Find the dimensions of the rectangular box with largest volume if the total surface area is given as 4 cm2. (Let x, y, and z be the dimensions of the rectangular box.)
(x, y, z) =

We are given a problem regarding trigonometric identities and asked to resolve for theta.

Recall that:

Therefore, we have:

In radians, we have:

The notation P(F|E) means the probability of event F given event E.

In probability notation, P(F|E) represents the conditional probability of event F occurring given that event E has already occurred. It is read as "the probability of F given E." The vertical bar "|" indicates "given" or "conditional on." This notation allows us to calculate the probability of one event happening, taking into account the occurrence of another event. For example, P(F|E) would represent the probability of rain (event F) given that the weather forecast predicts a cloudy day (event E). The conditional probability allows us to analyze how events are related and make more accurate predictions or assessments based on the given information.

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Answer:

see below

Step-by-step explanation:

Opposite sides are congruent (AB = DC).

Opposite angels are congruent (D = B).

Consecutive angles are supplementary (A + D = 180°).

If one angle is right, then all angles are right.

The four properties of parallelogram are:

i) Opposite sides are parallel & equal.

ii) Sum of adjacent interior angles is 180°

iii) Opposite angles are equal.

iv) Diagonals bisect each other.

The quadrilateral with two pairs of parallel sides is known as a parallelogram. Equal in length and width on both sides is required. Four vertices make up a parallelogram, which also has four edges.

A parallelogram is a two-dimensional (2D) shape that has two matching pairs of opposite sides that are parallel and equal in length. The angles inside the two sides of the shape must add up to 180 degrees, which means that all of the angles must add up to 360 degrees.

A rectangle that has been pushed over slightly is all that a parallelogram really is. Because of this, finding the area of a parallelogram can be done using the same formula as finding the area of a rectangle.

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The number of basketball trophies in Donovan's collection is 19

From the information given, let;

We have that;

x = 2y - 13       (1)

x + y = 35     (2)

Now, let's substitute the value of x as 13 - y in (2)

2y - 13 + y = 35

collect like terms

3y = 35 + 13

3y = 48

Make 'y' the subject

y = 48/3

y = 16

Donovan's collection =  2y - 13 = 2 (16) - 13 = 32- 13 = 19

Thus, the number of basketball trophies in Donovan's collection is 19

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Answer:

BCA

Step-by-step explanation:

The interior angle measures at stages A, B, and C are approximately 71.7 degrees, 133.4 degrees, and 175.0 degrees, respectively. Therefore, the angles in descending order are C, B, and A.

Let's label the stages A, B, and C. To find the interior angles at each stage, we can use the Law of Cosines:

cos(A) = (b^2 + c^2 - a^2) / 2bc

cos(B) = (c^2 + a^2 - b^2) / 2ca

cos(C) = (a^2 + b^2 - c^2) / 2ab

where a, b, and c are the distances between the centers of the stages.

Using the given distances, we have:

a = 100, b = 135, c = 210

cos(A) = (135^2 + 210^2 - 100^2) / (2*135*210) ≈ 0.309

cos(B) = (210^2 + 100^2 - 135^2) / (2*210*100) ≈ -0.692

cos(C) = (100^2 + 135^2 - 210^2) / (2*100*135) ≈ -0.905

To find the interior angles, we can take the inverse cosine (also known as arccosine) of each value:

A ≈ 71.7 degrees

B ≈ 133.4 degrees

C ≈ 175.0 degrees

So the interior angle measures at stages A, B, and C are approximately 71.7 degrees, 133.4 degrees, and 175.0 degrees, respectively. Therefore, the angles in descending order are C, B, and A.

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Step 1: Transform the subtraction of integers problem into the addition of integers problem. Here’s how:

First, keep the first number (known as the minuend).

Second, change the operation from subtraction to addition.

Third, get the opposite sign of the second number (known as the subtrahend)

Finally, proceed with the regular addition of integers.

Step 2: Proceed with the regular addition of the integers.

⊗ Note that you will eventually add integers. So for your convenience, here’s the quick summary of the rules on how to add integers.

Case 1:  Adding two integers having the same sign

Add their absolute values then keep the common sign.

Case 2:  Adding two integers with different signs

Subtract their absolute values (larger absolute value minus smaller absolute value) then take the sign of the number with the larger absolute value.

Answer:

When you subtract an integer from another interger you decrease the value of it.

Step-by-step explanation:

For example -9 plus negtive -9 is -18, it's almost like adding.

Answer:

6(−3−x)−2x=14

simplify

-18-6x-2x=14

simplify

-8x-18=14

add 18

-8x=32

divide by -8

x=4

Hope This Helps!!!

The error message displayed in Excel Solver when attempting to solve an unbounded problem is "Solver could not find a bounded solution."

This error message indicates that the Solver was unable to find a solution that satisfies all the constraints while still remaining within the defined bounds. An unbounded problem is one in which the objective function can be improved without limit, meaning that there is no upper limit on the optimal solution.

This can occur when there are no constraints on the variables, or when the constraints are too loose to define a unique optimal solution. In such cases, the Solver may continue to search for a solution without ever converging to a final answer. It is important to review the constraints and variables in the problem to ensure that they are properly defined and that the Solver is set up correctly.

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After considering the given data we conclude that there truth table is possible and is placed in the given figures concerning every sub question.

A truth table is a overview that projects  the truth-value of one or more compound propositions for each possible combination of truth-values of the propositions starting up the compound ones.
Every row of the table represents a possible combination of truth-values for the component propositions of the compound, and the count of rows is described by the range of possible combinations.
For instance, if the compound has just two component propositions, it comprises  four possibilities and then four rows to the table. The truth-value of the compound is projected on each row comprising the truth functional operator.
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(i) T-interval

(ii) F. Because I don't have a large number of professors and I don't know the standard deviation of all FSU professors' heights.

What is standard deviation?

Standard deviation is a measure of the amount of variation or dispersion of a set of data values from the mean value.

When constructing a confidence interval for the mean of a population using a sample, we use either a Z-interval or a T-interval based on the sample size and whether we know the population standard deviation.

If the sample size is large (usually taken to be greater than or equal to 30) and/or we know the population standard deviation, then we can use a Z-interval.

However, if the sample size is small (usually less than 30) and/or we don't know the population standard deviation, we should use a T-interval.

In this case, we don't have a large sample size (just the professors the student has this term), and we don't know the standard deviation of all FSU professors' heights, so we would use a T-interval.

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The given statement is an example of "Principle of specificity or specific adaption to imposed demands (SAID Principle) ".

What is Principle of specificity ?

According to the specificity of training principle, each physical activity has a very unique physiological response. For instance, someone who jogs can anticipate that both their running performance and their level of aerobic fitness will be favorable.

if someone repeatedly lifts heavy weights, that person will produce higher levels of maximal strength.

This an example of  "Principle of specificity or specific adaption to imposed demands (SAID Principle) "

Tenet according to which the body will adjust to the unique demands imposed upon it.

Higher degrees of endurance can be attained by regularly lifting lesser weights for a large number of repetitions.

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Using the conversion factor, 3 1/3 yards is equal to 120 inches

To convert yards to inches, we need to know the conversion factor between these two units. One yard is equal to 36 inches.

Therefore, to convert 3 1/3 yards to inches, we can use the following steps:

Convert the whole number of yards to inches: 3 yards x 36 inches/yard = 108 inches

Convert the remaining fraction of a yard to inches: 1/3 yard x 36 inches/yard = 12 inches

Add the results of steps 1 and 2 to get the total number of inches: 108 inches + 12 inches = 120 inches

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Answer:

Since there are (12) inches in 1 yard (divide) 3 1/3 by (36)

so 3 1/3 yards = (16) inches.

Step-by-step explanation:

when you see (   ) it means it's the Answer

Answer:

The expected profit from the game can be calculated as the revenue from ticket sales minus the investment cost:

Expected profit = $89,399 - $23,197 = $66,202

The expected loss if it rains can be calculated as the investment cost:

Expected loss = $23,197

To find the net result, we need to use the probability of the game happening (1 - 0.28 = 0.72) and the probability of it raining (0.28):

Net result = (0.72) * (Expected profit) + (0.28) * (Expected loss)

Net result = (0.72) * ($66,202) + (0.28) * ($23,197)

Net result = $47,683.44

Since the net result is positive, the expected outcome is a profit of $47,683.44.

There is an expected profit of $57,963.32.

To calculate the expected profit or loss, we need to consider two possible scenarios:

Scenario 1: It doesn't rain on the day of the game, and the club is able to sell tickets worth $89,399.

Scenario 2: It rains on the day of the game, and the club loses the entire investment of $23,197.

To calculate the expected profit, we need to multiply the revenue from scenario 1 by the probability of it happening, which is (1 - 0.28) = 0.72 (since there's a 28% chance of rain). So, the expected profit is:

Expected profit = 0.72 x $89,399 = $64,451.28

To calculate the expected loss, we need to multiply the investment from scenario 2 by the probability of it happening, which is 0.28 (since there's a 28% chance of rain). So, the expected loss is:

Expected loss = 0.28 x $23,197 = $6,487.96

To find the net result, we subtract the expected loss from the expected profit:

Net result = Expected profit - Expected loss = $64,451.28 - $6,487.96 = $57,963.32

Therefore, there is an expected profit of $57,963.32.

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These descriptors can be classified as a geographic distribution, expressed mathematically as a percentage of the total population living within a certain radius or certain counties.

These descriptors can best be classified as a geographic distribution. Specifically, the 70% of season ticket holders within 30 miles of the stadium can be expressed mathematically as a percentage of the total population living within that radius. The equation for this would be:

P = (70/100) * T

Where P is the percentage of the total population living within 30 miles of the stadium, and T is the total population within that radius.

The 40% of season ticket holders living within three different counties can also be expressed mathematically as a percentage of the total population living within those counties. The equation for this would be:

P = (40/100) * T

Where P is the percentage of the total population living within the three counties, and T is the total population within those counties.

Therefore, these descriptors can be classified as a geographic distribution, expressed mathematically as a percentage of the total population living within a certain radius or certain counties.

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Answer:

Vertex: (6, 18)

Step-by-step explanation:

Given the quadratic function, m(x) = -2(x - 3)(x - 9):

Perform the FOIL method on the two binomials, (x - 3)(x - 9) without distributing -2:

m(x) = -2[(x - 3)(x - 9)]

Combine like terms:

m(x) = -2(x² - 9x - 3x + 27)

m(x) = -2(x² - 12x + 27)

where: a = 1, b = -12, and c = 27

Since the axis of symmetry occurs at x = h, then we can use the following formula to solve for the x-coordinate (h ) of the vertex, (h, k):

\(x = \frac{-b}{2a}\)

Substitute a = 1 and b = -12 into the formula:

\(x = \frac{-b}{2a}\)

\(x = \frac{-(-12)}{2(1)} = \frac{12}{2} = 6\)

Therefore, the x-coordinate (h) of the vertex is 6.  

Next, substitute the value of h into x² - 12x + 27 to find the y-coordinate (k ) of the vertex:

k = x² - 12x + 27

k = (6)² - 12(6) + 27

k = 36 - 72 + 27

k = 18

Therefore, the vertex of the quadratic function occurs at point (6, 18), in which it is the maximum point on the graph.

When the principal is $3500 and the annual interest rate is 1.83%, compounded daily, the balance in the account receiving compound interest after 6 years is $4,036.32.

To find the amount A in the account earning compound interest after 6 years when the principal is $3500, we need to use the compound interest formula:

\(A = P(1 + \frac{r}{n})^{nt}\)

Where:

P = principal = $3500

r = annual interest rate = 1.83% = 0.0183 (as a decimal)

n = number of times the interest is compounded per year = 365 (daily compounding)

t = time in years = 6

Substituting these values into the formula, we get:

\(A = 3500(1 + \frac{0.0183}{365})^{(365*6)}\)

\(A = 3500(1.00005)^{2190}\)

A = $4,036.32

Therefore, the amount in the account earning compound interest after 6 years when the principal is $3500, with an annual interest rate of 1.83% compounded daily, is $4,036.32.

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Answer: I cant really see it beacuse how you angled it...

Step-by-step explanation:

The line

Can be written as:

This is the same line in the slope-intercept form:

Then, the original line has an slope of -2.

To find the slope of a perpendicular line to this one we need to remmeber that two lines are perpendicular if and only if

Plugging the value of the original line we have:

Therefore a line perpendicular to the line 10x+5y=10 has slope 1/2 or 0.5.

The first five terms of each sequence can be written from the nth term of the sequence and the type of sequence are, arithmetic, geometric, geometric, geometric, and geometric respectively.

It is given that:

The sequences are:

1. a(1) = 7, a(n) = a(n - 1) - 3 for n > 2.

Plug n = 2 in the a(n)

a(2) = a(2 - 1) - 3

a(2) = a(1) - 3

a(2) = 7 - 3

a(2) = 4

lug n = 3

a(3) = 1

The first five terms are:

7, 4, 1, -2, -5 (arithmetic sequence)

2. b(1) = 2, b(n) = 2[b(n - 1) - 1] for n > 2.

Similarly,

The first five terms are:

2, 2, 2, 2, 2 (geometric sequence)

3. c(1) = 3. c(n) = 10 • c(n - 1) for n > 2.

The first five terms are:

3, 30, 300, 3000, 30000 (geometric sequence)

4. d(1) = 1, d(n) = n • d(n - 1) for n > 2.​

1, 2, 6, 24, 48 (geometric sequence)

Thus, the first five terms of each sequence can be written from the nth term of the sequence and the type of sequence are, arithmetic, geometric, geometric, geometric, and geometric respectively.

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Write the first five terms of each sequence. Determine whether each sequence is arithmetic, geometric, or other.

1. a(1) = 7, a(n) = a(n - 1) - 3 for n > 2.

2. b(1) = 2, b(n) = 2 • b(n - 1) - 1 for n > 2.

3. c(1) = 3. c(n) = 10 • c(n - 1) for n > 2.

4. d(1) = 1, d(n) = n • d(n - 1) for n > 2.​

The algebraic expression is (2x + 7) - (2x - 4) and the solution is 11

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

Algebraic tile

To make use of the variable x, we have the following equation

(2x + 7) - (2x - 4)

Open the brackets

So, we have the following representation

(2x + 7) - (2x - 4) = 2x + 7 - 2x + 4

Evaluate the like terms

(2x + 7) - (2x - 4) = 11

Hence, the solution is 11

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Answer:

Division!

Step-by-step explanation:

(1/6) ÷ (3/7)

(1/6)(7/3)

= 7 / 18

The type of data that would be best displayed in a dot plot is the correspondent to the third option.

A dot plot is a plot where in the horizontal axis different numbers or properties (discrete set, usually we want smaller ranges, just so the graph are easier to read.) are marked, and above these, we mark dots, that represents how many times these are repeated on the data set.

We don't want large ranges (like in the first option 725 to 2450) because it means that we need to mark 725 points, or we need to find a common factor so each point represents more than one unit.

So, we need to have discrete data and with ranges not to large. The only option that meets both conditions is the third one, where on the horizontal axis we would have each of the 15 school dental clinics, and the dots would represent the number of dentist volunteering on each of them.

Then the correct option is the third one.

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Answer:

3rd option

Step-by-step explanation:

Answer:

I'm sorry if you get it wrong but it's 11.33%

Step-by-step explanation:

I searched it up

correct answer is random sample

A simple random sample, also known as an SRS, is a subset of people (also known as a sample) picked at random from a larger group of people (also known as a population) with an equal probability. It is a method of choosing a sample at random. Each subset of k people in SRS has the same chance of getting selected for the sample as any other subset of k people. [1] An objective sampling strategy is a straightforward random sample. Simple random sampling is a fundamental kind of sampling that may be used in combination with other, more sophisticated sampling techniques.

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Answer:

im sorry what ???

Step-by-step explanation:

i cant draw like that i only have 2 hands :(

The new price of the flight is $208.25

In this question, we have the following parameters

Discount proportion = 15%

Cost of flight = $245

This means that

New price = Cost of flight x (1 - Discount proportion)

Substitute the known values in the above equation, so, we have the following representation

New price = $245 x (1 - 15%)

Evaluate the product

New price = $208.25

Hence, th new price is $208.25

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The value of double integral is: (1/2) (1 - e) (1 - e).

To solve this integral, we will use the method of iterated integration. Let's first integrate with respect to x, treating y as a constant:

∫ e to 1 ( x ⋅ ln ( y ) / √ y y ⋅ ln ( x ) / √ x ) dx

Using substitution, let u = ln(x), du = 1/x dx, we get:

= ∫ e to 1 ( u / √ y y ) du

= [ ∫ e to 1 ( u / √ y y ) du ]

Now we integrate with respect to u:

= [ [ (1/2) u² ] from e to 1 ]

= (1/2) (1 - e)

Now, we integrate the remaining expression with respect to y:

= ∫ e to 1 (1/2) (1 - e) dy

= (1/2) (1 - e) [ y ] from e to 1

= (1/2) (1 - e) (1 - e)

So the value of given double integral is (1/2) (1 - e) (1 - e).

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Answer:

x₁(2x₁x₂² - x₂ - 3) - 3x₂

Step-by-step explanation:

The expression you provided is a polynomial in two variables, x₁ and x₂. Let's simplify it step by step:

2x₁²x₂² - x₁x₂ - 3x₁ - 3x₂

To simplify, we can look for common terms that can be factored out:

x₁(2x₁x₂² - x₂ - 3) - 3x₂

Now let's simplify the expression inside the parentheses:

2x₁x₂² - x₂ - 3