The function f(x) = 5,000(0.972)X, where x is the time in years, models a declining
lemming population. Approximately how many lemmings will there be in 4 years?
(Round your answer to the nearest whole number, and enter the number only.)

Answer:

3

Step-by-step explanation:

Answer:

y = 8.5

Step-by-step explanation:

7y - 4 = 9y +13 - 4y  

First arrange to combine like terms.

7y - 4 = 9y - 4y + 13

7y - 4 = 5y + 13     Subtract 5y from each side

7y - 5y - 4 = 5y - 5y + 13

7y - 5y - 4 = 13

2y - 4 = 13   Add 4 to each side

2y - 4 + 4 = 13 + 4

2y = 13 + 4

2y = 17   Divide each side by 2

2y/2 = 17/2

y = 17/2 or 8\(\frac{1}{2}\) or 8.5

The regression equation for the given data set is y = -0.51x + 100.12.

To find the regression equation, we need to first calculate the slope and intercept of the regression line. Using the formula for slope (b) and intercept (a) of the regression line, we get:

b = r(Sy/Sx)

a = y-bar - b(x-bar)

where r is the correlation coefficient, Sy and Sx are the standard deviations of y and x respectively, and y-bar and x-bar are the means of y and x respectively.

Using the given data, we can calculate the means, standard deviations, and correlation coefficient. Then, we can substitute these values into the formulas to get the regression equation.

After calculating, we get the equation y = -0.51x + 100.12. This equation represents the line of best fit for the given data, which can be used to predict the value of y for any given value of x.

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The Matlab & Simulink model consists of a Clock block to generate a time signal, a Gain block to multiply the time signal by 2, and a Differential Equation block to solve the given differential equation. The Scope block is used to visualize the behavior of the variable x over time.

To construct a Matlab & Simulink model for the given mathematical model, we can use Simulink's Differential Equation block and a Clock and Gain block. Here's a step-by-step guide:

1. Open Simulink in Matlab.

2. Drag and drop a Clock block from the Simulink Library Browser into the model.

3. Drag and drop a Gain block from the Simulink Library Browser into the model.

4. Double-click on the Gain block and set the Gain value to 2.

5. Drag and drop a Differential Equation block from the Simulink Library Browser into the model.

6. Double-click on the Differential Equation block and enter the equation `d²x + 3 + 4*x + 6 = 5*cos(2*t)`.

7. Connect the output of the Clock block to the input of the Gain block, and the output of the Gain block to the input of the Differential Equation block.

8. Connect the output of the Differential Equation block to a Scope block from the Simulink Library Browser.

9. Run the simulation.

The Scope block will show the behavior of the value of x over time according to the given mathematical model.

In conclusion, The Clock block provides the independent variable t, and the Differential Equation block evaluates the given equation to compute the value of x. The simulation shows the dynamic response of x as influenced by the equation and the time signal.

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To find the relative frequency of boys who want to go to the water park, we need to divide the number of boys who want to go to the water park by the total number of boys in the sample:

Relative frequency = Number of boys who want to go to the water park / Total number of boys

Assuming you have the necessary data, you can compute this value by dividing the number of boys who want to go to the water park by the total number of boys and rounding the result to the nearest hundredth.

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The weighted mean takes into account the weight of each investment and can provide a more accurate measure of the overall rate of return on the portfolio than the mean or median.

The weighted mean, mean, and median overall rate of return on this investment portfolio can be calculated using the following formulas:

Weighted Mean: Weighted mean = (R1 x W1) + (R2 x W2) + (R3 x W3) + ...

Mean: Mean = (R1 + R2 + R3 + ...) / N

Median: Median = (N + 1) / 2

where R1, R2, etc. are the returns on individual investments, W1, W2, etc. are the weights assigned to each investment, and N is the total number of investments in the portfolio.

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Answer:

Angle O congruent to Angle S, because this would pass the SAS proof. (Side Angle Side)

We know that it took 18 hours to drive 666 miles. If we divide the distance by the hours (666 miles)/(18 hours)

We find that 666/18= 37 miles per hour . which means we travel 37 miles each hour.

So, we can estimate that driving 37 miles it will take 1 hour (the distance to Chicago).

Answer:

666/18=37miles/hour

it would take 1 hour to drive 37 miles

The answer to 4x10^7 is much larger than 4x10^3. In fact, it is 10,000 times larger.

This is because the exponent (the number after the "^" symbol) indicates how many zeros are added after the number. So, 4x10^7 means that there are seven zeros added after the 4, while 4x10^3 only has three zeros added after the 4. To understand this better, let's break it down.

4x10^7 is equivalent to 4,000,000 (4 million) while 4x10^3 is equivalent to 4,000.

Therefore, if we divide 4x10^7 by 4x10^3, we get 1,0000 or 10,000. This means that 4x10^7 is 10,000 times larger than 4x10^3.

It's important to understand exponents as they are commonly used in math and science and help to represent very large or very small numbers in a compact way.

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The words that characterize the triangle which are the desired slopes and lengths are;

Slope of \(\overline{FG}\) = \(-2\frac{2}{3}\)

Slope of \(\overline{GH}\) = 1/5

Slope of \(\overline{FH}\) = -7/8

Length of \(\overline{FG}\) = √(73)

Length of \(\overline{GH}\) = √(26)

Length of \(\overline{FH}\) = √(113)

The slope of a segment is the ratio of the rise to the run of the line representing the segment when plotted on a graph.

The required slopes and lengths, obtained from a similar question are;

Slope of the segment \(\overline{FG}\)

The formula for the slope, m, of a line with coordinate points (x₁, y₁), and (x₂, y₂) is presented as follows;

\(m = \dfrac{y_2 - y_1}{x_2 - x_1}\)

The slope of the segment  \(\overline{FG}\) with coordinates of the points F(7, 1), and G(4, 9) is therefore;

The slope the segment \(\overline{GH}\) is found as follows;

The coordinates of the points are; G(4, 9) and H(-1, 8)

The slope the segment \(\overline{FH}\) is found as follows;

The coordinates of the points are; F(7, 1) and H(-1, 8)

The length of the segments can be found using the formula for finding the distance, d, between two points (x₁, y₁), and (x₂, y₂) is presented as follows;

d = √((x₂ - x₁)² + (y₂ - y₁)²)

The lengths of the three sides of the triangle ΔFGH are different, therefore, triangle ΔFGH is a scalene triangle

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Answer:

160

Step-by-step explanation:

360-170-30=160 subtract all angles from 360

Answer:

140°

Step-by-step explanation:

oh, come on, this is like "you have 8 apples as a mixture of red and green apples. 5 apples are red, how many are green ?".

it is the same here.

the total angle is 170°.

now we know a part of it is 30°.

how large is the rest ?

well, it is 170 - 30 = 140°

Answer:

  C.  142°

Step-by-step explanation:

You want the angle between vectors u=3i+√3j and v=-2i-5j.

There are a number of ways the angle between the vectors can be found. For example, the dot-product relation can give you the cosine of the angle:

  u•v = |u|·|v|·cos(θ) . . . . . . where θ is the angle of interest

You can find the angles of the vectors individually, and subtract those:

  u = |u|∠α

  v = |v|∠β

  θ = α - β

When the vectors are expressed as complex numbers, the angle between them is the angle of their quotient:

  \(\dfrac{\vec{u}}{\vec{v}}=\dfrac{|\vec{u}|\angle\alpha}{|\vec{v}|\angle\beta}=\dfrac{|\vec{u}|}{|\vec{v}|}\angle(\alpha-\beta)=\dfrac{|\vec{u}|}{|\vec{v}|}\angle\theta\)

This method is used in the calculation shown in the first attachment. The angle between u and v is about 142°.

A graphing program can draw the vectors and measure the angle between them. This is shown in the second attachment.

__

Additional comment

The approach using the quotient of the vectors written as complex numbers is simply computed using a calculator with appropriate complex number functions. There doesn't seem to be any 3D equivalent.

The dot-product relation will work with 3D vectors as well as 2D vectors.

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Answer:

1.70

Step-by-step explanation:

15.30 ÷ 9 = 1.70

1.70 dollars per chicken wing

I hope this helps

Answer:

Solve for be is 56

Step-by-step explanation:

That the answer

Answer:

I think 20

because her starting point was 5 and her ending point was 25 and the difference is 20

Answer:

B) 20

Step-by-step explanation:

Substituting these values back into equation (i), we get D = 4(3) = 12. There are 3 nickels, 12 dimes, and 3 quarters in the collection.

Let's assume the number of nickels is N, the number of dimes is D, and the number of quarters is Q. From the given information, we can deduce three equations:

(i) D = 4N (since there are 4 times more dimes than nickels),

(ii) N + D + Q = 18 (since there are 18 coins in total), and

(iii) 5N + 10D + 25Q = 290 (since the total value of the coins is 290 cents or $2.90).

To solve these equations, we can substitute the value of D from equation (i) into equations (ii) and (iii).

Substituting D = 4N into equation (ii), we get N + 4N + Q = 18, which simplifies to 5N + Q = 18.

Substituting D = 4N into equation (iii), we get 5N + 10(4N) + 25Q = 290, which simplifies to 45N + 25Q = 290.

Now we have a system of two equations with two variables (N and Q). By solving these equations simultaneously, we find N = 3 and Q = 3.

Substituting these values back into equation (i), we get D = 4(3) = 12.

Therefore, there are 3 nickels, 12 dimes, and 3 quarters in the collection.

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Answer:

Olivia spent 129 minutes or 2:15 doing all the homework

Step-by-step explanation:

Answer: 47.4 or -42.6/negative

Step-by-step explanation: i tried my best

An acute triangle

Step-by-step explanation:

Using a calculator, these measurements fit an acute scalene triangle.

Answer:

acute

Step-by-step explanation:

A metric can be used to help us determine the extent of how much an outcome is achieved.

A metric is a quantifiable gauge that is employed to assess, scrutinize, and appraise diverse facets of a system, procedure, or outcome. It furnishes a standardized and unbiased approach to gauge and monitor performance or advancement towards particular objectives or goals. Metrics are commonly formulated based on precise criteria or prerequisites and can manifest as numerical or qualitative in essence.

They find application in various domains such as commerce, finance, science, engineering, and myriad others to evaluate performance, facilitate well-informed decisions, and oversee progress over time.

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Yes Kevin's comparison in the number line is correct because 10.9 is less than 11.5.

A number line is described as a picture of a graduated straight line that serves as visual representation of the real numbers.

We can agree with Kevin  after referencing the decimal value chart or decimal comparisons below.

o   t     h

10  9

11   5

A number line can also be referred to as a  pictorial representation of numbers on a straight line that is used for  comparing and ordering numbers.

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Answer: 11

Step-by-step explanation:

The following ordered pair is given as {(1, -1), (2,0), (3,1)} for the given data of movement of arrow.

A set comprises elements or members that can be mathematical objects of any sort, including numbers, symbols, points in space, lines, other geometric forms, variables, or even other sets. A set is the mathematical model for a collection of various things.

An ordered pair consists of two items. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples, or 2-length sequences.

An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence. In order to understand a point visually, it might be helpful to position it on the Cartesian plane. An ordered pair's numerical values may be fractions or integers.

The following ordered pair is given as {(1, -1), (2,0), (3,1)} for the given data of movement of arrow.

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Answer:

D

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The number of novels purchased was 9 novels.

Let the number of novels purchased be x and the number of magazines purchased be y.

Hence, \(x + y = 11.\)

Let the selling price of novels be a and that of magazines be b.

Therefore, \(ax + by = 20.\)

Similarly, given the price of magazines and novels as shown below:

\(a=  2\\b = 1\)

We can use the given equations above to find the number of novels purchased.

To find the value of x, we substitute the value of a and b into the equations,

\(ax + by = $20$2x + $1y \\= $20\)

We can also use the equation we found from \(x + y = 11,\) and solve for \(y:y = 11 - x\)

We can now substitute this value of y into the equation\(2x + 1y = 202x + 1(11 - x) \\= 201x \\=9x \\= 9 novels\)

Therefore, the number of novels purchased was 9 novels.

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