Park rangers in Yosemite estimated the number of racoons in one hiking area. The rangers tagged 15 racoons in the hiking area. The following week they captured 40 racoons. If the park rangers estimated there were 75 in the area, how many of the captured racoons were tagged.

The values of a and b are 4 and -3

To solve for a, we make use of the function f(x).

x    f(x)

2     4

0     5

2     a

3     7

Remove the x values 0 and 3

x    f(x)

2     4

2     a

The above table implies that:

f(2) = 4 and f(2) = a

Substitute 4 for f(2) in f(2) = a

4 = a

Rewrite as:

a = 4

To solve for b, we make use of the function g(x).

x    g(x)

2     b

0     0

2     -3

3     -4

Remove the x values 0 and 3

x    g(x)

2     b

2     -3

The above table implies that:

f(2) = b and f(2) = -3

Substitute -3 for f(2) in f(2) = b

-3 = b

Rewrite as:

b = -3

Hence, the values of a and b are 4 and -3

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Complete question

Use the Symmetry of a Function to Find Coordinates

f is an even function             g is an odd function

x    f(x)                                        x             g(x)

2     4                                          2              b

0     5                                          0              0

2     a                                          2              -3

3     7                                          3              -4

Find a and b

Answer:

4, 3

Step-by-step explanation:

Answer:

8.25

Step-by-step explanation:

The pmf provides the probabilities of having 1, 2, or 3 children in the family based on the condition that the family stops having children once it has three children of the same gender.

To find the probability mass function (pmf) of the number of children in the family, we need to consider the possible values of x (the number of children) and their corresponding probabilities.
Let's analyze the possibilities:

1. x = 1 (only one child): The probability of having either a boy or a girl is 0.5. Therefore, P(x=1) = P(B or G) = 0.5.

2. x = 2 (two children): The possible outcomes are BB, GG, or BG (in any order). Each of these outcomes has a probability of 0.5 * 0.5 = 0.25. Therefore, P(x=2) = P(BB or GG or BG) = 0.25 + 0.25 + 0.25 = 0.75.

3. x = 3 (three children): The only outcome that satisfies the condition is BBB or GGG (in any order). Each of these outcomes has a probability of 0.5 * 0.5 * 0.5 = 0.125. Therefore, P(x=3) = P(BBB or GGG) = 0.125 + 0.125 = 0.25.

From the above analysis, we have:

P(x=1) = 0.5
P(x=2) = 0.75
P(x=3) = 0.25

To summarize, the pmf of x (the number of children in the family) is:
P(x=1) = 0.5, P(x=2) = 0.75, P(x=3) = 0.25.

The pmf provides the probabilities of having 1, 2, or 3 children in the family based on the condition that the family stops having children once it has three children of the same gender.

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The inverse Laplace transform of the given function F(s) is:

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A scatter plot is a graphical representation of the association between variables.

A scatter plot is a visual tool used to display the relationship or association between two numerical variables. It consists of a series of data points plotted on a graph, where each point represents the values of the two variables. The horizontal axis typically represents the independent variable, while the vertical axis represents the dependent variable.

By examining the pattern of the data points on the scatter plot, one can identify whether there is a positive, negative, or no correlation between the variables. Scatter plots are helpful in identifying trends, outliers, clusters, or any other patterns in the data. They provide a quick and intuitive way to assess the relationship between variables and are widely used in various fields, such as statistics, data analysis, and scientific research.

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Answer:

x=-9

Step-by-step explanation:

-2x+5=23

-5 on both sides

-2x=18

/-2 on both sides

x=-9

The calculated value of f(2) is 182 given that the function f(x) = 5(6)ˣ + 2

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

f(x) = 5(6)ˣ + 2

To calculate the value of f(2), we set x = 2

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

f(2) = 5(6)² + 2

Evaluate the exponent

This gives

f(2) = 5 * 36 + 2

Evaluate the product

This gives

f(2) = 180 + 2

So, we have

f(2) = 182

Hence, the value of f(2) is 182

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Answer: 6*4 or 8*3

Step-by-step explanation:

12^2=24

Answer:

x equals 14 - 7y

Step-by-step explanation:

x + 7y = 14

From this, take 7y to the other side. On shifting it to the other side of the equation, its sign changes to negative.

x = 14 - 7y

Then, we get x equals 14 - 7y.

Answer:

OA.1

Step-by-step explanation:

Function: f(x)=3x+4

A

f(5)=3(5)+4=19

Input

Function

Output

To evaluate a function, use the input value, which is typically an x value, in the function. Then, perform all calculations to determine the output value, which is typically a y value.

Recall that a function is a rule that produces an output value from an input value.

A function can only have one y value for any given x value. A vertical line test can be used to check this; if a vertical line crosses more than two points on the function, it is not a function.

To repeat the previous problem with a reliability of 98 percent, we need to find the value of C10 for which the Weibull distribution function gives a probability of 0.98 when X is at its 10th percentile. Using the Weibull parameters from example 11-3, we have a shape parameter (beta) of 2.5 and a scale parameter (eta) of 5.

To find C10, we can use the inverse Weibull distribution function, which is given by:

X = eta * (-ln(1 - p))^1/beta

where p is the probability (0.98), eta is the scale parameter (5), and beta is the shape parameter (2.5).

Substituting the values, we get:

C10 = eta * (-ln(1 - 0.98))^1/beta = 5 * (-ln(0.02))^0.4 = 13.86

Therefore, we expect to obtain a larger value for C10 with a reliability of 98 percent compared to the result in the previous problem, where the reliability was 90 percent. This is because the higher the reliability requirement, the more reliable the system needs to be, which means it needs to have a longer life. Hence, the value of C10, which represents the life at which 10 percent of the units fail, will be larger for a higher reliability requirement.

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Take the square root of each side.

\(\sf \sqrt{x^{2} } =\sqrt{25} \\\\\\ x=\± 5\)

Answer:

\(a_{n}=2+3(n-1)\)

Step-by-step explanation:

Step 1. To find the equation that describes the pattern, we use the arithmetic sequence formula:

\(a_{n}=a_{1}+d(n-1)\)

Where a_n is the n'th terms and d is the common ratio between the numbers.

Step 2. The sequence we have is:

2 5 8 11

The first term is:

\(a_{1}=2\)

And the common ratio or the difference between consecutive numbers is:

3 2+3=8 5+3=8  8+3=11

This will be the value of d:

d=3

Step 3. Substituting a_1 and d into the formula:

\(a_{n} =a_{1}+d(n-1)\\a_{n}=2+3(n-1)\)

This is the equation that represents the number pattern, it represents that we add three each time to the previous number in the sequence.

Hence, the correct answer is \(a_{n}=2+3(n-1)\)



The differential equation to be solved is Nxy - 0.5ye-0.1x for osx54 with y(0) = 6.5 dx. This can be solved using Euler's method in MATLAB.

Follow the steps below.

Step 1: Create a function file - The differential equation needs to be defined in a function file first. Let's create a function file named "odefun.m".function dydx = odefun(x,y)

dydx = N*x*y - 0.5*y*exp(-0.1*x);

where N is a constant value that needs to be defined.

Step 2: Define the given values - Define the given values such as N, initial value y(0), and step size dx.

N = ...; %

Define N herey 0 = 6.5; %

Define initial value of y here. dx = ...; %

Define step size here

Step 3: Use Euler's method to solve the differential equation - Now, use Euler's method to solve the differential equation using a for loop. The MATLAB code is as follows: x = 0:dx:54; %

Define range of x values here y = zeros(size(x)); %

Initialize y as a vector of zeros y(1) = y0; %

Assign initial value of y to y(1) for i = 1: length(x)-1 dydx = odefun(x(i),y(i)); y(i+1) = y(i) + dydx*dx; end

Step 4: Plot the solution - Finally, plot the solution using the MATLAB command plot(x,y).

The complete MATLAB code is given below:

N = ...; %

Define N here y0 = 6.5; %

Define initial value of y here dx = ...; %

Define step size here x = 0:dx:54; %

Define range of x values here y = zeros(size(x)); % Initialize y as a vector of zeros y(1) = y0; %

Assign initial value of y to y(1) for i = 1: length(x)-1 dydx = odefun(x(i),y(i)); y(i+1) = y(i) + dydx*dx; end plot(x,y)

The plot of the solution will be displayed.

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The value of x is 0.01

Angles can be measured using one of two standard units. Degrees are the most widely used unit of measurement. A straight angle is 90° since a circle has 360 equal degrees. We'll just take into account angles between 0° and 360° for the time being; however, we'll take into account angles higher than 360° and negative angles later, in the section on trigonometric functions.

Minutes and seconds can be used to further split degrees, but this separation is less common than it once was. Minutes are the 60 equal pieces that make up each degree. Thus, seven and a half degrees can also be written as seven degrees and thirty minutes, or seven°30'. Additionally, each minute is divided into 60 equal seconds.

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The missing factor in the second equation is 1, and the completed equation is: -24y + (-5) = -4(6y + 5/4)

We know that the GCF of -24y and -20 is 4. To find the missing factor in each equation, we can divide both terms by the GCF of 4.

For the first equation, we have:

-24y = 4 * (-6y)

Dividing both sides by 4, we get:

-6y = -24/4

Simplifying, we get:

-6y = -6

Therefore, the missing factor in the first equation is -1, and the completed equation is:

-24y + 20 = -4(6y - 5)

For the second equation, we have:

-20 = 4 * (-5)

Dividing both sides by 4, we get:

-5 = -20/4

Simplifying, we get:

-5 = -5/1

Therefore, the missing factor in the second equation is 1, and the completed equation is:

-24y + (-5) = -4(6y + 5/4)

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Answer:

2. n(2n+5)=26.

Step-by-step explanation:

If Sam has n stamps, and Nate has 5 more than twice that amount, the equation would be: 2. n(2n+5)=26.

In the present situation, the equation that best suits the sinusoidal function is given as:

(C) y = -12cos(1/12x)+ 12.

What is the meaning of a sinusoidal function?

A sinusoidal function is a function which oscillates smoothly, on a periodic basis, between high and low values. It is a sine-based function. Such a type of function is known as a sinusoidal function.

The cosine function, on the other hand, is just a horizontal shift of the sine function, can be used as a foundation for the sinusoidal functions.

A  mathematical curve also called as the sine wave, a sinusoidal wave or simply a sinusoid, can be described in terms of sine-trigonometric function, whose graph it is. It is a particularly a continuous wave or a smooth periodic function.

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Answer: 0.1056

Step-by-step explanation:

Given: Chipotle Burritos are normal distributed with

Mean =  200 mm

Standard deviation = 8 mm

Let x be the length of a random burrito.

The probability that a burrito picked at random is shorter than 190mm will be :

\(P(x<190)=P(\dfrac{x-\mu}{\sigma}<\dfrac{190-200}{8})\\\\=P(z<-1.25)\ \ \ [z=\dfrac{x-\mu}{\sigma}]\\\\=1-P(z<1.25)\\\\=1-0.8944\\\\=0.1056\)

Hence, the probability that a burrito picked at random is shorter than 190mm is 0.1056.

Answer:

the answer

is b

i hope that helps

Answer:

8 ^ 20

Step-by-step explanation:

(8 ^ 10) ^2

We know that a^ b^ c = a^ ( b*c)

8 ^ (10*2)

8 ^ 20

The speed of the train with time is given on a speed time graph

obtained from a past questions website drawn and attached here.

Correct response:

Given:

Length of the train = 220 m

Time at which the train crossed the bridge = 9:30

Length of the bridge = 1,400 m

The plot of the graph of the motion of the train obtained from a past papers website and created with MS Excel is attached;

From the attached graph, we have;

The speed of the train at 9:30 = 126 km/h

Required:

The time it took the train to completely cross the bridge.

Solution:

\(126 \, km/h = 126 \, km/hr \times \dfrac{1,000 \, m}{1 \, km} \times \dfrac{1 \ hr}{3,600 \, s} = \mathbf{ 35 \, m/s}\)

Therefore, the time it took the train to completely cross the bridge is given as follows;

Distance traveled = 1,400 m + 220 m = 1,620 m

The time it took the train to completely cross the bridge is t ≈ 46.29 s

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Answer:

b

Step-by-step explanation:

The mean is calculated by adding up all the numbers in the data set and dividing by the total number of values. In this case, the sum of the numbers is 105 and there are 16 values, so the mean is 6.56 cups of coffee per week on average.

To find the median, we need to arrange the numbers in order from smallest to largest. The ordered list is: 1, 1, 2, 2, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 36. The median is the middle value, which is 6.

In this case, the median is a better measure of central tendency because the data set includes an outlier value of 36 cups per week. This single value skews the mean and makes it less representative of the majority of employees' coffee consumption. The median, on the other hand, is not affected by outliers and represents the middle value in the data set, which is more reflective of the typical coffee consumption for this office.

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The component form of the vector that describes the drummer's movement is <4, -3>.

The component form of a vector is given by the difference between the coordinates of the endpoints.

The initial point is (1, 4) and the final point is (5, 1).

Thus, the horizontal component is the difference between the x-coordinates, which is 5 - 1 = 4,

and the vertical component is the difference between the y-coordinates, which is 1 - 4 = -3.

Therefore, the component form of the vector that describes the drummer's movement is <4, -3>.

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Answer:

I believe that the answer is 9

Step-by-step explanation:

You just replace x with 3

Answer:

x = 6

Step-by-step explanation:

4(x - 3) + 5x - x^2

Substitute x with 3

4(3 - 3) + 5(3) - 3^2

Solve via PMDAS so Parenthesis first

4(0) + 5(3) - 3^2

Multiply then the rest is Self-Explanatory

15 - 9

x = 6

Hope this helped!

The reflexive closure of a relation on a set is the smallest reflexive relation that contains the original relation. In other words, it is the addition of pairs that ensure every element in the set is related to itself. To form the reflexive closure, we need to add pairs that relate each element in the set to itself.

To form the reflexive closure of relation r on the set {0, 1, 2, 3}, we need to add ordered pairs that ensure every element in the set is related to itself. In other words, we need to add pairs of the form (x, x) for each element x in the set that is not already present in relation r.

In this case, the reflexive closure of relation r would require adding the following ordered pairs: (0, 0), (1, 1), (2, 2), and (3, 3). These pairs ensure that every element in the set {0, 1, 2, 3} is related to itself, making the relation reflexive. These pairs ensure that every element is related to itself, satisfying the reflexivity property.

By adding these additional ordered pairs, we have modified relation r to include reflexivity, as every element now has a direct relation to itself in the set.

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Answer:

the profit is $1.66 per pastry

Step-by-step explanation:

Answer:

The profit is 20 cents per pastry

Step-by-step explanation: