To solve the triangle, we have;
Angle Q = [tex]112^{o}[/tex]
QR = 30.0
PR = 40.2
What is a sine rule?A sine rule is a trigonometric function that can be applied to determined the unknown side, or angle of a none right triangle.
From the information given in the question, to solve the triangle;
P + R + Q = 180
42 + 26 + Q = 180
Q = 180 - 68
= 112
Q = [tex]112^{o}[/tex]
Applying the sine rule,
QR/Sin P = PR/Sin Q = PQ/Sin R
PR/Sin Q = PQ/Sin R
PR/Sin 112 = 19/ Sin 26
PRSin 26 = 19*Sin 112
= 17.6165
PR = 17.6165/ 0.4384
= 40.1836
PR = 40.2
Also,
QR/Sin P = PQ/Sin R
QR/Sin 42 = 19/ Sin 26
QRSin 26 = 19*Sin 42
= 12.7135
QR = 12.7135/ 0.4384
= 28.9998
QR = 30
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A rocket can rise to a height of
h(t)=t^3+0.6t^2 feet in t seconds. Find its velocity and acceleration 8 seconds after it is launched,
Velocity = ____
Acceleration = _____
To find the velocity and acceleration 8 seconds after the rocket is launched, we need to find the first and second derivatives of the height function with respect to time.
The first derivative of h(t) gives the velocity function v(t):
v(t) = h'(t) = 3t^2 + 1.2t
Substituting t = 8 into this equation gives us the velocity of the rocket at 8 seconds after launch:
v(8) = 3(8)^2 + 1.2(8) = 204.8 feet per second
So the velocity of the rocket 8 seconds after launch is 204.8 feet per second.
The second derivative of h(t) gives the acceleration function a(t):
a(t) = h''(t) = 6t + 1.2
Substituting t = 8 into this equation gives us the acceleration of the rocket at 8 seconds after launch:
a(8) = 6(8) + 1.2 = 49.2 feet per second squared
So the acceleration of the rocket 8 seconds after launch is 49.2 feet per second squared.
To find the velocity and acceleration of the rocket 8 seconds after it is launched, we need to determine the first and second derivatives of the height function h(t) with respect to time t.
Given h(t) = t^3 + 0.6t^2, let's find its first and second derivatives:
1. Velocity (first derivative of h(t)):
v(t) = dh/dt = 3t^2 + 1.2t
2. Acceleration (second derivative of h(t)):
a(t) = d^2h/dt^2 = d(v(t))/dt = 6t + 1.2
Now, let's evaluate the velocity and acceleration at t = 8 seconds:
Velocity at t=8:
v(8) = 3(8^2) + 1.2(8) = 192 + 9.6 = 201.6 ft/s
Acceleration at t=8:
a(8) = 6(8) + 1.2 = 48 + 1.2 = 49.2 ft/s^2
So, 8 seconds after the rocket is launched, its velocity is 201.6 ft/s and its acceleration is 49.2 ft/s^2.
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A city's population in the year x=1953 was y=2,695,750. In 1971 the population was 2,694,850. Compute a slope of the population growth or decline and choose the most accurate statement
The negative slope indicates a decline in population over the 18-year period. The most accurate statement based on this information is that the city's population experienced a decline of approximately 50 people per year on average between 1953 and 1971.
To compute the slope of the population growth or decline, we need to use the formula:
slope = (y2 - y1) / (x2 - x1)
where y2 is the final population, y1 is the initial population, x2 is the final year, and x1 is the initial year.
Plugging in the values we have:
slope = (2,694,850 - 2,695,750) / (1971 - 1953)
slope = -900 / 18
slope = -50
The negative slope indicates a decline in population over the 18-year period.
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Please help!!! Find the total surface area of the following cone. Leave your answer in terms of pi.
4 cm
3 cm
SA = [?]π cm²
Answer:
24π cm²
Concepts Applied:
SA (TSA) of a cone = π · r · ( l+r )
Relation between l, h, and r i.e. l²=h²+r²
(h: cone height, r: base radius, l: slant height)
Step-by-step explanation:
Calculating the Slant height:
l²=h²+r²
l = sqrt(h²+r²)
l = sqrt(16+9)
l = sqrt(25)
l = +5 cm (distance is a scalar quantity)
Calculating the TSA:
= π · 3 · (5+3)
= 24π cm²
Answer:
34π cm^2 is the correct answer
Find the maximum sum of two positive numbers (not necessarily
integers), each of which is in [1,450], and whose product is
450.
The maximum sum of two positive numbers in the range [1, 450] with a product of 450 is approximately 42.42.
How to find sum of two positive numbers?
1. Let the two numbers be x and y.
2. Given that their product is 450, we have the equation xy = 450.
3. To find the maximum sum, we will use the fact that the sum of two numbers is maximum when they are equal. So, x = y.
4. From the product equation, we get x * x = 450, which implies x^2 = 450.
5. Taking the square root of both sides, we have x = √450 ≈ 21.21 (approximately).
6. Since x = y, the maximum sum is x + y = 21.21 + 21.21 ≈ 42.42.
Therefore, the maximum sum of two positive numbers in the range [1, 450] with a product of 450 is approximately 42.42.
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Sketch the angle in standard form whose terminal side passes through the point (-5, 12). Find the exact value for each trigonometric function.
The exact value for each trigonometric function are -12/13, -5/13 and 12/5
To find the reference angle, we can use the properties of right triangles. We can draw a line from the point (-5, 12) to the x-axis to form a right triangle. The hypotenuse of the triangle is the distance from the point (-5, 12) to the origin, which is the square root of the sum of the squares of the x and y coordinates:
√((-5)² + 12²) = 13
The reference angle is the acute angle between the x-axis and the adjacent side of the triangle, which is the x-coordinate of the point (-5, 12) divided by the hypotenuse:
cosθ = -5/13
θ = arccos(-5/13)
θ ≈ 2.214 radians
The angle's standard form is given by the equation:
θ = n(2π) ± α
where n is an integer, and α is the angle's reference angle. Since the point (-5, 12) is in the second quadrant, the angle's terminal side intersects the unit circle at an angle of θ = π + α. Therefore, the standard form of the angle is:
θ = (2n + 1)π - arccos(-5/13)
To find the exact value of the trigonometric functions of this angle, we can use the properties of the unit circle. Since the sine function is positive in the second quadrant, we have:
sinθ = sin(π + α) = -sinα = -12/13
Similarly, since the cosine function is negative in the second quadrant, we have:
cosθ = cos(π + α) = -cosα = -5/13
Finally, since the tangent function is the ratio of the sine and cosine functions, we have:
tanθ = tan(π + α) = -tanα = 12/5
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A
Fill in the blank. If one line has a slope of 0. 5 and another distinct line has a
slope of those two lines are
A. Parallel
B. Not correlated
C. Perpendicular
e
D. Undefined
Is urgent , no link plis
If one line has a slope of 0. 5 and another distinct line has a slope of those two lines are Parallel. The correct answer is A.
Two lines are parallel if and only if they have the same slope. If two distinct lines have different slopes, then they cannot be parallel. In this case, one line has a slope of 0.5 and the other line's slope is unknown, so we cannot determine whether they are parallel or not just by looking at their slopes.
However, if the other line's slope is perpendicular to 0.5, then the lines would be perpendicular. Two lines are perpendicular if and only if the product of their slopes is -1. Therefore, if the other line's slope is -2, then the lines would be perpendicular (0.5 * -2 = -1).
If the other line's slope is undefined (i.e., the line is vertical), then the lines would not be parallel or perpendicular, but rather they would be skew lines.
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Sophie deposited money into an account in which interest is compounded semiannually at a rate of 3.3%. She made no other deposits or withdrawals and the total amount in her account after 11 years was $19,786.19. How much did she deposit? Round answer to nearest whole number. Do not include units in the answer. Be sure to attach your work for credit.
Applying the compound interest formula, rounding to the nearest whole number, we get that Sophie deposited approximately $11,200.
How to Apply the Compound Interest Formula to Find How Much was Deposited?We can use the formula for compound interest to solve this problem:
A = P * (1 + r/n)^(nt)
where A is the ending balance, P is the principal (the amount Sophie deposited), r is the annual interest rate (3.3%), n is the number of times the interest is compounded per year (2 for semiannual), and t is the number of years.
Substituting the given values, we get:
19786.19 = P * (1 + 0.033/2)^(2*11)
Simplifying and solving for P, we get:
P = 19786.19 / (1 + 0.033/2)^(2*11)
P ≈ 11200
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Terri is beginning a science experiment in the lab. The instructions call for 227 milligrams of potassium. Calculate the difference between this amount and 1 gram
The difference between the amount of potassium called for in the experiment (0.227 grams) and 1 gram is 0.773 grams.
The amount of potassium called for in the experiment is 227 milligrams. To convert milligrams to grams, we divide by 1000: 227/1000 = 0.227 grams.
The amount of 1 gram is larger than 0.227 grams. To find the difference between the two amounts, we subtract the smaller amount from the larger amount:
1 gram - 0.227 grams = 0.773 grams
Therefore, the difference between the amount of potassium called for in the experiment (0.227 grams) and 1 gram is 0.773 grams.
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data from the bureau of labor statistics reports that the typical manufacturing worker in wisconsin in 1997 earned a weekly salary of $424.20. suppose you wanted to see if this were true just in the far southeastern portion of the state. you obtain a sample of tax returns for manufacturing workers in racine and kenosha for the year 1997. your sample consists of 54 workers and has a mean weekly salary of $432.69 with a standard deviation of $33.90 at a 90% confidence level test the claim that manufacturing workers in racine and kenosha had the same salary as workers across the state. what will be your critical value?
The critical value for this hypothesis test is 1.676.
To test the claim that manufacturing workers in Racine and Kenosha had the same salary as workers across the state, we can conduct a hypothesis test with the following null and alternative hypotheses:
Null hypothesis: The mean weekly salary of manufacturing workers in Racine and Kenosha is equal to $424.20.Alternative hypothesis: The mean weekly salary of manufacturing workers in Racine and Kenosha is different from $424.20.We can use a t-test for the sample mean to test this hypothesis. At a 90% confidence level, we have a significance level of alpha = 0.10. Since this is a two-tailed test (we are testing for a difference in either direction), we will split the significance level evenly between the two tails, so alpha/2 = 0.05.
We need to calculate the critical value of the t-distribution with n-1 degrees of freedom, where n is the sample size. In this case, n = 54, so the degrees of freedom is 53. We can use a t-distribution table or a calculator to find the critical value. For a two-tailed test with alpha/2 = 0.05 and 53 degrees of freedom, the critical value is approximately 1.676.
Therefore, the critical value for this hypothesis test is 1.676.
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What is the circumference of the following circle?
Use 3.14 for πpi and enter your answer as a decimal.
The calculated value of the circumference of the circle is 31.4 units
What is the circumference of the following circle?From the question, we have the following parameters that can be used in our computation:
Radius, r = 5
Using the above as a guide, we have the following:
Circumference = 2 * π * r
Substitute the known values in the above equation, so, we have the following representation
Circumference = 2 * 5 * 3.14
Evaluate the products
Circumference = 31.4
HEnce, the value of the circumference is 31.4 units
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Hallie and Mattie donated blue jeans to the clothing drive. Hallie donated 4 pairs of blue jeans. Mattie donated 6 pairs of blue jeans. Write a ratio to represent the relationship between Hallie's donation of jeans and Mattie's donation of jeans.
6:14
2 to 3
2 over 4
1 to 10
the correct ratio to represent the relationship between Hallie's donation of jeans and Mattie's donation of jeans is 2:3. Thus, option B is correct.
What is the ratio?To write a ratio to represent the relationship between Hallie's donation of jeans and Mattie's donation of jeans, we need to find the common factor between the number of pairs of blue jeans each person donated.
Hallie donated 4 pairs of blue jeans, and Mattie donated 6 pairs of blue jeans.
The common factor between 4 and 6 is 2. We can divide both 4 and 6 by 2 to get:
Hallie donated 2 pairs of blue jeans.
Mattie donated 3 pairs of blue jeans.
Now we can write the ratio of Hallie's donation to Mattie's donation as:
2:3
Therefore, the correct ratio to represent the relationship between Hallie's donation of jeans and Mattie's donation of jeans is 2:3.
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Mr robins earns a commission on each airfare he books. At the end of the day he had booked 208. 60 worth of airfare and earned 31. 29
Mr. Robins earns a commission of 15% on the airfares he books, as he earned $31.29 on $208.60 worth of airfare bookings.
Let x be the amount of commission earned by Mr. Robins on the airfares he booked. Then, we can write the equation:
x = 15% of $208.60
Simplifying this equation, we get:
x = 0.15 x $208.60
x = $31.29
Therefore, Mr. Robins earned a commission of $31.29 on $208.60 worth of airfare bookings. To verify this, we can calculate his commission rate as:
Commission rate = Commission earned / Airfare bookings
Commission rate = $31.29 / $208.60
Commission rate = 0.15 or 15%
Hence, Mr. Robins earns a commission of 15% on the airfares he books.
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suppose discrete random variables x and y have a joint distribution: a. what is the expectation of x y? that is, what is e(x y)?
The expectation of the product of two discrete random variables x and y is given by E(xy) = ∑(x∑(yP(x,y))) where P(x,y) is the joint probability distribution of x and y.
To find the expectation of the product of two random variables, we need to use the formula:
E(XY) = ΣΣ(xy)p(x,y)
where p(x,y) is the joint probability mass function of X and Y.
So, for the given joint distribution of X and Y, we have:
E(XY) = ΣΣ(xy)p(x,y)
We need to sum this over all possible values of X and Y. If the joint distribution is given in a table or a function form, we can simply plug in the values of X and Y and calculate the sum.
However, without any specific information about the joint distribution of X and Y, it is impossible to calculate the expectation of X times Y. We would need to know either the joint probability mass function or the joint probability density function of X and Y.
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Lulu has 10 feet of ribbon she uses 1 1/3 feet ribbon for a project she uses the rest of the ribbon to make bows she uses 8 inches of ribbon for each bowl how many does lulu make?
The number of bows Lulu can make from the remaining ribbon is 13 bows.
To find the remaining ribbon, first, convert 1 1/3 to an improper fraction (1*3 + 1 = 4, so 1 1/3 = 4/3). Now, subtract 4/3 from 10 feet.
10 - (4/3) = (30/3) - (4/3) = 26/3 feet of ribbon remaining.
She uses 8 inches of ribbon for each bow. Since there are 12 inches in a foot, convert the remaining ribbon to inches:
(26/3) * 12 = 104 inches of ribbon remaining.
Now, divide 104 inches by the 8 inches required for each bow to find the number of bows she can make:
104 / 8 = 13 bows.
Lulu can make 13 bows with the remaining ribbon.
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Use an integer to describe the situations.
6 meters above sea level ___
sea level ___
Answer:
An integer to describe 6 meters above the sea level would be meters.
As per the question statement, We are supposed to use an integer to describe the following situation "6 meters above sea level".
We assume that sea level is the datum line and anything above that would be positive and below that would be negative.
So 6 meters above the sea level can be described as .
Integers: Set of whole number containing both positive and negative values of it.
PLS MARK BRAINLIEST
Step-by-step explanation:
f(x)=1/2x^4+2x^3 is concave up when f”(x) is
The function f(x) = (¹/₂)x⁴ +2x³ is concave up when f''(x) > 0, which is true when x > 0 or x < -2.
What is the concavity of the function?The concavity of a function is determined by taking the second derivative.
f'(x) = 2x³ + 6x²
f''(x) = 6x² + 12x
To find out when f(x) is concave up, we need to determine when f''(x) is positive;
f''(x) > 0
6x² + 12x > 0
6x(x + 2) > 0
When x > 0, both factors are positive, and the inequality is true.
When x < -2, both factors are negative, and the inequality is true.
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i need help quickk please
The true statements about the rectangular prism are Prism B has a greater volume than Prism C, Prism B has the greatest volume, and Prism A has the least volume.
What is the volume of each of the prisms?To understand, the differences between the prisms and therefore to verify the statements about them, let's calculate the volume of each by using the formula length x width x height.
Prism A: 2 x 2 x 3= 12 cubic units
Prism B: 2 x 3 x 4 = 24 cubic units
Prism C: 3 x 2 x 3 = 18cubic units
Based on this, the statements A, D, and E are correct.
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Box plot percentage of data values are greater than 16?
The percentage of the data values that are greater than 16, as shown in the box plot is: 75%.
What is a Box Plot?A box plot shows how the data points of a data set are distributed, in such a way that, 25% of the data points lie below the lower quartile, % lie below the median, and 75% lie below the upper quartile.
In the box plot given, the values that are greater than 16 lie above the upper quartile, which equals about 75% of the data values.
Therefore, the percentage of the data values that are greater than 65, as shown in the box plot is: 75%.
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Given that cos α = -8/17 and that 0° <= α <= 360°, find two values of α, to two decimal places.
Therefore, two possible values of α are approximately 138.19° and 221.81°.
What purpose does sin serve?Sin 180 has a precise value of zero. One of the fundamental trigonometric functions is sine, which is used to calculate the angle or sides of a right-angled triangle.
Given that cos = -8/17, we must determine two potential values for.
We can construct a right triangle with the adjacent side equal to -8 and the hypotenuse equal to 17, and then use the Pythagorean theorem to calculate the opposite side since cos = adjacent/hypotenuse.
The Pythagorean theorem gives us:
opposite² = hypotenuse² - adjacent²
opposite² = 17² - (-8)²
opposite² = 225
opposite = ±15
Both the x and y coordinates are negative in the second quadrant, resulting in:
cos α = -8/17
sin α = -15/17
Consequently, may have the following value: = 180° - arccos(-8/17) 138.19° (rounded to two decimal places)
The x coordinate is negative and the y coordinate is positive in the third quadrant, resulting in:
cos α = -8/17
sin α = 15/17
Therefore, another possible value of α is:
α = 360° - cos(-8/17)
≈ 221.81°
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Let F(X) = - 8 - x^2, find the following:
(f(7) - f(3))/ 7 -3
A relation is a set of ordered pairs that define the relationship between two sets. And, a function is a relation in which each element of the domain is connected to a single element of the codomain. The evaluated function is -10.
To find the expression (f(7) - f(3))/ 7 -3, we need to first find f(7) and f(3).
Using the given function F(X) = - 8 - x^2, we can find:
f(7) = -8 - 7^2 = -57
f(3) = -8 - 3^2 = -17
Now, we can substitute these values into the expression:
(f(7) - f(3))/ 7 -3 = (-57 - (-17))/ (7-3) = -40/4 = -10
Therefore, the answer is -10.
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The histogram shows the number of people who viewed each showing of scary night at one movie theater during its opening week the seat capacity of the theater is 300 for what fraction of the shows was the theater half full or less than half explain
For approximately 64% of the shows, the theater was half full or less than half full.
Since the seat capacity of the theater is 300, half full would be 150 seats or less. Looking at the histogram, we can see that there are 3 bars representing showings with 150 or less viewers.
The first bar represents showings with 0-50 viewers. From the histogram, it looks like there were about 5 showings with this number of viewers.
The second bar represents showings with 50-100 viewers. From the histogram, it looks like there were about 8 showings with this number of viewers.
The third bar represents showings with 100-150 viewers. From the histogram, it looks like there were about 3 showings with this number of viewers.
So the total number of showings with 150 or less viewers is 5+8+3 = 16.
Since the histogram shows a total of 25 showings, the fraction of shows that was half full or less than half is:
16/25 = 0.64 or 64%
Therefore, for approximately 64% of the shows, the theater was half full or less than half full.
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2. Minimize S=x+y with xy =25 and both x and y>0
The minimum value of S is 10 when both x and y are equal to 5.
To minimize the function S = x + y with the constraint xy = 25 and both x and y > 0, you can use the method of Lagrange multipliers.
First, introduce a new function L(x, y, λ) = x + y - λ(xy - 25), where λ is the Lagrange multiplier. Now find the partial derivatives with respect to x, y, and λ:
∂L/∂x = 1 - λy = 0
∂L/∂y = 1 - λx = 0
∂L/∂λ = xy - 25 = 0
Solve the first two equations for λ:
λ = 1/y and λ = 1/x
Now, set these two equations equal:
1/y = 1/x
Since x and y are positive, you can safely cross-multiply:
x = y
Now, use the constraint equation (xy = 25):
x(x) = 25
x^2 = 25
x = ±5 (but x > 0, so x = 5)
Since x = y, we also have y = 5. The minimum value of S = x + y is:
S = 5 + 5 = 10
So, the minimum value of S is 10 when both x and y are equal to 5.
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Find the measure of the angle indicated. Assume that the lines which appear tangent are tangent.
Answer:
65°-----------------------------
The measure of the angle formed outside of circle is half the difference of major and minor arc measures.
It means the measure of angle T is:
m∠T = 1/2((360 - 115) - 115) = 180 - 115 = 65The measure of the angle indicated in the diagram is 50 degrees.
What is Tangent ?
In geometry, the tangent is a trigonometric function that relates the opposite side and adjacent side of a right triangle. More specifically, for a given angle θ, the tangent of θ (denoted by tan θ) is defined as the ratio of the length of the opposite side to the length of the adjacent side of the right triangle containing that angle.
In the given figure, the two lines are tangent to the circle with center O. Let's call the point where the two lines intersect point P.
We know that the angle formed by a tangent line and a radius of a circle is always 90 degrees. Therefore, we can draw a radius OP from the center of the circle to point P and we know that angle POQ (where Q is the point where the radius intersects the circle) is 90 degrees.
We also know that angle OPQ is 40 degrees (as given in the diagram).
Since the sum of the angles in a triangle is 180 degrees, we can find angle OQP as follows:
angle OQP = 180 - angle OPQ - angle POQ
= 180 - 40 - 90
= 50 degrees
Therefore, the measure of the angle indicated in the diagram is 50 degrees.
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X varies jointly as y and z.
Write an equation that express each relationship. Then solve the equation for y.
An equation that express each relationship for the joint variation is X = kyz. Solving for y will give the equation y = X/(kz)
What is joint variationJoint variation is a mathematical concept that describes the relationship between two or more variables.
If X varies jointly as y and z, we can express this relationship mathematically using the formula:
X = k × y × z
X = kyz
where k is a constant of proportionality.
We can solve for y by dividing both sides by kz follows:
X/kz = kyz/kz
X/(kz) = y
Therefore, the equation that express each relationship for the joint variation is X = kyz. And the equation solved for y is y = X/(kz).
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If a woman making $29,000 a year receives a cost-of-living increase of 2. 6%, what will her new salary be?
To find the new salary after a 2.6% increase, we need to add 2.6% of the original salary to the original salary.
2.6% of $29,000 can be calculated as:
(2.6/100) x $29,000 = $754
Therefore, the new salary will be:
$29,000 + $754 = $29,754
So the woman's new salary will be $29,754.
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(I need these answered fast and with work and explanation)
A)What is the conditional probability of being on the marching band, given that you know
the student plays a team sport? Show your work.
b. What is the probability of being on the marching band, and how is this different from part
(a)? Explain completely.
C.
Are the two events, {on the marching band) and {on a team sport} associated? Use
probabilities to explain why or why not
We know that the P(Marching Band and Team Sport) ≠ P(Marching Band) * P(Team Sport), the two events are dependent and associated.
A) The conditional probability of being on the marching band given that the student plays a team sport can be calculated using the formula:
P(Marching Band | Team Sport) = P(Marching Band and Team Sport) / P(Team Sport)
where P(Marching Band and Team Sport) is the probability of being on the marching band and playing a team sport, and P(Team Sport) is the probability of playing a team sport.
Let's say that out of a total of 500 students, 100 students play a team sport and 50 of them are also on the marching band. Then,
P(Marching Band and Team Sport) = 50/500 = 0.1
P(Team Sport) = 100/500 = 0.2
Plugging these values into the formula, we get:
P(Marching Band | Team Sport) = 0.1 / 0.2 = 0.5
Therefore, the conditional probability of being on the marching band given that the student plays a team sport is 0.5 or 50%.
b. The probability of being on the marching band can be calculated as:
P(Marching Band) = (Number of students on the marching band) / (Total number of students)
Let's say that out of the same 500 students, 75 students are on the marching band. Then,
P(Marching Band) = 75/500 = 0.15 or 15%
The difference between part (a) and part (b) is that in part (a), we are given additional information (the student plays a team sport) and we want to find the probability of being on the marching band. In part (b), we are simply asked for the probability of being on the marching band without any other information.
c. The two events, {on the marching band} and {on a team sport}, may or may not be associated. We can use probabilities to determine whether they are associated or not.
If the probability of being on the marching band and playing a team sport is different from the product of the probabilities of being on the marching band and playing a team sport separately, then the events are dependent and associated. If they are the same, then the events are independent and not associated.
Let's calculate the probabilities:
P(Marching Band and Team Sport) = 50/500 = 0.1
P(Marching Band) = 75/500 = 0.15
P(Team Sport) = 100/500 = 0.2
Product of the probabilities:
P(Marching Band) * P(Team Sport) = 0.15 * 0.2 = 0.03
Since P(Marching Band and Team Sport) ≠ P(Marching Band) * P(Team Sport), the two events are dependent and associated. This means that knowing whether a student is on the marching band affects the probability of them playing a team sport, and vice versa.
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A company has two machines. During any day, each machine that is working at the beginning of the day has a 1 3 chance of breaking down. If a machine breaks down during the day, it is sent to a repair facility and will be working two days after it breaks down. (Thus, if a machine breaks down during day 3, it will be working at the beginning of day 5. ) Letting the state of the system be the number of machines working at the beginning of the day, formulate a transition probability matrix for this situation
With probability 1, both machines are in the repair facility, and we move to state 2 (both machines working) two days later.
What is the probability that both machines are working at the beginning of the day?Let the state of the system be the number of machines working at the beginning of the day. We have two machines, so the state space is {0, 1, 2}.
Let the probability of transitioning from state i to state j be P(i,j).
To fill in the entries of the transition probability matrix, we need to consider the possible transitions between states.
If both machines are working at the beginning of the day (state 2):
With probability 1/9, both machines break down, and we move to state 0 (neither machine working).With probability 4/9, one machine breaks down and one machine continues to work, and we move to state 1 (one machine working).With probability 4/9, both machines continue to work, and we stay in state 2.If one machine is working at the beginning of the day (state 1):
With probability 1/3, the working machine breaks down, and we move to state 0 (neither machine working).With probability 2/3, the working machine continues to work, and we stay in state 1.If neither machine is working at the beginning of the day (state 0):
With probability 1, both machines are in the repair facility, and we move to state 2 (both machines working) two days later.Putting this all together, we get the following transition probability matrix:
| | 0 | 1 | 2 |
|---|----------|----------|----------|
| 0 | 0 | 0 | 1 |
| 1 | 1/3 | 2/3 | 0 |
| 2 | 1/9 | 4/9 | 4/9 |
For example, the entry in row 1 and column 2 represents the probability of transitioning from state 1 (one machine working) to state 2 (both machines working) and is 4/9.
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If ad and bd are tangent to circle c, and ad= 13 and bd= 4x-3 find the value of x.
If ad and bd are tangent to circle c, and ad= 13 and bd= 4x-3, then the value of x is 4 or 4.5
To solve this problem, we'll need to use some geometry and algebra.
Using the Pythagorean theorem, we can set up two equations:
OA² + AD² = OD² (for right triangle OAD)
OB² + BD² = OD² (for right triangle OBD)
In these equations, "OD" is the radius of the circle. We don't know this value yet, but we can express it in terms of "x" using the fact that "BD" = 4x-3.
Now, we can simplify these equations by substituting in the values we know. We get:
OA² + 13² = OD²
OB² + (4x-3)² = OD²
This means we can set up the equation:
OA = OB
Now we can substitute in the expressions we found for "OA" and "OB" earlier:
√(OD² - 13²) = √(OD² - (4x-3)²)
We can then square both sides to eliminate the square roots:
OD² - 13² = OD² - (4x-3)²
Simplifying this equation, we get:
169 = (4x-3)²
Taking the square root of both sides (and remembering to include the positive and negative solutions), we get:
4x-3 = ±13
Solving for "x," we get two possible values:
x = 4
x = 4.5
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Use a triple integral to find the volume of the solid bounded by the parabolic cylinder y = 2x2 and the planes z = 0,2= 2 and y = 4.
Using the triple integral to find the volume of the solid bounded by the parabolic cylinder is 32/15 cubic units.
The given solid is bounded by the parabolic cylinder y = 2x², the plane z = 0, the plane z = 2, and the plane y = 4.
To find the volume of the solid using a triple integral, we can set up the integral as follows:
∫∫∫E dV
where E is the region of integration in three dimensions.
Region E can be described as:
0 ≤ z ≤ 2
0 ≤ y ≤ 4
0 ≤ x ≤ √(y/2)
Therefore, the triple integral can be written as:
∫0² ∫[tex]0^4[/tex] ∫[tex]0^{\sqrt(y/2)}[/tex] dx dy dz
Evaluating the integral gives us the volume of the solid:
V = ∫0² ∫[tex]0^4[/tex] ∫[tex]0^{\sqrt(y/2)}[/tex] dx dy dz = 32/15
Hence, the volume of the solid is 32/15 cubic units.
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HELP!!!!!! WILL GIVE BRAINLIEST!!!!!!!!!
1. The value of d is 10
2. measure of angle BSR is 120°
3. measure of angle RSM is 60°
What are angles on a straight line?The sum of angles on a straight line is 180°. This angles are adjascent angles.
angle BSR and RSM are on a straight line, therefore;
10d+20+6d = 180
16d = 180-20
16d = 160
d = 160/16
d = 10
therefore the value of d is 10
angle BSR = 10d+20 = 10×10+20
= 100+20 = 120°
angle RSM = 6d = 6 × 10
= 60°
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