Select ALL the correct answers.
The base of a pentagon lies on ray AB as shown.

An illustration showing a pentagon lying on ray AB, which when extended forms an exterior angle and is marked as 2x plus 14 degrees. The interior angle next to this exterior angle measures 7x plus 13 degrees.

Determine which statements are true.

(2x + 14)° = 48°
x = 7°
(2x + 14)° + (7x + 13)° = 180°
(7x + 13)° = 132°
(2x + 14)° = 90°

A reliable test is one that can measure what it is supposed to measure consistently, yield the same results when given a second time, and provide an unbiased score, ensuring that the results obtained are valid and reliable. Answer is D.

The reliability of a test refers to its consistency and stability over time and under different conditions. It is the extent to which a test is able to yield the same results repeatedly. A reliable test should be able to measure what it is supposed to measure consistently, without any errors or fluctuations. Additionally, it should provide an unbiased score, which means that it should not be influenced by any external factors such as personal biases or environmental factors. Therefore, the answer to the question is D, all of the above.

More on reliable test: https://brainly.com/question/27873337

#SPJ11

A triangular distribution that has a mode of 0 and a lower limit of -2.45 and an upper limit of 2.45 is similar to a symmetric distribution with finite bounds, such as the uniform distribution.

The triangular distribution is a continuous probability distribution that has a triangular shape, where the maximum occurs at the mode and the distribution is symmetric around the mode.

In this case, since the mode is 0, the distribution is symmetric around 0. The limits of -2.45 and 2.45 create a range of possible values for the distribution, similar to how the bounds of a uniform distribution create a range of possible values.

However, unlike the uniform distribution, the triangular distribution has a higher probability density near the mode, and a lower probability density near the bounds.

To know more about mode refer to-

https://brainly.com/question/30891252

#SPJ11

40 + 18x + 2x2 = 0 Solving 40 + 18x + 2x2 = 0 ... Factor out the Greatest Common Factor (GCF), '2'.

________________________________

_________________________________

When a charged capacitor is connected to a metal conductor, the charges on the capacitor plates induce charges of opposite sign on the surface of the metal. These charges redistribute themselves in such a way that the electric field inside the metal is zero.

This is due to the fact that the charges inside the metal are free to move, and so they will rearrange themselves until the electric field inside the metal is exactly balanced by the induced charges on the surface. Therefore, the electric field magnitude E inside the metal is zero. This means that the electric field on the internal cap is also zero, as the metal is in contact with the cap.

However, if the capacitor is disconnected from the metal, the electric field on the internal cap will be the same as it was before the metal was introduced. It is important to note that this only holds true for conductive materials. If the material were an insulator, the electric field inside the material would not be zero and would depend on the properties of the material.

To know more about electric field click here

brainly.com/question/8971780

#SPJ11

When comparing the strength of a rectangular wire versus a round wire, the rectangular wire is typically stronger. This is due to the fact that the rectangular wire has a larger cross-sectional area, which contributes to its overall strength. The rectangular wire's wider and flatter shape allows it to withstand greater force before deforming, making it more suitable for heavy loads and high-stress applications.

In terms of beams versus cantilevers, it is essential to understand the differences between these two structural elements. A beam is a horizontal structural member that is supported at both ends, while a cantilever is a horizontal structural member that is supported only at one end. Beams and cantilevers are used in various applications, such as bridges and buildings.

In general, a beam is stronger than a cantilever, as it has support at both ends, distributing the load more evenly across its length. This means that beams can carry more weight and are less likely to experience deformation or failure when compared to cantilevers. Cantilevers, on the other hand, have a single support, resulting in a higher concentration of stress at the fixed end. This makes cantilevers more susceptible to bending and deflection under heavy loads.

In summary, rectangular wires are typically stronger than round wires, and beams are stronger than cantilevers. Rectangular wires have a larger cross-sectional area, providing greater strength, while beams have support at both ends, allowing them to carry more weight without deforming.

To know more about strength : brainly.com/question/9367718

#SPJ11

The above question is a mathematical proof of the relationship between Lines and angles related to a Rhombus. See the proof below.

We know,

A Rhombus is a parallelogram with four sides (that is a quadrilateral). It's sides however are all of equal length.

we have,

∠DEC ≅ ∠BFC  Reason = All Right Angles with Equal dimensions are congruent.

∠C ≅ ∠C  Reason = It is the same angle for the two Right angles above which are congruent, hence Reflexive Property.

Δ DEC ≅ Δ BFC  Reason = Angle Angle Side. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

 ≅   Reason = The corresponding parts of congruent triangles are congruent. Also, it is a parallelogram with all congruent sides.

ABCD is a Rhombus Reason = Its sides are all congruent.

Learn more about Rhombus at;

brainly.com/question/20627264

#SPJ1

complete question:

Given: ABCD is a parallelogram, FC is congruent to EC, DE bisects BC and BF bisects DC Prove: ABCD is a rhombus

The probability that the average hourly rate of the 100 registered web developers sampled exceeds $35.5 is approximately 0.106, rounded off to the third decimal place.

The mean of the distribution of the hourly rate of registered web developers is $\mu = 35$ and the standard deviation is $\sigma = 4$. We are interested in finding the probability that the average hourly rate of the 100 registered web developers sampled exceeds $35.5$.

We can use the central limit theorem to approximate the sampling distribution of the sample mean. According to the central limit theorem, the sampling distribution of the sample mean will be approximately normal with mean $\mu_{\bar{x}} = \mu = 35$ and standard deviation $\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} = \frac{4}{{100}} = 0.4$.

Let $X$ be the sample mean hourly rate of the 100 registered web developers. Then we need to find $P(X > 35.5)$.

Standardizing $X$,we get:

Using a standard normal table or calculator, we can find the probability $P(Z > 1.25) \approximately 0.1056$. Therefore, the probability that the average hourly rate of the 100 registered web developers sampled exceeds $35.5$ is approximately 0.106, rounded off to the third decimal place

Many researchers do not explicitly refer to significance levels. Instead, they simply obtain the P value and use it (or let the reader use it) to assess the strength of the evidence against the null hypothesis.

In statistical hypothesis testing, the null hypothesis is the default or initial assumption that there is no relationship or difference between two or more groups being compared.

The goal of hypothesis testing is to determine whether the evidence in the sample provides enough evidence to reject the null hypothesis and support the alternative hypothesis.

This decision is made based on the significance level, which is the probability of rejecting the null hypothesis when it is actually true.

The significance level is typically set at 0.05 (or 5%), which means that there is a 5% chance of rejecting the null hypothesis even if it is true.

Instead of reporting a significance level, some researchers report the P value, which is the probability of obtaining a test statistic as extreme or more extreme than the one observed, assuming that the null hypothesis is true.

If the P value is less than the significance level, then the null hypothesis is rejected, and the results are considered statistically significant. If the P value is greater than the significance level, then the null hypothesis is not rejected, and the results are considered not statistically significant.

Therefore, the P value can be used to assess the strength of the evidence against the null hypothesis, without explicitly referring to a significance level.

The smaller the P value, the stronger the evidence against the null hypothesis, and the more likely it is that the alternative hypothesis is true.

The larger the P value, the weaker the evidence against the null hypothesis, and the less likely it is that the alternative hypothesis is true.

For similar question on strength :

https://brainly.com/question/9367718

#SPJ11

Many researchers do no longer explicitly refer to importance levels. Instead, they virtually achieve the P fee and use it (or let the reader use it) to determine the power of the proof in opposition to the null hypothesis.

In statistical speculation testing, the null speculation is the default or preliminary assumption that there is no relationship or distinction between two or extra businesses being compared.

The purpose of speculation checking out is to decide whether or not the proof in the pattern gives ample proof to reject the null hypothesis and help the choice hypothesis.

This choice is made primarily based on the magnitude level, which is the chance of rejecting the null speculation when it is in reality true.

The importance degree is normally set at 0.05 (or 5%), which capability that there is a 5% risk of rejecting the null speculation even if it is true.

Instead of reporting a magnitude level, some researchers file the P value, which is the chance of acquiring a check statistic as severe or greater severe than the one observed, assuming that the null speculation is true.

If the P fee is much less than the magnitude level, then the null speculation is rejected, and the consequences are viewed statistically significant.

If the P cost is larger than the importance level, then the null speculation is now not rejected, and the consequences are regarded no longer statistically significant.

Therefore, the P price can be used to verify the electricity of the proof towards the null hypothesis, besides explicitly referring to a magnitude level.

The smaller the P value, the better the proof towards the null hypothesis, and the extra possibly it is that the choice speculation is true.

The large the P value, the weaker the proof in opposition to the null hypothesis, and the much less in all likelihood it is that the choice speculation is true.

For comparable query on power :

https://brainly.com/question/29575208

#SPJ11

The probability of getting exactly one success in 8 trials is 0.3217. The probability of getting at most 4 successes in 8 trials is 1. The probability of getting at least 5 successes in 8 trials is 0.7708.

(a) The probability of getting exactly 1 success in 8 trials with a success probability of 0.35 is given by the binomial probability formula as:

[tex]P(x = 1) = (8 choose 1) * 0.35^1 * 0.65^7 = 0.3217[/tex]

Therefore, the probability of getting exactly one success in 8 trials is 0.3217.

(b) The probability of getting at most 4 successes in 8 trials can be calculated by adding the probabilities of getting 0, 1, 2, 3, or 4 successes:

P(x ≤ 4) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4)

Using the binomial probability formula as before, we get:

P(x ≤ 4) = 0.1142 + 0.3217 + 0.3574 + 0.1826 + 0.0477 = 1

Therefore, the probability of getting at most 4 successes in 8 trials is 1.

(c) The probability of getting at least 5 successes in 8 trials can be calculated by adding the probabilities of getting 5, 6, 7, or 8 successes:

P(x ≥ 5) = P(x = 5) + P(x = 6) + P(x = 7) + P(x = 8)

Using the binomial probability formula as before, we get:

P(x ≥ 5) = 0.2271 + 0.3118 + 0.1923 + 0.0396 = 0.7708

Therefore, the probability of getting at least 5 successes in 8 trials is 0.7708.

To know more about probability refer to-

https://brainly.com/question/30034780

#SPJ11

We can start by calculating the interest that Rahul has to pay on the loan.

The formula for simple interest is:

I = P * r * t

where:

- I is the interest

- P is the principal amount (the amount of money Shashwat lent to Rahul)

- r is the annual interest rate (10% per annum, or 0.10)

- t is the time in years (2.5 years)

Substituting the given values, we get:

I = 44000 * 0.10 * 2.5 = Rs 11,000

Therefore, the total amount that Rahul has to pay Shashwat is Rs 44,000 (the principal) + Rs 11,000 (the interest) = Rs 55,000.

However, Rahul paid only Rs 40,000 and a cow. Let's assume the value of the cow is x.

So, the total amount received by Shashwat is:

Rs 40,000 + x

We know that this amount is equal to the total amount that Rahul had to pay, which is Rs 55,000.

Therefore, we can set up an equation:

Rs 40,000 + x = Rs 55,000

Solving for x, we get:

x = Rs 15,000

So the cost of the cow was Rs 15,000.

Answer:4000

Step-by-step explanation:

The percentage of adults who have an IQ score higher than 128 points using the z score is 0.26%.

Given that,

The distribution of IQ scores for adults can be modeled with a normal distribution.

Mean, μ = 100

Standard deviation, σ = 10

We have to find the percentage of adults who have an IQ score higher than 128 points.

z score = (x - μ) / σ

            = (128 - 100) / 10

            = 2.8

Percent of adults who are below 2.8 = 0.9974

Percent of adults who are above 2.8 = 1 - 0.0026 = 0.26%

Hence the required percentage is 0.26%.

Learn more about z score here :

https://brainly.com/question/15016913

#SPJ4

The lower confidence interval for the mean life of the new type of LED at a 95% confidence level is [5084.7,∞ )

To calculate the lower confidence interval for the mean life of the new type of LED, we can use the formula:

Lower confidence limit = sample mean - (critical value) x (standard error)

where the standard error is the standard deviation of the sample mean, given by:

standard error = sample standard deviation / √sample size

The critical value depends on the confidence level and the degrees of freedom, which for a sample of size 9 is 8 (n-1).

For a 95% confidence level, the critical value with 8 degrees of freedom is 2.306. Substituting the given values into the formula, we get:

Lower confidence limit = 5200 - 2.306 x (150 /√9 )

= 5200 - 115.3

= 5084.7

Therefore, the lower confidence interval for the mean life of the new type of LED at a 95% confidence level is [5084.7,∞ )

Learn more about interval

brainly.com/question/9726380

#SPJ11

The requreid equation in the form x-b=c that has the solution set x <= -14 is:

x - (-14) = 0 or x + 14 = 0

The absolute value of a number is always positive, so the absolute value of any number is greater than or equal to 0. Therefore, the absolute value of any number will never be less than -14.

To write an absolute value equation in the form x-b=c, we need to isolate the absolute value on one side and simplify.

|x| <= -14 can be rewritten as:

x <= -14 (since the absolute value of any number is always greater than or equal to 0)

So the equation in the form x-b=c that has the solution set x <= -14 is:

x - (-14) = 0 or x + 14 = 0

Learn more about the absolute value function here:

https://brainly.com/question/14364803

#SPJ1

The correct statement is: provided that the sample size is reasonably large (for any population).

The Central Limit Theorem states that, under certain conditions, the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.

These conditions include a random sample from the population and a sufficiently large sample size (typically, n > 30 is considered large enough).

Therefore, the Central Limit Theorem is important because it allows us to make inferences about the population mean using the normal distribution, even if we do not know the population distribution.

This is useful in many applications of statistics, including hypothesis testing, confidence intervals, and estimating population parameters

Learn more about Central Limit Theorem

brainly.com/question/18403552

#SPJ11

The probability of seeing a shooting star during the first 15 minutes of the hour is approximately 19.95%

To solve this problem, we need to use conditional probability. We want to find the probability of seeing a shooting star during the first 15 minutes of the hour given that the chances of seeing a shooting star in any given hour are 80%.

First, we need to determine the probability of seeing a shooting star in the first 15 minutes of the hour. Since the probability is uniform for the entire hour, we can assume that the probability of seeing a shooting star in any given minute is 80% divided by 60 (the number of minutes in an hour), which is approximately 1.33%.

To find the probability of seeing a shooting star during the first 15 minutes of the hour, we need to add up the probabilities of seeing a shooting star in each of the 15 minutes. This can be calculated as follows:

P(seeing a shooting star in the first 15 minutes) = P(seeing a shooting star in minute 1) + P(seeing a shooting star in minute 2) + ... + P(seeing a shooting star in minute 15)
= 15 x 1.33%
= 19.95%

Therefore, the probability of seeing a shooting star during the first 15 minutes of the hour is approximately 19.95%. This means that if you go out star gazing again and the chances of seeing a shooting star are 80%, there is a 19.95% chance that you will see one during the first 15 minutes of the hour you are out.

Know more about   shooting star  here:

https://brainly.com/question/31451954

#SPJ11

`

On average, there were approximately 8547 visitors in the park at any particular time last year.

To find out how many visitors were in the park at any particular time last year on average, we can use the following formula:

Average number of visitors = Total number of hours spent by all visitors / Number of hours in a year

First, we need to calculate the total number of hours spent by all visitors:

Total number of hours spent by all visitors = Number of visitors x Average number of hours per visitor

Total number of hours spent by all visitors = 3400000 x 22 = 74800000 hours

Next, we need to calculate the number of hours in a year. Since a year has 365 days, and each day has 24 hours, the total number of hours in a year is:

Number of hours in a year = 365 x 24 = 8760 hours

Finally, we can calculate the average number of visitors in the park at any particular time last year:

Average number of visitors = Total number of hours spent by all visitors / Number of hours in a year

Average number of visitors = 74800000 / 8760 = 8547.032

Rounding to the nearest integer, we get:

Average number of visitors = 8547

Therefore, on average, there were approximately 8547 visitors in the park at any particular time last year.

Learn more about average number of visitors

brainly.com/question/15264137

#SPJ11

The calculated value of the expected number of spin is 216

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

Yellow or purple outcomes = 12

P(Yellow or purple) = 1/18

using the above as a guide, we have the following:

Yellow or purple outcomes = P(Yellow or purple) * Expected number of spin

So, we have

1/18 * Expected number of spin = 12

Rewrite as

Expected number of spin = 12 * 18

Evaluate

Expected number of spin = 216

Hence, the expected number of spin is 216

Read more about expected value at

https://brainly.com/question/15858152

#SPJ1

Given information:

Raoul collects sports cards.

He has six baseball cards, three football cards, four hockey cards, and three basketball cards.

Raoul has a total of 6 + 3 + 4 + 3 = 16 sports cards.

The number of hockey cards he has is 4.

Therefore, the fraction of his sports cards that are hockey cards is:

4/16

Simplifying the fraction by dividing both the numerator and denominator by 4, we get:

1/4.

So, 1/4 of Raoul's sports cards are hockey cards.

To learn more about the probability;

brainly.com/question/11234923

#SPJ4

Answer: -117

Step-by-step explanation: I added a photo of the work to show you what I did to get the answer, hope it helps!

Answer: 0.355625 ounces

Step-by-step explanation:

if one pound is 16 ounces then 1:16. In this case, the 16 is 5.60 because it’s a pound worth. So that being said you have to divide 5.60 by 16

Answer: 5(x squared+7x+4)

Answer:

in order to get the GCF u must 1st factorize it

5x^2+35x+20

5(x^2+7x+4) ..we factorize by dividing the num. by 5

so yhe GCF is 5

To convert 72 feet per day to a different unit, we can use unit conversion factors:

1 day = 24 hours

1 hour = 60 minutes

1 foot = 12 inches

So, we can set up the following calculation:

72 feet/day × (1 day/24 hours) × (1 hour/60 minutes) × (12 inches/1 foot) = 0.1 inches/minute

Therefore, the converted rate is in units of inches per minute.

Answer: (4) inches/minute

The probability of landing on Deep Space Transmitter is 2 out of 16 spins, or 2/16, which simplifies to 1/8 or 12.5%.

Based on the data, the probability of landing on Deep Space Transmitter is 2 out of 16 spins, or 2/16, which simplifies to 1/8 or 12.5%.

Probability is a numerical value, ranging from 0 to 1, assigned in the delineation of the likelihood of an event happening.

A 0 mark portrays that an incident is inconceivable, while a 1 proposes that it will certainly arise. In order to measure probability, one must split the favored outcomes by the sum total of prospective happenings in given circumstances.

Read more about probability here:

https://brainly.com/question/25870256

#SPJ1

Kimberly just got a new board game, Adventures in Space. Each player is gl

eship to start. When players land on a square with a picture of a rocket, they spin the

her and get a special part to put onto their spaceship. The spinner is divided into six

qual sections. Before the game starts, Kimberly spins the spinner 16 times to see what

gets.

Escape pod = 2 times

Asteroid shield = 1 time

Teleport pad = 3 times

Turbo boost button = 4 times

Deep space transmitter = 2 times

Antimatter generator = 4 times

based on the data, what is the probability of the transmitter landing on deep space transmitter

There are 3,276,000 possible license plates in the given country if no repetitions of letters or digits are allowed.

Assuming that there are 26 letters in the alphabet and 10 digits (0-9) available for use:

There are 26 choices for the first letter and 25 choices for the second letter (because we can't repeat the first letter), giving us a total of 26 x 25 = 650 possible letter combinations.

Similarly, there are 10 choices for the first digit, 9 choices for the second digit, 8 choices for the third digit, and 7 choices for the fourth digit (because we can't repeat any of the previous digits), giving us a total of 10 x 9 x 8 x 7 = 5,040 possible digit combinations.

To calculate the total number of possible license plates, we can multiply the number of letter combinations by the number of digit combinations:

650 x 5,040 = 3,276,000

Therefore, there are 3,276,000 possible license plates in the given country if no repetitions of letters or digits are allowed.

for such more question on word problem

https://brainly.com/question/1781657

#SPJ11

The determination of a one-sided or two-sided alternative hypothesis for the racquet-spinning study would depend on the specific research question being asked and the direction of the effect being tested.

On the other hand, if the research question is whether there is a significant difference in tennis serve performance between racquet-spinning and no spinning.

Regardless of the direction of the effect, then a two-sided alternative hypothesis would be appropriate. In this case, the alternative hypothesis would state that there is a significant difference in serve performance between racquet-spinning and no spinning.

While the null hypothesis would state that there is no significant difference in serve performance between the two conditions.

Learn more about racquet-spinning

brainly.com/question/30702125

#SPJ11

C: Parametric tests are more likely to get significant results compared to nonparametric tests.

Parametric tests are statistical tests that assume certain characteristics about the data, such as normal distribution and homogeneity of variance.

Parametric tests are statistical tests that make certain assumptions about the data, such as the normal distribution of the population. These tests have more statistical power and are more likely to find significant results if these assumptions hold.

Nonparametric tests, on the other hand, do not make any assumptions about the data's distribution and are useful for non-normally distributed data. They have less statistical power and are less likely to find significant results.

However, if the assumptions of parametric tests are not met, they may lead to incorrect conclusions.

Therefore, it is important to choose the appropriate test based on the data and research question.

Learn more about statistical tests

brainly.com/question/14128303

#SPJ11

The circumference of the circle in terms of π is 63π

Circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle.

The circumference of a circle is expressed as;

C = 2πr

where c is the circumference and r is the radius. For example a circle with diameter 7 cm will have circumference of ;

C = 22/7 × 7 = 22 cm

Similarly, the radius of the circle above is 31½ = 63/2

therefore it's circumference

= 2 × π × 63/2

= 63π

therefore the circumference of the circle is 63π

learn more about circumference of circle from

https://brainly.com/question/18571680

#SPJ1

Therefore, the median of an exponential distribution with λ = 0.3 arrivals per minute is approximately 2.31 minutes.

The exponential distribution is a continuous probability distribution that describes the time between events occurring at a constant rate. It has a probability density function of [tex]f(x) = λe^(-λx)[/tex], where λ is the rate parameter.

To find the median of an exponential distribution with a rate parameter λ = 0.3 arrivals per minute, we need to find the value x such that P(X ≤ x) = 0.5, where X is a random variable following the exponential distribution.

We know that the cumulative distribution function (CDF) of the exponential distribution is [tex]F(x) = 1 - e^(-λx)[/tex]. Setting this equal to 0.5 and solving for x, we get:

[tex]0.5 = 1 - e^(-0.3x)\\e^(-0.3x) = 0.5\\ln(e^(-0.3x)) = ln(0.5)[/tex]

-0.3x = ln(0.5)

x = ln(0.5) / (-0.3)

Using a calculator, we get x ≈ 2.31.

To know more about  median refer to-

https://brainly.com/question/30891252

#SPJ11