the population, p, of a species of fish is decreasing at a rate that is proportional to the population itself. if p=400000 when t=2 and p=350000 when t=4, what is the population when t=10?

The probability that the sample mean income is between 38 and 53 thousand dollars is approximately 0.678, or 67.8%.

To find the probability that the sample mean income is between 38 and 53 thousand dollars, we'll use the terms mean, standard deviation, sample size, and z-scores in our calculations.

Here's a step-by-step explanation:

1. Calculate the mean and standard deviation of the sample distribution:
Mean (µ) = 47 (given)
Standard deviation (σ) = 44 (given)
Sample size (n) = 35 (given)

2. Calculate the standard error (SE):
SE = σ / √n = 44 / √35 ≈ 7.44

3. Convert the given range of sample mean incomes (38 and 53) to z-scores:
z1 = (38 - µ) / SE = (38 - 47) / 7.44 ≈ -1.21
z2 = (53 - µ) / SE = (53 - 47) / 7.44 ≈ 0.81

4. Use a z-table or calculator to find the probability between the two z-scores:
P(-1.21 < Z < 0.81) = P(Z < 0.81) - P(Z < -1.21)

≈ 0.791 - 0.113 = 0.678

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Answer:

471 cm^3

(none of the answers above are correct)

Step-by-step explanation:

Volume of cylinder = πr^2 × h

= 3.14 × 5^2 × 6

= 3.14 × 25 × 6

= 471 cm^3

Answer:

3*81/100

Step-by-step explanation:

According to the information, the volume of the solid resulting from the region enclosed by the curves y = 6 - 2x and y = 2 being rotated about the x-axis is (128π/3) cubic units.

To find the volume of the solid formed by rotating the region enclosed by the curves about the x-axis, we can use the method of cylindrical shells.

First, determine the limits of integration. In this case, we need to find the x-values at which the two curves intersect. Setting the equations y = 6 - 2x and y = 2 equal to each other, we can solve for x:

So, the limits of integration are x = 0 to x = 2.

Secondly, set up the integral. The volume of each cylindrical shell can be calculated as V = 2πrh, where r is the distance from the axis of rotation (x-axis) to the shell, and h is the height of the shell (the difference in y-values between the curves).

The radius r is simply x, and the height h is given by h = (6 - 2x) - 2 = 4 - 2x.

Thirdly, integrate the expression. The integral that represents the volume of the solid is:

Simplifying this expression and integrating, we get:

So, the volume of the solid is (16π/3) cubic units, or approximately 16.8 cubic units.

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Answer:

x = -0.01685

(Is the equation written correctly?  This feels like a very unfortunate number)

Step-by-step explanation:

(2x+5/60-95x-3/30=3/2

2x+(5/60)-95x-(3/30)=3/2

2*(2x+(5/60)-95x-(3/30))=3     [Multiply both sides by 2]

4x+(10/60)-190x-(6/30))=3      

(2/30)-186x-(6/30))=3              [Simplify]

-186x-(4/30)=3

-186x=3+(4/30)

-186x=(90/30)+(4/30)

x = (94/30)/(-186)

x = -0.01685

Answer:

x = 0 or x = 7

Step-by-step explanation:

I have showed all steps on the image, if you have any other questions you can ask.

The equation which represents the relationship between 'h' the number of hours, and c, the total cost is y = 250x+850.

A straight line equation is a mathematical equation that describes the relationship between the coordinate points on that straight line. It can be written in several ways and indicates the slope, x-intercept, & y-intercept of a line.

Now, as per the given question;

The attorney charges price for an initial meeting = $850.

And, the charges for each hour is = $250.

Thus, the equation which shows the given situation is-

y = 250x + 850.

In which, 250 is the value of the slope 'm'.

The y- intercept is shown by 850.

Thus, the total cost will be found out by equation  y = 250x+850.

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{Y(t), t ≥ 0} is a Martingale when Y(t) = B₂(t) – t

To show that {Y(t), t ≥ 0} is a Martingale, we need to prove that E[Y(t)|F(s)] = Y(s) for all s ≤ t, where F(s) is the sigma-algebra generated by B(u), 0 ≤ u ≤ s.

Using the hint, we can compute E[Y(t)|F(s)] as follows:

E[Y(t)|F(s)] = E[B₂(t) - t |F(s)]

= E[B₂(t)|F(s)] - t   (by linearity of conditional expectation)

= B₂(s) - t  (since B₂(t) - t is a Martingale)

Therefore, we have shown that E[Y(t)|F(s)] = Y(s) for all s ≤ t, and thus {Y(t), t ≥ 0} is a Martingale.

To compute E[Y(t)], we can use the definition of a Martingale: E[Y(t)] = E[Y(0)] = E[B₂(0)] - 0 = 0.

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Given question is incomplete, the complete question is below

.Show that {Y(t), t ≥ 0} is a Martingale when

Y(t) = B₂(t) – t

What is E[Y(t)]?

Hint: First compute E[Y(t)|B(u), 0 ≤ u ≤ s].

Answer:

4

Step-by-step explanation:

The mean is another word for average

Add the number of goals

3+7+2 = 12

Divide by the number of data points

12/3 = 4

The mean is 4

Answer:

4

Step-by-step explanation:

Hope this helps

Answer:

I think the answer should be two and a half pieces

Answer:

information

Step-by-step explanation:

I don't know information I guess

The angle x in the diagram is 98 degrees.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angle, alternate exterior angles, vertically opposite angles, same side interior angles etc.

Therefore, let's find the angle of x using the angle relationships as follows:

The size of the angle x can be found as follows:

82 + x = 180(same side interior angles)

Same side interior angles are supplementary.

Hence,

82 + x = 180

x = 180 - 82

x = 98 degrees

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Answer:

The pizza restaurant put 1/10 of the sauce on each pizza.

Step-by-step explanation:

Take the 3/5, and on a calculator divide the 3 by the 5:

0.6

Then, take the 0.6 and divide it by the 6 pizzas:

0.1, converted into a fraction equals 1/10.

The pizza restaurant put 1/10 of the sauce on each pizza.

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 10 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

Solution

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given logarithmic expression

STEP 2: Find the value of x

State the rule of logarithm that applies

Apply the rule

Hence, the value of x is approximately 10.56

Answer:

$287.88

Step-by-step explanation:

Multiply 119.95 by 3.

You get 359.85

Multiply that by 80% or 0.8

The answer is 287.88

Answer:

5.15

Step-by-step explanation:

I hope this helps have a great day

Answer:

y = - 5/2

Step-by-step explanation:

The error represented in this scenario is an inappropriate task allocation or a mismatch between job responsibilities and the assigned task during the interview process.

The primary role of a customer service representative is to interact with customers, address their concerns, and log calls professionally and efficiently. In contrast, performing a detailed analysis of call-in data falls under the domain of data analysis or business intelligence roles.

By asking the candidate to perform a task unrelated to their potential job responsibilities, the company may not accurately assess the candidate's aptitude for customer service tasks. This error could lead to selecting a candidate who may excel in data analysis but may not possess the necessary communication and problem-solving skills required for a customer service representative position.

To avoid this error, the company should focus on evaluating candidates based on their skills, experience, and performance in tasks directly relevant to the customer service role.

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The numbers that represent A, B and C in the table for the cubic functions are: A = -12, B = -9 and C = 8

In mathematics, a cubic function is defined as a function of the form f(x) = ax³ + bx² + cx + d.

Where the coefficients a, b, c, and d are real numbers, and the variable x takes real values, and a ≠ 0. This means that, it is both a polynomial function of degree three, and a real function.

We are given the expression:

y = 3x³ + x² - 7x - 6

When x = -2, we have:

y = 3(-2)³ + (-2)² - 7(-2) - 6

y = -24 + 4 + 14 - 6

y = -12

When x = 1, we have:

y = 3(1)³ + (1)² - 7(1) - 6

y = 3 + 1 - 13

y = -9

When x = 2, we have:

y = 3(2)³ + (2)² - 7(2) - 6

y = 24 + 4 - 14 - 6

y = 8

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Answer:

53.9

Step-by-step explanation:

:)

1.2 seconds  it take the sunglasses to hit the ground

To find how long it takes for the sunglasses to hit the ground, we need to find the value of x when h = 0.

We can set the function equal to 0 and solve for x:

-16x² + 24 = 0

Dividing both sides by -16 gives:

x² - (24/-16) = 0

x² - 1.5 = 0

x² = 1.5

x = ±√1.5

x = √1.5 seconds for the sunglasses to hit the ground.

we get x = 1.2 seconds.

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The verification that PAP^-1 = I shows that the matrix A and its inverse A^-1 work together to transform and restore the base vectors, maintaining the integrity of the original coordinate system.

In linear algebra, matrices are used to represent linear transformations. When we have a matrix A and a base, we can apply the matrix transformation to the base vectors to see how they are affected. In this case, we are given a matrix A and a base p, and we want to verify that when we apply the transformation to the base vectors and then invert the result, we get the identity matrix I.

Let's break down the steps to understand the process:

We start with the base p, which consists of a set of vectors. These vectors serve as a coordinate system or a frame of reference.

Next, we apply the matrix transformation A to each vector in the base p. This means we take each vector from the base and multiply it by the matrix A. This multiplication represents how each vector is transformed or stretched, rotated, or skewed by the matrix.

After applying the matrix transformation, we obtain a new set of vectors, which we can call Ap. These vectors represent the transformed base under the influence of matrix A.

Now, we want to revert the transformation and go back to the original base p. To do this, we need to find the inverse of matrix A, denoted as A^-1.

We take the transformed vectors Ap and multiply them by the inverse matrix A^-1. This step effectively undoes the transformation and brings us back to the original base p.

Finally, we observe that the resulting vectors are exactly the same as the original base p. In other words, when we apply the transformation A to the base p and then invert the result, we end up with the original base vectors. This is precisely what the identity matrix I represents – the base vectors unchanged.

Geometrically, we can interpret this as follows: The matrix A represents a linear transformation that acts on the base p, altering the orientation and magnitude of the vectors. The inverse matrix A^-1 undoes this transformation, bringing the vectors back to their original positions and magnitudes. Therefore, the action of A with respect to this base p can be seen as a transformation and reversion process, where A distorts the base and A^-1 restores it.

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Answer:

5

Step-by-step explanation:

5x3 = 15 also you can divide 15 and 3 which equals to 5

Answer:

5

Step-by-step

The answer is 5 because if you count by 3's until you get to 15, you'll have your answer 5. Also known as...

15/3

or

5 times 3.

The sampling distribution of the sample mean would have a mean of 112 pounds and a standard deviation of 1.4142 pounds.

The sampling distribution of the sample mean would follow a normal distribution with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size.

Given that the population mean weight is claimed to be 112 pounds and the population standard deviation for the mean weight is claimed to be 20 pounds, the sampling distribution of the sample mean would be:

Mean of the sampling distribution = Population mean = 112 pounds

Standard deviation of the sampling distribution = Population standard deviation / Square root of sample size

= 20 pounds / sqrt(200)

= 1.4142 pounds

Therefore, standard deviation of the sampling distribution is 1.4142

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To find the exact length of the polar curve r = 5cos(θ), where 0 ≤ θ ≤ (3π)/4, we can use the arc length formula for polar curves:

L = ∫[θ₁ to θ₂] √(r(θ)² + (dr(θ)/dθ)²) dθ

In this case, we have r(θ) = 5cos(θ). Let's calculate dr(θ)/dθ:

dr(θ)/dθ = -5sin(θ)

Substituting these values into the arc length formula:

L = ∫[0 to (3π)/4] √((5cos(θ))² + (-5sin(θ))²) dθ

 = ∫[0 to (3π)/4] √(25cos²(θ) + 25sin²(θ)) dθ

 = ∫[0 to (3π)/4] √(25(cos²(θ) + sin²(θ))) dθ

 = ∫[0 to (3π)/4] √(25) dθ

 = 5∫[0 to (3π)/4] dθ

 = 5[θ]₀^(3π)/4

 = 5[(3π)/4 - 0]

 = 5(3π)/4

Therefore, the exact length of the polar curve r = 5cos(θ), where 0 ≤ θ ≤ (3π)/4, is (5(3π)/4) units.

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Step-by-step explanation:

cot = sqrt (8)     tan = 1/sqrt(8)  

  then :      Φ = arctan (1/sqrt8) = 19.47 degrees

           sin (19.47 degrees) = .33333...

              csc Φ = 1/sin Φ  =   3                    

Answer: The value of cosec(theta) is 3.

Step-by-step explanation:

consider Cot(theta) as cos(theta)/sin(theta). The given value of cot(theta) is the square root of 8.  {mark this as equation 1}

We also know that the cot(theta) of a triangle is the ratio of its Base to its Height, with the opposite side making an angle theta.

Thus, this clearly means that the ratio of the base and height of the triangle is equal to the square root of 8. If we consider the ratio to be the simplest terms, this means that the value of the base is the square root of 8 and the height has a value of 1.

Using this information we can calculate the hypotenuse of the triangle by Pythagorus theoram.

Therefore, the value of the hypotenuse is equal to the square root of the sum of squares of the base and height.

Therefore the value of hypotenuse=square root of 9=+-3.

Since theta is in the first quadrant, The value of the hypotenuse is considered to be positive. Therefore, the value of the hypotenuse is +3.

Now, the value of cos(theta) is the ratio to the base by the hypotenuse. This means the value of cos(theta) is the square root of 8 divided by 3.

Using this value of cos(theta) in equation 1, we can say that 1/sin(theta)=square root of 8 /(square root of 8 divided by 3)

Upon simplifying, the value of 1/sin(theta)=3

1/sin(theta)=Cosec(theta), therefore the value of cosec(theta) is 3.

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