The percentage of body weight the dog lost is 9.2%. Mary would weigh 52.664 kg after losing the same percentage of body weight as her dog.
A) To find the percentage of body weight the dog lost, first, calculate the actual weight loss: 25 kg - 2.3 kg = 22.7 kg. Then, divide the weight loss (2.3 kg) by the original weight (25 kg) and multiply by 100 to get the percentage: (2.3 kg / 25 kg) * 100 = 9.2%.
B) If Mary lost the same percentage of her body weight as the dog did, she would lose 9.2% of her weight. To calculate this, multiply her original weight (58 kg) by the percentage (9.2%): 58 kg * 0.092 = 5.336 kg. Now, subtract this weight loss from her original weight to find her new weight: 58 kg - 5.336 kg = 52.664 kg. So, Mary would weigh 52.664 kg after losing the same percentage of body weight as her dog.
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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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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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find the limit of the sequence \displaystyle a_n = \frac{(\cos n)}{7^n}.
The limit of the sequence a_n is 0. The sequence a_n = (cos n)/[tex]7^n[/tex] oscillates between -1/[tex]7^n[/tex] and 1/[tex]7^n[/tex] since the cosine function is bounded between -1 and 1. Therefore, by the squeeze theorem, the limit of the sequence is 0 as n approaches infinity.
The cosine function oscillates between -1 and 1, so we have:
-1/[tex]7^n[/tex] ≤ cos(n)/7^n ≤ 1/[tex]7^n[/tex]
Dividing each term by [tex]7^n[/tex], we obtain:
-1/[tex]7^n[/tex] ≤ a_n ≤ 1/[tex]7^n[/tex]
By the squeeze theorem, since -1/[tex]7^n[/tex] and 1/[tex]7^n[/tex] both approach zero as n approaches infinity, we have:
lim a_n = 0
Therefore, the limit of the sequence a_n is 0.
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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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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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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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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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The population of a town is decreasing at a rate of
1.5% per year. in 2007 there were 19265 people. write
an exponential decay function to model this situation
where t represents the number of years since 2007
and y is the amount of people. then estimate the
population for 2031 (?? years later) to the nearest
person.
The exponential decay function to model this situation where t represents the number of years since 2007 and y is the amount of people is y = 19265 * (1 - 0.015)^t. The population for 2031 will be approximately 14,814 people.
To write an exponential decay function for this situation, you can use the formula:
y = P * (1 - r)^t
where y is the population at time t, P is the initial population, r is the annual decrease rate, and t represents the number of years since 2007.
In this case, P = 19265, r = 0.015 (1.5% expressed as a decimal), and t represents the number of years since 2007.
So, the exponential decay function is:
y = 19265 * (1 - 0.015)^t
To estimate the population for 2031, find the difference in years between 2031 and 2007 (2031 - 2007 = 24 years), and plug it into the formula as t:
y = 19265 * (1 - 0.015)^24
y ≈ 14814
So, the estimated population in 2031 will be approximately 14,814 people, rounded to the nearest person.
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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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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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which amount is greater than four hundred forty-five and fifty-seven hundredths? a. four hundred forty-five and five tenths b. four hundred forty-five and seven tenths c. four hundred forty-five and five thousandths d. four hundred forty-five and fifty-seven thousandths
The amount which is greater than the given amount four hundred forty-five and fifty-seven hundredths is given by option b. 445.7.
Amount representing the number is 445.57.
Amount greater than this number,
Compare the decimal parts of the numbers given in the options.
445.5 has a decimal part of 0.5, which is not greater than 0.57.
Option a is not greater than 445.57.
445.7 has a decimal part of 0.7, which is greater than 0.57.
Option b is greater than 445.57.
445.005 has a decimal part of 0.005, which is less than 0.57.
Option c is not greater than 445.57.
445.057 has a decimal part of 0.057, which is not greater than 0.57.
Option d is not greater than 445.57.
Therefore, the only option that is greater than 445.57 is option b. 445.7.
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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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Write an equation in slope-intercept form to represent the
table.
x: 0, 1.5, 4, 6.5, 7
y: 6.4, 4.6, 1.6, -1.4, -2
Answer:
y=1.2x-6.4
Step-by-step explanation:
get slope
y2-y1/x2-x1
6.4 - 4.6/0-(-1.5)
1.8/1.5=1.2
get formula
y-y1=m(x-x1)
y-4.6=1.2(x-1.5)
y-4.6=1.2x-1.8
y-4.6=1.2x-1.8
y=1.2x-6.4
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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A fisherman kept records of the weight in pounds of the fish caught on the fishing trip 10, 9, 2, 12, 10, 12, 8, 14, 11, 3, 6, 9, 7, 15. What does the shape of the distribution in the histogram tell you about the situation
The shape of the distribution in the histogram can tell us about the distribution of weights of fish caught by the fisherman.
Looking at the given data set, we can see that the weights of the fish caught vary from as low as 2 pounds to as high as 15 pounds. The histogram of this data set can help us to fantasize the distribution of these weights. Grounded on the shape of the histogram, we can see that the distribution is kindly slanted to the right, with a long tail extending towards the advanced end of the weights.
This suggests that there were further fish caught that counted lower than the mean weight of the catch, with smaller fish caught that counted further than the mean weight. also, the presence of a many outliers( similar as the fish that counted 15 pounds) suggests that there may have been some larger or unusual fish caught on the trip.
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Hannah decided to make finger gelatin for a huge children’s party. She had to make 8 packs of gelatin. Each pack needed 2 cups of water. How many quarts of water will she need?
She will need 4 quarts of water.
Given Hannah decided to make finger gelatin for a huge children’s party. She had to make 8 packs of gelatin. Each pack needed 2 cups of water.
Since each pack of gelatin requires 2 cups of water, Hannah will need a total of:
8 packs x 2 cups/pack = 16 cups of water
To convert cups to quarts, we need to divide the number of cups by 4 (since there are 4 cups in a quart):
16 cups ÷ 4 cups/quart = 4 quarts
Therefore, Hannah will need 4 quarts of water to make 8 packs of finger gelatin for the children’s party.
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Mia is participating in a kite-flying competition. She wanted to find out how long is the string needed for fly her kite 33 meters from the ground if she is 56 meters away from the kite.
how do i do this assignment while showing the work?
The length of the string needed is 65 meters
What is an equation?An equation is an expression that shows how numbers and variables using mathematical operators.
Pythagoras theorem shows the relationship between the sides of a right angle triangle.
To find the length of string, Mia needs. A triangle is formed with hypotenuse (l) represent the length of string. The height of the kite (h) = 33 m which is the triangle height; while the 56 m is the base of the triangle (b). Hence:
l² = b² + h²
l² = 33² + 56²
l = 65 meters
The length of the string needed is 65 meters
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how to calculate the length of ED AND BE
With regard to the similar triangles,
The length of ED is 6.5cm.The length of BE is 14.4 cm.How is this so?In ΔACD
BE ∥ CD
In ΔACD and ΔABE
BE ∥ CD
∠ACD =∠ABE (corresponding angles)
∠ADC = ∠AEB (corresponding angles)
∠A = ∠A (common angle)
ACD ∼ ΔABE
So, The corresponding sides are in proportion.
Now, find ED
AB/BC = AE/ED
ED = AE (BC/AB)
ED = 26(5/20)
ED = 6.5cm
For BE
AB/AC = BE/CD
BE = CD (AB/AC)
BE = 18 (20/25)
BE = 14.4cm
Now, find BE
Therefore, the length of ED is 6.5cm and the length of BE is 14.4 cm.
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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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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
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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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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A basketball coach wants to purchase shooting shirts for each member of a basketball team.
The cost of shooting shirts can be represented by the equation C = 0. 2x^2 + 1. 6x + 15, where
C is the amount it cost to purchase x shooting shirts. How many shooting shirts can the
basketball coach order for $300?
C = 2x? + 1. 6x + 15
The basketball coach can order approximately 34 shooting shirts for $300.
To determine the number of shooting shirts the basketball coach can order for $300, we need to solve the equation C = 0.2x^2 + 1.6x + 15, where C represents the cost and x represents the number of shooting shirts.
The equation is given as C = 0.2x^2 + 1.6x + 15.
To find the number of shooting shirts for $300, we set the cost C equal to 300 and solve for x:
0.2x^2 + 1.6x + 15 = 300
0.2x^2 + 1.6x + 15 - 300 = 0
0.2x^2 + 1.6x - 285 = 0
Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
For this equation, a = 0.2, b = 1.6, and c = -285. Plugging in these values into the quadratic formula:
x = (-1.6 ± sqrt(1.6^2 - 4 * 0.2 * -285)) / (2 * 0.2)
Simplifying the equation further:
x = (-1.6 ± sqrt(2.56 + 228)) / 0.4
x = (-1.6 ± sqrt(230.56)) / 0.4
x = (-1.6 ± 15.18) / 0.4
Now we have two solutions:
x1 = (-1.6 + 15.18) / 0.4 = 33.95
x2 = (-1.6 - 15.18) / 0.4 = -44.95
Since the number of shooting shirts cannot be negative, we discard the negative solution.
Therefore, the basketball coach can order approximately 34 shooting shirts for $300.
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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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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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Qn in attachment. ..
Answer:
option c
Step-by-step explanation:
n²-1/2
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Using the equation of the line of best fit, estimate the number of coffee drinks sold on a day that 32 ice cream treats
were sold.
write an explanation that justifies your conclusion.
The number of coffee drinks sold on a day that 32 ice cream treats were sold using the equation of line of best fit is y = 32m + b, where y represents the number of coffee drinks sold and ice cream treats that were sold = 32.
To estimate the number of coffee drinks sold on a day that 32 ice cream treats were sold, we would need to use the equation of the line of best fit. This equation represents the trend of the data collected and can be used to make predictions based on that trend.
Assuming that the data collected shows a positive correlation between the number of ice cream treats sold and the number of coffee drinks sold, we can use the equation of the line of best fit to estimate the number of coffee drinks sold on a day that 32 ice cream treats were sold.
Let's say that the equation of the line of best fit is y = mx + b, where y represents the number of coffee drinks sold and x represents the number of ice cream treats sold. Using the data collected, we can find the values of m and b that best fit the trend.
Once we have the equation, we can substitute x = 32 into the equation and solve for y. This will give us an estimate of the number of coffee drinks sold on a day that 32 ice cream treats were sold.
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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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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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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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