Parallelogram proof please

The critical values of x are 31.319, 18.475, and 28.869 for each case respectively.

To find the critical values of x (x₂), we'll use the chi-square distribution table. The critical values depend on the degrees of freedom (df) and the significance level (α).

1. For n=14 and α=0.005:
  Degrees of freedom (df) = n - 1 = 14 - 1 = 13
  From the chi-square table, x₂ (13, 0.005) ≈ 31.319

2. For n=8 and α=0.01:
  Degrees of freedom (df) = n - 1 = 8 - 1 = 7
  From the chi-square table, x₂ (7, 0.01) ≈ 18.475

3. For n=18 and α=0.02:
  Degrees of freedom (df) = n - 1 = 18 - 1 = 17
  From the chi-square table, x₂ (17, 0.02) ≈ 28.869

Know more about critical values here:

https://brainly.com/question/30168469

#SPJ11

To solve this problem, we need to first find the average number of shoppers in the new store at any time.

We know that during business hours, 90 shoppers per hour enter the store and each stays an average of 12 minutes.

To find the average number of shoppers at any time, we need to convert the time each shopper spends in the store to hours:

12 minutes = 0.2 hours

So, on average, each shopper takes up 0.2 hours in the store.

Therefore, the average number of shoppers in the new store at any time is:

90 shoppers/hour x 0.2 hours/shopper = 18 shoppers

Now we can find the percent less that the average number of shoppers in the new store is compared to the original store:

Percent less = (Original - New) / Original x 100%

Percent less = (45 - 18) / 45 x 100%

Percent less = 27 / 45 x 100%

Percent less = 60%

So the answer is A. 60.
To find the average number of shoppers in the new store at any time, we can use the formula:

Average number of shoppers at any time = (Number of shoppers per hour * Average time spent in store) / 60

For the new store:
Average number of shoppers at any time = (90 shoppers per hour * 12 minutes) / 60
Average number of shoppers at any time = 1080 / 60 = 18 shoppers

Now we will find the percentage difference between the average number of shoppers in the original store (45 shoppers) and the new store (18 shoppers):

Percentage difference = ((Original store shoppers - New store shoppers) / Original store shoppers) * 100
Percentage difference = ((45 - 18) / 45) * 100
Percentage difference = (27 / 45) * 100 = 60%

So the average number of shoppers in the new store at any time is 60% less than the average number of shoppers in the original store at any time. Your answer: A. 60

Visit here to learn more about average brainly.com/question/27646993

#SPJ11

The Pacific Northwest region of america is located within the upper northwest corner of the united states of america, bordering to the Pacific Ocean. The state this is most generally located in this place is Washington,

That's home to numerous fundamental cities which include Seattle and Olympia. Oregon, that's located simply south of Washington, is also taken into consideration to be part of the Pacific Northwest.

The vicinity is thought for its various geography, which incorporates lush forests, rugged coastlines, and towering mountains such as Mount Rainier and Mount Hood.

The Pacific Northwest is likewise domestic to a vibrant tradition and economy, with industries which include generation, aerospace, and outside pastime gambling massive roles within the place's boom and development.

Learn more about Pacific Northwest region:-

https://brainly.com/question/31127995

#SPJ4

The equation in point slope form is y -6 = 3(x + 3)

(x₁, y₁) = (-3, 6)

(x₂, y₂) = (-2, 9)

Slope of the line,

m = (y₂ - y₁)/(x₂ - x₁)

m = (9 - 6)/(-2 - -3)

m = 3

Therefore, the equation in point slope form is given as,

(y - y₁) = m(x - x₁)

y - 6 = 3(x - -3)

y -6 = 3(x + 3)

To learn more about equation in point slope form, click:

https://brainly.com/question/28934380

#SPJ1

The given problem is a hypothesis testing problem, specifically a one-sample proportion test.

The null hypothesis is that the proportion of stuffed animals sold is 0.7, and the alternative hypothesis is that it is greater than 0.7. The sample proportion is 400/500=0.8, and we need to test whether this result is statistically significant at a 1% level of significance. We assume a normal distribution for the sample proportion and use a one-tailed z-test to calculate the p-value and make a conclusion about the null hypothesis.

Know more about hypothesis here:

https://brainly.com/question/29519577

#SPJ11

The solution of the linear equation 3(x - 6) - 8x = 2 + 5*(2x + 1) is x = -5/3

Here we want to solve the equation:

3(x - 6) - 8x = 2 + 5*(2x + 1)

First, simplify both sides:

3x - 18 - 8x = 2 + 10x + 5

-5x - 18 = 10x + 7

Now group like terms:

-18 - 7 = 10x + 5x

-25 = 15x

-25/15 = x

-5/3 = x

That is the solution.,

Learn more about linear equations at.

https://brainly.com/question/1884491

#SPJ1

Answer: its-134

Step-by-step explanation:

first you find both of the numbers then subtract the answers to both

x = -1 and x = 3 are the solutions to the equation [tex]-x^2+2x+3=0[/tex].

To solve the quadratic equation[tex]-x^2+2x+3=0[/tex], we can use the quadratic formula:

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

In this case, a = -1, b = 2, and c = 3, so we can substitute these values into the formula:

[tex]x = \frac{(-2 \pm \sqrt{2^2 - 4*1*3)} }{2*-1}[/tex]

x = (-2 ± sqrt(16)) / (-2)

x = (-2 ± 4) / (-2)

Simplifying this expression, we get:

x₁ = (-2 + 4) / (-2) = -1

x₂ = (-2 - 4) / (-2) = 3

Therefore, the solutions to the equation [tex]-x^2+2x+3=0[/tex] are x = -1 and x = 3.

Learn more about Quadratic equations here:

https://brainly.com/question/22364785

#SPJ1

Step-by-step explanation:

The length l meter of the cylinder will be 80 meters on rounding to the nearest whole number.

The volume of cylinder is given by the formula -

Volume = πr²h, where r refers to the radius of the base of cylinder and h is the height of the cylinder. Now, keep the values in formula to find the height or length of the cylinder.

156000 = π× 25² × l

l = 156000/(π × 25 × 25)

Rewriting the equation and performing multiplication

l = 79.45 meters

Rounding to the nearest whole number, the length will be 80 meters.

Hence, the length of the cylinder is 80 meters.

Learn more about cylinder -

https://brainly.com/question/23935577

#SPJ1

The complete question is attached in figure.

If "exponential-function" is "5ˣ + 6", then (a) Domain: All real numbers

Range: All real numbers greater than 6.

The "Domain" of an exponential function is all real numbers, since any real number can be raised to a power. The range, depends on the value of the base and any vertical shift that is applied to the function.

In the given function F(x) = 5ˣ + 6, the base is 5 which is greater than 1. Therefore, as x approaches negative infinity, F(x) approaches 6, and as x approaches positive infinity, F(x) grows without bound.

It means that the range of the function is all real-numbers greater than 6.

Therefore, the correct option is (a).

Learn more about Domain and Range here

https://brainly.com/question/27242650

#SPJ1

The given question is incomplete, the complete question is

What are the domain and range of the exponential function below?

F(x) = 5ˣ + 6,

(a) Domain: All real numbers

Range: All real numbers greater than 6

(b) Domain: All real numbers greater than 0

Range: All real numbers greater than 0

(c) Domain: All real numbers greater than 0

Range: All real numbers greater than 6

(d) Domain: All real numbers

Range: All real numbers greater than 0

An expression for the given model can be simplified as -x - 2.

Given a model.

The model consists of 2 times x and 3 times -x.

This can be written as 2x + (3 × -x) = 2x - 3x = -x

It also consists of some 1's and '-1's.

In the first column, there are 3 1's = 3

Next, there are 2 1's and 1 '-1' = 2 + -1 = 1

Next, there are 3 '-1's = -1 + -1 + -1 = -3

Next also = -1 + -1 + -1 = -3

So summing up all these,

Expression is -x + 3 + 1 - 3 - 3 = -x - 2

Hence the required expression is -x - 2.

Learn more about Expressions here :

https://brainly.com/question/13947055

#SPJ1

Using a Z-table, the probability of having a z-score less than 9.33 is virtually 1.000, or 100%.

The stand time for commercial jets is a random variable with a mean of 2 minutes and a standard deviation of 3 minutes. Assuming the distribution of times is approximately normal, we can calculate the probability of certain events.

(a) To find the probability that the wait time is less than 30 minutes, we can standardize the value and use a standard normal distribution table (also known as a Z-table).

First, calculate the z-score:
z = (X - μ) / σ
z = (30 - 2) / 3
z = 28 / 3
z ≈ 9.33

This means it is almost certain that the wait time will be less than 30 minutes.

Know more about probability here:

https://brainly.com/question/30034780

#SPJ11

Tatum earns more than Real.

We have,

Real works 36 hours a week and makes $612.

Tatum works 34 hours a week and makes $663

So, per hour earning of Real is

= 612 / 36

= $17

and, per hour earning of Tatum is

= 663 / 34

= $19.5

Thus, Tatum earns more than Real.

Learn more about Unitary Method here:

https://brainly.com/question/22056199

#SPJ1

The correct surface area of the cylinder is  878.06 sq. cm.

From the net of the cylinder we have the diameter of the circular bases of the cylinder.

So, the radius of the circle would be,

r = 13/2

Using the formula for area of circle the surface area of two circular bases would be,

A₁ = 2 × π × r²

A₁ = 2 × π × (13/2)²

A₁ = π × 169/2

A₁ = 265.46 sq. cm.

The length of the rectangle would be equal to the circumference of the circle.

So, the length of the rectangle would be,

l = 2× π × r

l = 2× π × (13/2)

l = 13 × π

l = 40.84 cm

Using the formula for the area of rectangle,

A₂ = l × w

A₂ = 40.84 × 15

A₂ = 612.6 sq. cm.

So, the total surface area of the cylinder would be,

A = A₁ + A₂

A = 265.46 +  612.6

A = 878.06 sq. cm.

This means that the surface area claimed by Talia is incorrect.

Therefore, the correct surface area of the cylinder =  878.06 sq. cm.

Learn more about the surface area of cylinder here:

https://brainly.com/question/22074027

#SPJ1

Using a z-table or calculator, we can find that the probability of getting a z-score less than -3.14 is approximately 0.0008 (rounded to four decimal places as requested).

Using the Empirical Rule and the concept of probability, I can help you find the requested probability. The Empirical Rule, also known as the 68-95-99.7 rule, states that for a normal distribution:

- Approximately 68% of the data falls within 1 standard deviation (SD) of the mean
- Approximately 95% of the data falls within 2 SDs of the mean
- Approximately 99.7% of the data falls within 3 SDs of the mean

You are asked to find the probability P(z < -3.14). Since -3.14 is slightly beyond -3 SDs from the mean, we know that less than 0.15% of the data falls in that area, as 99.7% of the data is within ±3 SDs.

However, to get a more precise probability, we need to use a standard normal (Z) table or calculator. When looking up z = -3.14, we find that the probability P(z < -3.14) is approximately 0.0008.

So, the probability you are looking for is 0.0008.

Learn more about probability here:

https://brainly.com/question/11234923

#SPJ11

The values of the trigonometry are as follows

8. cos x = 9/17

10. sin x = 0.8

12. cos x = 4/5

From trigonometry: cos² x + sin² x = 1

Let the angle be x

8.

cos² x + sin² x = 1

cos² x + (4√13)/17 = 1

cos² x = 1 - (4√13)/17

cos² x = 81 / 289

cos x = √(81 / 289)

cos x = 9/17

10.

sec x = 5/3 and sec x = 1 / cos x, therefore

cos x = 3/5

x = arc cos 3/5

x = 53.1301

sin x = 0.8

12.

sec x = 5/4 and sec x = 1 / cos x, therefore

cos x = 4/5

Learn more about trigonometry at

https://brainly.com/question/24349828

#SPJ1

Answer:

  10

Step-by-step explanation:

You want a number such that the square root of the sum of it and 8 is 3 times the square root of 2.

The relation in the problem statement is ...

  √(x +8) = 3√2

Squaring both sides, we have ...

  x +8 = 3²·2 = 18

  x = 10 . . . . . . . . . subtract 8

The number is 10.

<95141404393>

To find the probability that a customer has to wait more than 4 minutes, we need to use the normal distribution and standard deviation.

If the manager knows the standard deviation, we can use it to calculate the z-score and find the probability using a standard normal distribution table. However, since the standard deviation is not given in this question, we will assume that the distribution of waiting times is approximately normal and use the empirical rule.
The empirical rule states that for a normal distribution, approximately 68% of the values lie within one standard deviation of the mean, approximately 95% lie within two standard deviations, and approximately 99.7% lie within three standard deviations.
Since the average time that customers wait is 3 minutes, and we want to find the probability that a customer waits more than 4 minutes, we need to calculate how many standard deviations away from the mean 4 minutes is.
z = (x - μ) / σ
where x = 4, μ = 3, and σ is the standard deviation. Since we don't know the value of σ, we can't calculate the z-score directly. However, we can make a reasonable assumption that the standard deviation is around 1 minute. This is based on the empirical rule which states that approximately 68% of the values lie within one standard deviation of the mean.
So, σ = 1 minute, and
z = (4 - 3) / 1 = 1
Now we can use a standard normal distribution table to find the probability of a z-score of 1 or greater. From the table, we can see that the probability of a z-score of 1 or greater is approximately 0.1587.
Therefore, the probability that a customer has to wait more than 4 minutes is approximately 0.1587 or 15.87%.

To find the probability that a customer at the fast-food restaurant has to wait more than 4 minutes, we'll use the exponential distribution.
1. First, let's find the rate parameter, which is the reciprocal of the average waiting time: λ = 1 / average waiting time. In this case, λ = 1 / 3 ≈ 0.3333.
2. Now, we'll use the cumulative distribution function (CDF) of the exponential distribution to find the probability of waiting less than or equal to 4 minutes: P(X ≤ 4) = 1 - e^(-λx) = 1 - e^(-0.3333 × 4) ≈ 0.7364.
3. To find the probability of waiting more than 4 minutes, subtract the CDF value from 1: P(X > 4) = 1 - P(X ≤ 4) = 1 - 0.7364 ≈ 0.2636.
So, the probability that a customer at the fast-food restaurant has to wait more than 4 minutes is approximately 0.2636 or 26.36%.

Visit here to learn more about standard deviation:

brainly.com/question/23907081

#SPJ11

Step-by-step explanation:

solve for y

x-4y =24

-4y = 24-x

 y = x/4 - 6    slope = 1/4, the coefficient of the x term

a perpendicular line has the negative inverse,  change the sign and flip the fraction upside down to get -4/1 or -4

y=-4x + b.  plug in the point x=-2, y=7 to calculate b the y intercept

7=-4(-2) + b

b = 7-8 =-1

y=-4x -1 is the perpendicular line through (-2,7)

general equation in slope intercept form is y=mx +b.  m=-4,  b=-1

The area of the parallelogram in the middle outlined in purple is 6 square units

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

So, we have

The area of the parallelogram in the middle is calculated as

Area = base * height

So, we have

Area = (5 - 3) * (6 - 3)

Evaluate

Area = 6

Hence, the area is 6

Read more about area at

https://brainly.com/question/24487155

#SPJ1

A confounding variable is a variable that is related to both the independent variable (hours of revision) and the dependent variable (performance in a college-level Spanish language exam).

In this study, potential confounding variables could include the students' prior knowledge of Spanish, their natural ability in language learning, their level of motivation, their access to study resources, and their level of stress or anxiety. These factors could impact both the amount of time a student spends revising and their performance on the exam, making it difficult to determine if the hours of revision directly caused any changes in exam performance. To control for these confounding variables, researchers may consider randomly assigning students to different revision time groups, measuring these other factors, or using statistical analysis techniques to adjust for these variables.
In your study on the effect of revision hours on college-level Spanish language exam performance among 100 college students, potential confounding variables could include:

1. Prior knowledge of Spanish: Students with previous experience in learning Spanish may perform better than those without, regardless of revision hours.
2. Study habits: The quality of study methods can influence the effectiveness of revision hours.
3. Language aptitude: Some students may naturally possess a higher aptitude for language learning, affecting their exam performance.
4. Instructor quality: The effectiveness of the Spanish language instructor can influence student performance.
5. Sleep and stress levels: Adequate sleep and low stress levels can improve a student's ability to retain information during revision.

To learn more about Instructor visit;

brainly.com/question/14450776

#SPJ11

Answer:

No solution

Step-by-step explanation:

How many solutions does 5 = -5 ?

5 ≠ -5

So, there is no solution

Given that P(Xi > 0), we can infer that the probability of Xi being positive has implications on the convergence properties of the sequence and the limiting constant 'a'.

Based on the information given, we can say that the probability of xi being greater than zero is positive, i.e., p(xi > 0) > 0. This means that xi has a positive probability of taking values greater than zero.

Moreover, since the sequence of random variables converges in probability to a constant a, we can say that for any ε > 0,

lim P(|xi - a| > ε) = 0

This implies that as n approaches infinity, the probability that xi deviates from a by more than ε approaches zero.

Thus, we can conclude that the sequence of random variables xi is "almost surely" bounded away from zero as n approaches infinity, and the limit of the sequence is the constant a.
. Considering a sequence of random variables X1, X2, ..., Xn that converges in probability to a constant 'a', we can say that the probability of each Xi being greater than 0, denoted as P(Xi > 0), is relevant to understanding the limiting behavior of the sequence.

As the sequence converges in probability to 'a', it means that for any given ε > 0, the probability that the absolute difference between Xi and 'a' is greater than ε approaches 0 as n approaches infinity:

lim (n→∞) P(|Xi - a| > ε) = 0

Given that P(Xi > 0), we can infer that the probability of Xi being positive has implications on the convergence properties of the sequence and the limiting constant 'a'.

learn more about probability

https://brainly.com/question/28920252

#SPJ11

Carl Friedrich Gauss, the "Prince of Mathematicians," made groundbreaking contributions to number theory, geometry, physics, and statistics, leaving a lasting impact on the field of mathematics.

We have,

Carl Friedrich Gauss, known as the "Prince of Mathematicians," made significant contributions to number theory, geometry, physics, and statistics.

He formulated the fundamental theorem of arithmetic, developed concepts in differential geometry such as intrinsic curvature and Gaussian curvature, and formulated Gauss's law for electric fields.

Gauss's work laid the foundation for modern mathematics and his emphasis on rigor and precision influenced subsequent generations of mathematicians.

His legacy as one of the greatest mathematicians of all time is based on his profound theorems, laws, and concepts that continue to shape the field.

Thus,

Carl Friedrich Gauss, the "Prince of Mathematicians," made groundbreaking contributions to number theory, geometry, physics, and statistics, leaving a lasting impact on the field of mathematics.

Learn more about mathematicians here:

https://brainly.com/question/30613629

#SPJ12

The solution to the exponential equation 64^a = 8^(a + 2) is given as follows:

a = 2.

The exponential equation in this problem is defined as follows:

64^a = 8^(a + 2)

64 is the second power of 8, hence:

64 = 8².

Applying the power of power rule, we have that:

64^a = 8^2a.

Hence:

8^2a = 8^(a + 2)

The exponential function is one to one, hence we can obtain the value of a as follows:

2a = a + 2

a = 2.

More can be learned about exponential equations at https://brainly.com/question/2456547

#SPJ1

Answer: x=-4

Step-by-step explanation:

i'm assuming that you meant 92-17x=24 instead of -24 because that gives the answer -4

the goal of these equations is to get all the x variables on one side and all of the constants on the other side.

92-17x=-24

92-17x -92 =24 -92

-17x=-68

divide both sides by -17

x = -4

Once the issue is resolved, the seller can try to create or match the product with an ASIN again.

This error message is related to Amazon's Global Trade Item Number (GTIN) requirements. Amazon requires that sellers provide valid GTINs (such as UPC, EAN, or ISBN) for their products. The error message indicates that the SKU (Stock Keeping Unit) provided by the seller does not match any existing ASIN (Amazon Standard Identification Number) and contains invalid attribute values required for the creation of a new ASIN.

To fix this error, the seller should check that the SKU and attribute values are correct and that the product has a valid GTIN. The seller may need to obtain a valid GTIN for their product or correct any errors in the attribute values. Once the issue is resolved, the seller can try to create or match the product with an ASIN again.

To learn more about again visit:

https://brainly.com/question/27993468

#SPJ11

For part (a), we use the product rule and chain rule of differentiation:

y = x^2 sin(8x)

dy/dx = (2x sin(8x)) + (x^2 cos(8x) * 8)

dy/dx = 2x sin(8x) + 8x^2 cos(8x)

So, the differential of y = x^2 sin(8x) is dy = (2x sin(8x) + 8x^2 cos(8x)) dx.

For part (b), the differential is simply the derivative of y with respect to x, since y is not a function of x in this case:

y = 4+

dy/dx = 0

So, the differential of y = 4+ is dy = 0 dx.

To find the differential of each function, we will use the derivative rules. Let's solve each part step-by-step:

(a) y = x^2 sin(8x)

To find the differential (dy) of this function, we will need to find the derivative of y with respect to x (dy/dx). In this case, we will use the product rule, which states that if y = uv, where u and v are functions of x, then:

dy/dx = u(dv/dx) + v(du/dx)

Let u = x^2 and v = sin(8x).

Now, we need to find du/dx and dv/dx:

du/dx = 2x (by using the power rule)
dv/dx = 8*cos(8x) (by using the chain rule)

Now apply the product rule:

dy/dx = x^2 * 8*cos(8x) + sin(8x) * 2x
dy/dx = 8x^2*cos(8x) + 2x*sin(8x)

So, the differential of the function y = x^2*sin(8x) is dy/dx = 8x^2*cos(8x) + 2x*sin(8x).

(b) y = 4

To find the differential (dy) of this function, we will find the derivative of y with respect to x (dy/dx).

Since y is a constant function (it doesn't depend on x), its derivative is simply:

dy/dx = 0

So, the differential of the function y = 4 is dy/dx = 0.

learn more about differential here: brainly.in/question/13142910

#SPJ11