A population numbers 17,000 organisms initially and decreases by 4% each year.
Suppose P represents population, and t the number of years of growth. Write an exponential model to represent this situation.

Answer:

x = 13

Step-by-step explanation:

Given: f ( x ) = 4.5 x 2 − 3 x + 2 To determine the critical points, we must first calculate the first derivative of the function.

Differentiate the given function with respect to x using the power rule of differentiation, d d x x n = n x n − 1.

f ′ (x) =    d        (4.5 x 2 − 3 x + 2)

        ______        

            d x  

Apply sum rule: d d x (f(x)) + g (x) = d d x f (x) + d d x g (x) } f ′ ( x) = d d x (4.5 x^2) + d d x (−3 x) + d d x (x) f ′ (x) = 9 x − 3

To determine the critical points, set f ′ (x) = 0 . 9 x − 3 = 0 9 x = 3 {∴ x = 13}

Therefore, the tangent line to f(x) is horizontal at the point x = 13

Hope this helps, have a nice day/night! :D

The factored form of the polynomial is (5x^(3))(-x^(3)+3x+4).

To factor the polynomial with a negative coefficient, -5x^(6)+15x^(4)+20x^(3), we can use the content loaded factor method. This method involves factoring out the greatest common factor (GCF) of all the terms in the polynomial.

The GCF of -5x^(6), 15x^(4), and 20x^(3) is 5x^(3). So, we can factor out 5x^(3) from each term:

-5x^(6) = -(5x^(3))(x^(3))
15x^(4) = (5x^(3))(3x)
20x^(3) = (5x^(3))(4)

Now, we can rewrite the polynomial as:

-5x^(6)+15x^(4)+20x^(3) = (5x^(3))(-x^(3)+3x+4)

So, the factored form of the polynomial is (5x^(3))(-x^(3)+3x+4).

In summary, the polynomial -5x^(6)+15x^(4)+20x^(3) can be factored as (5x^(3))(-x^(3)+3x+4) using the content loaded factor method.

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Answer:

True false true

Step-by-step explanation:

I think so

The length of the rectangle is approximately 41.34 inches.

Let's assume the width of the rectangle is represented by the variable w. According to the given information, the length of the rectangle is four less than twice the width, which can be expressed as 2w - 4.

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 128 inches. Since a rectangle has two pairs of equal sides, we can set up the equation:

2w + 2(2w - 4) = 128.

Simplifying the equation, we get:

2w + 4w - 8 = 128,

6w - 8 = 128,

6w = 136,

w = 22.67.

So, the width of the rectangle is approximately 22.67 inches. To find the length, we can substitute this value back into the expression 2w - 4:

2(22.67) - 4 = 41.34.

Therefore, the length of the rectangle is approximately 41.34 inches.

In summary, the length of the rectangle is approximately 41.34 inches. This is determined by setting up a system of equations based on the given information: the perimeter of the rectangle being 128 inches and the length being four less than twice the width.

By solving the system of equations, we find that the width is approximately 22.67 inches, and substituting this value back, we obtain the length of approximately 41.34 inches.

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The number of terms in the series is 9, which corresponds to answer option c) 9.

In this arithmetic series, the first term is given as 123 and the common difference is 12. The sum of the series is given as 1113.

To find the number of terms in the series, we can use the formula for the sum of an arithmetic series:

S = (n/2) * (2a + (n-1)d)

Where S is the sum of the series, n is the number of terms, a is the first term, and d is the common difference.

In this case, we are given S as 1113, a as 123, and d as 12. Plugging in these values into the formula, we can solve for n:

1113 = (n/2) * (2(123) + (n-1)(12))

Simplifying this equation:

1113 = (n/2) * (246 + 12n - 12)

1113 = (n/2) * (234 + 12n)

Multiplying both sides by 2:

2226 = n(234 + 12n)

Rearranging the equation:

\(12n^2\) + 234n - 2226 = 0

Using the quadratic formula to solve for n, we find that n = 9.

Therefore, the number of terms in the series is 9, which corresponds to answer option c) 9.

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The U.S. Census Bureau takes a census every 10 years, which means that they attempt to count every person living in the United States and collect data on various demographic and social characteristics.

A sample is a subset of a larger population, selected in a way that it represents the characteristics of the population from which it is drawn. The purpose of sampling is to estimate or infer something about the population based on the characteristics of the sample.

On the other hand, a census is a survey or count that attempts to measure every member of a population.

In a census, data is collected on every individual or item in a population, rather than just a representative sample.

If you wanted to estimate the average income of households in a city, you could select a sample of households and estimate the average income based on the incomes of the sampled households.

This would be an example of sampling.

Alternatively, you could conduct a census of every household in the city, collecting income data from every household, and calculate the exact average income of all households in the city.

The purpose of the census is to provide a complete and accurate count of the population, which can then be used to allocate political representation and government funding, as well as to provide data for research and planning purposes.

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Recall that a reflection over a line y=k transforms the point (x,y) into:

Therefore the given sequence of transformations will change point (x,y) into:

Answer:

Since the original coordinates are P(-4,3), Q(0,3), and B(-3,-1), the coordinates of image 2 are:

Answer:

-1

Step-by-step explanation:

First we combine like terms, so y2 - 5y = - 3y

Now we get - 3y = 3

Then we divide both sides by - 3

Now we get y =-1

Answer:

Step-by-step explanation:

The answer is y= +/- 5 sqrt 37/2

The probability that the dart hits the bullseye is 0.04

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

Dart board of diameter 40 cm

Bullseye of diameter 8 cm

The areas of the above shapes are

Dart board = 3.14 * (40/2) * (40/2) = 1256

Bullseye = 3.14 * (8/2) * (8/2) =50.24

The probability is then calculated as

P = Bullseye/Dart board

So, we have

P = 50.24/1256

Evaluate

P = 0.04

Hence, the probability is 0.04

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Answer: the engineer counted t/26 trucks

Step-by-step explanation:

Hi yess my user name is my number teehee

where are the choices? Since its a select all that apply u should send what the options are

Kareem has 7 more strips of wood siding than vinyl siding.

What is a siding?

A siding is a brief railroad track with one or both ends opening into the main track, used to switch one of two meeting trains until the other has passed. Or a siding is any of a number of different forms of weatherproof face for frame buildings, made up of individual sections fastened together as shingles, plain or shaped boards, various sheet metal components, or other composition materials.

Number of vinyl siding strips = 2623/313 = 8.38 ≈ 8 strips

Number of wooden siding strips = 3334/214 = 15.57 ≈ 15 strips

Therefore, extra strips of wooden siding = 15 - 8 = 7 strips

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Answer:

the only thing I can do is get a refund for the convenience of the day and I'll be there in a few minutes to get a refund for the convenience of the day and I'll be there in a few minutes to get a refund for the convenience of the day and I'll be there in a few minutes to get a

Answer:

A

Step-by-step explanation:

The probability that the sample proportion will be at least k is 0.7580.

Let P be the probability that any one person in the population will cooperate and respond to the questions. We are looking for the probability that at least k people out of n in the sample will cooperate and respond to the questions. Let X be the number of people who cooperate and respond to the questions in the sample. X follows the binomial distribution with parameters n and P.To calculate this, use the following formula:

Z = (X - μ) / σ

Here, X = number of people who cooperate and respond to the questions in the sample

μ = E(X) = np,  σ = sqrt(npq)

q = 1 - P

Now, to calculate the probability, first calculate μ = np =

σ = sqrt(npq)

Then, find the z-score using z = (k - μ) / σ.

Now, use the z-table to find the probability corresponding to the z-score obtained in the previous step. The probability obtained from the z-table is the probability that the sample proportion will be at least k.

The probability that the sample proportion will be at least k is 0.7580.

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The measure of angle of elevation is the angle between the horizontal line of sight and the line of sight to an object above the horizon.

The measure of angle of elevation is the angle between the horizontal line of sight and the line of sight to an object above the horizon. To calculate the angle of elevation, first draw a horizontal line and draw a line from the observer’s eye level to the object. Then draw a line from the object to the same point on the horizontal line. The angle formed by the lines is the angle of elevation. Use a protractor to measure the angle and record the measurement. To calculate the angle of depression, draw a line from the object to the observer’s eye level and draw a line from the same point to the horizontal line. The angle formed by the lines is the angle of depression. Use a protractor to measure the angle and record the measurement.

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Answer:

a) x = 5

b) x = 4

Step-by-step explanation:

a) x:2 = 10:4

Product of extremes = Product of means

=> x*4 = 10*2

=> 4x = 20

Dividing both sides by 4

=> x = 5

b) 3:x = 6:8

Product of extremes = Product of Means

=> 3*8 = 6*x

=> 24 = 6x

Dividing both sides by 6

=> x = 4

Answer:

Solution,

\(a. \: \: \frac{x}{2} = \frac{10}{4} \\ \: \: or \: x \times 4 = 10 \times 2 \: ( \: cross \: multiplication) \\ \: \: or \: 4x = 20 \\ or \:x = \frac{20}{4} \\ \: \: \: x = 5\)

\(b. \: \frac{3}{x} = \frac{6}{8} \\ or \: 6 \times x = 3 \times 8 \: ( \: cross \: multiplication) \\ or \: 6x = 24 \\ \: or \: x = \frac{24}{6} \\ x = 4\)

Hope this helps...

Good luck on your assignment

The degree 3 polynomial with the zeros {1, 4, 2} and a leading coefficient equal to 1 is:

p(x) = x^3 -7x^2 + 14x - 8

We know that for a polynomial of degree n, with a leading coefficient "a" and the zeros {x₁, x₂, ..., xₙ} can be written as:

p(x) = a*(x - x₁)*(x - x₂)*...*(x - xₙ)

Knowing that here we have a polynomial of degree n = 3, with a leading coefficient a = 1, and the zeros {1, 4, 2}

Replacing these in the above form, we get:

p(x) = 1*(x - 1)*(x - 4)*(x - 2)

Now we can expand that to get:

p(x) = (x^2 - x - 4x + 4)*(x - 2) = (x^2 - 5x + 4)*(x - 2)

p(x) = x^3 - 5x^2 + 4x - 2x^2 + 10x - 8

p(x) = x^3 -7x^2 + 14x - 8

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Answer:

mathematically it means the sum of 1 and 3 gives or equals to 3

Step-by-step explanation:

Answer: A. The researcher computes difference scores to compute a t statistic

B. If the researcher has n number of participants to use in the experiment, then the degrees of freedom will be the same in a repeated-measures experiment or in a matched-subjects experiment

C. The researcher must compute an estimated standard error for the mean difference score to compute a t statistic.

D. Participants in both types of experiments are all measured the same number of times

A matched-subjects experiment produced a t statistic with a df of 9. How many subjects participated in this study?

A. 20

B. 10

C. 18

D. 9

For a repeated-measures experiment comparing two treatment conditions, the t statistic has a df of 11. How many subjects participated in this study?

A. 12

B. 22

C. 24

D. 11

Step-by-step explanation:

Step-by-step explanation:

-√81=-√(9)²=-9

A number inside a Square root cannot ne negative. So, the second one is not a real no.

Answer:

\( - \sqrt{81} = - 9 \\ \sqrt{ - 25 = - 5} \)

Step-by-step explanation:

-81/9 9+9+9+9+9+9+9+9+9(81)

-9

-25/5 (5+5+5+5+5(25)

-5

Answer:

3

Step-by-step explanation:

Factor the numerator and denominator and cancel the common factors.

Answer:

2.25 or fraction 9/4

Step-by-step explanation:

We do not have enough evidence to show that the proportion of households owning a cat has increased from 30%.

The appropriate null and alternative hypotheses in this scenario would be:

H0: p = 0.30 (the proportion of households owning a cat is equal to 30%)
Ha: p > 0.30 (the proportion of households owning a cat has increased from 30%)

To determine if there is enough evidence to support the alternative hypothesis, we can conduct a hypothesis test using a significance level (alpha) of 0.05. We would calculate the test statistic using the formula:

z = (sample proportion - population proportion) / standard error

In this case, the sample proportion is 0.35, the population proportion is 0.30, and the standard error can be calculated using the formula:

SE = sqrt[(p * q) / n]

where p is the population proportion (0.30), q is 1 - p (0.70), and n is the sample size (210).

Plugging in these values, we get:

SE = sqrt[(0.30 * 0.70) / 210] = 0.038

Then, we can calculate the test statistic:

z = (0.35 - 0.30) / 0.038 = 1.32

To determine if this test statistic is significant, we can compare it to the critical value from a z-table. For a one-tailed test at a significance level of 0.05, the critical value is 1.645. Since our test statistic of 1.32 is less than the critical value of 1.645, we fail to reject the null hypothesis.

Therefore, we do not have enough evidence to show that the proportion of households owning a cat has increased from 30%.

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Answer:

Use the graph to complete the statements.

The two variables are  

✔ bananas and days

✔ days

✔ bananas

✔ days

✔ bananas

Got it right lol uwu

The statement first "The number of bananas is the independent variable, and the cost in dollars is the dependent variable" is correct.

A line graph is a graph made up of segments of straight lines that connect the depicted data points.

here, we have,

On a coordinate plane, the points (1, 2), (2, 4), (3, 6), (4, 8), and (5, 10) are plotted.

We have:

The line goes through points (1, 0.27) and (2, 0.54).

The x-axis represents the independent variable

The y-axis represents the dependent variable.

Thus, the statement first "The number of bananas is the independent variable, and the cost in dollars is the dependent variable" is correct.

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The algebraic expression that can be represented by the statement is -5x/2 = 10

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

The negation of the product of five times a number divided by two is ten

Represent the variable with y

So, we have the following representation

The negation of the product of five times x divided by two is ten

Express the product as an actual product

So, we have the following representation

The negation of 5x divided by two is ten

Express the quotient as an actual quotient

So, we have the following representation

The negation of the 5x/2 is ten

Lastly, we have

-5x/2 = 10

Hence, the expression is -5x/2 = 10

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The equation of line which has slope -3/4 and passes through a point (-5,4) is given by          

y = -3/4x  +1/4

We have been given,

                       Slope = m = -3/4

                       Point = (x1,y1) = (-5,4)

The general slope-intercept form is given as,

              y = mx + c

                 where m = slope

                               c = intercept

Further, the formula to find the equation of line when we have been given one point and the slope is as follows,

            (y-y1) = m(x-x1)            (1)

Now putting the required value in equation (1) we will get,

       (y-4) = -3/4(x+5)

        y-4 = -3/4x – 15/4

         y = -3/4x – 15/4 + 4

         y = -3/4x  +1/4

Thus, the equation of line which has slope -3/4 and passes through a point (-5,4) is given by          

y = -3/4x  +1/4

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The orthonormal basis for V is: {v1 = 1/√(2), v2 = (t - √(2)/2)/√(2), v3 = (√(3)/2)t^2 - (√(6)/2)t}. To produce an orthonormal basis for V, we need to find a set of vectors that are linearly independent and can span the space V. Since we are working with polynomials of degree less than 2, we can write them in the form:

p(t) = at^2 + bt + c

where a, b, and c are real coefficients.

To find the basis, we can start with the standard basis for V, which is {1, t, t^2}. We can then use the Gram-Schmidt process to produce an orthonormal basis.

Here are the steps:

1. Normalize the first vector in the basis, which is 1, to obtain:

v1 = 1/√(2)

2. Calculate the projection of t onto v1 and subtract it from t to obtain the second vector in the basis:

v2 = (t - (t, v1)v1)/∥(t - (t, v1)v1)∥

where (t, v1) is the inner product of t and v1.

Simplifying, we get:

v2 = (t - √(2)/2)/√(2)

3. Finally, calculate the projection of t^2 onto v1 and v2, and subtract these projections from t^2 to obtain the third vector in the basis:

v3 = (t^2 - (t^2, v1)v1 - (t^2, v2)v2)/∥(t^2 - (t^2, v1)v1 - (t^2, v2)v2)∥

where (t^2, v1) and (t^2, v2) are the inner products of t^2 with v1 and v2, respectively.

Simplifying, we get:

v3 = (√(3)/2)t^2 - (√(6)/2)t

Therefore, the orthonormal basis for V is:

{v1 = 1/√(2), v2 = (t - √(2)/2)/√(2), v3 = (√(3)/2)t^2 - (√(6)/2)t}

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The absolute threshold is defined as the minimum detectable stimulus or intensity.

The absolute threshold refers to the minimum amount or level of a stimulus that is required for it to be detected or perceived by an individual. It is the point at which a stimulus becomes perceptible or noticeable to a person.

In sensory psychology, the absolute threshold is typically measured in terms of the lowest intensity or magnitude of a stimulus that can be detected accurately by a person at least 50% of the time. It represents the boundary between the absence of perception and the presence of perception.

The absolute threshold can vary depending on the sensory modality being tested. For example, in vision, it may refer to the minimum amount of light required for a person to see an object. In hearing, it may represent the minimum sound intensity needed for an individual to hear a tone.

Several factors can influence the absolute threshold, including individual differences, physiological factors, and the nature of the stimulus itself. Factors such as sensory acuity, attention, fatigue, and background noise can all affect an individual's ability to detect a stimulus.

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Answer:

$5

Step-by-step explanation:

The opposite of multiplication is division.

$15/Raking = 3 times more pay than mowing the lawn.

Divide $15/Raking by 3 and you'll get the pay for mowing the lawn.

15/3 = 5

Answer:

5

Step-by-step explanation: