Replace the values of mand n to show the solutions of this equation.
X^2 + 6x - 5=0

X=m + n
_

Given that each individual has a  \(\frac{1}{n}\) chance of receiving their own name, we may indicate whether or not person I received their own name by using a sequence of n identically distributed Bernoulli random variables with

\(P=\frac{1}{n}\) .

The total number of people who received their own name is the sum of these Bernoullis. The linearity of expectation causes the expected value of the sum to equal the sum of their respective expected values.

Since each summand has expected value  \(\frac{1}{n}\)  and there are n of them, the expected value is one.

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`a(26) = (-1)^(27) * F(26) = -196418`

To find the value of `a(26)` in the sequence `a(n)` where `a(0) = 1, a(1) = -1`, and `a(n) = a(n-1) + a(n-2)` for all `n ≥ 2`, to work our way up the sequence until we reach the desired term.

However, the process can be tedious and time-consuming. Instead, we can use a closed-form formula for the Fibonacci sequence, which is related to this sequence. Let's first write out the first few terms of the sequence: `1, -1, 0, -1, -1, -2, -3, -5, -8, -13, -21, -34, -55, -89, -144, -233, -377, -610, -987, -1597, -2584, -4181, -6765, -10946, -17711, -28657, ...`

Notice that the first two terms are `a(0) = 1` and `a(1) = -1`, which is similar to the first two terms of the Fibonacci sequence, `

F(0) = 0` and `F(1) = 1`. In fact, this sequence is obtained by subtracting the terms of the Fibonacci sequence from each other: `a(n) = F(n-1) - F(n)`. Thus, we have the closed-form formula for `a(n)` in terms of `n`:`a(n) = F(n-1) - F(n) = (-1)^(n+1) * F(n)`where `F(n)` is the `n`-th Fibonacci number.

So, to find `a(26)`, we simply find the 26th Fibonacci number, which is `F(26) = 196418`, and then multiply it by `-1` raised to the power of `27` (`n+1 = 26+1 = 27`), which is `-1`.

Therefore, `a(26) = (-1)^(27) * F(26) = -196418`

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Answer:

y=3

Step-by-step explanation:

The correct option is "sample statistic." A sample statistic is a numerical summary of a sample. In this case, the sample statistic is the percentage of golfers in the sample who own golf clubs made in the USA, which is 37%.

The population parameter is the true value of a characteristic of the entire population, which is often unknown and estimated based on the sample data. In this case, the population parameter would be the percentage of all golfers who own golf clubs made in the USA, which we do not know based on the information given.

A confidence level is a measure of the uncertainty associated with statistical inference, such as a confidence interval. It is often expressed as a percentage, such as 95% or 99%. However, no confidence level is mentioned in the question.

A confidence interval is a range of values that is likely to contain the true value of a population parameter, based on the sample data and a specified level of confidence. Again, no confidence interval is mentioned in the question.

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The more precise estimator ẏ₁ is the most efficient in estimating the average salary. With given values, the confidence interval is calculated to determine whether to accept the claim of a $50,000 mean salary.



In this scenario, we have two estimators for the average salary: ẏ₁, which uses precise data, and ẏ₂, which includes less precise data. The efficiency of the estimators depends on the variance of the data. If we compare the variances, Var(ẏ₁) = 0% and Var(ẏ₂) = o²(1 + 3c). Since Var(ẏ₁) is zero, it implies that ẏ₁ is the most efficient estimator. The answer does not depend on the value of c.

In the second part, with c = 0, we have Var(Y) = o². Given N = 300, s² = 20,000,000, and ẏ₁ = $48,000, we can use these values to construct a confidence interval. Using a 1% significance level, the critical value is 2.57 (from the standard normal distribution). The confidence interval is given by ẏ₁ ± 2.57 * sqrt(s²/N), which results in $48,000 ± 2.57 * sqrt(20,000,000/300). If this interval contains $50,000, we would accept your friend's claim; otherwise, we would reject it.

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The maximum value of the data is given as follows:

75.

A box and whisker plot shows these five metrics from a data-set, listed and explained as follows:

The maximum value on the box plot is the end of the plot, hence it is of 75.

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Answer: $3.32

Step-by-step explanation:

-0.3853 = (x - 3.4) / 0.2

Solving for x, we get:

X = 3.32

Therefore, the price for which only 35% of milk vendors is lower than $3.32.

The height of the escalator is as calculated using trigonometric ratios.

We know that in a right angled triangle the trigonometric ratios are

tan θ = perpendicular ÷ base

For a right angled triangle the tanθ is defined as the ratio of the perpendicular to the base of the triangle . The side opposite the angle θ is the perpendicular and the side adjacent to the θ is the base .

Now it is given that for every 2 feet vertically moved the horizontal distance moved is 3 feet.

Now using the trigonometric ratio of tanθ

tan θ = 2 / 3

Now we will use this ratio to calculate the vertical height for horizontal movement of 90 feet .

Now, the height is given as h .

∴ tan θ = h / 90

or, 2 / 3 = h / 90

or, h = 60 feet

Therefore the height of the escalator is 60 feet.

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The range, variance, and standard deviation are measures of variation that can provide insights into the prices of Big Mac hamburgers in different countries.

The range is the difference between the highest and lowest values in the data set. The variance measures the average squared deviation from the mean, while the standard deviation is the square root of the variance.

Without the actual data provided, I am unable to calculate the range, variance, and standard deviation. However, I can explain what these measures of variation generally tell us about the prices of Big Mac hamburgers in different countries.

The range alone, which is the difference between the highest and lowest prices, can indicate the extent of variability among the prices of Big Macs in different countries. If the range is large, it suggests significant differences in prices among the countries. However, the range alone does not provide information about the distribution of prices or the average price.

The variance and standard deviation, on the other hand, provide a more comprehensive understanding of the variability in prices. If the variance and standard deviation are high, it indicates that the prices of Big Macs vary greatly from the mean price, suggesting a wider spread of prices among the countries. This can be influenced by factors such as local economic conditions, exchange rates, and purchasing power.

In conclusion, the measures of variation, including the range, variance, and standard deviation, provide insights into the differences and spread of Big Mac prices in different countries. They help us understand the variability and potential factors influencing the prices, but they do not directly indicate whether prices are higher or lower in wealthier countries.

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The method that produces less CO2 per kg of aluminum produced among the given two eventualities is: Electrolysis with C electrodes of AlO3 in cryolite uses 3.35 kWh/kg Al.

Aluminum is produced by electrolysis of Al2O3 dissolved in a cryolite melt.

Carbon electrodes are used for the reduction reaction. CO2 is formed by the oxidation of the C electrodes.

Stoichiometric amounts of CO2 are produced by oxidation of C electrodes in the electrolysis with C electrodes of AlO3 in cryolite which uses 3.35 kWh/kg Al, and it is less than the amount of CO2 produced in the direct electrolysis of AlO3 in cryolite which uses 6.7 kWh/kg Al produced.

Therefore, Electrolysis with C electrodes of AlO3 in cryolite uses 3.35 kWh/kg Al is the method that produces less CO2 per kg of aluminum produced.

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The equation of the tangent line to the curve y = 2x cos(n) at the point (π, -π) is y = -2x + (2π + 2nπ sin(n) - π), where m = -2 - 2nπ sin(n) and b = 2π + 2nπ sin(n) - π.

To find the equation of the tangent line, we need to find the derivative of y with respect to x, and then evaluate it at the given point (π, -π) to find the slope of the tangent line. Then we can use the point-slope form of a line to find the equation of the tangent line in the form y = mx + b.

Taking the derivative of y with respect to x, we get:

dy/dx = 2cos(n) - 2n x sin(n)

Evaluating this derivative at x = π, we get:

dy/dx |x=π = 2cos(n) - 2n π sin(n)

Substituting x = π and y = -π into the original equation, we get:

-π = 2πcos(n)

cos(n) = -1/2

Since we want the equation of the tangent line at the point (π, -π), we can substitute x = π and y = -π into the point-slope form of a line:

y - (-π) = m(x - π)

Simplifying, we get:

y = m(x - π) - π

Substituting cos(n) = -1/2, we have:

dy/dx |x=π = 2cos(n) - 2n π sin(n) = -2 - 2nπ sin(n)

Setting this equal to the slope of the tangent line, we have:

m = -2 - 2nπ sin(n)

Substituting this value of m into the equation of the tangent line, we have:

y = (-2 - 2nπ sin(n))(x - π) - π

Therefore, the equation of the tangent line is:

y = -2x + (2π + 2nπ sin(n) - π)

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Complete question:

Find the equation of the tangent line to the curve y = 2x cos(n) at the point (π, -π). The equation of this tangent line can be written in the form y = mx + b, where m and b are constants. Find the values of m and b.

Answer:

They should leave $12.90 or round up to $13

Step-by-step explanation:

To find out the tip amount:

Convert 20% to .20

Multiply .20 x 64.50

=12.9

Answer:

12.90

Step-by-step explanation:

64.50×0.20=12.90

64.50+12.90=77.40

Answer:

YES

Step-by-step explanation:

1:4 can be written as: \(\frac{1}{4} \\ \), and we know to make and equivalent fraction you multiply by a constant. so,

\(\frac{1}{4} \\\)×\(\frac{5}{5} \)=\(\frac{5}{20} \) (5:20)

Hope this helps!

Answer:

a.

perimeter of rectangular = 2 times length + 2 times wide = 2L + 2W = 2 (L + W)

since L is x m and W is y meter, then

perimeter = 2 (L + W) = 2 (x + y)

p = 2(x + y)

(the correct is actually this one

70 ≤ 2(x+y) ≤ 96

b. minimum perimeter

to find minimum perimeter, use the minimum length (which is 20) and minimum wide (which is 15)

p(min) = 2 * ( x(min) + y(min))

p(min) = 2 * (20 + 15)

p(min) = 2 * (35) = 70

c. maximum perimeter

to find maximum perimeter, use the maximum length (which is 30) and maximum wide (which is 18)

p(miax) = 2 * ( x(max) + y(max))

p(max) = 2 * (30 + 18)

p(max) = 2 * (48) = 96 m

Answer:

Step-by-step explanation:

100800 cans.

Using proportions, it is found that 100,800 cans can be produced in a 7-hour day.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

Considering that one hour has 3600 seconds, the rule of three for this problem is given as follows:

0.04 cans - 0.01 seconds.

x cans - 7 x 3600 seconds.

Applying cross multiplication:

0.01x = 0.04 x 7 x 3600

x = 0.04 x 7 x 3600/0.01

x = 100,800

100,800 cans can be produced in a 7-hour day.

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Answer:

It took Brayden 3 months to complete a book.

Step-by-step explanation:

6 divided by 2 = 3

The correct answer is that the probability of a cash flow being between $16,000 and $19,000 is approximately 18.59%.

To calculate the probability of a cash flow being between $16,000 and $19,000, we can use the standard deviation and assume a normal distribution.

We are given that the average cash flow is $14,000 with a standard deviation of $5,000. These values are necessary to calculate the probability.

The probability of a cash flow falling within a certain range can be determined by converting the values to z-scores, which represent the number of standard deviations away from the mean.

First, we calculate the z-score for $16,000 using the formula: z = (x - μ) / σ, where x is the cash flow value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z1 = (16,000 - 14,000) / 5,000.

z1 = 2,000 / 5,000 = 0.4.

Next, we calculate the z-score for $19,000: z2 = (19,000 - 14,000) / 5,000.

z2 = 5,000 / 5,000 = 1.

Now that we have the z-scores, we can use a standard normal distribution table or calculator to find the corresponding probabilities.

Subtracting the probability corresponding to the lower z-score from the probability corresponding to the higher z-score will give us the probability of the cash flow falling between $16,000 and $19,000.

Looking up the z-scores in a standard normal distribution table or using a calculator, we find the probability for z1 is 0.6554 and the probability for z2 is 0.8413.

Therefore, the probability of the cash flow being between $16,000 and $19,000 is 0.8413 - 0.6554 = 0.1859, which is approximately 18.59%.

So, the correct answer is that the probability of a cash flow being between $16,000 and $19,000 is approximately 18.59%.

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The probability of a cash flow between $16,000 and $19,000 is approximately 18.59%.

To calculate the probability of a cash flow being between $16,000 and $19,000, we can use the standard deviation and assume a normal distribution.

We are given that the average cash flow is $14,000 with a standard deviation of $5,000. These values are necessary to calculate the probability.

The probability of a cash flow falling within a certain range can be determined by converting the values to z-scores, which represent the number of standard deviations away from the mean.

First, we calculate the z-score for $16,000 using the formula: z = (x - μ) / σ, where x is the cash flow value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z1 = (16,000 - 14,000) / 5,000.

z1 = 2,000 / 5,000 = 0.4.

Next, we calculate the z-score for $19,000: z2 = (19,000 - 14,000) / 5,000.

z2 = 5,000 / 5,000 = 1.

Now that we have the z-scores, we can use a standard normal distribution table or calculator to find the corresponding probabilities.

Subtracting the probability corresponding to the lower z-score from the probability corresponding to the higher z-score will give us the probability of the cash flow falling between $16,000 and $19,000.

Looking up the z-scores in a standard normal distribution table or using a calculator, we find the probability for z1 is 0.6554 and the probability for z2 is 0.8413.

Therefore, the probability of the cash flow being between $16,000 and $19,000 is 0.8413 - 0.6554 = 0.1859, which is approximately 18.59%.

So, the correct answer is that the probability of a cash flow being between $16,000 and $19,000 is approximately 18.59%.

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Answer:

5 and 4

Step-by-step explanation:

Answer:

45° degrees I think

Step-by-step explanation:

because in total there is 180 degrees in a triangle and if you subtract 40 and 95 you are left with 45

Yes, Micah created the boxplot correctly.

A boxplot, also known as a box-and-whisker plot, is a graphical representation of a dataset that provides a summary of its distribution. It consists of several key features: the minimum value, the lower quartile (Q1), the median (Q2), the upper quartile (Q3), and the maximum value.

Micah correctly identified these key features in the boxplot. The minimum value represents the smallest time taken by any student in the class to complete the drills, and in this case, it is 1 minute. The maximum value represents the largest time taken, which is 10 minutes. These values are denoted by the horizontal lines, also known as whiskers, extending from the box.

The box in the middle of the plot represents the interquartile range (IQR), which is the range between the lower and upper quartiles. The lower quartile (Q1) is the time taken by the 25th percentile of students to complete the drills. In this case, it is 2 minutes. The upper quartile (Q3) is the time taken by the 75th percentile of students, and here it is 5 minutes. The median (Q2) represents the middle value of the dataset, dividing it into two equal halves. In this case, the median is also 5 minutes.

The boxplot accurately represents these key features and allows us to visualize the spread, central tendency, and skewness of the data. It provides a concise summary of the distribution and helps identify any outliers or unusual values.

In summary, Micah created the boxplot correctly by accurately representing the minimum, maximum, median, and quartiles of the dataset. The boxplot effectively conveys the distribution of the time taken by the third-graders to complete their multiplication drills.

The topic related to this question is statistics, specifically boxplots and data visualization, which is typically covered in high school math courses or statistics lessons.

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Complete Question

The histogram shows the time it takes a class of 22 third-graders to finish their multiplication drills. Time to Complete Drills Number of Students 1 1 2 7 & ch 10 5 Time, minutes Micah created a boxplot to assist in analyzing the data set. Did Micah create the boxplot correctly? Why or why not? Be sure to address the key features of a boxplot.

the solution to the equation log3 x=4 is x = 81.The equation "log3 x=4" is a logarithmic equation with a base of 3.

It means that 3 raised to the power of 4 is equal to x. In other words, x is the value that satisfies the equation 3^4 = x.

To solve this equation, we need to isolate the variable x. We can do this by taking the exponential of both sides of the equation with a base of 3. This will cancel out the logarithm on the left side of the equation, leaving us with:

3^(log3 x) = 3^4

The base of the exponential function and the logarithmic function cancel each other out, and we're left with:

x = 81

Therefore, the solution to the equation log3 x=4 is x = 81.

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Answer:

6 games on each of the three shelves

Step-by-step explanation:

The total of  22 books minus the 4 books on the top shelf leaves 18 remaining books. You take that 18 and divide by 3 since there are three more shelves. This will leave you with a total of 6 books on each of the other shelves

22 - 4 = 18

18 / 3 = 6

Answer:

12 possible roots

Step-by-step explanation:

we can use the rational zeros theorem which says that in order to find the possible roots for a polynomial we need to divide the factors of the constant by the factors of the coefficient of the leading term

which in this case is:

±(1, 2, 3, 4, 6, 12)/(1)

±1, 2, 3, 4, 6, 12

so we have 12 possible roots

Answer:

x = 20

y = 25

Step-by-step explanation:

Vertical angles are always congruent, that is a theorem.

Set the vertical pairs equal to each other.

182 - 4x = 5x + 2

The lowest of the two coefficients is 4x, so that will be added to both sides.

4x + 5x = 9x

Simplify

9x + 2 = 182

Subtract both sides by 2

9x = 180

Divide by 9

180/9 = 20

x = 20

Plug in the 20 to get the angle measure.

182 - 80 = 102

the vertical pairs are 102 degrees

There is another theorem that sets the two angles outside as congruent.

So set 4y + 2 = 102

Subtract 2

100

Divide 4, which equals 25

y = 25

True, a half step is the shortest distance that can exist between two pitch-sounding frequencies. In Western musical notation, a half step is thought to be the shortest interval, or space between two notes.

The smallest musical interval typically utilized in Western tonal music is a semitone, sometimes known as a half step or a half tone. It is described as the space in a 12-tone scale between two neighbouring notes. For instance, there is a semitone's distance between C and C. Any interval in a 12-note scale that is almost evenly divided into semitones can be described in terms of the proper number of semitones, for example, a whole tone or major second is two semitones wide, a major third is four semitones wide, and a perfect fifth is seven semitones wide.

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Answer:

Less

Step-by-step explanation:

\(6.17 < 6.187 \)

This general solution satisfies the given differential equation y" - 6y + 9y = e³1 t² for t > 0.

The general solution of the given differential equation y" - 6y + 9y = e³1 t² for t > 0 can be obtained using the method of Variation of Parameters. It involves finding particular solutions and then combining them with the complementary solution to obtain the general solution.

To solve the differential equation using Variation of Parameters, we first find the complementary solution by assuming y = e^(rt). Substituting this into the differential equation gives us the characteristic equation r² - 6r + 9 = 0, which factors to (r - 3)² = 0. Hence, the complementary solution is y_c = (c₁ + c₂t)e^(3t).

Next, we find the particular solution using the method of Variation of Parameters.

We assume a particular solution of the form y_p = u₁(t)e^(3t), where u₁(t) is an unknown function.

Differentiating y_p twice, we get y_p'' = (u₁'' + 6u₁' + 9u₁)e^(3t).

Substituting y_p and its derivatives into the differential equation, we obtain u₁''e^(3t) = e³1 t².

To determine u₁(t), we solve the following system of equations: u₁'' + 6u₁' + 9u₁ = t² and u₁''e^(3t) = e³1 t².

By solving this system, we find u₁(t) = (1/9)t⁴e^(-3t).

Finally, the general solution is obtained by combining the complementary and particular solutions: y = y_c + y_p = (c₁ + c₂t)e^(3t) + (1/9)t⁴e^(-3t).

This general solution satisfies the given differential equation y" - 6y + 9y = e³1 t² for t > 0.

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Answer:

72.26ft

Step-by-step explanation: