Common information for 3 and 4 The probability of contracting a stomach virus while visiting Mexico is 23%. Find the probability that amongst 12 students visiting Mexico 3. Exactly five students contract a stomach virus:

None  of the given pairs of lines are perpendicular. The answer is none of the above (E).

To determine which two lines are perpendicular, we need to check whether the slopes of the lines are negative reciprocals of each other. If they are, then the lines are perpendicular.

The slope of a line can be determined by examining the coefficient of x in the line's equation.

For Equation A, the slope is -3 (the coefficient of x is 3, and the slope is the negative of the coefficient).
For Equation B, the slope is 3 (the coefficient of x is 6, and the slope is the coefficient divided by -2).
For Equation C, the slope is 3 (the coefficient of x is 3).
For Equation D, the slope is 13.

Now we can check which two lines have slopes that are negative reciprocals of each other. The negative reciprocal of 3 is -1/3, and the negative reciprocal of -3 is 1/3. None of the pairs of lines have slopes that are negative reciprocals of each other. Therefore, none of the given pairs of lines are perpendicular. The answer is none of the above (E).

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Any point on the unit circle may be expressed as (cos, sin), which denotes the angle formed between the radius of the point and the positive x-axis.

In a right triangle, the sine of an angle is defined as the length of the side opposite the angle divided by the length of the hypotenuse, and the cosine of an angle is defined as the length of the adjacent side divided by the length of the hypotenuse.

By definition, the cosine of θ is x (the length of the adjacent side) divided by 1 (the length of the hypotenuse), or simply x/1, which is just x. Similarly, the sine of θ is y (the length of the opposite side) divided by 1 (the length of the hypotenuse), or simply y/1, which is just y.

So we have shown that, for any point (x, y) on the unit circle, the cosine of the angle θ between the positive x-axis and the radius to the point is equal to x, and the sine of θ is equal to y.

Therefore, we can write any point on the unit circle as (cosθ, sinθ), where θ is the angle between the positive x-axis and the radius of the point.

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The solution is :

The sum of money deposited is approximately $22,021.74

Here, we have,

The given interest and amounts of the deposit are outlined as follows;

The simple interest per annum, R = 0.325%

The number of years the money is deposited, T = 4 years

The total amount received (Interest + Initial deposit), A = $50,650

We have;

I = P × R × T

Where;

P = The principal (initial amount deposited)

R = The (annual) interest rate = 0.325%

T = The time = 4 years

Therefore;

The total amount received, A = P + I

P + I = P + P × R × T = P × (1 + R × T)

∴ A = P + I = P × (1 + R × T)

P = A/(1 + R × T)

Plugging in the values, gives;

P = 50,650/(1 + 0.325 × 4) = 506,500/23 ≈ 22,021.74

The sum of money deposited, P = $22,021.74

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complete question:

A sum of money is deposited in a bank which offers a simple interest rate of 0.325% per annum. At

the end of the 4 years, the total amount receives is $50 650. Find the sum of money deposited.

The term that refers to the fact that the distance between two or more points is equal is "equidistant".

In geometry, the concept of equidistance is important when dealing with circles, which are sets of points that are equidistant from a single point called the center. This property is what allows circles to be defined in terms of their radius, which is the distance between the center and any point on the circle.

Equidistance is also important in other areas of mathematics and science. For example, in physics, equidistant points can be used to define a plane or surface that is perpendicular to a given line or axis. This is useful in many applications, such as designing electronic circuit boards or constructing buildings.

The concept of equidistance is not limited to mathematics and science, however. It can also be applied in everyday life. For instance, if you are planning a road trip and want to visit several destinations that are equidistant from your starting point, you can use this information to help plan your route and estimate your travel time.

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Correlation refers to the statistical relationship between two or more variables. A strong correlation means that there is a significant association between the variables, while a weak correlation suggests that there is little to no relationship between them.

Additionally, correlations can be either positive or negative. A positive correlation means that as one variable increases, so does the other, while a negative correlation means that as one variable increases, the other decreases.

To determine the strength and direction of a correlation, one can use a correlation coefficient. This measure ranges from -1 to +1, with -1 indicating a perfect negative correlation, 0 indicating no correlation, and +1 indicating a perfect positive correlation. When the correlation coefficient is close to -1 or +1, this suggests a strong correlation, while coefficients closer to 0 indicate a weaker correlation.

Overall, understanding the correlation between variables is essential for analyzing data and making informed decisions. By recognizing the strength and direction of a correlation, one can gain insights into the relationships between different variables and how they impact one another.

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After analysing the given data we conclude that the measure of <ABD is 117 degrees, under the condition that <ABC has a measure of 40°.

Now in order to evaluate the angle we have to relie on the principles of angle to derive a formula
The formula is
180 - ( remaining angles) = ( unknown angle)
Now, to find the measure of <ABD, we can apply the fact that the sum of the angles in a triangle is 180 degrees. It is known that <ABC has a measure of 40 degrees and <CBD has a measure of 23 degrees. Since <ABC and <CBD share a ray, we can add their measures to get the measure of <ABD.
Placing the values in the formula
Therefore,
<ABD = 180 - 40 - 23
= 117 degrees.
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The value of the random variable x0 such that P (x > x0) = 0.025 is approximately 55.88.

To find the value of x0 such that P(x > x0) = 0.025, we need to use the standard normal distribution table or a calculator to find the corresponding z-score.

First, we need to standardize x using the formula:

z = (x - µ) / σ

where µ = 50 and σ = 3.

So,

z = (x - 50) / 3

Now, we want to find the z-score that corresponds to a probability of 0.025 in the right tail of the standard normal distribution. From the standard normal distribution table, we can see that the z-score for this probability is approximately 1.96.

Therefore,

1.96 = (x0 - 50) / 3

Multiplying both sides by 3, we get:

x0 - 50 = 1.96 * 3

x0 - 50 = 5.88

Adding 50 to both sides, we get:

x0 = 55.88

So, the value of the random variable x0 such that P(x > x0) = 0.025 is approximately 55.88.

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After three years with a monthly deposit of $250 and an APR of 8.4%, you will have approximately $10,093.46 towards the purchase of a boat.

To calculate the amount you will have towards the purchase of a boat after three years with an APR (Annual Percentage Rate) of 8.4% and monthly deposits of $250, we can use the formula for the future value of a series of regular deposits:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the deposits

P is the monthly deposit amount ($250)

r is the monthly interest rate (8.4% / 12 = 0.007)

n is the number of periods (3 years * 12 months = 36)

Let's calculate the future value:

FV = $250 * [(1 + 0.007)^36 - 1] / 0.007

FV ≈ $10,093.46

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Answer:

(-2, ∞)

Step-by-step explanation:

The domain of a function is how far the x goes left and right.

We see the x starts at -2 and goes forever.

So, the Domain of the function is (-2, ∞)

The total number of tickets that Joe win at the park is 240 if the fraction of 3/ is used.

Given that,

Joe had been saving up all of his tickets from his day at the amusement park.

Let x be the total number of tickets he saved.

He used a fraction of  ⅗ of them on a stuffed bear for his sister.

x - (3/5 x) = 96

2/5 x = 96

Multiplying both sides by 5/2, we get,

x = 96 × 5/2

x = 240

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Answer:

  No, it is not reasonable.

Step-by-step explanation:

Given an 8-inch pizza costs $14.35, you want to know if an estimated cost of $28.70 is reasonable for a 16-inch pizza.

The scale factor for area is the square of the scale factor for linear dimensions such as diameter.

The ratio of diameters is ...

  (16 in)/(8 in) = 2

Then the ratio of areas will be 2² = 4. The larger pizza will have 4 times the area of the smaller one.

If cost is based on area, then a better estimate of the cost of a 16-inch pizza is ...

  4 × $14.35 = $57.40

Marco's estimate of $28.70 is not reasonable. A better estimate is $57.40.

__

Additional comment

The area is given by the formula ...

  A = (π/4)d²

When the diameter is doubled, the area becomes ...

  A' = (π/4)(2d)² = 4×(π/4)d² = 4A

You can see that the scale factor 2 was squared when we expanded (2d)² to 2²·d² = 4d².

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The area of Kimberly's wall hanging will be 32 square units.

Given that:

Points, A(1, 5), B(1, 9), C(7, 9), D(7, 5), E(5, 3), and F(3, 3)

The area of a two-dimensional figure is the area that its perimeter encloses. The quantity of unit squares that occupy a closed figure's surface is its region.

The polygon is shown in the graph below.

The area of the polygon is given as,

A = Area of rectangle + Area of trapezium

A = 4 x 6 + 1/2 x (6 + 2) x 2

A = 24 + 8

A = 32 square units

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The amount of candy remaining in the dispenser is 10.35 cups. There are 10.05 cups of candy remaining in the dispenser.

The candy dispenser can hold 15 cups of candy. If the dispenser is 75% full, then it contains 75% of 15 cups, which is:

0.75 x 15 = 11.25 cups

After a few hours, 8% of the candy has been sold. This means that 8% of 15 cups has been sold, which is:

0.08 x 15 = 1.2 cups

To find out how much candy remains in the dispenser, we need to subtract the amount sold from the amount that was initially in the dispenser. So, the amount of candy remaining in the dispenser is:

11.25 - 1.2 = 10.05 cups

Therefore, there are 10.05 cups of candy remaining in the dispenser.

Alternatively, we can calculate the amount of candy remaining in the dispenser directly as follows:

The dispenser is 75% full, which means that 25% of its capacity is empty. Therefore, the empty space in the dispenser is:

0.25 x 15 = 3.75 cups

If 8% of the candy has been sold, then 92% of the candy remains in the dispenser. Therefore, the amount of candy remaining in the dispenser is:

0.92 x (15 - 3.75) = 0.92 x 11.25 = 10.35 cups

This gives us the same answer as before, which is that there are 10.05 cups of candy remaining in the dispenser.

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The size of the angle y as required to be determined in the task content is; 60°.

As evident in the task content, the base of the triangle is; 9.1 cm.

Recall the area of a right triangle is; A = bh / 2

Therefore, to determine the height h given an area of 23.66 cm²; we have that;

23.66 = 9.1h / 2

h = (2 × 23.66) / 9.1

h = 5.2 cm.

Ultimately, to determine the size of y from trigonometric ratios;

tan y = 9.1 / 5.2

y = tan-¹ (9.1/5.2)

y = 60° to the nearest integer.

Ultimately, the size of the angle y as required in the task content is; 60°.

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The number 25% represents the proportion of the entire population of students at the school who have period 4 lunch. Therefore, it is a option D- parameter.

A statistic is a numerical summary of a sample, while a parameter is a numerical summary of a population. In this case, the proportion of students who have period 4 lunch in the sample of 40 students is 30%, which is a statistic. The proportion of students who have period 4 lunch in the entire population of 380 students is 25%, which is a parameter.

It's important to distinguish between a sample and a population because statistical conclusions drawn from a sample cannot be automatically generalized to the population from which the sample was drawn. In other words, the characteristics of a sample may not perfectly reflect the characteristics of the larger population, due to random sampling variation. Therefore, when making statistical inferences or drawing conclusions about a population, it's important to use appropriate sampling methods and to carefully consider the limitations and assumptions of statistical analyses.

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We should use the one mean z-test for large samples (size 30 or more) when dealing with quantitative data, the sample size is at least 30, and the population standard deviation is known.

When to use the one mean z-test for large samples (size 30 or more).
we should use the one mean z-test for large samples in the following situations:
Sample size (n) is greater than or equal to 30:

The one mean z-test is appropriate for large samples, typically when the sample size is 30 or more.

This is because the Central Limit Theorem states that for a sufficiently large sample size, the sampling distribution of the mean is approximately normally distributed.

Population standard deviation (σ) is known:

The one mean z-test requires knowledge of the population standard deviation.

If the population standard deviation is unknown, you should use the t-test instead.
The variable of interest is quantitative:

The one mean z-test is designed for quantitative data (interval or ratio scale).

If you are dealing with categorical or ordinal data,  would need to use different tests, such as the chi-square test or Mann-Whitney U test.

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Answer:

y-5=3(x+4)

Step-by-step explanation:

point slope form: y-y1=m(x-x1)

plug in 5 for y1, -4 for x1

y-5=3(x+4)

The answer is (A) k < 0. When k is negative, f'(x) is negative on (-1,1), which means that f(x) is strictly decreasing on (-1,1).  The correct answer is option a.

To determine for what values of k the function [tex]f(x) = kx/(x^2+1)[/tex]is strictly decreasing on the interval (-1, 1), we need to find the first derivative of f(x) and then examine its sign.

We have:

[tex]f(x) = kx/(x^2+1)\\f'(x) = (k(x^2+1) - kx(2x))/(x^2+1)^2\\f'(x) = k(1-x^2)/(x^2+1)^2[/tex]

To determine when f(x) is strictly decreasing on (-1,1), we need f'(x) to be negative on that interval. Therefore, we need [tex](1-x^2)/(x^2+1)^2[/tex] to be negative on (-1,1).

Note that [tex](1-x^2)[/tex] is always non-negative on the interval (-1,1), so for f'(x) to be negative, we need [tex](x^2+1)^2[/tex] to be positive. Since [tex](x^2+1)^2[/tex] is always positive, we can conclude that f'(x) is negative on the interval (-1,1) if and only if k < 0.

Therefore, the answer is (A) k < 0. When k is negative, f'(x) is negative on (-1,1), which means that f(x) is strictly decreasing on (-1,1). When k is zero or positive, f'(x) is zero or positive on (-1,1), respectively, which means that f(x) is not strictly decreasing on (-1,1).

The correct answer is option a.

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Answer:

Domain: [1,3]

Range: [0.5,1.5]

Step-by-step explanation:

Domain: x-values

Range: y-values

Answer:

A

Step-by-step explanation:

PLAto

The symbol for a hectare is "ha." A hectare is a unit of area measurement, primarily used in the field of agriculture and land management. It is equal to 10,000 square meters or approximately 2.47 acres.

The term "hectare" is derived from the metric prefix "hecto," which means one hundred, and the unit of area "are," which equals 100 square meters. Therefore, a hectare is equivalent to 100 ares (100 x 100 square meters).

The hectare is widely used in many countries around the world to describe the size of agricultural land, forests, parks, and other large areas. Its use is more common in countries that have adopted the metric system, such as in Europe and Asia. In contrast, countries like the United States often use acres as their primary unit of land measurement.

In summary, "ha" is the symbol used to represent a hectare, a unit of area measurement often utilized in agriculture and land management. It is equivalent to 10,000 square meters or about 2.47 acres and is commonly used in countries that follow the metric system.

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Answer:

We can use proportion to estimate the number of households that have a dog in the town of Nowaday.

From the data given in the random sample, we know that 24 out of 60 households had a dog. This can be written as:

24/60 = x/3000

where x is the number of households in the town that have a dog.

To solve for x, we can cross-multiply and simplify:

24 x 3000 = 60 x x

x = (24 x 3000) / 60

x = 1,200

Therefore, we can estimate that approximately 1,200 households in the town of Nowaday have a dog.

The mean of the Poisson distribution is 0.1.

The mean of a Poisson distribution is given by µ, which is the expected number of occurrences in the specified interval. In this case, µ = 0.1, which means we expect to have 0.1 occurrences in the specified interval.

The mean can also be calculated by using the formula µ = ΣxP(x), where ΣxP(x) is the sum of the product of each value of x and its corresponding probability.

µ = (0 × 0.9048) + (1 × 0.0905) + (2 × 0.0045) + (3 × 0.0002)

µ = 0 + 0.0905 + 0.009 + 0.0006

µ = 0.1

Therefore, the mean of the Poisson distribution is 0.1.

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The normal approximation to the sampling distribution of a proportion can be used when both np and n(1-p) are greater than or equal to 10.

In this problem, we are selecting an SRS of size n=100 from a large population with a proportion p of successes. We need to find the value of p that would make it safe.

To use the normal approximation to the sampling distribution of p.

For each given value of p, we can calculate np and n(1-p), and then determine whether both of these values are greater than or equal to 10.

a) p = 0.85

np = 85, n(1-p) = 15

Both np and n(1-p) are greater than or equal to 10, so the normal approximation is safe.

b) p = 0.975

np = 97.5, n(1-p) = 2.5

Only np is greater than or equal to 10, so the normal approximation is safe.

c) p = 0.999

np = 99.9, n(1-p) = 0.1

Only np is greater than or equal to 10, so the normal approximation is safe.

d) p = 0.01

np = 1, n(1-p) = 99

Only n(1-p) is greater than or equal to 10, so the normal approximation is safe.

e) p = 0.09

np = 9, n(1-p) = 91

Only n(1-p) is greater than or equal to 10, so the normal approximation is safe.

Therefore, for all given values of p, it is safe to use the normal approximation to the sampling distribution of p.

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Table 3 shows a relationship between x and y, where y is always equal to 8 less than the product of x and 3.

We are given that y is always equal to 8 less than the product of x and 3, which can be written as y = 3x - 8. We can create a table of values for x and y using this equation.

Table 1:

+x y

1 -5

2 -2

3 1

4 4

5 7

Table 2:

x y

1 -7

2 -4

3 -1

4 2

5 5

Table 3:

x y

1 -5

2 1

3 7

4 13

5 19

Checking each table, we can see that only Table 3 satisfies the condition that y is always equal to 8 less than the product of x and 3. Therefore, Table 3 shows the relationship between x and y as given in the question.

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Which table shows a relationship between x and y, where y is always equal to 8 less than the product of x and 3?

we can conclude that there is significant evidence to support the claim that μ is less than 10.

We need to compare the test statistic with the critical value to determine whether to reject or fail to reject the null hypothesis. Since the test statistic (-2.50) is less than the critical value (-1.645), we can reject the null hypothesis at the 5% level of significance.

The conclusion is that there is sufficient evidence to support the alternative hypothesis Ha: μ < 10. This means that the sample data suggests that the true population mean is less than 10, and we can reject the possibility that the population mean is greater than or equal to 10.

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