If y varies directly with x and y=-16 when x=8, find y when x=2

the distance between point A and point B is approximately 777.9 feet.

what is  distance ?

Distance is a numerical measurement of how far apart two objects or points are from each other. It is a fundamental concept in mathematics and physics, and it can be defined in different ways depending on the context.

In the given question,

Let's denote the distance between Jeriel and point A as x, and the distance between Jeriel and point B as y. We want to find the distance between point A and point B, which we can call d.

From the first measurement, we can draw a right triangle with one leg of length x, another leg of length 113, and an acute angle of 8 degrees. The angle opposite the leg of length 113 is 90 degrees minus 8 degrees, or 82 degrees. We can use tangent to find x:

tan(8) = 113/x

x = 113/tan(8)

x =802.5

From the second measurement, we can draw another right triangle with one leg of length y, another leg of length 113, and an acute angle of 52 degrees. The angle opposite the leg of length 113 is 90 degrees minus 52 degrees, or 38 degrees. We can use tangent to find y:

tan(52) = 113/y

y = 113/tan(52)

y =72.4

Now we can use the Law of Cosines to find d:

d² = x² + y² - 2xy cos(130)

where 130 degrees is the angle between the sides of length x and y. We can simplify this equation and substitute the values we found for x and y:

d² = (802.5)² + (72.4)² - 2(802.5)(72.4) cos(130)

d =777.9

Therefore, the distance between point A and point B is approximately 777.9 feet.

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The values which satisfy the given equation 2/3×(p-q)=1 is given by option b.  p= 5/2 , q= 1.

Equation is equal to,

2/3×(p-q)=1

Simplifying the equation multiply both the sides by 3/2we get,

2/3 × (p-q) = 1

⇒2/3 × (p-q) × 3/2 = 1 × 3/2

⇒ (p-q) = 3/2

Now check all the values of p and q which satisfy this equation,

p = 3/2, q = 1

⇒ (p-q) = (3/2 - 1)

⇒ (p-q) = 1/2

It is not equal to 3/2,

So option a) is not a solution.

p = 5/2, q = 1

⇒ (p-q) = (5/2 - 1)

⇒ (p-q) = 3/2

It is equals to 3/2.

So option b) is a solution.

p = 3/2, q = 5/2

⇒ (p-q) = (3/2 - 5/2)

⇒ (p-q)  = -1

It is not equal to 3/2,

So option c) is not a solution.

p = 1, q = 1/2

⇒(p-q) = (1 - 1/2)

⇒(p-q) = 1/2

It is not equal to 3/2,

So option d) is not a solution.

Therefore, the only values that satisfies the equation 2/3 × (p-q) = 1 is option b) p= 5/2 , q= 1.

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The above question is incomplete , the complete question is:

Consider the equation 2/3 × (p-q) = 1. Which of these can be the values of p and q?

a) p = 3/2, q= 1

b) p= 5/2 , q= 1

c) p= 3/2 , q= 5/2

d) p= 1, q= 1/2

There are 302,702,400 possible baseball teams of nine that can be formed with three designated pitchers and 12 multitalented players who can play any of the remaining positions.

Since three players are designated as pitchers, we need to choose three players out of the total 15 players on the team. This can be done in C(15, 3) ways, where C(n, r) represents the number of combinations of r objects selected from a set of n objects.

For the remaining six positions, any of the 12 multitalented players can be assigned to any of the positions, which means that there are 12 choices for the first position, 11 choices for the second position, and so on, down to 7 choices for the sixth position.

Therefore, the total number of baseball teams of nine that can be formed is:

C(15, 3) x 12 x 11 x 10 x 9 x 8 x 7

which simplifies to:

(15 x 14 x 13 / 3 x 2 x 1) x (12 x 11 x 10 x 9 x 8 x 7)

= 455 x 665,280

= 302,702,400

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To determine the creation date of system volumes on an older Apple computer, and the most effective methods for obtaining this information, such as checking file metadata or using file recovery tools.

The best way for Melissa to approach discovering the creation date of the system volumes on an older Apple computer would be to check the file metadata.

File metadata includes information about when a file was created, modified, or accessed, and can be accessed by;

right-clicking on the file and selecting "Get Info" or by using the Terminal command "ls -l" in the directory where the system volumes are located.

Alternatively, Melissa could use a file recovery tool such as Disk Drill or EaseUS Data Recovery to scan the hard drive for deleted files that may contain information about the creation date of the system volumes.

It is important to note that using file recovery tools can potentially overwrite or corrupt existing data, so caution should be exercised when using these tools.

If Melissa is unable to find the creation date of the system volumes through these methods, she could also try contacting Apple support or consulting online forums for assistance

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1. The characters in "The Town Mouse and the Country Mouse" are two mice who are cousins. The town mouse is described as elegant, refined, and sophisticated, while the country mouse is simple and unsophisticated.

2. The main idea of the story is that one should be content with their simple life rather than crave for a luxurious life full of dangers and uncertainties.

"The Town Mouse and the Country Mouse" is a fable, a short story that teaches a moral or lesson. It tells the story of two cousins, a town mouse and a country mouse, who visit each other's homes and experience each other's way of life. The town mouse lives in luxury and eats rich food, but is always in danger from the cat, while the country mouse lives a simple life but is safe and content.

3. The sequence of events in the story is as follows:

4. Important details in the story include the description of the town and country mice, the differences in their lifestyles, and their reactions to each other's homes. These details are important because they emphasize the theme of the story, which is that it's better to be content with one's simple life than to crave for a luxurious but dangerous life.

5. I think "The Town Mouse and the Country Mouse" is a great story because it teaches an important lesson in a fun and engaging way. The characters are well-developed, and the plot is entertaining, making it easy for readers to understand the message.

6. One question I have about the writing is whether the author intended the story to be a commentary on social class and wealth.

7. A fable is a short story that teaches a moral or lesson. Fables usually feature animals or other non-human characters that can talk and behave like humans.

8. The moral of "The Town Mouse and the Country Mouse" is that it's better to be content with a simple life than to crave for luxury and danger. The story shows that the country mouse is happier and safer in his simple life than the town mouse, who is always in danger despite his luxurious lifestyle. This lesson teaches readers to be satisfied with what they have rather than always craving for more.

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town mouse and country mouse are cousins, the town mouse is working hard, (keep up the good work bud,) and the city mouse is relaxing, one day, town mouse was invited to city mouse’s city, they were relaxing, and then, a dog almost killed the mouses.

Standard deviation and median are less affected by extreme scores, while mode is not affected at all since it represents the most frequently occurring value.

The measure of variation affected most by a few extreme scores is the range, as it considers only the difference between the highest and lowest values in a dataset. However, the mean can also be influenced by extreme scores, causing it to deviate from the central tendency. Standard deviation and median are less affected by extreme scores, while the mode is not affected at all since it represents the most frequently occurring value.

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The measure of variation affected most by a few extreme scores is the range. The range is the difference between the

highest and lowest values in a data set. Extreme scores significantly increase the range, making it a sensitive measure

of variation.

The measure of variation that is affected most by a few extreme scores is the standard deviation.

The reason for this is that the standard deviation is calculated by taking the square root of the sum of squared

deviations from the mean, and the squared deviations from the mean are particularly sensitive to extreme scores.

On the other hand, the mode, range, median, and mean are less affected by a few extreme scores.

The mode is simply the most frequently occurring value in a dataset and is not affected by extreme scores.

The range is the difference between the highest and lowest values in a dataset and can be affected by extreme scores, but only to a limited extent.

The median is the middle value in a dataset, and it is also not affected by extreme scores unless they are extreme

enough to change the position of the middle value.

The mean is the average value in a dataset, and while it can be influenced by extreme scores, its effect is typically less

pronounced than on the standard deviation.

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Based on the table, a relationship which best predicts the end behavior of the graph of f(x) include the following: C. as, x → ∞, f(x) → –∞, And as x → –∞, f(x) → ∞.

In Mathematics and Geometry, a function f(x) is generally considered as an odd function if the following condition holds for all x-values (both positive x-values and negative x-values) in the domain of function f(x):

-f(x) = f(-x) - f (x) = f(-x)

This ultimately implies that, the larger the x-values or independent values (domain) is, the smaller would be the y-values or output values (range). On the other hand (conversely), the smaller the x-values or independent values (domain) is, the larger would be the y-values or output values (range);

x → ∞, f(x) → –∞, And as x → –∞, f(x) → ∞.

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The graph is a positive association

The graphs shows a linear relationship

There is outliers in coordinate (3, 105) and clusters from domain value of 8

Variable association refers to the relationship between two variables, and it can be either positive or negative. A positive association means that as one variable increases, the other variable tends to increase as well, while a negative association means that as one variable increases, the other variable tends to decrease.

Linear association specifically refers to the relationship between two variables that can be best represented by a straight line. This means that as one variable increases or decreases, the other variable changes proportionally.

Specialty in statistics can refer to two different concepts: outliers and clusters.

Outliers are data points that are significantly different from the other data points in a dataset. These points can have a large effect on statistical analysis and can distort results, so they are often removed or treated separately.

Clusters refer to groups of data points that are close together in a dataset. These clusters can indicate that there are subpopulations within the dataset or that there is a relationship between the variables being studied. Clusters can also be used to identify patterns or trends in the data.

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The p-value is greater than 0.05, the researcher would fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that the average number of sick days taken per year by workers is greater than 5.

It appears that some values are missing in your question, specifically the sample mean and the population standard deviation.

Without these values, I cannot provide a complete answer to your question.

A general idea of how to approach this type of hypothesis test.

To test whether the average number of sick days a worker takes per year is greater than 5, the researcher would need to set up the following hypotheses:

Null hypothesis (H0):

The average number of sick days taken per year by workers is equal to or less than 5.

Alternative hypothesis (Ha):

The average number of sick days taken per year by workers is greater than 5.

The next step would be to collect a random sample of workers and calculate their sample mean and sample standard deviation.

Based on these values, the researcher would then calculate the t-value using the formula:

t = (sample mean - hypothesized population mean) / (sample standard deviation / sqrt(sample size))

The hypothesized population mean in this case is 5, the sample size is 28, and the sample mean and sample standard deviation would be substituted in.

Once the t-value is calculated, the researcher would then use a t-distribution table to find the corresponding p-value based on the degrees of freedom (sample size minus 1) and the level of significance (0.05).

If the p-value is less than 0.05, the researcher would reject the null hypothesis and conclude that there is enough evidence to support the claim that the average number of sick days taken per year by workers is greater than 5.

The specific critical t-value would be based on the degrees of freedom and level of significance.

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Answer:

four less than three times a number

The measure of angle A and angle B are 30° and 60° respectively.

The figure in the image is a right-triangle.

To find the measure of angle A and angle B, we use the trigonometric ratio.

Solving for the measure of angle A:

sinθ = opposite / hypotenuse

opposite of angle A = 8

hypotenuse = 16

Plug in the values

sinθ = 8/16

sinθ = 1/2

θ = sin⁻¹( 1/2 )

θ = 30°

Solving for angle B

cosB = adjacent / Hypotenuse

adjeacent of angle B = 8

Hypotenuse = 16

Plug in the given values

cosB = 8/16

cosB = 1/2

B = cos⁻¹( 1/2 )

B = 60°

Therefore angle A is 30 degrees and angle B is 60 degree.

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The probability that at most a fifth of the buyers would prefer green is approximately 0.0198

This problem can be solved by using the binomial distribution. Let X be the number of buyers out of 15 who prefer green. Then X follows a binomial distribution with parameters n = 15 and p = 0.6.

We want to find the probability that at most a fifth of the buyers would prefer green. This means we want to find P(X ≤ 3), since a fifth of 15 is 3.

Using the binomial probability formula, we have

P(X ≤ 3) = Σ P(X = k) for k = 0 to 3

= P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= (15 choose 0) (0.6)⁰ (0.4)¹⁵ + (15 choose 1) (0.6)¹(0.4)¹⁴ + (15 choose 2) (0.6)² (0.4)¹³ + (15 choose 3) (0.6)³ (0.4)¹²

= 0.0000265 + 0.000397 + 0.00312 + 0.0163

Add the number

= 0.0198

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Answer: 4.5

The interquartile range IQR is the range in values from the first quartile Q1 to the third quartile Q3. Find the IQR by subtracting Q1 from Q3.

The value of the test statistic is approximately 2.84. Its significance can't be determined.

To determine whether or not there is a significant difference between the hourly wages of two companies, we need to conduct a hypothesis test.

The null hypothesis states that there is no significant difference between the hourly wages of the two companies, while the alternative hypothesis states that there is a significant difference.

The test statistic for this hypothesis test is calculated using the formula:

[tex]t = (x1 - x2) / (s1^2/n1 + s2^2/n2)^(1/2)[/tex]

where x1, x2 are the sample means for companies A and B, s1 and s2 are the sample standard deviations for companies A and B, and n1 and n2 are the sample sizes for companies A and B.

Plugging in given values, we get:

[tex]t = (6.75 - 6.25) / [(1^2/80) + (0.95^2/60)]^(1/2)[/tex]

t = 0.5 / 0.1759

t = 2.8437

Without knowing the significance level or the degrees of freedom, we cannot determine whether or not the test statistic is statistically significant.

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The value of the test statistic is 2.75.

To determine the test statistic for comparing the hourly wages of two companies, the researcher would need to conduct a two-sample t-test with equal variances.

The formula for the test statistic is:

[tex]t = (\bar x1 - \barx2) / [s_p \times \sqrt(1/n1 + 1/n2)][/tex]

where:

[tex]\bar x1[/tex] and[tex]\bar x2[/tex] are the sample means for Company A and Company B, respectively

[tex]s_p[/tex] is the pooled standard deviation of the two samples, calculated as:

[tex]s_p = sqrt [((n1 - 1) \times s1^2 + (n2 - 1) \times s2^2) / (n1 + n2 - 2)][/tex]

n1 and n2 are the sample sizes for Company A and Company B, respectively

s1 and s2 are the sample standard deviations for Company A and Company B, respectively.

Plugging in the given values, we get:

[tex]t = (6.75 - 6.25) / [\sqrt(((80-1)\times 1^2 + (60-1)\times 0.95^2)/(80+60-2)) \times \sqrt(1/80 + 1/60)][/tex]

[tex]t = 2.75[/tex]

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The upper and lower values of the range of the dataset are: Option E: -12 and 104

The range of a dataset is defined as the difference between the highest and lowest values of that dataset when arranged in ascending or descending order.

The dataset is given by:

36, 45, 40, 36, 84, 72, 20, 53, 32, 45, 64, 76

The lowest value = 20

Highest value = 84

Thus:

Upper value of range will be: 80 + 24 = 104

Lower value of range will be: 20 - 32 = -12

There is no outlier

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If total sales were $624 and customers bought 7 times as many pens as flashlights, then the number of pens sold is 84.

Let's start by assigning variables to represent the unknown quantities.

Let x be the number of flashlights sold.

Then, since "customers bought 7 times as many pens as flashlights," the number of pens sold would be 7x.

The total sales can be expressed as the sum of the sales of each item:

10x (sales from flashlights) + 6(7x) (sales from pens) = 624

Simplifying this equation

10x + 42x = 624

52x = 624

x = 12

So, the number of flashlights sold is 12.

And the number of pens sold would be 7x = 7(12) = 84.

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a. The distribution of x1 x2 is z1z2 ~ Cauchy(0,1). (b) The probability that x1 x2 is greater than 16 is 0.1056. (c) The distribution of 3x1 + 2x2 + x3, is given as N(38, 29).

A probability density function (PDF) expresses the likelihood that a continuous random variable will take a specified value or fall within a predetermined range of values. It is a derivative of the cumulative distribution function (CDF), which is the likelihood that a random variable will have a value that is less than or equal to a certain value.

The CDF is a function that converts every potential value of the random variable to a probability between 0 and 1, and it is defined for both discrete and continuous random variables.

a. Covert the x1 and x3 into standard normal variables by subtracting their means and dividing by their standard deviations:

z1 = (x1 - 4) / 2 ~ N(0,1)

z2 = (x2 - 8) / 3 ~ N(0,1)

The product is thus:

z1z2 ~ Cauchy(0,1)

b. The probability that x1 x2 is greater than 16:

Y / z1 ~ Cauchy(0,1)

Now,

z1 = Y / (z1z2) ~ Cauchy(0,1)

Here, the probability that x1 x2 > 16 is:

P(x1 x2 > 16) = P(Y / z1 > 16 / z1) = P(z1 < -Y / 16) + P(z1 > Y / 16)

= 2 * P(z1 < -Y / 16)

Substituting the value of z1 and Y we have:

P(x1 x2 > 16) = 2 * P(z1 < -16z1z2 / (9)) = 2 * Φ(-16z2 / 3) ≈ 0.1056

Hence, the probability that x1 x2 is greater than 16 is 0.1056.

c) The distribution of 3x1 + 2x2 + x3, is given as:

[tex]3x1 + 2x2 + x3 \~ N(34 + 28 + 12, 3^22^2 + 2^23^2 + 4^2) = N(38, 29)[/tex]

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Solving the equations we get the average cost of movie tickets for Japan is $17.42 and Switzerland is $13.07.

What is equation?

An equation is a mathematical statement which is made by two expressions connected by an equal sign. For example, 3x – 8 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 8.

Let, the cost for 1 movie ticket in Japan = $x

the cost for 1 movie ticket in Switzerland = $y

It would cost $78.40 to buy three tickets in Japan plus two tickets in Switzerland.

So the first equation will be,

3x+2y= 78.40 ------------(1)

Three tickets in Switzerland plus two tickets in Japan would cost $74.05

From this the 2nd equation will be,

2x+3y= 74.05 --------------(2)

Multiplying equation (1) by 2 and multiplying equation (2) by 3 we get,

6x+4y= 156.8 --------------(3)

6x+9y= 222.15 ------------(4)

equation (4)- (3) gives,

5y= 65.35

y= 13.07

putting this value in equation (1) we get,

x= (78.40- 2× 13.07)/ 3

 = 17.42

Hence, the average cost of movie tickets for Japan is $17.42 and Switzerland is $13.07.

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There are 19 people who own a cat or a dog.

A number is a mathematical object used to represent quantity, measurement, or a count of something. It can be an integer (whole number), a rational number (fraction), an irrational number (such as pi), or a real number (which includes all rational and irrational numbers).

To find the number of people who own a cat or a dog, we need to add the number of people who own only cats to the number of people who own only dogs, and then add the number of people who own both cats and dogs.

Let's start by finding the number of people who own only cats. We know that 16 people own cats, and 5 people own both cats and dogs. Therefore, the number of people who own only cats is:

16 - 5 = 11

Next, let's find the number of people who own only dogs. We know that 8 people own dogs, and 5 people own both cats and dogs. Therefore, the number of people who own only dogs is:

8 - 5 = 3

Finally, we can add the number of people who own only cats to the number of people who own only dogs, and then add the number of people who own both cats and dogs:

11 + 3 + 5 = 19

So, there are 19 people who own a cat or a dog.

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The correct answer is option b. Burger Quick, because it has a larger mean.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves using mathematical and computational methods to gather, analyze, and interpret data from various fields, including business, economics, medicine, engineering, psychology, and social sciences. Statistics allows researchers and analysts to draw conclusions and make predictions based on data, and is used in a wide range of applications, from designing experiments and conducting surveys to testing hypotheses and making decisions based on data-driven insights.

Burger Quick typically has more wait time, because it has a larger interquartile range (IQR) and a larger upper whisker on the box plot, indicating that there is more variability in the wait times and some customers have experienced longer wait times. Although the median wait time for Burger Quick is also larger, it is the IQR and upper whisker that provide more evidence for the longer wait times. The mean is not shown on the box plot and therefore cannot be used to determine which drive-thru typically has more wait time.

Therefore, the correct answer is option b. Burger Quick, because it has a larger mean.

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Answer:

0.81

Step-by-step explanation:

[tex]\frac{100-19}{100} =0.81[/tex]

Answer:

x = 16

Step-by-step explanation:

A point that moves on a coordinate line is said to be in simple harmonic motion if its distance d from the origin at time

t  is given by either d = a sin ωt or d = a cos ωt.

Simple harmonic motion, or SHM for short, is a particular kind of periodic motion of a body that results from a dynamic

equilibrium between an inertial force that is proportional to the body's acceleration away from the static equilibrium

position and a restoring force on the moving object that is directly proportional to the size of the object's displacement

and acts towards the object's equilibrium position. If friction or any other energy dissipation is not present, it leads to an

oscillation that is represented by a sinusoid and that lasts indefinitely.

The oscillation of a mass on a spring when it is subject to the linear elastic restoring force specified by Hooke's law is a

good example of simple harmonic motion, which may be used as a mathematical model for many different motions.

The motion has a single resonant frequency and is sinusoidal in time. Simple harmonic motion can be used to simulate

a variety of other phenomena, such as the motion of a simple pendulum, though it is only a good approximation when

the angle of the swing is small; for more information, see small-angle approximation. In order for the model to be

accurate, the net force acting on the object at the end of the pendulum must be proportional to the displacement.

Molecular vibration can also be modelled using straightforward harmonic motion.

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Answer:

2x+7>-13

Step-by-step explanation:

Let the unknown number be x.

Since the problem starts off with "7 more than twice a number," we need to find twice the number first. Let's multiply x by 2:

we end up with 2x.

Let's return to "7 more than twice a number..."

This means that the value is 7 more than 2x, so let's add 7 to 2x:

we end up with 2x+7.

Now, let's take a look at "...is greater than negative 13."

Our new value, 2x+7, is greater than -13.

So, we can write:

2x+7>-13

From the given information , the brand which is a "better-buy" is (c) Brand C .

To determine which brand is the better buy, we calculate the "price-per-ounce" for each brand.

To find the "price-per-ounce" we divide "the cost" by "the number of ounces",

On dividing cost by ounces,

We get,

⇒ For Brand A: $2.16 for 18 ounces,

The "price-per-ounce" is = $2.16/18 = $0.12 per ounce.

⇒ For Brand B: $1.50 for 12 ounces,

The "price-per-ounce" is = $1.50/12 = $0.125 per ounce.

⇒ For Brand C: $2.26 for 20 ounces,

The "price-per-ounce" = $2.26/20 = $0.113 per ounce.

⇒ For Brand D: $1.95 for 16 ounces,

The "price-per-ounce" is = $1.95/16 = $0.122 per ounce.

On comparing the price per ounce, we see that "Brand C" has the lowest price per ounce at $0.113, which makes it the better buy among the options given.

Therefore, the correct answer is (c) Brand C.

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The given question is incomplete, the complete question is

Given the following information, choose the brand that is the better buy.

Brand A: $2.16 for 18 ounces

Brand B: $1.50 for 12 ounces

Brand C: $2.26 for 20 ounces

Brand D: $1.95 for 16 ounces

(a) Brand A

(b) Brand B

(c) Brand C

(d) Brand D

The value of x is -6.5.

First, substitute the value of y into the equation:

2x - 3(-7) = 8

Now, solve for x:

2x + 21 = 8

Subtract 21 from both sides:

2x = -13

Divide by 2:

x = -13/2 or -6.5

So, the value of x is -6.5.

We started with the given equation and information:

Equation: 2x - 3y = 8

Given: y = -7

Our task is to find the value of 'x' using the given information which was solved above and of which we substituted the value of y into the equation, simplified, subtracted and divided and got the answer to the equation which is -6.5.

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Given the equation 2x - 3y = 8 and y = -7, find the value of x.

|z| = 0.669 < 1.96, we fail to reject the null hypothesis at any significance level up to α = 0.05.

In other words, we do not have enough evidence to conclude that the true proportion of executives who would agree with the statement is different from one-half.

The null hypothesis that the true proportion of all such executives.

Agree with this statement is one-half, we can use a two-sample z-test for proportions.

Let p be the true proportion of executives who would agree with the statement and let. [tex]\^p[/tex] be the sample proportion.

Under the null hypothesis, the test statistic z is given by:

[tex]z = (\^p - 0.5) / \sqrt(0.5 \times 0.5 / n),[/tex]

n is the sample size (104 in this case).

This test statistic follows a standard normal distribution under the null hypothesis.

To reject the null hypothesis at a significance level α, we need to find the critical values.[tex]z\alpha/2[/tex] and [tex]-z\alpha/2[/tex] such that [tex]P(Z > z\alpha/2) = \alpha/2[/tex] and[tex]P(Z < -z\alpha/2) = \alpha/2[/tex], where Z is a standard normal random variable.

The lowest level of significance at which the null hypothesis can be rejected against a two-sided alternative.

The smallest α such that [tex]|z| > z\alpha/2.[/tex]

The two-sided alternative implies that we are interested in deviations from the null value of 0.5 in either direction.

Using the given information, we have:

[tex]\^p = 50/104 = 0.4808,[/tex]

n = 104.

Substituting these values into the formula for z, we get:

[tex]z = (0.4808 - 0.5) / \sqrt(0.5 \times 0.5 / 104) = -0.669.[/tex]

The critical value [tex]z\alpha/2[/tex], we look up the corresponding value in the standard normal distribution table.

[tex]z\alpha/2[/tex] such that [tex]P(Z > z\alpha/2) = \alpha/2[/tex], or equivalently, [tex]P(Z < -z\alpha/2) = \alpha/2[/tex]. Since the standard normal distribution is symmetric, we can look up the value of zα/2 that satisfies. [tex]P(Z > z\alpha/2) = \alpha/2[/tex], and then take its absolute value to find. [tex]-z\alpha/2.[/tex]

Using a standard normal distribution table, we find that z0.025 = 1.96 (rounded to two decimal places).

The critical values for rejecting the null hypothesis at a significance level α are:

[tex]z\alpha/2[/tex] = ±1.96.

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Step-by-step explanation:

-49+14p=-22+5p

-49+22=5p-14p

-27=-9p

p=3

Answer:

Step-by-step explanation:

yeah she is... i think.. this is twisting my mind rn