An equiangular hexagon has side lengths of 6, 8, 12, 6, 8, and 12 in that order. What is the area of this hexagon

The length of the missing side for the triangle is equal to 5.96 to the nearest tenth hundredth using the sine rule.

The sine rule is a relationship between the size of an angle in a triangle and the opposing side.

First, we find the angle opposite the side length 5 as follows;

180 - (34 + 118) = 28 {sum of interior angles of a triangle}

Using the sine rule;

5/sin28° = ?/sin34°

? = (5 × sin34°)/sin28° {cross multiplication}

? = 5.9556

Therefore, the length of the missing side for the triangle is equal to 5.96 to the nearest tenth hundredth using the sine rule.

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To construct a frequency distribution for categorical data, you need to follow a systematic approach. Firstly, identify the categories or groups present in the data set.

Then, count the number of observations that appear in each category. This step is crucial as it helps you understand the distribution and frequency of each category within the dataset.

Once you have the count of observations for each category, you can proceed to calculate the relative frequencies, which are obtained by dividing the number of observations in a specific category by the total number of observations in the dataset. This step enables you to comprehend the proportion of each category in relation to the entire dataset.

Lastly, organize and present the data in a meaningful format, such as a table or a chart, to help visualize the distribution of the categorical data effectively. By following these steps, you can successfully construct a frequency distribution for categorical data and analyze the trends and patterns that emerge.

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Answer:

P = $140 (the principal amount)

r = 6% per year (the annual interest rate)

n = 12 (the number of times the interest is compounded per year, since it is compounded monthly)

t = 15 years (the time period)

A(15) = $140(1 + 0.06/12)^(12*15)

A(15) = $140(1 + 0.005)^180

A(15) = $281.49

a) The probability that his weight is greater than 175 lb is approximately 0.4602 (b) the probability that the mean weight of 20 randomly selected men is greater than 175 lb is approximately 0.6772.

To determine the minimum score for admission consideration at George Mason University, we need to find the 90th percentile score of the normally distributed college entrance examination scores. The mean score is 550 and the standard deviation is 100.

Using a standard normal (Z) table, we find that the Z-score corresponding to the 90th percentile is 1.28. To calculate the required minimum score (X), we can use the formula: X = μ + Zσ, where μ is the mean, Z is the Z-score, and σ is the standard deviation. Thus, X = 550 + (1.28)(100) = 550 + 128 = 678. An applicant must score at least 678 to be considered for admission.

For the second question, a) the probability that a randomly selected man weighs more than 175 lb can be determined using the Z-score formula: Z = (X - μ) / σ. Plugging in the values, Z = (175 - 172) / 29 ≈ 0.10. Checking the Z-table, we find the probability to be approximately 0.4602.

b) To find the probability that the mean weight of 20 randomly selected men is greater than 175 lb, we first determine the standard error (SE) of the sample mean using the formula: SE = σ / √n, where σ is the population standard deviation and n is the sample size. In this case, SE = 29 / √20 ≈ 6.48. Now, we calculate the Z-score: Z = (175 - 172) / 6.48 ≈ 0.46. Referring to the Z-table, the probability is approximately 0.6772.

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There are 43,200 number of ways to arrange the letters in UNIVERSALLY so that no two vowels occur consecutively and the consonants appear in alphabetical order.

To find the number of ways to arrange the letters in UNIVERSALLY so that no two vowels occur consecutively and the consonants appear in alphabetical order, follow these steps:

1. Identify the vowels and consonants: Vowels are U, I, E, A, and Y; consonants are N, R, S, S, L, and L.

2. Arrange the consonants in alphabetical order: L, L, N, R, S, S.

3. Count the number of positions available for placing the vowels: There are 7 positions available for the vowels (between the consonants and at the beginning and the end of the word), which are _ L _ L _ N _ R _ S _ S _.

4. Count the permutations of the vowels: There are 5 vowels with the letters U, I, E, A, and Y occurring once. So there are 5! = 120 permutations.

5. Consider the consonants with repeating letters: Since there are two Ls and two Ss, we must divide the total permutations by the product of the repetitions (2! for L and 2! for S). Therefore, there are 6!/(2!*2!) = 360 arrangements for consonants.

6. Combine the permutations of vowels and consonants: To find the total number of ways to arrange the letters, multiply the permutations of vowels (120) by the arrangements for consonants (360).

120 * 360 = 43,200

So, there are 43,200 ways to arrange the letters in UNIVERSALLY so that no two vowels occur consecutively and the consonants appear in alphabetical order.

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The corresponding matrix is equal to its transpose conjugate, satisfying the property of Hermitian operators.

To demonstrate that a Hermitian operator Q has matrix elements satisfying Qmn = Qnm*, we first need to understand the properties of Hermitian operators and orthonormal bases.

A Hermitian operator Q is defined as an operator that satisfies Q† = Q, where Q† is the adjoint of Q. In the context of matrix representations, this means that the Hermitian matrix is equal to its conjugate transpose.

An orthonormal basis consists of a set of orthogonal unit vectors, which means that any two distinct vectors in the set have a dot product equal to zero, and the dot product of a vector with itself equals one.

Now, let's consider the matrix elements Qmn and Qnm. Given an orthonormal basis {|n⟩} and a Hermitian operator Q, we can write:

Qmn = ⟨m|Q|n⟩
Qnm = ⟨n|Q|m⟩

To prove the relationship Qmn = Qnm*, we need to show that the adjoint of the operator Q acts on the basis states in the following manner:

⟨m|Q†|n⟩ = ⟨n|Q|m⟩*

Since Q is Hermitian, we have Q† = Q, which gives us:

⟨m|Q|n⟩ = ⟨n|Q|m⟩*

This equation shows that the matrix element Qmn is equal to the complex conjugate of the matrix element Qnm.

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The height of the carpenter's creation is 8 feet and the width is 7 feet.

To solve this problem, we can use two equations. The first equation is based on the relationship between the width and height:

width = 3(height) - 17

The second equation is based on the amount of lumber the carpenter has available:

2(width) + 2(height) = 30

We can substitute the first equation into the second equation to solve for height:

2(3(height) - 17) + 2(height) = 30

6(height) - 34 + 2(height) = 30

8(height) = 64

height = 8

Using the first equation, we can solve for the width:

width = 3(8) - 17 = 24 - 17 = 7

Therefore, the height is 8 feet and the width is 7 feet.

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Answer:

I hope this helps !

Step-by-step explanation:

Using the central angle theorem, the degree measure of x is 53°.

The length of AB is 18.8 units.

Given a circle.

We have the central angle theorem,

We have that the angle subtended by an arc of a circle at the center is twice the angle subtended by the same arc at any point on the circle.

Here, the arc is semicircle.

Angle subtended by semicircle at the center= 180°

So, ∠ADB = 180° / 2 = 90°

Interior angles of a triangle sum up to 180°.

x = 180 - (37 + 90) = 53°

sin (x) = BD / AB

sin (53) = 15 / AB

AB = 15 / sin (53)

AB = 18.78 ≈ 18.8 units

Hence the measure of x is 53° and the length of AB is 18.8 units.

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The surface area of the actual Kaaba is 1260 square meters.

To find the surface area of the actual Kaaba, we need to know the dimensions of the real Kaaba. Since we know the dimensions of Kamal's replica and the scale factor, we can use proportion to find the dimensions of the actual Kaaba.

Let x be the length of the actual Kaaba in meters.

Then we have:

x/24 = 50

x = 24 × 50 = 1200 cm = 12 meters

Similarly, the width and height of the actual Kaaba can be found using the same method:

Width of actual Kaaba = 21 cm × 50 = 1050 cm = 10.5 meters

Height of actual Kaaba = 30 cm × 50 = 1500 cm = 15 meters

Now we can find the surface area of the actual Kaaba. The surface area of a rectangular prism (which the Kaaba resembles) is given by:

Surface area = 2lw + 2lh + 2wh

Plugging in the values we found, we get:

Surface area = 2(1210.5) + 2(1215) + 2(10.5 × 15) = 1260 square meters

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Answer: False, normal distribution describes continuous random variables and not discrete random variables

Step-by-step explanation: To describe discrete random variables other patterns of distributions can be used like binomial distribution. Therefore it is not recommended to use normal distribution for them.

Although in rare cases values of discrete variables can be approximated via normal distribution too but these won't be accurate values hence highly unstable.

The amount of cream in the coffee cup and the amount of coffee in the pitcher of cream remain the same.

When a spoonful of cream is taken from the pitcher and put into the coffee cup, the amount of cream in the pitcher decreases and the amount of cream in the coffee cup increases.

However, when a spoonful of the mixture is put back into the pitcher, the amount of cream in the pitcher increases again and the amount of cream in the coffee cup decreases.

Since the amount of coffee in the pitcher and the cup remains constant throughout this process, there is no net increase or decrease in the amount of coffee or cream in either container.

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Significant correlations are useful statistical tools for identifying relationships between variables, but they are not able to indicate causality.

While they can demonstrate the strength of the effect through the correlation coefficient, the size of the effect by examining the magnitude of the relationship, and the probability level by evaluating the likelihood that the observed relationship occurred by chance, they cannot prove that one variable directly causes changes in another variable.

Correlations can only show that two variables are related, but they do not provide information about the nature of that relationship. It is important to remember that correlation does not imply causation. There might be other factors, known as confounding variables, that affect both variables and create the appearance of a relationship where none truly exists.

To determine causality, researchers must conduct controlled experiments where they manipulate the independent variable and observe the effect on the dependent variable, while holding all other factors constant. This allows them to isolate the cause-and-effect relationship between the two variables and draw more accurate conclusions.

In summary, while significant correlations can provide valuable information about the strength, size, and probability level of the relationship between variables, they cannot establish causality. To determine if one variable truly causes changes in another, controlled experiments must be conducted.

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Answer:

-4

Step-by-step explanation:

H=4x-4

4x-4(4) write into equation

4x-16 multiply the fours

x=-4 divide both sides by four and you get your answer

Therefore, It will take approximately 5.68 hours for the colony of cells to reach 500, based on the given exponential equation.

In order to find out how many hours it will take for the colony of cells to reach 500, we can set up an exponential equation. Let's call the number of hours it takes for the colony to reach 500 "x". Using the information given in the problem, we know that the number of cells in the colony can be represented by the equation 10 * 3^x = 500.
To solve for x, we can divide both sides by 10 and take the logarithm of both sides. This gives us x = log(500/10) / log(3) ≈ 5.68 hours. Therefore, it will take approximately 5.68 hours for the colony of cells to reach 500.
Therefore, It will take approximately 5.68 hours for the colony of cells to reach 500, based on the given exponential equation.

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The null hypothesis is that the mean shearing strength of the rivets is equal to or greater than 725 lbs. The alternative hypothesis is that the mean shearing strength is less than 725 lbs. There is evidence at the 0.10 level of significance

Using a one-tailed test with a significance level of 0.10, we can determine if the sample data provides evidence to reject the null hypothesis in favor of the alternative.

The null hypothesis can be stated as H₀: µ ≥ 725, and the alternative hypothesis can be stated as H₁: µ < 725.

To test this hypothesis, we can use a t-test with a t-statistic of:

t = ([tex]\bar{X}[/tex] - µ₀) / (s / √n)

Where [tex]\bar{X}[/tex] is the sample mean, µ₀ is the null hypothesis mean (725 lbs.), s is the sample standard deviation, and n is the sample size.

Plugging in the given values, we get:

t = (720 - 725) / (20 / √50) = -1.77

Using 49 degrees of freedom (n-1), at a significance level of 0.10 and a one-tailed test, the critical t-value is -1.645. Since our calculated t-value (-1.77) is less than the critical t-value, we can reject the null hypothesis in favor of the alternative.

This means that there is evidence at the 0.10 level of significance that the mean shearing strength of the rivets is below 725 lbs.

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In terms of probability, we can say that the probability of selecting a coffee maker with a defective cord is 5.0% or 0.05. The percentage of coffee makers with a defective cord.

To find the probability of a coffee maker having a defective cord, we'll use the given information about faulty switches and defective cords.

We know that:
1. 6.0% of coffee makers have either a faulty switch or a defective cord.
2. 1.5% have a faulty switch.
3. 0.5% have both defects.

Using the formula for the probability of the union of two events (A or B) - P(A ∪ B) = P(A) + P(B) - P(A ∩ B), where A represents the event of a faulty switch, B represents the event of a defective cord, and A ∩ B represents both defects:

P(A ∪ B) = 6.0% (either a faulty switch or a defective cord)
P(A) = 1.5% (faulty switch)
P(A ∩ B) = 0.5% (both defects)

We need to find P(B), the probability of a coffee maker having a defective cord.

Using the formula, we can write:
6.0% = 1.5% + P(B) - 0.5%

Now, we'll solve for P(B):
6.0% = 1.0% + P(B)
P(B) = 6.0% - 1.0%
P(B) = 5.0%

Therefore, the probability (percent) of a coffee maker having a defective cord is 5.0%.

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It appears that your question is related to the validity of a test measuring academic ability in high school students and its correlation with freshman year college grades. The terms are "predictive validity" and "correlation."

When a test of academic ability given to high school students is found to be correlated with grades during the freshman year at college, it indicates that the test has predictive validity. Predictive validity refers to the extent to which a test or assessment can effectively predict an individual's future performance or outcome. In this case, the academic ability test serves as a predictor of the students' academic performance in their first year of college.

A positive correlation between the test scores and college grades means that higher test scores are generally associated with better college grades and vice versa. This relationship suggests that the test is a useful tool for predicting academic success at the college level. However, it is important to keep in mind that correlation does not necessarily imply causation, and there may be other factors influencing the students' performance in college.

In conclusion, a test of academic ability given to high school students that is correlated with freshman year college grades demonstrates predictive validity, suggesting that the test can effectively predict future academic success. The correlation between the test scores and college grades is an essential consideration when evaluating the usefulness of such a test in predicting academic performance at the college level.

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To prove that e(h) has a minimum at h = 3€/M, we need to first understand the terms involved. The upper bound for total numerical error E h2 eh) + M h 6 refers to the maximum possible error in a numerical computation.

It includes two types of error: the truncation error (E h2) which results from approximating a mathematical function using a finite number of terms, and the round-off error (eh) which results from the limited precision of computer arithmetic.
The numerical error e(h) is a function of the step size h used in numerical approximations. It is given by e(h) = E h2 + M h 6 + eh.
Now, to prove that e(h) has a minimum at h = 3€/M, we can take the derivative of e(h) with respect to h and set it to zero.
de(h)/dh = 2Eh - Mh5 + eh'
Setting this equal to zero, we get:
2Eh - Mh5 + eh' = 0
Rearranging and solving for h, we get:
h = (2E/Me')^(1/4)
Substituting this value of h in e(h), we get:
e(h) = (4/3)^(3/4) * (EM)^(1/4) * eh'
Since eh' is a constant, e(h) is minimized when EM is minimized.
Therefore, we need to find the minimum value of EM, which is achieved when h = 3€/M.
Thus, we can conclude that e(h) has a minimum at h = 3€/M.

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The mean is 172, the variance is 34.4, and the standard deviation is 5.86.

The United States has a system of bicameralism, which means that each state has two chambers in its legislature: a lower chamber (such as the Assembly or House of Representatives) and an upper chamber (such as the Senate).

The number of constituents per district in each chamber varies from state to state, and it is usually determined by the state's constitution or by a state redistricting commission.

As of the 2010 census, Texas had about 811,147 constituents per state senate district.

However, this is not the highest number of constituents per senator among all the states.

In fact, the state with the highest number of constituents per senator is California.

According to the U.S. Census Bureau, as of the 2010 census, California had a population of approximately 37.3 million people.

The state's constitution provides for 40 state senators, which means that each senator represents approximately 933,000 constituents.

This is significantly higher than the number of constituents per senator in Texas.

The high number of constituents per senator in California can be attributed to the state's large population and the fact that the number of state senators has not kept up with population growth.

The last time the number of state senators in California was increased was in 1973, when the state's population was around 20 million people.

In conclusion, while Texas has a high number of constituents per state senate district, it is not the only state with a high number of constituents per senator.

California has a significantly higher number of constituents per senator, due to its large population and the fact that the number of state senators has not kept up with population growth.

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Answer: If the question is how many halves will you need in total, then the answer is 14 halves in total or 7 wholes      

Step-by-step explanation:

Answer:

That's a total of 7 cupcakes.

Step-by-step explanation:

5 halves is 2 1/2.

6 halves is 3.

3 halves is 1 1/2.

2 + 3 + 1 + (1/2 + 1/2)

2 + 3 + 1 + (1)

2 + 3 + 1 + 1

5 + 1 + 1

6 + 1

7

If the sampled points are spatially correlated in kriging, then one would expect an increase in the semivariance with an increase in the distance between sampled points.

Step-by-step explanation:

1. Kriging is a geostatistical interpolation technique used to estimate values at unsampled locations based on sampled data points.
2. Spatial correlation refers to the relationship between values at different locations in space.
3. Semivariance is a measure of how much the values at different locations vary, and it is used to quantify the spatial correlation in kriging.
4. When the sampled points are spatially correlated, the semivariance will generally increase as the distance between sampled points increases.
5. This increase in semivariance with distance is due to the fact that points that are farther apart are less likely to have similar values than points that are closer together.

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This domain may be rewritten as:

[tex][tex]-3\le x\le4\, and\, 4[/tex]

Thus, option C is correct.

In the graph, we can see the domain by looking at the x values in which the function is defined.

As we can see, the left part of the graph starts at point (-3, 9) and it is filled so it includes it. So, the domain "starts" at x = -3, values below it are undefined on the function.

The quadratic part ends at point (4, 16), so at x = 4 and including it. However, the linear part starts at (4, -1), excluding the point, so at the exact point one ends, the other starts, and no x value is left out on the the transition from one part to the other.

Then, the linear part is defined until point (9, -3.xxx). We don't know exactly the value of the y coordinate, bu the x = 9 is enough for use to know that the function is only defined until x = 9, including it.

Putting these together, we see that the function is defined between the x values of -3 and 9, including both, so the domain is:

[tex][tex]-3\le x\le9\,[/tex]

As the proper alternative divided this interval into the quadratic and linear sections, we don't have an accurate alternative.

So, this domain may be rewritten as:

[tex][tex]-3\le x\le4\, and\, 4[/tex]

Thus, option C is correct.

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If the z-score falls below the critical value, we reject the null hypothesis and conclude that the proportion of people who own cats is indeed smaller than 30%.

The null hypothesis is typically denoted as H0, and the alternative hypothesis is denoted as H1 or Ha. In this case, the hypotheses would be:

H0: The proportion of people who own cats is equal to or greater than 30%.

H1: The proportion of people who own cats is less than 30%.

We can represent this symbolically as:

H0: p >= 0.3

H1: p < 0.3

where p represents the true proportion of people who own cats in the population.

To test this claim, we can use a one-tailed z-test for proportions, where we calculate the z-score of the sample proportion and compare it to the critical value of the standard normal distribution at the chosen significance level (0.05 in this case).

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This hypothesis aims to determine if the random sample of 2,000 U.S. adults taking an average of 5,863 steps per day with a standard deviation of 2,870 is strong evidence to support the claim that U.S. adults take fewer steps than the 7,000 steps threshold.

The alternative hypothesis in this scenario would be that the average number of steps taken by U.S. adults is less than 7,000 per day. This hypothesis is being tested to determine if there is strong evidence that the true average number of steps per day is lower than the commonly accepted average. The random sample of 2000 U.S. adults helps to ensure that the results are representative of the larger population. The alternative hypothesis for this study would be: "On average, U.S. adults take fewer than 7,000 steps per day."

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The confidence level for the given interval of 13.45 to 14.15 days is 95%, which means that we can be 95% confident that the true mean survival time falls within this range.

Based on the given information, we know that a random sample of 25 rats exposed to 10Sv of radiation has a mean lifetime of x=13.8 days. We also know that the LD100 is 14 days, and that the lifetimes for this level of exposure follow a normal distribution with unknown mean and standard deviation 0.75.

The report states that a confidence interval for the true mean survival time extends from 13.45 to 14.15 days, which means that we can be 95% confident that the true mean survival time falls within this range. This is because the confidence level for this interval is 95%.

To calculate this, we can use the formula:

Confidence level = 1 - alpha

where alpha is the significance level, which is typically set to 0.05 for a 95% confidence level. This means that there is a 5% chance that the true mean survival time is outside the given interval.

In conclusion, the confidence level for the given interval of 13.45 to 14.15 days is 95%, which means that we can be 95% confident that the true mean survival time falls within this range.

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The speed of the boat in still water is 8 miles per hour.

Let's call the speed of the boat in still water "x" (in miles per hour).

When Mackenzie rows downstream, the current is helping her, so the effective speed of the boat is (x + 4) miles per hour. The distance traveled is 96 miles. We can use the formula:

distance = rate × time

to set up an equation for the downstream trip:

96 = (x + 4) t

where "t" is the time (in hours) it takes for the downstream trip.

For the upstream trip, the current is working against Mackenzie, so the effective speed of the boat is (x - 4) miles per hour. The distance traveled is still 96 miles, but this time the trip takes 16 hours longer than the downstream trip. So we can set up another equation:

96 = (x - 4) (t + 16)

Now we have two equations with two unknowns (x and t). We can solve for t in the first equation and substitute into the second equation:

96 = (x - 4) (t + 16)

96 = (x - 4) (96/(x + 4) + 16)

Simplifying, we get:

96 = (x - 4) (96/(x + 4) + 16)

96 = 96(x - 4)/(x + 4) + 16(x - 4)

96(x + 4) = 96(x - 4) + 16(x + 4)(x - 4)

96x + 384 = 96x - 384 + 16(x^2 - 16)

96x + 384 = 96x - 384 + 16x^2 - 256

16x^2 = 256 + 384 + 384

16x^2 = 1024

x^2 = 64

x = 8

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The probability that the cycle time exceeds 60 minutes given that it exceeds 55 minutes is 2/1 or simply 1, which means it is certain that the cycle time exceeds 60 minutes if it exceeds 55 minutes.

Given that the cycle time for trucks hauling concrete to a highway construction site is uniformly distributed over the interval 50 to 70 minutes, we know that the probability density function is:

f(x) = 1 / (70 - 50) = 1/20, for 50 <= x <= 70

To find the probability that the cycle time exceeds 60 minutes given that it exceeds 55 minutes, we need to use conditional probability:

P(X > 60 | X > 55) = P(X > 60 and X > 55) / P(X > 55)

We can simplify this by noticing that if X is greater than 55, then it must be between 55 and 70, and therefore:

P(X > 55) = P(55 <= X <= 70) = (70 - 55) / (70 - 50) = 1/4

Similarly, we can rewrite the numerator as:

P(X > 60 and X > 55) = P(X > 60)

since if X is greater than 60, it is also greater than 55.

Now, to find P(X > 60), we integrate the density function from 60 to 70:

P(X > 60) = ∫60^70 (1/20) dx = (1/20) × (70 - 60) = 1/2

Putting it all together:

P(X > 60 | X > 55) = P(X > 60 and X > 55) / P(X > 55)

= P(X > 60) / P(X > 55)

= (1/2) / (1/4)

= 2

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The absolute maximum value of f on the interval [-1,3] is -3 and the absolute minimum value is approximately -1.732.

To find the absolute maximum and minimum values of f(t) = t - (3/t) on the interval [-1, 3], we need to perform the following steps:

1. Find the critical points by taking the derivative of the function and setting it to zero.
2. Evaluate the function at the critical points and the endpoints of the interval.
3. Compare the values to determine the absolute maximum and minimum.

Step 1: Find the critical points.

f(t) = t - (3/t)
To find the derivative, use the power rule and the quotient rule:
f'(t) = 1 - (-3/t^2) = 1 + 3/t^2

Set the derivative equal to zero and solve for t:
1 + 3/t^2 = 0
3/t^2 = -1
t^2 = 3/-1
Since there are no real solutions for t^2 = -3, there are no critical points.

Step 2: Evaluate the function at the endpoints of the interval.

f(-1) = -1 - (3/-1) = -1 + 3 = 2
f(3) = 3 - (3/3) = 3 - 1 = 2

Step 3: Compare the values.
Evaluating f at the critical point and at the endpoints of the interval, we get:
f(-1) = -4
f(3) = -3
f(√3) = √3 - 3/√3 ≈ -1.732
Since there are no critical points and the values at the endpoints are equal, the absolute maximum and minimum values are both 2. Therefore, the absolute maximum and minimum values of the function on the interval [-1, 3] are both 2.

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