(08.02)
The scores of several classmates on a math test are shown below:
91
points
77
points
90
points
79
points
81
points
85
points
86
points
76
points
75
points
80
points
What is the median score for these students? (4 points)

The product that is less than 2 is A. 7/9x2 because the fraction 7/9 is less than 1. When multiplied by 2, the product is still less than 2.


A. 7/9x2
1. Calculate 7/9 * 2
2. 14/9 (7/9 * 2 = 14/9)
3. 14/9 is less than 2 because the numerator (14) is less than twice the denominator (9*2 = 18)

B. 5/4x2
1. Calculate 5/4 * 2
2. 10/4 (5/4 * 2 = 10/4)
3. 10/4 simplifies to 5/2 which is greater than 2

C. 6/3x2
1. Calculate 6/3 * 2
2. 12/3 (6/3 * 2 = 12/3)
3. 12/3 simplifies to 4, which is greater than 2

D. 11/5x2
1. Calculate 11/5 * 2
2. 22/5 (11/5 * 2 = 22/5)
3. 22/5 is greater than 2 because the numerator (22) is more than twice the denominator (5*2 = 10)

Your answer: A. 7/9x2 is less than 2 because the fraction is less than 1 and the product of the fraction and 2 results in a value smaller than 2.

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The probability of at most 1 person leaving the elevator on each floor when assuming that every person is equally likely to leave the elevator on any floor depends on the number of floors in the building and can be calculated using the binomial distribution formula.

Assuming that every person is equally likely to leave the elevator on any floor, the probability that on each floor at most 1 person leaves the elevator can be calculated using the binomial distribution.

Let's say there are n floors in the building. The probability of at most 1 person leaving the elevator on each floor is the probability that 0 or 1 person leaves the elevator on each floor. This can be calculated as follows:

P(at most 1 person leaves the elevator on each floor) = P(0 people leave on floor 1) x P(0 or 1 people leave on floor 2) x P(0 or 1 people leave on floor 3) x ... x P(0 or 1 people leave on floor n)

Now, since we are assuming that every person is equally likely to leave the elevator on any floor, the probability of 0 people leaving the elevator on any floor is (n-1)/n and the probability of 1 person leaving the elevator on any floor is 1/n. Therefore, we can calculate the probability of at most 1 person leaving the elevator on each floor as:

P(at most 1 person leaves the elevator on each floor) = (n-1)/n * (1/n + (n-1)/n)^(n-1)

Simplifying this expression, we get:

P(at most 1 person leaves the elevator on each floor) = (n-1)/n * (2/n)^(n-1)

For example, if there are 5 floors in the building, the probability of at most 1 person leaving the elevator on each floor is:

P(at most 1 person leaves the elevator on each floor) = 4/5 * (2/5)^4
P(at most 1 person leaves the elevator on each floor) = 0.08192

Therefore, the probability of at most 1 person leaving the elevator on each floor when assuming that every person is equally likely to leave the elevator on any floor depends on the number of floors in the building and can be calculated using the binomial distribution formula.

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i like mantises! their cute funky bugs. they can turn their heads 180 degrees and are the only insect that can move their head. there are around 2,000 spices of them, most live in tropics, but 18 types are in north America. I have a praying mantis pet, and her name is creature, shes about 6 inches long!

The better buy is given by the following brand:

Brand A.

The better buy is obtained applying the proportions in the context of the problem.

A proportion is applied as the cost per ounce is given dividing the total cost by the number of ounces.

Then the better buy is given by the option with the lowest cost per ounce.

The cost per ounce for each brand is given as follows:

$8 per ounce is a lesser cost than $9.3 per ounce, hence the better buy is given by Brand A.

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In graph theory, a vertex cover of a graph is a set of vertices that covers all the edges in the graph. On the other hand, an independent set is a set of vertices that have no edges connecting them.

In this context, it is important to note that a vertex cover and an independent set are mutually exclusive.

That is, a vertex cannot belong to both the vertex cover and the independent set simultaneously.

In many cases, the determination of the minimum size of a vertex cover is one of the fundamental problems in graph theory.

Similarly, the determination of the maximum size of an independent set in a graph is also a significant problem in graph theory. The problems are typically addressed using various algorithms and heuristics.

However, in some cases, it is possible to establish the relationship between the vertex cover and the independent set in a graph. For instance, if a graph is a bipartite graph, then the vertex cover and the independent set are the same size.

This result is known as König's theorem and is one of the most important results in graph theory. In conclusion, the fact that each vertex belongs to the vertex cover or the independent set is not a coincidence.

It is a fundamental property of graphs that has significant implications for various problems in graph theory.

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The center of the ellipse will be (3, 0). And the lengths of the major and minor axes will be 4.4721 and 2, respectively.

Ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called foci adds up to a constant. It is taken from the cone by cutting it at an angle.

The equation of the ellipse is given below.

5x² + y² − 30x + 40 = 0

Convert the ellipse into standard form. Then we have

5x² + y² − 30x + 40 = 0

5[x² − 6x] + y² + 40 = 0

5[x² − 6x + 9] − 45 + y² + 40 = 0

5(x − 3)² + y² = 5

(x − 3)² + y² / 5 = 1

The equation center of the ellipse is (3, 0). Then the major axis is given as,

Major axis = 2 √5

Major axis = 4.4721

Then the minor axis is given as,

Minor axis = 2 x 1

Minor axis = 2

The center of the ellipse will be (3, 0). And the lengths of the major and minor axes will be 4.4721 and 2, respectively.

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The correct equation is given below.

5x² + y² − 30x + 40 = 0.

Case 2

The quadratic equation x² - 14 · x + 48 = 0 have the following roots: x₁ = 6 and x₂ = 8. (Correct choice: B)

Case 3

We need to add + 64 to both sides. (Correct choice: B)

Case 4

We need to add + 16 to both sides. (Correct choice: C)

In this problem we find three cases of quadratic equation that are not perfect square trinomials, these equations can be rewritten partially in that form by algebra properties. Completing the square offers a quick method to determine the roots of quadratic equations with integer coefficients. Now we proceed to determine the solutions corresponding to each case:

Case 2

x² - 14 · x + 48 = 0

x² - 14 · x + 49 = 1

(x - 7)² = 1

x - 7 = ± 1

x = 7 ± 1

The roots of the quadratic equation x² - 14 · x + 48 = 0 are x₁ = 6 and x₂ = 8, respectively.

Case 3

x² - 16 · x = - 21

x² - 16 · x + 64 = 64 - 21

(x + 8)² = 43

The first step consists in adding both sides by + 64.

Case 4

x² - 8 · x = 0

x² - 8 · x + 16 = 16

(x - 4)² = 16

The first step consists in adding both sides by + 16.

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Answer:

-4n + 49

Step-by-step explanation:

it is going down by 4 each step, hence, -4 and 45 -- 4 = 45 + 4 = 49.

Answer:

Step-by-step explanation:

45, 41, 37, 33, 29, ....

a₁ = 45

a₂ = 45 - 4 = 41

a₃ = 41 - 4 = 37

a₄ = 37 - 4 = 33

a₅ = 33 - 4 = 29

...

It's an arithmetic sequence.

a₁ = 45, d = -4

A general term of an arithmetic sequence:

aₙ = a₁ + (n - 1)d

Substitute:

aₙ = 45 + (n - 1) · (-4) = 45 - 4n + 4 = -4n + 49

Answer:

its all black;-; that just color black

Step-by-step explanation:

how we going to see it if that is black

The first one and the last one.

-Since they both include a negative and a positive

-The one you have chosen is incorrect because a negative divided by a negative becomes a positive

Answer:

Step-by-step explanation:

3,-3

Answer:

15²+2³= 225+8= 233

Step-by-step explanation:

hope it helps you

Answer:

≈ 254,47 in^2

Step-by-step explanation:

Given:

d (diameter) = 18 in

Find: A (area) - ?

First, we have to find the length of the radius (r):

\(r = \frac{1}{2} \times d\)

\(r = \frac{1}{2} \times 18 = 9 \: in\)

Now, we can find the area (a):

\(a = \pi {r}^{2} = \pi \times {9}^{2} = 81\pi \: {in}^{2} ≈254.47 \: {in}^{2} \)

The probability that exactly four of the selected bulbs from the pack of 10 bulbs is defective is 1/120.

For the given question;

Thus, the probability that exactly four of the selected is defective.

P = ⁴C₄  / ¹⁰C₃

P = 1/120

Thus, the probability that exactly four of the selected is defective is 1/120.

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The pitch of the roof is 0.3.

Pitch:

The pitch can be expressed numerically as a fraction. The pitch fraction represents a certain amount of vertical rise over the entire span.

Here it is given that the rise in the roof is 3.6m and a rum of 12m,

We have to find the pitch of the roof.

As is already given in the statement that the slope of a roof is called its pitch.

By this we get the slope:

Slope = 3.6/12

= 3/10

= 0.3

Therefore we get the pitch of the roof at 0.3.

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The domain is the set of all the x-values used by those points.

  { -1, 0, 3, -5, -3 }

The order does not matter.

The task requires analyzing a list of departments and performing several tasks related to relationship codes, activity relationship diagrams, reason codes, a worksheet, and a dimensionless block diagram.

We need to consider the number of departments. Since we have 7 departments listed, the number of relationship codes can be calculated using the formula: (n * (n-1)) / 2, where n is the number of departments.

Substituting the value of n = 7, we get:

Relationship Codes = (7 * (7-1)) / 2

= (7 * 6) / 2

= 42 / 2

= 21

Therefore, there will be 21 relationship codes in the chart.

Create an activity relationship diagram:

An activity relationship diagram visually represents the relationships between departments. Here is a basic diagram representing the given departments:

Receiving --+

           +-- Assembly & Shipping -- Offices

Fabrication--+

           +-- Painting -- Stores

Restrooms & Lockers

Populate the diagram with codes for all the relationships:

To populate the diagram with codes, we can assign a unique code to each relationship. Here's an example of assigning codes to the relationships in the diagram:

Receiving (R) --+

               +-- Assembly & Shipping (AS) -- Offices (O)

Fabrication (F)--+

               +-- Painting (P) -- Stores (S)

Restrooms & Lockers (RL)

What is the percentage of codes in each category? Does it follow the standard percentages?

To determine the percentage of codes in each category, we need to count the number of codes in each category and calculate the percentage relative to the total number of codes (21).

In this case, we have the following categories and their respective codes:

Production: R, F, AS, P (4 codes)

Administration: O, S (2 codes)

Support: RL (1 code)

Percentage of Production codes = (4 / 21) * 100 ≈ 19.05%

Percentage of Administration codes = (2 / 21) * 100 ≈ 9.52%

Percentage of Support codes = (1 / 21) * 100 ≈ 4.76%

These percentages do not necessarily follow any standard percentages. The distribution of codes among categories can vary depending on the specific organization or context.

Provide at least 3 reason codes for the chart:

Reason codes are used to provide explanations or justifications for the relationships depicted in the chart. Here are three example reason codes for the given chart:

R01: Receiving department receives raw materials and supplies from external sources.

AS01: Assembly & Shipping department assembles products and prepares them for shipment.

O01: Offices department provides administrative support and management functions for the organization.

Create a worksheet to assist in the creation of the dimensionless block diagram:

Here's an example of a worksheet that can assist in creating the dimensionless block diagram:

Relationship Code From Department To Department

R Receiving Fabrication

F Fabrication Painting

AS Assembly & Shipping Offices

P Painting Stores

RL Restrooms & Lockers -

O Offices -

S Stores -

This worksheet lists the relationship codes along with the corresponding "From" and "To" departments.

Create a dimensionless block diagram for your data B. Show the flow through the dimensionless block diagram:

A dimensionless block diagram represents the flow of activities or information between different departments. Here's an example of a dimensionless block diagram based on the given data:

Receiving --> Fabrication --> Painting --> Stores

                  |

                  v

        Assembly & Shipping --> Offices

                  |

                  v

       Restrooms & Lockers

The arrows indicate the flow of activities or information from one department to another.

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The three pairs of side lengths are possible measurements for the triangle are: GH = 8√3, GI = 16, HI=7, GI= 14 and GH = 2√3, HI = 2

Given an equilateral triangle which has all sides equal, says 2 unit each. It also has the angles equal which is 60°. If the triangle is divided into 2 equal halves we will have a triangle similar to the one provided with half angle of 30°, another angle 60° and a right angle of 90°.

This gives us a right angle and we can then apply the law of Pythagoras to get the value of the unknown sides after being divided.

Using the diagram,

GI = 2 (original size)

HI = 1 (half of original size)

GH = ? (the unknown)

By using Pythagoras theorem,

GI² = HI² + GH²

2² = 1² + GH²

4 = 1 + GH²

GH² = 4 - 1 = 3

GH = √3

GH = √3 , GI = 2, HI = 1

Now we have to compare each option to these values and select whichever one is a factor

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Answer:

its the 2 one you welcome

Answer:

1 1/2

Step-by-step explanation:

it is one whole and a half

If a language L is regular, then the tail of the language, Lt, is also regular because we can construct a new finite automaton for Lt by adding a new start state and connecting it to the old start state by an ε-transition, and by adding all states that are reachable from an accepting state by an ε-transition.

To show that if a language L is regular, the tail of the language, Lt, is also regular, we need to first understand the concepts of language tails and regular languages.

A language tail is a subset of a language that consists of strings starting at a certain point. In other words, given a language L over an alphabet Σ, the tail of L with respect to a string w is a subset of L that consists of all strings that start with w. The tail of L with respect to the empty string is L itself.

A regular language is a language that can be expressed by a regular expression or generated by a finite automaton. A finite automaton is a mathematical model for a machine that reads a sequence of characters from an input tape and transitions between different states according to the input.

The tail of a regular language is also a regular language. This is because if a language L is regular, then it can be recognized by a finite automaton. We can construct a new finite automaton for the tail of L by starting with the original automaton and adding a new start state that is connected to the old start state by an ε-transition.

This new start state is the start state for the tail language. The accepting states for the tail language are the same as the accepting states for the original language, except that we have to add all states that are reachable from an accepting state by an ε-transition.

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The power series has a center at 0, a radius of convergence of 5, and converges for values of x within the interval (-5, 5).

To find the center, radius of convergence, and interval of convergence for the power series

\(\[ \sum_{n=1}^{\infty} \frac{x^{n}}{5^{n} \cdot n^{5}} \]\)

we can use the ratio test. Let's apply the ratio test

lim n→∞ ∣aₙ+1 / aₙ∣ =  lim n→ ∞ ∣[xⁿ⁺¹/5ⁿ⁺¹(n+1)⁵]/[xⁿ/5ⁿn⁵]∣

= lim n → ∞ ∣[xⁿ⁺¹5ⁿn⁵/(n+1)⁵xⁿ5ⁿ⁺¹]∣

Simplifying the expression:

lim → ∞ ∣xn⁵/5(n+1)∣ = ∣ x/ 5 ∣ lim→∞ n⁵ /( n + 1 )⁵

Now, we can evaluate the limit of the second term

lim→∞ n⁵ /( n + 1 )⁵  = lim → ∞ (n/( n + 1 ))⁵ = 1

Therefore, the limit simplifies to:

∣ x/5 ∣

For the series to converge, we need this expression to be less than 1. Hence, ∣ x/5 ∣ <1

Multiplying both sides by 5, we get

∣x∣<5

So, the radius of convergence is 5. The center is the value of x around which the series converges, which is 0. Thus, the series converges for x in the interval (−5,5).

Therefore, the center is 0, the radius of convergence is 5, and the interval of convergence is (−5,5).

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Answer:

18 tests

Step-by-step explanation:

Create a proportion where x is the number of tests after 9 weeks:

\(\frac{10}{5}\) = \(\frac{x}{9}\)

Cross multiply and solve for x:

5x = 90

x = 18

So, after 9 weeks, Vera will have taken 18 tests

Answer:

18

Step-by-step explanation:

18

10 tests     =   x tests

/ 5 weeks =   / 9 weeks

10* 9= x5

90/5=  18

Answer:

59180

Step-by-step explanation:

Reduce 118/360 to lowest terms

The simplest form of 118360 is 59180.

I hope this helps   :)

Answer:

$40000

Step-by-step explanation:

The nearest thousand dollar is rounding the thousand value from its hundred value, which in this case is 4. Since 4 is less than half of 10, the thousand value must round down to $40000.

Answer:

$40000.00

Step-by-step explanation:

Report this answer if its incorrect ^_^

In 7th-grade math, you can use  methods like using a protractor, angle addition, and subtraction, angle bisectors,complementary and supplementary angles, properties of parallel lines, and using triangles to find angles:

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Answer - 4/45

They say no replacement so it would be

2/10 * 4/9 = 4/45

To determine if the polynomial is even, odd, or neither, we substitute -x for x in the polynomial and simplify. -3(-x)² + 6(-x) = -3x² - 6x. Since the polynomial is not equal to its negation, it is neither even nor odd.

To write the equation of the line with an x-intercept at -6 and a y-intercept at 2, we can use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept.

In this case, the y-intercept is given as 2, so the equation becomes y = mx + 2. To find the slope, we can use the formula (y2 - y1) / (x2 - x1) with the given points (-6, 0) and (0, 2). We find that the slope is 1/3. Thus, the equation of the line is y = (1/3)x + 2.

For the polynomial f(x) = -3x² + 6x, the degree is 2 and the leading coefficient is -3. The end behavior of the graph is determined by the degree and leading coefficient. Since the leading coefficient is negative, the graph will be "downward" or "concave down" as x approaches positive or negative infinity.

To find the zeros, we set the polynomial equal to zero and solve for x. -3x² + 6x = 0. Factoring out x, we get x(-3x + 6) = 0. This gives us two solutions: x = 0 and x = 2.

The x-intercept is the point where the graph intersects the x-axis, and since it occurs when y = 0, we substitute y = 0 into the polynomial and solve for x. -3x² + 6x = 0. Factoring out x, we get x(-3x + 6) = 0. This gives us two x-intercepts: (0, 0) and (2, 0).

To determine if the polynomial is even, odd, or neither, we substitute -x for x in the polynomial and simplify. -3(-x)² + 6(-x) = -3x² - 6x. Since the polynomial is not equal to its negation, it is neither even nor odd.

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Answer: 5 ft

Step-by-step explanation:

Area = 100 sq. ft

Length = x + 15ft

Width = x

Area of rectangle= L x W

100= (x + 15) x X

100= X^2 + 15x

X^2 + 15x -100 = 0

X^2 +20x - 5x - 100 = 0

x(x +20) - 5(x +20) = 0

(x+20)(x-5)= 0

solving for x:

x+20 = 0

x= -20

or

x-5 = 0

x = 5

Since width cannot be negative, the width is 5 feet

Given the equation:

Answer:

slope: 6

y-intercept: -4

easy: y = 6x -4