What is the longest line segment that can be drawn in a right rectangular prism that is 13 cm long 9 cm wide and 7 cm tall

a. P(1) = 0.3556, P(2) = 0.3111, P(3) = 0.0444; Py(1) = 0.5333, Py(2) = 0.4444, Py(3) = 0.1222 b. P(N = 1 | M = 2) ≈ 0.2574 c.P(M = 2, N = 3) ≈ 0.038 d.  Pr(M>N) = 0.5333.

a. The marginal probability function of m is given by P(m) = Σn P(m, n) and that of n is given by P(n) = Σm P(m, n).

Thus, the marginal PDFs are: P(1) = 1/5 + 8/45 + 2/15 = 0.3556 P(2) = 7/45 + 4/45 + 1/15 = 0.3111

P(3) = 1/9 + 2/45 + 1/45 = 0.0444 P(1) + P(2) + P(3) = 1 Py(1) = 1/5 + 7/45 + 2/15 = 0.5333

Py(2) = 8/45 + 4/45 + 1/15 = 0.4444 Py(3) = 2/15 + 1/15 + 1/45 = 0.1222 Py(1) + Py(2) + Py(3) = 1.

b. We need to find P(N = 1 | M = 2).

From the joint probability distribution table, we can see that P(N = 1, M = 2) = 8/45. P(M = 2) = 0.3111.

Using the conditional probability formula, P(N = 1 | M = 2) = P(N = 1, M = 2)/P(M = 2) = 8/45 ÷ 0.3111 ≈ 0.2574

c. We need to find the probability that M = E and N = N.

Since the two random variables are independent, we can simply multiply their probabilities: P(M = E, N = N) = P(M = E) × P(N = N).

The probability distribution of M is given by: M=1 with probability 0.3556 M=2 with probability 0.3111 M=3 with probability 0.0444

The probability distribution of N is given by: N=1 with probability 0.5333 N=2 with probability 0.4444 N=3 with probability 0.1222

Therefore, P(M = 2, N = 3) = P(M = 2) × P(N = 3) = 0.3111 × 0.1222 ≈ 0.038

d. We need to find P(M > N).

There are three possible pairs of values for (M, N) such that M > N: (M = 2, N = 1), (M = 3, N = 1), and (M = 3, N = 2).

The probabilities of these pairs of values are: P(M = 2, N = 1) = 1/5 P(M = 3, N = 1) = 1/9 P(M = 3, N = 2) = 1/15

Therefore, P(M > N) = P(M = 2, N = 1) + P(M = 3, N = 1) + P(M = 3, N = 2) = 1/5 + 1/9 + 1/15 = 0.5333.

Answer: a. P(1) = 0.3556, P(2) = 0.3111, P(3) = 0.0444; Py(1) = 0.5333, Py(2) = 0.4444, Py(3) = 0.1222 b. 0.2574 c. 0.038 d. 0.5333

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Answer:

See the attached file

Step-by-step explanation:

Given data

Say numbers of printer made per hour = 5 printers

Hence in 1 hour, they will make 5 printers

in 4 hours they will make

=4*5

=20 printers

The graph of this situation when plotted will give a straight line graph

Kindly find attached a straight line graph for your reference

Answer:

opposite of 55 degrees would be KL

opposite of 97 degrees would be ML

opposite of 28 degrees would be MK

Step-by-step explanation:

mark me brainliest if right!!!

Answer: 30 minutes so 1/2 hour

Step-by-step explanation:

Because 3 miles = 1 hour

1.5 times 2 = 3

divide 2 on both sides

Answer:

2 hours

Step-by-step explanation:

divide3 by 1.5 and that is how long it will take you

Answer:

x = [-b ±√(b² - 4ac)]/2a

Step-by-step explanation:

ax² + bx + c = 0

dividing through by a, we have

ax²/a + bx/a + c/a = 0

x² + bx/a + c/a = 0

x² + bx/a = -c/a

we now add th square of half the coefficient of x to both sides, thus

x² + bx/a + (b/2a)² = -c/a +  (b/2a)²

simplifying the left hand side and right hand side, we have

(x + b/2a)² = -c/a + b²/4a²

re-arranging, we have

(x + b/2a)² = b²/4a² - c/a

taking L.C.M of the right hand side, we have

(x + b/2a)² = (b² - 4ac)/4a²

taking square-root of both sides, we have

√(x + b/2a)² = ±√[(b² - 4ac)/4a²]

x + b/2a = ±√(b² - 4ac)/2a

So, x = -b/2a ±√(b² - 4ac)/2a

taking the L.C.M of the right hand side, we have

x = [-b ±√(b² - 4ac)]/2a

Answer:

5x

Step-by-step explanation:

got it right on edg

Answer:

B: 6.5 inches

Step-by-step explanation:

Given,  

Area of the rectangle = 45.5 sq. inches  

The Base of the rectangle = 7 inches  

45.5 = l * 7  

l = 45.5/7

l = 6.5 inches

Answer:

silly billy your a tree with branches and leaves hogwarts has an olw that deleivers letters

Step-by-step explanation:

Answer:

360

Step-by-step explanation:

Given that f is a continuous function on R, f(x) > 0 for all x, and [tex]f(x)^{2}[/tex] = 2f for all x ≥ 0, we need to show that f(x) = x for all x ≥ 0.

Let's assume that there exists a value a ≥ 0 for which f(a) ≠ a. Since f(x) is continuous, the Intermediate Value Theorem can be applied. Consider the function g(x) = f(x) - x. Since g(a) ≠ 0, either g(a) > 0 or g(a) < 0.

If g(a) > 0, it implies that f(a) - a > 0, which leads to f(a) > a. But this contradicts the given condition that f(x) > 0 for all x. Hence, g(a) cannot be greater than 0.

Similarly, if g(a) < 0, it implies that f(a) - a < 0, which leads to f(a) < a. Again, this contradicts the given condition that f(x) > 0 for all x. Therefore, g(a) cannot be less than 0.

Since g(a) cannot be greater than 0 or less than 0, the only possibility is that g(a) = 0, which implies f(a) = a. This holds true for all a ≥ 0. Hence, we can conclude that f(x) = x for all x ≥ 0.

Therefore, based on the given conditions, we have shown that f(x) = x for all x ≥ 0.

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The binary expansion 1100101 base 2 can be converted to base 4 and base 10. In base 4, the expansion is 313 and in base 10, it is 101.

To convert the binary expansion 1100101 base 2 to base 4, we group the binary digits into pairs from right to left. Starting from the rightmost pair, we convert each pair to its equivalent base 4 digit. In this case, the pairs are 01, 01, 10, and 11, which correspond to the base 4 digits 1, 1, 3, and 3, respectively. So the base 4 expansion is 313.

To convert the binary expansion 1100101 base 2 to base 10, we can use the positional value system. Each binary digit represents a power of 2. Starting from the rightmost digit, we assign powers of 2 to each digit in increasing order from right to left. In this case, the digits are 1, 0, 1, 0, 0, 1, and 1, which correspond to the powers of 2^6, 2^5, 2^4, 2^3, 2^2, 2^1, and 2^0, respectively. Evaluating these powers of 2, we get 64, 0, 16, 0, 0, 2, and 1. we obtain 64 + 0 + 16 + 0 + 0 + 2 + 1 = 101 in base 10.

Therefore, the binary expansion 1100101 base 2 is equivalent to 313 base 4 and 101 base 10.

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we can conclude that 12/17 is the larger fraction between 12/17 and 12/19 using the part-whole meaning of a fraction.

To determine which fraction is larger between 12/17 and 12/19 using the part-whole meaning of a fraction, we need to compare the sizes of the parts (numerators) relative to the wholes (denominators) for both fractions.

Let's consider the fractions 12/17 and 12/19:

For 12/17:

- The numerator, 12, represents a part of the whole.

- The denominator, 17, represents the total number of equal parts into which the whole is divided.

For 12/19:

- The numerator, 12, also represents a part of the whole.

- The denominator, 19, represents the total number of equal parts into which the whole is divided.

Since the numerators are the same (both 12) and we are comparing the fractions with the same numerator, the fraction with the smaller denominator represents larger parts or more significant portions of the whole.

Comparing the denominators, we can see that 17 is smaller than 19. This means that the whole in 12/19 is divided into fewer parts compared to the whole in 12/17. Therefore, each part of the whole in 12/17 is larger than each part in 12/19.

As a result, we can conclude that 12/17 is the larger fraction between 12/17 and 12/19 using the part-whole meaning of a fraction.

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18 cm is correct .

Step-by-step explanation:

The sum of two smaller sides is greater that the largest side.

It is given that the two sides of a triangle measure 8 cm and 15 cm.

Case 1: Let 8 cm and 15 cm. are smaller side. So,

Third side < 8 + 15

Third side < 23

It means 3rd side must be less than 23

Case 2: Let 15 cm is the largest side.

15 < Third side + 8

15 - 8 < Third side

7 < Third side

It means 3rd side must be greater than 7.

Since only 18 is less than 23 and greater than 7, therefore the possible length of third sides is 18 cm and option 2 is correct.

Answer:

Meryann brought 6 friends to the party

Step-by-step explanation:

y=9x+24

24 is your constant because the cost for all the pizza won't change

9x will change, so x represents the number of friends she brought

and y will be 78 because it's the total amount of money

78=9x+24

all you have to do is solve this equation

54=9x

x=6

Answer:

Meryann had 6 friends at the party.

Step-by-step explanation:

Total cost = $78

Pizza cost = $24

1 Movie Ticket = $9

Movie Tickets = Total Cost - Pizza Cost

Movie Tickets = $78 - $24 = $54

No. of Friends = Movie Tickets ÷ Movie Ticket

No. of Friends = $54 ÷ $9 = 6

No. of Friends = 6

Answer:

He should have done 8^2 + 15^2= x^2 because the hypotenuse is always the longest side and in Pythagorean theorem C represents the longest side

[tex] {x}^{2} = {(8)}^{2} + {(15)}^{2} [/tex]

[tex] {x}^{2} = 64 + 225[/tex]

[tex] {x}^{2} = 289[/tex]

[tex]x = \sqrt{289} [/tex]

[tex]x = 17[/tex]

Answer:

The length is 86 yards.

Step-by-step explanation:

63 is the width so,

63 + 63 = 126

Now subtract this from the total perimeter,

298 - 126 = 172

and divide by 2 because there are sides with the same length

172/2 = 86

The length is 86.

The equation that represents the sentence "0.7 increased by a number is 3.8" is d) 0.7 + n = 3.8

To understand why this equation is the correct representation, let's break it down. The phrase "a number" can be represented by the variable n, which stands for an unknown value. The phrase "0.7 increased by" implies addition, and the number 0.7 is being added to the variable n. The result of this addition should be equal to 3.8, as stated in the sentence.

Therefore, we have the equation 0.7 + n = 3.8, which indicates that when we add 0.7 to the unknown number represented by n, we obtain a value of 3.8. This equation accurately captures the relationship described in the sentence, making option d, 0.7 + n = 3.8, the correct choice.

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Answer:

(1, - 1)

Step-by-step explanation:

The solution to a system of equations given graphically is at the point of intersection of the 2 lines.

The lines intersect at (1, - 1)

Then (1, - 1 ) is the solution to the system.

Answer:

answer is a

Step-by-step explanation:

first solve

solve for gcf

flip

divide

then you add

and you get 0.928838

The correct answer is The logic behind the Secant method is to iteratively update two initial guesses, x0 and x1, based on the function evaluations at those points. The formula x2 = x1 - (f(x1) * (x1 - x0)) / (f(x1) - f(x0)) is used to update the guesses and obtain a new approximation, x2

Here's an example MATLAB code that implements the Secant method to find the root of a function:

% Function to find the root of

function y = myFunction(x)

[tex]y = x^3 - 5*x^2 + 6*x - 2;[/tex]

end

% Secant method

x0 = 0; % Initial guess x0

x1 = 1; % Initial guess x1

approx_error = 1; % Initial approximation error

while approx_error > 0.001 % Set the desired approximation error threshold

[tex]x2 = x1 - (myFunction(x1) * (x1 - x0)) / (myFunction(x1) - myFunction(x0));[/tex]

[tex]approx_error = abs((x2 - x1) / x2) * 100; % Calculate the approximation[/tex]error

   x0 = x1;

   x1 = x2;

The logic behind the Secant method is to iteratively update two initial guesses, x0 and x1, based on the function evaluations at those points. The formula x2 = x1 - (f(x1) * (x1 - x0)) / (f(x1) - f(x0)) is used to update the guesses and obtain a new approximation, x2. The iteration continues until the approximation error, calculated as the absolute difference between x2 and x1 divided by x2, falls below the desired threshold (in this case, 0.001).

To compare the Secant method with the False-position method, you can apply both methods to the same function and compare their convergence and accuracy. You can also analyze the number of iterations required for each method to achieve a certain level of approximation error.

Please note that in order to generate graphs and screenshots with results, it would be best to run the code in a MATLAB environment and visualize the results directly.

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A net income forecast for Excellence Corporation is made by an analyst for the next fiscal year. Low-end estimate of net income is $261,000High-end estimate is $312,000. Net income follows a continuous uniform distribution. To find: The probability that net income will be greater than or equal to $299,500. In order to solve the problem, we need to calculate the probability that net income will be between $299,500 and $312,000.

Then, we will subtract it from the probability that net income will be between $261,000 and $312,000. This difference will give us the required probability. P(261000 <= X <= 312000) = (312000-261000) / (312000-261000) = 0.2P(299500 <= X <= 312000) = (312000-299500) / (312000-261000) = 0.55P(X >= 299500) = P(299500 <= X <= 312000) - P(261000 <= X <= 312000) = 0.55 - 0.2= 0.35 or 35%.

Thus, the probability that net income will be greater than or equal to $299,500 is 35%. Therefore, the answer is: 24.5%.

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Approximately 48 subjects are needed to estimate the mean number of books read the previous year within six books with 90% confidence.

To estimate the mean number of books read the previous year within a certain margin of error, we need to determine the sample size required. In this case, we want to estimate the mean with a 90% confidence level and a margin of error of ±6 books.

The formula to calculate the required sample size is given by:

Since the standard deviation is unknown, we can use the initial survey result, s = 13.6 books, as an estimate for σ. However, this may result in a larger sample size than necessary.

Referring to the critical values table, we find the z-value corresponding to a 90% confidence level is approximately 1.645. Plugging in the values into the formula:

Since the sample size must be a whole number, we round up to the nearest subject. Therefore, approximately 48 subjects are needed to estimate the mean number of books read the previous year within six books with 90% confidence.

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Answer:

17.7 cm

Step-by-step explanation:

One of the legs of a right triangle measures 12 cm and the other leg measures 13 cm find the measure of the hypotenuse if necessary round the nearest 10th

To find the Hypotenuse of a right angle triangle, we solve using Pythagoras Theorem

Hypotenuse ² = Opposite ² + Adjacent ²

Hypotenuse = √Opposite ² + Adjacent ²

Opposite = 12 cm

Adjacent = 13 cm

Hence,

Hypotenuse = √12² + 13²

= √144 + 169

= 17.691806013 cm

Approximately = 17.7 cm

Therefore, the measure of the Hypotenuse is 17.7 cm

Answer:

c

Step-by-step explanation:

Answer:

Step-by-step explanation:

Putting values in the equation

A = 1/2(7)(8 + 14)

= 1/2(7)(22)

= 1/2(154)

= 77 ft. sq

Option A is the correct answer

An edge is formed when two faces come together. The number of edges in the given solid is 18.

An edge is formed when two faces come together. A cube, for example, has 12 edges, a cylinder has two, and a spherical has none.

The number of edges in the given solid is 18.

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Therefore, the margin of error of a 98% confidence interval estimate of the percentage of the population that favor free tuition is 4.2%.

The margin of error is the difference between the sample statistic and the population parameter. It shows how much the sample result can deviate from the actual population parameter.Here, the sample size n = 750, and the proportion of adults in the US who favor free tuition for four-year colleges is p = 330/750 = 0.44.Using the z-distribution, we can calculate the margin of error for the 98% confidence interval as follows:zα/2 = z0.01/2 = 2.33margin of error = zα/2 * √(p(1-p)/n)margin of error = 2.33 * √(0.44(1-0.44)/750)margin of error ≈ 0.042 or 4.2%Therefore, the margin of error of a 98% confidence interval estimate of the percentage of the population that favor free tuition is 4.2%.

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