There are 240 people at a meeting. They each give a valentines card to every other person. How many cards were given

The correct 4-bit combination for the decimal number 9 is 1001. To explain it in a long answer, we need to understand binary representation. In binary, each digit can either be 0 or 1, and the value of the digit depends on its position.

The rightmost digit represents the value 2^0 (which is 1), the next digit to the left represents the value 2^1 (which is 2), the next represents 2^2 (which is 4), and so on. To convert decimal number 9 to binary, we can start by finding the highest power of 2 that is less than or equal to 9, which is 2^3 (which is 8). We can subtract 8 from 9, and the remainder is 1. This means the leftmost digit in the binary representation is 1.

We repeat the same process with the remainder, which is 1, and find the highest power of 2 that is less than or equal to 1, which is 2^0 (which is 1). We subtract 1 from 1, and the remainder is 0. This means the rightmost digit in the binary representation is 0. Thus, the binary representation of decimal number 9 is 1001, which is the correct 4-bit combination.

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Answer:

Avg BC= 10.873 m

Step-by-step explanation:

See a picture

The factored function is given as follows:

[tex]x^4 + 2x^3 - 20x^2 + 64x - 32 = (x^2 + 6x - 4)(x^2 - 4x + 8)[/tex]

The function for this problem is defined as follows:

[tex]y = x^4 + 2x^3 - 20x^2 + 64x - 32[/tex]

The zeros are given as follows:

Hence the function is factored as follows:

[tex]x^4 + 2x^3 - 20x^2 + 64x - 32 = (ax^2 + bx + c)(x - 2 + 2i)(x - 2 - 2i)[/tex]

(we have the multiplication of two second degree polynomials resulting in a fourth degree polynomial, we must obtain the other second degree polynomial).

[tex]x^4 + 2x^3 - 20x^2 + 64x - 32 = (ax^2 + bx + c)(x^2 - 4x + 8)[/tex]

[tex]x^4 + 2x^3 - 20x^2 + 64x - 32 = ax^4 + (-4 + b)x^3 + \cdots + 8c[/tex]

(it is not necessary to make the calculations in the middle of the function as they are not needed to obtain the constants).

Hence the value of a is given as follows:

a = 1.

The value of b is given as follows:

-4 + b = 2

b = 6.

The value of c is given as follows:

8c = -32

c = -4.

Hence the factored expression is of:

[tex]x^4 + 2x^3 - 20x^2 + 64x - 32 = (x^2 + 6x - 4)(x^2 - 4x + 8)[/tex]

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Answer:

113.1 cm³

Step-by-step explanation:

diameter = 2 X radius

Volume of sphere = (4/3) X π X r ³

= (4/3) π (3)³

= 36π

= 113.1 cm³ to nearest tenth

Answer:

Step-by-step explanation:

Given two of three numbers correct, you want to find the correct value for the third number of 8 faces, 7 vertices, and 10 edges.

The relation between faces, vertices, and edges is ...

  F + V = E + 2

The given numbers are off by 3:

  8 + 7 = 15 ≠ 12 = 10 + 2

We can decrease the numbers of Faces or Vertices by 3, or we can increase the number of Edges by 3.

The numbers will be correct if we change to ...

#95141404393

If c and d are positive, then -c/2>d/2  is an example of a positive fraction c/d that satisfies the inequality -50 (c/d) > - 50

We know that c/d is a positive fraction,

so c>0 and d>0.

Multiplying both sides of the inequality by -d (which is negative since d>0), we get:

-50(c/d)>-50(-d)

-50c>50d

Dividing both sides by 50 (which is positive), we get:

-c>d

-c/2>d/2

Since c and d are positive, this is an example of a positive fraction c/d that satisfies the inequality -c/2>d/2

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All the correct statements are,

⇒ the absolute value a number is from 0 on a number line

⇒ The additive inverse of a number

⇒ Horizontal left and right

⇒ An integer number or its opposite

⇒ Straight vertical and down

⇒ A set of two opposite numbers that equal zero when combined.

We have to given that;

To fill the blanks in all the statement.

Hence, We get;

We know that;

⇒ The absolute value a number is from 0 on a number line

⇒ The additive inverse of a number

⇒ Horizontal left and right

⇒ An integer number or its opposite

⇒ Straight vertical and down

⇒ A set of two opposite numbers that equal zero when combined.

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Answer:

51

Step-by-step explanation:

Sum of interior angles in a triangle is 180.

x + 90 + 39 = 180

x + 129 = 180

x = 180 - 129

x = 51

Answer:

51 degrees

Step-by-step explanation:

We are asked to find angle x.

To find angle x, we have to write an equation to find it.

We know that one angle is 39 degrees, and the other is 90 degrees because of the small box.  We also know that all 3 angles in a triangle have to add up to 180.

Here's the equation for this:

180=39+90+x

simplify

180=129+x

subtract 129 from both sides

51=x

So, angle x is 51 degrees.

Hope this helps! :)

Answer:

.125 = 3.25/l

.125l = 3.25, so l = 26 feet

.125 = 2.5/w

.125w = 2.5, so w = 20 feet

A = lw = (26 feet)(20 feet)

= 520 square feet

The correct answer is A.

There is insufficient evidence to conclude that the mean blood pressure for women is different from the mean blood pressure for men. To determine whether the mean blood pressure for women is equal to the mean blood pressure for men, a t-test is conducted using the sample data of 16 women (group 1) and their respective brothers' blood pressures (group 2).

The null hypothesis states that the means are equal, and the alternative hypothesis suggests they are different. The test statistic is calculated, critical points are identified, and the null hypothesis is either accepted or rejected based on the test results.

To carry out the t-test, we first calculate the test statistic. The formula for the test statistic (t) in this case is:

t = (x1 - x2) / sqrt((s1^2 / n1) + (s2^2 / n2))

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Given:

x1 = 119.4 (average blood pressure for women)

x2 = 121.2 (average blood pressure for men)

s2d = 25 (pooled sample variance)

n1 = n2 = 16 (sample sizes)

α = 0.05 (Type I error value)

Now, we can calculate the test statistic:

t = (119.4 - 121.2) / sqrt((25/16) + (25/16))

 = -1.8 / sqrt(3.125 + 3.125)

 = -1.8 / sqrt(6.25)

 = -1.8 / 2.5

 = -0.72

Next, we determine the relevant critical point(s) for the t-test. Since the sample size is small (n1 = n2 = 16), we refer to the t-distribution with degrees of freedom equal to n1 + n2 - 2 = 30 - 2 = 28. Using a significance level (α) of 0.05, the critical value for a two-tailed test is approximately ±2.048.

Since the absolute value of the test statistic (0.72) is less than the critical value (2.048), we fail to reject the null hypothesis.

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In a hypothesis testing context, before examining the data, one should typically decide whether the alternative hypothesis is one-sided or two-sided. This decision is based on the specific research question and the expected direction of the effect being tested.

It helps determine the appropriate statistical test and the formulation of the null and alternative hypotheses.

The computation of the p-value and the decision of whether or not to reject the null hypothesis are made after examining the data and conducting the statistical analysis. The p-value is a measure of the strength of the evidence against the null hypothesis, and it is compared to a predetermined significance level to make a decision. If the p-value is below the significance level, the null hypothesis is typically rejected in favor of the alternative hypothesis.

Therefore, the correct answer is (c) decided whether the alternative hypothesis is one-sided or two-sided.

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The value of the measure of Arc CDE is,

⇒ Arc CDE = 128 degree

Since, An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Here, A circle is shown in figure.

And, By circle we have;

The measure of Arc CDE is,

⇒ Arc CDE = 128 degree

Thus, The value of the measure of Arc CDE is,

⇒ Arc CDE = 128 degree

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We can expect approximately 9 rats to die after being injected with cancerous cells based on probability.

To answer your question, we will use the given probability and the number of rats injected to find the expected number of rats that would die.

1. The probability that a rat injected with cancerous cells will live is 0.8.
2. Therefore, the probability that a rat will die is 1 - 0.8 = 0.2 (since the sum of probabilities of all possible outcomes should be equal to 1).
3. We have 45 rats injected with cancerous cells.
4. To find the expected number of rats that would die, multiply the total number of rats by the probability of a rat dying: 45 rats * 0.2 = 9 rats.

So, we can expect approximately 9 rats to die after being injected with cancerous cells.

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Models should be produced of the function C(x) = 10 + 2 x is 329.4 .

Cost of manufacturing is

C(x) = 10 + 2 x

Sale price in soles of each model is

P(x) = 20 - [tex]\frac{6x^{2} }{800}[/tex]

U(x) is the utility function

U(x) = x P(x) - C(x)

U(x) = x (20 - [tex]\frac{6x^{2} }{800}[/tex]  ) - (10 +2x)

U(x) = 20x - [tex]\frac{6x^{3} }{800}[/tex]   - 10 - 2x

U(x) = 18x - [tex]\frac{6x^{3} }{800}[/tex] - 10

U'(x) = 18 - 18x²/800

For maximum model U'(x) = 0

18 - 18x²/800 = 0

18x²/800 = 18

x² = 800

x = √800

x = 20√2

U(x) = 18(20√2 ) - [tex]\frac{6(20\sqrt{2} )^{2} }{800}[/tex] - 10

U(x) = 329.5

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The question is in Spanish question in English :

The manufacturing costs of models are modeled to the following function. C(x) = 10 + 2x. The manufacturer estimates that the sale price in soles of each model is given by: P(x) = 20- 6x2/800 How many models should be produced?

Answer: y=x²+5x−24

Step-by-step explanation:

The experimental probability that Sue will hit the bullseye on her next toss is 2/7.

We have,

The proportion of outcomes where a specific event occurs in all trials, not in a hypothetical sample space but in a real experiment, is known as the empirical probability, relative frequency, or experimental probability of an event.

Here, we have

Given: Sue is playing darts. So far, she has hit the bullseye 4 times and missed the bullseye 10 times.

We have to find the experimental probability that Sue will hit the bullseye on her next toss.

experimental probability = 4/(4+10) = 4/14 = 2/7

The next toss = P = 2/7

Hence,  the experimental probability that Sue will hit the bullseye on her next toss is 2/7.

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complete question:

Sue is playing darts. So far, she has hit the bullseye 4 times and missed the bullseye 10 times. What is the experimental probability that Sue will hit the bullseye on her next toss?

Answer:

Step-by-step explanation:

a= 3(x+11)

B=9(x+8)

C=5(x+5)

D=3(3x+2)

There are 10 boys in Mr. Johnson's class, and the total number of Students in the class is:10 + 15 = 25

If the ratio of boys to girls in Mr. Johnson's class is 2 to 3, this means that for every 2 boys, there are 3 girls. Let's represent the number of boys in the class as "b". Then we can set up the following proportion:2/3 = b/15

To solve for "b", we can cross-multiply:2 x 15 = 3 x b

30 = 3b

b = 10

Therefore, there are 10 boys in Mr. Johnson's class, and the total number of students in the class is:10 + 15 = 25

It's worth noting that we could have also found the number of girls in the class by using the ratio. Since the ratio of boys to girls is 2 to 3, this means that the total number of parts in the ratio is 2 + 3 = 5. To find the number of girls, we can divide the total number of students (25) by the total number of parts (5) and then multiply by the number of parts representing girls (3):(25/5) x 3 = 15

So we can see that there are indeed 15 girls in the class.

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A quartic polynomials is more complicated than quadratic or cubic polynomials. There are no obvious linear or quadratic factors. It is possible that the polynomial x^4 + x^3 + 2x^2 + x + 2 is irreducible over F3.

The polynomial 2x³ + 2x² + 2 over the field F₃, we first notice that we can factor out a 2 from all three terms to obtain:

2(x³ + x² + 1)

Now we need to factor the polynomial x³ + x² + 1 over F₃. One way to do this is to simply plug in all possible values for x (which are 0, 1, and 2 in F₃) and see if any of them result in a zero polynomial. We find that none of them do, so we know that x³ + x² + 1 is irreducible over F₃.

Therefore, our final factorization of 2x³ + 2x² + 2 over F₃ is:

2(x³ + x² + 1)

(b) To factor the polynomial x⁴ + x³ + 2x² + x + 2 over F₃, we can start by plugging in all possible values for x and checking if any of them result in a zero polynomial. Doing so, we find that x = 1 is a root of the polynomial, which means that x - 1 is a factor. Using polynomial long division or synthetic division, we can divide x⁴ + x³ + 2x² + x + 2 by x - 1 to obtain:

x⁴ + x³ + 2x² + x + 2 = (x - 1)(x³ + 2x² + 4x + 2)

Now we need to factor the cubic polynomial x³ + 2x² + 4x + 2 over F₃. Again, we can plug in all possible values for x and check for roots, but we won't find any in this case. However, we can use the fact that the sum of the coefficients of the polynomial is zero (1 + 2 + 4 + 2 = 0 in F₃) to infer that x = 1 is a root mod 3, and therefore x - 1 is a factor. Dividing x³ + 2x² + 4x + 2 by x - 1 using polynomial long division or synthetic division, we obtain:

x³ + 2x² + 4x + 2 = (x - 1)(x² + 3x + 2)

Now we need to factor the quadratic polynomial x² + 3x + 2 over F₃. We can do this by factoring it as (x + 1)(x + 2), since (x + 1)(x + 2) = x² + 3x + 2 mod 3.

Therefore, our final factorization of x⁴ + x³ + 2x² + x + 2 over F₃ is:

(x - 1)(x + 1)(x + 2)²

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A matrix with orthonormal columns satisfies this condition and is therefore orthogonal. The statement is false. A matrix with orthonormal columns is an orthogonal matrix if the matrix is also square.

An orthogonal matrix is a square matrix whose columns and rows are orthonormal, which means they are orthogonal (perpendicular) to each other and have a magnitude of 1. If a matrix has orthonormal columns but is not square, it cannot be considered an orthogonal matrix.

The statement "A matrix with orthonormal columns is an orthogonal matrix" is false, and the correct answer is (B) - A matrix with orthonormal columns is an orthogonal matrix if the matrix is also square.

In summary, a matrix with orthonormal columns is not necessarily an orthogonal matrix. The statement is only true if the matrix is also square.

To explain, an orthogonal matrix is a square matrix where all columns (and rows) are orthonormal, meaning they are of unit length and orthogonal to each other. However, a matrix with orthonormal columns does not necessarily meet the requirements of being square and having orthonormal rows. In fact, a rectangular matrix with orthonormal columns cannot have orthonormal rows.

Therefore, the only way for a matrix with orthonormal columns to be an orthogonal matrix is if it is also square. This is because a square matrix has an equal number of rows and columns, which ensures that its columns and rows are orthonormal to each other, and hence it is an orthogonal matrix.

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[tex]6\sqrt{5} \ cis(\frac{11\pi}{6}) \div 3\sqrt{6} \ cis (\frac{\pi}{2} )[/tex] can be expressed in polar form as[tex]6\sqrt{5} \ cis(\frac{11\pi}{6}) \div 3\sqrt{6} \ cis (\frac{\pi}{2} )=\underline{\frac{\sqrt{30} }{3} } \ cis\ (\underline{\frac{4\pi}{3}})[/tex] . Therefore the values to be dragged in the box are [tex]\frac{\sqrt{30} }{3}[/tex]  and [tex]\frac{4\pi}{3}[/tex].

We have to express in polar form, polar form of complex number:

[tex]r(cos\theta+isin\theta) \rightarrow rcis\theta[/tex]

where, r = modulus of complex number

[tex]\theta[/tex] = argument of complex number

The division of two complex number, [tex]z=[/tex] [tex]r_{1} cis \theta_{1}[/tex] and [tex]x=[/tex] [tex]r_{2} cis \theta_{2}[/tex]

[tex]\frac{z}{x} = \frac{r_{1} }{r_{2} }\ cis(\theta_{1}- \theta_{2})[/tex]

Similarly, let a = [tex]6\sqrt{5} \ cis(\frac{11\pi}{6})[/tex]

                    b = [tex]3\sqrt{6} \ cis(\frac{pi}{2})[/tex]

[tex]\frac{a}{b}= \frac{6\sqrt{5} }{3\sqrt{6} } \ cis (\frac{11\pi }{6}- \frac{\pi}{2} )[/tex]

 [tex]= \frac{{\sqrt{2}}\times\sqrt{2}\times\sqrt{5} }{\sqrt{2} \times\sqrt{3} } \ cis(\frac{11\pi-3\pi}{6} )[/tex]

 [tex]=\sqrt{\frac{10}{3} }\ cis\ \frac{8\pi}{6}[/tex]

[tex]\frac{a}{b}= \sqrt{\frac{10}{3} } \ cis\ \frac{4\pi}{3}[/tex]

It can also be written as, [tex]\frac{a}{b}= \frac{\sqrt{30} }{3} \ cis\ \frac{4\pi}{3}[/tex]

⇒ [tex]6\sqrt{5} \ cis(\frac{11\pi}{6}) \div 3\sqrt{6} \ cis (\frac{\pi}{2} )= \frac{\sqrt{30} }{3} \ cis\ \frac{4\pi}{3}[/tex]

Comparing it with the question we get:

[tex]6\sqrt{5} \ cis(\frac{11\pi}{6}) \div 3\sqrt{6} \ cis (\frac{\pi}{2} )=\underline{\frac{\sqrt{30} }{3} } \ cis\ (\underline{\frac{4\pi}{3}})[/tex]

Therefore, the first blank is [tex]\frac{\sqrt{30} }{3}[/tex] and the second blank is [tex]\frac{4\pi}{3}[/tex].

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(i) (CUD-E) specified using set builder notation:

(CUD-E) = {x ∈ R | (x > 0 ∧ x ≤ 10) ∨ (x > 9 ∧ x ≤ 15) ∧ x ∉ {1, 2, 3}}

(ii) (CE) specified using interval notation and set operations concisely:

(CE) = (0, 10] ∩ {1, 2, 3} = {1, 2, 3}

(iii) (CDF) specified using the most concise notation:

(CDF) = (C ∩ D) ∩ F

(b) Proof using the element argument method:

Given: A and B are sets such that P(A) ≤ P(B).

To prove: A ≤ B.

Proof:

1. Let x be an arbitrary element in A.

2. Since x is in A, by definition, x is a subset of A. Hence, x ⊆ A.

3. Since x ⊆ A and A ≤ B, by the definition of ≤, x ⊆ B.

4. Therefore, x is a subset of B. Hence, x ∈ P(B), where P(B) is the power set of B.

5. Since x ∈ P(B), by definition, x is a subset of B. Hence, x ⊆ B.

6. Since x is an arbitrary element in A and x ⊆ B, by definition, A ≤ B.

7. Therefore, if P(A) ≤ P(B), then A ≤ B.

In this proof, we used the fact that if x is an element of A, then x is a subset of A. Also, if x is a subset of A and A ≤ B, then x is a subset of B. These properties are based on the definitions of subsets and the order relation between sets.

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The probabilities of hitting the next bat are  Mitchell = 5/12 and Travis= 9/20

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

Mitchell hits 5 out of 12 times

Travis hits 9 out of 20 times

The probabilities of hitting the next bat is calculated as

P(Hit) = Hit/Total number of times

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

P(Mitchell Hit) = 5/12

P(Travis Hit) = 9/20

Hence, the probabilities of hitting the next bat are 5/12 and 9/20

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By the Mean Value Theorem, there exists a value c in the interval [1,4] such that f'(c) is equal to the average rate of change of f on the interval [1,4], which is (f(4) - f(1))/(4-1).

We can start by computing f(4) and f(1):

f(4) = 5cos(2(4^2)) + ln(4+1) - 3 = -0.841 + 1.609 - 3 = -1.232

f(1) = 5cos(2(1^2)) + ln(1+1) - 3 = 2.531 - 0.693 - 3 = -1.162

Then, we can compute the average rate of change:

(f(4) - f(1))/(4-1) = (-1.232 - (-1.162))/3 = -0.023

To satisfy the conclusion of the Mean Value Theorem, we need to find a value c in the interval [1,4] such that f'(c) = -0.023. From the given expression for f'(x), we can see that there is no value of c that satisfies this equation, since f'(x) can never be negative. Therefore, there is no value of c that satisfies the conclusion of the Mean Value Theorem applied to f on the interval [1,4].

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The function r(t) for the line passing through the points p(8,3,3) and q(6,8,7) is r(t) = <8-2t, 3+5t, 3+4t>

We can use the vector form of the equation of a line to find a function r(t) for the line passing through the points p(8,3,3) and q(6,8,7).

Let's first find the direction vector of the line by subtracting the coordinates of the two points:

q - p = <6-8, 8-3, 7-3> = <-2, 5, 4>

Now, we can write the vector equation of the line in terms of a parameter t as:

r(t) = p + t(q - p)

Substituting the values of p and q, we get:

r(t) = <8, 3, 3> + t<-2, 5, 4>

Expanding, we get:

r(t) = <8-2t, 3+5t, 3+4t>

Therefore, the function r(t) for the line passing through the points p(8,3,3) and q(6,8,7) is:

r(t) = <8-2t, 3+5t, 3+4t>

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The exact length of the curve is 8/3 (5sqrt(26) - 1).

To find the length of the curve, we can use the arc length formula:

L = ∫[tex][a,b]sqrt(dx/dt)^2 + (dy/dt)^2 dt[/tex]

where a and b are the starting and ending values of the parameter t, and dx/dt and dy/dt are the derivatives of x and y with respect to t, respectively.

Plugging in the given equations, we get:

[tex]dx/dt = 24t[/tex]

[tex]dy/dt = 24t^2[/tex]

Therefore,

[tex](sqrt(dx/dt)^2 + (dy/dt)^2) = sqrt((24t)^2 + (24t^2)^2) = sqrt(576t^2 + 576t^4)[/tex]

Substituting these expressions into the arc length formula, we get:

L = ∫[tex][0,2]sqrt(576t^2 + 576t^4) dt[/tex]

We can factor out 576t^2 from the square root:

L = ∫[tex][0,2]sqrt(576t^2(1 + t^2)) dt[/tex]

And then simplify the expression inside the square root:

L = ∫[tex][0,2]24t sqrt(1 + t^2) dt[/tex]

This integral can be evaluated using the substitution[tex]u = 1 + t^2, du/dt = 2t, dt = du/2t:[/tex]

L = ∫[tex][1,5]12 sqrt(u) du[/tex]

Now we can use the power rule of integration to evaluate this integral:

[tex]L = [8/3 u^(3/2)]_1^5 = 8/3 (5sqrt(26) - 1)[/tex]

Therefore, the exact length of the curve is 8/3 (5sqrt(26) - 1).

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The probability density function on [0 1] is 36, the correct option is C.

We are given that;

Function f(x) = ke-^(3x+2)

Now,

The function f(x) = ke^(-3x+2) is a probability density function on [0 1] if and only if the integral of f(x) from 0 to 1 is equal to 1.

∫(0 to 1) ke^(-3x+2) dx = -1/3ke^(-3x+2) from 0 to 1 = -1/3ke^-1 + 1/3ke^2

For f(x) to be a probability density function, the above expression must be equal to 1. Therefore,

-1/3ke^-1 + 1/3ke^2 = 1

Solving for k gives us k = 36

Therefore, by probability the answer will be 36.

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The association in this graph can best be described as C. Negative linear.

A negative linear association is one that moves from the left to the right. In this kind of association, the predictor increases while the response decreases. The linear nature of this association is seen in the straight line formed from the plot.

A positive linear association would fall from the right towards the left side and a non-linear association will form a curve. So, the association in the table is negative linear.

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The probability of rolling a sum greater than 5 when rolling a pair of standard six-sided dice is 5/6 or approximately 0.833.

To determine the probability of rolling a sum greater than 5, we can first find the total number of possible outcomes when rolling two dice, which is 36 (6 possible outcomes for each of the 6 sides on the first die). We can then count the number of outcomes where the sum of the two dice is greater than 5, which includes the outcomes (2,4), (2,5), (2,6), (3,3), (3,4), (3,5), (3,6), (4,2), (4,3), (4,4), (4,5), (4,6), (5,2), (5,3), (5,4), (5,5), (5,6), (6,2), (6,3), (6,4), (6,5), and (6,6). There are 21 such outcomes, so the probability of rolling a sum greater than 5 is 21/36, which simplifies to 5/6 or approximately 0.833.

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