Therefore , the solution of the given problem of unitary method comes out to be the athletes completed a total of 12 laps.
What is an unitary method ?Finish the project using the tried-and-true basic methodology, the actual variables, and any pertinent knowledge you gain from the broad and specific questions. In response, customers might be given another opportunity to sample expression the products. We'll miss out on important breakthroughs in programming comprehension if these changes don't take place.
Here,
In accordance with the information provided, for each sprint around the track, the runners jogged three times. So, three times as many laps are jogged around the track.
Furthermore, it is known that the runners jogged six more laps than they ran. Therefore, we can construct the following equation:
Jogging laps equals sprinting laps plus six.
=> 3x = x + 6
=> 3x - x = 6
=> 2x = 6
=> x = 6/2
=> x = 3
Total laps equal 3x + x = 4x times the amount of jogged and sprinting laps.
By changing the value of x, we obtain:
Laps completed = 4 (3) = 12
As a result, the athletes completed a total of 12 laps.
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The probability that a contestant played an electric guitar is 0.8, the probability that a contestant was dressed in sequins is 0.4, and the probability that a contestant played an electric guitar or was dressed in sequins is 0.9.
What is the probability that a randomly chosen contestant played an electric guitar and was dressed in sequins?
By probability, the likelihood that a candidate chosen at random played an electric guitar and wore sequins is 0.3.
explain probability.Using probabilities, one can determine how likely something is to occur.. It is represented by a number between 0 and 1, with 1 denoting a certain event and 0 an impossibility.
For instance, you can get either heads or tails when you flip a coin. There is only one way to get heads and two outcomes, hence the probability of receiving heads is 0.52.
The likelihood that a competitor played an electric guitar is 0.8, the likelihood that they were wearing sequins is 0.4, and the combined likelihood that they both played an electric guitar and wore sequins is 0.91.
The following formula can be used to determine the likelihood that a competitor chosen at random played an electric guitar and wore sequins:
P(A and B) equals P(A) times P(B|A)
where there are two events, A and B.
In this instance, A stands for the competitor who played an electric guitar, and B is for the person who wore sequins.
P(A) is known to equal 0.8. and P(B) = 0.4.
We also know that P(A or B) = 0.9.
Using the following equation to determine the likelihood of two events occurring together:
P(A or B) = P(A) + P(B) - P(A and B)
we can find P(A and B):
P(A and B)
= 0.8 + 0.4 - 0.9
= 0.3
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What is the rate of change?
In which quadrant of the coordinate plane will you find the point (-3, -2)?
Answer:
Quadrant III
Step-by-step explanation:
The point has a negative x AND y value, so it would be in Quadrant III
Taking a look at the quadrant graph will help you.
Question is in the screenshot (matrices)
Value of matrix X=[tex]\left[\begin{array}{ccc}-31/135 & 1/45 \\14/135&1/45 \\ \end{array}\right][/tex]
Define matricesMatrices are a type of mathematical object that consists of a rectangular array of numbers or other mathematical objects, such as variables, functions, or even other matrices. Matrices are widely used in mathematics, science, engineering, computer graphics, and other fields to represent and manipulate data, perform transformations, and solve systems of equations.
A matrix can be represented using a set of ordered pairs, where each pair represents a specific element of the matrix, and the position of the element is determined by its row and column indices. For example, a 3x3 matrix can be represented as:
| a11 a12 a13 |
| a21 a22 a23 |
| a31 a32 a33 |
Given matrix;
A=[tex]\left[\begin{array}{ccc}-1&-2 \\2&2 \\ \end{array}\right][/tex]
B=[tex]\left[\begin{array}{ccc}-6&5 \\2&-1 \\ \end{array}\right][/tex]
C=[tex]\left[\begin{array}{ccc}-3&1 \\2&0 \\ \end{array}\right][/tex]
Solving the equation
(A-4B)X=C
[tex]\left[\begin{array}{ccc}-1&-2 \\2&2 \\ \end{array}\right][/tex]- 4 [tex]\left[\begin{array}{ccc}-6&5 \\2&-1 \\ \end{array}\right][/tex]X=[tex]\left[\begin{array}{ccc}-3&1 \\2&0 \\ \end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}23&-22 \\-6&6 \\ \end{array}\right][/tex] X=[tex]\left[\begin{array}{ccc}-3&1 \\2&0 \\ \end{array}\right][/tex]
Taking the inverse and multiplying it with RHS, we get
X=[tex]\left[\begin{array}{ccc}-31/135 & 1/45 \\14/135&1/45 \\ \end{array}\right][/tex]
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Question 3(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
5, 5, 6, 8, 10, 15, 18, 20, 20, 20, 20, 20, 20
A graph titled Donations to Charity in Dollars. The x-axis is labeled 1 to 5, 6 to 10, 11 to 15, and 16 to 20. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 1 to 5, up to 3 above 6 to 10, up to 1 above 11 to 15, and up to 7 above 16 to 20.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The range of 13 is the most accurate to use, since the data is skewed.
The IQR of 13 is the most accurate to use, since the data is skewed.
The range of 20 is the most accurate to use to show that they have plenty of money.
The IQR of 20 is the most accurate to use to show that they need more money.
The IQR of 13 is more appropriate to use than the range of 13, as it provides a more accurate representation of the variability in the data when the data is skewed. Thus, option B is correct.
What is the accurate and IQR?The range is the difference between the maximum and minimum values in a dataset, and it is affected by extreme values, which can result in a misleading representation of the variability in the data.
if the data is skewed or contains outliers, the range may not accurately represent the variability in the data.
However, it is not appropriate to use the range of 20 to show that they have plenty of money or the IQR of 20 to show.
Therefore, in this case, the IQR of 13 is more appropriate to use than the range of 13, as it provides a more accurate representation of the variability in the data when the data is skewed.
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Simplify the radical
-√81m^3
Answer:
9m^3
Step-by-step explanation:
since there is a square root remove it and find it square which is 9
An architect is designing a house. He wants the bedroom to have the dimensions of 9 ft by 5 ft by 7 ft. The architect doubles one dimension to create the den. Does that mean the den will have double the volume of the bedroom?
Answer:
Yes
Step-by-step explanation:
The definition of dimension is Length, Width, and Height so if he doubles the dimensions it will be double. The volume is 630.
Enter the surface area of the figure
The surface area of the figure, given the diameter of the base and the height, would be 353.43 square millimeters.
How to find the area ?We can use the formula for the surface area of a cone:
Surface Area = πr² + πr√(r² + h²)
where r is the radius of the base and h is the height of the cone.
Since the diameter of the base is 9mm, the radius is half of that, or 4.5mm. The height of the cone is 20mm. Plugging these values into the formula, we get:
Surface Area = π(4.5)² + π(4.5)√(4.5² + 20²)
Surface Area = π(20.25) + π(4.5)√(436.25)
Surface Area = 353.43 millimeters²
Therefore, the surface area of the cone is approximately 353.43 square millimeters.
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What is the equation of this circle in general form?
Responses
x2+y2−2x−6y−26=0
x squared plus y squared minus 2 x minus 6 y minus 26 equals 0
x2+y2+2x+6y−26=0
x squared plus y squared plus 2 x plus 6 y minus 26 equals 0
x² + y² + 2x + 6y + 4 = 0
x, ² +, y, ² + 2, x, + 6, y, + 4 = 0
x2+y2−2x−6y+4=0
x squared plus y squared minus 2 x minus 6 y plus 4 equals 0
The equation of this circle in general form is: (x - 1)^2 + (y - 3)^2 = 36
How to find the equation of the circle in general formTo find the equation of a circle in general form, we need to complete the square for both x and y terms.
x^2 + y^2 - 2x - 6y - 26 = 0
First, we will complete the square for x terms:
x^2 - 2x + y^2 - 6y - 26 = 0
(x - 1)^2 - 1 + y^2 - 6y - 26 = 0
(x - 1)^2 + y^2 = 27
Now, we will complete the square for y terms:
(x - 1)^2 + (y - 3)^2 = 36
Therefore, the equation of this circle in general form is: (x - 1)^2 + (y - 3)^2 = 36
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Answer:
x2+y2−2x−6y−26=0
Step-by-step explanation:
Just took the test.
help! as soon as possible
The quadrilateral is a type of "kite", as the pair of adjacent angles are equal.
Explain about the features of kite:A quadrilateral known as a kite has four sides that may be grouped into two adjacent pairs of equal-length sides, and the diagonals cross each other at right angles. The quadrilateral is a polygon with four sides.
Kite's two diagonals meet at a right angle to form its properties.A kite's primary diagonal is symmetrical.The diagonal's primary opposed angles are equal.A set of congruent triangles having a common base can be thought of as the kite.The kite is split into two isosceles triangles by the shorter diagonal.Thus, the quadrilateral is a type of "kite", as the pair of adjacent angles are equal.
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Solve for s. . ...................
Answer:
[tex]S = \dfrac{v^2 - u^2}{2a}[/tex]
Step-by-step explanation:
We can solve for S using algebraic manipulation.
[tex]v^2 = u^2 + 2aS[/tex]
↓ subtract [tex]u^2[/tex] from both sides
[tex]v^2 - u^2 = 2aS[/tex]
↓ divide both sides by [tex]2a[/tex]
[tex]\dfrac{v^2 - u^2}{2a} = S[/tex]
[tex]\boxed{S = \dfrac{v^2 - u^2}{2a}}[/tex]
[tex]\sf \boxed{\sf S=\dfrac{v^{2}-u^{2} }{2a}}[/tex]
Step-by-step explanation:1. Write the expression.[tex]\sf v^{2} =u^{2} +2aS[/tex]
2. Subtract "u²" from both sides of the equation.[tex]\sf v^{2}-u^{2} =u^{2} +2aS-u^{2}\\ \\v^{2}-u^{2} =2aS[/tex]
3. Dividie by "2" and "a" on both sides of the equation.[tex]\sf \dfrac{v^{2}-u^{2} }{2a} =\dfrac{2aS}{2a} \\ \\ \\\dfrac{v^{2}-u^{2} }{2a} =S\\ \\ \\\boxed{\sf S=\dfrac{v^{2}-u^{2} }{2a}}.[/tex]
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The rainfall in a town, measured in inches over the last 7 days has been: 1 , 3 , 0 , 2 , 2 , 1 , 3 Find the median rainfall.
Answer: 2
Step-by-step explanation: 0 1 1 2 2 3 3 order
011 2 middle one 233
Marina is drawing a plan for a new garden. The rectangle plotted in the coordinate plane represents the garden, measured in feet. To surround the garden with a stone path, how many feet of stone does she need? 4 feet 6 feet 10 feet 20 feet
If Mariana needs to surround the garden with a stone-path, then she would need 20 feet of stone, Option (d) is correct.
The "Perimeter" of a rectangle is defined as the "total-length" of the outer boundary.
The length of the rectangle can be calculated as the difference between the x-coordinates of the vertices on the same vertical side.
In this case, the "x-coordinates" of vertices on same vertical side are 4 and -2.
So, the length of the rectangle is = 4 -(-2) = 6 feet.
Similarly, the width of rectangle is calculated as difference between "y-coordinates" of vertices on same horizontal side.
In this case, the "y-coordinates" of vertices on same horizontal side are 1 and -3.
So, the width of the rectangle is = 1 -(-3) = 4 feet,
To surround rectangle with a stone path, Marina need to add length of stone needed for the perimeter of rectangle, which is sum of all four sides.
The perimeter (P) is ⇒ P = 2(length + width),
Substituting the values,
We get,
⇒ P = 2(6 + 4) = 2(10) = 20 feet
Therefore, the correct option is (d).
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The given question is incomplete, the complete question is
Marina is drawing a plan for a new garden. The rectangle with the vertex (4,1) , (4,-3) , (-2,-3) , (-2,1)in the coordinate plane represents the garden, measured in feet. To surround the garden with a stone path, how many feet of stone does she need?
(a) 4 feet
(b) 6 feet
(c) 10 feet
(d) 20 feet
Answer:
20 feet because ik from experience
Select the correct answer.
Kristen gathered data from her classmates about the age and contents of their backpacks. She displayed the data in two scatter plots.
Does either scatter plot indicate a positive correlation between the variables?
A. Only plot A
B. Only plot B
C. Both plot A and plot B
D. Neither plot A nor plot B
Plot B shows a negative correlation between the age and the number of items in the backpack, while plot A does not show any clear correlation. Therefore, the correct answer is B. Only plot B.
In plot A, the data points appear scattered and do not show a clear trend or pattern.
In plot B, the data points are mostly clustered around a diagonal line that slopes downward from left to right, indicating a negative correlation between the age and the number of items in the backpack. Since the question asks for a positive correlation, the correct option is B. Only plot B.
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--The given question is incomplete, the complete question is given
" Question
Select the correct answer.
Kristen gathered data from her classmates about the age and contents of their backpacks. She displayed the data in two scatter plots.
Does either scatter plot indicate a positive correlation between the variables?
A. Only plot A
B. Only plot B
C. Both plot A and plot B
D. Neither plot A nor plot B"--
Solve for x.
5)
X=
555
X-87
Answer:
x=162
Step-by-step explanation:
55+x-87+50=180
x+18=180
x=162
A wall 12 feet long makes a corner with a wal
that is 14 feet long. The other ends of the walls
are about 18.44 feet apart. Do the walls form a
right angle? Explain.
Yes, the walls form a right angle.
To determine if the walls form a right angle, we can use the Pythagorean theorem. The question states that a wall 12 feet long makes a corner with a wall that is 14 feet long, and the other ends of the walls are about 18.44 feet apart.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, let's consider the 12-foot and 14-foot walls as the two shorter sides, and the 18.44-foot distance as the potential hypotenuse.
Step 1: Calculate the square of the lengths of the 12-foot and 14-foot walls.
12² = 144
14² = 196
Step 2: Calculate the sum of the squares of these two sides.
144 + 196 = 340
Step 3: Calculate the square of the length of the 18.44-foot distance.
18.44² ≈ 339.95
Since 339.95 is very close to 340, we can conclude that the walls form a right angle.
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select the correct answer from each drop-down menu. a candy company designs a package to hold chocolates. the height of the container is 13 inches and the diameter of its bottom is 9 inches. diagram shows a shape with circular base and curved surface meeting at a point. the diameter of the base is labeled 9 inches and the height of the shape is labeled 13 inches. which shape best models the package, and what is the approximate surface area of the package? the best model for the package is a . the approximate surface area is square inches.
The candy company's package can be modeled as a right circular cone with a height of 13 inches and a base diameter of 9 inches.
The circular base of the cone holds the chocolates, while the curved surface extends up to a point at the top. To calculate the surface area, we need to find the area of the circular base and the area of the curved surface. The formula for the area of a circle is pi times the radius squared, so the radius of the base is 4.5 inches.
The area of the base is pi times the radius squared, or approximately 63.62 square inches. The formula for the curved surface area of a cone is pi times the radius times the slant height, which is the square root of the height squared plus the base radius squared. Substituting the given values into the formula, the curved surface area is approximately 207.35 square inches. Thus, the approximate surface area of the package is the sum of the area of the base and the curved surface area, or approximately 271.97 square inches.
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The following data shows the grades that an 8th grade mathematics class received on a recent exam.
{99, 94, 91, 79, 88, 94, 92, 93, 90, 89, 77, 75, 65, 90, 87, 93, 92, 82, 65, 60, 78}
Part A: Determine the best graphical representation to display the data. Explain why the type of graph you chose is an appropriate display for the data. (6 points)
Part B: Explain, in words, how to create the graphical display you chose in Part A. Be sure to include a title, axis label(s), scale for axis if needed, and a clear process of how to graph the data. (6 points)
The resulting histogram would show the distribution of the grades on the exam, with the bins and frequency of data points clearly displayed. The title, axis labels, and scales would provide context for the graph and make it easy to interpret the data.
What is graph?In mathematics and computer science, a graph is a collection of points, called vertices or nodes, that are connected by lines, called edges or arcs. Graphs can be used to model and analyze relationships between objects or data, such as social networks, transportation systems, or web pages.
Here,
Part A:
The best graphical representation to display the given data is a histogram. A histogram is a bar graph-like representation of data that divides the data into intervals or bins and shows the frequency of each interval. Histograms are appropriate for displaying continuous data, which the grades on the exam can be considered as, and can also show the distribution of the data.
Part B:
To create a histogram of the given data, follow these steps:
Choose the number of bins or intervals. In this case, we can choose a reasonable number of bins, such as 6-8, to display the distribution of the grades.
Determine the range of the data. The lowest grade is 60 and the highest is 99, so the range is 99-60 = 39.
Calculate the bin size. The bin size is calculated by dividing the range by the number of bins. For example, if we choose 6 bins, the bin size would be 39/6 ≈ 6.5. Since it is difficult to have bins that are fractions of a point, we can round the bin size up to the nearest whole number to get a bin size of 7.
Create the bins. Starting from the lowest grade, create intervals or bins of size 7 that cover the range of the data. For example, the first bin would be 60-66, the second bin would be 67-73, and so on.
Count the frequency of data points that fall into each bin. For example, there are 2 data points in the first bin, 3 data points in the second bin, and so on.
Draw the histogram. On the horizontal axis, label and scale the bins. On the vertical axis, label and scale the frequency of data points in each bin. Draw a rectangle above each bin with a height equal to the frequency of data points in that bin.
Title: Grades on Recent 8th Grade Mathematics Exam
X-axis label: Grades
Y-axis label: Frequency
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=
O QUADRATIC FUNCTIONS AND EQUATIONS
Solving a quadratic equation using the square root prope
V
2
Solve 3w +9=90, where w is a real number.
Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.
If there is no solution, click on "No solution".
W
w = 0
No
solution
The solution for the given quadratic equation is √27.
What is a quadratic equation?
A quadratic equation is any algebraic equation that can be written in the standard form as where variable 'x' is an unknown number and where a, b, and c are known values, with a ≠ 0.
We are given a quadratic equation in variable 'w' as 3[tex]w^{2}[/tex] + 9 = 90.
Now, on solving the given equation , we get
⇒ 3[tex]w^{2}[/tex] + 9 = 90
⇒ 3[tex]w^{2}[/tex] = 81
⇒ [tex]w^{2}[/tex] = 27
⇒ w = √27
Hence, the solution for the given quadratic equation is √27.
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The complete question has been attached below.
help me plsssssssss
Answer: 13. 30
Step-by-step explanation:
13. Area = 18x * 10y = 180xy
Length = 6th
With ?
180xy = 6xy x width
180 x/6xy
Width = 30
14. 3^(9-5)= 3^4 = 81 the truck weighs 81 times as the driver
3^5
Solve for e: - 12e =6q -4
Answer:
e = - [tex]\frac{1}{2}[/tex] q + [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
- 12e = 6q - 4 ( divide through by - 12 )
e = [tex]\frac{6}{-12}[/tex] q - [tex]\frac{4}{-12}[/tex] , that is
e = - [tex]\frac{1}{2}[/tex] q + [tex]\frac{1}{3}[/tex]
LOT OF POINTS AND BRAINLIEST IF YOU'RE RIGHT:
Public opinion in the large city of Hillwood is that 62 percent of the residents are in favor of increasing taxes to fund afterschool programs and 38 percent are against the increase. What is the approximate probability that more than 180 of the residents surveyed will be against increasing taxes if a random sample of 450 residents are surveyed? (4 points)
Answer:
0.16%
Step-by-step explanation:
Imagine you are a politician who wants to increase taxes in your city. You decide to conduct a survey among 450 residents to see how many of them are against your proposal. You know that the probability of finding someone who is against increasing taxes is 0.38. You hope that the survey will show that most people support your idea, or at least that the opposition is not too strong. However, when you get the results, you are shocked to see that more than 180 people are against increasing taxes. How unlucky are you? Well, let's do some math. This is a binomial probability problem. The probability of success (being against increasing taxes) is p = 0.38 and the number of trials (residents surveyed) is n = 450. The question asks for the probability of more than 180 successes, which is equivalent to the probability of at least 181 successes. Using a binomial calculator, the answer is approximately 0.0016 or 0.16%. That means that there is only a 0.16% chance of getting at least 181 people against increasing taxes in a sample of 450 residents. That's very rare and unlucky indeed! You might want to reconsider your proposal or find a better way to convince people that paying more taxes is good for them.
Can someone please help me get this answer
Answer:
C. 15 + 18x ≥ 95
Step-by-step explanation:
Given: She has $15 saved so far
She earns $18.00 for each lawn she mows (each lawn she mows = x)
The inequality has to be greater or equal to $95.00, so she can have enough to buy a pair of shoes.
15 + 18x ≥ 95
trigonometry question, I solved some of it got stuck at one part. please help
The simplified form of the given expression is:
(cosx * (tanx + 1) + 1) / cosx
How to simplify trigonometric identity?To solve the given expression, we can start by simplifying it using trigonometric identities.
Given expression: tanx / (1 + secx) + (1 + secx) / tanx
Step 1: Simplify denominators
We can rewrite secx as 1/cosx, and tanx as sinx/cosx. Using these identities, we get:
tanx / (1 + 1/cosx) + (1 + 1/cosx) / (sinx/cosx)
Step 2: Find the least common denominator (LCD)
The LCD is cosx, as it is the common denominator for both fractions.
Step 3: Combine the fractions
Using the LCD, we can combine the fractions:
[(tanx * cosx) + (1 + 1/cosx)(cosx)] / cosx
Step 4: Simplify the numerator
Multiplying through by cosx to simplify the numerator, we get:
[tanx * cosx + (cosx + 1)] / cosx
Step 5: Combine like terms
Combining like terms in the numerator, we get:
[tanx * cosx + cosx + 1] / cosx
Step 6: Factor out cosx
We can factor out cosx from the numerator:
cosx * (tanx + 1) + 1 / cosx
So, the simplified form of the given expression is:
(cosx * (tanx + 1) + 1) / cosx
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QUESTION IS - simplify . tanx/1+secx + 1+secx/tan x
Graph y=4/7x−2.
Use the line tool and select two points on the line to graph the line.
Answer:
Therefore, the answer is: The graph of the equation is a straight line passing through the points (0, -2), (7, 2), and (-7, -6).
Step-by-step explanation:
The given equation is y = (4/7)x - 2.
To graph this equation, we need to plot points on a coordinate plane. We can do this by choosing values of x and then finding the corresponding values of y using the equation.
Let's choose some values of x and find the corresponding values of y:
When x = 0, y = (4/7)(0) - 2 = -2
When x = 7, y = (4/7)(7) - 2 = 2
When x = -7, y = (4/7)(-7) - 2 = -6
We now have three points: (0, -2), (7, 2), and (-7, -6). We can plot these points on a coordinate plane and draw a line through them to get the graph of the equation.
Suppose that we would like to determine the proportion of U.S. citizens who have brown hair. To estimate this, we randomly select 100 people and we find that 63 of them have brown hair. Construct a 95% confidence interval for the proportion of people with brown hair in the U.S.
we are 95% confident that the true proportion of people with brown hair in the U.S. falls between 0.532 and 0.728.
To construct a 95% confidence interval for the proportion of people with brown hair in the U.S., we can use the following formula:
[tex]Confidence Interval = p± z \sqrt{\frac{p(1-p)}{n} }[/tex]
where p is the proportion of people with brown hair in our sample, z is the critical value for a 95% confidence level (which is 1.96), and n is the sample size.
In this case, our sample proportion is , and our sample size is 100. Plugging these values into the formula, we get:
[tex]Confidence Interval = 0.63 ± 1.96\sqrt{\frac{0.63(1-0.63)}{100} }[/tex]
Simplifying the expression inside the square root, we get:
[tex]Confidence Interval= 0.63 ± 0.098[/tex]
Therefore, the 95% confidence interval for the proportion of people with brown hair in the U.S. is:
[tex]\frac{63}{100} = 0.63[/tex](0.532, 0.728)
This means that we are 95% confident that the true proportion of people with brown hair in the U.S. falls between 0.532 and 0.728.
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a cube is made up of 27 equal sized cubes. if all faces of the large cube are painted, how many small cubes will not have any paint on any of their faces?
If a large cube is made up of 27 equal-sized smaller cubes, and all faces of the large cube are painted, then the cubes on the interior of the large cube will not have any paint on any of their faces.
The large cube consists of 27 smaller cubes arranged in a 3x3x3 pattern. The smaller cubes on the exterior faces of the large cube will have some of their faces painted, while the smaller cubes on the interior will not have any of their faces painted.
To calculate the number of smaller cubes that will not have any paint on any of their faces, we need to subtract the smaller cubes on the exterior faces from the total number of smaller cubes in the large cube.
The number of smaller cubes on the exterior faces of the large cube can be calculated as follows:
There are 9 smaller cubes on each of the six faces of the large cube (3x3=9), for a total of 54 smaller cubes on the exterior faces.
So, the total number of smaller cubes in the large cube is 27, and the number of smaller cubes on the exterior faces is 54. Therefore, the number of smaller cubes that will not have any paint on any of their faces is:
27 - 54 = -27
Since we cannot have a negative number of cubes, the correct answer is 0. There will be 0 smaller cubes that will not have any paint on any of their faces.
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There is a raffle with 250 tickets, each costing $16. One ticket will win a $240 prize, one ticket will win a $130 prize, one ticket will win a $120 prize, one ticket will win a $70 prize, and the other tickets will win nothing. If you buy a ticket, what is the expected profit?
If you buy a ticket, you can expect to make a profit of approximately $0.96 on average.
To calculate the expected profit, we need to consider the probability of winning each prize and the value of each prize.
The probability of winning each prize can be calculated by dividing the number of winning tickets by the total number of tickets. There is 1 winning ticket for each prize, so the probability of winning each prize is:
$240 prize: 1/250
$130 prize: 1/250
$120 prize: 1/250
$70 prize: 1/250
The value of each prize is already given, so we can multiply the probability of winning each prize by its value and sum the results to find the expected profit:
Expected profit = (1/250 x $240) + (1/250 x $130) + (1/250 x $120) + (1/250 x $70) - ($16)
Expected profit = $0.96
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Britney had a math quiz yesterday. She got 7 questions correct for every 2 that she got incorrect.
If Britney got 10 more questions correct than she got incorrect, how many questions were on the quiz?
Answer:18
Step-by-step explanation:
Populations that can be modeled by the modified logistic equation dt can either trend toward extinction or exhibit unbounded growth in finite time, depending on the initial population size. If b 0.0015 and a 0.2, use phase portrait analysis to determine which of the two limiting behaviors will be exhibited by populations with the indicated initial sizes Initial population is 286 individuals Initial population is 16 individuals a. Doomsday scenario: Population will exhibit unbounded growth in finite time b. Population will trend towards extinction
We can conclude:
a) For an initial population size of 286, the population will trend towards extinction.
b) For an initial population size of 16, the population will exhibit unbounded growth in finite time.
What is differential equations?
Differential equations are mathematical equations that describe the relationship between an unknown function and its derivatives (or differentials).
The modified logistic equation is given by:
dP/dt = aP - bP²
where P is the population size, and a and b are positive constants.
To determine the limiting behavior of the population, we need to analyze the phase portrait of the differential equation. This can be done by finding the equilibria of the system, and then examining the direction of the vector field near each equilibrium.
The equilibria of the system occur when dP/dt = 0. This leads to two possible equilibria:
P = 0, and P = a/b
The direction of the vector field near each equilibrium can be determined by examining the sign of dP/dt for values of P slightly greater and less than the equilibrium value.
Near P = 0, dP/dt = aP > 0 for P > 0, indicating that the population will grow in this region.
Near P = a/b, dP/dt = -bP² < 0 for P slightly greater than a/b, indicating that the population will decrease in this region.
Based on this analysis, we can conclude:
a) For an initial population size of 286, the population will trend towards extinction. This is because 286 is larger than a/b, so the population starts in the region where the vector field is pointing towards extinction.
b) For an initial population size of 16, the population will exhibit unbounded growth in finite time.
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