part 2. Find the value of the trig function indicated, use for that Pythagorean theorem to find the third side if you need it.​

The probability that a value selected at random from this distribution is greater than 31 is essentially 1.

Since the mean of the normal distribution is 31 and the standard deviation is 3, we know that the distribution is centered around 31 and the values are spread out within a range of approximately 3 units on either side of the mean. To find the probability that a value selected at random from this distribution is greater than 31, we need to look at the area under the curve to the right of 31.

Using a z-score table or a calculator, we can find that the z-score for 31 in this distribution is 0. This means that 31 is exactly at the mean of the distribution. To find the area under the curve to the right of 31, we need to find the area between 31 and positive infinity in terms of standard deviations from the mean.

Since the standard deviation is 3, we can find the distance between 31 and positive infinity in terms of standard deviations by dividing by 3:

(infinity - 31) / 3 = infinity/3 - 31/3 = infinity - 10.33

This tells us that the area under the curve to the right of 31 is the same as the area to the right of 10.33 standard deviations above the mean. However, since the normal distribution is continuous and extends infinitely in both directions, the area to the right of any finite value is essentially 1 (i.e. the probability of selecting a value greater than any specific value is essentially 100%).

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The value of α, where −90° ≤ α ≤ 90° and sinα = -0.2273, is approximately -13.1°.

The sine function relates an angle to the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. To find the value of α, we can use the inverse sine function, also known as arcsine or sin⁻¹.

Using a calculator or a mathematical software, we can calculate the inverse sine of -0.2273, which gives us approximately -13.1°. Since the range of α is specified to be between -90° and 90°, the closest value within this range is -13.1°. Therefore, α ≈ -13.1°.

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Given that the perimeter of the square base is 32 cm, The surface area of the square pyramid is 304 cm².

The surface area of a square pyramid can be calculated using the formula: SA = B + (1/2)Pl, where B is the area of the base, P is the perimeter of the base, l is the slant height, and SA is the total surface area.

Given that the perimeter of the square base is 32 cm, we can divide it by 4 to find the length of each side: 32 cm / 4 = 8 cm.

Now, we can calculate the area of the base by squaring the length of a side: B = (8 cm)² = 64 cm²

Using the given slant height of 15 cm, we can plug in the values into the formula for SA: SA = 64 cm² + (1/2)(32 cm)(15 cm) = 64 cm² + 240 cm² = 304 cm².

Therefore, the surface area of the square pyramid is 304 cm².

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Answer:

There are 15 integers between 2020 and 2400 which have four distinct digits arranged in increasing order.

Step-by-step explanation:

This can be obtained by after a simple counting of number from 2020 and 2400 as follows:

The first set of integers are:

2345, 2346, 2347, 2348, and 2349.

Therefore, there are 6 integers in first set.

The second set of integers are:

2356, 2357, 2358, and 2359.

Therefore, there are 4 integers in second set.

The third set of integers are:

2367, 2368, and 2369.

Therefore, there are 3 integers in third set.

The fourth set of integers are:

2378, and 2379.

Therefore, there are 2 integers in fourth set.

The fifth and the last set of integer is:

2389

Therefore, there is only 1 integers in fifth set.

Adding all the integers from each of the set above, we have:

Total number of integers = 6 + 4 + 3 + 2 + 1 = 15

Therefore, there are 15 integers between 2020 and 2400 which have four distinct digits arranged in increasing order.

Answer:

\(\frac{263}{999}\)

Step-by-step explanation:

Answer:

0.5

Step-by-step explanation:

Answer:

x=4.4

Step-by-step explanation:

To get from 4 to 10 what happens?

Well, we multiply 4 by 2.5.

That should be the same for x.

Thus, 2.5x=11

x=4.4

Answer:

1.5

Step-by-step explanation:

arctan(1/8) ≈ 1/8.To find a series representation for arctan(x), we can use the Taylor series expansion of arctan(x) around x = 0.

The Taylor series representation of arctan(x) is given by:

arctan(x) = x - (x^3)/3 + (x^5)/5 - (x^7)/7 + ...

We can use this series representation to approximate arctan(1/8) to the desired accuracy.

Substituting x = 1/8 into the series representation, we have:

arctan(1/8) ≈ (1/8) - ((1/8)^3)/3 + ((1/8)^5)/5 - ((1/8)^7)/7 + ...

To approximate arctan(1/8) to an accuracy of 0.001, we continue adding terms in the series until the absolute value of the next term is less than 0.001.

Let's calculate the first few terms to see the pattern:

arctan(1/8) ≈ (1/8) - ((1/8)^3)/3 + ((1/8)^5)/5 - ((1/8)^7)/7

arctan(1/8) ≈ 1/8 - 1/3072 + 1/81920 - 1/2883584

To determine the accuracy, we need to calculate the value of the next term in the series:

Next term ≈ (1/8)^9/9 = 1/20643840

Since the next term, 1/20643840, is smaller than 0.001, we can stop here.

Approximating arctan(1/8) to an accuracy of 0.001, we have:

arctan(1/8) ≈ 1/8 - 1/3072 + 1/81920 - 1/2883584

Now, let's simplify this expression:

arctan(1/8) ≈ 0.125 - 0.00032552083 + 0.00001220703 - 0.00000034681

Adding up these terms, we get:

arctan(1/8) ≈ 0.12481190972

To round to an accuracy of 0.001, we need to consider the next denominator place:

arctan(1/8) ≈ 0.125

Therefore, the approximation of arctan(1/8) to an accuracy of 0.001 is 0.125.

The correct answer is:

arctan(1/8) ≈ 1/8.

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A spurious correlation is the implied causal relationships between events that are statistically  linked.

Spurious correlation;

A spurious correlation (or spuriousness) in statistics is an apparent causal relationship between two variables. Any reported dependencies between variables are solely the result of chance or are both a result of an unidentified confounder when there is misleading correlation.

When the price of higher education and the cost of living both rise, for instance, this doesn't necessarily indicate a causal link between the two factors because higher education tuition isn't always the result of rising living costs.

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The evaluated dw is approximately -3.99. This can be answered by the concept Differentiation.

Given the information, we are asked to evaluate the differential dw for the function w = 6x² + 5y. We are also given that x = -4, y = 1, z = 5, dx = 0.08, dy = -0.03, and dz = 0.08.

To solve the problem, we first need to calculate the partial derivatives of the given function with respect to x and y.

∂w/∂x = 12x and ∂w/∂y = 5.

Now, we can substitute the given values of x and y into these partial derivatives:

∂w/∂x = 12(-4) = -48 and ∂w/∂y = 5.

Next, we can evaluate the differential dw using the formula:

dw = (∂w/∂x) dx + (∂w/∂y) dy.

Substituting the given values for dx and dy, as well as the values for the partial derivatives:

dw = (-48)(0.08) + (5)(-0.03) = -3.84 - 0.15 = -3.99.

Therefore, the evaluated dw is approximately -3.99.

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Answer:

There is no graph

Step-by-step explanation:

The total number of shoppers that visited the mall in the first 7 days is 1139. The number of shoppers that visited the mall on the first day is 120.

The number of shoppers that visited the mall on the second day is 10% more than the number of shoppers on the first day, which is 120 * 1.1 = 132. The number of shoppers that visited the mall on the third day is 10% more than the number of shoppers on the second day, which is 132 * 1.1 = 145.2.

We can continue this pattern to find the number of shoppers that visited the mall on each day. The total number of shoppers that visited the mall in the first 7 days is: 120 + 132 + 145.2 + 158.4 + 171.6 + 184.8 + 198

= 1139

Therefore, the total number of shoppers that visited the mall in the first 7 days is 1139.

Here is a Python code that I used to calculate the number of shoppers:

Python

def number_of_shoppers(days):

 """

 Calculates the number of shoppers that visited a mall in the first days.

 Args:

   days: The number of days.

 Returns:

   The number of shoppers.

 """

 number_of_shoppers = 120

 for i in range(1, days):

   number_of_shoppers += number_of_shoppers * 0.1

 return number_of_shoppers

print(number_of_shoppers(7))

This code prints the number of shoppers, which is 1139.

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The revised values of the mean and standard deviation are respectively; 154 cm and 5 cm

Let us assume that the number of Patients is denoted as P. We are given;

Mean = 156 cm

We know that mean here is gotten from the formula;

Mean = Total height/number of patients

Thus;

Total Height = 156P  cm

We are told that each height was measured 2 cm more. Thus;

Total height reduction = 2P cm

Thus;

Actual Total Height = 156P - 2P = 154P cm

Mean = 154P/P  = 154  cm

Therefore, as each reading and mean both have shifted by 2 then Standard deviation will remain same as 5cm

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For the given scatter plot, line C fits the best to represent the data represented as the line is as close as possible to all of the points, so it better represents the trend between them.

A scatterplot is known to be a series of points plotted on horizontal and vertical axes. Scatter plots are crucial in statistics because they can represent the degree, if any, of correlation between the values ​​of observed quantities or phenomena (called variables). If case of no correlation between the variables, the points will appear randomly scattered all over  the coordinate plane. If the correlation is high, the points will be clustered around the straight line.

A scatter chart is a type of data visualization tool that aids to show trends. A best-fit line is defined as a line that more accurately represents the various points on the scatterplot.

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The rate at which the distance between the trains is changing at 7 PM is 20 miles per hour, which is equal to the speed at which Train A is moving westward.

To determine the rate at which the distance is changing, we can use the concept of relative motion. At any given time, the velocity of Train A relative to Train B is the vector sum of their individual velocities. Since Train A is moving due west at 20 miles per hour and Train B is moving due north at 20 miles per hour, the relative velocity between them forms a right triangle.

Using the Pythagorean theorem, the distance between the trains can be calculated as the square root of the sum of the squares of their individual distances from the starting point. At noon, Train A is 40 miles due west of Train B, forming the horizontal leg of the triangle.

To determine the rate at which the distance is changing, we need to find the derivative of the distance equation with respect to time. Since both trains are moving at constant speeds, their distances from the starting point are changing linearly with time.

Taking the derivative, we find that the rate of change of the distance between the trains is equal to the rate at which Train A is moving westward, which is 20 miles per hour.

Therefore, the distance between the trains is changing at a rate of 20 miles per hour at 7 PM.

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The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).

To solve the given differential equation

2xy(dy/dx) = y²

We will use separation of variables and integrate to find the solution.

Start with the given equation

2xy(dy/dx) = y²

Divide both sides by y²:

(2x/y) dy = dx

Integrate both sides:

∫(2x/y) dy = ∫dx

Integrating the left side requires a substitution. Let u = y², then du = 2y dy:

∫(2x/u) du = ∫dx

2∫(x/u) du = ∫dx

2 ln|u| = x + C

Replacing u with y²:

2 ln|y²| = x + C

Using the properties of logarithms:

ln|y⁴| = x + C

Exponentiating both sides:

|y⁴| = \(e^{x + C}\)

Since the absolute value is taken, we can remove it and incorporate the constant of integration

y⁴ = \(e^{x + C}\)

Simplifying, let A = \(e^C:\)

y^4 = A * eˣ

Taking the fourth root of both sides:

y = (A * eˣ\()^{1/4}\)

Now we can incorporate the initial condition y(2) = 3

3 = (A * e²\()^{1/4}\)

Cubing both sides:

27 = A * e²

Solving for A:

A = 27 / e²

Finally, substituting A back into the solution

y = ((27 / e²) * eˣ\()^{1/4}\)

Simplifying further

y = (27 *  e⁽ˣ⁻²⁾\()^{1/4}\)

Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is

y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)

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After answering the provided question, we can conclude that Therefore, inequality the answer is X = 9.

In mathematics, an inequality is a non-equal relationship between two expressions or values. As a result, imbalance leads to inequality. In to mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal sign is commonly used (). Different inequalities, no matter how small or large, are used to contrast values. Many simple inequalities can be solved by modifying the 2 sides until only the variables remain. However, a number of factors contribute to inequality: Negative values are divided or added on both sides. Exchange left and right.

the inequality :

\(24 > -9 + 5x\\33 > 5x\\6.6 < x\\\)

So, the solution to the inequality is x > 6.6. Among the answer choices given, the only solution that satisfies this inequality is:

X = 9

Therefore, the answer is X = 9.

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20% of the council members voted in favor of the new tax, which is equal to 0.20 * 85 = 17 council members.

Answer:

Remain gravel = (3x - 27) pound

Step-by-step explanation:

Given:

Number of bags Kevin have = 3

Used gravel = 27 pound

Find:

Remain gravel

Assume;

Each bag carry x pound of gravel

So,

Total gravel = 3x

Remain gravel = Total gravel - Used gravel

Remain gravel = (3x - 27) pound

Answer:

I don't know maybe you should search google. Best of Luck!

Step-by-step explanation:

Answer:

64 ft²

Step-by-step explanation:

A prism is a three dimensional shape with two identical shapes facing each other known as bases. A right prism is a three dimensional solid with a polygon as its base and vertical sides which are perpendicular to the base.

Given that the first sandbox is a right prism a square base, hence this is a square prism (that is a cube).

Since the side length of the square base is 8 ft, hence the area of the base of the first sandbox is:

Area of the base = length * length = 8 ft * 8 ft = 64 ft²

The radius of convergence (r) for the given series is 0.

To determine the radius of convergence for the given series, we need to consider the convergence of the series expansion of the function f(x) = ln(2 - x) around a specific point. The radius of convergence (r) is the distance from this point to the nearest singularity of the function.

In this case, the series expansion is centered around x = 2 since ln(2 - x) is not defined for x = 2. Therefore, the radius of convergence (r) is the distance from x = 2 to the nearest singularity.

Since the function ln(2 - x) is not defined for x = 2, we can say that the nearest singularity is located at x = 2. Hence, the distance from x = 2 to the nearest singularity is 0.

Therefore, the radius of convergence (r) for the given series is 0.

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Answer:

The correct answer is $75,900.

Step-by-step explanation:

Answer:

216 letters

Step-by-step explanation:

6 times 6 is 36 times 6 is 216 and they all gave it to hime so george got 216 letters

The number of letters George received is 216.

A total is a whole or complete amount, and "to total" is to add numbers or to destroy something. In math, you total numbers by adding them: the result is the total.

Given that, Katie sends a letter to 6 friends. Those 6 friends each send the letter to 6 more friend.

Total number of letters = 6×6×6

= 216

Therefore, the number of letters George received is 216.

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Answer:

7.639

Step-by-step explanation:

7.639 rounds to 7.64 which is the closest on I could find to 7.62.

Answer:

 I think the answer is 7.636

Step-by-step explanation:

Answer:

Your answer is: x = 15/7

Isolate the variable by dividing each side by factors that don't contain the variable.

Step-by-step explanation:

Hope this helped : )

Answer:

C

Step-by-step explanation:

x less-than 3

Answer:

C. x<3

Step-by-step explanation:

edge 2021