Need some little help on this

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Explanation:

The sequence is not arithmetic because the distance between adjacent terms keeps increasing. For instance, the gap from 0.4 to 1.6 is 1.6-0.4 = 1.2, while the gap from 1.6 to 6.4 is 6.4-1.6 = 4.8. There is no common difference, so we can rule out choices A and B.

To check if we have a geometric sequence, divide each term by its previous term

(term2)/(term1) = (1.6)/(0.4) = 4

(term3)/(term2) = (6.4)/(1.6) = 4

(term4)/(term3) = (25.6)/(6.4) = 4

Each time we get 4 as a result, so this sequence is geometric and the common ratio is r = 4.

Put another way: each new term is found by multiplying the previous term by 4.

0.4*4 = 1.6

1.6*4 = 6.4

6.4*4 = 25.6

This all leads to D being the answer.

Side note: the nth term of this geometric sequence is \(a_n = 0.4*(4)^{n-1}\) where n is a positive integer and starts at n = 1.

A randomized controlled trial in which each subject is assigned to a combination of at least two independent variables is an example of a Factorial Design.

In statistics, a full factorial experiment is one in which all potential combinations of the levels across all of the factors are taken into account by the experimental units. A full factorial experiment has two or more factors with discrete possible values or "levels" in its design. A fully crossed design is another name for a full factorial design. Using such an experiment, the researcher can examine how each element affects the response variable as well as how different factors interact with one another.

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The expression for output is 6 greater than three times the input is y = 3x + 6.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the output is 6 greater than three times the input the expression can be written as:-

y = 3x + 6

Therefore, y = 3x + 6 is an expression for an output that is six times greater than the input.

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Solution:-

= 6⁴/6²

\( = {6}^{4 - 2} \) ⠀⠀{ a^m/a^n = a^(m - n) }

= 6²

Thus, Option c.) 6² is correct!

Answer:

3² + 6 × 2² - 4² ÷ 2³ = 31.

Step-by-step explanation:

Answer:

31

Step-by-step explanation:

3^2=9

2^2=4

-4^2= -16

2^3=8

9+6*4-16/8=31

Mean is used to measure the center of a set of values. It is good for summarizing values which are generally pretty similar to each other.

Mean is more usually referred to as the average. It is calculated by adding up all of the values and dividing by the total number of values. It is a good way for summarizing the center of values which are commonly very similar to each other.

The mean is the most often used measure of central tendency since it uses all values in the data set to give us an average. For data from skewed distributions, the median is better than the mean because it is not influenced by large values.

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Although part of your question is missing, you might be referring to this full question: _________ is used to measure the center of a set of values. It is good for summarizing values that are generally pretty similar to each other.

A substantial interaction between age and educational status was discovered by a researcher who was creating a regression equation to predict income (y) in thousands of dollars from age (x1) and educational status (x2) (x3)

A dummy variable, educational status has the values 0 for no college degree and 1 for a college degree.

The regression formula is y = 0 + 1x1 + 2x2 + 3x1x2 where 0 is the intercept, 1 is the age regression coefficient, 2 is the educational status regression coefficient, and 3 is the regression coefficient for the interaction between age and educational status.

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We have proved that (2*10²)*(3*10⁵) = 3.5*10⁷+2.5*10⁷  .

In the given question

we have to prove that

(2*10²)*(3*10⁵) = 3.5*10⁷+2.5*10⁷

For proving we will solve the LHS and RHS separately and then equate them .

First Solving LHS

we have

=(2*10²)*(3*10⁵)

=(2*3)*(10²*10⁵)

=6*10²⁺⁵       ...( because aⁿ.aˣ = aⁿ⁺ˣ )

=6*10⁷    ...(i)

Now solving RHS

we have

=3.5*10⁷+2.5*10⁷

taking 10⁷ common , we get

=(3.5+2.5)*10⁷

Adding the terms in the bracket we get

=6*10⁷     ...(ii)

As we can see that from equation (i) and (ii) we have LHS=RHS

Hence proved that (2*10²)*(3*10⁵) = 3.5*10⁷+2.5*10⁷

Therefore , Proved that (2*10²)*(3*10⁵) = 3.5*10⁷+2.5*10⁷  .

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Answer:

below

Step-by-step explanation:

Domain is the set of all x values a function can have

 this one goes from    - inf to the asymtope at x = 2

(-∞, 2)     domain

range is the y values the function can have

   looks like 0   to - inf

(- ∞, 0]       ( but it COULD be  ( -∞, 0)    <===cannot tell from graph)

Answer:

944

Step-by-step explanation:

\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-16}~,~\stackrel{y_1}{11})\qquad (\stackrel{x_2}{16}~,~\stackrel{y_2}{4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~16 - (-16)~~)^2 + (~~4 - 11~~)^2} \implies d=\sqrt{(16 +16)^2 + (4 -11)^2} \\\\\\ d=\sqrt{( 32 )^2 + ( -7 )^2} \implies d=\sqrt{ 1024 + 49 } \implies d=\sqrt{ 1073 }\implies d\approx 32.76\)

To accumulate $2,176,097.00 in his retirement account by age 65, Derek needs to make annual deposits of $5,000.00 starting on his 27th birthday and ending on his 65th birthday, assuming an 8.00% interest rate.

To determine the annual deposits Derek needs to make, we can use the future value of an ordinary annuity formula. First, we calculate the number of years between Derek's 25th and 65th birthdays, which is 65 - 25 = 40 years. Next, we calculate the future value of the retirement account using the given interest rate of 8.00%. Using the formula:

Future Value = Present Value * (1 + interest rate)^number of periods

In this case, the future value is $2,176,097.00, the interest rate is 8.00%, and the number of periods is 40. We can rearrange the formula to solve for the present value:Present Value = Future Value / (1 + interest rate)^number of periods

Substituting the values:Present Value = $2,176,097.00 / (1 + 0.08)^40 = $123,529.31 (rounded to 2 decimal places)

Now, we need to find the annual deposit amount. Since Derek starts making deposits on his 27th birthday and ends on his 65th birthday, he makes deposits for 65 - 27 = 38 years.Annual Deposit = Present Value / ((1 + interest rate)^number of periods - 1)Substituting the values:

Annual Deposit = $123,529.31 / ((1 + 0.08)^38 - 1) = $5,000.00 (rounded to 2 decimal places)Therefore, Derek must make annual deposits of $5,000.00 into his retirement account starting on his 27th birthday and ending on his 65th birthday to accumulate $2,176,097.00 by the time he turns 65.

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The correct answer is A. The statement is false. If λ+5 is a factor of the characteristic polynomial of A, then −5 is an eigenvalue of A. In order for 5 to be an eigenvalue of A, the characteristic polynomial would need to have a factor of λ−5. This is because the eigenvalues of a matrix A are the roots of its characteristic polynomial, which is given by det(A-λI) where I is the identity matrix.

If λ+5 is a factor of the characteristic polynomial, then det(A-(λ+5)I)=0. This implies that A has an eigenvector corresponding to eigenvalue -(λ+5), which is -5 in this case. Therefore, 5 is not necessarily an eigenvalue of A. Moreover, the diagonal of A-λI contains the eigenvalues of A, not λ+5 as mentioned in option B. Option C is also incorrect because having λ+5 as a factor of the characteristic polynomial does not necessarily mean that λ=5 is a root of the polynomial. Option D is also incorrect because the factors of the characteristic polynomial are used to determine both the eigenvalues and eigenvectors of a matrix.

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The statement is false. If λ+5 is a factor of the characteristic polynomial of A, then it means that λ=-5 is an eigenvalue of A, not 5. This is because the characteristic polynomial is defined as det(A-λI), where I is the identity matrix and det is the determinant function. Setting λ+5 as a factor means that det(A-(-5)I) = 0, which implies that -5 is an eigenvalue of A.

Therefore, in order for 5 to be an eigenvalue of A, the characteristic polynomial would need to have a factor of λ-5, not λ+5. It is also important to note that while the characteristic polynomial is useful for determining both the eigenvalues and eigenvectors of a matrix, the factors of the polynomial only determine the eigenvalues, not the eigenvectors.

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6. C. Given

7. C. L is the midpoint of EM

8. .D . Definition of midpoint

9. B . < FLE= <ALM

10. C .ASA Postulate

Answer:

20 months

Step-by-step explanation:

The number of edges that the prism has is

When a plane intersects a prism, the shape formed is known as the cross section. The cross section of the prism will have the same form as the base if it is divided by a plane that runs horizontally and parallel to the base.

A prism is a 3-dimensional object with two congruent and parallel bases (which are polyggonal) connected by rectangular lateral faces. The number of edges of a prism is equal to the sum of the number of edges of the two bases and the number of lateral faces.

Each base of the prism has n edges, so the two bases together have 2n edges. The number of lateral faces of the prism is equal to the number of edges of one of its bases, so there are n lateral faces. Each lateral face has 4 edges, so the total number of edges of the lateral faces is 4n.

Therefore, the total number of edges of the prism is equal to the sum of the number of edges of the two bases (2n) and the number of lateral faces (4n), which is 2n + 4n = 6n.

In conclusion, the cross section of a prism is an n-sided polygon and the prism has n + 2 edges.

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The value of x is 5 from the diagram.

The sum of interior angle of a triangle is 180 degrees. Hence:

From the information given,;

73 = 8y - 7 (base angles are equal)

8y = 80

y = 10

Take the sum of the angles:

73  + 6x + 4 + 73 = 180

6x + 150 = 180

6x = 30

x= 5

Hence the value of x is 5 from the diagram.

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The value of x is 5.

Since triangle ABC is an isoceles triangle, angle A = Angle C(base angles of an isoceles triangle are equal)

Since angle A = 73° and angle C = (8y - 7)°

angle A = angle C

⇒ 73 = 8y - 7

Adding 7 to both sides, we have

73 + 7 = 8y - 7 + 7

80 = 8y

Dividing both sides by 8, we have

y = 80/8

y = 10

Also, angle A + angle B + angle C = 180° (sum of angles in a triangle)

73 + 6x + 4 + 8y - 7 = 180

Collecting like terms, we have

73 + 4 - 7 + 6x + 8y = 180

6x + 8y + 70 = 180

Subtracting 70 from both sides, we have

6x + 8y + 70 - 70 = 180 - 70

6x + 8y = 110

Making x subject of the formula, we have

6x = 110 - 8y

x = (110 - 8y)/6

Substituting the value of y into the equation, we have

x = (110 - 8y)/6

x = (110 - 8 × 10)/6

x = (110 - 80)/6

x = 30/6

x = 5

So, the value of x is 5.

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Answer:

5 (4 x + 5)

That is the answer

5 is a factor if 20 and 25 and 4x + 5 cannot be furthor be simplified.

the value of x= 3

and the value of y=5

Answer:

Step-by-step explanation:

       \(\begin{cases}6x=2y+8&\\ 4x+5y+10=47&\end{cases}\)

\(\Longleftrightarrow \begin{cases}12x=4y+16&\\ 12x+15y+30=141&\end{cases}\)

\(\Longleftrightarrow \begin{cases}12x=4y+16&\\ (4y+16)+15y=111&\end{cases}\)

\(\Longleftrightarrow \begin{cases}12x=4y+16&\\ 19y+16=111&\end{cases}\)

\(\Longleftrightarrow \begin{cases}12x=4y+16&\\ 19y=95&\end{cases}\)

\(\Longleftrightarrow \begin{cases}12x=4y+16&\\ y=\frac{95}{19}=5 &\end{cases}\)

\(\Longleftrightarrow \begin{cases}12x=20+16=36&\\ y=5 &\end{cases}\)

\(\Longleftrightarrow \begin{cases}x=3&\\ y=5 &\end{cases}\)

The diver's velocity during the first 2 sec of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

Given data: Initial velocity, u = 0 ft/sec

Acceleration, a = g = 32.2 ft/sec²

The maximum rate of fall, vmax = 80 mph

Time, t = 2 seconds

Air resistance constant, Ar = 0.2

We are supposed to determine the sky diver's velocity during the first 2 seconds of fall using the modified Euler method.

The governing equation for the velocity of the skydiver is given by the following:

ma = -m * g + k * v²

where, m = mass of the skydive

r, g = acceleration due to gravity, k = air resistance constant, and v = velocity of the skydiver.

The equation can be written as,

v' = -g + (k / m) * v²

Here, v' = dv/dt = acceleration

Hence, the modified Euler's formula for the velocity can be written as

v1 = v0 + h * v'0.5 * (v'0 + v'1)

where, v0 = 0 ft/sec, h = 2 sec, and v'0 = -g + (k / m) * v0² = -g = -32.2 ft/sec²

As the initial velocity of the skydiver is zero, we can write

v1 = 0 + 2 * (-32.2 + (0.2 / 68.956) * 0²)0.5 * (-32.2 + (-32.2 + (0.2 / 68.956) * 0.5² * (-32.2 + (-32.2 + (0.2 / 68.956) * 0²)))

v1 = 62.732 mph

Therefore, the skydiver's velocity during the first 2 seconds of fall using the modified Euler method with Ar= 0.2 is 62.732 mph.

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To find the average, one adds up all the scores and then divides by the total number of scores.

Joan had to find the average of the scores of her friends. To find the average, one adds up all the scores and then divides by the total number of scores. In this case, Joan had to find the sum of 10 different scores of her friends and then divide by 10. This will give her the average of the scores of her friends, which is a single value representing the central tendency of the scores. The average is a commonly used statistical measure that provides an overall idea of the data. In this case, the average of the scores of Joan's friends will give her an idea of the overall performance of her friends in the test she is preparing for.

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We can conclude that it is extremely unlikely to obtain a sample mean greater than 904.8 minutes if the design engineer's claim about the population variance and mean is true.

We can use the Central Limit Theorem to approximate the distribution of the sample means.

Under the given assumptions, the mean of the sampling distribution of the sample means is equal to the population mean, which is 886886 minutes, and the standard deviation of the sampling distribution of the sample means is equal to the population standard deviation divided by the square root of the sample size, which is\(\sqrt{84648464/145145} = 41.77\) minutes.

Therefore, we can standardize the sample mean using the formula:

\(z = (\bar{x} - \mu) / (\sigma / \sqrt{n } )\)

where \(\bar{x}\)  is the sample mean, \(\mu\)  is the population mean, sigma is the population standard deviation, and n is the sample size.

Plugging in the values we get:

z = (904.8 - 886886) / (41.77) = -21115.47

The probability of getting a sample mean greater than 904.8 minutes can be calculated as the area under the standard normal curve to the right of z = -21115.47.

This probability is essentially zero, since the standard normal distribution is symmetric and nearly all of its area is to the left of -6.

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Answer:

Step-by-step explanation:

Given:

Find f⁻¹(10):

Ordered pair is (10, 3)

Put 10 in f^{-1}(x)

The pair is (10,3)

Answer:

18

Step-by-step explanation:

You can forget about how many people their our in whole and focus on 6 x the amount they get, which is 3.

Answer:

4

Step-by-step explanation:

8*3=24 so there are 24 slices

24/6=4

so 6 people get 4 slices each

Answer:

12 because 12/30 is equal to 40% and 2/5 is is equal to 40% too

The population standard deviation by the square root of the sample size.

According to the central limit theorem, when multiple samples are taken from a population, the mean of the sample means will converge to the population mean.

In this case, if we repeatedly roll a standard die and calculate the mean of each sample, the mean of these sample means will approach 3.5, which is the population mean of the die.

The standard error of the mean is a measure of the variability of the sample means around the population mean. It can be calculated by dividing the population standard deviation by the square root of the sample size.

Since the sample size is not provided, we cannot determine the exact value of the standard error of the mean in this scenario.

In summary, the mean of the sample means will approach 3.5 (the population mean), while the standard error of the mean depends on the sample size and is not specified in this context.

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When comparing means of three or more conditions, an analysis of variance (ANOVA) should be used instead of multiple t-tests. This is because using multiple t-tests increases the risk of a type I error, where a significant difference is found when there is none. ANOVA controls for this by using a single test to determine if there is a significant difference between the means. Additionally, using multiple t-tests increases the risk of a type II error, where a significant difference is not found when there is one.

ANOVA is also more likely to detect statistical significance between the means because it takes into account the variability within each condition as well as the variability between conditions. This increases the power of the test and reduces the chances of missing a significant difference between the means.

When using ANOVA, the results can indicate that there are no differences between any of the population means (option a), that at least one of the three population means is different from another population mean (option b), that all three of the population means are different from each other (option c), or that one population mean is different from one of the other population means, but not the other population mean (option d).

Finally, ANOVA provides a measure of effect size, typically reported as r2, which indicates the proportion of variability in the data that can be attributed to the differences between the conditions. This can be useful in determining the practical significance of the results.

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