Marco is interested in the number of penguins who live on a particular ice floe. He decides to take an aerial photo of
the floe and create a 20 by 20 grid on the photo. He randomly selects 3 cells and counts the number of penguins in
each. He then finds the mean number of penguins for those 3 cells. Marco repeats this process for a total of 50
samples and makes a dotplot of the 50 means. This graph is an approximation of
O stratified random sampling.
the distribution of sample data.
the distribution of the population.
the sampling distribution of means.
the sampling distribution of proportions,
M

Answer:

f⁻¹(x) = 2ˣ / 9

Step-by-step explanation:

f(x) = log₂ (9x)

y = log₂ (9x)

swap y and x:    x = log₂ (9y)

solve y: 9y = 2ˣ        y = 2ˣ / 9

f⁻¹(x) = 2ˣ / 9

The equation of the inverse of the function f(x) = log2 (9x) should be considered as the \(f^{-1}(x) = 2^x / 9\)

Since

f(x) = log₂ (9x)

So,

y = log₂ (9x)

Now

swap y and x so    x = log₂ (9y)

And, now we have to solve for y

9y = 2ˣ      

y = 2ˣ / 9

f⁻¹(x) = 2ˣ / 9

Hence, The equation of the inverse of the function f(x) = log2 (9x) should be considered as the \(f^{-1}(x) = 2^x / 9\)

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I think it would be ef because they are across from each other.

Answer:

lineAF, CE, EF

Step-by-step explanation:

Every line except AB, because a line don't curve.

Hope u understood.

Please mark as brainliest

Thank You

Answer:

$4

Step-by-step explanation:

2/100 x 200 = 4

the curve of function 1 "y = 56(1.13ˣ)" fits the best to the given dot plot.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Given, three functions and their graphs but only function 1 "y = 56(1.13ˣ)"

fit the best to the given dot plot.

The curve of best fit estimates a straight line or curve that minimizes the distance between itself and where observations fall in some data set.

The curve of best fit is used to show a trend or correlation between the dependent variable and independent variable(s). It can be depicted visually, or as a mathematical expression.

Thus. Figure 1 is the best suited for the dot plot.

So the value of the item at time x = 13

y = 56(1.13¹³)

y = 274.28

Therefore, the curve of function 1 "y = 56(1.13ˣ)" fits the best to the given dot plot.

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Answer:

y-4=3(x+2)

Step-by-step explanation:

Plug into point slope equation with slope m and point (x1,y1)

y-y1=m(x-x1)

y-4=3(x+2)

The probability that the point does not land in triangle T is 7/8 or 0.875.

The probability that a randomly placed point inside a rectangle does not land in triangle T. To answer this question, we need to calculate the areas of the rectangle and triangle T and then find the probability.
Let's assume the dimensions of the rectangle are 6 units by 4 units, which gives it an area of 24 square units. For triangle T, it seems to have a base of 3 units and a height of 2 units. Using the formula for the area of a triangle (0.5 * base * height), the area of triangle T is 3 square units.
Now, to find the probability of the point not landing in triangle T, we will first determine the area of the remaining space in the rectangle. This can be found by subtracting the area of triangle T from the total area of the rectangle:
Area of remaining space = Area of rectangle - Area of triangle T
Area of remaining space = 24 square units - 3 square units = 21 square units
Finally, the probability of the point not landing in triangle T is the ratio of the remaining space area to the total rectangle area:
Probability = (Area of remaining space) / (Area of rectangle)
Probability = 21 square units / 24 square units = 7/8
Therefore, the probability that the point does not land in triangle T is 7/8 or 0.875.

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The derivative of f(x) = cos(x² - x) is \(3(2x - 1)cos(x^{2} - x)sin(x^{2} - x).\)

To find the derivative of the function f(x) = cos(x² - x), we can use the chain rule.

The chain rule states that if we have a composite function, such as cos(g(x)), the derivative of this composite function is given by the derivative of the outer function multiplied by the derivative of the inner function.

In this case, the outer function is cos(u), where u = x² - x, and the inner function is u = x² - x.

The derivative of the outer function cos(u) is -sin(u).

To find the derivative of the inner function u = x² - x, we apply the power rule and the constant rule. The power rule states that the derivative of x^n, where n is a constant, is nx^(n-1), and the constant rule states that the derivative of a constant times a function is equal to the constant times the derivative of the function.

Applying the power rule and the constant rule, we find that the derivative of u = x² - x is du/dx = 2x - 1.

Now, using the chain rule, the derivative of f(x) = cos(x² - x) is given by:

df/dx = \(-sin(x^{2} - x) * (2x - 1)\)

Simplifying, we have:

df/dx = -\(2xsin(xx^{2} - x) + sin(x^{2} - x)\)

Therefore, the correct answer is option a. 3(2x-1)cos(x²-x)sin(x²-x).

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Answer:

only (0,5)

Step-by-step explanation:

(0,5) is in the shaded region on the graph, so it is a solution.

One other point is in the unshaded region so it is NOT a solution. The other two points are on the dashed line, so they are NOT solutions. If the line was solid (not dashed) they would work, but since the line is dashed they are NOT solutions.

Answer:

A. (0,5)

Step-by-step explanation:

By applying the simple concept of algebra, the equation showing the number of Kenny's baseball cards (b) is b = 82 + 159. So it can be concluded that the number of Kenny's baseball cards is 241 cards.

The use of algebra in everyday life.

Algebra is a branch of mathematics that uses numbers, symbols, or letters to solve math problems. In everyday life, algebra is often used, starting from simple mathematical operations, to financial planning, calculating time/mileage, and so on.

In the above questions, we can take some notes as follows:

Baseball cards sold (x) = 82 cards.

Remaining baseball cards (y) = 159 cards.

The number of baseball cards owned by Kenny (b):

b = x + y

  = 159 + 82

  = 241 cards

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Answer:

2n^3

Step-by-step explanation:

twice a number cubed

n=number

Answer:

199 cm²

Step-by-step explanation:

in the picture

Answer: An atom of iron has 26 protons and 32 neutrons. The atomic number of iron is 26. the mass number of this iron atom is 55.845 U

Hope this helps :)

It is not impossible to construct a frame for a finite population or a target population, but it is impossible to construct a frame for a sampled population.

A frame is a list or map of all the units in a population, which is used to select a sample for a survey or study. If a population is finite, it is possible to list all the units in the population and create a frame. Similarly, if the target population is well-defined and can be identified, a frame can be constructed.

However, if the population is sampled, the frame cannot be constructed because the population is unknown and constantly changing. Therefore, it is impossible to construct a frame for a sampled population.

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The complete question is :

Is it impossible to construct a frame for a sampled population, a finite population, or a target population?

To determine if a math club can afford to rent a van from Vince's Vans, use a number line and an inequality equation. The number line represents the distance of 180 miles, while the inequality equation represents the cost of renting the van.

To determine if the math club can afford to rent the van from Vince's Vans, we can use two representations: a number line and an inequality equation.

1. Number Line Representation:
First, we can create a number line to represent the distance of 180 miles. We'll mark the starting point (school) as 0 and the ending point (science museum) as 180. Then, we can represent the amount of money the club has, $150, as a point on the number line. If the point representing $150 is to the right of or on the point representing 180, it means the club can afford to rent the van.

2. Inequality Equation Representation:
We can also use an inequality equation to represent this situation. Let's say the cost of renting the van is represented by the variable "c". The inequality equation would be "c ≤ 150", indicating that the cost of renting the van should be less than or equal to $150 for the club to afford it. If the rental cost satisfies this condition, the club can afford to rent the van.

By using both the number line and the inequality equation, we can determine if the math club can afford to rent the van from Vince's Vans based on the given information.

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Answer: 97

Step-by-step explanation: hope this is right.

The pool's new size will be 10 by 5 centimetres, where 1 centimetre equals 5 metres.

An object can be resized by scaling. It can be to make the thing bigger or smaller.

assuming a rectangular pool with dimensions of 50 by 25 metres

Drawing the pool at scale, with 1 cm equaling 5 metres, as follows:

1 cm = 5m .... 1

For the length;

L = 50 m ..... 2

Divide expressions 1 and 2 together;

1/L = 5/50

5L = 50

L = 50/5

L = 10 cm

For the width:

Original width = 25 meters

Get the new width

1/W = 5/25

5W = 25

W = 25/5

W = 5 cm

This demonstrates that the pool's new size will be 10 cm by 5 cm.

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The complete question and image of rectangular pool attached below,

The inequality that represents all the solutions of -2(3x + 6) ≥ 4(x + 7) is x ≤ -4

From the question, we have the following parameters that can be used in our computation:

-2(3x + 6) ≥ 4(x + 7)

Divide both sides of the inequality by -2

So, we have the following representation

3x + 6 ≤ -2(x + 7)

Open the brackets

This gives

3x + 6 ≤ -2x - 14

Add 2x to both sides of the inequality

So, we have the following representations

5x + 6 ≤ -14

Subtract 6 from both sides of the inequality

So, we have the following representations

5x ≤ -20

Divide both side of the inequality

x ≤ -4

Hence, the solution is x ≤ -4

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Answer:

ummmmmmmmmmmmmmmmmmm t=4

Answer:

C) festive

Step-by-step explanation:

I'm not completely sure but it's the best choice!

Hope this helps! :)

tell me if i'm wrong

After spending h hours sitting the dog and 2 days sitting the cat, Tamara earned a total of $(7h+30)

What is a mathematical equation?

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

What are the types of equations?

Given, Tamera spent h hours sitting the dog.

As she gets paid $7 per hour petting the dog, she earns a total $(7×h), which is $7h

Also, she spent 2 days sitting the cats.

She gets paid $15 per day sitting the cats, she earns a total $(15×2), which is $30

Thus, she earns a total of $7h + $30, which is $(30+7h)

Tamara earned a total $(30+7h)

After spending h hours sitting the dog and 2 days sitting the cat, Tamara earned a total of $(7h+30)

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The correct angle for a ladder is about 75 degrees from the ground, and you have a 15-foot ladder.

You need to determine how far from the house you should position the ladder's base if you know these fact.
Step 1: It is crucial to keep in mind that the height of the ladder is the same as the vertical distance between the base and the wall.
Step 2: Consider the height of the ladder to be the "opposite" side of the triangle, and the distance you want to find as the "adjacent" side of the triangle. In this scenario, we're looking for the distance from the house (the base of the ladder) to the wall, which will be the adjacent side.
Step 3: To figure out the length of the adjacent side, we'll need to use the tangent of the angle, which is given by the following formula:tan(θ) = opposite/adjacent
Step 4: The angle is 75 degrees, and the opposite side's length is 15 feet, so we can solve for the adjacent side as follows: tan(75) = 15/adjacent
Step 5: Rearranging the equation: adjacent = 15/tan(75)Step 6: Using a calculator, tan(75) is approximately 3.732, so: adjacent = 15/3.732 ≈ 4.01

Therefore, the base of the ladder should be approximately 4.01 feet from the wall (rounded to the hundredths place).

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The correct proof that proves that BE ≅ CF is the proof in option C. (see attachment).

Recall the following:

The isosceles triangle ABC given is shown in the image attached below.

To prove that, BE ≅ CF, establish the fact that △ABE ≅ △ACF by the AAS Congruence Theorem.

Since △ABE ≅ △ACF, therefore BE ≅ CF by the CPCTC Theorem.

Thus, the correct proof that proves that BE ≅ CF is the proof in option C. (see attachment).

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Answer:

9.8 units

Step-by-step explanation:

distance = sqrt (x2 - x1)^2 + ( y2 - y1)^2

sqrt (-3 - (-6))^2 + (5 - 1)^2

sqrt (9)^2 + (4)^2

sqrt 81 + 16

sqrt 97

9.848857802

Answer:

We can begin by finding the total surface area of the can. The area of the label is given as 66π square inches. Since the label is wrapped around the outside of the can, the area covered by it is the lateral surface area of the cylinder. The lateral surface area of a cylinder is given by 2πrh, where r is the radius and h is the height of the cylinder. We can write the equation for the lateral surface area as: 2πrh = 66π Simplifying this equation, we get: rh = 33 We also know that the radius of the can is given as 3 inches. Substituting this value in the above equation, we get: 3h = 33 Solving for h, we get: h = 11 inches Therefore, the height of the can is 11 inches.

In multivariable calculus, the tangent plane is a plane that "touches" a surface at a given point and has the same slope or gradient as the surface at that point.

To find the equation for the tangent plane at the point P0(2, 1, 2) on the surface 2x^2 + 4y^2 +3z^2 = 24, we need to find the gradient vector of the surface at P0, which gives us the normal vector of the plane. Then, we can use the point-normal form of the equation for a plane to find the equation of the tangent plane.

The gradient vector of the surface is given by:

grad(2x^2 + 4y^2 +3z^2) = (4x, 8y, 6z)

At P0(2, 1, 2), the gradient vector is (8, 8, 12), which is the normal vector of the tangent plane.

Using the point-normal form of the equation for a plane, we have:

8(x - 2) + 8(y - 1) + 12(z - 2) = 0

Simplifying, we get:

4x + 4y + 3z = 20

Therefore, the correct equation for the tangent plane is D. 5x + 4y + 3z = 20.

To find the equations for the normal line, we need to use the direction vector of the line, which is the same as the normal vector of the tangent plane. Thus, the direction vector of the line is (8, 8, 12).

The equations for the normal line can be expressed as:

x = 2 + 8t

y = 1 + 8t

z = 2 + 12t

where t is a parameter that can take any real value.

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Answer:

480 people

Step-by-step explanation: 180/x=37.5/100 cross multiply. x=480.

X is a continuous uniform random variable with a mean of 9.5 am and a variance of 1/12.

Since X denotes a random delivery time anywhere between 9 am and 10 am, X is a continuous random variable that follows a uniform distribution.

The uniform distribution is a probability distribution where all values between a lower bound (a) and an upper bound (b) have equal probability.

In this case, a = 9 am and b = 10 am, so the probability density function of X can be expressed as:

f(x) = 1/(b-a) = 1/(10-9) = 1

for 9 ≤ x ≤ 10, and f(x) = 0 otherwise.

The expected value or mean of X can be calculated as the average of the lower and upper bounds:

E[X] = (a + b)/2 = (9 + 10)/2 = 9.5 am

The variance of X is given by:

\(Var[X] = (b - a)^2/12 = (10 - 9)^2/12 = 1/12\)

Therefore, X is a continuous uniform random variable with a mean of 9.5 am and a variance of 1/12.

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Answer:

Option C 5a+(2b + 3c)

Answer:

-2,2

Step-by-step explanation:

To solve this problem, we can use the concept of the sampling distribution of the sample mean. The mean number of cups of coffee consumed in a day by all occupants is 2.0 with a standard deviation of 0.6.  Since the sample size is large (125 employees) and the population standard deviation is known, we can approximate the sampling distribution of the sample mean as a normal distribution.

The mean of the sampling distribution is equal to the population mean, which is 2.0 cups per day  Now, we need to calculate the z-score for the value of 240 cups per day using the formula:

z = (x - μ) / σ,

where x is the desired value (240 cups per day), μ is the mean of the sampling distribution (2.0 cups per day), and σ is the standard deviation of the sampling distribution (0.6 / sqrt(125)).

Plugging in the values, we have:

z = (240 - 2) / (0.6 / sqrt(125)) ≈ 58.01.

Finally, we can use a standard normal distribution table or a calculator to find the probability of obtaining a z-score greater than 58.01. However, since this z-score is extremely large, the probability will be very close to zero.

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