Find the length of AB

a. The contingency table for the given data is attached file below.

b. The proportion of lizards that were either species A or B is 0.605.

c. The probability that a species C lizard in this study did not survive is 0.4667.

a.

The contingency table for the given data is attached file below.

b.

The proportion of lizards that were either species A or B can be calculated as:

P(A or B) = (15+8)/(15+8+6+9+4)

P(A or B) = 23/38

P(A or B) = 0.605

c.

The probability that a species C lizard in this study did not survive can be calculated as:

P(Not survive| C) = 7/15

= 0.4667

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Answer:

(2,-2)

Step-by-step explanation:

(5+(-1))/2=4/2=2

(-5+1)/=-4/2=-2

The Phillips curve describes the relationship between the unemployment rate and the rate of change of wages. Option C is the correct option.

What is  Phillips curve?

The relationship between the rate of inflation and the unemployment rate is represented by the Phillips curve. The analysis of wage inflation and unemployment in the United Kingdom from 1861 to 1957 by A. W. H. Phillips, despite having forerunners, is a significant development in the field of macroeconomics. When unemployment was high, wages rose slowly; when unemployment was low, wages rose quickly, according to Phillips' research.

According to Phillips' hypothesis, as the unemployment rate declines, the labor market becomes more competitive and firms are forced to raise wages more quickly in order to recruit qualified workers. The pressure decreased as unemployment rates rose. The average relationship between wage behavior and unemployment over the course of the business cycle was represented by Phillips' "curve."

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Analysis of variance is used to test for equality of several population means.

ANOVA could also be utilized to predict the dependent variable of even more with around 2 categories and seems to be compared to the general population extra influential throughout this circumstance.

Throughout addition, ANOVA variants typically include covariates that encourage somebody to manipulate numerically for confounding factors as well as to recognize interactions wherein the factor progressives the implications of some other factor.

ANOVA (Analysis of Variance) was developed by Ronald Fisher.

ANOVA means the Analysis of Variance, is collection of statistical models & linked estimation processes, like variation among & between groups. It is used in analyzing differences among various means.

Therefore, Analysis of variance is used to test for equality of several population means.

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The average number of exclusive relationships Duke students have been in is between 2.972 and 3.428.

So, we can estimate with 90% confidence that the average number of exclusive relationships Duke students have been in is between 2.972 and 3.428.

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Step-by-step explanation:

the correct answer is option a 6a-7

The answer is D) 10gh

Answer: I think the correct answer would be d

Step-by-step explanation:

Any value calculated from this survey would be considered a statistic.

To determine whether the given value is a statistic or a parameter, consider the following:

A statistic is a numerical value calculated from a sample of the population, while a parameter is a numerical value that describes a characteristic of the entire population.

In this case, the health and fitness club surveys 40 members. This is a sample of the population, not the entire population.

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Answer:

d = - 1

Step-by-step explanation:

The common difference d between consecutive terms is

6 - 7 = 5 - 6 = 4 - 5 = - 1

Answer:

Step-by-step explanation:

The solution to the given Inequality is a > 12 and the graph is as attached.

We are given the Inequality as;

8a - 30 > 66

Now, use addition property of equality to add 30 to both sides to get;

8a - 30 + 30 > 66 + 30

8a > 96

Now, use division property of equality to divide both sides by 8 to get;

8a/8 > 96/8

a > 12

The graph of this is as attached.

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The solution to this equation –3x + 1 + 10x = x + 4 include the following: A. x = 1/2.

In order to create a list of steps and determine the solution to the equation, we would have to rearrange the variables and constants, and then collect like terms as follows;

–3x + 1 + 10x = x + 4

-3x + 10x - x = 4 - 1

6x = 3

By dividing both sides of the equation by 6, we have the following:

6x = 3

x = 3/6

x = 1/2

In conclusion, we can reasonably infer and logically deduce that solution to this equation –3x + 1 + 10x = x + 4 is 1/2 or 0.5.

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Complete Question:

Solve the equation.

–3x + 1 + 10x = x + 4

x = 1/2

x = 5/6

x = 12

x = 18

Answer:

D.

Step-by-step explanation:

Its D. Bruh

The process has to continue for approximately 2.86 minutes until there are 20 grams of salt in the tank.

We can use a mass balance approach to solve this problem. Let's start by calculating the amount of salt in the tank at any given time. We know that initially there are 5 grams of salt in 20 liters of water, so the concentration of salt is:

c1 = 5 g / 20 L = 0.25 g/L

As brine with a concentration of 2 grams per liter is added at a rate of 3 liters a minute, the concentration of salt in the tank increases at a rate of:

dc/dt = 2 g/L * 3 L/min = 6 g/min

At the same time, the tank is being drained at 3 liters a minute, so the volume of the tank remains constant. This means that the total amount of salt in the tank is changing at a rate of:

dm/dt = dc/dt * V = (6 g/min) * (20 L) = 120 g/min

We want to know how long the process has to continue until there are 20 grams of salt in the tank, which means we need to solve for the time t when the total amount of salt in the tank reaches 20 grams:

m = 5 g + (6 g/min) * t - (3 L/min) * t * (0.25 g/L) = 20 g

Simplifying this equation, we get:

6t - 0.75t = 15

5.25t = 15

t = 2.86 minutes

Therefore, the process has to continue for approximately 2.86 minutes until there are 20 grams of salt in the tank.

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The quadratic function passing through the point (1,12) and whose x-intercepts are (−2,0) and (3,0) is f(x) = 6x² - 6x - 36, The quadratic function whose vertex is (3,−9) and which is passing through the point (−1,15) is f(x) = -¼x² + (3/2)x - (9/4).

Formula for the quadratic function passing through the point (1,12) and whose x-intercepts are (−2,0) and (3,0) can be obtained as follows:

Using the x-intercepts to get the factors of the quadratic function: f(x) = a(x + 2)(x - 3).

Since the graph passes through (1, 12), we can substitute these coordinates to get a value for the coefficient a:12 = a(1 + 2)(1 - 3)12 = -6a6 = aTherefore, the formula for the quadratic function is:f(x) = 6(x + 2)(x - 3).

The answer   is  = 6(x + 2)(x - 3)To write this in standard form, we need to multiply out the brackets:f(x) = 6(x² - x - 6)f(x) = 6x² - 6x - 36.

The final answer  in standard form is f(x) = 6x² - 6x - 36.b) The formula for the quadratic function whose vertex is (3,−9) and which is passing through the point (−1,15) can be obtained as follows:

Using the vertex form of a quadratic function:f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.Substitute the coordinates of the vertex to get:f(x) = a(x - 3)² - 9We still need to find the value of a.

To do this, we can use the point (-1, 15) that the parabola passes through:15 = a(-1 - 3)² - 915 = 16a24a = -6a = -¼Substitute a into the equation:f(x) = -¼(x - 3)² - 9.

The  answer f(x) = -¼(x - 3)² - 9.

To write this in standard form, we need to multiply out the brackets and simplify:f(x) = -¼(x² - 6x + 9) - 9f(x) = -¼x² + (3/2)x - (9/4)The final answer  in standard form is f(x) = -¼x² + (3/2)x - (9/4).

In conclusion, the quadratic function passing through the point (1,12) and whose x-intercepts are (−2,0) and (3,0) is f(x) = 6x² - 6x - 36, whereas, the quadratic function whose vertex is (3,−9) and which is passing through the point (−1,15) is f(x) = -¼x² + (3/2)x - (9/4).

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Answer:

  0.92

Step-by-step explanation:

Each year, the value declines. This eliminates choices A and D.

The decline from 33000 to 30360 is slightly less than 10%, so the multiplier from one year to the next is slightly more than 1 -10% = 90%. The only choice in range is ...

  0.92 . . . . the third listed choice

Answer:

b =345

Step-by-step explanation:

The solution is w ≤ 20

The inequality equation is w ≤ 20

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Let the number be w

A = quotient of a number w and five is at most four

Substituting the values in the equation , we get

w / 5 ≤ 4   be equation (1)

Multiply by 5 on both sides of the equation , we get

w ≤ ( 4 x 5 )

w ≤ 20

Therefore , the value of A is w ≤ 20

Hence , the inequality equation is w ≤ 20

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Y in represents the following in this linear regression Y = α₀+α₁X+α₂X₂+ε: C. dependent variable.

In Mathematics and Geometry, a regression line is a statistical line that best describes the behavior of a data set. This ultimately implies that, a regression line simply refers to a line which best fits a set of data.

In Mathematics and Geometry, the general functional form of a linear regression can be modeled by this mathematical equation;

Y = α₀+α₁X+α₂X₂+ε

Where:

In conclusion, Y represent the dependent variable or response variable in a linear regression.

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There are 3 ways to select a senator from a state if you wish to make a 3-senator committee in which no two senators are from the same state.

There are two senators from each of the 50 states, we wish to create a committee of three senators so that no two senators are from the same state.

Therefore, the total number of ways to choose a 3-senator committee is: 2 C 98 + 3 = 2,941 ways.

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Converting 33 cubic feet to cubic centimeters would give 934454. 4 cubic centimeters

It is important to note that conversion of units requires the appropriate equivalent values

For

I cubic foot is equivalent to 28316. 8 cubic centimeters

But we were given

33 cubic feet for the conversion

If 1 cubic foot = 28316. 8 cubic centimeters

Then 33 cubic feet = x

Cross multiply, we get

x = 28316. 8 × 33

x = 934454. 4 cubic centimeters

Thus, converting 33 cubic feet to cubic centimeters would give 934454. 4 cubic centimeters

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The point estimate of the difference between the mean number of miles that Buffalo residents travel per day and the mean number of miles that Boston residents travel per day is 4.3 miles/day. The 95% confidence interval for the difference between the two population means is (2.08, 6.52) miles/day.

a)

The point estimate of the difference between the mean number of miles that Buffalo residents travel per day and the mean number of miles that Boston residents travel per day can be calculated as:

Point estimate = Mean of Buffalo residents - Mean of Boston residents

Point estimate = 22.5 miles/day - 18.2 miles/day

Point estimate ≈ 4.3 miles/day

Therefore, the point estimate of the difference between the mean number of miles that Buffalo residents travel per day and the mean number of miles that Boston residents travel per day is 4.3 miles/day.

b)

To calculate the 95% confidence interval for the difference between the two population means, we can use the formula:

Confidence interval = (Point estimate) ± (Critical value) * (Standard error)

The critical value depends on the desired confidence level and the sample size. Since the sample sizes are relatively large (70 and 40), we can approximate the critical value using a Z-distribution.

For a 95% confidence level, the critical value for a two-tailed test is approximately 1.96.

The standard error can be calculated as:

Standard error = sqrt((s1^2 / n1) + (s2^2 / n2))

where s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Standard error = sqrt((8.5^2 / 70) + (7.1^2 / 40))

Standard error ≈ 1.1307

Now, we can calculate the confidence interval:

Confidence interval = 4.3 ± 1.96 * 1.1307

Confidence interval ≈ (2.08, 6.52)

Therefore, the 95% confidence interval for the difference between the two population means is (2.08, 6.52) miles/day.

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Hey there!☺

\(Answer:\boxed{a=19}\)

\(Explanation:\)

\(-4(10-a)=36\) Equation

−4(10 − a) = 36  Simplify both sides

(−4)(10) + (−4)(−a) = 36 Distribute

−40 + 4a = 36

4a − 40 = 36

4a - 40 + 40 = 36 + 40 Add 40 to both sides

4a = 76

4a/4 = 76/4 Divide both sides by 4

76/4 = 19 Simplify 76/4

a = 19

Hope this helps!

We will get that the angle theta is:

θ = β/2

Remember that the sum of the interior angles of any triangle must be equal to 180°.

Now, looking at the triangle in the left, we can see that the top angle is equal to:

180 - 2α

The right angle is equal to:

180 - 2β

And the left angle is α

Then we can write:

α + (180 - 2α) + (180 - 2β) = 180

-α - 2β = -180

α = 180 - 2β

Now we can go to the other triangle, where theta is, and write:

α + β + 2θ = 180

Replacing what we found above, we get:

180 - 2β + β + 2θ = 180

-β + 2θ = 0

θ = β/2

That is the best simplification we can get with the given diagram.

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Answer:  15

Step-by-step explanation:

(r+1)th term of \((a+b)^n\) is given by:-

\(T_{r+1}=\ ^nC_r(a)^{n-r}b^r\)

For \((a+b)^6\) , n= 6

\(T_3=T_{2+1}=\ ^6C_2(a)^{6-2}(b)^2\\\\\)

\(=\ \dfrac{6!}{4!2!}a^4b^2\ \ \ [^nC_r=\dfrac{n!}{r!(n-r)!}]\\\\=\dfrac{6\times5\times4!}{4!\times2}a^4b^2\\\\=3\times5a^4b^2\\\\ =15a^4b^2\)

Hence, the coefficient of the third term in the binomial expansion of  \((a+b)^6\) is 15.

Answer:

15

Step-by-step explanation:

1. the distribution function of X is \(F_X(x)\) = 1 - \(e^{-x\) for x ≥ 0, and the distribution function of Y is \(F_Y(y)\) = 1 for y ≥ 0.

2. The function F(x, y) is not the joint distribution function of any pair (X, Y) of random variables.

Let's analyze each case separately:

(a) F(x, y) = 1 - \(e^{-x - y\) if x, y ≥ 0, and F(x, y) = 0 otherwise.

To determine if F is the joint distribution function of some pair (X, Y) of random variables, we need to check if F satisfies the properties of a distribution function:

1. Non-negativity: F(x, y) ≥ 0 for all (x, y).

2. Monotonicity: F(x, y) is non-decreasing in both x and y.

3. Right-continuity: F(x, y) is right-continuous in both x and y.

4. Marginal distribution: The marginal distribution functions, \(F_X(x)\) and \(F_Y(y)\), can be obtained by integrating F(x, y) over the respective variables.

In this case, the function F(x, y) satisfies the properties of a distribution function:

1. Non-negativity: F(x, y) = 1 - \(e^{-x - y\) ≥ 0 for all x, y ≥ 0.

2. Monotonicity: The partial derivatives of F(x, y) with respect to x and y are non-negative for x, y ≥ 0, which implies that F(x, y) is non-decreasing in both x and y.

3. Right-continuity: The function F(x, y) is continuous for all x, y ≥ 0.

4. Marginal distribution: To find the marginal distribution functions, we can integrate F(x, y) over the respective variables.

Let's find the distribution functions of X and Y separately:

\(F_X(x)\) = ∫[0 to ∞] F(x, y) dy

      = ∫[0 to ∞] (1 - \(e^{-x - y\)) dy

      = [y - \(e^{-x - y\)]|[0 to ∞]

      = ∞ - (0 - \(e^{-x - 0\))

      = 1 - e\(e^{-x\)

\(F_Y(y)\) = ∫[0 to ∞] F(x, y) dx

      = ∫[0 to ∞] (1 - \(e^{-x - y\)) dx

      = [x - \(e^{-x - y\)]|[0 to ∞]

      = ∞ - (0 - \(e^{-\infty - y\))

      = 1

Therefore, the distribution function of X is \(F_X(x)\) = 1 - \(e^{-x\) for x ≥ 0, and the distribution function of Y is \(F_Y(y)\) = 1 for y ≥ 0.

(b) F(x, y) = 1 - \(e^{-x\) = x \(e^{ - y\) if 0 ≤ x ≤ y, and F(x, y) = 0 otherwise.

Let's analyze this case using the same criteria:

1. Non-negativity: F(x, y) = 1 - \(e^{-x\) = x \(e^{- y\) ≥ 0 for 0 ≤ x ≤ y.

2. Monotonicity: The partial derivatives of F(x, y) with respect to x and y are positive for 0 ≤ x ≤ y, indicating that F(x, y) is increasing in both x and y.

3. Right-continuity: F(x, y) is continuous for 0 ≤ x ≤ y.

4. Marginal distribution: We need to find the marginal distribution functions \(F_X(x)\) and \(F_Y(y)\) by integrating F(x, y) over the respective variables.

Let's find the distribution functions of X and Y separately:

\(F_X(x)\) = ∫[x to ∞] F(x, y) dy

      = ∫[x to ∞] (1 - \(e^{-x\)) dy

      = (y - \(e^{-x\) y)|[x to ∞]

      = ∞ - (x - \(e^{-x\) x)

      = 1 - x \(e^{-x\) for x ≥ 0

\(F_Y(y)\) = ∫[0 to y] F(x, y) dx

      = ∫[0 to y] (1 - \(e^{-x\) y \(e^{- y\)) dx

      = (x -\(e^{-x\) x \(e^{- y\))|[0 to y]

      = y -\(e^{- y\) y \(e^{- y\)

      = y(1 - \(e^{ - y\)) for y ≥ 0

Therefore, the distribution function of X is F_X(x) = 1 - x \(e^{-x\) for x ≥ 0, and the distribution function of Y is \(F_Y(y)\) = y(1 - \(e^{- y\)) for y ≥ 0.

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Answer:

Negative:)

Step-by-step explanation:

Answer:

0.56

Step-by-step explanation:

14/25 = 14×4/25×4

=56/100

=0.56

The synthetic division of the polynomial, (2x⁴ + 4x³ + 2x² + 8x + 8) / (x + 2) =  2x³ + 2x + 4.

The division of the polynomial is determined as follows;

(2x⁴ + 4x³ + 2x² + 8x + 8) / (x + 2)

                     2x³ + 2x + 4

                   -------------------------

     x + 2   √(2x⁴ + 4x³ + 2x² + 8x + 8)

                - (2x⁴ + 4x³)

                 -------------------------------------

                                        2x² + 8x + 8

                                     - (2x² + 4x)

                                   ------------------------

                                                  4x + 8

                                               - (4x + 8)

                                              -------------------

                                                       0

Thus, the synthetic division of the polynomial, (2x⁴ + 4x³ + 2x² + 8x + 8) / (x + 2) =  2x³ + 2x + 4.

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The domain of the function A(n) which represents the amount of wax left in the jar after making candles is; n = {n: 0<= n <= 16}.

According to the task content, it follows that tge function given to represent the use of wax to make candles is;

A(n)=800−50n

Hence, since the domain of a function is the set of all possible values of n, it follows that the possible values of n spans from the least to the highest as follows;

When none of the wax is used for candles;

800 = 800 -50n.

0 = -50n

n = 0.

When all of the wax is used for candles;

0 = 800 - 50n

-800 = -50n

n = 16.

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