Verify the following identity. sin^2 x + cos 2x = cos^2 x To transform the left side into the right side, should be changed to and the left side simplified.

The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent

To determine the correct statement, we need to know the properties of a parallelogram.

These properties includes;

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Answer:

Divide Using Synthetic Division.

d. It is impossible to determine how the Gini coefficient will change as it will depend on the original income distribution.

The Gini coefficient is a measure of income inequality in a society. It takes into account the entire income distribution, not just the average or total increase in income. The change in the Gini coefficient depends on how the income increase is distributed among different income groups.

If the income increase is distributed equally among all households, then the Gini coefficient would stay the same because the relative income differences between households remain unchanged. However, if the income increase is concentrated among higher-income households, it is likely that the Gini coefficient would increase, indicating a higher level of income inequality.

On the other hand, if the income increase is disproportionately distributed to lower-income households, it is possible for the Gini coefficient to decrease, indicating a reduction in income inequality.

Therefore, without knowing the initial income distribution and how the income increase is distributed across households, it is impossible to determine how the Gini coefficient will change over the 10-year period.

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Answer:

Albert was born in the year 2000!

Step-by-step explanation:

2006 Kyle is 10

10 - 4 = 6

So, Albert was 6 years old in 2006

6 - 6 = 0

2006 - 6 = 2000

Kyle was born in the year 2000.

Answer:

A) 4 years old

B) 2000

Step-by-step explanation:

A) 2004 Kyle was 8 years old. Two years pass which makes Kyle 10. Kyle is 4 years older than his cousin 10-4 equal 6. Albert was 6 in 2006. 6-2 equal 4

B) Albert is 6 (2006) which means he was born in 2000.

Answer: The final answer is:\(`I = -2π / [ab (a² + b² - 2abcos(t))^(1/2)]`\)

Explanation: We have to use contour integration to evaluate the integral cos20 -do, [. a²+6²-2abcose where b> a > 0.

Let \(f(z) = cos(20 - z) / [a² + b² - 2abcos(z - 6)] .\)

The denominator in the integral looks like\(cos(z - 6) = Re(e^(i(z-6)) ).\)

Therefore, we have \(cos(20 - z) = Re(e^(i(20 - z)))\)

Thus, we can write the integral as follows: `I = ∮ |z|=1 f(z) dz `

By Cauchy's Residue Theorem, the integral of f(z) over any closed curve in the complex plane is equal to `2πi` times the sum of residues of f(z) at its poles within the curve.

If we use the parametrization \(`z = 6 + b/a + re^(it)`\) with `0 <= t <= 2π`, then the integral becomes:

\(`I = -i ∫ 0^{2π} dt (a² + b² - 2abcos(t) ) / [ a² + b² - 2abcos(t) + 2ib(asin((r/a)sin(t-θ))]`\)

This integral can be computed using the residue theorem. If we define

\(`g(z) = 1 / [ a² + b² - 2abcos(t) + 2ib(asin((r/a)sin(t-θ))]`,\)

then the residue of g(z) at `z = 6 + b/a + i(asin((r/a)sin(t-θ))` is given by:

\(`Res(g, z) = lim_{z->6+b/a+i(asin((r/a)sin(t-θ)))} (z - (6 + b/a + i(asin((r/a)sin(t-θ))))) g(z) / [a² + b² - 2abcos(t)]`\)

We can compute this residue using L'Hopital's Rule.

After some algebraic manipulation, we can show that the residue is:\(`Res(g, z) = -1 / [ab (a² + b² - 2abcos(t))^(1/2)]`\)

Hence, by the residue theorem, we have: \(`I = -2πi / [ab (a² + b² - 2abcos(t))^(1/2)]`\)

Therefore, the final answer is:\(`I = -2π / [ab (a² + b² - 2abcos(t))^(1/2)]`\)

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Answer: 9+24r

Step-by-step explanation:

Answer: -13

Step-by-step explanation:

Answer:

56 is the answer so it's A, C and E.

Step-by-step explanation:

Answer:

1. 30 minutes to walk 9 miles.

2. 33.33 minutes to walk 10 miles.

Step-by-step explanation:

I divided 20 by 6, and got 3.33. If you multiply 3.33 by 9 you get 30, and if you  multiply 3.33 by 10 you get 33.33.

So the right answer is 1.8

Look at the attached picture

Hope it will help you

Good luck on your assignment

The required solutions to the following hardening coefficient are:

a) false

b) true

c) false

d) false

e) true

a) F - The statement is false.

Revised statement: The hardening coefficient is indicative of the material's strength. The higher the work-hardening coefficient, the greater the strength of the material.

b) T - The statement is true.

c) F - The statement is false.

Revised statement: The effective strain is not a state variable that depends solely on the initial and final states of the system, but rather on the deformation path followed by the material.

d) F - The statement is false.

Revised statement: At the moment when necking appears during the tensile test, the total deformation accumulated in the direction parallel to the width of the sheet is not 0.5. The actual value needs to be calculated or provided.

e) T - The statement is true.

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Answer:

Step-by-step explanation:

In this problem (word problem), we are examined on how to express equations from words.

let us initialize some variables

let the length of the first piece (the short piece) be x

and that of the second(the longer piece) be 5x

given that the total length is 96 cm

Also from the problem statement, the total length can be expressed as

5x+x= 96

6x= 96

divide both sides by 6 to solve for x

x= 96/6

x= 16

now the longer side = 5x

        the longer side= 5*6

       the longer side = 30 cm

Answer:

y = 4x - 5

Step-by-step explanation:

move the 2y to the left side of the equation and move the 0 to the right side of the equation in which it becomes -2y = -8x+ 10 then divide the whole equation by -2 since y cannot be negative and have a coefficient. so then the equation becomes y = 4x - 5.

The value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

(1). angle B = 180 - (22 + 90) {sum of interior angles of a triangle}

angle B = 68°

Given that the triangle ∆ABC is similar to the triangle ∆PQR.

(2). PQ/7.5cm = 12cm/18cm

PQ = (12cm × 7.5cm)/18cm {cross multiplication}

PQ = 5cm

(3). 13cm/BC = 12cm/18cm

BC = (13cm × 18cm)/12cm {cross multiplication}

BC = 19.5cm

(4). area of ∆PQR = 1/2 × 12cm × 5cm

area of ∆PQR = 6cm × 5cm

area of ∆PQR = 30cm²

Therefore, the value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

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Answer: x-5 / x

Step-by-step explanation:

because…

Answer:

\(\frac{x - 5}{x}\)

Step-by-step explanation:

\(\frac{\frac{x - 5}{x + 4} }{\frac{x}{x + 4} }\)

It can also be written as :-

\(=> \frac{x - 5}{x + 4} \div \frac{x}{x + 4}\)

\(=> \frac{x - 5}{x + 4} \times \frac{x + 4}{x}\)

Cancel x + 4 from numerator and denominator.

\(=> \frac{x - 5}{x}\)

Answer:

It will take you 1/2 hour to catch up.

Step-by-step explanation:

We Know

You are biking at a speed of 18 miles per hour.

You are 3 miles behind your friend, who is biking at a speed of 12 miles per hour.

The equation will be:

18h = 12h + 3

Find the amount of time it takes for you to catch up.

18h = 12h + 3

6h = 3

h = 3/6 = 1/2 hour

So, it will take you 1/2 hour to catch up.

Answer:

5.25inches

Step-by-step explanation:

difference in height = 68.5-63.25 =5.25

Height of Mario Hm = 68.5 inches

Height of Tyler Ht = 63.25 inches

Evidently, Hm > Ht

Now difference = Hm - Ht = 68.5 - 63.25

= 5.25 inches

Answer: Mario is 5.25 inches taller than Tyler.

Answer:

55.9%

Step-by-step explanation:

To find the percentage of girls in the class, we can use the following formula:

Percentage = (Number of girls / Total number of students) * 100

Number of girls = 19

Total number of students = 34

Percentage = (19 / 34) * 100

                   = 55.88235 % ≈ 55.9 % ( rounded off to one decimal place)

Using the formula of combination and probability theorem , The answer is b) 75.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.

The formula for combination is:

\(C(n,r) = \frac {n!}{r!(n-r)!}\)

selecting 1 blue ball from 5 blue balls = C(5,1)

=5

selecting 2 orange balls from 6 balls = C(6,2)

=15

Total ways of selection = 5*15=75

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True, the residual for John is unusual.

The difference between the standard deviations of the observed values and the anticipated values, as illustrated by the points in a regression analysis, is referred to statistically as residual standard deviation.

Regression analysis is a statistical technique used to demonstrate the relationship between two different variables and to assess how well one variable can be predicted based on the behavior of another.

The standard deviation of points surrounding a fitted line or the standard error of estimation is another name for residual standard deviation.

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ANSWER:

AAA Similarity Theorem

STEP-BY-STEP EXPLANATION:

We can see that the two triangles have the same interior angles and are corresponding.

Therefore, we can state that these two triangles are congruent using the AAA Similarity Theorem, where if two triangles have equal corresponding angles, then their corresponding sides are proportional and the triangles are similar.

The probability is 0.0132.

Here we have mean and standard deviations for air samples from large cities.

According to large samples, the law sample average calculated from large samples is approximately equal to the population average.  

As here sample is taken from a large city, the sample is considered a large sample. Hence mean is approximately equal to the population mean. Also, it is considered a random sample is representative of the population and the sample standard deviation is approximate to the population standard deviation. Hence we can say that carbon monoxide concentrations in air samples from this city are normally distributed.

So here we have

μ = 12

σ = 9 , n = 100

Hence here we need to find,

= p (x > 14)

= p((x-μ /(σ/√n)) > 14-12/9/√100)

= p ( z > 2.22 )

= 1 - p ( z < 2.22 )

= 1 - 0.9868 (using excel formula = norm.s.dist(2.22,1))

= 0.0132

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To determine the number of calories per cup of popcorn and per ounce of soda, we can set up a system of equations based on the given information about the total calories consumed by Roselle and Carmel. By solving the system, we can find the desired calorie values.
the number of calories per cup of popcorn is 40 and the number of calories per ounce of soda is 18.

Let's denote the number of calories per cup of popcorn as x and the number of calories per ounce of soda as y.
From the given information, we can set up the following system of equations:
2x + 7y = 206 ...(1) (for Roselle)
1x + 12y = 256 ...(2) (for Carmel)
To solve this system, we can use the method of substitution or elimination. Let's use the elimination method.
Multiplying equation (1) by 12 and equation (2) by 2, we get:
24x + 84y = 2472 ...(3)
2x + 24y = 512 ...(4)
Now, subtract equation (4) from equation (3) to eliminate x:
(24x + 84y) - (2x + 24y) = 2472 - 512
Simplifying the equation, we have:
22x + 60y = 1960
Next, isolate x by dividing both sides by 22:
x = (1960 - 60y) / 22
Now, we can substitute this value of x into equation (1) to solve for y:
2[(1960 - 60y) / 22] + 7y = 206
Simplifying the equation, we have:
3920 - 120y + 154y = 22 * 206
Combining like terms, we get:
34y = 4532 - 3920
Simplifying further, we have:
34y = 612
Dividing both sides by 34, we find:
y = 18
Substituting this value of y back into equation (1), we can solve for x:
2x + 7(18) = 206
Simplifying the equation, we have:
2x + 126 = 206
Subtracting 126 from both sides, we get:
2x = 80
Dividing both sides by 2, we find:
x = 40
Therefore, the number of calories per cup of popcorn is 40 and the number of calories per ounce of soda is 18.

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Answer:

y = -2x - 8

Step-by-step explanation:

Step-by-step explanation:

Acute angle means less than 90 degrees....so it is in the first Quadrant and sin and cos will be positive values

Trig identity

sin^2 + cos^2 = 1

sin^2 + .6^2 = 1    shows sin = .8

The tan  =   sin/ cos =  .8/.6 = 1.33

The polygon will have 9 sides.

The required polygon is a nonagon.

A polygon is named on the basis of the number of sides it has, as a polygon having 5 sides is a pentagon, a polygon having 6 sides is a hexagon, a polygon having 7 sides is a heptagon, and so on., and the addition of their interior angles is (n - 2) 180°.

To identify the polygon, we need to know the number of sides of the polygon. We know that the sum of internal angles of an n - sided polygon is

(n - 2) 180°.

For the given polygon, the internal angles added up to 1260 degree. Equate  (n - 2) 180° to 1260 degree and solve the resulting equation for n.

(n - 2) 180° = 1260°

n - 2 =  1260°/ 180°

n - 2 = 7

n = 7 + 2

n = 9

The given polygon will have 9 sides.

=> The required polygon is a nonagon.

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A pricing policy change for a hardware store, all products containing the word "saw" in their description have been discounted by 15%, and all products containing the word "hammer" in their description have been discounted by 7%.

This statement describes a pricing strategy employed by SaleCo hardware store, which involves offering discounts on certain products. Specifically, the store has lowered prices on saws and hammers by 15% and 7%, respectively.

Discounting is a common pricing strategy used by businesses to stimulate sales and attract customers.

By lowering the prices of certain products, a store can increase the perceived value of these items and make them more appealing to customers.

This can result in increased sales, which can ultimately lead to higher profits.

The store has chosen to discount saws and hammers.

These products are likely to be in high demand among customers who engage in woodworking or DIY projects, and the discounts are intended to attract these customers and encourage them to make a purchase.

The discounts offered by SaleCo on saws and hammers are relatively modest, with a 15% discount on saws and a 7% discount on hammers. Even small discounts can have a significant impact on sales if they are applied to high-demand products.

The pricing strategy employed by SaleCo is a common one in the retail industry, and it is intended to stimulate sales and attract customers.

By offering discounts on saws and hammers, the store is hoping to increase its customer base and generate more revenue.

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The statement provides two quantities, A and B, expressed as ratios of positive integers c and d. The relationship between the quantities A and B cannot be determined from the information given.

The statement provides two quantities, A and B, expressed as ratios of positive integers c and d. However, no specific values or constraints are given for c and d. Without knowing the specific values or any relationship between c and d, it is impossible to determine the relationship between A and B.

The relative magnitudes of A and B will depend on the values of c and d. If the value of c is greater than d, then A would be greater than B. Conversely, if the value of d is greater than c, then B would be greater than A. However, without any information about the values of c and d or any relationship between them, we cannot determine the relationship between A and B.

Therefore, based on the given information, the relationship between quantities A and B cannot be determined.

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Step-by-step explanation:

always remember : the sum of all angles in a triangle is 180°.

so, one angle is 90° (it is a right triangle).

the second angle is 48°.

therefore,

180 = 90 + 48 + third angle

third angle = 180 - 90 - 48 = 42°

so, C is correct.