Find the Pearson correlation coefficient r for the given points. Round any intermediate calculations to no less than six decimal places, and round your final answer to three decimal places.

(1,6)
, (2,10)
, (3,4)
, (4,4)
, (5,8)
, (6,2)
, (7,2)

Answer:

Step-by-step explanation:

SA=2r^{2}+2rh=175.84

Answer: 87

Step-by-step explanation:

(74+85+x)/3  = 82

3(82)=74+85+x

246 = 74+85 + x

246-74-85=x

x= 87

Answer:

  (a)  65.85 km²

Step-by-step explanation:

You want the area of a sector with radius 7 km and central angle 154°.

The formula for the area of a sector is ...

  A = 1/2r²θ . . . . where r is the radius and θ is the central angle in radians

  A = 1/2(7 km)²(154·π/180) ≈ 65.85 km²

The area of the shaded sector is about 65.85 square km.

__

Additional comment

The last two answer choices can be eliminated because their units are distance units, not area units.

The area of the circle is πr², about 154 km². The shaded part is less than half, but somewhat more than 1/7, so will be less than 77 and more than 22 km². For this problem, a rough estimate of the area can tell you which is the reasonable answer choice.

Therefore , the solution of the given problem of volume comes out to be  1.5 centimetres is the appropriate height measurement option A.

The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Two instances of cubic units are the numbers cm3 and in3. However, an object's bulk can be used to determine its dimensions. Typically, an object's weight is transformed into mass units like kilogrammes and kilos.

Here,

The technique used by the classmate made a mistake by rearranging the measurements in the formula. The right equation to use to determine a rectangle prism's volume is:

=> V = lwh

where the prism's length, breadth, and height are indicated by l, w, and h, respectively.

The colleague in this instance applied the formula:

=>  h = 1.5(1.2)(2.5)

which, rather than the height, is the method for calculating the volume.

We must rewrite the volume formula to determine the height:

=>  V = lwh

=>  h = V/lw

Now that we know the numbers to substitute, we can determine the height:

=>  h = 1.5(1.2)(2.5) / (1.2)(2.5)

=>  h = 1.5 cm

Consequently, 1.5 centimetres is the appropriate height measurement (option A).

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The required perimeter of the rectangle is 42 cm.

A quadrilateral with four right edges is a rectangle. It can also be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equivalent. A square is a rectangle with four equally long edges.

Let's assume that the width of the rectangle is w cm.

The length of the rectangle is twice the width, which means that the length is 2w cm.

The area of the rectangle is given as 98 square cm, so we have:

[tex]$$A = lw = (2w)w = 2w^2 = 98$$[/tex]

Solving for w, we get:

[tex]$$w^2 = 49$$[/tex]

[tex]$$w = \pm 7$$[/tex]

Since the width of the rectangle cannot be negative, we take w = 7 cm.

Then, the length of the rectangle is 2w = 14 cm.

The perimeter of the rectangle is given by:

[tex]$$P = 2l + 2w = 2(14) + 2(7) = 28 + 14 = 42 \text{ cm}$$[/tex]

Therefore, the perimeter of the rectangle is 42 cm.

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Answer:

Step-by-step explanation:

I'm sorry, but I cannot accurately calculate the driver's average speed without additional information such as the distance traveled and the time taken.

However, I can help you calculate the cost of fuel if the driver fills up half of the tank's capacity:

Half of the tank's capacity is 28/2 = 14 litres.

The cost of fuel per litre is R17.98.

Therefore, the cost of filling up half the tank is 14 x R17.98 = R251.72.

So, if the price of fuel is R17.98 per litre and the driver fills up half the tank, they will pay R251.72 for fuel.

Answer:

As per the given information, Paul's profit from selling b bottles of water is given by the formula:

P(b) = 1.05b - 279

Here, b represents the number of bottles sold, and P(b) represents the profit made by Paul in dollars.

We can find the profit made by Paul by substituting the given value of b in the above equation. For example, if Paul sells 100 bottles of water, then his profit can be calculated as follows:

P(100) = 1.05(100) - 279

= 105 - 279

= -174

So, if Paul sells 100 bottles of water, he will make a profit of $174.

Note that the profit is negative in the above example, which means that Paul will incur a loss if he sells only 100 bottles of water. To make a profit, he needs to sell more than 265 bottles of water. We can find this by setting P(b) equal to zero and solving for b as follows:

P(b) = 1.05b - 279 = 0

1.05b = 279

b = 265.71

Therefore, Paul needs to sell more than 265 bottles of water to make a profit.

Paul's profit from selling bottled water is described by the formula P(b)=1.05b-279. This suggests he makes $1.05 per bottle minus an initial cost of $279. To break even, Paul must sell approximately 266 bottles.

The question involves understanding of linear functions in the context of a real-world problem. Paul is planning to sell bottled water at the local carnival. His profit function, P(b), represented by the formula P(b)=1.05b-279, describes how his profit changes based on the number of bottles, b, he sells. This formula suggests that for every bottle Paul sells, he makes a profit of $1.05 with the subtraction of $279, which probably represents his initial costs. To break even, Paul has to sell enough water such that his profit, P(b), is zero. Solving the equation P(b)=0 gives b=279/1.05. This means Paul needs to sell approximately 266 bottles of water to break even. Any sales beyond this would generate profit.

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We expect the cube to show a two 8 times out of 48 rolls.

Six faces, numbered from 1 to 6, make up a typical number cube. When the cube is rolled, there is an equal chance that every face will show up. As a result, there is a 1/6 chance that the cube will roll a two on any given roll.

We can use the calculation for the anticipated value of a discrete random variable to get the expected number of times the cube will reveal a two in 48 rolls:

E(X) = np

where n is the number of trials (in this example, 48 rolls), p is the probability of success on each trial (in this case, 1/6), and X is the random variable (in this case, the number of times the cube reveals a two).

When we change the values, we obtain:

E(X) = 48 * (1/6) = 8

Hence, we anticipate that the cube will display a two 8 times out of every 48 rolls.

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The total number of seats available for the baseball game can be calculated by adding the number of box and club seats available whch is found to be 25,200.

The game of baseball can be used to teach various mathematical concepts, such as probability, statistics, graphing, estimation, and basic arithmetic. The game can also be used to introduce concepts such as geometry and trigonometry, as well as to build problem-solving skills.

The total number of seats available can be calculated by adding the number of box and club seats available, which is

12,600 + 5400 = 18,000.

This total can then be multiplied by the respective percentages of the other two categories to get the total number of seats available.

For instance, the total number of bleacher seats available can be calculated by multiplying 12,000 by 18%.

12,000 x 0.18 = 2,160

Similarly, the total number of grandstand seats available can be calculated by multiplying 12,000 by 42%.

12,000 x 0.42 = 5,040

Hence, the total number of seats available for the baseball game is

18,000 + 2,160 + 5,040 = 25,200.

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Answer:

1.49 minutes

Step-by-step explanation:

Let the number of minutes be x.

Deandre paid $17.43 for $7 to start  and 7 cents per minute.

Mathematically,

7x+7=17.43

7x= 17.43-7

7x = 10.43

∴ x = 10.43/7

x = 1.49 minutes.

Hope this helps! :)

The statement " If a and x are positive numbers and a ≠ 1, then[tex]log_a(x^r) = r * log_a(x)[/tex] for any real number r" is true .

To prove the equation, we can start with the definition of logarithms:

[tex]log_a(x) = y[/tex] if and only if [tex]a^y = x[/tex]

Using this definition, we can rewrite both sides of the equation as exponents:

[tex]log_a(x^r) = y[/tex] if and only if [tex]a^y = x^r[/tex]

[tex]r * log_a(x) = y[/tex] if and only [tex]a^y = x^r[/tex]

Since [tex]a^y = x^r[/tex] in both case, we have:

[tex]log_a(x^r) = r * log_a(x)[/tex]

Therefore, the equation [tex]log_a(x^r) = r * log_a(x)[/tex] holds for any positive numbers a and x (where a ≠ 1) and any real number r.

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The  least positive multiple of 199 is still 199

To find the least positive multiple of 199, we can start by multiplying 199 by 1, 2, 3, and so on until we find a multiple that is a positive integer.

199 x 1 = 199

199 x 2 = 398

199 x 3 = 597

199 x 4 = 796

Notice that the product of 199 and any positive integer greater than 1 will have at least three digits. Therefore, the least positive multiple of 199 is 199 itself.

Therefore, the least positive multiple of 199 is 199.

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The probability of the ball landing on a number that is less than six is:

5/38.

The word "probability" derives from the Latin word "probitatem," which means "credibility, probability," from the noun probabilis in the 14th century (see probable). The phrase was first used in a mathematical meaning in 1718.

American roulette has five numbers that are less than six, namely 1, 2, 3, 4, and 5.

The odds of the ball landing on a number less than six are 5 to 1 out of a total of 38 outcomes (the 36 digits plus 0 and 00).

Hence, the likelihood that the ball will land on a number smaller than six is:

5/38.

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Answer:

Step-by-step explanation:

The equation would be

f(x) = (x - 1)^2 + 1

Answer:

7.111 per pound of seed.

Step-by-step explanation:

64/9 = 7.111

Answer:

Step-by-step explanation:

If the shapes are similar - then their lengths are proportional.

You can make a ratio and solve for the missing variable.

You must match the corresponding sides.

[tex]\frac{32}{48}[/tex] = [tex]\frac{d}{36}[/tex]

Cross mulitiply the "diagonal values" and divide by the value

diagonal from the variable.

32 × 36 = 48d

1152 = 48d

1152/48 = 48d/48

24 = d

Answer:

3

Step-by-step explanation:

the coordinates are the answers for X and Y.

x+3y=20

n+3n=20

n=5

y=ax-10

5=5a-10

a=3

Answer:

To solve the problem, we need to determine the number of ways to choose 2 girls out of 8 and 2 boys out of 4, and then multiply those numbers together to get the total number of arrangements.

The number of ways to choose 2 girls out of 8 is given by the combination formula:

C(8,2) = 8! / (2! * 6!) = 28

Similarly, the number of ways to choose 2 boys out of 4 is:

C(4,2) = 4! / (2! * 2!) = 6

Therefore, the total number of different arrangements of 2 girls and 2 boys that can be chosen from the 12 students is:

28 x 6 = 168

So there are 168 different arrangements possible.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the number of different arrangements, we can use combinations.

The number of ways to choose 2 girls out of 8 is C(8,2) = 28.

The number of ways to choose 2 boys out of 4 is C(4,2) = 6.

So, the total number of ways to choose 2 girls and 2 boys from 8 girls and 4 boys is:

C(8,2) * C(4,2) = 28 * 6 = 168

Therefore, there are 168 different arrangements for the piano teacher to take 4 of her 12 students to the concert.

Answer: 5 Miles and 1,241 Yards and 2 Feet

Step-by-step explanation: There are 5,280 ft in a mile. To convert to miles, you can do 30,125/5,280. This will give you 5 miles with a remainder of 3,725 ft.

Next, we convert to yards. There are 3 yards in a foot. For this you can do 3,725/3. This will give you 1,241 yd. with a remainder of 2 feet.

Combine these and it will give you 5 miles and 1,241 yd. and 2 ft.

To check your work, you can do (5*5,280)+(3,725*3)+2=30,125.

Please reply back if you have any question.

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The linear regression line is: Y = 0.51X - 14.05

A number is a mathematical object used to count, measure, and label. It is a fundamental concept in mathematics and is used in nearly every branch of the discipline. In everyday life, the notion of numbers is used to count objects, keep track of scores, measure amounts, and label objects.

City TV Commercials Car Sales

A 60 20

B 50 15

C 70 25

D 45 17

E 55 19

Calculating the linear regression line:

m = Slope = (NΣXY - (ΣX)(ΣY)) / (NΣX2 - (ΣX)2)

= (5(1475) - (325)(95)) / (5(5850) - (325)2)

= (7375 - 30875) / (29250 - 105625)

= -38500 / -75375

= 0.51

b = Intercept = (ΣY - m(ΣX)) / N

= (95 - 0.51(325)) / 5

= (95 - 165.25) / 5

= -70.25 / 5

= -14.05

Therefore, the linear regression line is:

Y = 0.51X - 14.05.

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complete question:

An automobile company is running a new television commercial in five cities with approximately the same population. The following table shows the number of times

the commercials run on TV each day and the number of car sales in the hundreds. Finds the linear regression line for the data gen in the table Round any intermediate

calculations to no less than a decimal place, and round the coefficients to two decimal places.

The mean of the data-set represented by the frequency table is given as follows:

d) 13.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

We have a frequency distribution, hence each observation is considered to be the midpoint of each interval, and thus the sum of the observations is given as follows:

5 x 4 + 10 x 7 + 15 x 9 + 20 x 5 = 325.

The number of observations is given as follows:

4 + 7 + 9 + 5 = 25.

Hence the mean is given as follows:

325/25 = 13.

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The expression which is equivalent to the given expression for all values of x is; 7x + 8.

As evident from the task content; the given expression whose equivalent is required to be determined is; x + 8 + 4x + 2x.

Therefore, by collecting like terms; we have that;

x + 4x + 2x + 8

By adding like terms; we have;

7x + 8.

Ultimately, the expression which is equivalent to the given expression is; 7x + 8.

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Answer:

p=10m.

Step-by-step explanation:

For every painting Sydney sells, $10 is saved.

Answer:

Step-by-step explanation:

a, YES,  x is a solution as 4 + 2 = 6.

b. looks like there's a missing symbol here.

The volume of the Cylinder formed  approximately 16.37 cubic units.

What is a cylinder?

A cylinder is a three-dimensional geometric shape that has two parallel circular bases, connected by a curved lateral surface. It is similar to a prism, but instead of having polygons as its bases, it has circles. The lateral surface of a cylinder is formed by the set of all straight lines connecting the points on the edge of one base to the corresponding points on the edge of the other base.

Now,

To find the volume of the solid formed by rotating the region enclosed by x=0, x=1, y=0, y=5+x⁸about the y-axis, we can use the method of cylindrical shells.

First, we need to express the equation y=5+x⁸ in terms of x, so we can integrate with respect to x:

y = 5 + x⁸

y - 5 = x⁸

x = (y - 5)¹/⁸

Next, we need to determine the limits of integration. The region is bounded by x=0 and x=1, so we integrate from x=0 to x=1.

Volume of a cylindrical shell is

V = 2πrhΔx

In this case, the radius r is simply x, the height h is y, and Δx is dx. So, we have:

V = 2πxy dx

V = 2πx(5+x^8) dx

V = 10πx dx + 2πx⁸ dx

Integrating with respect to x from x=0 to x=1, we get:

V = [5π + 2π/10] - [0 + 0]

V = 5.2π

Therefore, the volume of the solid formed by rotating the region enclosed by x=0, x=1, y=0, y=5+x⁸ about the y-axis is approximately 16.37 cubic units.

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The Scotch Bonnet seashell is 3/4 inches shorter than the combined lengths of the two Alphabet Cone seashells.

What is length ?

Length is a physical quantity that describes the size or distance of an object in one dimension. It is typically measured in units such as meters, feet, inches, or centimeters, and can refer to the distance between two points or the size of an object in one direction. In geometry, length is a fundamental concept that is used to define other geometrical properties such as area, volume, and perimeter. In general, length can be defined as the extent of something along its longest dimension, and it is a crucial parameter in many fields, including physics, engineering, architecture, and mathematics.

According to the question:

The combined length of two Alphabet Cone seashells is:

1(3/4) inches + 1(3/4) inches = 3(1/2) inches

The length of the Scotch Bonnet seashell is:

2(1/8) inches

To find the difference in length, we can subtract the length of the Scotch Bonnet seashell from the combined length of the two Alphabet Cone seashells:

3(1/2) inches - 2(1/8) inches = 3(4/8) inches - 2(1/8) inches

Simplifying the expression, we get:

3(4/8) inches - 2(1/8) inches = 3(2/8) inches = 3/4 inches

Therefore, the Scotch Bonnet seashell is 3/4 inches shorter than the combined lengths of the two Alphabet Cone seashells.

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Tabi's bill includes $248.94 in charges and $34.99 in interest.

Let x be the amount of interest that Tabi was charged, in dollars.

According to the problem, the new charges are $213.95 more than the interest, so the amount of new charges is x + $213.95.

The total bill, which includes the charges and interest, is $283.93.

Therefore, we can write an equation:

x + (x + $213.95) = $283.93

Simplifying and solving for x, we get:

2x + $213.95 = $283.93

2x = $69.98

x = $34.99

So the amount of interest charged is $34.99.

To find the amount of charges, we can use the equation for new charges:

x + $213.95 = $34.99 + $213.95 = $248.94

So the amount of charges is $248.94.

Therefore, Tabi's bill includes $248.94 in charges and $34.99 in interest.

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Marlo can draw two different isosceles right triangles and third vertices are (-0.5, 5) and (-0.5, 7)

An isosceles triangle is a type of triangle in which two sides of the triangle have the same length.

Since the triangle is isosceles, its third vertex must lie on the line that is perpendicular to the line passing through the two given vertices and passes through the midpoint of that line.

The midpoint of the two points (-3,6) and (2,6) connecting the line segment is

((-3+2)/2,    (6+6)/2) = (-0.5, 6)

The line passing through (-3,6) and (2,6) has equation y = 6. The line perpendicular to it passing through (-0.5,6) has equation x = -0.5.

Therefore, the third vertex of the isosceles right triangle must have coordinates (-0.5, y), where y is an integer.

To find how many different isosceles right triangles can be drawn, we need to find how many different integer values of y satisfy the condition that the distance between (-3, 6) and (-0.5, y) is the same as the distance between (2, 6) and (-0.5, y).

We know that the distance formula, So,

[tex]\sqrt{((2 - (-0.5))^2 + (6 - y)^2)}[/tex] = [tex]\sqrt{((-3 - (-0.5))^2 + (6 - y)^2)}[/tex]

Simplifying this equation gives:

(2.5)² = (3.5)²

y = 6 ± 1

Therefore, there are two possible values of y, 5 and 7, which correspond to the two possible third vertices of the isosceles right triangle: (-0.5, 5) and (-0.5, 7). So, Marlo can draw two different isosceles right triangles with two vertices at (-3, 6) and (2, 6) such that the coordinates of the third vertex are both integers.

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Answer: To find the height of the ramp, we need to use the Pythagorean theorem, which relates the lengths of the sides of a right triangle. In this case, the ramp, porch, and ground form a right triangle, with the height of the ramp being the missing side.

We know that the ramp begins 96 centimeters from the porch and is 100 centimeters long. Let's represent the height of the ramp with the variable "h". Then, we can write the Pythagorean theorem equation:

h^2 + 96^2 = 100^2

Simplifying this equation, we get:

h^2 + 9216 = 10000

Subtracting 9216 from both sides, we get:

h^2 = 784

Taking the square root of both sides, we get:

h = 28

Therefore, the height of the ramp is 28 centimeters.

Step-by-step explanation: