you spin the spinner once.


what is p(less than 4)?

write your answer as a fraction or whole number

Answer:

If the probability of getting a two on a biased dice is 0.1, then the probability of not getting a two is 0.9.

To find the expected number of times a two is rolled in 250 rolls:

Expected value = (probability of an event occurring) x (number of trials)

Expected number of twos = 0.1 x 250 = 25

To find the expected number of times a number other than two is rolled in 250 rolls:

Expected number of non-twos = 0.9 x 250 = 225

Therefore, we would expect to roll a two 25 times and a number other than two 225 times in 250 rolls of this biased dice.

Answer:

0.790, or 79%.

Step-by-step explanation:

If the probability of getting a two on a biased dice is 0.1, then the probability of not getting a two is 0.9.

We can use the binomial distribution to calculate the probability of getting a certain number of twos in 250 rolls of the dice. The formula for the binomial distribution is:

P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

Where:

P(X = k) is the probability of getting exactly k twos

n is the number of trials (250 rolls)

k is the number of successes (getting a two)

p is the probability of success (0.1)

(1-p) is the probability of failure (0.9)

C(n, k) is the number of ways to choose k successes from n trials (n choose k)

To calculate the probability of getting exactly k twos in 250 rolls, we plug in the values for n, k, p, and (1-p) into the formula:

P(X = k) = C(250, k) * 0.1^k * 0.9^(250-k)

We can use a calculator or a software program to find the probabilities for different values of k. Here are some examples:

The probability of getting no twos (k = 0) is P(X = 0) = C(250, 0) * 0.1^0 * 0.9^250 = 0.057

The probability of getting exactly one two (k = 1) is P(X = 1) = C(250, 1) * 0.1^1 * 0.9^249 = 0.153

The probability of getting at least two twos (k >= 2) is the complement of the probability of getting zero or one two:

P(X >= 2) = 1 - P(X = 0) - P(X = 1)

= 1 - 0.057 - 0.153

= 0.790

Therefore, the probability of getting at least two twos in 250 rolls of the biased dice is approximately 0.790, or 79%.

please leave a star

Answer: yes, yes, no

Explanation: In order for a figure to be a triangle, the two smallest sides must add up to be larger than the biggest side. The reason why the last one isn't a triangle is because 6+8 EQUALS 14 and is not greater than 14.

By using system of equations, there are 43 free DVD rentals and 46 boxes of microwave popcorn were given away during the promotional campaign.

Let's use the following variables

x: the number of free DVD rentals given away

y: the number of boxes of microwave popcorn given away

We can set up a system of equations to represent the given information:

x + y = 89 (total number of new members signed up)

1x + 2y = 135 (total cost of the incentives)

We can solve for x or y in the first equation and substitute into the second equation

x = 89 - y

1(89 - y) + 2y = 135

89 - y + 2y = 135

y = 46

Substituting y = 46 into the first equation:

x + 46 = 89

x = 43

Therefore, 43 free DVD rentals and 46 boxes of microwave popcorn.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Here is real answer :>

Answer:

153

Step-by-step explanation:

The relationship in the row is below

4³ +2³ +1³ =64 + 8 +1 = 72

1³ + 2³ +6³= 1 + 8 + 216

3³ + 1³ + 5³ = 27 +1 +125 = 153

All numbers below the first level are raised to power 3 and added together

The distance traveled is equal to sin^2(θ), as seen before.

To find the distance traveled by a particle with position (x, y) as t varies in the given time interval, we need to first find the parametric equations for x and y in terms of t, and then compute the arc length of the curve.

Given x = sin^2(t) and y = cos^2(t), we first find the derivatives of x and y with respect to t:
dx/dt = 2 * sin(t) * cos(t)
dy/dt = -2 * sin(t) * cos(t)

Next, we compute the square root of the sum of the squares of the derivatives:
sqrt((dx/dt)^2 + (dy/dt)^2) = sqrt((2 * sin(t) * cos(t))^2 + (-2 * sin(t) * cos(t))^2) = sqrt(4 * sin^2(t) * cos^2(t) + 4 * sin^2(t) * cos^2(t)) = 2 * sin(t) * cos(t)

Now, we can find the distance traveled by integrating the above expression with respect to t over the given time interval (0, θ):

Distance traveled = ∫(2 * sin(t) * cos(t) dt) from 0 to θ

Using the substitution u = sin(t), du = cos(t) dt, we get:

Distance traveled = ∫(2 * u du) from 0 to sin(θ)

Now, integrating with respect to u, we get:

Distance traveled = u^2 | from 0 to sin(θ) = (sin^2(θ)) - (0^2) = sin^2(θ)

The length of the curve can be computed as the arc length:

Length of the curve = ∫(2 * sin(t) * cos(t) dt) from 0 to θ

As we computed earlier, the distance traveled is equal to sin^2(θ). Therefore, the distance traveled by the particle is the same as the length of the curve.

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The histograms demonstrate that as sample size increases, the distribution of sample means becomes more normal, which is in line with the central limit theorem.

Histograms can be used to graphically represent a probability distribution, which is a measure of how likely it is that a random variable will take on a particular value.

The central limit theorem states that as the sample size increases, the sampling distribution of the mean approaches a normal distribution, regardless of the shape of the population distribution.

The histograms demonstrate this by showing the distribution of sample means for different sample sizes. As the sample size increases, the shape of the histogram becomes more normal, with a narrower and taller distribution.

Therefore, this demonstrates that the central limit theorem holds true, as the distribution of sample means becomes more normal as sample size increases, regardless of the shape of the population distribution.

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By standard deviation, The required number of motels that charged 118 or less per night is 87 (approx).

We are to determine how many motels charged 118 or less per night. We can use the normal distribution table to find out the z-score for the 75th percentile. We can then use this z-score to find out the price of lodging per night for the 118th percentile.

The formula to calculate the z-score is:[tex]z=\frac{X-\mu}{\sigma}[/tex], where X is the price of lodging per night, [tex]$\mu$[/tex]is the mean rate, [tex]$\sigma$[/tex] is the standard deviation.

The z-score for the 75th percentile is found using the normal distribution table as: z = 0.67 (approx). For the 75th percentile, the motel charged $118 per night. Therefore, we can write the formula as:[tex]0.67 = \frac{118 - 91}{14}[/tex] Simplifying, we get: [tex]0.67 = \frac{27}{14}[/tex]

Therefore, we can conclude that:118 = 91 + 14 [tex]\times[/tex] 0.67 Or, X = [tex]\mu[/tex] + z[tex]\sigma[/tex]= 91 + 0.67 [tex]\times[/tex] 14 = 100.38. Thus, motels that charged 118 or less per night can be found as follows: [tex]$$P(X \leq 118)[/tex]=[tex]P(Z \leq z)$$$$[/tex] = [tex]P(Z \leq 0.67)$$$$[/tex]= 0.7486.

Hence, the number of motels that charged 118 or less per night is:

0.7486 [tex]\times[/tex]116 = 87.06. Rounding it to the nearest integer, we get: 87 (approx). Therefore, the required number of motels that charged 118 or less per night is 87 (approx).

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Forecast for August with an alpha of 0.7 and forecast of June 164 are to be calculated using exponential smoothing.

Exponential smoothing is a forecasting method that uses a weighted average of past time-series values to forecast future values. In a time-series, data values are obtained over time, such as over months or years, and then plotted in sequence.

The weights decrease exponentially as the observations get older. The EWMA formula used in exponential smoothing is as follows:

St=α × Yt-1+(1-α) × St-1

where,St is the smoothed statistic for the current period tYt is the original observation for the current period tSt-1 is the smoothed statistic for the previous period t-1α is the smoothing parameter 0≤α≤1, and usually close to 0.1.The smoothed statistic is also called the exponentially weighted moving average (EWMA).Calculating the forecast for August with alpha=0.7 and forecast of June 164 as follows:

St=α × Yt-1+(1-α) × St-1St =0.7 × 164+(1-0.7) × 164St=164

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Answer:

To find the difference in degrees Celsius between Oklahoma's and New Jersey's record low temperatures, we first need to convert both temperatures to Celsius or Fahrenheit. Since Oklahoma's temperature is given in Fahrenheit and New Jersey's temperature is given in Celsius, we'll convert Oklahoma's temperature to Celsius.

Using the formula F = 1.8C + 32, we can solve for C:

-31°F = -35°C

(To see how we arrived at this conversion: first, we use the formula to convert Fahrenheit to Celsius: F = 1.8C + 32. Rearranging the equation, we can solve for C: (F - 32) / 1.8 = C. Plugging in -31°F for F, we get (-31 - 32) / 1.8 = -35°C)

Now we can find the difference in Celsius between the two temperatures:

|-35°C| - |-37°C| = |-2| = 2°C

So the difference in degrees Celsius between Oklahoma's and New Jersey's record low temperatures is 2°C.

The probability of a high school baseball player getting at least 6 hits in one game, given a 0.253 batting average, when he gets 8 at-bats, is 0.0197 or approximately 2%.


Given, the high school baseball player's batting average is 0.253, which means in 100 times he hits the ball, he will make 25.3 hits on average. We need to find the probability of getting at least 6 hits in a game when he gets 8 at-bats.

We will calculate the probability using the Binomial Probability formula. Here, the number of trials is 8, and the probability of success is 0.253. We need to find the probability of getting at least 6 hits.

P(X≥6) = 1 - P(X<6)

P(X<6) = ∑P(X=i), i=0 to 5

We can use the Binomial Probability Table to find these probabilities or use the Binomial Probability formula.

P(X<6) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)

= C(8,0) (0.253)^0 (1 - 0.253)^8 + C(8,1) (0.253)^1 (1 - 0.253)^7 + C(8,2) (0.253)^2 (1 - 0.253)^6 + C(8,3) (0.253)^3 (1 - 0.253)^5 + C(8,4) (0.253)^4 (1 - 0.253)^4 + C(8,5) (0.253)^5 (1 - 0.253)^3

≈ 0.9799

Therefore, P(X≥6) = 1 - 0.9799

= 0.0201 or approximately 2%.

Hence, approximately 0.0197 or 1.97% is the probability of a high school baseball player, who has a batting average of 0.253, obtaining at least 6 hits when given 8 at-bats during a single game.

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Answer: the answer would be 122

Step-by-step explanation:

To find the surface area you need to find the area of each face and add them together

2 (W L+H L+H W) = surface area  

2·(4·7+3·7+3·4)=122

Answer:

Step-by-step explanation:

Given dimensions of the rectangular prism ,

4"×3"×7"

We know, Total surface area of a cuboid= 2(lb+bh+hl)

where, l=length of the cuboid

 b= breadth " " "

 h= height " " "

Since, a rectangular prism holds the shape of a cuboid, therefore it's surface area should also be 2(lb+bh+hl)

Now, surface area of the rectangular prism = 2(4×3+3×7+7×4)

 =2(12+21+28)

 =2×61

 =122 square inches.

Answer:

No

Step-by-step explanation:

No. So if the number next to the "x" we're the same, it would have been. But they are different (one is -3 and one is 1/3)

2 3/4 cups of diced tomatoes should he put in the chili.

How many glasses should there be?

Simply said, a fraction is a portion of a whole. Mathematically, the number is expressed as a quotient with split numerator and denominator. The numerator and denominator of a simple fraction are both integers.

Tomatoes in cups expressed as a fraction higher than 1.

A mixed fraction is 2 3/4. Because it combines a full number with a fraction, it is known as that.

We must change the mixed fraction into an improper fraction in order to calculate the quantity of cups of tomatoes stated as a fraction greater than 1.

A fraction that has a larger numerator than denominator is said to be improper.

2 3/4 ⇒ ((2*4)+3)/4 ⇒ (8+3)/4 ⇒ 11/4

A fraction that is bigger than one is 11/4.

A fraction with the value 1 is 4/4. Hence, any fraction that has a numerator larger than one and less than four is a fraction. It is 11/4 in this instance.

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The circumference of the circle in terms of pi is 16π yards.

The circumference of a circle is the distance around the edge or perimeter of the circle. It is the length of a closed curve and can be measured by using a flexible measuring tape or a string to wrap around the circle. The formula for the circumference of a circle is C = 2πr, where C is the circumference, r is the radius of the circle, and π is the mathematical constant pi (approximately equal to 3.14159). The circumference of a circle is proportional to its radius and increases as the radius increases. Therefore, if we know the radius of a circle, we can use the formula to find its circumference, and if we know the circumference, we can use the formula to find the radius. The circumference is an important concept in geometry and is used in many real-world applications, such as calculating the length of a fence needed to enclose a circular garden or the distance traveled by a car moving around a circular racetrack.

Substituting the given value of the radius, we get:

C = 2π(8) = 16π

Therefore, the circumference of the circle in terms of pi is 16π yards.

So the answer is 16pi yards.

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Answer:

x = -32

Step-by-step explanation:

Given: (2x + 4) + 112 + 132 = 180

First, write it down:

(2x + 4) + 112 + 132 = 180

Then collect like terms:

2x = 180 - 112 - 132

Then calculate:

2x = -64  (Divide both sides by 2)

x = -32

The x-intercepts of the function 3 tan(3x) over the interval (π/6, 3π/6) are:

x = π/3 and x = 2π/3

What is function ?

A function is a mathematical object that takes one or more inputs, called the arguments or variables, and produces a unique output. The output is determined by a set of rules that specify how the function operates on the inputs. In other words, a function is a relationship between inputs and outputs.

Functions are typically denoted by a symbol or a name, such as f(x) or g(t). The input is usually represented by a variable, such as x or t, while the output is represented by the function value, such as f(x) or g(t).

Functions are used extensively in mathematics, science, engineering, and many other fields. They provide a way to model and analyze real-world phenomena, and they are essential tools for solving many problems in these fields. Examples of functions include polynomial functions, exponential functions, trigonometric functions, and logarithmic functions.

To find the x-intercept of the function 3 tan(3x) over the given interval, we need to find the values of x where the function equals zero.

Let's first simplify the function:

3 tan(3x) = 0

tan(3x) = 0

We know that tan(π/2) is undefined and that tan(π) = 0. Since the period of the tangent function is π, we can say that:

tan(3x) = 0 --> 3x = nπ for n ∈ ℤ

Now we solve for x:

3x = nπ

x = nπ/3

Since the interval is (π/6, 3π/6), we need to find the values of x that satisfy:

π/6 < x < 3π/6

π/6 < nπ/3 < 3π/6

1/2 < n < 3/2

So the values of x that satisfy the given condition are:

x = π/3 and x = 2π/3

Therefore, the x-intercepts of the function 3 tan(3x) over the interval (π/6, 3π/6) are:

x = π/3 and x = 2π/3

Expressed in terms of π, the x-intercepts are:

π/3π and 2π/3π, which simplify to:

x = 1/3 and x = 2/3.

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Answer:

44/5

Step-by-step explanation:

6 3/5 ÷ 3/4

6 3/5 = 33/5

33/5 ÷ 3/4 = 33/5 × 4/3 = 132/15 = 44/5

So, the answer is 44/5

Answer:

Step-by-step explanation:

1) Write the equation

[tex]\frac{3}{5}[/tex] ÷ [tex]\frac{3}{4}[/tex] = ?

2) Multiply by the reciprocal of [tex]\frac{3}{4}[/tex]

[tex]\frac{3}{5}[/tex] × [tex]\frac{4}{3}[/tex] =?

3) Cancel out the GCF 3

[tex]\frac{1}{5}[/tex] × 4 =?

4) Solve

[tex]\frac{4}{5}[/tex] or 0.8

The standard form of the equation of the circle with center and radius of square 2 divided by 4 is (x - 1/2)² + (y + 1/2)² = 1/8.

The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.

To use this formula, we first need to find the values of h, k, and r for the given circle with center and radius of square 2 divided by 4.

We know that the center of the circle is (h, k) = (2/4, -2/4) = (1/2, -1/2).

This means that h = 1/2 and k = -1/2.

The radius of the circle is r = square 2 divided by 4.

We can write this as r² = (square 2 divided by 4)² = 2/16 = 1/8.

Now we can substitute these values into the standard form equation to get:

(x - 1/2)² + (y + 1/2)² = 1/8

So the standard form of the equation of the circle with center and radius of square 2 divided by 4 is (x - 1/2)² + (y + 1/2)² = 1/8.

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The woman at the dinner party consumed 24 fluid ounces of wine containing approximately 4.8 standard drinks assuming the wine had an alcohol content of 12%. She exceeded the recommended limit for moderate drinking on that day.

Assuming each glass of wine contained 8 fluid ounces, the woman consumed a total of 24 fluid ounces of wine throughout the evening.

To determine the number of standard drinks ingested, we need to know the alcohol content of the wine. In the United States, a standard drink is defined as containing 0.6 fluid ounces or 14 grams of pure alcohol.

Assuming the wine had an alcohol content of 12% (which is a typical percentage for table wine), we can calculate the number of standard drinks ingested by using the following formula:

Number of standard drinks = (Volume of alcohol consumed in ounces x % alcohol by volume) / (0.6 ounces of alcohol per standard drink)

Number of standard drinks = (24 fl oz x 0.12) / 0.6 fl oz

Number of standard drinks = 4.8

Therefore, the woman consumed approximately 4.8 standard drinks.

To determine if she drank alcohol in moderation, we need to consider the recommended limits for moderate drinking. According to the National Institute on Alcohol Abuse and Alcoholism, moderate drinking is defined as up to one drink per day for women.

Since the woman consumed 4.8 standard drinks in one evening, she exceeded the recommended limit for moderate drinking for that day.

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A stadiometer can be used to measure height, age, and shoe size of learners. It is a simple device consisting of a ruler mounted on a vertical board, and the measurements can be taken in the Frankfort Plane position.

An instrument that can be used to measure height, age, and shoe size of learners is a stadiometer. A stadiometer is a device designed to measure the height of an individual, typically from the floor to the crown of the head. It consists of a ruler, graduated in metric or imperial units, mounted on a vertical board. To measure a person's height, they must stand against the board with their feet together and their head in the Frankfort Plane. The Frankfort Plane is an imaginary line running from the top of the ears to the bottom of the eyes. Once the person is standing in this position, the height is read off the ruler and recorded.

In addition to height measurement, a stadiometer can also be used to measure age and shoe size of learners. To measure age, the stadiometer must be calibrated with the average height of the population by age. Then, when the person is standing in the Frankfort Plane position, their age can be read off the ruler. To measure shoe size, the stadiometer must be calibrated with the average height of a person with a certain shoe size. Once the person is standing in the Frankfort Plane position, their shoe size can be read off the ruler.

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Therefore  the range of the quadratic function with vertex (-3, -1) is y ≥ -1 and the domain is all real number and the Domain is real numbers .

A quadratic function's vertex form is given by:

[tex]y = a(x - h)^2 + k[/tex]

where (h, k) is the parabola's vertex. In this instance, we have:

[tex]h = -3, k = -1[/tex]

So the quadratic function's equation is:

[tex]y = a(x + 3)^2 - 1[/tex]

To determine the function's range, we must first determine the minimum value of y. Because the squared term's coefficient is positive, the parabola opens upwards and the vertex is a minimum point. As a result, the range is:

Range: y ≥ -1

To determine the function's domain, we must first determine the set of all x-values for which the function is defined. Due to the fact that a quadratic function is defined for all real numbers, the domain is:

Domain: All real numbers

So the domain of the quadratic function with vertex (-3, -1) is all real numbers, and its range is y -1.

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The value of f(4) using recursive formula f(1) = 10 and f(n) = f(n-1) + 4 for n ≥ 2  is 22

Given that f(1) = 10 and f(n) = f(n-1) + 4 for n ≥ 2.

To find the value of f(4), we can use the recursive formula to work our way up from f(1) to f(4):

Using the above as a guide, we have the following:

f(2) = f(1) + 4 = 10 + 4 = 14

Next, we have

f(3) = f(2) + 4 = 14 + 4 = 18

Next, we have

f(4) = f(3) + 4 = 18 + 4 = 22

Therefore, the value of f(4) is 22.

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The probability that a librarian chooses a fiction book, then a nonfiction book, then a fiction book is approximately 0.305.

The solution to this problem is a probability calculation.

To calculate the probability of selecting a fiction book, then a nonfiction book, then a fiction book from a selection of 10 nonfiction books and eight fiction books, we need to use the multiplication rule of probability.

The multiplication rule states that the probability of two or more independent events happening together is equal to the product of their individual probabilities.

To apply this rule, we'll break down the question into three events:

Probability of choosing a fiction book = 8/18 = 4/9

Probability of choosing a nonfiction book (after selecting a fiction book) = 10/17

Probability of choosing a fiction book (after selecting a nonfiction book) = 8/16 = 1/2

Now we can use the multiplication rule:4/9 * 10/17 * 1/2 = 0.305 (rounded to three decimal places)

Therefore, the approximate probability that the librarian will choose a fiction book, then a nonfiction book, then a fiction book is 0.305.

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[tex]\frac{65x-14x+49-4}{14} = 36[/tex]The value of x is 9.

Inequality refers to a situation where there is a significant difference in the distribution of resources, opportunities, and power among individuals or groups in a society. It is a complex social and economic phenomenon that can manifest in various forms such as income inequality, wealth inequality, gender inequality, racial inequality, educational inequality, and healthcare inequality, among others.

Given by the question.

[tex]\frac{9x+7}{2} - \frac{7x-x+2}{7} = 36[/tex]

[tex]\frac{63x+44-14x+2x+4}{14} = 36[/tex]

[tex]\frac{65x-14x+49-4}{14} = 36[/tex]

[tex]51x+45=504\\51x= 459\\x=9[/tex]

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Answer:

7$

Step-by-step explanation:

✅

The coordinates of the vertices for the image if the preimage is translated 4 units down are A′(-4, -1), B′(0, 1), C′(-2, -4).

What is meant by preimage?

In geometry, a preimage is the original figure or shape before any transformation is applied. It is the initial configuration of the object that is being transformed. For example, if we have a square and we rotate it by 90 degrees, the original square is the preimage and the resulting figure after the rotation is the image.

To translate the preimage 4 units down, we need to subtract 4 from the y-coordinates of all vertices. Therefore, the coordinates of the image vertices are:

A′(-4, 3-4) = (-4, -1)

B′(0, 5-4) = (0, 1)

C′(-2, 0-4) = (-2, -4)

Therefore, the vertices of the image triangle are A′(-4, -1), B′(0, 1), and C′(-2, -4).

So, the correct option is: A′(-4, -1), B′(0, 1), C′(-2, -4).

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Answer:

N = N0 x 2^n

Step-by-step explanation:

The formula for calculating the number of bacteria cells after n generations is N = N0 x 2^n, where N is the total number of cells after n generations, N0 is the initial number of cells, and 2^n represents the number of times the population doubles after n generations. Assuming an initial population of 100 cells, there will be approximately 102,400 cells after 10 generations.

Answer:

The explicit formula for the number of bacteria cells after each generation can be written as:

N = N0 * r^n

Where:

N is the number of bacteria cells after n generations

N0 is the initial number of bacteria cells (at n=0)

r is the growth rate (how many new cells are produced per existing cell)

Assuming that each bacteria cell doubles in number with each generation (i.e. r=2), the formula can be simplified to:

N = N0 * 2^n

To find the number of cells after 10 generations, we can substitute n=10 into the formula:

N = N0 * 2^10

Since we don't have a specific value for N0, we can't find the exact number of cells after 10 generations. However, we can make some assumptions. For example, if we assume that there are initially 100 bacteria cells (N0=100), we can calculate:

N = 100 * 2^10 = 102,400

So, if each bacteria cell doubles in number with each generation and there were initially 100 cells, there will be 102,400 cells after 10 generations.

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Answer:

27 cubic units

Step-by-step explanation:

Since each small cube is a unit cube, then each small cube has side length 1 unit. Each side of the Rubik's cube has length 3 units.

V = s³ = 3³ = 27

Answer: 27 cubic units

The probability of selecting at least 2 corporations earned profits is 2/3.

A subfield of statistics known as probability studies random events and their likelihood of happening.

Using combination formula:

¹⁰C₂ =  [tex]\frac{10!}{(2! * (10-2)!)}[/tex]  =  45

This tells us that there are 45 possible ways to select two corporations from the list of 10.

To determine the number of ways that two corporations that both earned profits can be selected,

⁶C₂ =  [tex]\frac{6!}{(2! * (6-2)!)}[/tex]   = 15

So there are 15 ways to select two corporations that both earned profits.

Therefore, the probability of selecting two corporations that both earned profits is:

P(both earned profits) = 15/45 = 1/3

To find the probability of selecting one corporation that incurred a loss,

⁴C₁ × ⁶C₁ =  4 × 6 = 24

So there are 24 ways to select one corporation that incurred a loss and one corporation that earned a profit.

Therefore, the probability of selecting one corporation that incurred a loss is:

P(one incurred loss) = 24/45 = 8/15

If the IRS inspector selects 3 corporations from the list, we can use the complement rule to find the probability that at least 2 of them earned profits,

P(at least 2 earned profits) = 1 - P(none earned profits) - P(only 1 earned profit)

To find the probability that none of the three selected corporations earned profits,

⁴C₃ ÷ ¹⁰C₃ = 4/120 = 1/30

To find the probability that only one of the three selected corporations earned profits,

{ ⁶C₁ × ⁴C₂ } ÷ ¹⁰C₃   = 36/120 = 3/10

Therefore, the probability of selecting at least 2 corporations that earned profits is:

P(at least 2 earned profits) = 1 - 1/30 - 3/10 = 2/3

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