Which equation or inequality represents the following description?

Multiply the quantity 2 more than a number by 8. The result is at least 12 times the number subtracted from 76.

A. 8(2n) 76-12n
D. 8(2n)=76-12n

The differential equation describing the cell phone sales is \(\frac{{dy}}{{dt}} = 0.5357 \cdot y(t) \cdot \left(1 - \frac{{y(t)}}{{100}}\right)\).

Based on the given information, the cell phone sales growth is logistic, with a carrying capacity of 100 thousand units. When 28 thousand cell phones have been sold, the rate of sales increase is 10 thousand units per month.

The logistic growth differential equation is given by:

\(\frac{dy}{dt} = k \cdot y(t) \cdot \left(1 - \frac{y(t)}{M}\right)\)

where dy/dt is the rate of change in sales, y(t) is the number of cell phones sold after t months, k is the growth rate, and M is the carrying capacity.

In this case, y(t) = 28, dy/dt = 10, and M = 100. To find k, we can plug these values into the equation:

10 = \($k \cdot 28 \cdot \left(1 - \frac{28}{100}\right)$\)

Solving for k:

k ≈ 0.5357

Therefore, the differential equation describing the cell phone sales is:

\(\frac{{dy}}{{dt}} = 0.5357 \cdot y(t) \cdot \left(1 - \frac{{y(t)}}{{100}}\right)\)

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Options A , C , E ,  F , H are true for the statement population that is finding the probability.

Given that,

We have to choose the correct answer for the given statement that is finding the probability.

We know that,

Calculating a situation's probability allows us to determine its probability. Many things are difficult to determine with 100% accuracy. We can only anticipate the probability of an event occurring, or how likely it is, using it. A probability can be range 0 and 1, where 0 indicates an impossibility and 1 indicates a certainty. The probability of each event in a sample space is one.

Therefore, Options A , C , E ,  F , H are true for the statement population that is finding the probability.

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A random variable is said to be continuous if it is measured over an interval. Option b. "is measured over an interval" correctly describes a continuous random variable.

A continuous random variable can take on any value within a given interval, including decimal values. It represents measurements that can be infinitely divided and can take on an uncountable number of values. Examples of continuous random variables include the height of individuals, the time it takes to complete a task, or the temperature of a room. These variables are not restricted to specific discrete values and can vary continuously.

On the other hand, discrete random variables (options a, c, and d) can only take on a countable number of distinct values. Discrete random variables represent outcomes that are distinct and separate, such as the number of students in a class, the number of cars passing by, or the number of heads obtained when flipping a coin.

These variables do not have decimal values and cannot be measured over a continuous range.

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Answer:

\(f'(x)= \frac{13}{(2x+3)^2}\\\)

Step-by-step explanation:

\(f(x)= \frac{3x-2}{2x+3} \\\)

\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)

\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)

Answer:

Step-by-step explanation:

Remark

It's not 82.

You have to take the 62% off and then follow it with 20% from the new price.

Solution

62%

If you get a reduction of 62%, it means that you pay 100% - 62% = 38% of the marked price of $49.95.

38% price =49.95 * 62/100

38% price = 3096.9 / 100

38% price = $30.97

20%  Reduction

20% more means that you pay 100% - 20% = 80%

20% more reduction = 30.97 * 80/100

20% more reduction = 2478/100

20% more reduction = 24.78

Conclusion.

Your final price before taxes is $24.78

Answer:

f(x^3-8)=x^6-19x^3+90

Step-by-step explanation:

Answer:

Step-by-step explanation:

$40 per day represents the slope

Finding the y-intercept:

The function is then:

Answer:

The circumference is 44

Answer:

34.56

Step-by-step explanation:

C = 2πr = 2 · π · 5.5 ≈ 34.55752

(a) The function f(x) = 4x³ - 2 is injective (one-to-one) and surjective (onto).

(b) The inverse function of f is f⁻¹(x) = ∛((x + 2)/4).

(a) To show that the function f: R → R defined by f(x) = 4x³ - 2 is injective (one-to-one) and surjective (onto):

Injectivity: Suppose we have two values x₁ and x₂ in the domain such that f(x₁) = f(x₂). We need to prove that x₁ = x₂. So, let's assume 4x₁³ - 2 = 4x₂³ - 2. By simplifying, we get 4x₁³ = 4x₂³.

Dividing both sides by 4 gives us x₁³ = x₂³.

Taking the cube root of both sides gives x₁ = x₂. Therefore, the function f is injective.

Surjectivity: For surjectivity, we need to show that for every y in the codomain (R), there exists at least one x in the domain (R) such that f(x) = y. Let's take an arbitrary y ∈ R.

We need to find an x such that f(x) = y. Solving the equation 4x³ - 2 = y for x, we have x = ∛((y + 2)/4). Thus, for any y in the codomain, there exists an x in the domain such that f(x) = y. Therefore, the function f is surjective.

(b) To find f⁻¹(x) (the inverse function of f), we interchange the roles of x and f(x) in the original function equation and solve for x.

Start with y = 4x³ - 2 and solve for x:

y + 2 = 4x³

x³ = (y + 2)/4

x = ∛((y + 2)/4)

Thus, the inverse function of f is f⁻¹(x) = ∛((x + 2)/4).

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Karen is correct because

Step-by-step explanation:

10 to the 3rd power is 1000 and 560.9 divided by 1000 is 0.5609

In a regular polygon, each inside angle is the same. A polygon has a total of 360° in its outside angles. Interior angle of a polygon is equal to the sum of interior angles divided by the number of sides, according to the following formula. A polygon has a total of 360° in its outside angles.

In a regular polygon, all of the inside angles are equal. Interior angle of a polygon = sum of interior angles number of sides is the formula for estimating the magnitude of an interior angle. A polygon's external angles add up to 360°.

example

Triangles with three sides are a type of polygon. Given that it is curved and lacks sides and angles, a circle is a plane figure as well, but it is not regarded as a polygon.

As a result, we can state that while all two-dimensional shapes are polygons, not all polygonal figures are two-dimensional.

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Answer:

85 1/3

Step-by-step explanation:

All I did is multiply and got that.

I'm going to submit my finals, so hopefully it's not wrong. I don't think it's wrong though.

To write Acos(?0t) + Bsin(?0t) in the form r*sin(?0t - ?), we can use the identities. The relationship among R, r, ? and ? is:
R^2 = r^2 (1 + (A/B)^2), tan? = r/R = B/A

r = sqrt(A^2 + B^2)
tan? = B/A

Therefore, r = sqrt(A^2 + B^2) and tan? = B/A.

To determine the relationship among R, r, ? and ?, we can use the identity:

R^2 = r^2 + (tan?)^2

Therefore, R = sqrt(r^2 + (tan?)^2) and tan? = r/R. Substituting the expression for tan? from earlier, we get:

tan? = B/A = r/R

Solving for R, we get:

R = r/tan? = r/(B/A) = rA/B

And substituting the expression for R in terms of r and tan?, we get:

R = sqrt(r^2 + (r/R)^2) * A/B

Simplifying this expression, we get:

R^2 = r^2 + (A/B)^2 * r^2

R^2 = r^2 (1 + (A/B)^2)

Therefore, the relationship among R, r, ? and ? is:

R^2 = r^2 (1 + (A/B)^2)
tan? = r/R = B/A

To show that Acos(ω₀t) + Bsin(ω₀t) can be written in the form r*sin(ω₀t - θ), we can use trigonometric identities. We know that:

sin(a - b) = sin(a)cos(b) - cos(a)sin(b)

Comparing this to the given expression, we have:

Acos(ω₀t) + Bsin(ω₀t) = r*sin(ω₀t - θ) = r[sin(ω₀t)cos(θ) - cos(ω₀t)sin(θ)]

Now, let's equate the coefficients of sin(ω₀t) and cos(ω₀t):

A = -r*sin(θ)
B = r*cos(θ)

To find r and θ in terms of A and B, we can use the Pythagorean identity:

A² + B² = (-r*sin(θ))² + (r*cos(θ))² = r²(sin²(θ) + cos²(θ)) = r²

Therefore, r = √(A² + B²).

Now, to find θ, we can use the tangent function:

tan(θ) = -A/B

Now, for the second part, if Rcos(ω₀t - θ) = r*sin(ω₀t - θ), we can use the sine-to-cosine transformation:

Rcos(ω₀t - θ) = Rsin(ω₀t - θ + π/2)

This implies that:

R = r
θ + π/2 = θ'

So, the relationship among R, r, θ, and θ' is:

R = r
θ' = θ + π/2

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False. The probabilistic model assumes that the actual values of y have some random variability around the regression line, which is represented by the error term ε in the regression equation.

The expected value of y (E(y)) is the value predicted by the regression line for a given value of x, but the actual values of y may deviate from the regression line due to random variation. Therefore, while the regression line provides an estimate of the mean of the response variable for a given value of the predictor variable, it does not imply that all actual values of the response variable will fall precisely on the line.

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Answer:

-6x+2y=-18 = \(y = -9 + 3x\)

-3x-2y=54 = \(y = -27 - \frac{3x}{2}\)

Step-by-step explanation:

I hope I understood this correctly.

Answer:y= - 2x + 16

Step-by-step explanation:

An equation for C is C = 0.1t + 4.

An interpretation of the slope of the graph is that the total cost of using a computer increases by 0.1 per minute.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (5 - 4.5)/(10 - 5)

Slope (m) = 0.5/5

Slope (m) = 0.1

At data point (10, 5) and a slope of 0.1, a linear equation for C can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = 0.1(x - 10)

y = 0.1x + 5 - 1

y = 0.1x + 4 ≡ C = 0.1t + 4

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Grant can arrange 3 of his 10 plants on a window ledge in 720 ways.

To find the answer, we need to use the formula for permutations:

Permutations = n! / (n-r)!

Where:

- n is the total number of items

- r is the number of items to be arranged

- ! means factorial (e.g. 5! = 5 x 4 x 3 x 2 x 1)

In this case:

- n = 10 (the total number of plants)

- r = 3 (the number of plants to be arranged on the window ledge)

Plugging these values into the formula, we get:

Permutations = 10! / (10-3)! = 10! / 7! = (10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (7 x 6 x 5 x 4 x 3 x 2 x 1) = (10 x 9 x 8) / 1 = 720

Therefore, Grant can arrange 3 of his 10 plants on a window ledge in 720 ways.

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2(x - 2)

The given expression is:

3x−6x+x−4+4x

Collect like terms

3x - 6x + x + 4x - 4

Simplify the resulting expression

2x - 4

Factor out the common term (2) from the expression

2(x - 2)

Answer:

2(x−2)

Step-by-step explanation:

Solution Steps

3x−6x+x−4+4x

Combine 3x and −6x to get −3x.

−3x+x−4+4x

Combine −3x and x to get −2x.

−2x−4+4x

Combine −2x and 4x to get 2x.

2x−4

If the question is asking to look for the third angle, given angle a being 40° and angle b being 40° as well, then we must figure out the total ° that the triangle is (internally), which is 180°.

180 - (40 + 40)

180 - 80

100° is what angle C is

The amount of sugar in the entire shipment is 97(1)/(2) tons.

We are given that a shipment of sugar fills 2(1)/(5) containers. If each container holds 3(3)/(4) tons of sugar, we need to find the amount of sugar in the entire shipment.

Step-by-step explanation:

One container of sugar holds 3(3)/(4) tons of sugar. There are 2(1)/(5) containers of sugar in the shipment.

Amount of sugar in one container = 3(3)/(4) tons

Amount of sugar in 2(1)/(5) containers

= 2(1)/(5) × 3(3)/(4) tons

= 13/5 × 15/4 = 195/20

= 97(1)/(2) tons

Therefore, the amount of sugar in the entire shipment is 97(1)/(2) tons.

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An exponent is a number written above and to the right side of a value or number in math. The value or number is called the base, and the expression is read out as;

"Base raised to the power of exponent."

An example is given below;

In this example, 10 is the base and 3 is the EXPONENT.

The expression is now read out as,

"10 raised to the power of 3"

Note that even unknown values (such x as we commonly use in math) can also be an exponent or base. For example, we can have;

So basically, an exponent indicates the number of times a number is used to multiply itself.

Answer:

line graph i think

Step-by-step explanation:

i'm not sure, i don't even know but i tried

The line graph is best display the change over time to determine the change in the number of cars sold per month at a local car dealership.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

We have to given that;

Kelsey is trying to determine the change in the number of cars sold per month at a local car dealership.

Now, We know that;

The line graph is best display the change over time.

Hence, The line graph is best display the change over time to determine the change in the number of cars sold per month at a local car dealership.

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Answer:

8 people

Step-by-step explanation:

3 people to do the job in 16 hours so each of the people will mow 1/3 of the lawn during the 16 hours.

So if was a single person was mowing the lawn would take them 3 times longer 16*3 =48 hours

To mow the lawn in 6 hours will need 48 hours to be split in 6 hours so will get 48/6 = 8 people.

Answer: 48

Step-by-step explanation:

We need to find the least common multiple of 12 and 16.

Finding the prime factorizations of 12 and 16,

\(12=2^{2} \times 3\\\\16=2^{4}\)

Thus, the least common multiple is \(2^{4} \times 3=\boxed{48}\)

The type of sampling described, where the researchers intentionally select a sample with 50% straight and 50% LGBTQ+ respondents, is known as "disproportionate stratified sampling."

A. Disproportionate stratified sampling involves dividing the population into different groups (strata) based on certain characteristics and then intentionally selecting a different proportion of individuals from each group. In this case, the researchers are dividing the population based on sexual orientation (straight and LGBTQ+) and selecting an equal proportion from each group.

B. Availability sampling (also known as convenience sampling) refers to selecting individuals who are readily available or convenient for the researcher. This type of sampling does not guarantee representative or unbiased results and may introduce bias into the study.

C. Snowball sampling involves starting with a small number of participants who meet certain criteria and then asking them to refer other potential participants who also meet the criteria. This sampling method is often used when the target population is difficult to reach or identify, such as in hidden or marginalized communities.

D. Simple random sampling involves randomly selecting individuals from the population without any specific stratification or deliberate imbalance. Each individual in the population has an equal chance of being selected.

Given the description provided, the sampling method of intentionally selecting 50% straight and 50% LGBTQ+ respondents represents disproportionate stratified sampling.

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To compute the slope, intercept, and equation to predict the Price, we will use the formulae below:

For the equation

For the slope

For the intercept

In this case, we have the following data given:

Part A

Upon substituting the above into the formula, we will have

Hence slope = 141.41

Part B

Hence, Intercept =-292.099

PART C

The equation that can be used to predict Price from Capacity

Therefore, the equation is

Price=-292.099+(141.41)capacity

Part D

To predict the price of a 20.0TB disk, we will simply set the capacity= to 20 and then simplify

Hence, the predicted price is=2536.10

Answer:

75%=x-125

90%=x+250

subtract the second from the first

15%=375

100%=?

100%×375/15

100%=2500marked price is 2500

2500+250=2750

90%=2750

100%=?

cost price=3055.56

The historical rate of defective widgets produced by ACME Corporation was 7%. Approximately, 91.2 is the standard deviations is the point estimate from 7%.

In statistics, standard deviation is a measure of the amount of variation or distribution of a set of values. A low standard deviation indicates that the values ​​tend to be close to the ensemble mean (also called the expected value), while a high standard deviation indicates that the values ​​are spread over a wider range.

The standard deviation can be abbreviated SD, and is most commonly used in mathematical texts and equations with the lowercase Greek letter σ (sigma) for the population standard deviation, or the Latin letter s for the standard deviation of the sample.

The standard deviation of a random variable, sample, population, data set, or probability distribution is the square root of its variance. It is algebraically simpler than the mean absolute deviation, although less robust in practice. A useful property of the standard deviation is that, unlike the variance, it is expressed in the same units as the data.

According to the Question:

Given that:

Defective widgets produced by ACME corporation was 7%

Total sample was 856 widgets.

Therefore, the Standard Deviation estimates from 7% is:

856 of 7% = 91.2

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As a rough estimate, 100g of sugar is equivalent to 0.5 cups of granulated sugar.

Conversion is the process of changing units of measurement from one system to another.

In this case, we need to convert 100g of sugar into cups. However, the conversion factor for sugar varies depending on factors such as the type of sugar and how densely it is packed. For instance, powdered sugar is denser than granulated sugar, and so the conversion factor will differ.

In general, one cup of granulated sugar weighs around 200g, which means that 100g of sugar is equivalent to 0.5 cups. However, it is essential to note that this conversion factor is approximate and can vary depending on the quality and type of sugar used.

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Complete Question:

how many cup sugar in 100g?