The probability that 3 boys are selected for the relay team given that the first election was a girl is approximately 0.122, or 12.2%.
The Bayes theorem can be used,Let B represent the decision to select three boys for the relay team whereas A represents the scenario when a girl was chosen first.
P(B|A) is the conditional probability of B given A.
The Bayes theorem gives us:
P(B|A) is equal to P(A|B)*P(B)/P(A).
Given that the relay team consists of 3 boys, the probability that a girl would be chosen as the first team member is P(A|B). Therefore:
P(A|B) = 7/13 * 6/12 * 5/11 * 7/10 = 0.0871
P(B) represents the likelihood of choosing three males for the relay team in an arbitrary manner.
P(B) = (7C3 * 7C1) / (14C4) = 35/143
P(A) represents the likelihood that a girl will be chosen as the first team member without any restrictions.
P(A) = 7/14 = 1/2
Combining everything, we get the following: P(B|A) = P(A|B) * P(B) / P(A) = 0.0871 * 35/143 / (1/2) = 0.1220.122, or 12.2%.
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2. Consider this scatter plot.
a)
Draw a line of best fit on the picture of the scatterplot above. (2 pts.)
b) Is there a positive or negative association between a car's price and age? Explain your answer using as
much detail as possible. (3 pts.)
Answer:
Answer: A
Step-by-step explanation: cuz of the
pie chart
Select the correct answer from each drop-down menu.
Riley is swinging on a swing at the playground. Let t represent time, in seconds, and let represent Riley's horizontal distance, in inches, from
her starting position, as shown in the table.
t
0 0.75 1.5 2.25 3 3.75 4.5 5.25 6 6.75
f(t) 0 38.9 55 38.9 0-28.9 -55 -38.9 0 38.9
Note: When Riley swings in front of the starting position, f (t) is positive, and when Riley swings behind the starting position, f(t) is negative.
From the table, Riley is moving forward on the interval [0,
It takes Riley
Riley reaches a maximum distance of
seconds to swing forward, back, and then return to her starting position.
inches from her starting position.
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Reset
Next
Thus, Riley's maximum distance from the starting position is 55 inches.
Explain about the function:When an input value has a defined output value in reality, functions can be applied. For instance, how long a car has been driving affects how far it has travelled (the output) (the input).
Riley is swaying on a playground swing. As stated in the table, let t denote the passing of time in seconds and let f(t) denote Riley's horizontal displacement from her starting location in inches.
t: 0 ,0.75, 1.5, 2.25, 3, 3.75, 4.5, 5.25, 6, 6.75
f(t): 0 ,38.9, 55, 38.9, 0, -28.9, -55, -38.9, 0, 38.9
Recall that f(t) is positive when Riley swings closest to the starting position and negative when Riley swings in behind starting position.
So,
started from 0 and travelled distance of 55 inches in 1.5 seconds.
She is advancing by up to 1.5 seconds.
Then she begins to move backward, returning to her starting location after 3 seconds, and continuing to do so for an additional 4.5 seconds at a distance of -55.
Then begin to advance and return to the starting position after six seconds
Riley is advancing from the table on the interval [0, 1,5].Riley swings forward, backward, and then back to the starting position in six seconds. A is a few inches from where she started.Riley's maximum distance from the starting position is 55 inches.Know more about the function:
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Find the surface area
Round to the nearest tenth
Write a quadratic function with zeroes – 1 and 6. Write your answer using the variable x and in standard form with a leading coefficient of 1.
Answer:
If the zeroes of a quadratic function are -1 and 6, then its factored form is:
(x + 1)(x - 6) = 0
Expanding the left side:
x^2 - 5x - 6 = 0
So the quadratic function in standard form is:
f(x) = x^2 - 5x - 6
Answer:
f(x) = x^2 - 5x - 6
Step-by-step explanation:
To create a quadratic function with zeroes -1 and 6, we can start by using the zero product property to write out the factors of the equation:
(x + 1)(x - 6) = 0
Expanding the factors, we get:
x^2 - 5x - 6 = 0
This quadratic equation is in standard form with a leading coefficient of 1. Therefore, the quadratic function with zeroes -1 and 6 is:
f(x) = x^2 - 5x - 6
This function can also be graphed on the coordinate plane as a parabola with a vertex at (2.5, -10.25) and its axis of symmetry at x = 2.5. The graph would intersect the x-axis at -1 and 6, confirming that these are the zeroes of the function.
You are given that cos(A)=−5/13, with A in Quadrant II, and sin(B)=24/25, with B in Quadrant II. Find cos(A+B). Give your answer as a fraction.
The value for the trigonometric expression cos(A+B) is (5√7 - 288)/325
Explain trigonometry.
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It includes the study of trigonometric functions such as sine, cosine, and tangent, which are used to calculate unknown angles or sides of a triangle. Trigonometry has many practical applications in fields such as engineering, physics, and navigation.
According to the given information
We can use the trigonometric identity cos(A + B) = cos(A)cos(B) - sin(A)sin(B) to find cos(A + B).
Since cos(A) = -5/13 and A is in Quadrant II, we can use the Pythagorean identity sin²A + cos²A = 1 to find sin(A). Solving for sin(A), we get sin²A = 1 - cos²A = 1 - (-5/13)² = 144/169. Since A is in Quadrant II, sin(A) is positive, so sin(A) = √(144/169) = 12/13.
Similarly, since sin(B) = 24/25 and B is in Quadrant II, we can use the Pythagorean identity to find cos(B). Solving for cos(B), we get cos²B = 1 - sin²B = 1 - (24/25)² = 7/625. Since B is in Quadrant II, cos(B) is negative, so cos(B) = -√(7/625) = -√7/25.
Substituting these values into the identity for cos(A + B), we get:
cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
= (-5/13)(-√7/25) - (12/13)(24/25)
= (5√7)/(13*25) - (12*24)/(13*25)
= (5√7 - 288)/(13*25)
= (5√7 - 288)/325
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if tan68° = 1/m, express the following in terms of m:
1. tan22°
What is the probability of pulling a colored pair of socks from the drawer, if you have 3 pairs of white socks and 5 pairs of colored socks?
Negative 3 6/7 times negative 3 1/3
The expression Negative 3 6/7 times negative 3 1/3 has a value of -12 6/7
Evaluating the mathematical expressionWe have the following statement as the given parameter
Negative 3 6/7 times negative 3 1/3
Next, we rewrite the above statement using numbers and operators
-3 6/7 * 3 1/3
The above statement is a product expression that multiplies the values of -3 6/7 and 3 1/3
Also, there is no need to check if there are like terms in the expression or not
This is because we are multiplying the factors
So, we have
-3 6/7 * 3 1/3 = -27/7 * 10/3
Evaluate
-3 6/7 * 3 1/3 = -9/7 * 10
Rewrite as
-3 6/7 * 3 1/3 = -90/7
Simplify
-3 6/7 * 3 1/3 = -12 6/7
This means that the value of the expression is -12 6/7
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Error Analysis The bar graph shows the
results of a school election. A total of 150
students voted. Charlotte says that this
means 40 students voted for Candidate C.
How many students voted for Candidate C
in all? What was Charlotte's likely mistake?
Percent of Votes
40-C
32-
24-
16-
8-
In all how many students voted C
Answer:
To determine the number of students who voted for Candidate C, we need to first find what percent of the total votes they received. Looking at the graph, it appears that Candidate C received approximately 40% of the votes.
To find out how many students this represents, we can set up a proportion:
40% = C/150
Where C is the number of votes received by Candidate C.
To solve for C, we can cross-multiply:
0.4 x 150 = C
C = 60
Therefore, 60 students voted for Candidate C.
Charlotte's mistake was assuming that the percentage of votes for Candidate C directly corresponded to the number of students who voted for them. It's possible that more than one student voted for each candidate, and the percentage of votes represents the proportion of all votes each candidate received.
A bag contains 18 small red, 19 small black, 13 large black, and 15 large red T-shirts, and nothing else. What is the least number of T-shirts Alpa must take out of the bag (without looking at them) to be absolutely sure of having at least two T-shirts among them that differ only by size or only by color?
Alpa must take out at least 19 T-shirts from the bag to be absolutely sure of having at least two T-shirts among them that differ only by size or only by color.
What is the Pigeonhole Principle?
The Pigeonhole Principle is a fundamental concept in combinatorics, which is a branch of mathematics that deals with counting and analyzing the properties of sets of objects. The principle states that if there are more pigeons than pigeonholes, then at least one pigeonhole must contain more than one pigeon.
We can solve this problem using the Pigeonhole Principle, which states that if n+1 objects are distributed among n boxes, then there is at least one box that contains two or more objects.
In this case, we want to be sure that we have at least two T-shirts that differ only by size or only by color.
So we need to find the minimum number of T-shirts that we must take out of the bag to guarantee this.
Let's consider the worst-case scenario, where we take out all the T-shirts that are of one size or one color.
If we take out all 18 small red T-shirts, we still need to take out at least one more T-shirt to be sure that we have at least two T-shirts that differ only by size or only by color (since we could still get a small black T-shirt).
Similarly, if we take out all 19 small black T-shirts, we still need to take out at least one more T-shirt to be sure that we have at least two T-shirts that differ only by size or only by color.
If we take out all 13 large black T-shirts, we still need to take out at least one more T-shirt to be sure that we have at least two T-shirts that differ only by size or only by color.
If we take out all 15 large red T-shirts, we still need to take out at least one more T-shirt to be sure that we have at least two T-shirts that differ only by size or only by color.
So we need to take out at least 19 T-shirts to be sure that we have at least two T-shirts that differ only by size or only by color. (We add one to the largest number of T-shirts of one color or size.)
Therefore, Alpa must take out at least 19 T-shirts from the bag to be absolutely sure of having at least two T-shirts among them that differ only by size or only by color.
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If XZ ⊥ WY, XE = 4, and WY = 7, what is the perimeter of WXYZ, rounded to the nearest tenth?
The perimeter of the rhombus is approximately 7.6 units.
XZ is perpendicular to WY and XE is 4,
Since WXYZ is a rhombus because only the diagonal of the rhombus and square bisect each other at 90°
By the Pythagorean theorem, we have:
XE² = XY² + EY²
4² = XY² + (7/2)²
XY = 1.9
So the perimeter of WXYZ is 4(XY), rounded to the nearest tenth:
4(1.9) ≈ 7.6 units.
Therefore, the perimeter of the rhombus is approximately 7.6 units.
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francine can type 3,420 words in 1 hour and 30 minutes at this rate how any words can she type per minute
Francine can type 38 words per minute at this rate.
To find out how many words Francine can type per minute, we need to convert the time she took to type the words into minutes. Since there are 60 minutes in 1 hour, 1 hour and 30 minutes is equivalent to 1 × 60 + 30 = 90 minutes.
Next, we can use the formula:
words per minute = total words / total minutes
where "total words" is the number of words Francine typed (3,420) and "total minutes" is the time she took in minutes (90).
Substituting these values into the formula, we get:
words per minute = 3,420 / 90 = 38
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100 Points! Use synthetic substitution to find f(-3) and f(4) for 3x^4-4x^3+3x^2-5x-3. Photo attached. Please show as much work as possible. Thank you!
f(4) = 537. and f(-3) = 363. To find f(-3), we replace x with -3 in the expression similarly for x=4.
what is expression ?
In mathematics, an expression is a combination of mathematical symbols (such as numbers, variables, and operators) that represents a mathematical object or relationship.
In the given question,
To find f(-3), we replace x with -3 in the expression:
f(-3) = 3(-3)⁴ - 4(-3)³ + 3(-3)² - 5(-3) - 3
= 3(81) - 4(-27) + 3(9) + 15 - 3
= 243 + 108 + 15 - 3
= 363
Therefore, f(-3) = 363.
To find f(4), we replace x with 4 in the expression:
f(4) = 3(4)⁴ - 4(4)³ + 3(4)² - 5(4) - 3
= 3(256) - 4(64) + 3(16) - 20 - 3
= 768 - 256 + 48 - 23
= 537
Therefore, f(4) = 537.
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A square pyramid has a base with an area of 225 centimeters squared if the volume is 300 centimeters cubed how tall is the pyramid
The height of the square pyramid with base area 225 cm² and volume 300cm³ is equal to 4 centimeters.
Area of the base of square pyramid = 225 centimeters squared
Volume of the square pyramid = 300 centimeters cubed
Using the formula for the volume of a square pyramid,
V = (1/3) × B × h
where V is the volume,
B is the area of the base,
and h is the height of the pyramid.
Substitute this value into the formula we have,
⇒ 300 = (1/3) × 225 × h
Simplifying the equation , we get,
⇒ 900 = 225 × h
Dividing both sides by 225, we get,
⇒ h = 4
Therefore, the height of the square pyramid is 4 centimeters.
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PLEASE HELP - GIVING MANY POINTS!
After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. You notice the rainbow is the shape of a parabola.
The equation for this parabola is y = -x2 + 19.
In the distance, an airplane is taking off. As it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points.
Linear function: _________________ (You create an equation in y=mx+b form, that means the requirements above).
Create a table of at least four values for YOUR function that includes two points of intersection between the airplane and the rainbow.
x y
Is the linear function you created with your table positive or negative? Explain what it means in context.
What are the solutions or solution to the system of equations created? Explain what it or they represent.
Analyze the two functions. Answer the following reflection questions in complete sentences.
What is the domain and range of the rainbow?
Explain what the domain and range represent in context.
Do all of the values make sense in this situation? Why or why not?
What are the x- and y-intercepts of the rainbow?
Explain what each intercept represents in context.
The x-intercepts of the rainbow are (sqrt(19), 0) and (-sqrt(19), 0), while the y-intercept is (0, 19). In context, the x-intercepts represent the points where the rainbow touches the ground, while the y-intercept represents the highest point of the rainbow.
The linear functionLinear function: y = 3x + 1
x y
3 10
5 16
7 22
9 28
The linear function is positive, which means that the airplane's altitude is increasing as it moves towards the right on the graph. In context, this means that the airplane is ascending as it moves away from the observer towards the rainbow.
The system of equations created by the two functions is:
y = -x^2 + 19
y = 3x + 1
By substituting y in the second equation with the first equation, we get:
-x^2 + 19 = 3x + 1
Solving for x, we get:
x = -2 or x = 5
Substituting these values of x back into either of the equations, we get the corresponding values of y:
(-2, 7) and (5, 16)
These two solutions represent the points of intersection between the rainbow and the airplane's trajectory.
The domain of the rainbow is all real numbers, while the range is y ≤ 19. In context, this means that the rainbow can appear at any point in the observer's field of view, but its highest point is at y = 19.
All of the values in the domain and range make sense in this situation since they are within the physical limits of the observer's perception.
The x-intercepts of the rainbow are (sqrt(19), 0) and (-sqrt(19), 0), while the y-intercept is (0, 19). In context, the x-intercepts represent the points where the rainbow touches the ground, while the y-intercept represents the highest point of the rainbow.
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PLEASE Help me answer these 2 math questions!!!
1. The equation for the function is defined as follows: g(x) = (1/3)^x - 2.
2. The range of the function is given as follows: The set of real numbers less than -5.
How to define an exponential function?An exponential function has the definition presented as follows:
y = ab^x.
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.For item 1, the function has an horizontal asymptote at y = -2, hence it is defined as follows:
y = a(1/3)^x - 2.
When x = 0, y = -1, hence the parameter a is obtained as follows:
-1 = a - 2
a = 1.
Thus the function is:
g(x) = (1/3)^x - 2.
For item 2, we have that the function is:
Reflected over the y-axis, due to the negative sign of a.Has an horizontal asymptote at y = -5.Hence the range of the function is given as follows:
The set of real numbers less than -5.
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What fraction is equivalent to 1/4
The numbers are: 2,4,6,8,10,12
The price of an item has been reduced by 45%. The original price was $55. what is the price now?
Answer:
45% = 0.45
(you do this by bringing the decimal over 2 places)
multiply $55 and 0.45 to get $24.75
final answer = $24.75
What is the volume and surface area of a rectangular prism that is 11 ft long, 8 ft wide, and 4 ft tall?
Answer:
Here
Step-by-step explanation:
The volume of a rectangular prism is found by multiplying the length, width, and height.
Volume = Length x Width x Height
Volume = 11 ft x 8 ft x 4 ft
Volume = 352 cubic feet
The surface area of a rectangular prism is found by adding up the areas of all six faces.
Surface area = 2lw + 2lh + 2wh
Surface area = (2 x 11 ft x 8 ft) + (2 x 11 ft x 4 ft) + (2 x 8 ft x 4 ft)
Surface area = 176 + 88 + 64
Surface area = 328 square feet
Therefore, the volume of the rectangular prism is 352 cubic feet and the surface area is 328 square feet.
El m.c.m y m.c.d de 15 21 y 63
Find the area of a rectange with a base of 3/7 feet and a height of 9/10 feet
The area of the rectangle is 27/70 square feet.
Area of a rectangleThe area of a rectangle is given by the formula:
Area = base x height
Plugging in the given values, we get:
Area = (3/7) x (9/10)
Simplifying, we get:
Area = (27/70) square feet
Therefore, the area of the rectangle is 27/70 square feet.
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The Gallup Poll reported that 48% of Americans spend more than an hour a day using the Internet. If 4 people are selected at random, find the probability that they all spend more than an hour a day using the Internet. Please round the final answer to 2 or 3 decimal places. 4 people spend more than an hour a day using the internet
The probability that all 4 people spend more than an hour a day using the Internet is 0.053 or 5.3%.
The given problem is an example of a binomial probability distribution, where there are only two outcomes - success and failure. Here, success means spending more than an hour a day using the internet, and failure means spending an hour or less a day.
The probability of success is p = 0.48, and the probability of failure is q = 1 - p = 0.52.
To find the probability that all 4 people spend more than an hour a day using the Internet, we need to use the formula for the binomial probability distribution:
P(X = k) = (n choose k) * [tex]p^{k }* q^{(n-k)[/tex]
Here, n = 4 (the number of people selected), and k = 4 (the number of people who spend more than an hour a day using the Internet).
Plugging in the values, we get:
P(X = 4) = (4 choose 4) * 0.48⁴ * 0.52⁴⁻⁴ = 0.053
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Could this ordered pair be a solution to this equation?
y = 2x -1
(2, 3)
Step-by-step explanation:
yes .. when you put x=2 y will be 3 .. you get it?
Solve the system algebraically.
y= 3-1/2x
3x+4y=1
What is the value of x?
1. 17/2
1. -11
3. 11
Answer: x = -11
Step-by-step explanation:
Sub in y= 3-1/2x into 3x+4y=1 for y, and solve for x.
[tex]3x+4(3-\frac{1}{2}x) =1\\3x + 12 - 2x =1\\\\\ x = -11[/tex]
4.)Write an inequality.
Seven more than the quotient of a
number b and 15 is greater than 6
HELLLPPP ME PLSSS ITS URGENT
The ratio of the volume of both spheres is: 1/(24√3)
What is the volume of the sphere?The formula for the volume of a sphere is expressed as:
V = ⁴/₃πr³
where:
r is radius
V is volume
We are told that the radii of the two spheres have a ratio of 1:2√3. Thus:
Volume of sphere A/Volume of sphere B = (1:2√3)³
= 1/(24√3)
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A right triangle has side 9 and hypotenuse 15. Use the Pythagorean Theorem to find the length of the third side.
For pythagorean theorem the triangle is a 3, 4 ,5 triangle 15 would be the length 5, and 9 would be the lenght 3. So we would multiply each side to getthe answer your lookin for. Which the third side would be, I think im right, i just did this in my head but im only 11 so dont bully me plsssss
ANSWER 12
Determine the equation of the circle graphed below.
The equation for the circle graphed in the coordinate axis is:
(x - 5)^2 + (y - 6)^2 = 16
How to determine the equation for the circle?Remember that the equation for a circle whose center is at (a, b) and has a radius R is.
(x - a)^2 + (y - b)^2 = R^2
On the graph, we can see that the center of the circle is at (5, 6), and the radius of the circle is R = 4 units. Then the equation for the circle in the graph is:
(x - 5)^2 + (y - 6)^2 = 4^2
(x - 5)^2 + (y - 6)^2 = 16
That is the equation we wanted to find.
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Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?
y > x2 – 2
y ≥ –x2 + 5
To graph the solution set to the given system of inequalities, we first need to graph the functions f(x) = x^2 - 2 and g(x) = -x^2 + 5.
The graph of f(x) is a parabola that opens upward and has its vertex at (0, -2). The graph of g(x) is also a parabola, but it opens downward and has its vertex at (0, 5). We can plot these two graphs on the same coordinate plane as follows:
[Insert image of two parabolas on a coordinate plane]
Next, we need to shade the regions of the graph that satisfy the given inequalities. The first inequality y > x^2 - 2 represents the region above the parabola f(x) but below the line y = infinity. The second inequality y ≥ -x^2 + 5 represents the region at or above the parabola g(x). The solution set is the intersection of these two regions.
The shaded region represents all the points (x, y) that satisfy both inequalities, and therefore, the solution set to the system of inequalities.
The measure of an angle formed by two tangents to a circle is 80°. The radius of the circle is 8
centimeters. How far is the vertex of the angle from the center of the circle to the nearest centimeter?
Answer: So the vertex of the angle is located at the center of the circle, which is 8 centimeters away from the nearest centimeter.
Step-by-step explanation:
Let O be the center of the circle, and let A and B be the points of tangency of the two tangents with the circle. Since OA and OB are radii of the circle, they have the same length of 8 centimeters.
Let C be the vertex of the angle formed by the two tangents. Since the tangents are perpendicular to the radii at the points of tangency, we have that angle AOC = angle BOC = 90 degrees.
Since the measure of the angle formed by the two tangents is 80 degrees, we have that angle AOB = 180 - 80 - 80 = 20 degrees.
Let D be the foot of the perpendicular from C to line AB. Then angle OCD = 90 - 20/2 = 80 degrees, so triangle OCD is an isosceles triangle. Therefore, we have that OD = OC = 8 centimeters.
Finally, since triangle OCD is a right triangle, we can use the Pythagorean theorem to find the length of CD. We have:
CD^2 = OD^2 - OC^2 = 8^2 - 8^2 = 0
Therefore, CD = 0 centimeters.
So the vertex of the angle is located at the center of the circle, which is 8 centimeters away from the nearest centimeter.