Explain why these steps show that this formula is true whenever n is a positive integer. Multiple Choice A)We have completed the inductive step. so by the principle of mathematical induction, the statement is true for every positive integer n. B) We have completed both the basis step and the inductive step, so by the principle of mathematical induction, the statement is true for every real number C) We have completed both the basis step and the inductive step, so by the principle of mathematical induction, the statement is true for every integer 2
D) We have completed both the basis step and the inductive step, so by the principle of mathematical induction, the statement is true for every positive integer E) We have completed the inductive step, so by the principle of mathematical induction, the statement is true for every integer

Answer:

18.25

Step-by-step explanation:

Add 5.50 and 12.75

5.50 + 12.75 = 18.25

Answer: 18.25

Step-by-step explanation:

9514 1404 393

Answer:

  3.  m∠A < 80°

Step-by-step explanation:

The exterior angle NGS, marked as 80°, has a measure that is the sum of the measures of the remote interior angles: GAN, GNA.

If we assume that angle measures cannot be zero, then we must have ...

  m∠A +m∠N = 80°

  m∠A = 80° -m∠N

Since m∠N > 0, the measure of angle A must be less than 80°.

This conclusion matches choice 3.

No, Thomas does not work the same percentage of days each month, because there different number of days in different months.

Let us consider two different months: one with 30 days and another with 31 days.

In the month with 30 days, Thomas works 12/30 = 40% of the days.

In the month with 31 days, Thomas works 12/31 = approximately 39% of the days.

As we can see, the percentage of days that Thomas works varies depending on the number of days in the month. This is because the number of days that Thomas works is fixed at 12, while the number of days in the month changes.

Therefore, the percentage of days that Thomas works each month will depend on the number of days in the month, and will not be the same percentage each month.

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The given question is incomplete, the complete question is

Thomas works 12 days out of every month. Does Thomas work the same percent of days each month? Explain.

The range of the given function is -∞ ≤ y ≤ ∞

A function is an equation for which any x that can be put into the equation will produce exactly one output such as y out of the equation.

Given is a function, y = \(\sqrt[3]{x+8}\), we need to find the range, for the function,

we know that,

The range of function in two variables, that contains variables x, and y are those values of y, for which x is defined.

For example, consider the linear function, y = x

The set of values that, x can take for which y is defined called Domain of the function, x ∈ R.

And the set of values that, y can take for which x is defined called Range of the function, y ∈ R.

Therefore,

y = \(\sqrt[3]{x+8}\)

Taking cube on both sides

y³ = x+8

Therefore, x is defined for all real values of y, means for all real values of y, we are getting real values of x, so Range of the given function is,  y ∈ R.

Hence, the range of the given function is -∞ ≤ y ≤ ∞

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The mean difference in game scores over the six games is 12

The mean difference, or difference in means, measures the absolute difference between the mean value in two different groups.

Given the points by which a basketball team either won or lost 6 games.

- Won by 7 points = +7

- Lost by 10 points = -10

- Won by 8 points = +8

- Won by 11 points = +11

- Lost by 2 points = -2

- Won by 10 points = +10

Thus;

Mean difference of the 6 games is;

= (+7 - 10 + 8 + 11 - 2 + 10)/6

= 24/6

= 12

Hence, the mean difference in game scores over the six games is 12

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A) Function is increasing on (-∞, -1) and (7/2, ∞), and decreasing on (-1, 7/2).

b)  The local minimum value of f is; 5608/2197 at x = -42/13, and the local maximum value of f is 139/8 at x = 7/2.

(a) To determine the intervals on which f is increasing or decreasing, we need to determine the critical points and then check the sign of the derivative on the intervals between them.

f(x)=8x³-42x-48x + 4

f'(x) = 24x² - 90

Setting f'(x) = 0, we get

24x² - 90 = 0

24x² = 90

x =±  √3.75

So, the critical points are;

x = -1 and x = 7/2.

We can test the sign of f'(x) on the intervals as; (-∞, -1), (-1, 7/2), and (7/2, ∞).

f'(-2) = 72 > 0, so f is increasing on (-∞, -1).

f'(-1/2) = -25 < 0, so f is decreasing on (-1, 7/2).

f'(4) = 72 > 0, so f is increasing on (7/2, ∞).

Therefore, f is increasing on (-∞, -1) and (7/2, ∞), and decreasing on (-1, 7/2).

(b) To determine the local maximum and minimum values of f, we need to look at the critical points and the endpoints of the interval (-1, 7/2).

f(-1) = -49

f(7/2) = 139/8

f(-42/13) = 5608/2197

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Answer:

A Hexagon has 6 sides so 6 Vertices

The sum of the first fifteen terms of the given sequence is 220.

The given sequence can be expressed as: \($2, 8, 14, \dots$\), in which each term is six more than the preceding term. This is an arithmetic sequence, where the common difference between terms is 6. The formula to calculate the sum of the first n terms of an arithmetic sequence is given by \($S_n = \frac{n}{2}(a_1 + a_n)$\), where \($a_1$\) is the first term and \($a_n$\) is the nth term.

In the given sequence, the first term \($a_1$\) is 2 and the 15th term \($a_n$\) is 42. So, plugging these values to the formula gives us, \($S_{15} = \frac{15}{2}(2+42) = \frac{15\times 44}{2} = 220$\).

Therefore, the sum of the first fifteen terms of the given sequence is 220.

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To display all the equivalence relations on the set of the m smallest positive integers, we need to consider the different ways in which we can partition the set. The number of equivalence relations is related to the number of partitions, and it can be calculated using combinatorial techniques.

An equivalence relation on a set is a relation that is reflexive, symmetric, and transitive. In the case of the set of the m smallest positive integers, we can represent each equivalence relation as a partition of the set. A partition is a collection of non-empty disjoint subsets that, when combined, cover the entire set.

To find all the equivalence relations, we need to consider all possible partitions of the set. The number of partitions can be calculated using the concept of Bell numbers, which count the number of ways to partition a set. The formula for calculating the Bell number B(n) is recursive and involves summing the Stirling numbers of the second kind.

Once we have determined the number of partitions, we can generate each equivalence relation by listing the subsets that form each partition. Each subset represents an equivalence class, and the union of all the subsets gives the original set. In summary, to display all the equivalence relations on the set of the m smallest positive integers, we need to generate all possible partitions of the set. The number of equivalence relations is related to the number of partitions and can be calculated using combinatorial techniques such as Bell numbers. Each equivalence relation can be represented by listing the subsets that form each partition, with each subset representing an equivalence class.

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As the residual is positive, this tells us that Carlos is above average height for his shoe size.

The residual for each observation is the difference between predicted values of y (dependent variable) and observed values of y . Residual=actual y value−predicted y value, \(ri=yi^{-yi}\).

Given that, a = 1.313 and b = 56.143

So, the model is height = 1.313 x shoe size + 56.143

r = 0.837 so we have a strong linear relationship between height and shoe size

Residual = observed - predicted

For size 9, predicted = 1.313 x 9 + 56.143 = 67.96

Observed = 71

Residual = 71 - 67.96 = 3.04

Therefore, as the residual is positive, this tells us that Carlos is above average height for his shoe size.

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We will have that the pie chart should be:

Answer: a+b=b+a is a clear example of commutative property.

Step-by-step explanation: The commutative property applies to addition and multiplication. The property states that terms can “commute,” or move locations, and the result will not be affected. This is expressed as a+b=b+a for addition, and a×b=b×a for multiplication. The commutative property does not apply to subtraction or division.

Answer:

2.1

Step-by-step explanation:

8

10

−

2

5

)+0.9

=3(

4

5

−

2

5

)+0.9

=3(

2

5

)+0.9

=

6

5

+0.9

=2.1

Therefore, the value of angle A is approximately 76.16°, and the value of angle C is approximately 8.24°.

A triangle is a closed two-dimensional shape with three straight sides and three angles. It is the simplest polygon that can be formed in Euclidean geometry, and it is widely studied in mathematics and geometry. Triangles can be classified based on their sides and angles. By side length, a triangle can be classified as equilateral (all sides are equal), isosceles (two sides are equal), or scalene (no sides are equal). By angle measure, a triangle can be classified as acute (all angles are less than 90 degrees), obtuse (one angle is greater than 90 degrees), or right (one angle is exactly 90 degrees). Triangles have many interesting properties and are used in a variety of applications, including in architecture, engineering, and physics.

Here,

Sure, I can help you with that! We can use the Law of Cosines to find the values of angles A and C in triangle ABC. The Law of Cosines states that:

c² = a² + b² - 2ab cos(C)

where c is the side opposite angle C.

First, let's find the value of side c:

c² = a² + b² - 2ab cos(C)

c² = (782)² + (1435)² - 2(782)(1435) cos(115.6°)

c² = 613524 + 2055225 - 2238015.52

c²  = 594733.48

c = √(594733.48)

c ≈ 771.1 cm

Now, we can use the Law of Cosines again to find angle A:

cos(A) = (b² + c² - a²) / 2bc

cos(A) = (1435² + 771.1² - 782²) / (2 * 1435 * 771.1)

cos(A) = 0.2354

A = cos⁻¹*²³⁵⁴⁾

A ≈ 76.16°

Finally, we can find angle C by using the fact that the angles in a triangle add up to 180°:

C = 180° - A - B

C = 180° - 76.16° - 115.6°

C ≈ 8.24°

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Convert the scale to a ratios: 1:482. Determine the actual height of the train in millimeters by multiplying the model height by the scale factor: 102 x 483. Simplify the ratio: 1:2,3044. Convert millimeters to meters by dividing by 1,000: 102 ÷ 1,000 = 0.102 meters

Therefore, the actual height of the train is 0.102 meters.

Lin has a scale model of a modern train. The model is created at a scale of 1:48. The height of the model train is 102 millimeters. To find the actual height of the train in meters, we need to use the scale factor and convert the millimeters to meters.Steps to find the actual height of the train in meters:1. Convert the scale to a ratio: 1:482. Determine the actual height of the train in millimeters by multiplying the model height by the scale factor: 102 x 483. Simplify the ratio: 1:2,3044. Convert millimeters to meters by dividing by\(1,000: 102 ÷ 1,000 = 0.102\)meters

Therefore, the actual height of the train is 0.102 meters.

It is essential to use proper formatting and syntax while answering a question. HTML is a useful tool that helps in formatting the answer in a more organized way. Below is the formatted answer:Steps to find the actual height of the train in meters:1.

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Answer:

the data below are the tempretures on randomly

Step-by-step explanation:

Answer:

In plane Euclidean geometry, a rhombus is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

got it right on edge 2022

If a typical somatic cell has 64 chromosomes, each gamete of that organism is expected to have 32 chromosomes.

In sexually reproducing organisms, somatic cells are the cells that make up the body and contain a full set of chromosomes, which includes both sets of homologous chromosomes. Gametes, on the other hand, are the reproductive cells (sperm and egg) that contain half the number of chromosomes as somatic cells.

During the process of gamete formation, called meiosis, the number of chromosomes is halved. This reduction occurs in two stages: meiosis I and meiosis II. In meiosis I, the homologous chromosomes pair up and undergo crossing over, resulting in the shuffling of genetic material. Then, the homologous chromosomes separate, reducing the chromosome number by half. In meiosis II, similar to mitosis, the sister chromatids of each chromosome separate, resulting in the formation of four haploid daughter cells, which are the gametes.

Since a typical somatic cell has 64 chromosomes, the gametes produced through meiosis will have half that number, which is 32 chromosomes. These gametes, with 32 chromosomes, will combine during fertilization to restore the full set of chromosomes in the offspring, creating a diploid zygote with 64 chromosomes.

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The contractor would have to work for 20 hours on the site to earn $555 total pay

What is total cost function?

Total cost function is the sum of the fixed charge, which is fixed cost to the person paying the contractor when the contractor visits the site and charge per hour multiplied by the number of hours spent working

TC=a+bX

TC=total cost=$555

a=fixed charged=$55

b=charge per hour=variable element of contractor's pay=$25

X=number of hours spent working=unknown

$555=$55+$25X

$555-$55=$25X

$500=$25*X

X=$500/$25

X=20

The contractor needs to work for 20 hours in order to earn a total pay of $555

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The sum of the series Σ (6^(n-2) + 1 / (-8)^n) is 53 / 540.

To find the sum of the series, let's express it in sigma notation and then simplify it:

Σ (6^(n-2) + 1 / (-8)^n)

First, let's consider the first term of the series: 6^(n-2).

We can rewrite this term as 6^(-2) * 6^n.

Now, let's consider the second term of the series: 1 / (-8)^n.

Since (-8)^n can be written as (-1)^n * 8^n, we can rewrite the term as 1 / ((-1)^n * 8^n).

Combining the two terms, we have:

Σ (6^(-2) * 6^n + 1 / ((-1)^n * 8^n))

We can split this into two separate series:

Σ (6^(-2) * 6^n) + Σ (1 / ((-1)^n * 8^n))

Now, let's calculate each series separately.

For the first series, Σ (6^(-2) * 6^n), we have a geometric series with a common ratio of 6. The formula for the sum of a geometric series is:

Sum = a / (1 - r),

where a is the first term and r is the common ratio.

In this case, a = 6^(-2) and r = 6.

Sum of the first series = 6^(-2) / (1 - 6) = 6^(-2) / (-5) = -1 / (5 * 6^2) = -1 / 180.

For the second series, Σ (1 / ((-1)^n * 8^n)), we also have a geometric series, but with a common ratio of (-1/8).

Using the formula for the sum of a geometric series, we get:

Sum of the second series = 1 / (1 - (-1/8)) = 1 / (1 + 1/8) = 1 / (9/8) = 8/9.

Now, let's find the sum of the entire series by adding the sums of the two separate series:

Sum of the series = Sum of the first series + Sum of the second series

                 = -1/180 + 8/9

                 = (-1 + 160) / (180 * 9)

                 = 159 / 1620

                 = 53 / 540.

Therefore, the sum of the series Σ (6^(n-2) + 1 / (-8)^n) is 53 / 540.

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Answer:

Step-by-step explanation:

-3 + 4i

value = square( (-3)^2 + (4i)^2 ) = sqr(9 + 16) = sqr(25) = 5

The absolute value is like the Pythagoras theorem

Step-by-step explanation:

The equation of a circle written in the form (x−h)2+(y−k)2=r2 where (h,k) is the center and r is the radius. The circle centered at the origin with radius 1; its equation is x2+y2=1.

Hope it help!!!

The type of sampling used by the University of Iowa in their investigation of student drinking is C) Cluster sampling.

Cluster sampling is a method where the population is divided into groups, or clusters, and a random sample of these clusters is selected for the study. In the case of the University of Iowa's investigation, the population was the entire student body and the clusters were the different classrooms. By randomly selecting 10 classrooms and interviewing all the students in each of these groups, the University of Iowa was using cluster sampling.

Therefore, the correct answer is  C: cluster sampling.

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Domain: the smallest possible x-value to the largest possible x-value

In the case of this graph, we see the parabola starts at x = -3, and continues on forever.

Domain: [-3, infinity)

Range: the smallest possible y-value to the largest possible y-value

In the case of this graph, the parabola will continue to expand forever.

Range: (-infinity, infinity)

Therefore, while the domain has a restriction, the range does not and is all real numbers.

Hope this helps!