\(6+2n=-4(N-1)+6N\)

The solution for the trapezoid with median is:

1. If MY || LE, then MY || IK

2. MY = 52 cm

3. MY = 109 cm

4. IK = 10 cm

5. LE = 45 cm

The trapezoid mid-segment or median theorem states that "a line connecting the midpoints of the non-parallel sides (legs) is parallel to the bases". It measures half the sum of lengths of the bases. That is:

m = 1/2 (b₁ + b₂)

where b₁ and b₂ are the bases of the trapezoid.

No. 1

Since the midpoints of the non-parallel sides (legs) is parallel to the bases. Thus:

If MY || LE, then MY || IK

Note: || means parallel

No. 2

In this case, the midpoint is MY. IK and LE are the bases. Thus:

MY = 1/2 * (IK + LE)

MY = 1/2 * (56 + 48)

MY = 52 cm

No. 3

MY = 1/2 * (142 + 76)

MY = 109 cm

No. 4

45.7 = 1/2 * (IK + 85)

45.7 * 2 = IK + 85

95 = IK + 85

IK = 95 - 85

IK = 10 cm

No. 5

37.5 = 1/2 * (120 + LE)

37.5 * 2 = 120 + LE

75 = 120 + LE

LE = 120 - 75

LE = 45 cm

Learn more about trapezoid median theorem on:

https://brainly.com/question/26150828

#SPJ1

The required slopes are:

(a) slope = 4

(b) slope = 6/7

(c) slope =  -3

(d) slope = 4

(e) slope = -5/2

We know that,

When a line passing through (x₁, y₁) and (x₂, y₂)

Then  the slope of the line be,

slope (m) = (y₂ - y₁) / (x₂ - x₁)

Using this formula, calculate the slope for each given points

a. (9, 10) and (7, 2)

⇒ slope (m) = (2 - 10) / (7 - 9)

                    = -8/-2 = 4

So, the slope is 4.

b. (-8, -11) and (-1, -5)

⇒ slope (m) = (-5 - (-11)) / (-1 - (-8))

                    = 6/7

So, the slope is 6/7.

c. (5, -6) and (2, 3)

⇒ slope (m) = (3 - (-6)) / (2 - 5)

                    = 9/-3

                    = -3

So, the slope is -3.

d. (6, 3) and (5, -1)

⇒ slope (m) = (-1 - 3) / (5 - 6)

                    = -4/-1

                    = 4

So, the slope is 4.

e. (4, 7) and (6, 2)

⇒ slope (m) = (2 - 7) / (6 - 4)

                    = -5/2

So, the slope is -5/2.

Therefore, the slope of the line that joins (-8, -11) and (-1, -5) is 6/7.

Learn more about the equation of line visit:

https://brainly.com/question/18831322

#SPJ4

The 99% confidence limit will be option B which is (45, 55)

90% confidence limits for the population mean are (46,54)

mean = 46+54 / 2 = 50.

the margin of error E = 54-46/2 = 4

For 90% Confidence Z- Critical value is = 1.645

But the margin of error

E = ZS/√n

4=(1.645)S/√n

S/√n = 4 / 1.645

= 2.4316

For 95% confidence Z-critical value is 1.96

A 95% confidence interval is = mean ± E

(50 ± 1.96) S/√n = (50 ± 1.96)×2.4316

= 50+ 4.7660

= 45.2340, 54.7660

= (45, 55)

Hence the correct option is B which is (45, 55) as the 99% confidence limit.

To learn more about mean, median, and mode,

https://brainly.com/question/15323584

#SPJ4

The domain and the range of the function are (-∝, ∝) and (0, ∝), respectively

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

The graph

The above graph is an exponential function

The rule of an function is that

The domain is the set of all real values

In this case, the domain is (-∝, ∝)

For the range, we have

Range = (0, ∝)

Read more about domain and range at

brainly.com/question/27910766

#SPJ1

In the sequence of file folders, the number of yellow folders increases by 2 at each step. We can model this pattern using a linear function, where the number of yellow folders Y(n) at step n can be represented as Y(n) = 2n.

By observing the sequence of file folders, we can identify a pattern that the number of yellow folders increases by 2 at each step. This means that for each step n, the number of yellow folders Y(n) can be obtained by multiplying the step number n by 2.

Therefore, we can model the relationship between the step number and the number of yellow folders using a linear function. The function Y(n) = 2n represents this pattern, where Y(n) denotes the number of yellow folders at step n.

For example, at step 1, we have Y(1) = 2(1) = 2 yellow folders. At step 2, we have Y(2) = 2(2) = 4 yellow folders, and so on.

This linear model accurately captures the pattern observed in the sequence of file folders, where the number of yellow folders increases by 2 at each step.

To know more about  linear refer here:

https://brainly.com/question/21107621

#SPJ11

The within-group estimate of variance is the estimate of the variance of the population of individuals based on the variation among the scores in each of the actual groups studied.

The within-groups estimate of variance is the estimate of the variance of the population of individuals based on the variation among the:
Scores in each of the actual groups studied.
This estimate represents the variation within each group and helps in understanding the population's variance by looking at individual differences within the groups.

The estimated within-group variance is the sum of the within-group variances for each group in the model. Effectively, this is the sum of the variance of each value (j) from its group (i) divided by the sample size minus one.

Learn more about Variance:

brainly.com/question/13708253

#SPJ11

Answer:

70 students and 130 adults

Step-by-step explanation:

Graph theory is relevant in the design of network topologies such as roads, satellite air traffic control stations, etc. It helps in analyzing and optimizing network structures.

In the context of a Jamaica road area network managed by the National Works Agency (NWA), graph theory can be applied to study various theoretical properties.

A personalized road graph network with at least 20 nodes is created, and its features are explained based on graph theory principles. Additionally, the Dijkstra matrix is generated to support the properties of the depicted graph.

Graph theory provides a framework for studying and analyzing network structures. In the design of road networks, graph theory concepts can be applied to understand the connectivity, efficiency, and optimization of routes. For example, in the Jamaica road area network managed by the NWA, the personalized road graph network can be created to capture the relationships between different road intersections or nodes. The nodes represent locations, and the edges represent the road segments connecting them.

Theoretical properties of the road graph network can be analyzed using graph theory. These include concepts such as connectivity, shortest paths, degree centrality, and clustering coefficients.

Connectivity determines the connectivity between different parts of the road network, while shortest paths help identify the most efficient routes between nodes. Degree centrality measures the importance of a node in terms of the number of connections it has, and clustering coefficients analyze the presence of clusters or groups of nodes.

To support these properties, the Dijkstra matrix can be generated. The Dijkstra algorithm finds the shortest paths between nodes in a graph, which can be used to construct the Dijkstra matrix.

This matrix provides information about the distances or costs between nodes, aiding in the analysis of the road network's efficiency and connectivity.

In summary, graph theory plays a crucial role in the design and analysis of network topologies, including road networks. The personalized road graph network for the Jamaica road area network demonstrates how theoretical properties can be applied and analyzed using graph theory concepts.

The generated Dijkstra matrix further supports the understanding of the graph's properties, such as connectivity and shortest paths.


To learn more about graph theory visit:
brainly.com/question/29892828

#SPJ11

Answer:

65 sq ft

Step-by-step explanation:

SA(sq pyr) = area of base + 1/2(perimeter of base)x(slant height)

SA = 5² + 1/2(10)(8)

SA = 25 + 40

SA = 65

Answer: Its D i just took the test

Step-by-step explanation:

The complete question is:

Fred's Donuts is installing new equipment in its bakery. Many employees are fearful they will not be able to operate it. Which of the following courses of action is best for Fred to use to overcome this employee resistance?

A) threaten the employees who resist the change

B) present distorted facts to the employees

C) terminate employees who resist the change

D) educate employees and communicate with them

The answer is option D) educate employees and communicate with them.

Threatening employees (option A) is not a productive or ethical approach. It can create a negative and hostile work environment, leading to decreased morale and potential legal consequences.

Presenting distorted facts (option B) is dishonest and can lead to mistrust among employees. Providing accurate and transparent information is crucial for building trust and gaining employee support.

Terminating employees (option C) solely based on their resistance to change is not an effective solution. It is important to engage with employees and understand their concerns before considering any drastic actions such as termination.

Educating employees and communicating with them (option D) is the recommended approach. This involves providing thorough training on how to operate the new equipment, addressing any concerns or fears employees may have, and ensuring open lines of communication throughout the process. By involving employees in the decision-making and change implementation, they are more likely to feel valued and willing to adapt to the new equipment.

Overall, a collaborative and supportive approach that focuses on education, communication, and addressing employee concerns is the most effective way to overcome resistance to change in this scenario.

Learn more about employee resistance: https://brainly.com/question/33204926

#SPJ11

The equation that represent the relationship of the coffees is 3x + 5y = 68.

At a coffee shop, two sizes of coffee are sold. A medium coffee costs $3, and a large coffee costs $5.

The equation that represent the relationship between the number of medium coffees sold, x, and the number of large coffees sold, y, in an hour where sales totalled $68 is as follows:

where

Therefore, the equation is as follows:

3x + 5y = 68

learn more on equation here:https://brainly.com/question/14177953

#SPJ1

We use ANOVA to test for differences between population means by examining the amount of variability between the samples relative to the amount of variability within the samples. Hence, it is TRUE

The statistical analysis tool known as analysis of variance (ANOVA) divides the observed aggregate variability present in a data set into two categories: systematic variables and random components. The random factors have no statistical impact on the presented data set, whereas the systematic factors do. The ANOVA test is used by analysts to ascertain how independent factors in a regression analysis affect the dependent variable.

ANOVA basically stands for analysis of the variance.

Hence, according to above statements, given fact is true.

To learn more about anova, visit:

https://brainly.com/question/23638404

#SPJ4

Answer:

I'm assuming the double minus marks meant 5 and 6 were negative. Answer is 30.

Step-by-step explanation:

\(17+\abs(-12--5)-(-6)\\17+\abs(-12+5)-(-6)\\17+\abs(-7)-(-6)\\17+7-(-6)\\17+7--6\\24--6\\24+6\\30\)

Answer:The answer would be 28

Step-by-step explanation:17-6 is 11

                                            The absolute value of -12-5 is 17

                                               17+11=28

                                            So therefore the answer would be 28.

Answer:

Step-by-step explanation:

Discussion

A: incorrect. the minus turns the parabola upside down and you would get a maximum, not a minimum.

B: incorrect. The + 1 moves the parabola upwards not downwards.

C: incorrect. The - 3 turns the parabola upside down. You get a maximum, not a minimum.

D: correct. The parabola moves right (x - 3)^2 which anti intuitive, but it is correct. - 5 moves the parabola down. +8 the plus makes a minimum.

Answer:

x2 + 8 = 28

The value of x2 is 4.48

Step-by-step explanation:

Hope this is what you were asking for :)

Answer:

B. 40

Step-by-step explanation:

(4x-120)

plug in your x value

(4x40-120)

multiply

(160-120)

subtract

40

Answer/Step-by-step explanation:

To find the volume of a rectangular prism, multiply the length by the width by the height. The product of the formula will provide the volume of the box in cubic feet.

Volume formula: V = L x W x H

Answer: c

Step-by-step explanation:

Answer:

Step-by-step explanation:

Remember PEMDAS

2 - 8 : (2^4 : 2) =

2 - 8 : (16 : 2) =

2 - 8 : 8 =

2 - 1 =

The surface area of the box as a function of x will be f(x) = x² + 20000/x² where x is the length of the square base's edge.

Here it is given that the box has a square base.

This implies that length = breadth

Now, the volume of a box = lbh = 5000 cu in

where l is the length of the box. b is the breadth of the box, and h is the height of the box.

or, x²h = 5000

or, h = 5000/x²

Let the surface area function be f(x) where x is the length of the edge of the square base.

Since the box is open, the surface area will be

lb + 2bh + 2lh

= x² + 10000/x² + 10000/x

= x² + 20000/x²

Hence the surface area as a function of x will be

f(x) = x² + 20000/x²

To learn more about function visit

https://brainly.com/question/14002287

#SPJ4

Let's start by substituting the right-hand side of the equation into the left-hand side:

What does the math equation mean?

Two expressions are combined by the equal sign to form a mathematical statement known as an equation. For instance, a formula might be 3x - 5 = 16. After solving this equation, we learn that the value of the variable x is 7.

4y - 3 = 4(y + 1)

4y - 3 = 4y + 4

Now, we can isolate y by subtracting 4y from both sides:

0 = y + 4

-4 = y

So, there is a solution to the equation: y = -4. This means that Dawson is incorrect in saying that the equation has no solution.

Learn more about equation

https://brainly.com/question/2972832

#SPJ1

Answer:

I'm pretty sure that it's C.

Answer:

The mean number of deliveries for driver A is less than the mean for driver B by 1 MAD.

Step-by-step explanation:

Test appoved

A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = –16t² + 40t + 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are –0.2 s and 2.7 s.

the solution to be eliminated is -0.2s this is because time do not have negative values

ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a.

It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be real or complex.

Considering the given function, the answer is both real one is negative the other is positive.

The solution in this case represents time, and time of negative value do not apply in real life

Learn more about quadratic equation at:

https://brainly.com/question/1214333

#SPJ1

Answer:

eu não entendo seu idioma vale

Answer:

The factors that multiply to equal

x^2  - 13x  + 42 = 0

is

(x-6)(x-7) = 0

So,

(x-6) = 0

x = 6

(x-7) = 0

x = 7

6, and 7, are the solutions. They are asking for PRODUCT of the solutions, which means to multiply.

So, 6 times 7 = 42.

The answer is 42

By working with the exponential equation we will get:

i) N = 1000

ii) k = -0.02

iii) t = 34.66 seconds

Here we know that the equation:

\(N = 1000*e^{-k*t}\)

models the population at a time t.

i) When t = 0, we have:

\(N = 1000*e^{-k*0}\\N = 1000*1\\N = 1000\)

That is the initial population of bacteria.

ii) at t = 0, the rate of decay is -20 /min

the differentiation of the exponential gives:

\(N' = -k*1000*e^{-k*t}\)

And evaluating that in t = 0 should give -20., then:

\(-20 = -k*1000*e^{-k*t}\\\\-20 = -k*1000\\-20/1000 = -k\\-0.02 = -k\\0.02 = k\)

That is the value of k.

iii) Here we need to solve the equation:

\(500= 1000*e^{-0.02*t}\\\\0.5 = e^{-0.02*t}\\\\ln(0.5) = ln(e^{-0.02*t})\\\\ln(0.5) = -0.02*t\\\\ln(0.5)/ -0.02 = t\\ \\34.66 = t\)

So it will take 34.66 seconds to reach half of the initial population.

Learn more about exponential equation at:

https://brainly.com/question/11832081

#SPJ1

The output is given by:r= t-3

For the inputs,

t=17

The output is

r=17-3=14

For the input, t=20

The output is:

r=20-3=17

For the input, t=22

The output is

r=22-3=19.

For the input, t=24

The output is

r=24-3=21

The equation is 967.50 = 450 + 28.75p which models the situation. The team could bring 18 players to the tournament.

Setting up an equation based on the given information.

Let p be the number of players on the team.

Then the total amount of money spent on meals will be 28.75p.

The total amount of money spent on the bus and meals will be 450 + 28.75p.

Since they spent all the money they raised, the equation models the situation as follows:

967.50 = 450 + 28.75p

To solve for p, subtract 450 from both sides:

517.50 = 28.75p

Then divide both sides by 28.75:

p = 18

Therefore, the team could bring 18 players to the tournament.

Learn more about the equation here:

https://brainly.com/question/3228020

#SPJ1

The complete question is as follows:

Members of a baseball team raise $967.50 to go to a tournament. They rented a bus for $450.00 and budgeted $28.75 per player for meals. They will spend all the money they raised.

Write and solve an equation that models the situation and could be used to determine the number of players, p, the team could bring to the tournament.

Step-by-step explanation:

(9/8)÷(45/60)=27/32 cups per unit hour