Answers
The correct answer is [78.2, 82.3].
What do you mean by standard deviation?It is a statistical quantity that provides information about how far the individual values in a data set deviate from the mean (average) value.
The standard deviation is calculated by finding the square root of the variance, which is the average of the squares of the deviations of each value in the data set from the mean. The formula for standard deviation is:
σ = [tex]\sqrt{ \frac{1}{n}[/tex] × Σ ([tex]x_{i}[/tex] - μ)²
where:
σ is the standard deviation,
n is the number of values in the data set,
[tex]x_{i}[/tex] is each value in the data set,
μ is the mean of the data set,
Σ ([tex]x_{i}[/tex] - μ)² is the sum of the squares of the deviations of each value from the mean.
To calculate the 95% confidence interval for the population mean, we need to know the population standard deviation. Since we don't have that information, we will use the sample standard deviation as an estimate.
Using the sample data, the sample mean is 80.25 and the sample standard deviation is 2.83.
The 95% confidence interval for the population mean is calculated as follows:
CI = [tex]\bar x[/tex] ± t×[tex]\frac{s}{\sqrt{n} }[/tex]
where:
[tex]\bar x[/tex] = sample mean = 80.25
s = sample standard deviation = 2.83
t = t-statistic for a 95% confidence level with 11 degrees of freedom (n-1)
n = sample size = 12
Using a t-table, the t-statistic for a 95% confidence level with 11 degrees of freedom is 2.201.
CI = 80.25 ± 2.201 × [tex]\frac{2.83}{\sqrt{12} }[/tex]
CI = 80.25 ± 2.201 × 0.913
CI = 80.25 ± 2.006
CI = (78.24, 82.26)
Rounding off to the nearest tenth, the 95% confidence interval for the population mean is [78.2, 82.3].
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The complete question is:
Related Questions
Please help me with this question.
Answers
The area of the rectangle will be equal to 11 square units.
What is a matrix?
Matrix is defined as the arrangement of the numbers variables and expressions in the table as rows and columns.
A matrix is a structured table with columns and rows for arranging numbers, expressions, and even symbols. If the two matrices have equal row and column sizes, they can be added to, subtracted from, and multiplied element by element.
The area of the rectangle is calculated by finding the determinant of the matrix as below,
[tex]A = \left[\begin{array}{cc}3&-1&\\5&2&\\\end{array}\right][/tex]
A = ( 6 - ( -5 )
A = 6 + 5
Area = 11 square units
Hence, the value of the area of the rectangle is 11 square units.
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random variables and have the following distribution. x2 f(x1,x2) 0.00 10.00 20.00
x1 5.00 0.20 0.14 0.06
10.00 0.11 0.07 0.12
20.00 0.08 0.02 0.20
Find P(X +Y s 4). (write up to first decimal place)
Answers
P(X + Y < 4) = 0.53 rounded to the first decimal place.
To find the probability P(X + Y < 4),
we need to find the values of x1 and x2 that satisfy the condition
X + Y < 4, and then sum up the corresponding probabilities in the table.
We can start by plotting the points (x1, x2) on a graph and finding the region where X + Y < 4.
This region can be determined by shading in the portion of the graph that is below the line X + Y = 4.
Next, we need to find the values of x1 and x2 in the table that fall within this region and sum up their probabilities.
This gives us P(X + Y < 4) = 0.20 + 0.14 + 0.11 + 0.08 = 0.53.
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It might be useful to represent numbers in ways that simplify
calculations. Create an algebraic expression including at least one variable
and at least one number that can be simplified using minimum 3 of the
exponent laws:
Pls include steps
Answers
If an algebraic expression (x²)³ × x⁴ / x² [tex]x^{(2^3)}[/tex], then the simplified expression is [tex]x^{(2^3)}[/tex] using the exponent laws.
What is the expression?Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.
Consider the expression, as follows:
(x²)³ × x⁴ / x²
Use the exponent law "[tex]a^m \times a^n = a^(m+n)[/tex]" to simplify the first term:
(x²)³ × x⁴ = x⁽²ˣ⁶ ⁺⁴⁾ = x¹⁰
Use the exponent law "[tex]a^m / a^n = a^{(m-n)}[/tex]" to simplify the second term:
x¹⁰ / x² = x⁽¹⁰⁻²⁾ = x⁸
Use the exponent law "[tex](a^m)^n = a^(mn)[/tex]" to simplify the first term:
[tex]x^8 = x^{(24)} = x^{(2^3)}[/tex]
Simplified expression: [tex]x^{(2^3)[/tex]
Note: The laws used in this example are:
[tex]a^m \times a^n = a^(m+n)\\a^m / a^n = a^{(m-n)}\\(a^m)^n = a^{(m\timesn)}[/tex]
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Let the vector space P2 have the inner product
⟨p,q⟩=∫4−4p(x)q(x)dx
Find the following for p=2x, q=5x2.
Solution
(i) ⟨p,q⟩=
(ii) d(p,q)=
(iii) ∥p∥=
(iv) ∥q∥=
Answers
(p, q) = √4 - 4∫p(x)q(x)dx
And the vectors p = 2x and q = 5x^2, we can calculate their inner product as follows:
(p, q) = √4 - 4∫2x * 5x^2 dx = √4 - 4 * (5/3) * x^3 | from 0 to 1
(p, q) = √4 - 4 * (5/3) * 1^3 = √4 - 20/3
Therefore, the inner product of p = 2x and q = 5x^2 is √4 - 20/3.
the retail price of a tv is $600. The discount is 25% and tax is7%. how much do you pay for the tv?
Answers
Answer:
$ 481.50
Step-by-step explanation:
Discount:
Discount = 25% of retail price of TV
= 0.25 * 600
= $ 150
Price after discount = Retail price - discount
= 600 - 150
= $ 450
Tax:
Tax = 7% of 450
= 0.07 * 450
= $ 31.50
Amount to be paid:
Amount needs to be paid = price after discount + tax
= 450 + 31.50
= $ 481.50
The radius of Circle A is 6 cm. The radius of Circle B is 3 cm greater than the radius of Circle A. The radius of Circle C is 3 cm greater than the radius of Circle B. The radius of Circle D is 2 cm less than the radius of Circle C. What is the area of each circle? How many times greater than the area of Circle A is the area of Circle D?
Answers
Radius of Circle B = 6 cm + 3 cm = 9 cm
Radius of Circle C = 9 cm + 3 cm = 12 cm
Radius of Circle D = 12 cm - 2 cm = 10 cm
What is a circle's straightforward definition?
Simply put, a circle is a rounded shape without any edges or line segments. It has the geometric shape of a closed curve. The distance between the circle's points and its center is fixed.
The area of a circle is given by the formula: A = πr^2, where A is the area and r is the radius.
The area of Circle A is A = π(6 cm)^2 = 36π cm^2
The area of Circle B is A = π(9 cm)^2 = 81π cm^2
The area of Circle C is A = π(12 cm)^2 = 144π cm^2
The area of Circle D is A = π(10 cm)^2 = 100π cm^2
To find how many times greater than the area of Circle A is the area of Circle D, we can divide the area of Circle D by the area of Circle A:
100π cm^2 / 36π cm^2 = 2.78
The area of Circle D is 2.78 times greater than the area of Circle A.
Note: since π is a constant, we can ignore it for the purposes of comparing the areas of the circles. It will always be the same value and it will cancel out when dividing.
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Find f(a + 5).
f(x) = x² + 7
Answers
Answer:
[tex]f(x) = {x}^{2} + 7 \\ \dashrightarrow \: f(a + 5) = {(a + 5)}^{2} + 7 \\ \dashrightarrow \: f(a + 5) = {a}^{2} + 25 + 10a + 7 \\ \dashrightarrow \: \: \boxed{ f(a + 5) = {a}^{2} + 10a + 32}[/tex]
hope helpful! :)
Need Help please, here is screenshot
Answers
1)
The axis of symmetry is x = -6.
2)
Vertex is (-6, 26).
3)
f(x) has a maximum value.
4)
f(x) is concave down.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 7 is an equation.
We have,
f(x) = -x² - 12x - 10
This is in the form of ax² + bx + c.
a = -1, b = -12, c = -10
The axis of symmetry is x = -b/2a
x = 12/(-2)
x = -6
Now,
f(x) = -x² - 12x - 10
f(x) = -(x² + 12x + 10)
f(x) = - { (x² + 12x + 36) - 36 + 10}
f(x) = -(x + 6)² + 26
This is in the form of f(x) = a (x - h)² + k
a = -1, h = -6, k = 26
Vertex = (h, k) = (-6, 26)
Now,
f(x) = -x² - 12x - 10
f'(x) = -2x - 12
f''(x) = -2
It is a negative value.
This means f(x) has a maximum value.
Now,
From the graph, we see that f(x) is concave down.
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A population, f(x), after x years may be modeled with f(x)=2(3)^x. What is the initial amount , growth rate, domains and range?
Answers
Growth rate: 3
Domain: all real numbers
Range: all positive real numbers.
2 is the initial amount, growth rate is (3ˣ - 1) × 100% , domain of the function is all real numbers and range of the function is all positive real numbers
What is a function?A relation is a function if it has only One y-value for each x-value.
The given function is:
f(x) = 2(3)ˣ
To find the initial amount, we need to find f(0):
f(0) = 2(3)⁰ = 2(1) = 2
So the initial amount is 2.
To find the growth rate, we can use the formula:
growth rate = (f(x) - f(0)) / f(0) × 100%
= (2(3)ˣ - 2) / 2 × 100%
= (3ˣ - 1) × 100%
So the growth rate is (3ˣ - 1)×100%.
The domain of the function is all real numbers because the function is defined for all values of x.
The range of the function is all positive real numbers because the function is always positive for any value of x.
Specifically, the range of the function is (0, infinity).
Hence, 2 is the initial amount, growth rate is (3ˣ - 1) × 100% , domain of the function is all real numbers and range of the function is all positive real numbers
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Estimate each square root to the nearest tenth 372
Answers
Answer: 19.3
Step-by-step explanation: To solve this we can find numbers whose squares are close to 372. We know 20x20 = 400 and 19x19 = 361 so it has to be between these two.372 is closer to 361 meaning the square root of it is less than 19.5. Now we can just test numbers. 19.4x19.4 = 376ish and 19.3x19.3 is 372.49. This number is close enough so 19.3 is our answer.
Stuck on this please help!!
Answers
Basically, there are two different types of geometric shapes such as: Two – Dimensional Shapes.
Define area of geometrical shape?
The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.The area of shape is the space enclosed within the perimeter or the boundary of a given shape. We can calculate the area of shape for different geometrical shapes using specific mathematical formulae.The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.Area is measured in square units such as square inches, square feet or square meters. To find the area of a rectangle, multiply the length by the width. The formula is: A = L * W where A is the area, L is the length, W is the width, and * means multiply.To learn more about area refers to:
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Basically, there are two different types of geometric shapes such as: Two – Dimensional Shapes. Total area under graph = 15 + 12.56 + 3 + 20 = 50.56 sq. units
Define area of geometrical shape?The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.
The area of shape is the space enclosed within the perimeter or the boundary of a given shape. We can calculate the area of shape for different geometrical shapes using specific mathematical formulae.
The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.
Area is measured in square units such as square inches, square feet or square meters. To find the area of a rectangle, multiply the length by the width. The formula is: A = L * W where A is the area, L is the length, W is the width, and * means multiply.
The area under the graph will be -
area of rectangle = length × breadth
= 5 × 3 = 15 sq. unit
area of circle = πr²
= 3.14 × 2 × 2
= 12.56 sq units
area of triangle = 1/2 × base × height
= 1/2 × 3 ×2
= 3 sq. units
area of trapezium = a + b / 2 . h
= 5 + 3 / 2 . 5
= 20 sq. units
area of triangle = 1/2 × 2 × 5 = 5 sq. units
Total area under graph = 15 + 12.56 + 3 + 20 = 50.56 sq. units
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The times for the mile run of a large group of male college students are approximately Normal with mean 7.18 minutes and standard deviation 0.74 minutes. Use the 68-95-99.7 rule to answer the following questions. (Start by making a sketch of the density curve you can use to mark areas on.)
(a) What range of times covers the middle 68% of this distribution?
(b) What percent of these men run a mile in more than 8.57 minutes?
Answers
Considering the given data, we can calculate our answers of standard deviation as:
a) The range of times that covers the middle 68% of this distribution is 6.44 <= x <= 7.92
b) 97.9% of these men run a mile in more than 8.57 minutes.
(a) Using the 68-95-99.7 rule, we know that 68% of the data falls within 1 standard deviation of the mean. Hence, the middle 68% of times falls between the mean minus 1 standard deviation and the mean plus 1 standard deviation:
7.18 - 0.74 <= x <= 7.18 + 0.74
=> 6.44 <= x <= 7.92
(b) To find the percent of men who run a mile in more than 8.57 minutes, we need to find the area under the curve to the right of 8.57 minutes. This can be found by subtracting the area under the curve to the left of 8.57 from 100%. Using the standard normal distribution tables or a calculator, the standard score (z-score) for 8.57 can be found:
z = (8.57 - 7.18) / 0.74 = 2.10
Using standard normal distribution tables or a calculator, the area under the curve to the right of 2.10 can be found to be approximately 2.1%, so
100% - 2.1% = 97.9%
of these men run a mile in less than 8.57 minutes.
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If A(0, 4), B(5, y), and AB = 13. What is y?
Answers
The required value of y for the given segment AB is given as y = 16, -8.
A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.
here,
A(0, 4), B(5, y), and AB = 13.
Applying the distance formula,
D = √[[x₂ - x₁]² + [y₂- y₁]²]
Substitue the value in the above expression,
13 = √[[5 - 0]² + [y - 4]²]
169 = 25 + [y - 4]²
[y - 4]² = 144
y - 4 = ± 12
y = 16, -8
Thus, the required value of y for the given segment AB is given as y = 16, -8.
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Please help me with this question.
Answers
The center of mass coordinates of the given plane is -
COM{X, Y} = { [tex]$\int\limits^4_0 {\rho (x,y)/x} \, \;dx[/tex], [tex]$\int\limits^2_0 {\rho (x,y)/y} \, \;dy[/tex]}
What is center of mass?The center of mass is the point at which the whole mass of the body or system can be considered to be concentrated.
Given is the plane with the equation -
ρ(x, y) = (1 + x/2)
We can write the center of mass as -
X{C.M.} = [tex]$\int\limits^4_0 {\rho (x,y)/x} \, \;dx[/tex]
Y{C.M.} = [tex]$\int\limits^2_0 {\rho (x,y)/y} \, \;dy[/tex]
Therefore, the center of mass coordinates of the given plane is -
COM{X, Y} = { [tex]$\int\limits^4_0 {\rho (x,y)/x} \, \;dx[/tex], [tex]$\int\limits^2_0 {\rho (x,y)/y} \, \;dy[/tex]}
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How do i rewrite the sum in the form a(b+c) such that the integers b and c have no common factor. 36+72
Answers
Ans:-
[tex] \: [/tex]
[tex] \underline{ \boxed{ \bold{12( 3 + 6 )}}}[/tex][tex] \: [/tex]
Int b nd c can be divide by 12
[tex] \: [/tex]
[tex] \rm 12 × 3 = \bold{36}[/tex][tex] \: [/tex]
[tex] \rm 12 × 6 = \bold{72}[/tex][tex] \: [/tex]
The Sum In The Form a( b + c ):-
[tex] \: [/tex]
[tex] \rm \bold{12 ( 3 + 6 )}[/tex][tex] \: [/tex]
[tex] \underline{ \rm \: 36 + 72 \: }[/tex][tex] \: [/tex]
hope it helps! :)
assistance with This question please I’ll give you brainliest
Answers
Answer:
%6, 1/2, 0.6, 6/5
Step-by-step explanation:
Answer:
Bottom left option
Step-by-step explanation:
The four numbers present in this order are:
[tex]\frac{1}{2} = 0.5[/tex]
0.6
[tex]\frac{6}{5} = 1.2[/tex]
[tex]6 percent = \frac{6}{100}[/tex] = 0.06
The order of the numbers from least to greatest are:
6%, [tex]\frac{1}{2}[/tex], 0.6, [tex]\frac{6}{5}[/tex]
katie rents a car while spending her vacation travelling in australia. when she returns the car, she has driven 1400 miles and used about 56 gallons of gas. if gas costs an average of $5.099 per gallon, estimate how much she spent on fuel.
Answers
Katie spent approximately $285.544 on fuel during her vacation in Australia.
The Average Cost is the per unit cost of the product received by dividing the total cost (TC) by the total output (Q). By per unit cost of production, we mean that all the fixed and variable costs are considered for calculating the average cost. Thus, it is also called Per Unit Total Cost.
Symbolically, the average cost is expressed as:
AC = TC/Q
To estimate how much Katie spent on fuel, you need to multiply the number of gallons of gas she used (56 gallons) by the average cost of gas per gallon ($5.099):
56 gallons × $5.099/gallon = $285.544
So, Katie spent approximately $285.544 on fuel during her vacation in Australia.
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Please answer!!!
question: What is the triangle's base, b?
Answers
Answer:
b = 8 cm
Step-by-step explanation:
Area: 1/2*base*height
1/2*base*3=12
3*base=24
base=24/3
base=8 cm
Do the values in the table represent a proportional relationship?
Answers
Answer:
Yes
Step-by-step explanation:
Yes, they do since if you multiply the y by 2.5 it will give you all the answers you entered
The problem: Shawn thought of planning for his 18-year-old daughter going
off to college when she was born. Create a realistic compound interest
equation that shows the value of the investment that Shawn made using
A = P(1 + i
n)tn
Answers
The total value of the account after 18 years, deposit of $100,000 with monthly compounding and a rate of 5%, is given as follows:
$245,501.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.The parameters for this problem are given as follows:
[tex]P = 100000, r = 0.05, n = 12, t = 18[/tex]
Hence the balance is given as follows:
A(18) = 100000 x (1 + 0.05/12)^(12 x 18)
A(18) = $245,501.
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Simplify 10 • (2 + 5).
25
17
70
100
Answers
Answer: 70
Step-by-step explanation: To find this answer, we must use PEMDAS. So, we have parentheses (adding) and multiplying. The P is first, so we solve for parentheses first. So, 2 + 5 = 7. So, now we multiply. 10 * 7 = 70. Therefore 70 is our answer. I hope this helped!
1/4 of what is 1/5 thank you very much
Answers
Answer:
4/5
Step-by-step explanation:
Call our unknown variable ‘x’
X(1/4)=1/5
Therefor, x=4/5
The correlation coefficient may assume any value between _____ a) 0 and 1.b) −[infinity] and [infinity].c) 0 and 8.d) −1 and 1.e) −1 and 0.
Answers
The correlation coefficient may assume any value between -1 and 1. Correct answer: letter D.
This means that the coefficient may be negative, zero, or positive, with a value of -1 indicating a perfect negative correlation, 0 indicating no correlation, and 1 indicating a perfect positive correlation.
The correlation coefficient is a numerical measure of the degree of linear dependence between two variables. It is a statistic that measures the strength of the relationship between two variables. A correlation coefficient of 1 indicates a perfect positive correlation, a coefficient of -1 indicates a perfect negative correlation, and a coefficient of 0 indicates no correlation between the two variables.
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Tia owns a fruit shop and is selling a fresh lot of apples and oranges. She wants the ratio of apples to oranges sold to be 3 to 2. Tia wants to sell a total of 35 apples and oranges. How many apples should she sell?
Answers
The number of apples for the lot will be 21.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Tia owns a fruit shop and is selling a fresh lot of apples and oranges. She wants the ratio of apples to oranges sold to be 3 to 2. Tia wants to sell a total of 35 apples and oranges.
a /o = 3 / 2
a + o = 35
( 3 / 2)o + o = 35
5o = 70
o = 14
a + o = 35
a + 14 = 35
a = 21
Hence, the number of apples for the lot will be 21.
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Give the solution of the equation x+5/3=15
Answers
Answer:
x = 40/3
Step-by-step explanation:
x+5/3=15
x + 5/3 = 45/3
x = 40/3
Let's check
40/3 + 5/3 = 15
45/3 = 15
15 = 15
SO, x = 40/3 is the correct answer.
is 3²¹×5³¹×7²⁰ a multiple of 3⁵⁰×5³¹×7²⁰
Answers
Answer:
yes
Step-by-step explanation:
that is 3×3×3×3×3×3....×3 21 times and the other is 50 times,so u have to multiply 3²¹ with more 3s so u ger 3⁵⁰
a triangular prism (like a box of toblerone) of mass m, whose two ends are equilateral triangles parallel to the xy plane with side 2a, is centered on the origin with its axis along the z axis. find its moment of inertia for rotation about the z axis. without doing any integrals write down and explain its two products of inertia for rotation about the z axis.
Answers
The moment of inertia for rotation about the z axis is [tex]I & =\frac{a^2 M}{3}[/tex].
A triangular prism of mass m, whose two ends are equilateral triangles.
Two ends are equal.
The xy plane with side 2a, is centered on the origin with its axis along the z axis.
Find the moment of inertia for rotation the z-axis.
It is divide into 4 triangles with side 'a' k one side is 3cm.
[tex]$$\begin{aligned}& I_{\text {BiG }}=16 I_{\text {small }} . \\& I_{\text {BIG }}=4 I_{\text {small }}+P_{A T}\end{aligned}$$[/tex]
It is fact that the big triangle is made up from four small triangles. connected with parallel axis theorem.
Now, we have to find the distance from the center of mas of small outer triangles to the origin. so, that it is PAT.
[tex]$$\therefore z=2 \sqrt{x^2-\frac{a}{2} ^2}$$[/tex]
[tex]$$\begin{aligned}& =2 \sqrt{\left(\frac{a}{\sqrt{3}}\right)^2-\frac{a^2}{4}} \\& =2 \sqrt{\frac{a^2}{3}-\frac{a^2}{4}} \\I_{\text {Big }} & =\frac{\sqrt{3}}{3} a \cdot \\& \left.=4 I_{\text {small }}+3 m \frac{\sqrt{3}}{3} a\right)^2 \\I_{\text {Big }} & =4 I_{\text {small }}+\frac{3 m}{4} \frac{1}{3} a^2 \\& =\frac{a^2}{4}\end{aligned}$$[/tex]
⇒ Now, by using the [tex]$I_{\text {Big }}=I$[/tex]
⇒[tex]I & =4\left(\frac{\sqrt{2}}{16}\right)+\frac{a^2 M}{4} \\[/tex]
⇒[tex]4 I & =I+a^2 m[/tex]
⇒[tex]4 I-I & =a^2 m \\[/tex]
⇒[tex]3 I & =a^2 M . \\[/tex]
⇒[tex]I \quad & =\frac{a^2 M}{3}[/tex]
Therefore, the moment of inertia is [tex]I & =\frac{a^2 M}{3}[/tex].
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According to a recent poll, 27% of Americans get 30 minutes of exercise at least five days each week. Let's assume this
is the parameter value for the population. If a simple random sample of size were taken, what is the approximate
probability that , the proportion who exercise at least five days per week, is higher than 0.30?
Answers
The probability that the proportion of a sample is higher than 0.30 can be estimated using the Central Limit Theorem (CLT) which states that the distribution of the sample means approaches a normal distribution as the sample size increases. With a large sample size (n >= 30), we can use the normal distribution to approximate the distribution of the sample means.
Assuming the sample size is large, the standard error (SE) of the sample mean is given by
SE = sqrt(p * (1 - p) / n), where p is the population proportion (0.27) and n is the sample size.
With this information, we can find the Z-score corresponding to 0.30 using the formula: Z = (0.30 - 0.27) / SE
Since we don't know the sample size, we'll assume a conservative sample size of 30.
With a sample size of 30, the SE is approximately 0.039, and the Z-score is approximately 0.77.
Using a standard normal table, we can find the probability of a Z-score being greater than 0.77 is approximately 0.22.
Therefore, the approximate probability that the proportion who exercise at least five days per week is higher than 0.30 is 0.22.
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Write the equation of the function graphed below:
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An equation of the function graphed above include the following: f(x) = 2∛x - 4.
What is dilation?In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape.
Additionally, a geometric figure that is translated downward simply means subtracting a digit from the value on the y-coordinate of the pre-image or parent function.
By critically observing the graph of the function shown above, we can logically deduce that it is a cube root function that has been vertically shifted by a scale factor of 2 units and then translated downward by 4 units. Therefore, this can be modeled by this equation as follows;
f(x) = 2∛x - 4.
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A new sidewalk will be 4 feet wide, 140 feet long, and filled to a depth of 6 inches (0.5foot) with concrete. How many cubic yards of concrete are needed?
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Answer: 93 [tex]\frac{1}{3}[/tex] yards³
Step-by-step explanation:
We will find the volume in feet with this formula:
V = LWH
V = LWH
V = (140)(4)(0.5)
V = 280 feet³
There are 3 feet in a yard, and the question asks for yards, so we will divide:
280 feet³ / 3 = 93 [tex]\frac{1}{3}[/tex] yards³
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