Question 3 Evaluate (i) ∬_(2 1)^(3 5)▒(x+2y)dydx (ii) ∬_(1 0)^(2
y)▒(x√(y^2 )-x^2 )dydx

The approximate gauge of a wire with a diameter of 100 mils is AWG 12.

To determine the approximate gauge of a wire with a diameter of 100 mils, we can use the American Wire Gauge (AWG) standard, which is commonly used in North America for measuring wire sizes.

The AWG gauge number is inversely proportional to the diameter of the wire, which means that as the gauge number increases, the wire diameter decreases.

Using the AWG standard, we can estimate that a wire with a diameter of 100 mils (0.1 inches) is approximately AWG 12. This can be calculated using the formula:

diameter (mils) = 1000 x (0.005 x 92)^(36 - AWG)/39.

Solving for AWG, we get:

AWG = 36 - 39 x log10(diameter (mils)/1000)/(0.005 x 92)

Plugging in the diameter of 100 mils, we get:

AWG = 36 - 39 x log10(0.1/1000)/(0.005 x 92) ≈ 12

Therefore, the approximate gauge of a wire with a diameter of 100 mils is AWG 12.

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Answer:

9 and 16       hope this helps.

Step-by-step explanation:

Answer:

c)

Step-by-step explanation:

\(\frac{1}{2}\)(12*g) - h = \(\frac{1}{2}\)(12 * \(\frac{1}{4}\)) - \(\frac{1}{2}\) = 1/2 * 3 - 1/2 = 3/2 - 1/2 = 1

Answer:

Step-by-step explanation:

To find a missing numerator, look at the denominators of the fractions. One fraction has both a numerator and denominator. Find the number that this denominator is multiplied by to get to the denominator that is missing its numerator. Multiply the known numerator by this number to find the unknown numerator.

The smallest value within the class is the lower class limit, and the largest value within the class is the upper class limit.

A class limit is a set of boundary values in the form of a range that describes the lowest and highest data values that a class can contain. The lower class limit refers to the smallest data value in a class, whereas the upper class limit refers to the largest data value in a class. The width of a class is determined by the difference between the upper and lower class limits. Here are a few examples to give you a better understanding of how this works:

Class:              5-9 5 9

Lower Limit:    10-14 10 14

Upper Limit:    15-19 15 19

This shows class limits for three different classes.

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The percent increase in the temperature is 50%.

To understand more, check below explanation.

The temperature increases from 18° F to 27° F.

       Increase in temperature = 27 - 18 = 9

The percent increase in the temperature is computed as,

                                  \(=\frac{27-18}{18}*100\\ \\=\frac{9}{18}*100\\ \\=\frac{1}{2}*100=50\%\)

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x = 147 / 0.5446 ≈ 270.2 ft

To find the length of the guy wire for a radio transmission tower, trigonometry concepts are applied. Given a tower height of 160 feet, with the wire attached 13 feet from the top and making an angle of 29° with the ground, we can solve for the length of the guy wire, represented by x.

Using the Pythagorean theorem and considering the right triangle formed by the tower height, the wire attachment point, and the ground, we can set up the equation:

x = √((160 - 13)² + x²)

Next, we apply the tangent function to the given angle:

tan(29°) = (160 - 13) / x

Simplifying, we have:

0.5446 = 147 / x

To solve for x, we rearrange the equation:

x = 147 / 0.5446 ≈ 270.2 ft

Rounding to the nearest tenth of a foot, the length of the guy wire required is approximately 270.2 feet. This wire is attached 13 feet from the top of the tower and makes a 29° angle with the ground.

Trigonometry plays a crucial role in solving real-world problems involving angles and distances. It provides a mathematical framework for calculating unknown values based on known information, enabling accurate measurements and constructions.

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Answer:

β, α, γ

Step-by-step explanation:

The figure only shows us the side lengths of the triangle, but is asking for the angles.

Thus, we have to use the angle relationships of a triangle to answer the question.

⭐What are the angle relationships of a triangle?

α° is opposite of the side length with 9 cm.

β° is opposite of the side length with 12 cm.

γ° is opposite of the side length with 5 cm.

∴ The angles from highest to the least are β, α, γ

IF THIS RESPONSE HELPED YOU, PLEASE MARK IT THE BRAINLIEST :-)

Answer:

Step-by-step explanation:

The answer should be BAY but if i check it don't work

Answer:

50% chance because (10)/(20)=1/2=0.5=50%

Step-by-step explanation:

hope this helps

The trend projection for time period 18 is 197.6. The correct option is B

A mathematical equation used to represent the trend or pattern seen in a time series of data is called a linear trend expression, sometimes referred to as a linear trend model.

To find the trend projection for time period 18 using the given linear trend expression, we substitute t = 18 into the equation:

Yt = 129.2 + 3.8t

Y18 = 129.2 + 3.8 * 18

Y18 = 129.2 + 68.4

Y18 = 197.6

Therefore, the trend projection for time period 18 is 197.6.

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Two- tailed t- test, determined the 97.5% confidence level for p-value less than a significance level of 5%. So, researcher claims with 95% confidence that wearing earplugs will reduce the chance of hearing loss is also correct.

We have specify that a researcher wants to support the claim that wearing earplugs will reduce the chance of hearing loss.

Significance level= 5% = 0.05

P-value< 0.05

Now, the p-value for a two tailed test is computed by = 2× Area of the lower tail on one side. Here, P-value< 0.05, therefore Area of the lower tail on one side < 0.05 / 2

=> p-value for a one tailed test < 0.025

that represents the 97.5% confidence level. So, the researcher can actually claim here even at 97.5% confidence level that wearing earplugs will reduce the chance of hearing loss but even concluding at any confidence level less than 97.5% would be correct. Therefore the researcher is not incorrect in concluding here the given concluion at 95% confidence level.

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(a) Pseudocode for the algorithm that finds the first repeated integer in a given sequence of integers is as follows:

1. Initialize an empty set called "visited".

2. Traverse the given sequence of integers.

3. For each integer in the sequence, check if it is already in the "visited" set.

4. If the integer is in the "visited" set, return it as the first repeated integer.

5. Otherwise, add the integer to the "visited" set.

6. If there is no repeated integer, return "None".

(b) The worst-case time complexity of the algorithm is O(n), where n is the length of the sequence of integers.

Therefore, the time complexity of the algorithm increases linearly with the size of the input sequence.

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Answer:

B

Step-by-step explanation:

the shortest distance is a straight line from house to library. This line is the hypotenuse (h) of a right triangle formed by the 3 features on the map.

Using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

h² = 1.7² + 0.9² = 2.89 + 0.81 = 3.7 ( take square root of both sides )

h = \(\sqrt{3.7}\) ≈ 1.9 miles ( approximate shortest distance )

(a) F is increasing on the interval (-1/2, 1) and decreasing on (-∞, -1/2) and (1, +∞). (b) F has a local minimum at x = 1 with a value of -1. (c) F is concave up for all x and there are no inflection points.

(a) To find the intervals on which F is increasing or decreasing, we need to analyze the sign of the derivative of F.

\(F(x) = x^2 - x - ln(x)\)

Differentiating F(x) with respect to x:

F'(x) = 2x - 1 - (1/x)

Setting F'(x) = 0 to find critical points:

2x - 1 - (1/x) = 0

\(2x^2 - x - 1 = 0\)

Solving the quadratic equation, we find the critical points:

x = (-(-1) ± √(\((-1)^2\) - 4(2)(-1))) / (2(2))

x = (1 ± √(9)) / 4

x = (1 ± 3) / 4

So, the critical points are x = -1/2 and x = 1.

Now, we can analyze the intervals:

For x < -1/2, F'(x) < 0, indicating that F is decreasing.

For -1/2 < x < 1, F'(x) > 0, indicating that F is increasing.

For x > 1, F'(x) < 0, indicating that F is decreasing.

(b) To find the local maximum and minimum values of F, we need to analyze the critical points and the behavior of F at the endpoints of the intervals.

\(At x = -1/2, F(-1/2) = (-1/2)^2 - (-1/2) - ln(-1/2)\)

We cannot take the natural logarithm of a negative number, so F(-1/2) is undefined.

\(At x = 1, F(1) = 1^2 - 1 - ln(1) = -1\)

Therefore, there is no local maximum, but F has a local minimum at x = 1 with a value of -1.

(c) To find the intervals of concavity and the inflection point, we need to analyze the sign of the second derivative of F.

Differentiating F'(x) with respect to x:

\(F''(x) = 2 + (1/x^2)\)

Setting F''(x) = 0 to find possible inflection points:

\(2 + (1/x^2) = 0\\1/x^2 = -2\\x^2 = -1/2\)

There are no real solutions for x, so there are no inflection points.

Analyzing the intervals:

For x < 0, F''(x) > 0, indicating concave up.

For x > 0, F''(x) > 0, indicating concave up.

Therefore, F is concave up for all x.

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Answer:

6.8π in.²

Step-by-step explanation:

A = πr²

d = 18 in.

r = d/2 = 9 in.

A = π × (9 in.)²

A = 81π in.²

1/12 of the area is

81π in.² / 12 = 6.75π in.²

Answer: 6.8π in.²

To find the expected value of a discrete probability distribution, we multiply each possible outcome by its probability and then sum the products. In this case, we have:

E(X) = 0(3/16) + 1(3/16) + 2(1/8) + 3(1/2)

    = 0 + 3/16 + 1/4 + 3/2

    = 1.5

Therefore, the expected value of this distribution is 1.5.

In probability theory, the expected value (also known as the mean or average) of a discrete probability distribution is a measure of the central tendency of the distribution. It represents the theoretical long-term average of the values taken by a random variable over an infinite number of trials.

To find the expected value of a discrete probability distribution, we multiply each possible value of the random variable by its corresponding probability and add up the products. In other words, if X is a discrete random variable with possible values x1, x2, ..., xn and corresponding probabilities p1, p2, ..., pn, then the expected value E(X) is:

E(X) = x1 * p1 + x2 * p2 + ... + xn * pn

For example, consider the discrete probability distribution given in the table:

x     |  0  |  1  |  2  |  3  

pr(x) | 3/16| 3/16| 1/8 | 1/2

To find the expected value of this distribution, we multiply each possible value of X by its corresponding probability and add up the products:

E(X) = 0*(3/16) + 1*(3/16) + 2*(1/8) + 3*(1/2) = 0 + 0.1875 + 0.25 + 1.5 = 1.9375

Therefore, the expected value of this distribution is 1.9375.

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The number of puppies per kids is 20 puppies.

Given that, there are 180 puppies in the shelter with 9 kids.

Number of puppies per kids = Total number of puppies/Number of kids

= 180/9

= 20 puppies

Therefore, the number of puppies per kids is 20 puppies.

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The equation is a linear combination of three angles that add up to 180°, he might consider using systems of linear equations or other algebraic methods to solve for the variables.

given that za + 2d + g = 180°, some observations that could potentially be useful to Jason include:

Identifying any relationships or constraints between the variables za, d, and g that might help him simplify or solve the equation. For example, if he knows that za and g are complementary angles (i.e., they add up to 90°), he could substitute 90 - za for g in the equation to get a new expression in terms of za and d.

Using additional information about the angles or the situation to derive new equations or constraints that could help him solve for one or more variables. For example, if he knows that za and d are equal (i.e., za = d), he could substitute za for d in the equation to get a new expression in terms of za and g.

Identifying any patterns or structures in the equation that might suggest a particular approach or technique for solving it. For example, if he notices that the equation is a linear combination of three angles that add up to 180°, he might consider using systems of linear equations or other algebraic methods to solve for the variables.

Ultimately, the most effective observations for completing the proof will depend on the specific details of the problem and the approach that Jason is taking.

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The complete question:Jason knows that za + 2d + g = 180°. Which of the following observations, if true, would allow him to prove a statement or theorem related to the angles za, d, and g?

Answer: A. 0

Step-by-step explanation: To determine the number of solutions for the system of equations x - y = 7 and y = sqrt(3x + 3) - 2, we can substitute y in the first equation with the expression for y in the second equation, giving us x - (sqrt(3x + 3) - 2) = 7. Simplifying this equation, we get sqrt(3x + 3) = -x + 9.

Since the square root of a number is always non-negative, we can conclude that there are no solutions to this system of equations. Therefore, the answer is A. 0.

- Lizzy ˚ʚ♡ɞ˚

The normally distributed process has specifications of LSL = 75 and USL = 85 has a Cp of 2.22 , this process is capable and 0.08 defective parts can be expected per day.

To obtain the estimate of Cp, we first need to calculate the process capability index (Cpk) using the formula:

Cpk = min[(USL - mean) / (3 * standard deviation), (mean - LSL) / (3 * standard deviation)]

In this case, the sample mean is 80 and the sample standard deviation is 1.5, so:

Cpk = min[(85 - 80) / (3 * 1.5), (80 - 75) / (3 * 1.5)]
   = min[1.11, 1.11]
   = 1.11

To obtain Cp, we simply multiply Cpk by 2, since Cp = 2 * Cpk when the process is centered:

Cp = 2 * Cpk
  = 2 * 1.11
  = 2.22

Since Cp is greater than 1.0, this process is capable.

To calculate the expected number of defective parts per day, we need to know the proportion of parts that are defective.

Assuming that the process is centered, the proportion of parts that are defective can be estimated using the area under the normal distribution curve beyond the specification limits.

Since the process is normally distributed with mean 80 and standard deviation 1.5, we can use a standard normal distribution table to find the area beyond the limits:

Area beyond USL = P(Z > (USL - mean) / standard deviation) = P(Z > (85 - 80) / 1.5) = P(Z > 3.33) = 0.0004

Area beyond LSL = P(Z < (LSL - mean) / standard deviation) = P(Z < (75 - 80) / 1.5) = P(Z < -3.33) = 0.0004

So the proportion of parts that are defective is:

Proportion defective = 0.0004 + 0.0004 = 0.0008

To find the expected number of defective parts per day, we multiply this proportion by the number of parts produced per day:

Expected number of defective parts per day = 0.0008 * 100 = 0.08

So we would expect to see approximately 0.08 defective parts per day.

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The probability of selecting three packages that are satisfactory is 0.729.

we need to find the probability of selecting three packages that are satisfactory from the given satisfactory weight probability. P(satisfactory) = 90.0/100 = 0.9So, the probability of selecting the first satisfactory package is 0.9, for the second package is also 0.9, and for the third package is also 0.9.

∴ The probability of selecting three packages that are satisfactory P(3 satisfactory) = P(Satisfactory) × P(Satisfactory) × P(Satisfactory)P(3 satisfactory) = (0.9)³P(3 satisfactory) = 0.729.

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3.35 feet have a maximum inaccuracy of 0.005 feet.

The correct option is C.

When students consistently commit mistakes, an approach known as error analysis is frequently employed to determine the root of the problem. Reviewing student work is the first step in the process, after which misunderstood patterns are sought out. Mathematics mistakes can be conceptual, procedural, or factual, and they can happen for a variety of reasons.

The window is 3.35 feet long.

Find the biggest error you can

Half of the measuring unit is considered to be the maximum amount of measurement error.

3.35 feet are calculated to the nearest centimeter, or 0.01 feet

Consequently, the largest conceivable error is equal to half of the measurement unit.

= .01/2

= .005

Therefore, the maximum inaccuracy for 3.35 feet is 0.005 feet.

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The limiting distribution of wn = wn ~ N(0, 1)

We have: zn ~ χ^2(n) and wn = zn/n^2

We want to find the limiting distribution of wn as n approaches infinity. To do this, we can use the Central Limit Theorem (CLT), which states that the sum of independent and identically distributed random variables (in this case, zn/n^2) approaches a normal distribution as the sample size (n) increases, regardless of the underlying distribution.

To apply the CLT, we first need to find the mean and variance of wn:

\(E[wn] = E[zn/n^2] = E[zn]/n^2 = n/ n^2 = 1/n\)

\(Var[wn] = Var[zn/n^2] = Var[zn]/n^4 = 2n/n^4 = 2/n^3\)

As n approaches infinity, E[wn] approaches zero and Var[wn] approaches zero. Therefore, we can apply the CLT and conclude that:

wn ~ N(0, 1) where N(0, 1) represents a normal distribution with mean 0 and variance 1.

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Answer:

∅=30°

Step-by-step explanation:

\(sin\)∅\(=\frac{1}{\sqrt{3} }sin60^{0}\)

sin∅=\(\frac{\frac{\sqrt{3} }{2} }{\sqrt{3} } =\frac{\sqrt{3} }{2\sqrt{3} }=\frac{1}{2}\)

∅=\(sin^{-1}(\frac{1}{2})= 30^{0}\)

I hope this help you

Answer:

Step-by-step explanation:

x = 8

C.44  is the the correct to the question a net of a triangular prism is shown below 8ft 3ft 5ft 5ft 3ft 4ft A.120 B.96 C.44 D.108

Answer: C!!!!!!!

Step-by-step explanation:

Decomposers ( however you spell it ) are things that eat and uhh remove the waste and let other decompopers eat they waste

Answer:

p=10320^2

Step-by-step explanation:

formula:

p=4a

a=2580cm^2

Answer:

gallons

Step-by-step explanation:

There are no other options other then gallons

Cassie should use gallons to eliminate the need to write the value in scientific notation.

Volume represents the space that a substance or 3D shape occupies or contains.

Units of volume are cubic meter, litre, gallon etc.

Since teaspoons, cubic inches etc are smaller units of the volume so we need to represent the volume of the fish tank in scientific notation.

Gallon is the bigger unit of the volume so we do not need to write the value in scientific notation.

Hence, Cassie should use gallons to eliminate the need to write the value in scientific notation.

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