Chapter 3 Written Assignment A population of frogs has 1,200 members when an initial observation is made. The population is believed to be growing at a rate of 5.2% annually. a. Write a formula for the number of frogs, F, as function of years since the initial observation t. Form: F = a(b)(4 points) b. Find the number of frogs in the population after 8 years. Round to the nearest frog. (3 points) c. Use logarithms to determine the number of years for the population to reach 2000 frogs. (Round to the nearest year) (4 points)

Answer:

A. -(5y+2) + y = 5

Step-by-step explanation:

Solving the above Equation given to us in the Question,

-x + y = 5...... Equation 1

x - 5y = 2....... Equation 2

Step 1

We make x subject of the formula in Equation 2

---> x= 5y + 2

Step 2

This would be to substitute 5y + 2 for x in Equation 1

-x + y = 5...... Equation 1

-(5y+2) + y = 5

Hence, Option A is the correct option

Answer:

Step-by-step explanation:

Let the numbers be x and y

HCF is 8, so both numbers are multiples of 8 ⇒ x = 8n, y = 8m

As per property of numbers, the product of numbers is equal to product of their LCM and HCF:

Since LCM(x,y) = 80 we have:

Possible option:

Then the numbers are:

The base salary per year is $66,200, and she only gets the target for medication A, the 70% of the annual bonus of $22,500

(22,500 * 70)/ 100 = 15,750

So the total of her compensation (salary plus bonus) is:

$66,200 + $15,750 = $81950

Answer:

19,188

Step-by-step explanation:

hope this helps ;)

Answer: The probability of a student taking the SATs is p = 0.61. Let's consider the first student we sample. The probability that this student does not take the SATs is q = 1 - p = 0.39.

If the first student does not take the SATs, we need to sample another student. The probability that the second student does not take the SATs, given that the first student did not take the SATs, is still q = 0.39.

Similarly, if the second student also does not take the SATs, we need to sample a third student. The probability that the third student does not take the SATs, given that the first two students did not take the SATs, is still q = 0.39.

We continue this process until we find the first student who takes the SATs. Let X be the number of students we sample until we find the first student who takes the SATs. Then X can take on the values 1, 2, 3, and so on.

The probability that we find the first student who takes the SATs on the first try is p = 0.61. The probability that we find the first student who takes the SATs on the second try is (q)(p) = (0.39)(0.61) = 0.238.

Similarly, the probability that we find the first student who takes the SATs on the third try is (q)(q)(p) = (0.39)(0.39)(0.61) = 0.147.

In general, the probability that we find the first student who takes the SATs on the kth try is (q)^(k-1)(p).

Therefore, the probability that we find the first student who takes the SATs in exactly k tries is:

P(X=k) = (q)^(k-1)(p)

We want to find the probability of sampling five successive students at random until we find the first student to take the SATs. So we want to find:

P(X=1) ∗ P(X=2) ∗ P(X=3) ∗ P(X=4) ∗ P(X=5)

= p ∗ (q)(p) ∗ (q)(q)(p) ∗ (q)(q)(q)(p) ∗ (q)(q)(q)(q)(p)

= (0.61) ∗ (0.39)(0.61) ∗ (0.39)(0.39)(0.61) ∗ (0.39)(0.39)(0.39)(0.61) ∗ (0.39)(0.39)(0.39)(0.39)(0.61)

= 0.61 ∗ 0.238 ∗ 0.147 ∗ 0.0905 ∗ 0.0554

≈ 0.00028

Therefore, the probability of sampling five successive students at random until you find the first student to take the SATs is approximately 0.00028 or 0.028%.

Step-by-step explanation:

The difference quotient for the function is 8.

The function is given by:

f ( x ) = 8 x − 9, where h ≠ 0

To find f(a), substitute a for x in the function. So we have:

f ( a ) = 8 a − 9

To find f(a + h), substitute a + h for x in the function. So we have:

f ( a + h ) = 8 ( a + h ) − 9

The difference quotient can be found using the formula:

(f(a + h) - f(a))/h

Substituting the values found above, we have:

(8 ( a + h ) − 9 - (8 a − 9))/h

Expanding the brackets and simplifying, we have:

((8a + 8h) - 9 - 8a + 9)/h

= 8h/h

= 8

Therefore, the difference quotient for the function is 8.

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Answer:

the first option - 48s + 4.75

Step-by-step explanation:

The equation that can be used to find d, the diameter of a new soccer ball, is: |d - 8.65| = 0.05

What is diameter ?

Diameter is the distance across a circle passing through its center, and it is defined as the length of a straight line passing through the center of a circle and connecting two points on the circumference of the circle. In the case of a soccer ball, the diameter is the distance between two opposite points on the surface of the ball, passing through its center.

Radius is a term used in geometry to refer to the distance from the center of a circle to any point on its circumference. It is defined as half of the diameter of a circle. In the case of a soccer ball, the radius is the distance from the center of the ball to its surface. The radius is related to the diameter by the formula:

radius = diameter / 2

The minimum possible diameter of a soccer ball is:

d = 8.65 - 0.05 = 8.60 inches

The maximum possible diameter is:

d = 8.65 + 0.05 = 8.70 inches

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Answer:

graph{6x [-10, 10, -5, 5]}

Step-by-step explanation:

Start with

1. x = 0.

2. Here, y = 0 and your first dot.

3. Got to x = 1; And here is y = 6. So your second dot is at y = 6 and x = 1.

4. Connect both dots and you will get the graph below.

(sorry if dont make sense)

Answer: D.

Step-by-step explanation:

You can start out with the form AX = B and solve for matrix X that would yield the answer

Then X = (A^-1)(B)

A = [1    -1]

      [1     1]

A^-1 = (1/(1 - (1)(-1)))*[1    1]

                             [-1   1]

which can be written as (1/2) * [1    1]

                                                  [-1   1]

B = [26]

     [6]

(A^-1)(B) = (1/2)*[1    1] [6]

                        [-1   1] [26]

= (1/2)*[32]

          [20]

= [16]

  [10]

Answer:

Step-by-step explanation:

\(c^{2}+b^{2} = (4+a)^2 \\c = \sqrt{6^2+4^2}\\ c = \sqrt{36+16}\\ c = \sqrt{52} \\c^2 = 52\\a^2 + 6^2 = b^2\\\\52 + a^2 + 36 = 16 + a^2 + 8a\\ 8a = 72\\a = 9\)

Please mark my answer as brainliest .

The speed of the particle along the path c(t) = (cos(4t), sin(4t), 3t) at time t = 0 is E. 5.

To find the speed of the particle at time t = 0, we need to find the magnitude of its velocity vector at that time. The speed at which an object's position changes is represented by a velocity vector. A velocity vector's magnitude indicates an object's speed, whereas the vector's direction indicates its direction. According to the vector addition tenets, velocity vectors can be added or deleted.
The velocity vector is given by the derivative of the position vector:
c'(t) = (-4sin(4t), 4cos(4t), 3)

At t = 0, we have:
c'(0) = (-4sin(0), 4cos(0), 3) = (0, 4, 3)

The magnitude of this vector is:
|c'(0)| = sqrt(0^2 + 4^2 + 3^2) = sqrt(25) = 5

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The area of the figure composed of a rectnagle and a triangle is 128in².

The figure in the the image is composed of rectangle and a triangle.

The area of a rectangle = length × width

Area of a triangle = 1/2 × base × height

Hence;

Area of the composite figure will be;

A = area of a rectangle + area of a triangle

From the image;

Now, we solve for thr area of the composite figure.

A = area of a rectangle + area of a triangle

A = ( 12in × 9in ) + ( 1/2 × 5in × 8in )

A = ( 108in² ) + ( 20in² )

A = 128in²

Therefore, the total area of the figure id 128 squared inch.

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True. Since the square matrix that represents the DCT coefficient is an orthogonal matrix, its inverse and transpose are the same. This property is a fundamental characteristic of orthogonal matrices and holds true for all orthogonal matrices.

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False While it is true that the square matrix that represents the DCT coefficient is orthogonal, it does not mean that its inverse and transpose are the same.

the inverse of an orthogonal matrix is its transpose. However, the transpose of the matrix does not necessarily mean that it is the same as the inverse of the matrix. In the statement is false because the inverse and transpose of an orthogonal matrix are not always the same.


The Discrete Cosine Transform (DCT) coefficient matrix is an orthogonal matrix. In the case of orthogonal matrices, the inverse matrix is indeed equal to the transpose of the original matrix. This is because the product of an orthogonal matrix and its transpose results in the identity matrix.

Since the square matrix representing the DCT coefficient is an orthogonal matrix, its inverse and transpose are the same.

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No, Erica's calculation is wrong

Based on the given information and performing a one-sample t-test, the conclusion is that if the population mean (μ) is greater than 30.8294 km per litre, we reject the null hypothesis.

Given:

Sample mean (x') = 30 km per litre

Sample standard deviation (s) = 3.5 km per litre

Sample size (n) = 50

Significance level (α) = 0.05 (5%)

Null hypothesis \((H_0)\): The mean petrol consumption of the new car is equal to or higher than that of the existing car.

Alternative hypothesis \((H_1)\): The mean petrol consumption of the new car is lower than that of the existing car.

We'll calculate the test statistic (t-value) and compare it with the critical t-value.

The formula for the t-value is:

t = (x' - μ) / (s / √n)

where μ is the population mean (mean petrol consumption of the existing car).

First, we need to calculate the critical t-value from the t-distribution table. Since we have a significance level of 0.05 and (50 - 1) degrees of freedom, the critical t-value for a one-tailed test is approximately -1.677.

Now, let's calculate the t-value:

t = (30 - μ) / (3.5 / √50)

To reject the null hypothesis, the t-value should be less than the critical t-value.

Simplifying the equation:

t = (30 - μ) / (0.495)

To find the critical value, we compare it with the calculated t-value:

-1.677 > (30 - μ) / (0.495)

Multiplying both sides of the inequality by 0.495:

-0.8294 > 30 - μ

Rearranging the inequality:

μ > 30 + 0.8294

μ > 30.8294

Therefore, if the population mean (μ) is greater than 30.8294 km per litre, we reject the null hypothesis in favor of the alternative hypothesis, concluding that the mean petrol consumption of the new car is lower than that of the existing car.

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Rachel would end up with 12 chocolate bars.

Answer:

x=6 y=5.2

Step-by-step explanation:

To determine the probability of event A, we need to add the probabilities of the sample points e1, e4, and e6:

P(A) = P(e1) + P(e4) + P(e6)

To determine the probability of event B, we need to add the probabilities of the sample points e2, e4, and e7:

P(B) = P(e2) + P(e4) + P(e7)

To determine the probability of event C, we need to add the probabilities of the sample points e2, e3, e5, and e7:

P(C) = P(e2) + P(e3) + P(e5) + P(e7)

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Answer:

f(x) = x^3

The interval is -1 to 3

The intervals here are X

So we just plug in the x values with these 2 numbers.

F(x) is basically “y”

Y= x^3

For -1

y= (-1)^3

Y= -1

For 3

Y= 3^3

Y= 27

So now we have the y values we can’t forget the x values originally used to plug it in.

So for -1, the x value is -1 and y is -1, therefore

(-1,-1)

For 3, the x value is 3 and the y value is 27, therefore

(3,27)

Find the rate of change which is basically the slope, you do this by

(y2- y1)/(x2 - x1)

*1 and 2 are just subscripts*

It doesn’t matter for ay order so lets just do

-1 - 27 / -1 - 3

= -28 / -4

= 7

The answer is 7

The F statistic follows an F-distribution with (n-1) and (m-1) degrees of freedom. This distribution allows us to assess whether there is a significant difference between the variances of the two populations.

The question seems to be asking about the distribution of the F statistic when comparing the variances of two independent random samples.

Here is the answer: When comparing the variances of two independent random samples, the F statistic follows an F-distribution. In this case, if S1² and S2² are from independent random samples of size n and m respectively, taken from normal populations, then the F statistic is distributed as F with (n-1) and (m-1) degrees of freedom.

To understand why the F statistic follows an F-distribution, we need to consider the underlying theory. When comparing variances, we use the F statistic, which is calculated by dividing the sample variances (S1² and S2²) and taking the ratio of their respective degrees of freedom (n-1 and m-1).

The F-distribution is used because it is the ratio of two chi-squared distributions, which are themselves derived from normal distributions. The numerator chi-squared distribution represents the sum of squared deviations from the mean of the first sample, and the denominator chi-squared distribution represents the sum of squared deviations from the mean of the second sample.

The F-distribution is a right-skewed distribution, meaning it has a long right tail. This is because variances cannot be negative, and the F statistic is always positive. The shape of the F-distribution changes depending on the degrees of freedom, with higher degrees of freedom resulting in a more symmetrical distribution. In summary, when comparing variances of two independent random samples from normal populations, the F statistic follows an F-distribution with (n-1) and (m-1) degrees of freedom. This distribution allows us to assess whether there is a significant difference between the variances of the two populations.

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Answer:

Yes it is a function.

Step-by-step explanation:

By the way, don't click on any links, there's a bunch of raiders going around sharing links that will give you a virus, if you still have the virus, you should probably factory-reset your device, it could be taking your information.

To find the fraction of the square quilt block that is shaded, we need to count the number of shaded unit squares and divide it by the total number of unit squares in the quilt block. Let us begin by counting the number of shaded unit squares.

We notice that there are a total of 6 unit squares that are shaded. The unit squares that are shaded are the 2 squares that are completely shaded and the 4 squares that are half shaded due to the presence of triangles.

Next, we need to count the total number of unit squares in the quilt block. We notice that the quilt block is made up of 9 unit squares, each of which can be divided into 4 smaller unit squares. Thus, the total number of unit squares in the quilt block is 9 x 4 = 36.

Therefore, the fraction of the square quilt block that is shaded is 6/36 or 1/6.

To summarize, the shaded portion of the quilt block consists of 6 unit squares out of a total of 36 unit squares. Thus, the fraction of the square quilt block that is shaded is 1/6.

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Answer:

Step 2

Step-by-step explanation:

He messed up because while changing the denominator (number on the bottom), he forgot to change the numerator (number on top).

It should be 2/8 instead of 1/8.

Yes, It is possible for two sets of data to have the same slope but different correlation coefficients depending on the direction of the relationship between the variables.

Two sets of data, Set A and Set B. Both sets have the same slope but different correlation coefficients.

Set A

x-values: [1, 2, 3, 4, 5]

y-values: [2, 4, 6, 8, 10]

Set B

x-values: [1, 2, 3, 4, 5]

y-values: [10, 8, 6, 4, 2]

For Set A, the points lie on a straight line that increases as x increases. The line has a positive slope, indicating a positive relationship between x and y. This positive relationship results in a high correlation coefficient, indicating a strong linear relationship between the variables.

For Set B, the points also lie on a straight line, but it decreases as x increases. The line has the same slope as Set A, indicating the same rate of change between x and y. However, the negative relationship between x and y in Set B leads to a negative correlation coefficient. This negative correlation coefficient indicates a strong linear relationship but in the opposite direction compared to Set A.

So, although both sets of data have the same slope, the difference in the direction of the relationship between x and y results in different correlation coefficients. Set A has a positive correlation coefficient, while Set B has a negative correlation coefficient.

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The value of angle DAB is 90 degrees.

The value of angle ABC is  118 degrees.

The value of angle BCD is  90 degrees.

The measure of the missing angles of the quadrilateral inscribed in a circle is calculated by applying circle theorem as follows;

If line BD is the diameter, then we will have the following;

angle BCD = 90 degrees

angle DAB = 90 degrees

Now, the value of angle ABC is calculated as follows;

angle ABC = 180 - angle ADC ( opposite angles of a cyclic quadrilateral are supplementary).

angle ABC = 180 - 62⁰

angle ABC = 118⁰

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The given system of equations, -35x + 40y = 0, does not provide enough information to determine its consistency and independence. Further analysis or additional equations are needed to make a conclusive determination.

To determine the consistency and independence of a system of equations, we need to analyze the relationships between the equations and variables. In this case, the given system only consists of one equation: -35x + 40y = 0. Without any other equations or information, we cannot definitively classify the system as consistent and independent, consistent and dependent, or inconsistent.

A system of equations is considered consistent if there is at least one solution that satisfies all equations simultaneously. It is considered independent if each equation provides new and distinct information. On the other hand, a system is dependent if one or more equations can be derived from or are redundant with other equations in the system. However, since we only have one equation in this case, we cannot make any conclusions about the consistency and independence of the system without further information or additional equations.

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State whether the system is consistent and independent, consistent and dependent or inconsistent. -35x + 40y= 0 and 20x -y =0

To convert 5/16 inch to millimeters, you need to know the conversion factor between the two units. One inch is equal to approximately 25.4 millimeters.

When measuring length, there are different units of measurement that can be used such as inches and millimeters. Inches (") are commonly used in the imperial system, which is primarily used in the United States, whereas millimeters (mm) are part of the metric system which is widely used in many countries around the world. To convert 5/16 inch to millimeters, you would multiply 5/16 by 25.4.

So, 5/16 inch is roughly equal to 7.9375 mm

It's important to keep in mind that when converting measurements, it's important to be precise and use accurate conversion factors. Additionally, it's also important to consider the level of precision required for the task at hand. In general, inches are mostly used in the US and the UK, while millimeters are primarily used in other countries. It is important to use the right unit of measurement depending on the context of the task or situation. It's also important to note that when converting decimal inches to millimeters, it's important to use a calculator or perform the calculation with a high degree of accuracy, as the conversion factor is not exact.

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