The variables x and y vary inversely. Use the given values to write an equation relating x and y. Then find y when x = 2.

x = 1
y = 2

For Aₙ = aₙ₋₁ + n and a₁ = 4, the first four terms will be 4, 6, 9, 13 respectively.

We will use the recursive formula  aₙ = aₙ₋₁ + n for the recursive series to get the first four terms of the sequence, with a₁ set to 4 for the series.

a₁ = 4 (given),

a₂ = a₁+2

⇒ a₂ = 4+2

⇒ a₂ = 6,

a₃ = a₂+3

⇒ a₂ = 6+3

⇒ a₃ = 9,

a₄ = a₃+4

⇒ a₄ = 9+4

⇒ a₄ = 13,

As can be seen, one term is utilized to locate the next term in the sequence, which is why it is referred to as recursive. So the series' first four terms are 4, 6, 9, 13.

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Answer: 0.3.

Step-by-step explanation:

1.18-0.88= 0.3

Answer:

A quadratic trinomial in x with coefficient of x^2 equal to 1 is a perfect-square trinomial if the constant term is the square of 1/2 the coefficient of x.

[tex] {x}^{2} + 15x + {( \frac{15}{2} )}^{2} [/tex]

[tex] {x}^{2} + 15x + \frac{225}{4} [/tex]

[tex] {(x + \frac{15}{2} )}^{2} [/tex]

Answer:

The solution to the equation x^2=2 is an irrational number. Specifically, the exact value of the solution is the square root of 2, which cannot be expressed as a fraction of two integers and has a decimal expansion that goes on infinitely without repeating. Therefore, the correct answer is D.

Step-by-step explanation:

The equation x^2=2 can be solved by taking the square root of both sides of the equation. However, since the square root of 2 is not a rational number (meaning it cannot be expressed as a fraction of two integers), the solution to this equation is an irrational number.

To see why the square root of 2 is irrational, suppose it could be expressed as a fraction a/b, where a and b are integers with no common factors. Then, squaring both sides of this equation gives:

(a/b)^2 = 2

a^2/b^2 = 2

Multiplying both sides by b^2 gives:

a^2 = 2b^2

This means that a^2 is an even number, since it is equal to twice an integer (namely, 2b^2). But this implies that a itself must be even, since the square of an odd number is odd and the square of an even number is even. Therefore, we can write a=2k for some integer k.

Substituting this expression for a into the equation a^2=2b^2 gives:

(2k)^2 = 2b^2

4k^2 = 2b^2

2k^2 = b^2

This implies that b^2 is even, which means that b itself must be even (using the same argument as before). But this contradicts our assumption that a/b is a fraction with no common factors. Therefore, we have shown that the square root of 2 cannot be expressed as a fraction of two integers and is therefore an irrational number.

hope it helps!

The binormal vector B(t) is then defined as the cross product of the unit tangent vector and the unit normal vector: B(t) = T(t) x N(t).

In the context of vector calculus, given a curve in three-dimensional space parameterized by the arc length parameter t, the unit tangent vector T(t) and the unit normal vector N(t) are defined as follows:

The unit tangent vector T(t) is a vector tangent to the curve at the point P(t), and its direction is the direction of the curve's motion at P(t). It is given by the first derivative of the position vector r(t) with respect to t, divided by its magnitude:

T(t) = r'(t) / |r'(t)|

The unit normal vector N(t) is a vector perpendicular to the curve at the point P(t), and its direction is toward the center of curvature of the curve at P(t). It is given by the second derivative of the position vector r(t) with respect to t, divided by its magnitude:

N(t) = r''(t) / |r''(t)|

The binormal vector is a vector perpendicular to both T(t) and N(t), and its direction is determined by the right-hand rule. It is used to complete the Frenet-Serret formulas, which describe the geometry of a curve in terms of its curvature and torsion.

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The mean absolute deviation of the data is of:

1.25.

It represents the average by which the shoe sizes deviate from the mean shoe size.

The mean of the data-set in this problem is given as follows:

Mean = (6 + 8.5 + 6 + 9 + 10 + 7 + 8 + 9.5)/8

Mean = 8.

Then the deviations are given as follows:

Hence the MAD for the data-set is given as follows:

MAD = (2 + 0.5 + 2 + 1 + 2 + 1 + 0 + 1.5)/8

MAD = 1.25.

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the probability that the driver was not intoxicated is approximately 0.8545.

To find the probability that the driver was not intoxicated in a randomly selected pedestrian death, we first need to determine the total number of pedestrian deaths and the number of deaths where the driver was not intoxicated.

From the table:
- Driver Not Intoxicated & Pedestrian Intoxicated: 289
- Driver Not Intoxicated & Pedestrian Not Intoxicated: 545

Total pedestrian deaths = 62 + 80 + 289 + 545 = 976

Deaths with driver not intoxicated = 289 + 545 = 834

Now, we can calculate the probability:

Probability (Driver Not Intoxicated) = (Deaths with driver not intoxicated) / (Total pedestrian deaths) = 834 / 976 ≈ 0.8545

So, the probability that the driver was not intoxicated is approximately 0.8545.

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Since Mila has made 50% of her free-throws. The word or phrase that describes the probability that Mila will hit her next free throw is uncertain or unknown.

To determine the likelihood of successful free throws, divide the number of successful attempts by the total number of attempts, and then multiply by 100.

A forecast of an probability distribution of uncertainty is passed by a probability distribution, and this term ought to be subject to modification only upon having additional knowledge.

Due to the fact that Mila has made 50% of her free throws in all, one cannot say or predict with accuracy if she will make her next free throw

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The given angles are supplementary and the value of x is 86°.

Since both angles are composited above a straight line it makes the sum of angles 180°.

So, the given angles are supplementary.

As we know that supplementary angles are defined as when pairing of angles addition to 180° then they are called supplementary angles.

As per the given figure,

∠x° + ∠(x+8)° = 180°

x + x + 8 = 180

2x = 180 - 8

x = 172/2

x = 86°

Thus, the given angles are supplementary and the value of x is 86°.

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The mean response of the randomly selected 30 students is x, which is also the mean response of the entire class.

To find the mean response for the randomly selected students, we need to use the formula:

mean = (sum of all responses) / (number of students)

Since we are given that the # of students is 30, not 463, we need to adjust our calculation accordingly.

Let's say the sum of all the responses for the 30 students is S. Then the formula becomes:

mean = S / 30

We don't know the exact value of S, but we can use the information given to make an estimate. The mean response of the 30+463 students is x, so we can write:

(x) = (S + 463y) / (30+463)

where y is the mean response of the remaining 463 students. We want to solve for x, so we need to isolate it on one side of the equation:

(x) = (S + 463y) / (30+463)

x(30+463) = S + 463y

30x + 463x = S + 463y

493x = S + 463y

x = (S + 463y) / 493

Now we need to use the fact that y is not given, but we can make an assumption based on the information given. The mean response of the entire class is likely to be somewhere between the mean response of the randomly selected 30 students and the mean response of the remaining 463 students. So we can assume that:

y is close to x

This allows us to simplify the equation:

x = (S + 463x) / 493

Multiplying both sides by 493 gives:

493x = S + 463x

30x = S

So we can see that the sum of the responses for the 30 students is 30 times the mean response, which is x. Therefore:

S = 30x

Plugging this back into the formula for the mean, we get:

mean = S / 30

mean = (30x) / 30

mean = x

So the mean response of the randomly selected 30 students is x, which is also the mean response of the entire class.

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To answer these questions, we need to use the information provided in Figure 5.30. Let's first write down the given percentages for each technology:

Only use online coupons: 17.39%

Use online coupons and check prices online before shopping: 21.74%

Use a smart phone to save money: 15.22%

Don't use any of these technologies: 26.09%

Use online coupons and check prices online, but not a smart phone: 13.04%

Use a smart phone if they check prices online: 86.36%

Check prices online but not use online coupons or a smart phone: 4.35%

Now we can answer each question:

What is the probability that a shopper will check prices online before shopping?

This includes the percentage of shoppers who use online coupons and check prices online, plus the percentage of shoppers who only check prices online:

P(check prices online) = 21.74% + 4.35% = 26.09%

What is the probability that a shopper will use a smart phone to save money?

This is the percentage of shoppers who use a smart phone:

P(use a smart phone) = 15.22%

What is the probability that a shopper will use online coupons?

This includes the percentage of shoppers who only use online coupons, plus the percentage of shoppers who use online coupons and check prices online:

P(use online coupons) = 17.39% + 21.74% = 39.13%

What is the probability that a shopper will not use any of these technologies?

This is the percentage of shoppers who don't use any of the technologies:

P(not use any technology) = 26.09%

What is the probability that a shopper will check prices online and use online coupons but not use a smart phone?

This is the percentage of shoppers who use online coupons and check prices online, but not a smart phone:

P(check prices online and use online coupons but not a smart phone) = 13.04%

If a shopper checks prices online, what is the probability that he or she will use a smart phone?

This is the percentage of shoppers who use a smart phone if they check prices online:

P(use a smart phone | check prices online) = 86.36%

What is the probability that a shopper will check prices online but not use online coupons or a smart phone?

This is the percentage of shoppers who only check prices online:

P(check prices online only) = 4.35%

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Complete question:

A survey of shopping habits found the percentage of respondents that use technology for shopping as shown in figure 5.30. for example, 17.39% only use online coupons; 21.74% use online coupons and check prices online before shopping, and so on.

What is the probability that a shopper will check prices online before shopping?

What is the probability that a shopper will use a smart phone to save money?

What is the probability that a shopper will use online coupons?

What is the probability that a shopper will not use any of these technologies?

What is the probability that a shopper will check prices online and use online coupons but not use a smart phone?

If a shopper checks prices online, what is the probability that he or she will use a smart phone?

What is the probability that a shopper will check prices online but not use online coupons or a smart phone?

The sentence "After Tiara's lawn had been mowed, she cooled off in the swimming pool." contains a remote reference because the pronoun "she" is ambiguous and could refer to either Tiara or someone else. The sentence "After her lawn had been mowed, Tiara cooled off in the swimming pool." would avoid the remote reference by explicitly stating who cooled off in the pool.

Answer:

length-7 width-5

Step-by-step explanation:

I used to guess and check so if you give a good guess you can get it in two attempts

Answer:

Each employee worked for 8 regular hours and 2 overtime hours, so each employee worked for a total of 10 hours. The regular pay rate is $15.50 per hour, so each employee earned 8 hours x $15.50 = $124 for regular pay. For overtime pay, each employee worked for 2 hours x ($15.50 + $7.00) = $44 in total.

Step-by-step explanation:

Therefore, each employee earned a total of $124 + $44 = $168.

Since there are 3 employees, the total amount that the company paid the employees is $168 x 3 = $504.

Therefore, the company paid a total of $504 to its employees.

Answer:

$507

Step-by-step explanation:

The total rate for overtime work is $7.00 + $15.50 = $22.50

1 employee worked:

8 hours at $15.50 per hour

2 hours at $22.50 per hour

total for 1 employee:

8 × $15.50 + 2 × $22.50 = $124 + $45 = $169

total for 3 employees:

3 × $169 = $507

Given that in ∠ABC and ∠DEF, ∠C and ∠F are right angles and sinA = cos D.

The tabla can be completed as follows:

Angle Pair Related as

∠A and ∠D Complementary

∠B and ∠F Complementary

∠B and ∠E Neither

∠A and ∠E Congruent

∠E and ∠D Neither

∠B and ∠D Congruent

Complementary angles are two angles whose sum is 90 degrees.

Congruent angles are two or more angles whose values are the same.

Considering the given angles:

∠A and ∠D are complementary angles since sinA = cos D.

∠B and ∠F are complementary angles since they are both right angles

∠A and ∠E are congruent angles since sinA = sinE and both angles are acute angles.

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Answer:

It's the last one :)))

Step-by-step explanation:

It starts with only 1 14, so look at the dots and see if they have one dot above 14. They all do.

Next look at 11. It is only counted once. look in between 10 and 12 for 1 plot of 11. The first one doesn't have 11 plotted once. That one is not it.

Then look at 4. It is counted 3 times. look at the last two options and see if 4 is plotted 3 times. The second one only has it once. So it has to be the last one.

That's what came off the top of my head. Hope this helps! :)))

The third dot plot best corresponds to the data set  (14, 11, 4, 15, 12, 5, 17, 3, 6, 4, 6, 10, 4, 18, 5).

The given data set is (14, 11, 4, 15, 12, 5, 17, 3, 6, 4, 6, 10, 4, 18, 5)

We have to find the corresponding dot plot which matches the data set.

A dot plot is a graphical display of data using dots.

a simple form of data visualization that consists of data points plotted as dots on a graph with an x- and y-axis.

By observing the data set and plots the third dot plot matches the data set.

Hence, the third dot plot best corresponds to the data set  (14, 11, 4, 15, 12, 5, 17, 3, 6, 4, 6, 10, 4, 18, 5).

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The expression that has a value less than 1 is 3/4 x 4/4, the correct answer is option C. To decide which expression contains esteem less than 1, we got to rearrange each expression and compare it to 1.

A. 3/4 x 4/3

Increasing these divisions, we get:

(3/4) x (4/3) = 12/12 = 1

This expression rearranges to 1, which isn't less than 1.

B. 3/4 x 6/3

Duplicating these divisions, we get:

(3/4) x (6/3) = 18/12 = 3/2

This expression disentangles to 3/2, which is more prominent than 1.

C. 3/4 x 4/4

Duplicating these divisions, we get:

(3/4) x (4/4) = 12/16 = 3/4

This expression streamlines to 3/4, which is less than 1.

D. 3/4 x 8/4

Increasing these divisions, we get:

(3/4) x (8/4) = 24/16 = 3/2

This expression rearranges to 3/2, which is more prominent than 1.

thus, the expression that incorporates esteem less than 1 is alternative C, 3/4 x 4/4. 

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Answer:

w ≈ 137.6 feet

Step-by-step explanation:

using the tangent ratio in the right triangle formed

tan54° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{w}{100}[/tex] ( multiply both sides by 100 )

100 × tan54° = w , then

w ≈ 137.6 feet ( to the nearest tenth )

Answer:

E. 9, F. 10

Step-by-step explanation:

Area of the rectangle: 3b

Area of the white triangle: 3b/3

Area of shaded region: 3b/2

3b/2 > 12

3b > 24

b > 8

Answer: E. 9, F. 10

Answer:

56

Step-by-step explanation:

because of its answee

we need a sample size of at least 665 drivers to be 99% confident that the resulting estimate of the proportion of drivers who exceed the legal speed limit is off by less than 0.04.

To determine the sample size required to estimate a proportion with a given margin of error and confidence level, we can use the following formula:

n = (z^2 * p * q) / E^2

where:

n is the sample size

z is the z-score corresponding to the desired level of confidence. For 99% confidence, z = 2.576

p is the estimated proportion of drivers who exceed the legal speed limit (we can use a conservative estimate of 0.5 for p, which maximizes the sample size)

q = 1 - p

E is the maximum margin of error we allow in our estimate (0.04 in this case)

Substituting the values into the formula, we get:

n = (2.576^2 * 0.5 * 0.5) / 0.04^2

Simplifying, we get:

n = 664.33

Therefore, we need a sample size of at least 665 drivers to be 99% confident that the resulting estimate of the proportion of drivers who exceed the legal speed limit is off by less than 0.04.

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a) the equilibrium demand is 122. b) the equilibrium price is $3.63.

a) Equilibrium demand can be gotten by setting the demand equal to the supply:

√√9-0.1q = √0.1q+1 -2

Squaring both sides:

√9 - 0.1q = (0.1q + 1 - 2)²

9 - 0.1q = 0.01q² + 0.98q - 1

0.01q² + 1.08q - 8 = 0

Solving for q using the quadratic formula:

q = (-1.08 ± √(1.08² + 4(0.01)(8))) / (2(0.01))

q = (-1.08 ± 3.52) / 0.02

q = 122 or -130

Since we cannot have a negative quantity, the equilibrium demand is 122.

b) To find the equilibrium price, we can substitute q = 122 into either the demand or supply equation:

p = √√9-0.1q = √√9-0.1(122) ≈ $3.63

Therefore, the equilibrium price is approximately $3.63.

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Answer:

the answer's letter D "The car travels 60 miles every y minutes"

At Ying Ying's bakery, there's an 8% probability that a customer will report a food allergy.

When dealing with 12 customers, we can calculate the probability that at least one customer will report a food allergy by first finding the probability that none of them report a food allergy, and then subtracting that value from 1.

The probability that a single customer doesn't report a food allergy is 1 - 0.08 = 0.92. For all 12 customers not to report a food allergy, the probability is 0.92^12 = 0.3981 (rounded to four decimal places).

Now, subtract this probability from 1: 1 - 0.3981 = 0.6019.

Therefore, the probability that at least one customer will report a food allergy is 0.6019 or 60.19%.

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The probability that the mean life of 7 items will be longer than 7 years is approximately 0.0059, or 0.59%.

To solve this problem, we need to use the central limit theorem, which tells us that the sample mean of a normally distributed population is also normally distributed, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

So, in this case, the mean of the sample mean lifespan is also 5.6 years, and the standard deviation is 1.7 years / sqrt(7) = 0.644 years.

To find the probability that the mean life of 7 items is longer than 7 years, we need to standardize the sample mean using the z-score formula:

z = (x - mu) / (sigma / sqrt(n))
where x is the desired mean (in this case, 7 years), mu is the population mean (5.6 years), sigma is the population standard deviation (1.7 years), and n is the sample size (7).

Plugging in the values, we get:
z = (7 - 5.6) / (1.7 / sqrt(7)) = 2.52

Using a standard normal distribution table or calculator, we can find that the probability of a z-score being greater than 2.52 is approximately 0.0059.

Therefore, the probability that the mean life of 7 items will be longer than 7 years is approximately 0.0059, or 0.59%.

To answer your question, we need to find the probability that the mean life of 7 randomly purchased items will be longer than 7 years, given that their normally distributed lifespan has a mean of 5.6 years and a standard deviation of 1.7 years.

To do this, we first need to find the standard deviation of the sample mean, which is calculated as the population standard deviation divided by the square root of the sample size:

Standard deviation of the sample mean = 1.7 / √7 ≈ 0.642

Next, we'll calculate the z-score for the desired mean lifespan of 7 years:

Z = (7 - 5.6) / 0.642 ≈ 2.18

Now, we need to find the probability of having a z-score greater than 2.18, which represents the probability that the mean life of the 7 items will be longer than 7 years. You can use a standard normal (Z) table or an online calculator to find the area to the right of 2.18. This area represents the probability:

P(Z > 2.18) ≈ 0.0146

So, the probability that the mean life of the 7 randomly purchased items will be longer than 7 years is approximately 1.46%.

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The given statement " using an empirical (resampling) distribution includes sampling values outside the range of the actual data. " is True because while resampling techniques may generate values outside the range of the original data, this is not necessarily a cause for concern.

Resampling techniques, such as bootstrapping or permutation tests, involve repeatedly sampling from the observed data to create an empirical distribution. This empirical distribution can then be used to make statistical inferences and hypothesis testing.

In some cases, resampling may generate values that are outside the range of the original data. This occurs because the resampling process is not constrained by the actual data values, but rather by the probability distribution of the observed data.

While sampling values outside the range of the actual data may seem counterintuitive, it is not necessarily a problem. In fact, resampling can be a powerful tool for testing statistical hypotheses and estimating uncertainty, particularly when the underlying population distribution is unknown or complex.

However, it is important to be aware of the limitations and assumptions of resampling techniques, particularly when making inferences or drawing conclusions. For example, if the original data is highly skewed or contains outliers, resampling may not accurately capture the underlying distribution.

Overall, while resampling techniques may generate values outside the range of the original data, this is not necessarily a cause for concern. Instead, it highlights the flexibility and power of empirical methods for statistical analysis.

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The value of painting B increases then decreases between 2000 and 2020, which indicates that the graph of the data is nonlinear

The option that is true is option C

C. The graph that represents the value of painting B is nonlinear

A linear graph is a graph that is a straight line.

The value of the painting A in the year 2000 = $12,050

The value in the year 2020 = $16,100

The variation of the value of painting B are;

Year   [tex]{}[/tex] Amount

2000 [tex]{}[/tex] 14,200

2005 [tex]{}[/tex] 15075

2010 [tex]{}[/tex]  15950

2015 [tex]{}[/tex]  16,825

2020 [tex]{}[/tex] 15,950

Therefore, the value of painting B increases from 2000 to 2015 then decreases in 2020

Option (a) is incorrect

In 2015, the value of painting A = 12050 + 15 × (16100 - 12050)/(20) = 15, 087.5

The value of painting B in 2015 = 16,825 > 15,0875, therefore; option (b) is incorrect

The value of painting B increases and decreases as the number of years steadily increases, therefore, the graph that represents the value of painting B is nonlinear and option C is correct

The value of painting B in 2020, which is 15,950 is higher than the value of painting A in the same year (16,100), therefore, option d is incorrect

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According to the World Health Organization (WHO), the European and Mediterranean populations over the age of 20 have a high percentage of overweight people. In fact, the WHO estimates that approximately 55% of the population in this region is overweight or obese.

This is a significant percentage, and it is important to note that being overweight or obese can increase the risk of numerous health problems, including cardiovascular disease, diabetes, and certain types of cancer.

There are a number of factors that contribute to the high prevalence of overweight and obesity in this region, including changes in diet, decreased physical activity levels, and cultural factors. For example, many people in these regions consume a diet that is high in calories, fat, and sugar, while also engaging in sedentary behaviors.

Overall, the high percentage of overweight and obese individuals in the European and Mediterranean populations over the age of 20 is a cause for concern. It highlights the need for effective public health interventions to promote healthy lifestyles and prevent chronic disease.

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The OLS (Ordinary Least Squares) estimator is derived by: c. minimizing the sum of squared residuals. In a regression analysis, the OLS estimator aims to find the best-fitting line by minimizing the sum of the squared differences (or residuals) between the actual data points (yi) and the predicted values on the regression line.

The residuals represent the error between the actual and predicted values. Minimizing the sum of squared residuals ensures that the regression line fits the data as closely as possible, ultimately providing a reliable model for predicting future values based on the relationship between the independent variable (xi) and the dependent variable (yi).It is important to note that the standard error of the regression does not necessarily equal the standard error of the slope estimator, but they are related measures.

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