost that does not depend on the number of hours she rents the bike. Additionally, she pays $3.75 per hour she rents the bike, which is a variable cost that depends on the number of hours. Therefore, the total cost of renting a bike (y) can be expressed as the sum of the fixed cost ($2.50) and the variable cost ($3.75x), which gives the equation:
The absolute maximum value of f(x)= x^3 -3x^2 +12 on the closed interval [-2,4] occurs at x=a) 4b) 2c) 1d) 0e) -2
The absolute maximum value of f(x) on the closed interval [-2, 4] occurs at x = -2 and x = 0, and the maximum value is 16. So the answer is option (e) -2.
To find the absolute maximum value of the function f(x) = x³ - 3x² + 12 on the closed interval [-2, 4], we need to evaluate the function at the critical points and at the endpoints of the interval, and then choose the largest value.
To find the critical points, we take the derivative of the function and set it equal to zero
f'(x) = 3x² - 6x = 3x(x - 2)
Setting f'(x) = 0 gives x = 0 and x = 2 as critical points.
Next, we evaluate the function at the critical points and at the endpoints of the interval
f(-2) = (-2)³ - 3(-2)² + 12 = 16
f(0) = (0)³ - 3(0)² + 12 = 12
f(2) = (2)³ - 3(2)² + 12 = 4
f(4) = (4)³ - 3(4)² + 12 = 4
Therefore, the correct option is (e) -2
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The absolute maximum value occurs at x = 4, with a value of 28. So, the answer is a) 4.
We occasionally encounter operations with hills and valleys. Hill and valley points in polynomial functions typically have many locations. We are aware that these places, which can be categorized as maxima or minima, are the function's critical points. The valley points are referred to as minimal and the hill points are as maxima. We must determine the locations of the function's global maxima and global minima, which are known as the minimum and maximum values, respectively, due to the fact that there are several maxima and minima.
To find the absolute maximum value of the function [tex]f(x) = x^3 - 3x^2 + 12[/tex] on the closed interval [-2, 4], we need to examine the critical points and the endpoints of the interval.
First, find the critical points by taking the derivative of f(x) and setting it equal to 0:
[tex]f'(x) = 3x^2 - 6x\\0 = 3x^2 - 6x\\0 = 3x(x - 2)[/tex]
The critical points are x = 0 and x = 2.
Next, evaluate the function at the critical points and the interval endpoints:
[tex]f(-2) = (-2)^3 - 3(-2)^2 + 12 = -8 - 12 + 12 = -8\\f(0) = 0^3 - 3(0)^2 + 12 = 12\\f(2) = 2^3 - 3(2)^2 + 12 = 8 - 12 + 12 = 8\\f(4) = 4^3 - 3(4)^2 + 12 = 64 - 48 + 12 = 28[/tex]
The absolute maximum value occurs at x = 4, with a value of 28. So, the answer is a) 4.
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Which is more, 7,000,001 milligrams or 7 kilograms?
Question
The table of values shows the height of a windmill blade from the ground over time. This can be modeled by a sinusoidal function.
The table of values is attached
Which statements are true?
Select each correct answer.
The frequency of the function is 4.
The minimum value of the function is 5.8.
The amplitude of the function is 1.5.
The period of the function is 1/4.
Answer:
the amplíetude of the function is 1.5
Step-by-step explanation:
.
223/26 please help I can do it’s to hard!
Answer:
roughly 8.58
Step-by-step explanation:
long division I hope this helps bye !!! have a great day!!! :D
Ganymede, one of the moons of Jupiter, can be modeled by a sphere with a diameter of approximately 3,388 kilometers. The Moon of Earth, by comparison, can be modeled by a sphere with a diameter of approximately 1,245 kilometers. The volume of Ganymede is approximately how many times the volume of Earth’s Moon?
The volume of Ganymede is approximately 3.48 times the volume of the Moon, based on the given diameters of the two moons and the formula for the volume of a sphere.
What is volume of a sphere?The volume of a sphere is the amount of space occupied by the sphere in three-dimensional space. It can be calculated using the formula V = (4/3)πr³, where V is the volume of the sphere, r is the radius of the sphere, and π (pi) is a mathematical constant approximately equal to 3.14159. This formula states that the volume of a sphere is four-thirds of the product of pi and the cube of the sphere's radius.
In the given question,
The volume of a sphere can be calculated using the formula V = (4/3)πr³, where r is the radius of the sphere. Since we are given the diameters of the two moons, we can calculate their radii by dividing the diameters by 2. Therefore, the radius of Ganymede is 3,388/2 = 1,694 km, and the radius of the Moon is 1,245/2 = 622.5 km.
Now, we can calculate the volumes of the two moons:
V_Ganymede = (4/3)π(1694)³ ≈ 7.66 x 10^10 km³
V_Moon = (4/3)π(622.5)³ ≈ 2.2 x 10^10 km³
To find how many times larger Ganymede's volume is compared to the Moon's volume, we can divide the volume of Ganymede by the volume of the Moon:
V_Ganymede / V_Moon ≈ (7.66 x 10¹⁰) / (2.2 x 10¹⁰) ≈ 3.48
Therefore, the volume of Ganymede is approximately 3.48 times the volume of the Moon.
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NEED HELP ASAP, WILL GIVE BRAINLIEST!!
In the figure shown, angle 1 has a measure of 90° and angle 2 has measure of 38°. Using angles 4, 3, and 2 write an equation and solve for angle 3. Then solve for angle 6 & 5.
Equation for Angle 3-
Angle 3=
Angle 5=
Angle 6=
Answer:
Equation for Angle 3- 90-38=52
Angle 3= 52
Angle 5= 38
Angle 6= 52
Step-by-step explanation:
Angle is 90 degrees.
Angle 2 is 38 degrees.
If you are just looking at the bottom half(Angle 6, Angle 1, and Angle 2) They are all supposed to add up to equal 180 degrees because it is a supplementary angle.
So you add 90 and 38 and it gives you 52(Angle 6).
90+38+52=180
Then a complementary angle is two angles that equal 90 degrees.
So if you take Angle 2(38 degrees) and subtract it from 90, you get 52. Which is Angle 3.
You do the same with Angle 6 and Angle 5.
Angle 6(52 degrees) subtract from 90 and you get 38.
Then you add 38 and 52 and you get 90.
Then 180-90=90, so Angle 4 is 90 degrees.
have you ever been frustrated because you could not get a container of some sort to release the last bit of its contents? an article reported on an investigation of this issue for various consumer products. suppose five 6.0 oz tubes of toothpaste of a particular brand are randomly selected and squeezed until no more toothpaste will come out. then each tube is cut open and the amount remaining is weighed, resulting in the following data: 0.51, 0.63, 0.42, 0.5, 0.37. does it appear that the true average amount left is less than 10% of the advertised net contents?
The null hypothesis is that the true average amount left is equal to 10% of the advertised net contents. In In another case of true average amount is less than 10% of the advertised net contents.
Hence, we will utilize one-tailed t-test with a significance level of 0.05 to test this hypothesis.
The sample mean of the five tubes is (0.51+0.63+0.42+0.5+0.37)/5 = 0.486 ounces.
The sample standard deviation is √(((0.51-0.486)² + (0.63-0.486)² + (0.42-0.486)² + (0.5-0.486)² + (0.37-0.486)²)/4) = 0.107 ounces.
The t-statistic is calculated as
(mean sample - hypothe -sized mean)/( standard deviation sample/√( size sample))
= (0.486 - 0.6)/(0.107/√(5))
= -3.06.
The p-value for this test is 0.0249 which is less than our significance level of 0.05.
Therefore, we reject the null hypothesis and conclude that there is evidence that the true average amount left in a tube of toothpaste is less than 10% of the advertised net contents.
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a percentile is group of answer choices a common label on the vertical axis of histograms. is a numerical summary for categorical data. a measure of placement in a sorted quantitative dataset. is a numerical summary for ordinal data.
Percentiles provide information about the placement of data points in a quantitative dataset, histograms display the distribution of data, categorical data is grouped into categories, and ordinal data has an inherent order but no meaningful numerical differences.
Based on the terms you provided, we are looking for information about percentiles, histograms, categorical data, and ordinal data.
A percentile is a measure of placement in a sorted quantitative dataset.
It indicates the relative standing of a data point within the dataset.
For example, a score in the 80th percentile means that it is higher than 80% of the scores in the dataset.
A histogram is a graphical representation of the distribution of a dataset, typically used for continuous data.
The vertical axis of a histogram displays frequency or density, while the horizontal axis represents the data values divided into bins or intervals.
Categorical data is a type of data that can be divided into groups or categories, such as gender, ethnicity, or favorite color.
A numerical summary for categorical data usually involves counts or percentages for each category.
Ordinal data is a type of data where the order matters, but the difference between values is not meaningful, such as rankings or ratings.
A numerical summary for ordinal data can include measures of central tendency, such as the median or mode.
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I NEED HELP ON THIS ASAP!!!
The exponential function f(x) = 2^x is given by the blue graph on the given graph.
What is an horizontal asymptote?The horizontal asymptote of a function is the value of f(x) as x goes to infinity, as long as this value is different of infinity.
The function in this problem is defined as follows:
y = 2^x.
Two relevant numeric values are given as follows:
When x = -1, y = 2^(-1) = 1/2 = 0.5.When x = 0, y = 2^0 = 1.Hence the function is represented by the blue graph.
The horizontal asymptote is of y = 0, as when x goes to negative infinity, y goes to zero.
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What is the area of this tile?
And it isn’t 12 because I did that for the other one and got it wrong.
The area of this tile is 12 cm2.
What is area?Area is a two-dimensional measure of space, referring to the total surface area of a shape. It can be measured in terms of square units, such as square feet, meters, or kilometers. Area is an important concept in geometry and can be used to calculate the perimeter, circumference, and volume of a shape. Area calculations are also used in fields such as engineering, architecture, and construction.
Area is the size of a two-dimensional shape or the amount of space within a three-dimensional figure. It is a measure of how much space an object occupies.
The area of this tile can be calculated using the formula:
Area = Length x Width
In this case, the length of the tile is 6 cm and the width is 2 cm. Therefore, the area of the tile is 12 cm2.
To calculate the area, we multiplied the length and width of the tile. This formula is applicable to all rectangles, as the area of any rectangle is determined by multiplying the length and width.
It is important to note that the units used to measure the length and width must be the same in order to get an accurate area measurement. For example, if the length was measured in inches and the width in centimeters, then the area would be incorrect.
In conclusion, the area of this tile is 12 cm2.
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Solve for the value of t. (9t+3)º (4t-5)°
Answer:
13
Step-by-step explanation:
The given angles are on a straight line and they are supplementary angles which means their sum is 180°
According to the above mentioned information, we can write the following equation to find the value of t:
9t + 3 + 4t - 5 = 180
Add/subtract like terms.13t - 2 = 180
Add 2 to both sides of the equation.13t = 182
Divide both sides by 13.t = 14
Going to Market - Basics Math
QUESTION 5 of 10: Advertisers want to create "awareness," which is whether a consumer even knows about a business. If your business
starts with 3% awareness and grows awareness by 5% per week (compounded), how long will it take to reach 75% awareness? The formula
for compound growth is E= B x (1 + R), where E is ending value, B is beginning value, R is rate of growth, and T is the amount of time.
a) 12 weeks
b) 66 weeks
c) 83 weeks
d) 94 weeks
If your business starts with 3% awareness and grows awareness by 5% per week (compounded), how long will it take to reach 75% awareness is b) 66 weeks
What is Compound Growth?Compound growth denotes the procedure of generating profits not only on the investment's principal amount, but also on the accumulated interest.
It is essentially reallocating its earnings where the investor's interest is integrated with the beginning sum, while additional interest is contingent on this amplified amount.
The purposeful act of compounding can yield noteworthy accomplishments over time, since interest earned from pre-existing income inflates drastically in value due to accruing interest outlays, and hence boosts the final outcome substantially and rapidly- resulting in exponential growth of the given input.
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Can someone please help me on this?
Answer: angle(s) A on the left.
Step-by-step explanation:
Complementary angles are angles whose sum equals 90, which is a righ angle (forms a corner)
It cost Chile 17. 70$ to send 177 text messages. How much would it cost to send 97 text message
The total cost of sending 97 text messages is $9.70
How to find the unit cost?A unit cost is defined as the total expenditure incurred by a specific company to produce, store, and sell one unit of a specific product or service. Unit costs are also synonymous with cost of goods sold (COGS). This accounting measure also involves all of the fixed and variable costs associated with the production of a good or service.
Now, we are told that It cost Chile 17.70$ to send 177 text messages. Thus:
Unit cost of message = 17.70/177 = $0.1 per message
Thus:
Cost of 97 text messages = 97 * 0.1 = $9.7
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if the mean and standard deviation of a population are 436 and 103 respectively, what is the standard error of the mean for a sample of size 8?
The standard error of the mean for a sample of size 8 and population mean 436 is equals to the 36.42.
The standard error of the mean, or usually say standard error, shows how different the population mean from a sample mean. We have a population with population mean, [tex]\mu[/tex] = 436
Standard deviations for population, [tex] \sigma[/tex] = 103
Sample size, n = 8
We have to determine the value of standard error of the mean. SEM is calculated simply as dividing the standard deviation by the square root of the sample size, n. Mathematically,
[tex]SE = \frac{ \sigma}{\sqrt n}[/tex]
Substitues all known values in above formula, [tex]= \frac{ 103}{\sqrt 8}[/tex]
= 36.42
Hence, required standard error value is 36.42.
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ris poll asked a random sample of 1,015 adults nationwide the following question: are you afraid of being alone in an elevator? 10% of the people in the in the sample answered yes. the se of the sample % is about 0.94%. a) an approximate 95% confidence interval for the percentage of all american adults who are afraid of being alone in an elevator is closest to incorrect 9.94%-10.06% correct: 8.12%-11.88%
Answer: The correct answer is 8.12%-11.88%.
We can use the formula for a confidence interval for a proportion:
p ± z*SE
where p is the sample proportion, z* is the z-score corresponding to the desired level of confidence (in this case, 1.96 for a 95% confidence interval), and SE is the standard error of the proportion.
SE = sqrt(p*(1-p)/n) = sqrt(0.1*0.9/1015) = 0.0094
Plugging in the values, we get:
0.1 ± 1.96*0.0094
= 0.1 ± 0.0184
So the 95% confidence interval is (0.0816, 0.1184), which is equivalent to 8.12%-11.88%.
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