Which equations are true for x = –2 and x = 2? Select two options
x2 – 4 = 0
x2 = –4
3x2 + 12 = 0
4x2 = 16
2(x – 2)2 = 0

The Masters golf tournament belongs to a large scale event category, given the corresponding variations in its impacts such as attracting thousands of visitors and generating significant economic activity in the host city.

The Masters Golf Tournament belongs to a large-scale event category. Large-scale events typically have significant impacts, including attracting international attention, generating substantial economic benefits, and requiring considerable planning and resources.

In the case of the Masters Golf Tournament, it is an annual event held at Augusta National Golf Club in Georgia, USA, and it attracts professional golfers from around the world, as well as a global audience, creating corresponding variations in economic, social, and environmental impacts.

Learn more about economic benefits here:

brainly.com/question/30315394

#SPJ11

False, For this situation, the professor should not use a t test with related samples.

The scenario described in the question involves two independent samples (upper and lower classmen) and not related samples. A t-test for related samples is used when the same group of participants is measured twice, resulting in paired or dependent samples.

Since the variances of the two independent samples are equal, the appropriate test in this scenario is a two-sample t-test for equal variances. However, the sample size of 10 for each group is relatively small, and the normality assumption of the t-test may not hold. Therefore, the professor should first check the normality assumption of the data using a normal probability plot or a Shapiro-Wilk test. If the assumption is not met, nonparametric tests such as the Wilcoxon rank-sum test can be used as an alternative.

In summary, the correct statistical test for this scenario is a two-sample t-test for equal variances or a nonparametric alternative if the normality assumption is not met. The t-test for related samples is not appropriate in this case.

To learn more about t test here:

https://brainly.com/question/15870238

#SPJ1

The x-coordinate that makes this relation not a function.

A relation is not a function if one of the inputs (x-coordinates) is mapped into two or more different outputs.

Here we have the relation:

(4, 8), (-3, 6), (-3, 7), (1, 6)

If you look at the inputs, you can see that:

x = -3

Is mapped into two different outputs, so that is the x-coordinate that makes this not a function.

Learn more about functions at:

https://brainly.com/question/2328150

#SPJ1

Each part will be approximately 8.04 inches long.

We can express this as:

Length of each part = Total length of ribbon / Number of parts

In this case, the total length of the ribbon is 4 feet, and we want to divide it into six equal parts. So, we can substitute these values into the above formula:

Length of each part = 4 feet / 6 parts

To solve this division problem, we can either use a calculator or do long division:

4 / 6 = 0.6666666667

So, each part will be approximately 0.67 feet long. Alternatively, we can convert this to inches, which is a more common unit of measurement for small lengths:

0.67 feet x 12 inches/foot = 8.04 inches

To know more about length here

https://brainly.com/question/14806907

#SPJ4

Operating Income $21,950

Yes. The franchisees still earn target profit.

Requirement 1.

Contribution margin per unit $4.55

X Average sales volume units 7,000

Contribution margin $31,850

Less: Fixed expenses $7,800

Operating Income $24,050

Requirement 2.

Contribution margin per unit $4.05 ($6.50 - $2.45)

X Average sales volume units 7,500

Contribution margin $30,375

Less: Fixed expenses $8,425

Operating Income $21,950

Yes. The franchisees still earn the target profit.

Read more about franchisees here:

https://brainly.com/question/16826168

#SPJ1

A binomial distribution is characterized by two outcomes (success or failure) and a fixed number of trials with the same probability of success on each trial.

In this case, X represents the number of times you roll the dice before achieving a Yahtzee.

However, X is not a binomial distribution because it doesn't have a fixed number of trials. You continue rolling until you get a Yahtzee, which could take an unpredictable number of attempts. Instead, X follows a geometric distribution, which describes the number of trials needed for the first success in a sequence of Bernoulli trials.

Yes, X is binomial because it has the following properties:

1. There are a fixed number of trials (rolling the dice repeatedly)
2. Each trial is independent of the others (the outcome of one roll does not affect the outcome of the next)
3. There are only two possible outcomes for each trial (either a Yahtzee is rolled or it isn't)
4. The probability of success (rolling a Yahtzee) is constant for each trial (1/6 to the 5th power, or about 0.00077)

Visit here to learn more about binomial distribution  : https://brainly.com/question/31197941
#SPJ11

Answer:

Here is the correct answer:

y > -1, x < 3

Step-by-step explanation:

The top right one most closely approximates the data.

Answer:I'm gonna have to go with top right

Step-by-step explanation:

A linear line is a straight line, the image you gave wasn't to clear but it looks like the right one.

A main feature of nonprobability samples is that they involve personal judgment somewhere in the selection of sample elements. Unlike probability samples, where every element in the population has a known, non-zero chance of being selected, nonprobability samples rely on the researcher's discretion when choosing elements for the sample.

This subjective approach may introduce biases, as the sample might not be representative of the entire population. Unfortunately, hidden biases in nonprobability samples cannot be eliminated simply by increasing the sample size, since the selection process itself is not random.

Due to these potential biases and the non-random nature of the selection process, it is difficult to generalize results from nonprobability samples to the entire population with the same level of confidence as probability samples.

While samples can provide valuable insights in some research contexts, they lack the statistical rigor and representativeness nonprobability of probability samples.

learn more about probability here: brainly.com/question/31439116

#SPJ11

The final cost of filling up the tank with 750 liters of oil at a price of 81.5p per liter with a 7.5% discount is 56,540.62p.

The price of oil is 81.5p per litre. If we want to calculate the cost of filling up the tank, we need to know how many liters of oil we need to add.

To do this, we need to subtract the current amount of oil in the tank (450 liters) from the maximum capacity of the tank (1200 liters):

1200 - 450 = 750 liters

So we need to add 750 liters of oil to fill up the tank.

Next, we need to calculate the cost of adding 750 liters of oil at the price of 81.5p per liter:

750 x 81.5 = 61,125p

To calculate the discount, we first need to find 7.5% of the total cost. We can do this by multiplying the total cost by 7.5% expressed as a decimal:

61,125 x 0.075 = 4,584.38p

So the discount is 4,584.38p.

To find the final cost after the discount, we need to subtract the discount from the total cost:

61,125 - 4,584.38 = 56,540.62p

To learn more about discount here:

https://brainly.com/question/3541148

#SPJ1

Answer:

$16

Step-by-step explanation:

25% off of 100% = 75%

0.75x=12, where x is the original cost

x=16

For the conversion of polar coordinates into cartesian coordinates means (r, θ) changed into (x,y), the Cartesian equation for the polar equation r = 9 sin(θ), is equals to x² + y² - 9y = 0.

In the polar coordinate system has different characteristics. To convert polar coordinates to Cartesian or rectangular coordinates, solve for the x and y coordinates separately.

We have a polar equation, r = 9 sin(θ). We have to convert this polar equation into cartesian equation. To convert from polar coordinates (r, θ) to cartesian coordinates ( x, y ). So, we use the following equations, x = rcos(θ)

y = r sin(θ)

Now, x² + y² = r² sin²(θ) + r²cos(θ)

= r²( sin²(θ) + cos²(θ))

= r²

Here, we have r = 9 sin(θ)

=>[tex] r = 9 \frac{ 9y}{r}[/tex]

=> r² = 9y

So, we can write as, x² + y² = 9y

=> x² + y² - 9y = 0

Hence, required equation is x² + y² - 9y = 0.

For more information about Cartesian equation, visit :

https://brainly.com/question/14869452

#SPJ4

The best description of the shape and center of the dotplot is that distribution of math classes is unimodal symmetric with a center around 4 classes. The Option C is correct.

A dot plot shows the frequency of each value in a dataset. To identify if the distribution of classes is unimodal symmetric, we will check if the dots are roughly evenly distributed around a central line which is the 4 classes.

This indicates the distribution is symmetric. We have a single peak in the data. If there is only one prominent cluster of dots, then, the distribution is unimodal. So, the distribution of classes is unimodal symmetric on the dot plot.

Read more about unimodal symmetric

brainly.com/question/4245473

#SPJ1

Answer:

c

Step-by-step explanation:

took the test

The hypergeometric probabilities for the given values of n and x are:

(a) P(X = 2) = 0.5143

(b) P(X = 3) = 0.1429

(c) P(X = 0) = 0.3571

(d) P(X = 3) = 0.0714

The hypergeometric probability mass function is given by:

P(X = x) = (rCx)(N-rCn-x) / (NCn)

where N is the total number of items in the population, r is the number of "successes" in the population, n is the sample size, and x is the number of "successes" in the sample.

(a) For n = 4 and x = 2:

P(X = 2) = (4C2)(8-4C4-2) / (8C4)

= (6)(6) / (70)

= 0.5143

(b) For n = 6 and x = 3:

P(X = 3) = (4C3)(8-4C6-3) / (8C6)

= (4)(1) / (28)

= 0.1429

(c) For n = 3 and x = 0:

P(X = 0) = (4C0)(8-4C3-0) / (8C3)

= (1)(20) / (56)

= 0.3571

(d) For n = 3 and x = 3:

P(X = 3) = (4C3)(8-4C3-3) / (8C3)

= (4)(1) / (56)

= 0.0714

Therefore, the hypergeometric probabilities for the given values of n and x are:

(a) P(X = 2) = 0.5143

(b) P(X = 3) = 0.1429

(c) P(X = 0) = 0.3571

(d) P(X = 3) = 0.0714

To know more about  hypergeometric visit:

https://brainly.com/question/15245410

#SPJ4

a.  Outliers are observed values far from the main group of data.

In a histogram they are separated from the others by space.

Outliers must be looked at twice, once with and once without the outliers. C.

b. The median is more resistant, which indicates that it usually changes less than the mean when comparing data with and without outliers. A.

Outliers are data points that are significantly different from the other values in a data set.

These observations can be identified by looking at a histogram, where they are separated from the main group of data by a significant space.

Outliers can be mistakes or they may represent real but unusual values.

It is important to look at outliers in closer context to determine how to treat them.

Sometimes they may be included in the analysis, but other times they may be removed or corrected.
To determine which measure of center, mean or median, is more resistant to outliers, we need to understand what "resistant to outliers" means.

Resistance to outliers refers to how much a measure of center is affected by the presence of outliers.

A measure that is more resistant to outliers will change less when outliers are present.
The median is more resistant to outliers than the mean.

This means that the median usually changes less than the mean when comparing data with and without outliers.

The reason for this is that the median is calculated by taking the middle value of the data set, which is less affected by extreme values than the mean, which takes into account all values in the data set.
Outliers should be examined carefully in the context of the data set to determine how to treat them.

The median is more resistant to outliers than the mean, which makes it a better measure of center when outliers are present.

For similar questions on Outliers

https://brainly.com/question/29546240

#SPJ11

To prove that there exist infinitely many primes p ≡ 3 mod 4 without using Dirichlet's theorem, we can use a proof by contradiction.  Assume that there are only finitely many primes p ≡ 3 mod 4, say p1, p2, ..., pk. Let N be the product of all these primes, i.e. N = p1p2...pk.

1. Let's denote these finitely many primes as {p_1, p_2, ..., p_k}, where each prime p_i ≡ 3 mod 4.
2. Now consider the number N = (4 * p_1 * p_2 * ... * p_k) - 1. Notice that N ≡ 3 mod 4.
3. N has a unique prime factorization, and since N ≡ 3 mod 4, at least one of its prime factors must be congruent to 3 mod 4.
4. Since we assumed there are only finitely many primes congruent to 3 mod 4, we can check if any prime in the set {p_1, p_2, ..., p_k} divides N. Notice that for every prime p_i in the set, N ≡ -1 mod p_i, which means that no prime p_i can divide N.
5. This leads to a contradiction since N must have a prime factor congruent to 3 mod 4, but none of the primes in our set can divide N. Therefore, our initial assumption is incorrect.

So, there must be infinitely many primes p ≡ 3 mod 4.

Learn more about theorem here : brainly.com/question/30066983

#SPJ11

The regular cost per month for a Switch Gears Activity Box subscription is $12.

To find the regular cost per month, Derek needs to subtract the discount he received from the total cost and divide the result by the number of months in his subscription. Let x be the regular cost per month. Then, the equation can be written as follows:

8x - 15 = 81

In this equation, 8x represents the total cost of the 8-month subscription at the regular price. Subtracting $15 from this total cost gives the amount Derek actually paid. Therefore, 8x - 15 = $81.

To find the regular cost per month, Derek needs to isolate x on one side of the equation. He can do this by adding 15 to both sides of the equation, then dividing both sides by 8. The resulting equation is:

8x = 96

x = 12

Derek can now use this information to budget for future subscriptions or compare it to other subscription services.

To know more about equation here

https://brainly.com/question/10413253

#SPJ4

To construct a confidence interval for the standard deviation, we can use the chi-square distribution. The formula for the confidence interval is: ( n - 1 )S^2 / χ^2(α/2, n-1) ≤ σ^2 ≤ ( n - 1 )S^2 / χ^2(1-α/2, n-1),

where n is the sample size, S is the sample standard deviation, α is the level of significance (1-0.99 = 0.01), and χ^2 is the chi-square distribution with (n-1) degrees of freedom.

1. Identify the sample size (n), sample standard deviation (s), and the confidence level (99%).

n = 20
s = 1.76 mm
confidence level = 99%

Calculate the lower and upper bounds for the confidence interval of the population standard deviation (σ) using the sample standard deviation (s) and Chi-square values.

Lower bound: √((n-1) * s² / χ²_upper) = √(19 * 1.76² / 38.582) ≈ 1.25 mm
Upper bound: √((n-1) * s² / χ²_lower) = √(19 * 1.76² / 6.844) ≈ 2.57 mm
Interpret the confidence interval.

The 99% confidence interval for the standard deviation of the length of straws is (1.25 mm, 2.57 mm). This means that we are 99% confident that the true standard deviation of the straw lengths lies within this interval. The straw manufacturing company can use this information to assess the accuracy of their cutting machine.

Learn more about standard deviation here : brainly.com/question/23907081

#SPJ11

According to the National Survey on Drug Use and Health, approximately 18.53% of U.S. adults (ages 18 and older) experienced some form of mental illness in 2016.

Approximately 18.53% of U.S. adults suffered from mental illness in 2016. This percentage represents the prevalence of mental health disorders among the adult population, which is important to understand in order to address and provide support for those affected.

This includes a range of conditions such as anxiety disorders, depression, bipolar disorder, and schizophrenia. It's important to note that mental illness can vary in severity and can impact individuals differently, and seeking professional help can greatly improve one's quality of life.

Learn more about quality of life here:

brainly.com/question/13826088

#SPJ11

From the phenotypic variance (p) of the genetically variable and genetically identical plants, the value of the broad-sense heritability (H) of seed number for the roadside population of bluebonnets is equals to the 0.6.

We have, population of graduation studying students in bluebonnets along a roadside. Sample size of plants = 100

variance for plants = 25

=> standard deviations = 5

We have to determine the broad-sense heritability (H) of seed number for the roadside. Broad-sense heritability [tex]H2 = \frac{V_G }{ V_P} [/tex] ---(1)

The phenotypic variation [tex]V_P = V_G + V_E [/tex], here [tex] V_P = 25[/tex]

[tex]25 = V_G + V_E[/tex] ------(II)

In the identical population, [tex] V_G = 0[/tex] and here [tex] V_P = 10[/tex]

=> [tex]10 = 0 + V_E [/tex]

=> [tex]V_E= 10[/tex]

By substituting [tex]V_E[/tex] value in equation (II), we will determine [tex]25 = V_G + 10 [/tex]

=> [tex]V_G = 15[/tex]

Substitute the values of [tex]V_G and V_E [/tex] of the roadside population in equation (1), [tex]H²=\frac{15}{25}=0.6[/tex].

The key to the answer is assumption should be the genetic variance of the genetically identical plants is the same as the genetically variable population. In the event that we don't make this supposition, at that point our concern turns out to be very entangled in light of the fact that then we should likewise realize the genetic variance effect of the plant in its environment as well.

For more information about population, visit:

https://brainly.com/question/30913921

#SPJ4

The measures of the angles in the triangle are 30 degrees, 60 degrees, and 90 degrees.

In this case, we are given that the angles of the triangle are in the ratio of 1:2:3. This means that the three angles can be expressed as x, 2x, and 3x, where x is some constant factor.

To find the value of x, we need to use the fact that the sum of the angles in a triangle is 180 degrees. So, we can write an equation:

x + 2x + 3x = 180

Simplifying the equation, we get:

6x = 180

Dividing both sides by 6, we get:

x = 30

Now that we know the value of x, we can use that to find the measure of each angle in the triangle.

The first angle is x, which we know is 30 degrees.

The second angle is 2x, which is 2 times 30, or 60 degrees.

The third angle is 3x, which is 3 times 30, or 90 degrees.

To know more about triangle here

https://brainly.com/question/8587906

#SPJ4

Complete Question:

The angles of a triangle are in the ratio of 1:2:3. Find the measure of each angle of the triangle

The correct statistical null hypothesis (H0) for this study is option b: fish that are exposed to the herbicide have the same average enzyme level compared to fish that are not exposed.

In the study conducted by an environmental scientist to investigate the effect of exposure to an herbicide on the levels of a particular enzyme in a species of fish (species 1), the statistical null hypothesis (H0) for this study is:
B. Fish that are exposed to the herbicide have the same average enzyme level compared to fish that are not exposed.
The null hypothesis assumes that there is no significant difference between the treatment and control groups, meaning that the herbicide has no effect on the enzyme levels in the fish.

Visit here to learn more about herbicide:

brainly.com/question/31375814

#SPJ11

The explicit formula for this sequence 6, 12, 24, 48, 96, .. is equal to aₙ = 6 * 2ⁿ⁻¹.

The sequence shown above is a geometric sequence because each term is obtained by multiplying the previous term by 2. To find the explicit formula for this sequence, we can use the formula:

aₙ = a₁ * rⁿ⁻¹

where:

aₙ = the nth term of the sequence

a₁ = the first term of the sequence

r = the common ratio between terms

n = the position of the term in the sequence

In this case, a₁ = 6 and r = 2, so the formula becomes:

aₙ = 6 * 2ⁿ⁻¹

Using this formula, we can find any term in the sequence by plugging in the value of n. For example, to find the 7th term, we would plug in n = 7:

a₇ = 6 * 2⁷⁻¹ = 6 * 2⁶ = 384

To learn more about sequence click on,

https://brainly.com/question/29000744

#SPJ1

Answer: 7

Step-by-step explanation:

Assume that the number entered is x.

(The lowercase x is a variable and the uppercase X is the multiplication symbol.)

                                              (x-9)X3=xX(-3)+15

                                                  3x-27=-3x+15

                                                        6x=42

                                                          x=7

                                               The answer is 7.

Answer:

72 cm²

Step-by-step explanation:

We can split this composite figure into 3 simple shapes:

First, we can solve for the area of the rectangles:

A(rect) = length × width

A(rect1) = 4 × (9 - 3) = 24

A(rect2) = 10 × 3 = 30

Next, we can solve for the area of the triangle:

A(triangle) = (1/2) × base × height

A(triangle) = (1/2) × (10 - 4) × 6

A(triangle) = 3 × 6 = 18

Finally, we can add each the simple shapes' areas together to get the area of the whole figure.

A = A(rect1) + A(rect2) + A(triangle)

A = 24 + 30 + 18

A = 72 cm²

The angle of depression the plane should descend is 1.43 degrees.

A plane is flying at an altitude of 25,000 ft when it start it descent to the airport. The plane is a horizontal distance of 1000,000 ft from the airport.

Therefore, let's find the angle of depression.

Hence, this situation forms a right angle triangle.

Therefore,

tan ∅ = opposite / adjacent

where

Hence,

tan ∅ = 25000 / 1000000

∅ = tan⁻¹ 25 / 1000

∅ =  tan⁻¹  0.025

∅ = 1.43209618416

∅ = 1.43 degrees

learn more on right triangle here: https://brainly.com/question/3770177

#SPJ1

Logarithms are a useful tool in determining the acidity or basicity of a solution. pH is a measure of the concentration of hydrogen ions in a solution and is calculated using the formula pH = -log[H+].

A solution with a pH of 7 is considered neutral, while a pH below 7 indicates acidity and a pH above 7 indicates basicity.

Using logarithms, we can determine the pH of 7 solutions ranging from strong acid to neutral to strong base. To do this, we need to measure the concentration of hydrogen ions in each solution and then use the formula above to calculate the pH.

For example, if we have a solution with a hydrogen ion concentration of 0.001 M, we can calculate the pH as follows:

pH = -log(0.001) = 3

This solution would be considered a strong acid, as it has a pH below 7. Similarly, a solution with a hydrogen ion concentration of 10^-7 M (which is the same as a concentration of 1x10^-7 M) would have a pH of 7 and would be considered neutral.

Finally, a solution with a hydrogen ion concentration of 10^-11 M would have a pH of 11 and would be considered a strong base.

In summary, using logarithms, we can determine the acidity or basicity of a solution by calculating its pH. A pH of 7 is considered neutral, while a pH below 7 indicates acidity and a pH above 7 indicates basicity.

learn more about logarithms here : brainly.in/question/54090640

#SPJ11

The t-test cannot be used in this situation because the samples are not independent, and the variable's distribution is heavily skewed in at least one sample, violating the assumptions of normality and independence.

We cannot use the t-test for this situation for two reasons. Firstly, the samples are not independent as the same 40 subjects are used for both the men and women groups. Secondly, the variable's distribution is heavily skewed in at least one sample and the sample size is relatively small. These factors violate the assumptions of normality and independence that are required for the t-test to be valid. Therefore, alternative non-parametric tests should be considered, such as the Mann-Whitney U test or Wilcoxon rank-sum test, which do not require normality assumptions and can handle non-independent samples.

To know more about variable visit:

https://brainly.com/question/29696241

#SPJ4

If point C is 4.15 miles from point A and 5.33 miles from point B, the distance from Point A to Point B is approximately 4.15 miles.

To find the distance from Point A to Point B, we can use the Law of Cosines. The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. In this case, we can use the Law of Cosines to find the length of side AB, which is the distance we are trying to find.

Let a = 4.15, b = 5.33, and C = 37 degrees. Then, we have:

AB² = a² + b² - 2ab cos(C)

AB² = (4.15)² + (5.33)² - 2(4.15)(5.33) cos(37)

AB² = 17.2225

AB = √17.2225

AB ≈ 4.15 miles

In conclusion, we can use the Law of Cosines to find the distance between two points on opposite sides of a lake, given the lengths of two sides and the angle between them. We can use the formula to calculate the length of the third side, which is the distance we are trying to find.

To learn more about distance click on,

https://brainly.com/question/10104425

#SPJ1

Complete question is:

Mr creole must find the distance from Point A to Point B on opposite sides of a lake. He locates point C that is 4.15 miles from point A and 5.33 miles from point B. He measures the angle ACB to be 37. Find distance  from point A to point B.

The value of C is given as follows:

b. [tex]c = \sqrt{31}[/tex]

The Law of Cosines is a trigonometric formula that relates the lengths of the sides of a triangle to the cosine of one of its angles.

The Law of Cosines states that for any triangle with sides a, b, and c and angle C opposite to side c, the following equation holds true:

c^2 = a^2 + b^2 - 2ab cos(C)

The parameters for this problem are given as follows:

a = 5, b = 6 and C = 60º.

Hence the length C is obtained as follows:

c² = 5² + 6² - 2 x 5 x 6 x cosine of 60 degrees

c² = 31.

[tex]c = \sqrt{31}[/tex]

More can be learned about the law of cosines at https://brainly.com/question/4372174

#SPJ1