For the first question, to calculate a 95% confidence interval for the proportion of college students interested in taking summer courses using a sample size of 49 and a reported proportion of 70%, the range would be 57% to 83% (option A). And for the second question option b is the correct answer.
To calculate the confidence interval, we can use the following formula:
Confidence interval = sample proportion ± z-score × standard error
where the sample proportion is the proportion reported in the survey (70%), the z-score corresponds to the level of confidence (95%) and can be obtained from a standard normal distribution table (1.96 for a 95% confidence level), and the standard error can be calculated as follows:
Standard error = √(sample proportion × (1 - sample proportion) / sample size)
Plugging in the values, we get:
Standard error = √(0.70 × 0.30 / 49) ≈ 0.099
Then, the confidence interval can be calculated as:
Confidence interval = 0.70 ± 1.96 × 0.099 ≈ 0.57 to 0.83
Therefore, the correct answer is option A.
For the second question, to determine the sample size required to estimate the proportion of calls to the USC office that are reached during 12-1pm with a 3% margin of 415
To calculate the sample size, Paul needs to use the formula:
n = (Z^2 * p * q) / E^2
n = (1.96^2 * 0.5 * 0.5) / 0.03^2 = 415.24
Since we cannot have a fraction of a call, we round up to the nearest whole number, which gives us a sample size of 415 calls.
Therefore, Paul needs to include at least 415 calls in order to get answer to her question.
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find the least common denominator of the rational expressions?
The least common denominator (LCD) of the rational expressions is (x+1)(x-1).
When adding or subtracting rational expressions, we need to find a common denominator. The least common denominator (LCD) is the smallest multiple of the denominators of the rational expressions.
To find the LCD, we follow these steps:
Factor the denominators of the rational expressions.Identify the common factors.Take the product of the highest powers of each common factor.If there are any unique factors, include them as well.Simplify the resulting expression to obtain the LCD.Let's consider an example to illustrate this process:
Example:
Find the LCD of the rational expressions:
x/(x+1) and 1/(x-1)
Step 1: Factor the denominators:
x+1 and x-1
Step 2: Identify the common factors:
There are no common factors in this case.
Step 3: Take the product of the highest powers of each common factor:
Since there are no common factors, we skip this step.
Step 4: Include any unique factors:
The unique factors are x+1 and x-1.
Step 5: Simplify the resulting expression:
The LCD is (x+1)(x-1).
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The least common denominator of the rational expressions in this problem is given as follows:
4x(x + 5).
How to obtain the least common denominator?The rational expressions for this problem are defined as follows:
9/(4x + 20), 10/(x² + 5x).
The denominators are given as follows:
4x + 20.x² + 5x.The denominators can be simplified as follows:
4x + 20 = 4(x + 5).x² + 5x = x(x + 5).The least common denominator is the multiplication of the unique factors, hence it is given as follows:
4x(x + 5).
Missing InformationThe expression that completes this problem is given as follows:
9/(4x + 20), 10/(x² + 5x).
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please answer number 15 and 17
Answer:
15 ans rln 1 and 17 ans rln3
Consider the following sets A = {a,b}, B = {{/0},{a,b}} and C = A∪B. Write does all the elements of the following sets and report their cardinality:
1. 2^C (powerset)
2. C × C (cross-product)
In your answer make sure that you (1) Show your steps (2) Do not skip any steps and (3) Justify each step with the name of the law being used.
The cardinality of \(2^C\) (powerset of C) is 2⁴ = 16, and the cardinality of C × C (cross-product of C with itself) is 4 × 4 = 16.
To find the cardinality of \(2^C\) (powerset of C), we need to determine the number of possible subsets of set C. Set C is the union of sets A and B, which are given as A = {a, b} and B = {{/0}, {a, b}}. By combining the elements of A and B, we have C = {a, b, {/0}, {a, b}}.
The powerset of a set is the set of all possible subsets of that set, including the empty set and the set itself. In this case, we have four elements in C, so the cardinality of \(2^C\) is 2⁴ = 16. Each element in the powerset can be either included or excluded, resulting in 2⁴ = 16 possible subsets.
To find the cardinality of C × C (cross-product of C with itself), we need to determine the number of possible ordered pairs that can be formed by choosing one element from C for each position. Since C has four elements, there are four options for the first position and four options for the second position. Thus, the cardinality of C × C is 4 × 4 = 16.
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For the past 10 periods, MAD was 25 units while total demand was 1,000 units. What was mean absolute percent error (MAPE)?
Multiple choice question.
10%
25%
50%
75%
The mean absolute percent error (MAPE) is 25%.
The mean absolute percent error (MAPE) is a measure of forecasting accuracy that quantifies the average deviation between predicted and actual values as a percentage of the actual values. In this case, the mean absolute deviation (MAD) is given as 25 units for the past 10 periods, and the total demand is 1,000 units.
To calculate the MAPE, we need to divide the MAD by the total demand and multiply by 100 to express it as a percentage. In this scenario, the MAPE is calculated as follows:
MAPE = (MAD / Total Demand) * 100
= (25 / 1,000) * 100
= 2.5%
Therefore, the MAPE is 2.5%, which means that, on average, the forecasts have a 2.5% deviation from the actual demand.
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evaluate the expression 6x + 4 9/10 when x = 2/3.
x=2/3
6(2/3) + 4 9/10 =4 + 4 9/10 = 8 9/10
Answer:
2x-1=y,2y+3=x
Step-by-step explanation:
no explanation
Find the inverse of each function. Is the inverse a function? f(x)=(x-2)³
The inverse function is given by f⁻¹(x)=∛x+2 and the inverse is a function.
The opposite function is referred to as the inverse of a function. To map the dependent variable y based on the independent variable x, we should ideally utilize a function. The relationship that determines the value of x based on a certain value of y is known as an inverse function.
The domain of a function shifts to the range for an inverse function, and vice versa.
For a function that is mathematically denoted by the formula y=g(x), where g(x) is a polynomial of x. We use y to solve the equation for x.
Given function is in the form f(x)=(x-2)³
It can be written as
y=(x-2)³
Then we take the cube root on either sides of the equation.
∛y=x-2
or, x=∛y+2
So the inverse function is:
f⁻¹(x)=∛x+2
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i to the power of 6n+2 ? where n is a positive integer?
Answer:
The answer will always equal a positive when it comes to the n
Step-by-step explanation:
A recipe that would make 18 cupcakes
calls for 4 teaspoons of vanilla. How
many cupcakes is that per teaspoon?
Answer:
Hello there,
Let's solve,
It takes 4tsp for 18 cupcakes
thus for 1tsp it'll be,
= 18/4
= 4 and a half cupcake
That is one teaspoon of vanilla is needed for 4 and a half cupcakes.
All the best!
PLEASE HELPPPP ITS A BIG TEST AND I DON’T KNOW WHAT TO DO
Answer:
choice 2
Step-by-step explanation:
a translation is just a copy from one location to another
Is the ordered pair a solution of y ≥ 2x − 5? a. (3, 1) b. (1, −4)
Answer:
a. Yes
b. No
Step-by-step explanation:
To find if an ordered pair is a solution to the inequality, substitute its x and y values for the x and y in the inequality and solve. If the equation is true, then it is a solution. If it is not, then it is not a solution.
1) First, substitute the x and y values of (3, 1) into the inequality. So, substitute 3 for x and 1 for y:
\(1 \geq 2(3)-5\\1\geq 6-5\\1\geq 1\)
1 is greater than or equal to 1, so (3,1) is a solution.
2) Second, do the same with the point (1, -4). Substitute 1 for x and -4 for y:
\(-4\geq 2(1)-5\\\\-4\geq 2-5\\-4\geq -3\)
However, -4 is not greater than or equal to -3, thus (1, -4) is not a solution.
The ordered pair (3, 1) is the solution of the given inequality.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequality is y ≥ 2x-5.
A) The ordered pair is (3, 1)
Substitute (x, y)=(3, 1) in the given inequality, we get
1 ≥ 2(3)-5
1 ≥ 1
B) The ordered pair is (1, -4)
Substitute (x, y)=(1, -4) in the given inequality, we get
-4 ≥ 2(1)-5
-4 ≥ -3
Which is not true.
Therefore, the ordered pair (3, 1) is the solution of the given inequality.
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The data in the table represents a linear function x 0 2 4 6 y: -5 -2 1 4
what is the slope of the linear function which graph represents the data
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given: The table of linear function.
x : -3 , 0 , 3, 6
y : -6 , -2 , 2, 6
Slope=change in y over change in x
Passing point: (0,-2)
Point slope form:
Slope of the linear function
Linear function is
Hence, The slope of linear function is
The slope of the given linear function which graph represents the data is 3/2.
How to calculate slope of a linear function?The slope of a linear function can be calculated by finding the difference between two points on the graph and dividing it by the difference of the corresponding x-values of those points.
In this case, the two points are (2, -2) and (6, 4).
The difference between these y-values = 6,
and the difference between the x-values = 4.
Therefore, the slope of the linear function which graph represents the data = 6/4
= 3/2
This means that the linear function has a slope of 3/2 which summarizes that for every two units that x increases, y increases by three units.
If x increases from 0 to 4, y increases from -5 to 1, which is a difference of 6 units (4 x 3/2 = 6).
The linear function can be written as y = 3/2x -5.
This means that for any given x-value, the corresponding y-value can be calculated by multiplying 3/2 by the x-value and subtracting 5.
If x = 2, the y-value is -2,that is
(2* 3/2)- 5= -2
Therefore, the slope of the linear function which graph represents the data is 3/2.
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What is 120 mm in Inches
Answer:4.724
Step-by-step explanation:
Please I need help with quiz corrections should be easy if you are good at geometry!!
A right triangle, also known as a right-angled triangle, is a triangle that has one angle measuring 90 degrees.
What is a right angle triangle?Right triangles have some unique properties that make them useful in various applications, such as in geometry and trigonometry. For example, the Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
We know that;
Tan 45 = 14/x
x = 14
Sin 45 = 14/y
y = 20
Again;
Tan 60 = 16√3/x
x = 16√3 * 1/√3
x = 16
Sin 60 = 16√3/y
y = 16√3 ^ 2/√3
y = 32
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(1 point) how many different ways can a race with 6 runners be completed? (assume there is no tie.) your answer is : 36
There are 720 different ways can a race with 6 runners be completed.
What is a combination?
The process of combining or the condition of combining. a combination of things; an amalgamation of concepts. a grouping of notes: A chord is a grouping of notes. a grouping of people or entities acting together to impede commerce.
Here, we have
The winner can be chosen from all 6 runners, the second person can be chosen from 5 people, the third - from 4, and so on.
So the total number of possible results can be calculated as:
n = 6×5×4×3×2×1= 6!
= 720
Hence, there are 720 different ways can a race with 6 runners be completed.
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the longer leg of a right triangle is three times as long as the shorter leg. the hypotenuse is $\sqrt 5.$ what is the area of this triangle?
The area of the triangle is 3/4 units.
What is area of the triangle?
The total area that is bounded by a triangle's three sides is referred to as the triangle's area. In essence, it is equal to 1/2 of the height times the base, or A = 1/2 b h. Therefore, we need to know the triangular polygon's base (b) and height (h) in order to calculate its area.
Suppose
x is the shorter leg of the triangle.
As the longer leg of a right triangle is three times as long as the shorter leg.
⇒ 3x is the longer leg of the triangle.
The hypotenuse of the triangle is, √5.
By using Pythagorean theorem,
\(x^2 + (3x)^2 = (\sqrt{5} )^2\\x^2 + 9x^2 = 5\\10x^2 = 5\\x^2 = \frac{5}{10}\\ x^2 = \frac{1}{2} \\x = \frac{1}{\sqrt{2} }\)
⇒ Shorter leg of the triangle is 1/√2.
⇒ Longer leg of the triangle is 3/√2.
Now to find the area of the triangle.
Area of triangle = \(\frac{1}{2}(\frac{1}{\sqrt{2} })(\frac{3}{\sqrt{2} } )\)
\(A = \frac{3}{4}\)
Hence, the area of the triangle is 3/4 units.
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Draw a rectangle on graph paper with vertices whose coordinates are (-1, 2), (-1, -4), (3, -
4), and (3, 2).
(Graph paper provided in the jamboard in Q1).
Part A: Find the perimeter and area of the rectangle. Show your work.
Part B: Multiply the coordinates of the vertices of the rectangle by 3. State the new vertices.
Part C: Draw the rectangle whose vertices are those you found in Part B. Find the perimeter and area of this new rectangle.
Show your work.
Part D: Compare the perimeter of the rectangle in Part C to the perimeter of the original rectangle. (list each and then compare).
Part E: Compare the area of the rectangle in Part C to the area of the original rectangle. (list each and then compare).
The area of the new rectangle is 9 times the previous area and the perimeter of the new rectangle is 3 times the previous area
Part A: Find the perimeter and area of the rectangle.From the question, we have the following parameters that can be used in our computation:
(-1, 2), (-1, -4), (3, -4), and (3, 2).
See attachment for the points, where we have
Length = 4 and width = 6
Using area and perimeter formulas, we have
Area = 4 * 6 = 24
Perimeter = 2 * (4 + 6) = 20
Part B: Multiply the coordinates by 3Here, we have
New = (-3, 6), (-3, -12), (9, -12), and (9, 6).
Part C: Find the new perimeter and area of the rectangle.See attachment for the points, where we have
Length = 12 and width = 18
Using area and perimeter formulas, we have
Area = 12 * 18 = 216
Perimeter = 2 * (12 + 18) = 60
Part D: Comparison of the areasThe area of the new rectangle is 9 times the previous area
i.e. 216/24 = 9
Part E: Comparison of the perimetersThe perimeter of the new rectangle is 3 times the previous area
i.e. 60/20 = 3
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write an algebraic description for the sequence of Transformations that will map the preimage onto the image to show that the two circles are similar first transformation dilate the orgin (x,y) and (kx,ky)
The first transformation is a translation one unit up.
The second transformation is a translation of four units left.
The scale factor is 2.5.
According to the transformations above, the circles are similar, they are related with a scale factor of 2.5.
The equation of the preimage is
\(x^2+y^2=1\)The equation of the image is
\((x+4)^2+(x-1)^2=(2.5)^2\)Sheila is biking at a constant speed. She travels 54 meters in 9 seconds.
How many meters per second does Sheila travel?
Answer:
6 meters per second
Step-by-step explanation:
6 meters/ seconds
Step 1: Find the unit rate
total distance/total time
54/9
6 meters / seconds
Answer: 6 meters/ seconds
Please I need help
Write the equation for a parabola with a focus at (1,-4) and a directrix at x = 2.
X=?
Answer:
Step-by-step explanation:
The directrix is a vertical line, so the parabola is horizontal. The focus lies to the left of the directrix, so the parabola opens to the left.
For a left-opening parabola:
x = a(y-k)²+h,
a < 0,
vertex (h,k)
focal length p = 1/|4a|
focus (h-p, k)
directrix: x=h+p
Apply your data
focus (1,-4)
directrix x=2
vertex (1.5,-4).
focal length p = 0.5
a = -1/|4p| = -½
x = -½(y-2)²+ ½
please do these thank you look up to see what they are and fill out the answers
If 20 pounds of beans sold for $1.20, what was the price per pound of beans?
Answer:
0.06 Cent
Step-by-step explanation:
Per Pound= Every one
so 1.20 divided by 20
= 0.06
So the price per pound of beans is 0.06 Cent
Match the plot with a possible description of the sample.
60 70 80 90 100
Choose the correct answer below
A. Wait time (in minutes) for a sample of doctors offices
B.Ages (in years) of a sample of residents of a retirement home.
C. Highest yearly temperatures (F) for a sample of deserts.
D. Time (in hours_ spent watching TV in a day for a sample of teenagers.
Ages (in years) of a sample of retirement home inhabitants is option B. For the lowest wait time, the maximum frequency is anticipated to be right-skewed. A desert cannot have a maximum annual temperature of 60°F, and it is not conceivable to watch 60+ hours of TV in a single day.
Residents of senior living facilities are typically 84 years old. While there are many couples in these communities, the majority of people who live in independent living are women. Some people move in at or near the minimum age (often around 65), but most people do so between the ages of 75 and 84. Residents come from all different backgrounds.
Many people are choosing senior living in a community environment, including teachers, nurses, small business owners, big business CEOs, university professors, housewives, lawyers, engineers, musicians, and more. Current residents will attest that the rich diversity of origins fosters amazing interactions and relationships. And contrary to popular belief, the majority of residents of independent living are quite active.
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Correct Question:
Match the plot with a possible description of the sample.
60 70 80 90 100
Choose the correct answer below
A. Wait time (in minutes) for a sample of doctors offices
B. Ages (in years) of a sample of residents of a retirement home.
C. Highest yearly temperatures (F) for a sample of deserts.
D. Time (in hours_ spent watching TV in a day for a sample of teenagers.
17. Who am I? ___ Collection of one or more different types of variables, including arrays and pointers, that have been grouped under a single name for each manipulation.
a) template
b) array
c) structure
d) local variables
You are c) a structure. A structure is a collection of one or more different types of variables, including arrays and pointers, that have been grouped under a single name for each manipulation.
A structure is a user-defined data type that allows you to group together related data. For example, you could create a structure to store the name, age, and address of a person. The structure would have three variables, each of a different type: a string variable for the name, an integer variable for the age, and a string variable for the address.
The advantage of using a structure is that it allows you to treat the related data as a single unit. This makes it easier to manipulate the data and to pass the data to functions.
The other answer choices are incorrect. A template is a blueprint for creating a generic class or function. An array is a collection of elements of the same type. Local variables are variables that are declared within a function and that are only accessible within the function.
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The football player had an 80 yard gain on the play. Answer with integer(s)
345 x 564 divided by 3x - 2y
Answer:
-97290
Step-by-step explanation:
the base of a triangle is shrinking at a rate of 3 cm/min and the height of the triangle is increasing at a rate of 9 cm/min. find the rate (in cm2/min) at which the area of the triangle changes when the height is 16 cm and the base is 12 cm.
The rate-of-change of area of triangle is changing when height is 16 cm and base is 12 cm is 30 cm²/min.
We know that the area of a triangle is given by the formula
⇒ A = (1/2)×b×h, where b = length of base and h = height,
We are given that the base is shrinking at a rate of 3 cm/min,
So, we have db/dt = -3 cm/min.
We are also given that the height is increasing at a rate of 9 cm/min,
So, we have dh/dt = 9 cm/min.
We need to find the rate at which the area of the triangle is changing with respect to time (dA/dt), when h = 16 cm and b = 12 cm.
⇒ dA/dt = (1/2)(db/dt)(h) + (1/2)(b)(dh/dt)
Substituting the values,
We get,
⇒ dA/dt = (1/2)×(-3)×(16) + (1/2)×(12)×(9),
⇒ dA/dt = -24 + 54,
⇒ dA/dt = 30 cm²/min
Therefore, the rate at which the area of the triangle is 30 cm²/min.
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Which represents where f(x) = g(x)?
The equation represents the intersections. The correct option is A:
f(2) = g(2) = 0f(0) = g(0) = 4.Which represents where f(x) = g(x)?
If we have two functions:
y = f(x) and y = g(x), the equation:
f(x) = g(x) gives the value of x such that the two functions have the same output. So, that equation gives the intersection points between the two graphs.
By looking at the graph, we can see that we have two intersections, one at:
(2, 0) and other at (0, 4).
This means that:
f(2) = g(2) = 0f(0) = g(0) = 4.So the correct option is the first one.
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Which expression is equivalent to ∣∣b∣∣>6
?
Responses
b > –6 and b < 6
b > –6 and b < 6
b < –6 and b > 6
b < –6 and b > 6
Answer:
b > –6 and b < 6
Step-by-step explanation:
The expression "|b| > 6" means that the absolute value of b is greater than 6. Therefore, b can either be greater than 6 or less than -6. So, the equivalent expression is b > –6 and b < 6.
the number of moose in a national park is modeled by the function m that satisfies the logistic differential equation dmdt=0.6m(1−m200), where t is the time in years and m(0)=50. what is limt→[infinity]m(t)? a) 50. b) 200. c) 500. d) 1000. e) 2000.
The limit of m(t) as t approaches infinity is 200. So, option b) is correct.
To answer this question about the limit of m(t) as t approaches infinity, we can analyze the given logistic differential equation:
dm/dt = 0.6m(1 - m/200). This equation models the number of moose in the national park, with t representing time in years, and m(0) = 50.
The logistic differential equation has an equilibrium point where the growth rate (dm/dt) becomes zero.
To find this point, we set the equation equal to zero and solve for m:
0 = 0.6m(1 - m/200)
Dividing by 0.6 and simplifying, we get:
0 = m(1 - m/200)
0 = m(200 - m)
There are two possible solutions here:
m = 0 and m = 200.
However, since we know there are initially 50 moose (m(0) = 50), the stable equilibrium point must be m = 200.
So, option b) is correct.
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okay, youre sherlock, and im wtason.
Answer:
(3x²-x-2) (x+2) -first choice
Step-by-step explanation:
First we notice that when x → - ∞ the y or f(x) → -∞ because the graph goes on the negative side of the y-axis (down) as we move on the left ( where x is negative)
Second we notice that the graph touches the x-axis at x= -2 so one of the roots is -2
The equation (3x²-x-2) (x+2) has a root at -2 because x+2= 0 will give x=-2