4. Scatterplots Match these values of r with the five scatterplots shown below: 0.268, 0.992, -1, 0.746, and 1. 2.0 13- y-2 y14 12 -3 1.0 . 0.8 000 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.B 0.9 0.0 0.1 02 0.3 0

Answer:

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Answer:

There is one solution, x=2

Step-by-step explanation:

1/2x+6=4x-1

subtract 6 from both sides

1/2x=4x-7

subtract 4x from both sides

-7/2x=-7

multiply both sides by 2

-7x=-14

divide both sides by -7

x=2

Answer:

West Edmonton,Canada

Step-by-step explanation:

parking lot at Canada's West Edmonton Mall makes the Guinness Book of World Records as the largest parking lot in the world.

A Poisson random variable represents the number of occurrences of an event in a fixed interval of time or space. It is a discrete random variable, which means that it can only take on integer values, starting from zero. Therefore, the smallest numerical value that a Poisson random variable can be is zero.

This means that there is a possibility that the event will not occur at all during the given interval. For example, if we are counting the number of customers who visit a store in an hour, it is possible that no customers show up during that hour, resulting in a Poisson random variable of zero.

However, the probability of this occurring depends on the average rate of the event occurring, which is denoted by the parameter λ in the Poisson distribution. The larger the value of λ, the smaller the probability of a Poisson random variable being zero.

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Both options a. A = 129.9° and b. A = 53.1° are correct.

To find the possible values for angle A in triangle ABC, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

Using the Law of Sines, we have sin(A)/a = sin(B)/b. Plugging in the given values, we get sin(A)/36 = sin(51°)/35.

To find the two possible values for angle A, we can solve the equation sin(A)/36 = sin(51°)/35. Taking the arcsine of both sides, we have A = arcsin((sin(51°)/35)*36).

Calculating this expression, we find two possible values for angle A:

A ≈ 53.1° (rounded to the nearest tenth)

A ≈ 129.9° (rounded to the nearest tenth)

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Answer:

Line A, because it is closest to most data points

Step-by-step explanation:

That is your answer because Line A is the closest to most of the data points, while Line B is more farther away. Also, the line of best fit has nothing to do with the positive or negative association.

Answer:

Line A

Step-by-step explanation:

It is the closest to the data points

Answer:

1 and four

Step-by-step explanation:

Answer:

1 and 4

Step-by-step explanation:

A vertical angle is one of two opposite and equal angles formed by the intersection of two lines.

1 and 4

2 and 3

5 and 8

6 and 7

are all answers

Answer:

0.375

Step-by-step explanation:

3/8 = 0.375

Answer:

0.375

Step-by-step explanation:

Answer:

0 ≤ x < 1.12 and 34.18 < x ≤ 39.87

Step-by-step explanation:

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The options provided are range, quartile, mean absolute deviation, and interquartile range. We need to select the measure of spread that best represents the variability in the data.

In this case, the most suitable measure of spread for the data in the table is the range. The problem asks us to determine the most appropriate measure of spread for the given data in the table, which represents the population of different cities.

The range is a measure of spread that calculates the difference between the largest and smallest values in a dataset. In this case, the range would provide information about the spread of population values across the different cities. By subtracting the smallest population (325) from the largest population (600), we would obtain the range, which represents the extent of variability in the population sizes among the cities.

The range calculates the difference between the maximum and minimum values in a dataset and provides a straightforward measure of how spread out the data points are. Since the population values represent the size of different cities, the range will give us an idea of the extent of variation in population among the cities. Therefore, option A, range, is the correct answer in this scenario.

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The slope of the tangent line at (4, 54) is 45. So the equation of the tangent line to the curve y = x^3 - 3x + 2 at the point (4, 54) is y = 45x - 126.

To find the equation of the tangent line to the curve y = x^3 - 3x + 2 at the point (4, 54), we need to use calculus. First, we find the derivative of the function:

y' = 3x^2 - 3

Next, we plug in x = 4 to find the slope of the tangent line at that point:

y'(4) = 3(4)^2 - 3 = 45

So the slope of the tangent line at (4, 54) is 45. To find the equation of the line, we use the point-slope form of the equation:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the point on the line. Plugging in our values, we get:

y - 54 = 45(x - 4)

Simplifying, we get:

y - 54 = 45x - 180

y = 45x - 126

So the equation of the tangent line to the curve y = x^3 - 3x + 2 at the point (4, 54) is y = 45x - 126.

To find the equation of the tangent line to the curve y = x^3 - 3x + 2 at the point (4, 54), we need to first find the derivative of the function and then use the point-slope form of a line.

1. Find the derivative of the function with respect to x:
y'(x) = d/dx (x^3 - 3x + 2) = 3x^2 - 3

2. Evaluate the derivative at the given point (4, 54) to find the slope of the tangent line:
m = y'(4) = 3(4)^2 - 3 = 3(16) - 3 = 48

3. Use the point-slope form of a line (y - y1 = m(x - x1)):
y - 54 = 48(x - 4)

4. Simplify the equation:
y - 54 = 48x - 192
y = 48x - 138

So, the equation of the tangent line to the curve y = x^3 - 3x + 2 at the point (4, 54) is y = 48x - 138.

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The approximate probability that a married woman selected at random is taller than her husband is 8.85%.

We can use the concept of sampling distribution of the difference between two means to approximate the probability that a randomly selected married woman is taller than her husband.

Let X be the height of a married man and Y be the height of a married woman. Then, the probability that a woman is taller than her husband can be expressed as P(Y > X).

The sampling distribution of the difference between two means can be approximated by a normal distribution if the sample sizes are large enough. In this case, since we have a large sample of 400 couples, we can assume that the sampling distribution of the difference in heights between married men and women is approximately normal.

The mean of the difference in heights between married men and women is

65 - 70 = -5 inches

The standard deviation is the

√(3² + 2.5²) = 3.7 inches.

We can then standardize the difference using the formula:

Z = (Y - X - (-5))/3.7

P(Y > X) = P(Z > (0 - (-5))/3.7) = P(Z > 1.35)

Using a standard normal table or calculator, we find that the probability of a woman being taller than her husband is approximately 0.0885 or 8.85%.

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Complete question is:

A random sample of 400 married couples was selected from a large population of married couples.

Heights of married men are approximately normally distributed with mean 70 inches and standard deviation of 3 inches.

Heights of married women are approximately normally distributed with mean 65 inches and standard deviation 2.5 inches.

There were 20 couples in which the wife was taller than her husband, and there were 380 couples in which the wife was shorter than her husband

suppose that a married man is selected at random and a married woman is selected at random. find the approximate probability that the woman will be taller than the man.

Answer:

y = 0.027027027027027x + 14.540540540541

or

\(y = \frac{1}{37} x + \frac{538}{37}\)

Step-by-step explanation:

Answer:

1) 8 m^3

2) 125 + 25

3) 8

Step-by-step explanation:

1) It's a cube shape => length = width = height = 2 m

Volume = length × width × height = 2 × 2 × 2 = 8 m^3

2) 5^2 + 5^3 = 150

25 + 125 = 150

3) Now she is 8 years old (8 = 2^3)

Next year she'll be 9 years old (9 = 3^2)

The Normal distribution is symmetric and ranges from negative to positive infinity, while the Log-normal distribution is skewed and only takes positive values. To select the better fit for data, consider characteristics (positivity and skewness favor Log-normal, symmetry favors Normal), hypothesis testing, visualization, and statistical tests.

Let's analyze each section separately:
a) The major differences between the Normal and Log-normal distributions are:

Normal Distribution: The Normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution that is defined by its mean (μ) and standard deviation (σ). It follows a bell-shaped curve and is often used to model naturally occurring phenomena. The range of values extends from negative infinity to positive infinity.

Log-normal Distribution: The Log-normal distribution is a skewed probability distribution that arises when the logarithm of a random variable follows a normal distribution. It is characterized by its parameters mu (μ) and sigma (σ) of the underlying normal distribution. Unlike the Normal distribution, the Log-normal distribution only takes positive values.

b) Selecting which distribution fits the data better depends on the nature of the data and the research question at hand. Here are a few considerations:

1. Data Characteristics: If the data consists of positive values and the distribution appears to be skewed, the Log-normal distribution might be more appropriate. On the other hand, if the data is symmetric and unbounded, the Normal distribution may be a better fit.

2. Hypothesis Testing: If you have a specific hypothesis to test or a theoretical justification for choosing one distribution over the other, it is advisable to use that distribution.

3. Visualization: Plotting the data and comparing it to the shapes of the Normal and Log-normal distributions can provide visual insights into which distribution aligns better with the data.

4. Statistical Tests: Statistical tests such as the Kolmogorov-Smirnov test or the Anderson-Darling test can be used to assess the goodness-of-fit for each distribution and determine which one provides a better fit to the data.

In summary, selecting the appropriate distribution involves considering the characteristics of the data, the research question, and statistical tests. Visualization and hypothesis testing can further aid in determining the best fit distribution.

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Answer:0.25

Step-by-step explanation:3/12 = 0.25

Answer:

523.3 cm^3

Step-by-step explanation:

You have a formula for the volume of a sphere:  \(V=\frac{4}{3}\pi r^3\) but to use it, you need the radius, r .

The panel on the left shows  c = 31.4 cm (I am assuming  c  is the circumference, like the distance around the "equator" of the sphere).

What's the relationship of circumference of a circle (equator) to the radius?

\(c=2\pi r\)

So put 31.4 in for  c  in that last formula.

\(31.4 =2\pi r\)

If you use the approximate value of pi  \(\pi \approx 3.14\) that becomes

\(31.4 = 2(3.14)r\\\frac{31.4}{6.28} = r\\\\5=r\)

Aha!  The radius r  is 5 cm.  Now go back to the formula for volume:

\(V=\frac{4}{3} (3.14)(5^3)\\V=\frac{4}{3}(3.14)(125)\\V \approx 523.3 \text{ cm^3}\)

The area of Circle D is 3.36 times greater than the area of Circle A.

What is circle?

A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center.

We are given the following information about the radii of the four circles:

The radius of Circle A is 6 mm.

The radius of Circle B is 3 mm greater than the radius of Circle A, so it is 6 + 3 = 9 mm.

The radius of Circle C is 5 mm greater than the radius of Circle B, so it is 9 + 5 = 14 mm.

The radius of Circle D is 3 mm less than the radius of Circle C, so it is 14 - 3 = 11 mm.

The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius.

Therefore, we can calculate the areas of the four circles as follows:

The area of Circle A = π(6)² = 36π mm².

The area of Circle B = π(9)² = 81π mm².

The area of Circle C = π(14)² = 196π mm².

The area of Circle D = π(11)² = 121π mm².

To find out how many times greater the area of Circle D is than the area of Circle A, we can divide the area of Circle D by the area of Circle A:

Area of Circle D / Area of Circle A = (121π) / (36π) = 3.36

Therefore, the area of Circle D is 3.36 times greater than the area of Circle A.

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Answer:

3. B 10a

4. D 3

Step-by-step explanation:

the value of function lim (g(x)*h(x)) will be 10 a.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

Given, For g(x)=5 and h(x)=2x

\(\lim_{x \to \ a }(g(x)*h(x))\)

=> lim (5 * 2x)

=> lim 10x

=> 10a

for  G(x)= X-10 And H(x)= 2x,

g(x)/ h(x) = (x - 10)/2x

\(\lim_{x \to \ -2} g(x)/ h(x)\)

=> (-2- 10)/-4

=> 3

therefore, the value of function lim (g(x)*h(x)) will be 10 a.

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Answer:

(5x-4y)^2

Step-by-step explanation:

Both 25 and 16 are perfect squares, √25=5 and √16=4

The volume of the box is 432 cubic inches

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

The volume of the box is calculated as

Volume = Number of cubes * Volume of each cube

Where

Volume of each cube = 1 * 1 * 1

Volume of each cube = 1

Substitute the known values in the above equation, so, we have the following representation

Volume = 432 * 1

Evaluate

Volume = 432

Hence, the volume of the box is 432 cubic inches

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Step-by-step explanation:

the question is not complete

Answer:

18x^4 - 12x^3 + 57x^2 - 28x +35

Step-by-step explanation:

Step-by-step explanation:

(3×2+7)(6×2-4x+5)= -52x +221

Answer:

undefined

Step-by-step explanation:

the line is straight up and down, so undefined. 0 would be a horizontal line from left to right

Answer:

The order of arithmetic calculations is

B - Bracket

O - off

D - Division

M - Multiplication

A - Addition

S - Subtraction

Use this to solve

Answer:

1255.64

Step-by-step explanation:

Check the image above I solved it on google docs lol

Given:

City's population= 785,000.

Calculating of city's population:

\(\to \bold{785000 \cdot 8.5 \% = 785000 \cdot \frac{8.5}{100}=785000 \cdot \frac{\frac{85}{10}}{100}}\)

Calculating the complex fraction:

\(\to \bold{\frac{\frac{85}{10}}{100}, \text{write as 100 like} \ \frac{100}{1}}\)

\(\to \bold{785000 \cdot \frac{ \frac{85}{10}}{100}=785000 \cdot \frac{\frac{85}{10}}{\frac{100}{1}}=785000 \cdot \frac{85}{1000}=66725}\)

Therefore, \(\bold{8.5\% \ of\ 785000\ is\ {66725}}\)

Calculating \(\bold{9.4\%}\) of the city's population:

\(\to \bold{9.4\% (\frac{9.4}{100})}:\\\\\to \bold{785000 \cdot 9.4\% = 785000 \cdot \frac{9.4}{100}=785000 \cdot \frac{\frac{64}{10}}{100}}\)

Calculating the complex fraction:

\(\to \bold{ \frac{\frac{94}{10}}{100}\ \text{write 100 as} \ \frac{100}{1}}\\\\\to \bold{785000 \cdot \frac{\frac{94}{10}}{100}=785000 \cdot \frac{\frac{94}{10}}{\frac{100}{1}}=785000 \cdot \frac{94}{1000}=73790}\\\\\)

Therefore, \(\bold{9.4\%\ of\ 785000\ is\ {73790}}\)

So, the final answer is "Between 66725 and 73790 people use the transit system daily".

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Answer:1

Step-by-step explanation:

Answer:

The Answer is c

Step-by-step explanation:

g(-1)=1

Area of region A is equal to the sum of area of region B and area of region C when a right-angled triangle is formed by the diameters of three semi-circular regions A, B, and C.

Let the diameters of semicircle A, B and C be a, b and c respectively.

We know area of a semi-circular region of diameter d is

A = (1/2)(πd²/4)

A = πd²/8

Thus,

area of region A is πa²/8

area of region B is πb²/8

area of region C is πc²/8

The triangle formed is a right angled triangle, with hypotenuse a and legs b and c. By Pythagoras theorem

a² = b² + c²

Multiplying both sides by π/8

(π/8)a² = (π/8)(b² + c²)

πa²/8 = πb²/8 + πc²/8

Area of region A = Area of region B + Area of region C

Hence proved.

--The question is incomplete, answering to the question below--

"A right-angled triangle is formed by the diameters of three semi-circular regions A, B, and C as shown in the diagram. Show that area of region A = area of region B + area of region C."

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There are 12,376 different groups of six passengers that can be selected from the plane flight of 17 passengers.

To calculate the number of different groups of six passengers that can be selected from a plane flight with 17 passengers, we can use the concept of combinations.

The number of ways to choose a subset of k items from a set of n items is given by the combination formula:

C(n, k) = n! / (k!(n-k)!)

In this case, we need to select 6 passengers from a group of 17. Thus, we can calculate the number of different groups using the combination formula:

C(17, 6) = 17! / (6!(17-6)!)

        = 17! / (6!11!)

        = (17 * 16 * 15 * 14 * 13 * 12) / (6 * 5 * 4 * 3 * 2 * 1)

        = 12376

Therefore, there are 12,376 different groups of six passengers that can be selected from the plane flight of 17 passengers.

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