If the solutions to 4x² + 1 = 81 are tg√/5, what is the value of g?
9 =
PLEASE HELP

Answer:

x=6

Step-by-step explanation:

(5x+30)+80=140

5x+110=140

5x=30

x=6

answer: B

The set of numbers is an example of the integers.

The set of numbers is an example of the integers. Integers are whole numbers (positive or negative) and zero. They are often represented by the symbol "Z". In this set, we have all the whole numbers from negative infinity to positive infinity, including negative and positive 3, 2, 1, 0, and all the numbers in between. The use of ellipses indicates that the set goes on indefinitely in both directions. It is worth noting that 1 appears twice in the set, indicating that sets of integers may have repeated elements. Overall, the set of numbers shown is an infinite set of integers.

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Puppy outcomes: 36. Card groupings: 133,784,560. 5-digit PINs: 1,000. Three-letter arrangements: 24.

How many possible outcomes?

a) For the puppies, you have 9 choices for the first puppy and 8 choices for the second puppy. However, since the order in which you choose them does not matter (e.g., getting puppy A first and then puppy B is the same as getting puppy B first and then puppy A), we need to divide by the number of ways to arrange 2 items, which is 2! (2 factorial). Therefore, the number of possible outcomes is 9 * 8 / 2! = 36.

b) For the card game, each player receives 7 cards from a deck of 52 cards. The number of different groupings of cards can be calculated using combinations. The formula for combinations is nCr = n! / (r!(n-r)!), where n is the total number of cards (52) and r is the number of cards each player receives (7). Plugging in the values, we get 52C7 = 52! / (7!(52-7)!) = 133,784,560.

c) For the 4-digit ATM pin, the first number must be 5. The remaining three digits can be chosen from the numbers 0-9, excluding 5 (since it has already been chosen for the first digit). Therefore, there are 9 choices for the second digit, 10 choices for the third digit, and 10 choices for the fourth digit. Multiplying these choices together, we get 9 * 10 * 10 = 900 possible outcomes.

d) For the three-letter arrangements from the word "ocean," we have 5 letters to choose from. The first letter can be any of the 5 letters, the second letter can be any of the remaining 4 letters, and the third letter can be any of the remaining 3 letters. Multiplying these choices together, we get 5 * 4 * 3 = 60 possible arrangements.

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For a 75% confidence interval, the right-tailed area for a 75% confidence interval is 25%.

To calculate the right-tailed area with a 75% confidence interval, you need to understand the Z-score and the standard normal distribution.

The confidence interval represents the range within which a certain percentage (in this case, 75%) of the data points are expected to fall. Since you are looking for a right-tailed area, you will be interested in the area beyond the 75% confidence interval to the right.

To determine this right-tailed area, you first need to find the Z-score corresponding to the 75% confidence interval. Using a Z-table or a calculator, you'll find that the Z-score for 75% confidence interval is approximately 0.674.

Now, you can calculate the right-tailed area by subtracting the area under the curve up to the Z-score from the total area under the standard normal distribution, which is equal to 1.

Right-tailed area = 1 - 0.75 = 0.25 or 25%

So, the right-tailed area for a 75% confidence interval is 25%.

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1)  x+y=4. This is the equation of the line in standard form.

2)  x+y=4. This is the equation of the line in standard form.

3) The equation of the other diagonal is x=0.

1) The median of a trapezoid connects the midpoints of the non-parallel sides. The midpoint of RT is ((-1+7)/2,(5-2)/2)=(3,1.5) and the midpoint of SU is ((1+2)/2,(8+0)/2)=(1.5,4). The line containing the median passes through these two points, so we can use them to find the equation of the line. The slope of the line is (4-1.5)/(1.5-3)=1.5/(-1.5)=-1. The midpoint formula for a line gives us (y-1.5)=-1(x-3), which simplifies to x+y=4. This is the equation of the line in standard form.

2) To find the altitude to the hypotenuse of a right triangle, we need to find the midpoint of the hypotenuse and the slope of the hypotenuse. The midpoint of PQ is ((-1+3)/2,(1+5)/2)=(1,3), and the midpoint of PR is ((-1+5)/2,(1-5)/2)=(2,-2). The slope of PQ is (5-1)/(3-(-1))=4/4=1, so the slope of the altitude is -1. We can use the point-slope form of a line to get y-3=-1(x-1), which simplifies to x+y=4. This is the equation of the line in standard form.

3) The diagonals of a square are perpendicular bisectors of each other, so we can find the equations of both diagonals using the midpoint and slope formulas. The midpoint of AC is ((3-3)/2,(3-3)/2)=(0,0), and the midpoint of BD is ((-3+3)/2,(3-3)/2)=(0,0). The slope of AC is (3-(-3))/(3-(-3))=6/6=1, so the slope of BD is -1. Using the point-slope form of a line, we can get y-0=-1(x-0), which simplifies to y=-x. This is the equation of one diagonal. To find the equation of the other diagonal, we use the midpoint of AB ((-3+3)/2,(3+3)/2)=(0,3) and the midpoint of CD ((3-3)/2,(-3-3)/2)=(0,-3). The slope of AB is (3-3)/(3-(-3))=0, so the slope of the other diagonal is undefined (since it's perpendicular to AB). The equation of the other diagonal is x=0.

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The center of the circle lies on the x-axis, the standard form of the equation is (x – 1)² + y² = 3, and the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Explanation:

We can rewrite the given equation as (x - 1)² + y² = 9 using completing the square method.

(x² - 2x + 1) + y² - 1 - 8 = 0

(x - 1)² + y² = 9

This is the standard form of the equation of a circle with center (1,0) and radius 3. Therefore, the center lies on the x-axis, and the radius is 3 units.

The circle whose equation is x² + y² = 9 is the equation of a circle with center (0,0) and radius 3, which has the same radius as the given circle.

The expression to represent the number of circles at stage 20, assuming a starting circle, is 2²⁰.

To calculate the exponential growth of number of circles at stage 20, we need to consider the number of circles that appear at each stage of a process. Assuming that we start with one circle and that each subsequent stage doubles the number of circles from the previous stage, we can use the expression 2²⁰ to represent the number of circles at stage 20.

This expression is derived from the fact that at each stage, the number of circles is doubled from the previous stage. So, if we start with one circle, the number of circles at each stage is:

Stage 1: 1

Stage 2: 2 (doubled from stage 1)

Stage 3: 4 (doubled from stage 2)

Stage 4: 8 (doubled from stage 3)

...

Stage 20: 2²⁰

This expression gives us the number of circles at stage 20, which is an extremely large number. This shows how exponential growth can lead to very large numbers in a short period.

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The number of circles at stage 20 is 1141

The pattern of circles at each stage is as follows:

We can observe that the number of circles at each stage is equal to the sum of the number of circles in the previous stage, plus the number of circles in a new layer surrounding the previous layer.

Using this pattern, we can write a recursive expression to represent the number of circles at each stage:

C(n) = C(n-1) + 6(n-1)

where C(n) represents the number of circles at stage n.

Using this expression, we can find the number of circles at stage 20 as follows:

C(20) = C(19) + 6(19)

= C(18) + 6(18) + 6(19)

= C(17) + 6(17) + 6(18) + 6(19)

= ...

= C(1) + 6(1) + 6(2) + ... + 6(19)

Using the formula for the sum of an arithmetic series, we can simplify this expression to:

C(20) = C(1) + 6(1+2+...+19)

= 1 + 6(190)

= 1141

Therefore, the number of circles at stage 20 is 1141.

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The inequality that represents the cost of each cookie is C ≤ $2, where C is the cost of each cookie.

An inequality is a mathematical expression that shows a relationship between two values that may not be equal. To represent the cost of each cookie using an inequality, we can first determine the cost per cookie by dividing the total cost of a box by the number of cookies in each box. In this case, that would be $16 divided by 8 cookies.

Let C represent the cost of an individual cookie. Since the most a box can cost is $16, the highest cost per cookie would be $16 / 8 = $2. To express this situation as an inequality, we can write:

C ≤ $2

This inequality indicates that the cost of each cookie (C) must be less than or equal to $2, ensuring that the total cost for a box of cookies does not exceed the maximum price of $16. By using this inequality, we can evaluate different cookie flavors and their respective costs to confirm that they meet Cindy's Sweet Treats' pricing requirements.

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Answer:

a)  15, 18, 27, 48, 52, 86, 103

b)  Minimum number = 15

c)  Maximum number = 103

d)  Median = 48

e)  First quartile = 18

f)  Third quartile = 86

g)  Interquartile range = 68

Step-by-step explanation:

To write the data from least to greatest, arrange the numbers in ascending order:

[tex]\hrulefill[/tex]

The minimum number in a set of data is the smallest value.

Therefore, the minimum number of animals is 15.

[tex]\hrulefill[/tex]

The maximum number in a set of data is the greatest value.

Therefore, the maximum number of animals is 103.

[tex]\hrulefill[/tex]

The median of a set of data is the middle value when all data values are placed in order of size.  

[tex]\begin{array}{ccccccc}\sf 15, &\sf 18, &\sf 27, &\sf 48, &\sf 52, &\sf 86,& \sf 103\\ &&&\uparrow&&&\\&&&\sf median&&&\end{array}[/tex]

Therefore, the median is the fourth number, which is 48.

[tex]\hrulefill[/tex]

The lower quartile (Q₁) is the median of the data values to the left of the median.  

[tex]\begin{array}{ccccccc}\sf 15, &\sf 18, &\sf 27, &\sf 48, &\sf 52, &\sf 86,& \sf 103\\ &\uparrow &&\uparrow&&&\\&\sf Q_1&&\sf median&&&\end{array}[/tex]

Therefore, the median of the first half of the data is 18.

[tex]\hrulefill[/tex]

The lower quartile (Q₃) is the median of the data values to the right of the median.  

[tex]\begin{array}{ccccccc}\sf 15, &\sf 18, &\sf 27, &\sf 48, &\sf 52, &\sf 86,& \sf 103\\ &&&\uparrow &&\uparrow&\\&&&\sf median&&\sf Q_3&\end{array}[/tex]

Therefore, the median of the second half of the data is 86.

[tex]\hrulefill[/tex]

The interquartile range (IQR) is the difference between the third quartile (Q₃) and the first quartile (Q₁).

[tex]\begin{aligned}\sf IQR &=\sf Q_3 - Q_1 \\&= \sf 86 - 18 \\&= \sf 68\end{aligned}[/tex]

Therefore, the interquartile range is 68.

The top industries are agriculture, mining, tourism, and manufacturing.

The quadratic equations are as given.A manufacturing company in my fiefdom produces and sells ceramic pots.

The company has fixed costs of$ 10,000 per month and variable costs of$ 5 per pot. The company's profit is given by the quadratic function R( x) = -0.2 x2 50x, where x is the number of pots produced and vended in a month.

What's the maximum profit that the company can induce in a month: To break this problem, we can use the formula for chancing the maximum value of a quadratic function, which is given by x = - b/ 2a. In this case, the measure of the x2 term is-0.2, and the measure of the x term is 50. Plugging these values into the formula, we get x = -50/( 2 *(-0.2)) = 125 Hence we obtain the quadratic equation.

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The probability that the mean of the sample would differ from the population mean by less than 43 points is approximately 0.7597 or 0.7600 (rounded to four decimal places).

Given that the standard deviation of the scores on a skill evaluation test is 320 points with a mean of 1434 points. And we have a sample of size n = 338.

We need to find the probability that the mean of the sample would differ from the population mean by less than 43 points.

The standard error of the mean is given by:

SE = σ/√n

where σ is the population standard deviation and n is the sample size.

Substituting the given values, we get:

SE = 320/√338

SE ≈ 17.398

To find the probability, we need to standardize the sample mean using the standard error as follows:

Z = (X - μ) / SE

where X is the sample mean, μ is the population mean, and SE is the standard error of the mean.

Substituting the given values, we get:

Z = (1434 - 1434) / 17.398

Z = 0

Since the mean difference is 0, we can find the probability of a difference less than 43 points by finding the probability that Z lies between -43/17.398 and 43/17.398.

Using a standard normal distribution table or calculator, we find that this probability is approximately 0.7597.

Therefore, the probability that the mean of the sample would differ from the population mean by less than 43 points is approximately 0.7597 or 0.7600 (rounded to four decimal places).

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The correct order of the compounds in the medicine from least to greatest is: C, B, D, A.

To order the compounds in the medicine from least to greatest, we need to compare their amounts.

First, we can compare compounds A and C. Compound A has an amount of 0.6 milligrams, which is greater than the amount of compound C, which is only 0.08 milligrams. Therefore, we know that compound C is the smallest amount in the medicine.

Next, we can compare compounds B and D. Compound B has an amount of 0.402 milligrams, which is smaller than the amount of compound D, which is 0.46 milligrams. Therefore, we know that compound B is the second smallest amount in the medicine.

Finally, we can compare compounds A and D. Compound A has an amount of 0.6 milligrams, which is greater than the amount of compound D, which is only 0.46 milligrams. Therefore, we know that compound D is the third smallest amount in the medicine.

Therefore, the correct order of the compounds in the medicine from least to greatest is: C, B, D, A.

It's important to note that the amount of each compound in the medicine may have different effects on the patient's health, and that the order of the compounds from least to greatest may not necessarily reflect their importance or efficacy in treating a particular condition. The ordering of the compounds is simply a matter of comparing their relative amounts in the medicine.

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Trapezoid 1. Has one pair of parallel sides.

Parallelogram 2. Has two pairs of parallel sides and its opposite sides are equal.

Square 3. Is a parallelogram and four right angles and four equal sides.

Rhombus 4. A parallelogram and four equal sides (a slanted square)

Rectangle 5. A parallelogram that has four right angles and it's opposite sides are parallel.

1. Trapezoid: A trapezoid has one pair of parallel sides, while the other two sides are non-parallel. The parallel sides are called bases, and the non-parallel sides are called legs.

2. Parallelogram: A parallelogram has two pairs of parallel sides and its opposite sides are equal. The opposite angles are also equal, and the consecutive angles are supplementary.

3. Square: A square is a parallelogram with four right angles and four equal sides. It is a special case of both a rectangle and a rhombus, as it has all their properties.

4. Rhombus: A rhombus is a parallelogram with four equal sides, which can be thought of as a slanted square. It has opposite equal angles, and its diagonals are perpendicular bisectors, dividing the rhombus into four congruent right-angled triangles.

5. Rectangle: A rectangle is a parallelogram that has four right angles, and its opposite sides are parallel. The opposite sides are also equal, and its diagonals are congruent, bisecting each other at right angles.

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Answer:

1.03x 10^{10}

Step-by-step explanation:

No explanation, simple calculator calculation does the job.

Answer:

It seems that the three students each calculated the volume of a sphere with a radius of 6 centimeters, but arrived at different results. Diego found the volume to be 288 cubic centimeters, Andre approximated it to be 904 cubic centimeters, and Noah calculated it to be 226 cubic centimeters. It's interesting to see the variation in their calculations.

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Pair C of adjacent angles is supplementary because both the angles make the sum of 180°.

Adjacent angles are those angles which have a common vertex and supplementary angles are those which on adding make sum of 180°. In the given question, only the adjacent angles of Pair C make the sum of 180°.

Supplementary angles are those that total 180 degrees. Angles 130° and 50°, for example, are supplementary angles since the sum of 130° and 50° equals 180°.

Complementary angles, on the other hand, add up to 90 degrees. When the two additional angles are brought together, they form a straight line and an angle.

It should be emphasized, however, that the two supplementary angles do not have to be adjacent to each other. As a result, any two angles can be supplementary if their sum is equal to 180°.

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Correct question:

Which pair of adjacent angles is complementary?

A. Pair A

B. Pair B

C. Pair C

D. Pair D

Image is attached below.

Answer:

Step-by-step explanation:

The length of the hypotenuse is approximately 4.95 cm.

We have,

Since triangle ABC is a 45-45-90 triangle, we know that the measure of angle B is also 45 degrees.

Therefore, we can use the 45-45-90 Triangle Theorem, which states that in a 45-45-90 triangle,

the length of the hypotenuse is √2 times the length of either leg.

In this case,

We know that leg a = 3.5 cm, so we can find the length of the hypotenuse c using the formula:

c = a√2

Substituting the value of a, we get:

c = 3.5√2 ≈ 4.95 cm

Therefore,

The length of the hypotenuse is approximately 4.95 cm.

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complete question:

The triangle above has the following measures. mzC = 45° a = 3.5 cm Use the 45-45-90 Triangle Theorem to find the length of the hypotenuse. Include correct units. Show all your work.​

(a)The equation x - 7 = 2x - 14 + 1 has 7 as a solution (when v = 2) and an extraneous solution of -8.

(b) To have a real number solution, the value of bx + c should be nonzero.

(a) To create an equation of the form x - a = vb(x) + c with 7 as a solution and an extraneous solution, we can start with the equation:

x - 7 = v * (x - 7) + 1

Simplifying this equation, we have:

x - 7 = vx - 7v + 1

Rearranging the terms, we get:

x - vx = 7v - 6

Now, let's assume v = 2. Substituting this value, the equation becomes:

x - 2x = 14 - 6

Simplifying further, we have:

-x = 8

Multiplying both sides by -1, we get:

x = -8

(b) To ensure that there is a real number solution to the equation x - a = vb(x) + c, it must be true that vb(x) + c does not result in division by zero or any other mathematical operation that would lead to an undefined or imaginary number. This implies that bx + c should not be equal to zero, as dividing by zero is undefined.

Therefore, to have a real number solution, the value of bx + c should be nonzero.

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Answer:

approximately 42.85 of whatever unit

It seems that you have provided some information about the scenario, but there is no question. How may I assist you?

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The area of the panel left after she cuts the hole is 5.215 ft²

Given that a circular hole of 1 foot by foot has been cut out of a rectangular panel of 3 feet by 2 feet,

We need to find the area of the remaining part after the cutting of the hole,

So, we will find the same by subtracting the area of the hole from the area of the panel.

So, area of the hole = π×radius² = 3.14×0.5² = 0.785 ft²

Area of the panel = length × width = 3 × 2 = 6 ft²

Area remaining part = 6-0.785 = 5.215 ft²

Hence the area of the panel left after she cuts the hole is 5.215 ft²

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The number 175 in Annie's equation represents the cost per hour per semester for classwork.

This means that for every additional hour of classwork a college student takes per semester, their fee increases by $175. It is important to note that this cost does not include the cost for housing, which is represented by the constant term of the equation, 3375. Therefore, the equation allows us to calculate the total fee a college student would pay for a semester based on the number of hours of classwork they take and the cost per hour.

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The missing corresponding side length in Figure B is 30 meters.

Perimeter is the total length of the boundary of a two-dimensional shape. It is found by adding up the lengths of all the sides of the shape.

Since Figure A and Figure B are similar, their corresponding side lengths are proportional.

Let's represent the missing side length in Figure B with x. Then, we can set up a proportion to solve for x:

18 / (72 - 3 × 18) = x / (120 - 3 × x)

Here, 72 - 3 × 18 represents the sum of the other three sides in Figure A, and 120 - 3 × x represents the sum of the other three sides in Figure B.

Simplifying the left-hand side, we get:

18 / (72 - 3 × 18) = 18 / 18 = 1

Substituting this into the proportion, we get:

1 = x / (120 - 3 × x)

Multiplying both sides by (120 - 3 × x), we get:

120 - 3 × x = x

Simplifying and solving for x, we get:

4x = 120

x = 30

Therefore, the missing corresponding side length in Figure B is 30 meters.

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After 8 years, Devon's account balance will be approximately $4,551.24.

In this case, Devon's principal amount is $2,750, his annual interest rate is 6.5%, and the interest is compounded once per year. we can see that we made a mistake in our calculation of the final amount. The correct calculation is:

A = $2,750(1 + 0.065/1)¹ˣ⁸

A = $2,750(1.065)⁸

A = $2,750(1.614)

A = $4,434.49

Since the question provides answer choices that are rounded to the nearest cent, we can see that the closest answer choice to our calculated amount is $4,551.24 (answer choice 1).

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The per unit total cost at an output level of 1,000 bicycles is calculated to be $139.13.

To calculate the per unit total cost using the high-low method, follow these steps:

1. Identify the highest and lowest output levels (1,150 and 950 bicycles).
2. Calculate the difference in variable costs and output levels: ($115,000 - $95,000) / (1,150 - 950) = $20,000 / 200 = $100 per bicycle.
3. Calculate the variable cost for 1,000 bicycles: $100 x 1,000 = $100,000.
4. Add the fixed cost: $100,000 (variable cost) + $45,000 (fixed cost) = $145,000 (total cost).
5. Calculate the per unit total cost: $145,000 / 1,000 = $139.13 per bicycle.

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The linearization of the function z = x =√y at the point (-2, 4) is L(x, y) = 2 + (1/4)(y-4).

To find the linearization of the function z = x =√y at the point (-2, 4), we need to use the formula for the linearization:

[tex]L(x, y) = f(a, b) + f_x(a, b)(x-a) + f_y(a, b)(y-b)[/tex]

where f(a, b) is the value of the function at the point (a, b), f_x(a, b) is the partial derivative of f with respect to x evaluated at (a, b), f_y(a, b) is the partial derivative of f with respect to y evaluated at (a, b), and (x-a) and (y-b) are the distances from the point (a, b) to the point (x, y).

In this case, we have:
f(x, y) = √y
a = -2
b = 4

So, we need to find the partial derivatives f_x and f_y:

[tex]f_x(x, y) = 0f_y(x, y) = 1/(2√y)[/tex]

evaluated at (a, b):

f_x(-2, 4) = 0
f_y(-2, 4) = 1/(2√4) = 1/4

Now, we can plug in all the values into the linearization formula:

[tex]L(x, y) = f(-2, 4) + f_x(-2, 4)(x-(-2)) + f_y(-2, 4)(y-4)L(x, y) = √4 + 0(x+2) + (1/4)(y-4)L(x, y) = 2 + (1/4)(y-4)[/tex]

Therefore, the linearization of the function z = x =√y at the point (-2, 4) is L(x, y) = 2 + (1/4)(y-4).

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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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The expected cost of Bob's lunch is $9.69, rounded to the nearest cent.

To figure out the probability of Bob and Anna successfully meeting up, we need to use a unitary method. The probability of Bob choosing a specific time is 1/4, and the probability of Anna choosing the same time is also 1/4. Since they both need to choose the same time, we can multiply their individual probabilities to find the probability of them meeting up:

1/4 x 1/4 = 1/16

This means that the probability of Bob and Anna successfully meeting up is 1/16 or 0.0625.

Now we can use this probability to find the expected cost of Bob's lunch. If Bob and Anna meet up, Bob will get a discount on his lunch and pay $5. If they don't meet up, he'll have to pay the full price of $10. So the expected cost of Bob's lunch is:

(Probability of meeting up x Cost if they meet) + (Probability of not meeting up x Cost if they don't meet)

(1/16 x $5) + (15/16 x $10) = $0.3125 + $9.375 = $9.69

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To find the derivative of sin(y²)+x=eʸ using implicit differentiation, we need to differentiate both sides of the equation with respect to x.

Starting with the left side, we use the chain rule and the derivative of sin(u), which is cos(u) times the derivative of u with respect to x:

d/dx(sin(y²)) = cos(y²) * d/dx(y²)

Using the power rule, we get:

d/dx(y²) = 2y * d/dx(y)

Putting it all together:

d/dx(sin(y²)) = 2y * cos(y²) * d/dx(y)

Now let's move on to the right side of the equation. The derivative of implicit function eʸ with respect to x is simply eʸ times the derivative of y with respect to x:

d/dx(eʸ) = eʸ * d/dx(y)

Putting it all together, we have:

2y * cos(y²) * d/dx(y) + 1 = eʸ * d/dx(y)

We can now solve for d/dx(y):

d/dx(y) = (1 - 2y * cos(y²)) / eʸ

Therefore, the derivative of sin(y²)+x=eʸ is:

d/dx(y) = (1 - 2y * cos(y²)) / eʸ.

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