A polygon has vertices whose coordinates are A(1.4), B(4, -1), C(-1,-4), and D(-4,1). Use the midpoint formula to determine whether or not the diagonals of polygon ABCD bisect each other. In your final answer, include all of your calculations.​

Answer:

y = 29.2x + 24363

Step-by-step explanation:

X = number of years after 1984 ;

X:

0

3

10

17

22

Y:

25000

25077

22257

25437

25565

Using the online linear regression calculator, the line of best fit obtained after preparing the model parameters is ŷ = 29.2075X + 24363.44197

Approximately;

y = 29.2x + 24363

With :

y being the population value

x = number of years after 1984

Slope = 29.2

Intercept = 24363

By cross multiplication, the result for each pair of rational numbers are listed below:

Cross multiplication is a property involving multiplication and division between the terms of two rational numbers of the form:

a / b = c / d

Where a, b, c, d are real numbers. Combinations between a numerator and a denominator are multiplications and combinations between two numerators and two denominators are divisions. Now we proceed to solve on each case:

Case 11

4 / x = 2 / 7

4 · 7 = 2 · x

28 = 2 · x

x = 14

Case 12

19 / 10 = x / 12

19 · 12 = 10 · x

228 = 10 · x

x = 114 / 5

Case 13

(x - 1) / 6 = 13 / 19

(x - 1) · 19 = 13 · 6

(x - 1) · 19 = 78

x - 1 = 78 / 19

x = 1 + 78 / 19

x = 97 / 19

Case 14

5 / 17 = 19 / (x + 4)

5 · (x + 4) = 19 · 17

x + 4 = 323 / 5

x = 318 / 5

Case 15

10 / (2 · x - 9) = 20 / 9

10 · 9 = 20 · (2 · x - 9)

90 / 20 = 2 · x - 9

27 / 2 = 2 · x

27 / 4 = x

x = 27 / 4

Case 16

12 / 18 = (3 · x + 4) / 15

2 / 3 = (3 · x + 4) / 15

10 = 3 · x + 4

3 · x = 6

x = 2

Case 17

(x - 20) / 3 = (x - 11) / 18

18 · (x - 20) = 3 · (x - 11)

18 · x - 360 = 3 · x - 33

15 · x = 327

x = 109 / 5

Case 18

6 / (x + 16) = 7 / (3 · x + 3)

6 · (3 · x + 3) = 7 · (x + 16)

18 · x + 18 = 7 · x + 112

11 · x = 94

x = 94 / 11

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Answer:

yes, you can graph parametric equations there. (It's called Desmos, by the way, not “Demos.”) Click on the triple-bar symbol at the top left, which takes you to a drop-down menu. Scroll down that menu until you see the entries for parametric equations. Hope this helps!

Step-by-step explanation:

pls say thx

Answer:

3/12

Step-by-step explanation:

the entire bag has 12 skittles. there are only 3 red. This gives a fraction of red skittles/entire bag in order to get the probability. So this would be 3/12 in this most basic sense? I am not sure if you need to go further than this or not. Hope this helps!

To determine the necessary sample size to obtain an interval width of 50 ppm for a confidence level of 95%, we need to use the formula for sample size calculation for estimating a population mean.

The formula for sample size calculation is:

n = (Z * σ / E)^2

In this case, the desired margin of error is 50 ppm, which means the interval width is 2 * E = 50 ppm. Therefore, E = 25 ppm.

The Z-score corresponding to a 95% confidence level is approximately 1.96.

Given that the investigators made a rough guess of 175 for the value of σ (standard deviation) before collecting data.

We can substitute these values into the sample size formula:

n = (1.96 * 175 / 25)^2

Simplifying the calculation:

n = (7 * 175)^2

n = 1225^2

n ≈ 1,500,625

Therefore, a sample size of approximately 1,500,625 would be necessary to obtain an interval width of 50 ppm for a confidence level of 95%.

To obtain an interval width of 50 ppm with a confidence level of 95%, a sample size of approximately 1,500,625 is required. This is calculated using the formula for sample size estimation, considering a desired margin of error of 25 ppm and a standard deviation estimate of 175. The Z-score corresponding to a 95% confidence level is used to determine the sample size.

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Step-by-step explanation:

The answer is A

Bcz In a race runs faster whoever does it in less time

Answer:

Y=3x+5

Step-by-step explanation:

if s and l are independent, both should be accepted False.

If s and l are independent, it means that the occurrence of one event does not affect the occurrence of the other event. However, this does not necessarily mean that both events should be accepted. It depends on the specific criteria and requirements for acceptance of each event.

Therefore, the statement "if s and l are independent, both should be accepted" is false.


If s and l are independent, it means that they have no direct influence on each other. However, this does not necessarily mean that both should be accepted. The acceptance of s and l will depend on their individual merits and the specific context or criteria being considered.

The independence of s and l does not automatically imply that both should be accepted. Instead, evaluate each one separately based on the relevant factors.

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True. If s and l are independent variables, then accepting one does not affect the acceptance or rejection of the other. Therefore, both can be accepted if they meet the necessary criteria.

However, it's important to note that this assumption of independence should be confirmed through statistical analysis before making any conclusions.

If s and l are independent variables, then accepting one does not affect the acceptance or rejection of the other. This means that both can be accepted if they meet the necessary criteria. However, it's important to ensure that this assumption of independence is valid before making any conclusions. The independence of the variables can be tested through statistical analysis. Therefore, it's essential to examine the relationship between s and l before accepting or rejecting them. In general, if s and l are independent, then both can be accepted without any issues.

In conclusion, if s and l are independent variables, then both can be accepted. However, the independence assumption should be confirmed before making any decisions. This can be achieved through statistical analysis, which is a crucial step in data analysis.

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Answer: Y= -2/-18 or Y= 0.1111X=-2(-0.1111) +1or X=0.77778

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

\(\frac{5(x-2)}{3} = -x + 2\)

expand left side:

\(\frac{5(x-2)}{3} = -x + 2\\\\\frac{5x-10}{3} = -x + 2\)

multiply both sides by 3:

\(3(\frac{5x-10}{3}) = 3(-x + 2)\\\\ =5x - 10 = -3x + 6\)

Add 3x to both sides:

5x - 10 + 3x = -3x + 6 + 3x

8x - 10 = 6

add 10 to both sides:

8x - 10 + 10 = 6 + 10

8x = 16

divide both sides by 8:

8x/8 = 16/8

x = 2

The solution of the quadratic equation 8x² – 5x – 4 = 0 will be 1.085 and negative 0.460.

The solution of the equation means the value of the unknown or variable.

The quadratic equation is given below.

8x² – 5x – 4 = 0

Then we have

a = 8, b = -5, c = -4

Then the solutions will be

\(\rm x = \dfrac{-b\pm \sqrt{b^2 - 4ac}}{2a}\\\\\\\rm x = \dfrac{-(-5)\pm \sqrt{(-5)^2 - 4 * 8 * (-4)}}{2 * 8 }\\\\\\x = \dfrac{5 \pm 12.37}{16}\\\\\\x = \dfrac{5- 12.37}{16}, \dfrac{5 +12.37}{16}\)

On further solving, we have

x = 1.085, -0.460

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Answer:

E.  12

Step-by-step explanation:

The ratio of the lengths of the sides of a 30-60-90 triangle is

short leg : long leg : hypotenuse

1 : √3 : 2

The short leg is 4√3.

The long leg is √3 times the short leg.

a = 4√3 * √3 = 4 * √9 = 4 * 3 = 12

Answer: E.  12

We can use the Integral Test to test the convergence of this series.

The Integral Test states that if f(x) is a positive, continuous, and decreasing function for all x >= N, where N is some positive integer, and if a_n = f(n), then the series ∑a_n converges if and only if the improper integral ∫N^∞ f(x)dx converges.

In this case, we have:

a_n = ln(8n)/n

We can check that a_n is positive, continuous, and decreasing for n >= 5, so we can apply the Integral Test.

We have:

∫5^∞ ln(8x)/x dx

Let u = ln(8x), du/dx = 1/x dx

Substituting:

∫ln(40)^∞ u e^(-u) du

Integrating by parts:

v = -e^(-u), dv/du = e^(-u)

∫ln(40)^∞ u e^(-u) du = [-u e^(-u)]ln(40)^∞ - ∫ln(40)^∞ -e^(-u) du

= [-u e^(-u)]ln(40)^∞ + e^(-u)]ln(40)^∞

= [e^(-ln(40))-ln(40)e^(-ln(40))]+ln(40)e^(-ln(40))

= 1/40

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450 miles

Explanation

Step 1

Let

Step 2

how many times the distnce (E-M) is the distance(E-S)

so, the distance is

I hope this helps you

Answer:

y = -(×)+7

Step-by-step explanation:

y+2 = -× + 5

y = -(×) + 7

Answer:

40 pints

Step-by-step explanation:

1 gallon = 8 pints so 5x8= 40

Answer:

5-gallons=40 pints

Step-by-step explanation:

You need to multiply the number of gallons by 8.

5*8=40

40 pints would be the answer.

Answer:

268

Step-by-step explanation:

268+308-126=450

(a) To show that there can be at most 14 abundant circles, we can use the combination formula.

(b) There cannot be 14 abundant circles.

To see why, consider that each circle contains 4 points. If there were 14 abundant circles, then there would be a total of 14 * 4 = 56 points involved.

Since a circle abundant if it passes through at least 4 points of S, we can select any 4 points from the set S to form a circle. The number of ways to choose 4 points out of 8 is given by the combination formula:

C(8, 4) = 8! / (4!(8-4)!) = 70

Therefore, there can be at most 70 abundant circles.

However, this count includes some cases where multiple circles pass through the same 4 points. To eliminate these duplicates, we can consider the maximum number of unique sets of 4 points that can form abundant circles.

(b) There cannot be 14 abundant circles.

To see why, consider that each circle contains 4 points. If there were 14 abundant circles, then there would be a total of 14 * 4 = 56 points involved. However, we are given that the set S has only 8 points. Therefore, it is not possible to have 14 abundant circles.

The maximum number of abundant circles can be determined by considering the maximum number of unique sets of 4 points. Since there are C(8, 4) = 70 unique sets of 4 points, the maximum number of abundant circles is 70.

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Jake wants to post a 600 gram parcel and an 800 gram parcel.

He posts them Second Class.

He pays with a £10 note.

How much change should he get?

Siren moves toward you for 2 s but doesn't reach you, then reverses direction at t = 2 s and moves away. Option C is correct.

The graph shows the frequency you hear as you stand at rest at x = 0 on the x-axis.

At t = 0 s, the frequency of the sound wave is fo.

From t = 0 s to t = 2 s, the frequency of the sound wave increases as the siren moves toward you, however it does not reach you.

At t = 2 s, the siren reverses direction and moves away from you.

Therefore, the correct description of the siren's motion is Option C: It moves toward you for 2 s but doesn't reach you, then reverses direction at t = 2 s and moves away.

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1. When the scientist started, there were 1.9477 thousand frogs

2. The frog population in month 17 is 1.2499 thousand frogs.

3.  The frog population will be above 400 frogs in 3rd month.

1. To find how many frogs were there when the scientist started, we need to find the population at month 0, which can be calculated by evaluating S(x) at x = 0:

\(S(0) =-0.0523 - 25(0)^2 + 6.34(0) + 2\)

         =  1.9477    

   Therefore, there were approximately 1.9477 thousand (1,947.7) frogs when the scientist started.

2. To find the approximate frog population in month 17, we need to evaluate S(x) at x = 17:

\(S(17) =-0.0523 - 25(17)^2 + 6.34(17) + 2\)

≈ 1.2499

   Therefore, the approximate frog population in month 17 is 1.2499 thousand (1,249.9) frogs.

3. To find the approximate frog population in month 17, we need to solve the equation S(x) = 0.4 (since S(x) is in thousands):

\(-0.0523 - 25x^2 + 6.34x + 2 = 0.4\)

Simplifying and rearranging, we get:

\(25x^2 - 6.34x + 2.4523 = 0\)

Using the quadratic formula, we can solve for x:

\(x = (-b \pm \sqrt{(b^2 - 4ac)}) / 2a\)

where a = 25, b = -6.34, and c = 2.4523

Plugging in the values, we get:

\(x = (-(-6.34) \pm \sqrt{((-6.34)^2 - 4(25)(2.4523))}) / 2(25)\)

x ≈ 2.56 or x ≈ 0.16

We can ignore the negative root since the population cannot be negative.

Therefore, the frog population will be above 400 frogs in approximately the 3rd month (since we started counting from x = 0).

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Answer:

Not parallel  

Step-by-step explanation:

Could be   perpindicular    or   not parallel

If the family size sunscreen bottle holds 12 fl oz (fluid ounces) of sunscreen, while the regular bottle has 75% less, we will then convert the percentage into fluid ounces with the following calculation:

75/100×12=9

From the calculation above, we know the difference in the liquid content between both bottles; the regular size bottle of sunscreen has 9 fl oz (fluid ounces) less liquid content. So the liquid content of a regular sunscreen bottle is 3 fl oz (fluid ounces)

You asked an incomplete question, so I assume your complete question was:

"The family size bottle of sunscreen holds 12 fluid ounces of sunscreen. The regular bottle holds 75% less. How many fewer fluid ounces does the regular bottle hold?"

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A bicycle repair shop that offers two service packages: a tune-up and a complete overhaul.

The shop operates for 60 hours per week and receives an average of 180 bicycles each week. To analyze the capacity and utilization of the process, we need to consider the time taken at each stage and the demand for each service option. We'll break down the problem into multiple parts and provide a detailed explanation using mathematical terms.

a) Creating the Demand Matrix:

To create a demand matrix, we need to determine the number of bicycles going through each stage of the process. Let's denote the demand for tune-up as T and the demand for additional services as A.

Given that the average number of bicycles received per week is 180 and 25% of customers opt for additional services, we can calculate the demands as follows:

Demand for tune-up (T) = Total demand - Demand for additional services

T = 180 - (0.25 * 180)

T = 180 - 45

T = 135

Demand for additional services (A) = 0.25 * Total demand

A = 0.25 * 180

A = 45

Now, we can create a demand matrix based on the demand for each service option:

Demand Matrix:

Tune-up Additional Services Wheel Balancing

Tune-up  [135  0  0]

Additional [0  45  0]

Services

Total [ 135  45  0 ]

The demand matrix shows the number of bicycles flowing through each stage of the process.

b) Daily Capacity at Each Stage:

To calculate the daily capacity at each stage, we need to consider the time taken for each service option. Given that the shop operates for 60 hours per week, we can calculate the daily capacity at each stage:

Tune-up technician time per bicycle (\(T_{tuneup}\)) = 75 minutes

Additional services technician time per bicycle (\(T_{additional}\)) = 72 minutes

Wheel balancing specialist time per bicycle (\(T_{balancing}\)) = 20 minutes

Daily Capacity (C) = (60 hours * 60 minutes) / (\(T_{tuneup}\) + \(T_{additional}\) + \(T_{balancing}\))

Substituting the given values:

C = (60 * 60) / (75 + 72 + 20)

C = 21600 / 167

C ≈ 129.34 bicycles per day

Therefore, the daily capacity at each stage of the process is as follows:

Tune-up: 129 bicycles per day

Additional Services: 129 bicycles per day

Wheel Balancing: 129 bicycles per day

c) Implied Utilizations:

To find the implied utilizations, we need to compare the demand and the capacity at each stage of the process. Utilization can be calculated as the demand divided by the capacity.

Implied Utilization (U) = Demand / Daily Capacity

For the Tune-up stage:

\(U_{tuneup}\) = 135 / 129 ≈ 1.05

For the Additional Services stage:

\(U_{additional}\) = 45 / 129 ≈ 0.35

For the Wheel Balancing stage:

\(U_{balancing}\) = 0 / 129 = 0

The implied utilizations show how efficiently each stage of the process is being utilized. Utilization values greater than 1 indicate that the stage is operating beyond its capacity.

d) Weekly Capacity of the Process:

To calculate the weekly capacity of the process, we multiply the daily capacity by the number of days the shop is open per week:

Weekly Capacity = Daily Capacity * Number of days shop is open per week

Given that the shop is open for 60 hours per week, the number of days the shop is open per week can be calculated as follows:

Number of days shop is open per week = 60 hours / 24 hours per day = 2.5 days

Therefore, the weekly capacity of the process is:

Weekly Capacity = Daily Capacity * Number of days shop is open per week

Weekly Capacity = 129 bicycles per day * 2.5 days

Weekly Capacity = 322.5 bicycles per week

e) Flow Rate and Constraint Analysis:

To determine if the flow rate of the process is capacity-constrained or demand-constrained, we compare the weekly capacity to the demand for each service option.

Demand for Tune-up (\(T_{demand}\)) = 135 bicycles per week

Demand for Additional Services (\(A_{demand}\)) = 45 bicycles per week

Comparing the demands with the weekly capacity:

\(T_{demand}\) < Weekly Capacity (135 < 322.5)

\(A_{demand}\) < Weekly Capacity (45 < 322.5)

Since both the demands for tune-up and additional services are less than the weekly capacity, the flow rate of the process is demand-constrained. This means the shop has the capacity to handle the current demand without operating beyond its limits.

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We cannot reject null hypothesis because -1.68 is not smaller than the critical value of -2.064

Null Hypothesis: The null hypothesis assumes that any kind of difference between the chosen characteristics that you see in a set of data is due to chance. For example, if the expected earnings for the gambling game are truly equal to zero, then any difference between the average earnings in the data and zero is due to chance.

given that a two-tail test is conducted with a sample size of 25

and the value of the t statistic is -1.68. at the 5% level of significance

we know that the critical value is of -2.064

we cannot reject null hypothesis because -1.68 is not smaller than the critical value of -2.064

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Answer:

Step-by-step explanation:

They already said the domain of f(x) is x≥0.

The smallest value of f(x) is f(0) = 9.

Range of f(x) is y≥9.

The radicand of a square root must be non-negative, so the domain of f⁻¹(x) is x≥9.

The range is y≥0.

(2n + 1)² - (2n + 1) is an even number for all positive integral values of n.

How to simplify an expression?
Expressions are simplified when they are rewritten in a concise manner and without any similar phrases. When we combine like terms in an expression and, if necessary, solve all of the specified brackets, we are only left with unlike terms in the simplified expression that cannot be further reduced.
What is an even number?
An even number is any number that can be divided by 2 precisely. The last digit of an even number is always one of the following: 0, 2, 4, 6, or 8. Even numbers can include 2, 4, 6, 8, 10, 12, and 14. These are even numbers because they are simple to divide by two. It is important to remember that 2 is the smallest positive even natural number.

Given, the equation under consideration is y = (2n + 1)² - (2n + 1)
Upon simplifying and solving for y, we have:
y = (2n + 1)² - (2n + 1) = 4n² + 4n + 1 - 2n - 1 ⇒ y = 4n² + (4n - 2n) + (1 - 1)
⇒ y = 4n² + 2n + 0 ⇒ y = 2 (2n² + n) --(i)
On carefully analyzing (i), we can affirm that y is divisible by 2, thus confirming that (2n + 1)² - (2n + 1) is an even number for all positive integral values of n.
Therefore, (2n + 1)² - (2n + 1) is an even number for all positive integral values of n.

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