The measure of an exterior angle of a triangle is 40°. What is the sum of the measures of the corresponding remote interior angles?

Answer:

24x^7 = 24x^7

Step-by-step explanation:

Left side of equation: 3 times 8 times X = 24x

Then you raise it to the 7th power

Right side of the equation: 6 times 4 times X = 24x

Since the exponent is the same, you keep it as the 7th power

We aim to prove the equation Σ(6i^2 - 2i) = 2x^2(x + 1) for all integers x ≥ 1 using proof by induction. The formula will be verified for the base case x = 1 and then assuming it holds for an arbitrary value k

Base case (x = 1):

When x = 1, the left-hand side of the equation becomes Σ(6i^2 - 2i) from i = 1 to 1, which is equal to (6(1)^2 - 2(1)) = 4. The right-hand side becomes 2(1)^2(1 + 1) = 4. Thus, the equation holds true for x = 1.

Inductive step:

Assume the equation holds for an arbitrary value k, which means Σ(6i^2 - 2i) = \(2k^{2}\)(k + 1).

Now we need to prove that the equation also holds for k + 1:

Σ(\(6i^{2}\) - 2i) from i = 1 to k + 1 can be rewritten as Σ(6i^2 - 2i) from i = 1 to k plus the term when i = k + 1, which is (6(k + 1)^2 - 2(k + 1)).

Using the assumption, we can substitute Σ(6i^2 - 2i) from i = 1 to k with \(2k^{2}\)(k + 1):

Σ(6i^2 - 2i) from i = 1 to k + 1 = 2k^2(k + 1) + (6(k + 1)^2 - 2(k + 1)).

Simplifying the expression:

= \(2k^{2(k + 1) }\) + (\(6k^{2}\) + 12k + 6 - 2k - 2)

= \(2k^{2(k + 1) }\) + \(6k^{2}\) + 10k + 4

= \(2k^{2(k + 1) }\)+ 2(\(3k^{2}\) + 5k + 2)

= 2(\(k^{2}\) + 3k + 2)(k + 1)

= 2(k + 1)(k + 2)(k + 1)

=\(2(k + 1)^{2}\)(k + 2).

We have arrived at the right-hand side of the equation for k + 1, which matches the desired form 2(k + 1)^2(k + 2). Thus, the equation holds for k + 1.

By proving the base case and the inductive step, we conclude that the equation Σ(6i^2 - 2i) = 2x^2(x + 1) holds for all integers x ≥ 1 by proof by induction.

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The true statement is (d) the angle measures of trapezoid PQRS are equal to the corresponding angle measures of trapezoid KLMN

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

Trapezoid PQRS

The transformation is given as

As  a general rule of transformation, reflection and rotation are rigid transformations and they do not change the size and angles in a shape

This means that we get a congruent figure to that figure after the transformations

Thus, when PQRS is reflected and rotated 90° about the origin to form trapezoid KLMN, the trapezoid KLMN is congruent to trapezoid PQRS.

⇒  By the definition of congruence,

The corresponding sides and angle of trapezoid KLMN are congruent to that of trapezoid PQRS.

⇒ ∠P ≅ ∠K, ∠Q ≅ ∠L, ∠R ≅ ∠M and  ∠S ≅ ∠N

⇒ Option D) is correct.

Note:  KMLN is a trapezoid ⇒ Sum of the angle measures of trapezoid P'Q'R'S' is also 180°

Option A) is incorrect.

Since, trapezoid KMLN is congruent to trapezoid PQRS.

⇒ Option B) is incorrect.

We know that if two shapes are congruent then their area must be equal.

⇒ Area of trapezoid KMLN = Area of trapezoid PQRS

Thus, Option C) is incorrect.

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Complete question

Trapezoid PQRS is shown on the coordinate plane. If trapezoid PQRS is reflected across the y-axis and rotated 90° clockwise about the origin to form trapezoid KLMN, which must

A) The sum of the angle measures of trapezoid PQRS is 180° less than the sum of the angle measures of trapezoid KLMN.

B) Trapezoid PQRS is not congruent to trapezoid KLMN

C) The area of trapezoid PQRS is less than the area of trapezoid KLMN

D) The angle measures of trapezoid PQRS are equal to the corresponding angle measures of trapezoid KLMN

Answer:

It may be C or D

I think its C.

Sorry if I'm wrong.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

let the number be n then increasing - 7 by n is - 7 + n and

- 7 + n = 12 ( add 7 to both sides )

n = 19

The probability of at least one of your 10 lottery tickets being a winner is approximately 0.638 or 63.8%.

The probability of winning on a single lottery ticket is 1/8, which means that the probability of not winning is 7/8. If you buy 10 of these lottery tickets, the probability of not winning on any of them is:

(7/8)^10 = 0.362

This means that there is a 36.2% chance that none of your tickets will be a winner. To find the probability that at least one of your tickets will be a winner, we can use the complementary probability:

P(at least one winner) = 1 - P(no winners)

P(at least one winner) = 1 - 0.362

P(at least one winner) = 0.638

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Answer: 9x(3+1)/6-5

Step-by-step explanation: 9x(3+1)= 36

36/6-5=1

The Expression is 9 x (3+1)/ 6 -5 which gives value 1.

BODMAS rule is an acronym that is used to remember the order of operations to be followed while solving expressions in mathematics. It stands for B - Brackets, O - Order of powers or roots, (in some cases, 'of'), D - Division, M - Multiplication A - Addition, and S - Subtraction. It means that expressions having multiple operators need to be simplified from left to right in this order only.

Given:

9 x 3 + 1 divide by 6 - 5

So, we can write it as

9 x (3 + 1) ÷ 6 -5

Using the BODMAS rule

9 x (3+ 1)

= 9 x 4

and, (9 x 4) /6

= 36/6

= 6

and, 6-5 = 1

Hence, the Expression is 9 x (3+1)/ 6 -5.

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The function you're referring to is likely a periodic function, as Fourier series expansions are typically used for periodic functions.

The convergence of the Fourier series expansion depends on the properties of the function, such as its continuity and differentiability.

If the function is continuous and piecewise smooth, then the Fourier series will converge to the function itself.

However, if the function is not continuous or not piecewise smooth, then the Fourier series may not converge uniformly.

In some cases, the Fourier series may converge to a different function altogether, known as a Fourier series of the function.

Therefore, to determine the value at which the Fourier series converges, you would need to analyze the properties of the function itself.

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Answer:

See attachment 2

Step-by-step explanation:

See attachment 1 for complete question

\(Scale= 1 : 2000\)

Required

Fill in the table

The scale implies that:

To fill in the gaps of actual measurements, we simply multiply the scale measurement by 2000

To fill in the gaps of scalar measurements, we simply divide the actual measurement by 2000

For the flag height, we have:

\(Scale\ Measurement = 13.2\ cm\)

Using the analysis above:

\(Actual = 2000 * 13.2\ cm\)

\(Actual = 26400\ cm\)

Convert to meters

\(Actual = 26400m/100\)

\(Actual = 264m\)

For the flag length, we have:

\(Actual\ Measurement = 396\ m\)

Using the analysis above:

\(Scale\ Measurement = 396\ m /2000\)

\(Scale\ Measurement = 0.198\ m\)

Convert to centimeters

\(Scale\ Measurement = 0.198\ cm * 100\)

\(Scale\ Measurement = 19.8\ cm\)

For the height of crescent moon, we have:

\(Actual\ Measurement = 99\ m\)

Using the analysis above:

\(Scale\ Measurement = 99\ m /2000\)

\(Scale\ Measurement = 0.0495\ m\)

Convert to centimeters

\(Scale\ Measurement = 0.0495\ cm * 100\)

\(Scale\ Measurement = 4.95\ cm\)

See attachment 2 for completed table

The translation of the given  figure be  (x -7 , y + 4).

From the given figure,

We can see that ,

The coordinate of point T is (2,-2)

And the coordinate of point T' is (-5, 2)

Here T is initial position and T' is the position after translation,

Now we can see that

The figure is translating towards left direction,

And after that it translating towards upwards direction.

Therefore,

(2 - a , -2 + b) = (-5, 2)

Equating ordinate and mantissa we get,

a = 7 and b = 4

Now if any point of the figure has coordinate (x, y)

Then after such translation the position of point be,

⇒ (x -7 , y + 4)

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Databases of variants are crucial in helping to identify disease gene candidates. Here's how they are used:

1. Collect and store genetic variants: Databases collect and store genetic variants from various individuals, including those with specific diseases and those without.

2. Compare variants between groups: By comparing the variants in affected individuals to those in unaffected individuals, researchers can identify variants that are more common in the disease group. This helps to narrow down the list of potential disease-causing genes.

3. Calculate probability: Databases can be used to calculate the probability of certain variants appearing in the general population. If a variant is rare in the general population but more common in individuals with a specific disease, it may be more likely to be a disease-causing variant.

4. Filter out common variants: As you mentioned, variants that are common in the general population or present in individuals without the disease are less likely to cause a rare genetic disease. By filtering out these common variants, researchers can focus on rare variants that may have a stronger association with the disease.

5. Identify disease gene candidates: Through this process of comparing and filtering genetic variants, researchers can identify potential disease gene candidates that warrant further investigation.

In summary, databases of variants help researchers identify disease gene candidates by storing genetic information, enabling comparison between affected and unaffected individuals, calculating variant probabilities, filtering out common variants, and ultimately pinpointing rare variants that may be associated with specific genetic diseases.

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50%

since 98/2 = 49

Thats it

The wavelength of the wave is approximately 2.09m, and the speed of the wave is approximately 1.99m/s. values were obtained by analyzing given expression and utilizing relationships between wave parameters.

To find the wavelength, we can use the formula λ = v/f, where λ represents the wavelength, v represents the speed of the wave, and f represents the frequency of the wave. However, in the given expression, we are not directly given the frequency. Instead, we have the angular frequency ω, which is related to the frequency as ω = 2πf.By comparing the given expression with the general wave equation, we can identify that the wave number k = 3.00m^(-1). Since the wave number is related to the wavelength as k = 2π/λ, we can rearrange the equation to find the wavelength: λ = 2π/k. Plugging in value for k, we get λ = 2π/(3.00m^(-1)), which simplifies to approximately λ = 2.09m.

To determine the speed of the wave, we can use the formula v = λf, where v represents the speed of the wave, λ represents the wavelength, and f represents the frequency. As mentioned earlier, we have the angular frequency ω instead of the frequency f. However, we know that ω = 2πf, so we can rearrange this equation to find f = ω/(2π). Plugging in the given angular frequency ω = 6.00s^(-1), we get f = 6.00s^(-1)/(2π), which simplifies to approximately f = 0.955Hz.Now that we have the wavelength λ = 2.09m and the frequency f = 0.955Hz, we can use the formula v = λf to find the speed of the wave. Plugging in the values, we get v = (2.09m)(0.955Hz), which gives us the speed of the wave v = 1.99m/s.

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Answer:

The probability of rolling a sum greater than 1 when rolling two fair numbered cube is 1 or 36/36.

Step-by-step explanation:

There is no 1 as a sum when rolling two fair numbered cubes, so all the sums will be greater than 1.

Answer:

ans= (2)

Step-by-step explanation:

y=x²-1 is the only quadratic function there

1 is a linear function

3 is a cubic function

4 is a a constant function

Answer:

r = 8

Step-by-step explanation:

To find the radius with only the area you do r = \(\sqrt{A/\pi }\)

Since your area 64\(\pi\) = 201.0619298 then 201.0619298/\(\pi\) = 64

\(\sqrt{64}\) = 8

Hope this helps!!

Answer:

Hey! so the answer is X=7 and Y=6

Step-by-step explanation:

if you look at the pattern you'll see it adds up to 7 and 6 everytime so those are the answers.

Hoped this helped Im Eve btw. Hope you have a great day and consider marking this brainliest Thank you so much if you do! ✨

After multiplication of pair of complex numbers, the results of product are respectively 45, 41, 73

The complex number is a combination of real number and imaginary number. The representation of complex number is like, a + bi.

where a is real part and b is imaginary part, the value of i is √-1.

i × i = -1

i⁴ = 1

Given that, pair of complex numbers

(6 +3i )×( 6 - 3i) =  6×6 -6×3i + 6×3i - (3i × -3i)

                         = 36 - 18i + 18i + (-3i × 3i)

                         =  36 + 9

                         =  45

(4-5i) × (4+5i)   =  4×4 + 4×5i - 4×5i - (5i × -5i)

                        = 16 - 20i + 20i + (-5i × 5i)

                        = 16+25

                        = 41

(-3+8i) × (-3-8i) = -3×-3 + (-3× -8i) - 3×8i + (8i × -8i)

                        = 9 +24i-24i +64

                        =  73

Hence, The result of products are 45, 41, 73

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Answer: (6 + 3i)(6 − 3i) = 45, (4 − 5i)(4 + 5i) = 41, (−3 + 8i)(−3 − 8i) = 73

Step-by-step explanation:

True. The equation Ax = 0 gives an explicit description of its solution set.

When A is a matrix and x is a vector, the equation Ax = 0 represents a homogeneous system of linear equations. The solution set of this system consists of all vectors x that satisfy the equation and make the left-hand side equal to zero.

The explicit description of the solution set can be obtained by using techniques such as Gaussian elimination or matrix factorizations. These methods allow you to perform row operations on the augmented matrix [A | 0] to obtain the reduced row echelon form. The reduced row echelon form reveals the structure of the solution set by identifying pivot and free variables.

If there are no free variables (all columns of A are pivot columns), then the solution set consists of only the zero vector, x = 0. In this case, the solution set is a singleton set {0}.

If there are one or more free variables, you can express the solutions in terms of those variables. The free variables introduce parameters that allow for infinitely many solutions. The explicit description of the solution set will involve expressing the dependent variables (those corresponding to pivot columns) in terms of the free variables.

In summary, the equation Ax = 0 gives an explicit description of its solution set, either as the singleton set {0} or as a set of vectors expressed in terms of free variables.

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Answer:

1.02, 1.1, 1.101

Step-by-step explanation:

use a calculator

We can reject the null hypothesis and conclude that there is a significant difference in the average customer satisfaction ratings between Home Depot and Lowe's.

What is hypothesis?

A hypothesis is a proposed explanation or prediction that can be tested through empirical investigation.

To test the difference in the average customer satisfaction rating for Home Depot and Lowe's, we can perform a two-sample t-test. Let's go through the steps of conducting the hypothesis test:

Step 1: State the hypotheses:

Null Hypothesis (H₀): The average customer satisfaction rating for Home Depot is equal to the average customer satisfaction rating for Lowe's.

Alternative Hypothesis (H₁): The average customer satisfaction rating for Home Depot is different from the average customer satisfaction rating for Lowe's.

Step 2: Set the significance level (α):

Let's assume a significance level of α = 0.05. This means we want to have strong evidence to reject the null hypothesis if the p-value is less than 0.05.

Step 3: Collect the data and calculate the sample statistics:

We have the following customer satisfaction ratings:

Home Depot: 79, 81

Lowe's: 72, 78, 79, 76, 72

To calculate the sample statistics, we need to find the sample means and sample standard deviations for Home Depot and Lowe's.

Sample mean of Home Depot \((\bar x_1)\) = (79 + 81) / 2 = 80

Sample mean of Lowe's \((\bar x_2)\) = (72 + 78 + 79 + 76 + 72) / 5 = 75.4

To calculate the sample standard deviations, we need to find the differences between each rating and the respective sample mean, square the differences, sum them up, divide by n-1, and then take the square root.

Home Depot: [(79-80)² + (81-80)²] / (2-1) = 1 / 1 = 1

Lowe's: [(72-75.4)² + (78-75.4)² + (79-75.4)² + (76-75.4)² + (72-75.4)²] / (5-1) = 16.8 / 4 = 4.2

Step 4: Calculate the test statistic:

To calculate the test statistic, we use the formula:

\(t = (\bar x_1 - \bar x_2) / \sqrt((s_1^2/n_1) + (s_2^2/n_2))\)

Substituting the values:

\(t = (80 - 75.4) / \sqrt{((1^2/2) + (4.2^2/5))}\\\\t = 4.6 / \sqrt(0.5 + 1.68)\)

t ≈ \(4.6 / \sqrt(2.18)\)

t ≈ 4.6 / 1.476

t ≈ 3.116

Step 5: Determine the p-value:

We need to find the p-value associated with the calculated test statistic. Since this is a two-sided test, we need to find the probability of observing a test statistic as extreme as t = 3.116 or more extreme in either tail of the t-distribution.

Using a t-distribution table or statistical software, the p-value is found to be p ≈ 0.021.

Step 6: Make a decision:

Compare the p-value to the significance level. Since the p-value (0.021) is less than the significance level (0.05), we have enough evidence to reject the null hypothesis.

Step 7: State the conclusion:

Based on the sample data, there is sufficient evidence to conclude that the average customer satisfaction rating for Home Depot is different from the average customer satisfaction rating for Lowe's at a significance level of 0.05.

Therefore, we can reject the null hypothesis and conclude that there is a significant difference in the average customer satisfaction ratings between Home Depot and Lowe's.

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Answer:

A

Step-by-step explanation:

Answer: A. 11

Step-by-step explanation:

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The slope or gradient of the blue line from the given graph is -3.3.

The equation of line is shown in the graph.

The slope or gradient of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope or gradient = Rise/Run

From the given graph, the gradient of a line is

Slope = rise/run

= -4/1.2

= -3.3

Hence, the slope or gradient of the blue line from the given graph is -3.3.

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Answer:

B. 5.6

Step-by-step explanation:

The products of the lengths of the segments of each chord are equal.

5 × z = 7 × 4

5z = 28

z = 28/5

z = 5.6

Answer: B. 5.6

Answer:

the answer is 1.4N/kg

The coordinates for each point would be:

M': (2,-2)

N': (4, 2)

O': (8, -1)

If the rule is (x, y) = (x + 2, y - 6), this is how you solve this problem...

M to M': (0 + 2, 4 - 6), then (2, -2)

N to N':  (2 + 2, 8 - 6), then (4, 2)

O to O': (6 = 2, 5 - 6), then (8, -1)

The shaded part​ of the Venn Diagram is A n C n B'

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

The Venn diagram

From the given Venn Diagram, we have"

The shaded region includes the intersection of A and C without B

i.e. no region in B is shaded

Using the above (i.e. the Venn diagram) as a guide, we have the following:

The shaded region = A n C n B'

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