Triangles LMN and RWN are similar right triangles. What is the length of WR?
Round your answer to the nearest tenth.

We have two right-angled triangles that share a common side, with side lengths 6 and 10. Let's label the sides of the triangles as follows:

Triangle 1:

Side adjacent to the right angle: 6 (let's call it 'a')

Side opposite to the right angle: x (let's call it 'b')

Triangle 2:

Side adjacent to the right angle: x (let's call it 'c')

Side opposite to the right angle: 10 (let's call it 'd')

Using the Pythagorean theorem, we can write the following equations for each triangle:

Triangle 1:\(a^2 + b^2 = 6^2\)

Triangle 2: \(c^2 + d^2 = 10^2\)

Since the triangles share a common side, we know that b = c. Therefore, we can rewrite the equations as:

\(a^2 + b^2 = 6^2\\b^2 + d^2 = 10^2\)

Substituting b = c, we get:

\(a^2 + c^2 = 6^2\\c^2 + d^2 = 10^2\)

Now, let's add these two equations together:

\(a^2 + c^2 + c^2 + d^2 = 6^2 + 10^2\\a^2 + 2c^2 + d^2 = 36 + 100\\a^2 + 2c^2 + d^2 = 136\)

Since a^2 + 2c^2 + d^2 is equal to 136, we can conclude that x (b or c) is between 11 and 12

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Answer:

5

Step-by-step explanation:

Answer:

Angle of elevation= 180- (20- 55)

180- 75

105°

We will use Green's theorem to evaluate the line integral ∮C (2xy) dx + (xy²) dy, where C is the closed curve formed by traveling between specified points.

Green's theorem relates a line integral around a closed curve to a double integral over the region enclosed by the curve. It states that for a vector field F = (P, Q), the line integral ∮C P dx + Q dy around a closed curve C is equal to the double integral ∬R (Qx - Py) dA over the region R enclosed by C.

In this case, the vector field F = (2xy, xy²). To apply Green's theorem, we need to find the partial derivatives of P and Q with respect to x and y.

∂P/∂y = 2x and ∂Q/∂x = y²

Now, we can evaluate the double integral over the region R. The region R is the triangle formed by the points (-1, 2), (-1, -5), and (4, -4).

∬R (Qx - Py) dA = ∫∫R (y² - 2xy) dA

Using the given points, we can determine the limits of integration for x and y.

Finally, we evaluate the double integral using these limits of integration to obtain the value of the line integral ∮C (2xy) dx + (xy²) dy.

In summary, we use Green's theorem to relate the line integral to a double integral over the region enclosed by the curve. By evaluating this double integral, we can find the value of the line integral over the given closed curve.

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Answer:

She could make 5 of each type.

Step-by-step explanation:

If x is the number of 0.5 pound hamburgers and y is the number of 0.25 pound hamburgers:

0.5x + 0.25y = 3.75

Divide through by 0.25:

2x + y = 15

Some whole numbers which fit this relation  are x = 5 and y = 5.

Answer:

Step-by-step explanation:

Given:

Equation for the number of hamburgers:

simplified to:

Minimum number of each size is zero, then the maximum possible number is:

So possible numbers are within the range:

Answer:

147/200

Step-by-step explanation:

The coordinates of C are (-15, -3/4)

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

A = (-5,8)

B = (-5,-3).

m : n = 3: 1 i.e. three fourths

The coordinate is then calculated as

C = 1/(m + n) * (mx2 + nx1, my2 + ny1)

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

C = 3/4 * (3 * -5 + 1 * -5, 3 * -3 + 1 * 8)

Evaluate

C = (-15, -3/4)

Hence, the coordinate is (-15, -3/4)

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The algebraic expression x³y⁴ - x⁴y⁴ is factorized to be x³y⁴(1 - x) using their highest common factor HCF

The H.C.F. defines the highest common factor present in between given two or more numbers or mathematical expression.

The two terms x³y⁴ and x⁴y⁴ of the algebraic expression x³y⁴ - x⁴y⁴ have their highest common factor to be x³y⁴ such that:

x³y⁴ × 1 = x³y⁴

x³y⁴ × x = x⁴y⁴

and

x³y⁴ - x⁴y⁴ = x³y⁴ × 1 - x³y⁴ × x

x³y⁴ - x⁴y⁴ = x³y⁴(1 - x)

Therefore, the algebraic expression x³y⁴ - x⁴y⁴ is factorized to be x³y⁴(1 - x) using their highest common factor HCF

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Answer:

Step-by-step explanation:

One of four in number form is 1/4 this is the only thing I can tell you without knowing what the answer choices are or what the question is

The total number of sides of a regular polygon with each exterior angle of measure 30 degrees is equal to 12.

Let us consider 'n' be the number of sides of the regular polygon.

Let 'y' be the measure of each of the exterior angle of regular polygon.

y = 30 degrees

Measure of each of the exterior angle of regular polygon 'y'

= ( 360° ) / n

⇒ n = ( 360° / y )

Substitute the value we get,

⇒ n = ( 360° / 30° )

⇒ n = 12

Therefore, the number of sides of a regular polygon with each of the exterior angle 30 degrees is equal to 12.

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The above question is incomplete, the complete question is:

How many sides does a regular polygon have when each exterior angle measures 30 degrees?

Answer:

Step-by-step explanation:

22/25, 6, 6.21, 137/20, 6.885

Answer:

x = \(3\sqrt{13}\) = 10.8

Step-by-step explanation:

Both problems are done the same way.  I will do the first one and you do the second one.  OK?

Move the radius x to make a right triangle.  The 6 unit segment bisects the chord.  So, the legs of the right triangle are 6 and 9

The use the Pythagorean theorem to find x, which is the hypotenuse of the right triangle.   Now,

\(6^{2} + 9^{2} = x^{2}\)

\(x^{2} = 36 + 81 = 117\\x = \sqrt{117} = 3\sqrt{13}\)= 10.8

None of the answer choices are to the nearest tenth.  So, I am confused about that.

In  the second problem, the answer should be 11.2

The circumference of the circle is 2π x 2, or 12.57 units.

To find the circumference of a circle, we use the formula C = 2πr, where C is the circumference, π is a constant value of 3.14, and r is the radius of the circle. In this case, the radius of the circle is 2 units. So, we plug the values into the formula and get 2π x 2 = 12.57 units. This means that the circumference of the circle is 12.57 units. To put it another way, the circumference is equal to the diameter of the circle (2 units) multiplied by the value of pi (3.14). Therefore, the circumference of a circle with a radius of 2 units is 12.57 units.

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The mean of the time taken by a mechanic to rebuild the transmission of 2005 Chevrolet Cavalie μ = 8.4 hours The standard deviation of the time taken by a mechanic to rebuild the transmission of 2005 Chevrolet Cavalier, σ = 1.8 hours.

The sample size, n = 40 We have to find the probability that their mean rebuild time exceeds 8.7 hours. We know that the sampling distribution of the sample means is normally distributed with the following mean and standard deviation.

We have to find the probability that the sample mean rebuild time exceeds 8.7 hours or Now we need to standardize the sample mean using the formula can be found using the z-score table or a calculator. Therefore, the probability that the mean rebuild time of 40 mechanics exceeds 8.7 hours is 0.1489.

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There are 11,232,000 license plates consisting of three letters followed by three digits with no letter or digit repeated.

We can solve this problem using permutation, as we need to find the number of arrangements of three letters followed by three digits with no repetition.

There are 26 letters in the alphabet, so we can choose the first letter in 26 ways. For the second letter, we can choose from the remaining 25 letters, as we cannot use the same letter twice. Similarly, we can choose the third letter in 24 ways.

For the first digit, we have 10 options (0 to 9). For the second digit, we can choose from the remaining 9 digits (we cannot use the same digit twice). Similarly, we can choose the third digit in 8 ways.

Using the multiplication principle, we can find the total number of possible license plates:

26 × 25 × 24 × 10 × 9 × 8 = 11,232,000

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The simplified form of the expression is written as 11x³ - 39x -2x²/(x²- 9)(x+ 3)

Algebraic expressions are simply described as expressions that are composed of terms, variables, constants, factors and coefficients.

These expressions are also made up of arithmetic operations such as addition, multiplication, division, subtraction, etc

From the information given, we have that;

x -2/x + 3 + 10x/x² - 9

Find the lowest common denominator and simplify

(x-2)(x² - 9) + (x-3)(10x)  /(x²- 9)(x+ 3)

Now, expand the bracket, we get;

x³ - 9x - 2x² + 10x³ - 30x/(x²- 9)(x+ 3)

collect the like terms of the denominator and that of the numerator, we get;

11x³ - 39x -2x²/(x²- 9)(x+ 3)

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we know that 76% of the specialty soaps are made with fresh herbs, and we also know that there are a total of 350 specialty soap bars, so how many are made with fresh herbs?  well, just 76% of those 350

\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{76\% of 350}}{\left( \cfrac{76}{100} \right)350}\implies 266\)

The function f(x) = 8 - x^3/8 is a polynomial function of degree 3.

To see why, note that a polynomial function is a function of the form f(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0, where n is a non-negative integer and a_n, a_{n-1}, ..., a_1, a_0 are constants (coefficients). In this case, we have:

f(x) = 8 - x^3/8

= 8 - (1/8)x^3

= 0x^4 + 0x^3 + (-1/8)x^2 + 0x + 8

Thus, we can write f(x) as a polynomial function with degree 3, since the highest power of x that appears is x^3.

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a) The probability is 50%. b) The probability is 50%. c) The probability is 25%. d) The probability is 67%. e) The Mean is 5.5 gallons per minute. f) The standard Deviation is 0.5774 gallons per minute.

a) To find the probability that the machine is pumping more than 5.5 gallons per minute, we need to calculate the area under the uniform distribution curve to the right of 5.5. Since the distribution is uniform, the probability is equal to the ratio of the width of the interval to the total width of the distribution.

The width of the interval greater than 5.5 is (6.5 - 5.5) = 1 gallon per minute.

The total width of the distribution is (6.5 - 4.5) = 2 gallons per minute.

Therefore, the probability is 1/2 = 0.5 or 50%.

b) The probability that the machine is pumping less than 5.5 gallons per minute can be found by calculating the area under the uniform distribution curve to the left of 5.5. Since the distribution is uniform, the probability is equal to the ratio of the width of the interval to the total width of the distribution.

The width of the interval less than 5.5 is (5.5 - 4.5) = 1 gallon per minute.

The total width of the distribution is (6.5 - 4.5) = 2 gallons per minute.

Therefore, the probability is 1/2 = 0.5 or 50%.

c) To find the probability that the machine is pumping somewhere between 5.0 and 5.5 gallons per minute, we need to calculate the area under the uniform distribution curve between these two values. Again, since the distribution is uniform, the probability is equal to the ratio of the width of the interval to the total width of the distribution.

The width of the interval between 5.0 and 5.5 is (5.5 - 5.0) = 0.5 gallon per minute.

The total width of the distribution is (6.5 - 4.5) = 2 gallons per minute.

Therefore, the probability is 0.5/2 = 0.25 or 25%.

d) If we already know that the machine is pumping at least 5.0 gallons per minute, we can consider the remaining possible range of pumping rate, which is from 5.0 to 6.5 gallons per minute. The probability that the machine is pumping less than 6.0 gallons per minute can be calculated as the ratio of the width of the interval between 5.0 and 6.0 to the total width of the remaining possible range.

The width of the interval between 5.0 and 6.0 is (6.0 - 5.0) = 1 gallon per minute.

The total width of the remaining possible range is (6.5 - 5.0) = 1.5 gallons per minute.

Therefore, the probability is 1/1.5 ≈ 0.67 or 67%.

e) The mean of a uniform distribution is equal to the average of the minimum and maximum values. In this case, the minimum value is 4.5 and the maximum value is 6.5.

Mean = (4.5 + 6.5) / 2 = 5.5 gallons per minute.

f) The standard deviation of a uniform distribution can be calculated using the formula:

Standard Deviation = (Maximum Value - Minimum Value) / √12

Standard Deviation = (6.5 - 4.5) / √12 ≈ 0.5774 gallons per minute.

The complete question is:

A machine is set to pump cleanser into a process at the rate of 5 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by a uniform distribution over the interval 4.5 to 6.5 gallons per minute.

a) What is the probability that at the time the machine is checked it is pumping more than 5.5 gallons per minute?

b) What is the probability that at the time the machine is checked it is pumping less than 5.5 gallons per minute?

c) What is the probability that at the time the machine is checked it is pumping somewhere between 5.0 and 5.5 gallons per minute?

d) If we already know that the machine is pumping at least 5.0 gallons per minute, what is the probability that this machine is actually pumping less than 6.0 gallons per minute?

e) What is the mean of this uniform distribution?

20

f) What is the standard deviation of this uniform distribution?

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The best way to select a random sample of students is "Ask every 20th student during lunch in the school cafeteria".

The model approach to picking a random sample of students to gather data on teens' music tastes is to ensure that each student has an equal chance of getting chosen. This is known as random sampling, and it assists in reducing biases and ensuring that the sample is representative of the total population.

Option C, Asking every 20th kid during lunch in the school cafeteria, would be the best decision among the possibilities presented.

By picking every 20th student, a decent amount of randomization is achieved, and each student has an equal chance of being included in the sample.

When compared to the other choices, this technique generates a more representative sample.

Hence, the correct answer is C.

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100%

You calculate the increase, which is the final amount minus the initial amount.

You then divide the value of increase by the original amount (in our case, this was 8÷8).

You then multiply that amount by 100 to put it into a percentage.

Hope this helps!

The measure of angle x is 77 degrees.

We have two angles given: 65 degrees and 38 degrees. Let's call the measure of angle x as "x".

From the information, we have the measure of the missing angle of the angles in a triangle are 38°, 65° and x. Then we can set up an equation:

x + 65 + 38 = 180 (the sum of the measures of the angles in a triangle is 180)

Simplifying this equation, we get:

x + 103 = 180

x = 77

Therefore, the measure of angle x is 77 degrees.

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Complete question

Find the measure of the missing angle of the angles in a triangle are 38°, 65° and x.

Answer:

A)

\(\sqrt{290}\approx 17.0\text{ units}\)

B)

\(\sqrt{53}\approx7.3\text{ units}\)

Step-by-step explanation:

To find the distance between any two points, we can use the distance formula:

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2\)

Problem 1)

We have the two points (-4, 5) and (7, 18).

Let (-4, 5) be (x₁, y₁) and let (7, 18) be (x₂, y₂).

Substitute:

\(d=\sqrt{(7-(-4))^2+(18-5)^2}\)

Evaluate:

\(\begin{aligned}d&=\sqrt{(11)^2+(13)^2}\\&=\sqrt{121+169}\\&=\sqrt{290}\approx17.0\end{aligned}\)

Problem 2)

We have the two points (-2, -3) and (-4, 4).

Similarly, we will let (-2, -3) be (x₁, y₁) and (-4, 4) be (x₂, y₂).

Substitute:

\(d=\sqrt{(-4-(-2))^2+(4-(-3))^2\)

Evaluate:

\(\begin{aligned}d&=\sqrt{(-2)^2+(7)^2}\\&=\sqrt{4+49}\\&=\sqrt{53}\approx7.3\end{aligned}\)

Answer:

24

Step-by-step explanation:

l = 2√(r²-d²) = 2√(20²-16²) = 2√1440 = 24

The annual depreciation expense would be calculated as ($4,800 - $800) / 10 = $400. The journal entry for the first year would be:

Depreciation Expense=  $400, Accumulated Depreciation = $400

The journal entry for the first year, given the production of 300 units, would be:

Depreciation Expense         $600 (300 units * $2)

  Accumulated Depreciation    $600

The journal entry for the first year, using a double-declining-balance rate of 20% (twice the straight-line rate of 10%), would be:

Depreciation Expense         $960 ($4,800 * 20%)

  Accumulated Depreciation    $960

1. Straight-Line Depreciation:

The straight-line depreciation method allocates an equal amount of depreciation expense each year over the useful life of the equipment. In this case, the annual depreciation expense would be calculated as ($4,800 - $800) / 10 = $400. The journal entry for the first year would be:

Depreciation Expense         $400

  Accumulated Depreciation    $400

2. Units-of-Production Depreciation:

The units-of-production method bases depreciation on the actual units produced. The depreciation per unit is calculated as ($4,800 - $800) / 2,000 = $2 per unit. The journal entry for the first year, given the production of 300 units, would be:

Depreciation Expense         $600 (300 units * $2)

  Accumulated Depreciation    $600

3. Double-Declining-Balance Depreciation:

The double-declining-balance method accelerates depreciation in the early years of the asset's life. The depreciation rate is twice the straight-line rate. The journal entry for the first year, using a double-declining-balance rate of 20% (twice the straight-line rate of 10%), would be:

Depreciation Expense         $960 ($4,800 * 20%)

  Accumulated Depreciation    $960

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The major multivariate technique for examining variable interdependence is factor analysis.

Factor analysis is a multivariate statistical technique used to identify patterns in the relationships among a large number of variables. Specifically, it is used to examine variable interdependence, which refers to the degree to which variables are related to one another in a dataset.

In factor analysis, the goal is to identify underlying factors or dimensions that account for the observed patterns of correlation among the variables. By doing so, it is possible to reduce the number of variables to a smaller set of factors that capture the essential information contained in the original variables. This can be useful for a variety of purposes, such as data reduction, hypothesis testing, and exploratory data analysis.

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Answer: 8.22

Step-by-step explanation:

The relationship between the volume of a gas and the pressure on the gas is described by the equation V ∝ 1/P, where V is the volume and P is the pressure. This equation means that the volume and pressure of a gas are inversely proportional, so if the pressure increases, the volume will decrease and vice versa.

To find the volume of the gas when the pressure is increased from 66 pounds per square inch to 77 pounds per square inch, you can use the formula for inverse proportionality to solve for the new volume:

V1/V2 = P2/P1

Plugging in the known values, you get:

V1/V2 = 77 pounds per square inch / 66 pounds per square inch

= 1.16

Rearranging the equation to solve for V2, you get:

V2 = V1 * (P1/P2)

= 329329 cubic inches * (66 pounds per square inch / 77 pounds per square inch)

= 329329 cubic inches * (0.86)

= 283590 cubic inches

Rounding this volume to the nearest integer, the volume of the gas when the pressure is increased to 77 pounds per square inch is approximately 283,590 cubic inches.

Remember to divide, multiply, subtract, and drop down until each digit in the dividend has been divided in long division problems. The solution to the division issue is the quotient.

Long division is explained in the following steps:

Put the dividend and the divisor in their proper places.

Take the dividend's first digit from the left.

If this digit is more than or equal to the divisor, divide it by the divisor and write the quotient on top.

To calculate the difference, write the product below the dividend and subtract the result from the dividend. If this difference is less than the divisor and no numbers remain in the dividend, this is termed the residual and the division is completed. If there are more digits in the dividend to be handed down, we repeat the operation until there are no more digits more digit left in the dividend.

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Answer:

Always

Step-by-step explanation:

Similar figures are always the same shape, but not always the same size. If they have they same size, then they are also congruent.