In Northern California, Oceana's scientists tested 89
samples of fish labeled as snapper, and 38 came back
as rockfish. What's the experimental probability of buying
snapper mislabeled as rockfish?

To find the critical points at which profit is maximized given the total revenue TR = 4700 - 302 and total cost TC = 320/10,500, we need to compute the marginal revenue and marginal cost, equate MR = MC to find the optimal quantity Q∗, verify if Q∗ is a relative maximum point, and compute the maximum profit level (π) by evaluating π∗ = 9(π(Q∗)).

Marginal Revenue (MR) is the derivative of the total revenue function with respect to quantity (Q). In this case, MR = dTR/dQ. By taking the derivative of TR = 4700 - 302 with respect to Q, we can find the expression for MR.

Marginal Cost (MC) is the derivative of the total cost function with respect to quantity (Q). In this case, MC = dTC/dQ. By taking the derivative of TC = 320/10,500 with respect to Q, we can find the expression for MC.

To find the optimal quantity Q∗, we equate MR and MC by setting MR = MC and solve for Q. This is because profit is maximized when MR equals MC.

Once we have found Q∗, we need to verify if it is a relative maximum point. This can be done by checking the second derivative of the profit function and determining if it is negative at Q∗. If the second derivative is negative, it confirms that Q∗ is a relative maximum point.

Finally, to compute the maximum profit level (π∗), we evaluate π(Q∗) by substituting Q∗ into the profit function. In this case, we can multiply the value of π(Q∗) by 9 to obtain the maximum profit level (π∗).

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Answer:

1. acute angle, 2.right angle, 3.obtuse angle

Step-by-step explanation:

Answer:

If the game with 3 hits is ignored the data becomes:

a) The mean will increase.

With 3:

Without 3:

b) The median will remain as is.

Answer:

277.778 m/s

Step-by-step explanation:

just divide by 3.6

The integers in the set S that make the inequality 3(-5) > 3(7-2j) true are {-4, 6}.

To determine which integers in the set S = {-4, 4, 6, 21} make the inequality 3(-5) > 3(7-2j) true, we can simplify the inequality and compare the values.

First, let's simplify the inequality:

3(-5) > 3(7-2j)

-15 > 21 - 6j

Now, let's compare the values of -15 and 21 - 6j:

Since -15 is less than 21 - 6j, we can conclude that the inequality 3(-5) > 3(7-2j) is true.

Now, let's determine which integers in the set S satisfy the inequality. The integers in the set S that are less than 21 - 6j are:

-4 and 6

Therefore, the integers in the set S that make the inequality 3(-5) > 3(7-2j) true are {-4, 6}.

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The z-score corresponds to 0.275 is -0.63.

The specific number of skateboards corresponding to the z-score from part (a) is 20,468.

We have,

(a)

To find the z-score corresponding to a specific percentage of days, we can use the standard normal distribution table or a calculator.

In this case, we are given that 45% of the days had a production of skateboards less than the specific value.

Since the standard normal distribution is symmetrical, we can find the z-score corresponding to 45% by finding the z-score that corresponds to

(1 - 0.45) / 2 = 0.275, which is the area to the left of the z-score.

Using the standard normal distribution table or a calculator,

We find that the z-score corresponds to 0.275 is:

= -0.63.

(b)

To find the specific number of skateboards corresponding to the z-score, we can use the formula:

x = μ + zσ

where x is the specific number of skateboards, μ is the mean (20,500), z is the z-score (-0.63), and σ is the standard deviation (55).

Substituting the values.

x = 20,500 + (-0.63) x 55

x = 20,468.35

Rounding to the nearest whole number,

x = 20,468.

Therefore,

The z-score corresponds to 0.275 is -0.63.

The specific number of skateboards corresponding to the z-score from part (a) is 20,468.

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Answer:

\(k = 1\)

Step-by-step explanation:

Given

\(3y = 5x + k\)

Opposite points: \((1,-2)\) and \((-2,1)\)

Required

Find k

First, calculate the midpoint of the opposite points.

\((x,y) = 0.5(x_1 + x_2,y_1 + y_2)\)

This gives:

\((x,y) = 0.5(1 -2,-2 + 1)\)

\((x,y) = 0.5(-1,-1)\)

Open bracket

\((x,y) = (-0.5,-0.5)\)

The equation \(3y = 5x + k\) becomes:

\(3 * -0.5 = 5 * -0.5 + k\)

\(-1.5 = -2.5 + k\)

Solve for k

\(k = 2.5-1.5\)

\(k = 1\)

The 15 and 9 units side lengths of the parallelogram ABCD, and the 36° measure of the acute interior angle, A indicates the values of the ratios are;

1. AB:BC = 5:3

2. AB:CD = 1:1

3. m∠A : m∠C= 1 : 4

4. m∠B:m∠C = 4:1

5. AD: Perimeter ABCD = 3:16

A ratio is a representation of the number of times one quantity is contained in another quantity.

The shape of the quadrilateral ABCD in the question = A parallelogram

Length of AB = 15

Length of BC = 9

Measure of angle m∠A = 36°

Therefore;

1. AB:BC = 15:9 = 5:3

2. AB ≅ CD (Opposite sides of a parallelogram are congruent)

AB = CD (Definition of congruency)

AB = 15, therefore, CD = 15 transitive property

AB:CD = 15:15 = 1:1

3. ∠A ≅ ∠C (Opposite interior angles of a parallelogram are congruent)

Therefore; m∠A = m∠C = 36°

∠A and ∠D are supplementary angles (Same side interior angles formed between parallel lines)

Therefore; ∠A + ∠D = 180°

36° + ∠D = 180°

∠D = 180° - 36° = 144°

∠D = 144°

m∠A : m∠C = 36°:144° =1:4

m∠A : m∠C = 1:4

4. ∠B = ∠D = 144° (properties of a parallelogram)

m∠B : m∠C = 144° : 36° = 4:1

5. AD ≅ BC (opposite sides of a parallelogram)

AD = BC = 9 (definition of congruency)

The perimeter of the parallelogram ABCD = AB + BC + CD + DA

Therefore;

Perimeter of parallelogram ABCD = 15 + 9 + 15 + 9 = 48

AD:Perimeter of the ABCD  = 9 : 48  = 3 : 16

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Approximately 99.7% ( or 99.73% ) population  lies within  3 standard deviation   ( μ - 3σ , μ + 3σ ) = ( 38, 68 ) .

Why is there a standard deviation?

Empirical rule holds only for normal populations and states that

approximately 68% ( or 68.27%) population lies within  standard deviation

                          ( μ - σ , μ + σ ) = ( 48 , 58 )

Approximately 95% ( or 95.45% ) population  lies within 2  standard deviation  

                    ( μ - 2σ , μ + 2σ ) = ( 43, 63 )

Approximately 99.7% ( or 99.73% ) population  lies within  3 standard deviation  

                        ( μ - 3σ , μ + 3σ ) = ( 38, 68 )

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We know that with a 700 credit score we pay $23 per $1000 financed, then the monthly payment will be:

Therefore for a 700 credit score tour monthly payment is $657.50

Answer : $28.00

Step-by-step explanation: because it says on the chart the 590-619 it would be $28.00.

The percentage of Measurements that are 124.4 or higher is approximately 0.99%.

In order to determine the percentage of measurements that are 124.4 or higher in a population of measurements that is approximately normal with a mean of 95 and a standard deviation of 15, we need to use the z-score formula.

The z-score formula is used to standardize a distribution so that it can be compared to a normal distribution with a mean of 0 and a standard deviation of 1.

The formula for calculating the z-score is: z = (x - μ) / σWhere:x is the measurement we want to standardize.μ is the population mean.σ is the population standard deviation.

The first step is to calculate the z-score for the measurement of 124.4:z = (124.4 - 95) / 15z = 2.2933The second step is to find the percentage of measurements that are 124.4 or higher using a standard normal distribution table. We look up the area to the right of the z-score of 2.2933 in the table.

The closest value in the table is 0.9901, which corresponds to a z-score of 2.33. We know that the area to the left of a z-score of 2.33 is 0.9901, so the area to the right of a z-score of 2.33 is:1 - 0.9901 = 0.0099

This means that approximately 0.99% of the measurements are 124.4 or higher.

Therefore, the percentage of measurements that are 124.4 or higher is approximately 0.99%.

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She makes a minimum monthly payment of 62.52 dollars. Then the correct option is B.

The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.

May currently has a balance of $1,817.43 on her credit card.

If she must make a minimum monthly payment of 3.44% of her total balance.

Then the minimum payment will be given as

Minimum payment = 0.0344 × 1817.43

Minimum payment = 62.519 ≅ 62.52

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Answer:

\(64 \frac{1 3}{21} ft {}^{2} \)

Step-by-step explanation:

Area of the garden:

\((8 \frac{3}{7} \times 7 \frac{2}{3} )ft {}^{2} \\ \\ ( \frac{59}{7} \times \frac{23}{ 3} )ft {}^{2} \\ \\ = \frac{1357}{21} ft {}^{2} \\ \\ = 64 \frac{13}{21} ft {}^{2} \: (ans)\)

Answer:

the relation in the table is a function

the relation in the set of points is not a function

Step-by-step explanation:

the definition of a function is that one input (x) can only have one output (y). In the set of points, the input 4 appears twice, which means it is not a function.

The modulus of a complex number is defined as the distance between the complex number and the origin in the Argand plane.

The correct definition of the modulus of a complex number is option B: the distance between the complex number, denoted as z, and the origin in the Argand plane. The Argand plane is a two-dimensional plane where the real part of the complex number is represented on the x-axis, and the imaginary part is represented on the y-axis. In this plane, the complex number z is represented as a point with coordinates (a, b), where 'a' is the real part and 'b' is the imaginary part.

The modulus of z, denoted as |z|, can be calculated using the distance formula from Euclidean geometry. It is given by the square root of the sum of the squares of the real and imaginary parts of z. Mathematically, |z| = √(a^2 + b^2). This modulus represents the length of the line segment connecting the origin to the point (a, b) in the Argand plane.

In summary, the modulus of a complex number is defined as the distance between the complex number and the origin in the Argand plane. It is calculated using the square root of the sum of the squares of the real and imaginary parts of the complex number.

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(a) The probability of having at least one girl is 1 - 0.0625 = 0.9375 or 93.75%.

(b) The probability that all the children will be of the same gender is 0.0625 + 0.0625 = 0.125 or 12.5%.

The probability of having at least one girl can be calculated by finding the probability of having no girls and subtracting it from 1.

Assuming that the probability of having a boy or a girl is equal (0.5), the probability of having no girls is (0.5)^4 = 0.0625.

Therefore, the probability of having at least one girl is 1 - 0.0625 = 0.9375 or 93.75%.

(b) The probability that all the children will be of the same gender is 0.0625 + 0.0625 = 0.125 or 12.5%.

The probability that all the children will be of the same gender can be calculated by finding the probability of having all boys and adding it to the probability of having all girls.

The probability of having all boys is (0.5)^4 = 0.0625, and the probability of having all girls is also 0.0625.

Therefore, the probability that all the children will be of the same gender is 0.0625 + 0.0625 = 0.125 or 12.5%.

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Answer:

Step-by-step explanation:

Hello there!

Parallel lines have the same slope.

So if one line has a slope of 4, then the slope of the line parallel to it has a slope of 4 as well.

Hope it helps!

Please mark Brainliest!

~Just a determined gal

\(MysteriousNature\) here to help

Step 1. Identify the variables.

Step 2. Find the first constraint using the condition for the total number of books in each box.

The problem states "Christina needs to pack the boxes so there are at least 20 books in each box" This means that the sum of x and y must be at least 20, this is represented in the following inequality:

That is the first constraint.

Step 3. Find the second constraint using the condition for the weight of each box.

The problem states: "the boxes cannot weigh more than 30 pounds" and since the paperback books weigh 0.8 pounds and the hardcover books weigh 1.3 pounds each, the sum of their weights is:

This sum cannot be more than 30, which is represented by the following inequality:

Answer:

The set of constraints is

Answer:

150%

Step-by-step explanation:

15 / 10 =

1.5 =

150%

Answer:

5a^2/2

Step-by-step explanation:

Answer: 3.2

Step-by-step explanation:

1/2 a = 5a

0.2164 is probability that exactly 4 of the couples said that they paid for their honeymoon.

What are examples and probability?

If x = no of married couples out of 5 who paid for their honeymoon .

then X ~ ( 5 , 0.56 )

P (X = 4 ) =  5C4( 0.56 )⁴ ( 0.44)¹

                = 0.2164

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In what direction is the derivative of f(x,y) = xy + y2 at P(4,9) equal to zero

then, the value is (5,22).

Directional Derivative:

The directional derivative of a function

\(D_u\) f(x, y) at a point (x0,y0) in the direction of the unit vector \(u^{-}\), denoted

f(x0,y0), can be calculated by first evaluating the gradient of f at this

point :

∇f(x₀, y₀) = ⟨∂f/∂x(x₀, y₀),∂f/∂y (x₀, y₀)⟩

and then computing the dot product of this with the given unit vector:

\(D_u\) f(x₀, y₀) = ∇f(x₀, y₀) × \(u^{-}\)

If the directional derivative of a function at a point is zero in some direction, then the unit vector must be perpendicular to the gradient at that point.

Given that:

f(x, y) = xy + y² at P(4,9)

Now,

f(x, y) = xy + y²

⇒ fₓ = δ/δₓ f(x, y)

       = y

And,

(fₓ)₍₅,₉₎ = 4

 \(δ_y\) = \(δ\)/\(δ_y\) f(x, y)

      = (x + 2y)

      = 4 + 2× 9

      = 22

Therefore,

Δf₍₅,₉₎ = { y, x+2y}

        = {4,22}

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Answer:

5

Step-by-step explanation:

20000*7=140,000

1.4 * 10 to the 5 power,

So its order of magnitude is 5.

Using index notation, the expression can be written more compactly as:

∑(c_ix_i) = 40

In the given expression, we have three terms: \(c_{1}\)\(x_{1}\), \(c_{1}\)\(x_{2}\), and \(c_{3}\)\(x_{3}\). Each term represents the product of a coefficient (c₁, c₂, or c₃) and a variable (x₁, x₂, or x₃). The sum of these three terms equals 40.

In order to write this expression using index notation, we introduce the index i to represent the three variables. We can rewrite the terms as c_ix_i, where i takes the values 1, 2, and 3.

The notation ∑(c_ix_i) represents the sum of all terms c_ix_i over the range of i. In this case, it represents the sum of \(c_{1}\)x₁, \(c_{2}\)\(x_{2}\), and \(c_{3}\)\(x_{3}\).

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The number of shares he buy is $615.

Given that Barney just bought stock in Purple Dinosaur Industries and he paid a total of $7,380 and the price of the stock is $12 for one share.

We want to find the number of shares Barney buys.

The total amount barney should pay is $7380.

The price of the stock for one share is $12.

The total number of shares barney buy is 7380/12=615.

Hence, the number of shares barney should buy when he paid a total $7380 and the price of stock for one share is $12 is $615.

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The value of $40,000 in today's dollars, considering an annual discount rate of 8% and a time period of 10 years, is approximately $21,589.

To calculate the present value of $40,000 in 10 years with an annual discount rate of 8%, we can use the formula for present value:

Present Value = Future Value / (1 + Discount Rate)^Number of Periods

In this case, the future value is $40,000, the discount rate is 8%, and the number of periods is 10 years. Plugging in these values into the formula, we get:

Present Value = $40,000 / (1 + 0.08)^10

Present Value = $40,000 / (1.08)^10

Present Value ≈ $21,589

This means that the value of $40,000 in today's dollars, taking into account the time value of money and the discount rate, is approximately $21,589. This is because the discount rate of 8% accounts for the decrease in the value of money over time due to factors such as inflation and the opportunity cost of investing the money elsewhere.

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