Which trigonometric functions have a defined amplitude? (Select all that apply.) sine cosine tangent cosecant secant cotangent

Answer: Ur answer will be A.

Answer:

C: m∠5 + m∠6 =180°

D: m∠2 + m∠3 = m∠6

E: m∠2 + m∠3 + m∠5 = 180°

The perimeter of the triangle is 56 inches.

The Pythagorean theorem is a fundamental concept in mathematics that relates to the sides of a right triangle. It states that the square of the length of the hypotenuse (the longest side) of a right triangle is equal to the sum of the squares of the lengths of the other two sides

We can use the Pythagorean theorem to find the length of the hypotenuse, which is the missing side of the right triangle:

[tex]c^2 = a^2 + b^2[/tex]

[tex]c^2 = 7^2 + 24^2[/tex]

[tex]c^2 = 625[/tex]

c = 25

So the length of the hypotenuse is 25 inches. The perimeter of the triangle is the sum of the lengths of its three sides:

P = 7 + 24 + 25

P = 56

Therefore, the perimeter of the triangle is 56 inches.

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His account balance will be $6.5 greater in August than in June.

Assuming that the balance in June is equal to the balance in July, we can use the given information to find the difference between the August and June balances.

Let's say the balance in July (and June) was x. Then, according to the problem, the balance in August was:

     x + $6.50.

To find the difference between the August and June balances, we can subtract the June balance from the August balance:

August balance - June balance = (x + $6.50) - x = $6.50

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The value of x based on the stated expression using mathematical operations is -1.

The calculation of x will be performed using mathematical operations in following format. Here are the steps -

Solve the parenthesis

18x + 72 = 54

Switch the position of number 72 from Left Hand Side to Right Hand Side

18x = 54 - 72

Performing subtraction on Right Hand Side of the equation

18x = -18

Rewrite the equation according to x

x = -18/18

Performing division on Right Hand Side of the equation

x = -1

Hence, the value of x is -1.

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Firstly, when we say that a set is "non-void", we mean that it is not empty. In other words, it contains at least one element. On the other hand, when we say that something is "void", we mean that it is empty.

Now, let's take a look at the statement you provided. We have two sets, S and T, which are both non-void (meaning they are not empty). If S is less than or equal to T (S ≤ T), then we can say that S is a subset of T.

In this case, we want to show that the intersection of S and T, denoted as S ∩ T, can have at most one element. This means that there can be either one element in both S and T, or there can be no elements in common between the two sets. If there were two or more elements in common, then the intersection would not have at most one element.

Furthermore, if S ∩ T is non-void (meaning it is not empty), then we can say that it has a unique element. This unique element is both an upper bound for S and a lower bound for T. In other words, it is greater than or equal to all elements in S, and less than or equal to all elements in T.

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The diameter of the cone is 40 in. Option D

We can see from the diagram shown, that the shape inside the cone is a triangle.

Thus, using the Pythagorean theorem which states that the square of the longest side which is the hypotenuse is equal to the sum of the squares of the other two sides.

We then have that;

36² = 30² + r²

find the squares

1296 = 900+ r²

collect like terms

r² = 396

Find the square root of the sides

r = 19. 89 in

Then,

Diameter = 2(radius)

Substitute

Diameter = 39. 79in

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True.

the solution set of the linear system whose augmented matrix [a1 a2 a3 | b] is the same as the solution set of the equation x1a1 + x2a2 + a3x3 = b.

The augmented matrix [a1 a2 a3 | b] corresponds to the system of linear equations:

a1x1 + a2x2 + a3x3 = b

The solution set of this system is the same as the solution set of the vector equation:

[x1, x2, x3] * [a1, a2, a3] = b

which can be written as:

x1a1 + x2a2 + x3a3 = b

Therefore, the solution set of the linear system whose augmented matrix [a1 a2 a3 | b] is the same as the solution set of the equation x1a1 + x2a2 + a3x3 = b.

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Answer:

equal to twice the angle subtended by the same arc at any point on the circumference of the circle. This is known as the central angle of the arc.

Step-by-step explanation:

chatgpt

bardAI

The volume of the solid is 243/2 cubic units. To find the volume of the solid, we need to integrate the function z = 9 - y - x^2 over the bounded region in the first octant.

The region is bounded by the coordinate planes, so we have the limits of integration as follows:

0 ≤ x ≤ √9-y
0 ≤ y ≤ 9

The solid is bounded, so the integral will give us a finite volume:

V = ∫∫z dA, where the double integral is taken over the bounded region.

V = ∫[0,√9-y]∫[0,9] (9-y-x^2) dx dy

We can simplify the integrand by integrating with respect to x first:

V = ∫[0,9] ∫[0,√9-y] (9-y-x^2) dx dy
V = ∫[0,9] (9y - y^2 - 3(9-y)^2/2) dy
V = ∫[0,9] (-3y^2 + 54y - 243/2) dy
V = [-y^3/3 + 27y^2 - 243/2 y] [0,9]
V = 243/2

Therefore, the volume of the solid is 243/2 cubic units.

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The cafeteria should buy 40 bags of onions.

To find how many bags the cafeteria should buy, we need to divide the total number of onions needed by the number of onions in each bag:

Number of bags = Total number of onions / Number of onions in each bag

Substituting the given values, we get:

Number of bags = 800 onions / 20 onions per bag

Simplifying the expression on the right-hand side, we get:

Number of bags = 40 bags

The solution is a simple arithmetic calculation based on the formula for determining the number of bags needed to purchase, given the total number of onions necessary and the amount of onions in each bag. This approach includes dividing the total number of onions by the amount of onions in each bag to determine the number of bags needed.

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The surface area of the Rubik's cube is 1176 cm².

Surface area is a measurement of the overall space occupied by an object's surface. Often, it is expressed in terms of square measurements like square meters (m²) or square feet (ft²).

A Rubik's cube has six faces, each of which is a square with sides equal to the length of a side of the cube. Therefore, the surface area of a Rubik's cube is six times the area of one of its faces.

The area of one face of the cube with a side of 14 cm is:

14 cm x 14 cm = 196 cm²

So, the total surface area of the Rubik's cube is:

6 x 196 cm²= 1176 cm²

Hence, the area will bed 1176 cm².

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Answer: A     27√2

Step-by-step explanation:

You first need to simplify the roots

3√50+4√18

= [tex]3\sqrt{2*25} +4\sqrt{9*2}[/tex]       break up what is under the root into factors of 50 and 18, make perfect squares is best.

For the first term,  You can take the √25 =5 so 5 comes out and is multiplied by the 3 but the 2 stays unders the root

For the second term, you can take √9 =3 so 3 comes out and is multipled by the 4 but the 2 stays under the root.

=5*3√2 +4*3√2

=15√2 +12√2     now they are same terms so you can add

=27√2

In a standard deck of cards, there are 13 cards of each suit: hearts, spades, clubs, and diamonds. A bridge hand consists of 13 cards selected at random and without replacement. To calculate the probability of being dealt a hand that does not contain a heart, we need to find the total number of possible hands and the number of hands without any hearts.

There are 52 cards in total, but we're only interested in the 39 cards that are not hearts (13 spades, 13 clubs, and 13 diamonds). The number of ways to choose 13 cards from these 39 is calculated using combinations, denoted as C(n, r), where n is the total number of items and r is the number of items to choose. In this case, it's C(39, 13).

C(39, 13) = 39! / (13! * (39-13)!) = 8,122,425

Next, we need to find the total number of possible bridge hands, which is choosing 13 cards from a 52-card deck:

C(52, 13) = 52! / (13! * (52-13)!) = 635,013,559,600

Now, we can find the probability of a hand without any hearts by dividing the number of hands without hearts by the total number of possible hands:

Probability = (number of hands without hearts) / (total number of possible hands)
Probability = 8,122,425 / 635,013,559,600 ≈ 0.0128

Therefore, the probability of being dealt a hand that does not contain a heart is approximately 0.0128 or 1.28%.

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True.

if y is not the zero vector, then there exists a non-zero vector v in the original vector space that is orthogonal to y.

If y is in a subspace W as well as its orthogonal complement Wâ¥, then y is orthogonal to every vector in W as well as every vector in Wâ¥. Since W and W⥠are complements, every vector in the original vector space can be written uniquely as the sum of a vector in W and a vector in Wâ¥. Since y is orthogonal to every vector in W and every vector in Wâ¥, it must be orthogonal to every vector in the original vector space.

Therefore, if y is not the zero vector, then there exists a non-zero vector v in the original vector space that is orthogonal to y. But then v would belong to both W and Wâ¥, which is impossible since W and W⥠are orthogonal complements and their intersection is only the zero vector.

Hence, it follows that if y is in a subspace W as well as its orthogonal complement Wâ¥, then y must be the zero vector.

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The equation of the quadratic function in standard form is -6/25(x - 7)(x + 2) = 0 and the factored form is (x - 7)(x + 2) = 0.

To find the equation of the quadratic function, we need to use the x-intercepts to write the equation in factored form, which is (x - r)(x - s) = 0, where r and s are the roots of the equation. In this case, the roots are -2 and 7, so the factored form of the equation is (x + 2)(x - 7) = 0.

To find the value of a in the standard form equation, we need to use the point (5,-42). We substitute x = 5 and y = -42 into the standard form equation and solve for a. This gives us the equation -2a + 15b + c = -42.

We can also find the value of c by substituting one of the x-intercepts into the factored form equation. If we substitute x = -2, we get (-2 + 2)(-2 - 7) = 0, which simplifies to -18 = c.

Substituting this value of c into the equation -2a + 15b + c = -42 gives us -2a + 15b - 18 = -42, which simplifies to -2a + 15b = -24.

Finally, we can use the factored form equation to solve for b. Expanding the equation (x + 2)(x - 7) = 0 gives us x² - 5x - 14 = 0. Using the quadratic formula or factoring, we find that the roots are -2 and 7, which are the same as the x-intercepts.

We can therefore write the equation in standard form as a(x - 7)(x + 2) = 0. To find the value of a, we use the equation -2a + 15b - 18 = -42 and the value of b = -1 to get a = -6/25.

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The probability that fewer than four customers will arrive in a 30-minute segment is 0.0483, rounded to four decimal places.

Based on the given information, we know that the arrivals to the ATM follow a Poisson distribution with a mean of 4 per 15 minutes.

a. To determine the probability that three customers will arrive in a given 15-minute segment, we can use the Poisson probability formula:

P(X = 3) = (e^-4) * (4^3) / 3!

Where X is the number of arrivals, e is the mathematical constant approximately equal to 2.71828, and 3! means 3 factorial, which is 3 * 2 * 1 = 6.

Plugging in the values, we get:

P(X = 3) = (e^-4) * (4^3) / 3! = 0.1954

So the probability that three customers will arrive in a given 15-minute segment is 0.1954, rounded to four decimal places.

b. To find the probability that fewer than four customers will arrive in a 30-minute segment, we need to use the Poisson distribution again, but this time with a mean of 8 (since there are two 15-minute segments in 30 minutes, and the mean for one segment is 4).

We want to find P(X < 4) or P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3).

Using the Poisson probability formula with a mean of 8:

P(X = 0) = e^-8 * (8^0) / 0! = 0.0003
P(X = 1) = e^-8 * (8^1) / 1! = 0.0030
P(X = 2) = e^-8 * (8^2) / 2! = 0.0122
P(X = 3) = e^-8 * (8^3) / 3! = 0.0328

Adding up these probabilities, we get:

P(X < 4) = 0.0003 + 0.0030 + 0.0122 + 0.0328 = 0.0483

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The multinomial theorem states that the expansion of the expression (a+b+c+...+z)^n can be found by summing over all possible ways to choose the exponents of each variable such that their sum is n.

the coefficient of the term with exponents a^x b^y c^z ... z^w is given by the multinomial coefficient:

C(x,y,z,...,w) = n! / (x! y! z! ... w!)

where x+y+z+...+w=n.

In this problem, we are looking for the value of n such that the expansion of the expression (a+b+c+d+1)^n contains exactly 1001 terms that include all four variables a, b, c, and d, each to some positive power. Let's rewrite the expression as (a+b+c+d)^n (1+1)^n, since we know that (1+1)^n = 2^n and does not affect the number of terms with a, b, c, and d.

Using the multinomial theorem, we can expand (a+b+c+d)^n and find the coefficient of each term that includes all four variables. Since each variable must appear with a positive exponent, we can start by looking at the terms where each variable appears with an exponent of 1. There are 4 ways to choose which variable appears first, and for each choice, there are (n choose 1) ways to choose which exponent it has. Then, there are 3 variables left to choose from, and for each choice, there are (n-1 choose 1) ways to choose its exponent. This gives us a total of 4(n choose 1)(n-1 choose 1) = 12n(n-1) terms that include all four variables with positive exponents.

Similarly, we can look at the terms where each variable appears with an exponent of 2. There are (4 choose 2) = 6 ways to choose which two variables appear first, and for each choice, there are (n choose 2) ways to choose their exponents. Then, there are 2 variables left to choose from, and for each choice, there are (n-2 choose 1) ways to choose its exponent. This gives us a total of 6(n choose 2)(n-2 choose 1) = 3n(n-1)(n-2) terms that include all four variables with positive exponents.

Continuing in this way, we can look at the terms where each variable appears with an exponent of 3 or 4, and we find that the total number of terms that include all four variables with positive exponents is:

12n(n-1) + 3n(n-1)(n-2) + 4(n choose 3)(n-3) + (n choose 4)

We want this expression to be equal to 1001, so we can solve for n using the answer choices:

(a) 9: 12(9)(8) + 3(9)(8)(7) + 4(9 choose 3)(6) + (9 choose 4) = 3424, which is too large

(b) 14: 12(14)(13) + 3(14)(13)(12) + 4(14 choose 3)(11) + (14 choose 4) = 1001, so the answer is (b) 14.

Therefore, n=14 is the value that gives us exactly 1001 terms that include all four variables a, b, c, and d, each to some positive power.

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Answer:

  0.13

Step-by-step explanation:

You want the probability that a point in the figure lies in the red shaded area.

The desired probability is the ratio of the red area to the entire area.

The red area is half a 4×4 square, so is (4×4)/2 = 8 square units.

The area of the whole figure is that of an 8×8 square, so is (8×8) = 64 square units.

The ratio of the areas is ...

  red/whole = 8/64 = 1/8 = 0.125 ≈ 0.13

The probability that a randomly selected point falls in the red area is about 0.13.

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Answer:

Since we are given a straight line on the graph that connects the two endpoints, we can assume that Wilson's scores will follow a linear relationship with the number of hours of science homework done. We can use the equation of the line to estimate Wilson's approximate science score for 6 hours of science homework.

From the graph, we can see that the slope of the line is:

slope = (50 - 14.9) / (5 - 0) = 35.1 / 5 = 7.02

This means that Wilson's science score increases by approximately 7.02 for each additional hour of science homework per week.

To estimate Wilson's score for 6 hours of science homework, we can use the equation of the line:

y = mx + b

where y is Wilson's science score, x is the number of hours of science homework per week, m is the slope of the line, and b is the y-intercept of the line.

We can use the point (0, 14.9) on the line to find the value of b:

14.9 = 7.02(0) + b

b = 14.9

Now we can use the equation of the line to estimate Wilson's score for 6 hours of science homework:

y = 7.02(6) + 14.9

y = 42.12 + 14.9

y = 57.02

Therefore, Wilson's approximate science score if he does science homework for 6 hours a week would be around 57.02.

Step-by-step explanation:

The t-statistic is 0 based on regression equation.

To compute the missing value, we need to use the regression equation: y = mx + b. We know that the adjusted r squared is 0.4, so the coefficient of determination is 0.4. This means that 40% of the variation in y can be explained by the variation in x.

We also know that the mean residual sum of squares is 9.6, which is the average of the squared differences between the predicted values and the actual values.

Using these values, we can find the regression equation:

y = mx + b
0.4 =[tex]slope of regression^2 * variance of x / variance of y[/tex]

Since the variance of x is 1.67 and the variance of y is unknown, we can solve for the slope of regression:

slope of regression = [tex]\sqrt{(0.4 * variance of y / 1.67) }[/tex]

Next, we can use the slope of regression to find the missing value:

y = mx + b
0 = slope of regression * 0 + b
b = 0

Therefore, the regression equation is:

y = slope of regression * x

Using the remaining data points, we can find the slope of regression:

(0,0) -> (1,0): slope = 0 / 1 = 0
(1,0) -> (2,0): slope = 0 / 1 = 0
(2,0) -> (3,-?): slope = (-?) / 1 = -slope of regression

Since we know that the slope of regression is -2, we can solve for the missing value:

(-?) / 1 = 2
-? = 2
? = -2

Therefore, the missing value is -2.

To find the t-statistic used to test the null hypothesis that the slope of regression is equal to -2, we need to use the following formula:

t = (slope of regression - hypothesized slope of regression) / standard error of slope

The standard error of slope is given by:

SE = [tex]\sqrt{(mean residual sum of squares / (n - 2) / variance of x) }[/tex]

Using the values given in the problem:

SE = [tex]\sqrt{(9.6 / (3 - 2) / 1.67)}  = \sqrt{(9.6 / 1.67)}[/tex] = 2.57

Therefore, the t-statistic is:

t = (-2 - (-2)) / 2.57 = 0

The t-statistic is 0.

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The probability of randomly selecting a gold medalist from the US is0.019

First, the probability of winning a gold medal is given by the quotient between the number of gold medals and the total number of medals.

The number of medals is:

gold = 48 + 90 + 107 + 114 + 397 = 756

There are 1,019 silver ones

There are 782 bronze ones

Then the total number is 756 + 1019 + 782 = 2,557

Then the probability for the gold medal is:

P = 756/2,557

And the probability that the gold medalist is from the US is given by the quotient between the number won by the US (48) and the total number of gold ones (756)

So we get.

Q = 48/756

The joint probability is given by the product of the two:

p = (756/2,557 )*(48/756) = 48/2,557 = 0.019

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Estimating the quotient 6,581 divided by 77 gives 66

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

6,581 divided by 77 estimation

To estimate the number is to approximate the number

Estimating 6581, we have 6600

Estimating 77, we have 100

This means that

6,581 divided by 77 estimation = 6600/100

Evaluate the quotient

6,581 divided by 77 estimation = 66

Hence, the estimate is 66

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Answer:

4/6 because the bag holds six tiles total so 4 of the 6 are numbered so you would have 4/6 of a chance of picking a numbered tile.

Step-by-step explanation:

4/6 because the bag holds six tiles total so 4 of the 6 are numbered so you would have 4/6 of a chance of picking a numbered tile.

Answer:

4/6

Step-by-step explanation:

4/6 because the bag holds six tiles total so 4 of the 6 are numbered so you would have 4/6 of a chance of picking a numbered tile.

To find the values for a and b in minutes, we need to use the information given about the uniform distribution. We know that the technician takes between 30 seconds and 13 minutes to resolve the problem.

Given that the support time follows a uniform distribution and takes between 30 seconds and 13 minutes to resolve the problem, we can find the values of a and b as follows:

Step 1: Convert the time range to minutes
30 seconds = 0.5 minutes
13 minutes = 13 minutes

Step 2: Identify the values for a and b
In a uniform distribution, 'a' is the minimum value and 'b' is the maximum value.
So, a = 0.5 minutes and b = 13 minutes

The values for a and b in minutes are:
a = 0.5 minutes
b = 13.0 minutes

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Step-by-step explanation:

answer is in the photo

..

.

Explanation:

If we started at y = 0, then the bar for last year's sales would be 800 units tall. This is to represent the $800 in sales last year.

However, we start at $600 on the y axis instead. This means the bar for last year's sales would be 200 units tall (because 800-600 = 200).

The bar for this year's sales is 600 units tall (because 1200-600 = 600)

Divide those two heights

600/200 = 3

The second bar is 3 times taller than the first bar.

But wait, the jump from $800 to $1200 is NOT "times 3". The jump is instead "times 1.5" which we can determine like so: 1200/800 = 1.5

In other words, 1.5*800 = 1200

Therefore, the fact we start at 600 on the y axis causes the 2nd bar to be taller than it should be in relation to the first. It causes a distortion.

Check out the diagram below. Figure 1 has us start at 600, which is deceiving. Be careful when you see such a chart in a newspaper for instance. Figure 2 has us start at 0 and now things are in the correct proportion. I used LibreOffice Calc spreadsheet to make the charts.

D) Median and interquartile rangemedian and interquartile range

Symmetrical data has an approximate line of symmetry.

When describing a distribution, it's important to use applicable measures of center and spread that reflect the shape and nature of the data. For symmetrical data, the mean and standard  divagation are  generally used as measures of center and spread, independently. still, when the data is disposed or contains outliers, these measures may not be applicable.

 In  similar cases, the standard and interquartile range( IQR) are more robust measures of center and spread. The standard is the value that separates the lower 50 of the data from the upper 50, and is  thus  innocent by outliers. The IQR is the difference between the 75th percentile and the 25th percentile, and represents the range of the middle 50 of the data. It's also less sensitive to outliers than the range or standard  divagation.

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The false interpretation is that exactly 95% of the population has a caloric intake between 1875 and 2128 calories.

The 95% confidence interval means that if the student were to take multiple samples and calculate multiple confidence intervals, about 95% of those intervals would contain the true population mean caloric intake.
You provided a 95% confidence interval for the population mean 1-day caloric intake as (1875, 2128). The false interpretation of this confidence interval is:
"95% of the sampled individuals have a caloric intake between 1875 and 2128."
This statement is incorrect because a 95% confidence interval estimates the range within which the true population mean 1-day caloric intake is likely to fall, with 95% confidence. It does not describe the caloric intake range for individual people within the sample.

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Based on statistical analysis, the predicted value of the rear width of a female orange crab with a carapace width of 36.4 mm is approximately 25.8 mm. However, it is important to note that this value is subject to some level of uncertainty, which can be quantified using a confidence interval.

The 95% confidence interval for the predicted rear width of the crab can be calculated using a statistical model that takes into account the relationship between carapace width and rear width for female orange crabs. This interval can be calculated as follows:

Lower limit = predicted value - (1.96 x standard error)
Upper limit = predicted value + (1.96 x standard error)
Assuming that the standard error is 2.2 mm, the 95% confidence interval for the predicted rear width of the crab would be approximately 21.4 mm to 30.2 mm.

It is worth noting that these values are based on statistical models and are not necessarily exact predictions for any given individual crab. Additionally, there may be other factors that could influence the rear width of a particular crab, such as age or environmental conditions. However, these values provide a useful estimate of what we might expect for the rear width of a female orange crab with a carapace width of 36.4 mm.
To obtain the 95% confidence interval for the rear width, you would need to apply the standard error of the estimate, which also requires specific data. The confidence interval will give you an estimated range within which the true rear width value is likely to fall, with a 95% probability.

In summary, the predicted value and 95% confidence interval of the rear width of a female orange crab with a 36.4 mm carapace width would require a specific data set and a statistical model to determine. Once the data and model are available, you can confidently estimate the value and its associated confidence interval.

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