write the largest open interval on which f is the antiderivative for f.

True. The Monte Carlo simulation is a technique that uses random sampling to simulate real-life scenarios. It can be used to represent a long period of real-time by using a short period of simulated time.

This is because the simulation can generate a large number of random samples, which can provide a comprehensive picture of the possible outcomes in a shorter time frame.
The Monte Carlo simulation is a technique that can be used to represent a long period of real-time by a short period of simulated time. The statement is true. Monte Carlo simulations use random sampling and statistical models to estimate the probabilities of different outcomes, allowing for the analysis of complex systems over a long period of real-time in a shorter simulated time.

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The length of the radius of the circle is [tex]4\sqrt{73}[/tex].

Let, AB is the chord with a length of 24 centimeters. Line OD is the distance between the chord and the center of the circle. Line r is the radius.

By the chord bisector theorem, line OD bisects the chord AB and it is perpendicular to AB.

Thus, the length of segment AD would be half of the length of AB. i.e,

AD = 12.

As triangle AOD is a right triangle, use Pythagoras theorem in triangle AOD to find the radius of the circle.

[tex]OA^{2} =AD^{2} +OD^{2} \\r^{2} =12^{2} +32^{2} \\r^{2} =144+1024[/tex]

Further simplify,

[tex]r^{2} =\sqrt{1168}\\ r=4\sqrt{ 73[/tex]

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(L3) If there is no indication of congruent or equal segments, you are dealing with a(n) orthocenter .

The altitude is a piece of a perpendicular line that connects the triangle's vertex to either its opposite side or an extension of that side.The orthocenter is located inside the triangle if the triangle is acute, on the vertex that is farthest from the base if the triangle is obtuse, and on the base if the triangle is right-angled. The orthocenter is an important point in the study of triangles, as it has a variety of properties that are useful in problem-solving, such as its relationship with the circumcenter and centroid of a triangle.

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Bill has a total of 3 one-piece jumpsuits, 5 pairs of work pants, and 8 work shirts. To find the number of possible outfits he can wear to work, we can use the multiplication principle.

First, we need to determine how many choices Bill has for his top and bottom. He can either wear a jumpsuit or a combination of pants and a shirt. Therefore, he has 3 + (5 x 8) = 43 choices for his top and bottom.

Next, we can use the multiplication principle to determine the total number of possible outfits he can wear. Since he has 43 choices for his top and bottom, and each outfit combination is independent of the others, we can multiply the number of choices for his top and bottom by the number of one-piece jumpsuits he has.

Therefore, Bill has a total of 43 x 3 = 129 possible outfits he can wear to work.

In summary, Bill has 3 one-piece jumpsuits, 5 pairs of work pants, and 8 work shirts. He can wear either a jumpsuit or pants and a shirt to work. Using the multiplication principle, we determined that he has a total of 129 possible outfits he can wear.

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To form a triangle, the set of line segments must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, we need to check if the given line segments 8 cm, 4 cm, and 3 cm meet this requirement.

We can start by checking if the sum of the two smaller sides (3 cm and 4 cm) is greater than the largest side (8 cm). 3 cm + 4 cm = 7 cm, which is less than 8 cm. Therefore, these three line segments cannot form a triangle.

In general, for a set of line segments to form a triangle, the largest side must be smaller than the sum of the other two sides. In this case, the line segment of 8 cm is too long compared to the other two sides, which makes it impossible to form a triangle.

In conclusion, there are no line segments that meet the requirements to form a triangle with lengths of 8 cm, 4 cm, and 3 cm.

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To test whether the type of animal used for animal crackers is not uniformly distributed, we can use a chi-squared goodness-of-fit test.

The null hypothesis is that the type of animal used for animal crackers is uniformly distributed, while the alternative hypothesis is that it is not uniformly distributed.

We first calculate the expected counts under the assumption of a uniform distribution, which would be 686/6 = 114.33 for each animal.

Animal Observed Count Expected Count

Lion 100 114.33

Tiger 110 114.33

Bear 120 114.33

Rhino 116 114.33

Hippo 130 114.33

Zebra 110 114.33

The test statistic is the chi-squared statistic, which can be calculated as:

χ² = Σ(observed count - expected count)² / expected count

Using the table above, we calculate:

χ² = [(100-114.33)²/114.33] + [(110-114.33)²/114.33] + [(120-114.33)²/114.33] + [(116-114.33)²/114.33] + [(130-114.33)²/114.33] + [(110-114.33)²/114.33] = 7.956

The degrees of freedom for this test is (6-1) = 5.

Using a chi-squared distribution table or calculator, the p-value associated with this test statistic and degrees of freedom is approximately 0.1603.

Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, we do not have convincing evidence to suggest that the type of animal used for animal crackers is not uniformly distributed.

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Antonio started watching the movie at 5:17pm

If the movie ended at 7:00pm, and we know that the movie was 1 hour and 43 minutes long, we can then subtract 1 hour and 43 minutes from 7:00pm to find out what time Antonio started the movie.

To subtract 1 hour and 43 minutes from 7:00pm:

= 19:00 - 1:43

= 17:17

As a 24-hour mode, when we convert 17:17 to 12 hours, this gives us 5:17pm.

Note: The movie ended at 7:00pm

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Answer:

130 square metres

Step-by-step explanation:

The shaded area is a trapezium.

Therefore, the rule for its area is base1+base2/2xh

base1=6

base2=14

height = 13

Therefore, 6+14/2 x 13

= 130

Hope that helped!!! k

A higher slope indicates a stronger relationship between the variables, and the sign (positive or negative) indicates the direction of the relationship (positive: both variables increase together, negative: one variable increases while the other decreases).

When comparing the slopes of the regression lines for two models, you're essentially looking at the differences in their unstandardized coefficients. These coefficients represent the change in the dependent variable for each unit change in the independent variable, keeping all other variables constant.

In the unstandardized model you mentioned, the slope of 0.96 means that for every one-unit increase in the independent variable, the dependent variable is expected to increase by 0.96 units, on average. This helps us understand the strength and direction of the relationship between the two variables in the model.

To compare the slopes between two models, simply examine their unstandardized coefficients.

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The measures of the angle and side is given by:

Blank 1: (x) = 53

Blank 2: AB =

We know that the measure of semi circular central angle is 90 degrees.

So here angle BDA is 90 degrees. [Since the sum of all interior angles of a triangle is 180 degrees according to the Angle Sum Property]

So the sum of angle DAB and angle ABD is 90 degrees.

So, 37 + x = 90

x = 90 - 37

x = 53 degrees.

Now according to trigonometry, AB is Hypotenuse and DB is Base with respect to angle DBA.

Given that the length of side DB is 15 units.

cos(angle DBA) = DB/AB

cos 37 = 15/AB

AB = 15/cos 37

AB = 18.8 (approximated to one decimal place)

Hence the angle x is 53 degrees and side AB will be 18.8 (rounded off to one decimal place) units.

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The graph in the attachment shows that the system of equations, 3y + 3x = 2 and y + x = 8 has: C. No solution

The solution to a system of equations can be determined by finding the coordinate of the point where the lines that represent each of the equations intersect on a coordinate plane when graphed.

Given the system of equations as:

3y + 3x = 2

y + x = 8

The image below shows a red line which represents 3y + 3x = 2 and a blue line that represents y + x = 8. Both lines do not intersect at any point.

Therefore, there is no solution.

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Answer: $24.50

Step-by-step explanation:

We know that each battery  pack contains 4 batteries.

This mean that to get 28 batteries, you would need 7 packs (28/4)

7 battery packs x $3.50 = $24.50

∴, 28 batteries will cost $24.50

After one hour, approximately 364 people will have heard the news.

In general, if n people know the news, then the next round will add 3n new people who also know the news. Therefore, after k rounds (where k is the number of rounds that can fit in an hour), the total number of people who know the news will be:

n + 3n + 3²ⁿ + 3³ⁿ + ... + 3ˣⁿ

To simplify this expression, we can use the formula for the sum of a geometric series:

S = a(1 - rⁿ) / (1 - r)

where S is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms.

In this case, the first term = n ,

the common ratio = 3

and the number of terms = x

Therefore, we can write:

S = n(1 - 3ˣ) / (1 - 3)

Simplifying further, we get:

S = (3ˣ - 1)n / 2

Now we can substitute the values we know:

n = 4

x = 6

Therefore:

S = (3⁶ - 1)4 / 2 = 364

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Complete Question:

Luisa has great news, she communicates it to 3 people. Each of them tells 3 more. This is how a chain is set up, since each new person who learns the news communicates it to three others. It takes one person approximately 10 minutes to communicate the news to three others. If an hour has passed, how many people have heard the news?

Reject the null hypothesis; there is strong evidence to suggest that the Sharpies last longer than a mean of 14 hours.

What is null hypothesis?

In statistics, a null hypothesis is a statement that suggests there is no significant difference between two sets of data, or that any observed difference is due to chance or sampling variation.

Reject the null hypothesis; there is strong evidence to suggest that the Sharpies last longer than a mean of 14 hours.

The calculated t-value of 2.635 is greater than the critical t-value at the 5% significance level, which indicates that the sample mean is significantly different from the hypothesized population mean of 14 hours.

The p-value of 0.006 is also less than the significance level of 0.05, providing strong evidence against the null hypothesis.

Therefore, we can conclude that the Sharpies last longer than a mean of 14 continuous hours, based on the given data.

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Note that the complete statement is:

Note that the translation is -4 units in the x -direction (to the left), and4 units in the y- direction (upwards). That is (-4, 4) Units.

A translation moves  a form up, down, or from side to side, but it has n effect on its appearance . A transformation is an example of translation. A transformation is a method of modifying a shape's size or location. Every point in the shape is translated in the same direction by the same amount.

To go from ⊕ A to   ⊕ B, we can use a combination of translation and  reflection.

We can see that the center of  ⊕ A is at (1,0), and the c  enter of ⊕ B is at (-3,4).

To move from the center of ⊕ A to the center of ⊕ B, we need to translate by -4 units in the x-  direction and 4 units in the y-  direction. This will move the center of ⊕A to the point ( -3,   4), which is the center of ⊕   B.

hence, the translation is -4 units in the x -direction (to the left), and4 units in the y- direction (upwards). That is (-4, 4) Units.

NOte that ⊕ mean circle.

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Answer:

An odd number of data values will always have one middle value

B, D

Step-by-step explanation:

123

2

12345

3

1234567

4

ALWAYS

The amount she will need to pay is $6.95 .

The amount Anye will need is calculated as follows;

The total cost of the two coffees is 2 x $3.55 = $7.10

The total cost of the coffees and muffin is $7.10 + $2.85 = $9.95

Adding the $2 tip, the total cost becomes $9.95 + $2 = $11.95.

If Anye has a $5 gift card, the amount she will need to pay is calculated as;

= $11.95 - $5

= $6.95

Therefore, Anye will need $6.95 in cash to pay for the rest of the order.

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The reference angle for a rotation of 334° is 26°.

A reference angle is the smallest acute angle between the terminal side of an angle and the x-axis. To find the reference angle of a given angle, you need to subtract the nearest multiple of 360° from the given angle until the resulting angle is between 0° and 360°.

In this case, 334° is greater than 360°, so you can subtract 360° from it once to get 334° - 360° = -26°. Since the reference angle is always positive, you can take the absolute value of -26° to get 26°. Therefore, the reference angle for a rotation of 334° is 26°.

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The correct order of magnitudes is:

hurricane > tornado and 10 > 100

What is a sequence?

A sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms).

The diameter of a typical tornado is usually much smaller than that of a typical hurricane.

The diameter of a tornado can range from a few tens of meters to about 2 km, while the diameter of a hurricane can range from a few hundred kilometers to more than 1,000 km.

Therefore, the correct order of magnitudes for the diameter of a typical hurricane and a typical tornado, from largest to smallest, is:

10,000 (this is too large for both hurricanes and tornadoes)

1,000 (this is still too large for both hurricanes and tornadoes)

100 (this is a possible diameter for a tornado, but it's too small for a hurricane)

10 (this is a typical diameter for a tornado)

Hence, the correct order of magnitudes is:

hurricane > tornado and 10 > 100

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The answer is option 3: at least 22%, but less than 29%.

Let J be the random variable representing Jordan's arrival time, and let T be the random variable representing Taylor's arrival time.

Then, J is uniformly distributed between 8:00AM and 8:50AM, which means that J ~ U(480, 530) (measured in minutes past 12:00AM).

Similarly, T is uniformly distributed between 8:00AM and 8:30AM, which means that T ~ U(480, 510).

We want to find the probability that they meet, which means that Jordan arrives before Taylor leaves (within 10 minutes of Taylor's arrival time). Let's assume that Taylor arrives at time t (measured in minutes past 12:00AM). Then, Jordan needs to arrive between t-10 and t in order to meet Taylor.

The probability of this happening is:

P(J ∈ [t-10, t]) = (t - (t-10)) / (530 - 480) = 10/50 = 0.2

Since Taylor's arrival time is also uniformly distributed, we need to take the average of this probability over all possible values of t between 480 and 510:

P(meeting) = E[P(J ∈ [t-10, t])] for t ∈ [480, 510]

P(meeting) = (1/31) ∫₄₈₀ ⁴⁹⁰ [0.2] dt + (1/31) ∫₄₉₀ ⁵₀₀ [0.2] dt + (1/31) ∫₅₀₀ ⁵₁₀ [0.2] dt

P(meeting) = (1/31) [((0.2)(10)) + ((0.2)(20)) + ((0.2)(30))]

P(meeting) = 0.1935

Therefore, the probability that Jordan and Taylor meet is approximately 0.1935, which is between 16% and 22%.

Therefore, the answer is option 3: at least 22%, but less than 29%.

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a) The probability distribution are P(S₂ = -2) = 1/9, P(S₂ = -1) = 2/9, P(S₂ = 0) = 1/9, P(S₂ = 1) = 2/9, P(S₂ = 2) = 2/9, P(S₂ = 3) = 2/9, P(S₂ = 4) = 1/9

b) The probability that the particle's position S90,000 is less than or equal to 29,500 is approximately 0.0571.

In this problem, we are given a particle's initial position S₀ = 0, and its position Sₙ after n time intervals, where the position is a sum of n independent and identically distributed random displacements X₁, X₂, ..., Xₙ. Each displacement Xᵢ can take on one of three values: -1, 0, or 2, with equal probability 1/3 for each.

(a) To find the probability distribution of S₂ = X₁ + X₂, we can enumerate all possible values of S₂ and compute their probabilities. The possible values of S₂ are -2, -1, 0, 1, 2, 3, 4, and their respective probabilities are:

P(S₂ = -2) = P(X₁ = -1, X₂ = -1) = (1/3)² = 1/9

P(S₂ = -1) = P(X₁ = -1, X₂ = 0) + P(X₁ = 0, X₂ = -1) = 2(1/3)² = 2/9

P(S₂ = 0) = P(X₁ = 0, X₂ = 0) = (1/3)² = 1/9

P(S₂ = 1) = P(X₁ = 2, X₂ = -1) + P(X₁ = -1, X₂ = 2) = 2(1/3)² = 2/9

P(S₂ = 2) = P(X₁ = 2, X₂ = 0) + P(X₁ = 0, X₂ = 2) = 2(1/3)² = 2/9

P(S₂ = 3) = P(X₁ = 2, X₂ = 1) + P(X₁ = 1, X₂ = 2) = 2(1/3)² = 2/9

P(S₂ = 4) = P(X₁ = 2, X₂ = 2) = (1/3)² = 1/9

(b) To compute P(S90,000 ≤ 29,500), we can use the Central Limit Theorem (CLT) to approximate the distribution of S90,000. The CLT states that the sum of a large number of independent and identically distributed random variables tends to follow a normal distribution, regardless of the underlying distribution of the individual variables. For n large enough, we have:

S90,000 ≈ N(μ, σ²), where μ = nE(X) and σ² = nVar(X)

Here, n = 90,000, E(X) = (-1 + 0 + 2)/3 = 1/3, and Var(X) = [(2-1/3)² + (-1-1/3)² + (0-1/3)²]/3 = 10/9. Therefore, we have:

μ = 90,000(1/3) = 30,000

σ² = 90,000(10/9) ≈ 100,000

Now, we can standardize the variable Z = (S90,000 - μ)/σ and use a standard normal table or calculator to find the probability:

P(S90,000 ≤ 29,500) = P(Z ≤ (29,500 - 30,000)/√100,000) ≈ P(Z ≤ -1.58) ≈ 0.0571 (rounded to four decimal places)

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The solution to the system of equations is w = 0 and z = -2

Given equations are 3w - 4z = 8   ...(1)

2w + 3z = - 6          ...(2)

By multiplying the first equation by 3 and the second equation by 4, we get:

9w - 12z = 24        ...(3)

8w + 12z = -24      ....(4)

Adding equation (1) and (2)

17w + 0 = 0

w = 0

Putting the value of w in first equation

3(0) - 4z = 8

- 4z = 8

z = - 2

Therefore, the solution to the system of equations is w = 0 and z = -2

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We can estimate that about 31.5% + 43% = 74.5% of the observations are between 50 and 90.

To find out what percent of the observations are between 50 and 90, we need to first calculate the interquartile range (IQR).

The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). We can calculate Q1 and Q3 using the five-number summary:

Q1 = 35 + 0.25(50-35) = 42.5
Q3 = 70 + 0.25(90-70) = 77.5

So the IQR is: IQR = Q3 - Q1 = 77.5 - 42.5 = 35

Now we can use the IQR to estimate what percent of the observations are between 50 and 90. Since the data is roughly symmetric and follows a normal distribution, we can assume that about 50% of the data falls within one standard deviation of the mean. In this case, the IQR represents about one standard deviation of the data.

Therefore, we can estimate that about 68% of the observations fall within one IQR of the mean. Since the IQR spans from 35 to 77.5, we can estimate that about 68% of the observations fall between these values.

To estimate the percent of observations between 50 and 90, we need to determine how many standard deviations away from the mean these values are.

50 is (50 - 60)/35 = -0.29 standard deviations away from the mean.
90 is (90 - 60)/35 = 0.86 standard deviations away from the mean.

Using the empirical rule, we can estimate that about 63% of the observations fall within one standard deviation of the mean. Since 50 is less than one standard deviation away from the mean, we can estimate that less than 31.5% of the observations fall between 50 and the mean.

Similarly, we can estimate that about 86% of the observations fall within two standard deviations of the mean. Since 90 is less than two standard deviations away from the mean, we can estimate that less than 43% of the observations fall between the mean and 90.

Therefore, we can estimate that about 31.5% + 43% = 74.5% of the observations are between 50 and 90.

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The correct p-value for the test of H0: p = 0.25 versus H1: p > 0.25 is 0.375.

In this question, we are given two hypotheses:

H0: p = 0.25

H1: p < 0.25

The p-value for this test is 0.625. This means that if the null hypothesis is true, we would observe a sample proportion as extreme as, or more extreme than, the observed proportion with a probability of 0.625.

Now, we need to find the correct p-value for the alternative hypothesis:

H0: p = 0.25

H1: p > 0.25

Since the null hypothesis is that p = 0.25, the sampling distribution of the sample proportion is approximately normal with mean 0.25 and standard deviation √(0.25*(1-0.25)/n), where n is the sample size.

The observed sample proportion is not given in the question, so we cannot calculate the exact p-value. However, we can use the fact that the p-value is the area in the tail of the distribution beyond the observed sample proportion.

Since the alternative hypothesis is p > 0.25, the observed sample proportion is less than the null hypothesis value of 0.25. Therefore, the area in the right tail beyond the observed sample proportion is the complement of the original p-value of 0.625.

This means that the correct p-value for the test of H0: p = 0.25 versus H1: p > 0.25 is 1 - 0.625 = 0.375.

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A male at the 70th percentile has a body temperature of 98.26°F.

The body temperature of a male at the 70th percentile, we need to use the cumulative distribution function (CDF) of the normal distribution.

The CDF gives the probability that a random variable (in this case, body temperature) is less than or equal to a certain value.

A standard normal distribution table or a calculator to find the corresponding z-score for the 70th percentile, and then use the formula:

z = [tex](x - \mu) / \sigma[/tex]

x is the body temperature we want to find, mu is the mean, sigma is the standard deviation, and z is the z-score corresponding to the 70th percentile.

Using a standard normal distribution table, we find that the z-score for the 70th percentile is approximately 0.52.

Plugging in the values we have:

0.52 = (x - 98.1) / 0.30

Solving for x, we get:

x = 98.1 + 0.30 × 0.52

x = 98.26°F

To draw a well-labeled sketch to support the answer, we can start by drawing a normal distribution curve with the mean of 98.1°F and a standard deviation of 0.30°F.

The point on the x-axis corresponding to the body temperature of a male at the 70th percentile, which is 98.26°F.

The area under the curve to the left of this point, which represents the probability that a male has a body temperature less than or equal to 98.26°F.

The resulting sketch would look like this:

Normal Distribution Curve with 70th Percentile

The shaded area under the curve represents the probability that a male has a body temperature less than or equal to 98.26°F, is approximately 0.70 or 70%.

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There is not enough evidence to reject the claim that the mean time it takes smokers to quit smoking permanently is 13 years.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

To find the standardized test statistic (Z-score), we need to first calculate the sample mean and standard error of the mean.

Sample mean:

x = (17.8 + 21.1 + 19.7 + 9.5 + 18.5 + 13.2 + 13.6 + 10.7 + 19.1 + 7.5 + 11.3 + 7.6 + 21.8 + 9.2 + 21.6 + 9.8 + 19.3 + 21.9 + 22.6 + 15.5 + 12.4 + 9.5 + 14.9 + 7.7 + 12.9 + 17.6 + 14.1 + 19.4 + 17.1 + 17.3 + 15.4 + 22.5) / 32

x = 15.91875

Standard error of the mean:

SE = σ /√(n)

SE = 6.1 / √(32)

SE = 1.0823

Now we can calculate the Z-score:

Z = (x - μ) / SE

Z = (15.91875 - 13) / 1.0823

Z = 2.5707

we can find that the p-value associated with a Z-score of 2.5707 is approximately 0.0051.

Since the significance level (α) is 0.06, which is larger than the p-value, we fail to reject the null hypothesis.

Therefore, there is not enough evidence to reject the claim that the mean time it takes smokers to quit smoking permanently is 13 years.

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The simplified value of the expression given as 7^(3 +12)/7^5  is 7^10

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

7^3+^12-^75

Expess properly

So, we have the following representation

7^(3 +12)/7^5

Evaluate the sum of the exponents

So, we have the following representation

7^15/7^5

When the exponents are simplified, we have

7^10

Hence, the simplified expression of 7^(3 +12)/7^5  is 7^10

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The statement is true. Therefore, we have shown that [tex](rA)^{(-1)} = A^{(-1)}/r,[/tex]which implies that [tex](rA)^{(-1)} = r^{(-1)}\times A^{(-1)[/tex]. Hence, [tex](rA)^{(-1) }= rA^{(-1)[/tex], since r is nonzero.

To prove this, we can start with the definition of the inverse of a matrix:

If A is an invertible matrix, then its inverse, denoted as [tex]A^{(-1),[/tex] is the unique matrix such that [tex]A\times A^{(-1)} = A^{(-1)} \times A = I[/tex], where I is the identity matrix.

Now, let's consider the matrix rA, where r is a nonzero scalar. We want to find its inverse, denoted as [tex](rA)^{(-1)[/tex].

We can start by multiplying both sides of the equation [tex]A\times A^{(-1)} = I[/tex] by r:

[tex]rA\times A^{(-1)} = rI[/tex]

Next, we can multiply both sides of this equation by A from the left:

[tex]rA\times A^{(-1)}A = rIA\\rAI = rA = rA(A\times A^{(-1)})[/tex]

Now, we can use the associative property of matrix multiplication to rearrange the right-hand side of this equation:

[tex]rA\times(AA^(-1)) = (rAA)\times A^{(-1)}\\rA\times I = (rA)\times A^{(-1)}\\rA = (rA)\times A^{(-1)}[/tex]

Finally, we can multiply both sides of this equation by [tex](rA)^{(-1)[/tex] from the left to obtain:

[tex](rA)^{(-1)}rA = (rA)^{(-1)}(rA)\times A^{(-1)}\\I = A^{(-1)}[/tex]

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Answer:

Factor x^2 - 4 into (x - 2)(x + 2). Cancel out the x + 2 factor. Then multiply.

[tex] \frac{9x + 14}{ {x}^{2} - 4} \times \frac{x + 2}{x + 1} [/tex]

[tex] \frac{9x + 14}{(x - 2)(x + 2)} \times \frac{x + 2}{x + 1} [/tex]

[tex] \frac{9x + 14}{(x - 2)(x + 1)} [/tex]