Where is there a striking deviation in the dot plot above

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.

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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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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Answer:

[tex]x=44[/tex]

Step-by-step explanation:

lets say X is the cookies Ms. Jans Brought to her class
first she put half of then in the morning (that is [tex]x/2[/tex] of her cookies)
then she gave out 12 more. That is 12 less cookies.
the total cookies left is the total amount minus the half, minus the 12 cookies:
[tex]x-x/2-12=10[/tex]
From this equation we can solve for X
[tex]x/2=10+12[/tex]

 [tex]x=2(22)\\[/tex]

[tex]x=44[/tex]
Just for check, if she brought 44 cookies, and put 22 (half of then), she still have 22 cookies, then she 12 more, then only 10 are left. So 44 is the answer.

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:

In order of the expressions: 3 1/4, 3 1/3, 3 1/2, and 3 1/6

Step-by-step explanation:

All the names for the polygon are correct except for: C) GDFEABC.

In Mathematics, a polygon can be defined as a two-dimensional geometric figure that consists of straight line segments and finite number of sides. Additionally, some examples of a polygon include the following:

Generally speaking, the vertices of a regular polygon should be named in consecutive order either clockwise or anticlockwise (counterclockwise).

In conclusion, GDFEABC is an incorrect name for the given regular polygon.

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The correct option is (b) i.e. the total perimeter of the fence is 7x + y − 4 feet.

What is Perimeter?

Perimeter is the total length of the boundary or outer edge of a two-dimensional shape, such as a polygon, circle, or ellipse. It is the sum of the lengths of all the sides or arcs that make up the shape. For example, the perimeter of a square is the sum of the lengths of all its sides, while the perimeter of a circle is the circumference, which is the distance around the circle. The perimeter is often measured in units such as centimeters, meters, or feet, depending on the context of the problem.

Given : sides of the fence

            s₁ = 4x + 5

            s₂ =  y − 7

            s₃ = 3x − 2

We know that, perimeter of a triangle is sum of all three sides.

So, Perimeter of the fence =  s₁+ s₂+ s₃

                                            = 4x + 5 + y − 7 + 3x − 2

                                            = 7x + y - 4 ft.

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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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The area of the shaded part is 20m²

The space enclosed by the boundary of a plane figure is called its area. The area of a rectangle is length × width It is measured in square units like cm² and m².

To find the area of the square, we need to find the side length.

The side length is found by using Pythagoras theorem

each box is 1m, then 4 boxes is 4m and 2 boxes is 2m

therefore;

l= √ 4²+2²

l = √ 16+4

l = √20 = 2√5

area a square is l²

A = (2√5)²

A = 4× 5

A = 20m²

therefore the area of the shaded part is 20m²

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Answer:

Step-by-step explanation:

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

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:

p=10m.

Step-by-step explanation:

For every painting Sydney sells, $10 is saved.

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

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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The required radius of the hemisphere is approximately 20.27 inches.

Half of a sphere, with one edge flat and the other in the form of a bowl, makes up a hemisphere, a 3D geometric object. The northern and southern hemispheres, a bowl, mushrooms, and other objects are some of the most typical instances of hemispheres.

The volume V of a hemisphere with radius r is given by:

[tex]$V = \frac{2}{3}\pi r^3$$[/tex]

We are given that the volume of the hemisphere is 6043 cubic inches. So we have:

[tex]$$\begin{align*}\frac{2}{3}\pi r^3 &= 6043 \r^3 &= \frac{3}{2}\cdot 6043 \cdot \frac{1}{\pi} \r^3 &= 9051 \r &= \sqrt[3]{9051} \approx 20.27 \text{ in}\end{align*}[/tex]

Therefore, the radius of the hemisphere is approximately 20.27 inches.

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Answer: 3/2, 2/3, 1/3

Step-by-step explanation:

Answer:

The base of the ladder is pulled away from the wall at a rate of 2 feet/sec. b) Consider the triangle formed by the side of the house, the ladder,and the ground

Step-by-step explanation:

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:

Jeriel would have to pay $17

Step-by-step explanation:

t= hours

$3 per t hour +$8 fee

t=3

3(3)+8= $17

How much would Jeriel have to pay if he left his car in the lot for t hours:

3t+8

How much total money would Jeriel have to pay for parking if he left his car in the lot for 3 hours?

$17

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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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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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 scale factor of the smaller polygon to the larger polygon is 2. Therefore, the scale factor of the smaller triangle to the larger triangle is 6.

Scale factor refers to the ratio of any two corresponding lengths in two similar geometric figures. In other words, it is the ratio of the size of an object in one image or figure to the size of the same object in another image or figure, assuming that the two images or figures are proportional to each other. The scale factor can be used to determine the relationship between the sizes of the objects in the two figures or images.

Here,

1. The scale factor from the smaller polygon to the larger polygon is found by dividing the length of the larger polygon by the length of the smaller polygon:

scale factor = length of larger polygon / length of smaller polygon

scale factor = 14 / 7

= 2

2. The scale factor from the smaller triangle to the larger triangle is found by dividing the length of the larger triangle by the length of the smaller triangle:

scale factor = length of larger triangle / length of smaller triangle

scale factor = 24 / 4

= 6

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Plane Art include squares, rectangles, triangles, circles, pentagοns, οctοgen, hexagοns, οvals etc. A grοuping οf shapes is called pοlygοns, like squares and rectangles, but circles and οvals are nοt pοlygοns.

A plane is a twο-dimensiοnal surface measured by twο linearly independent pοints; a plane dοesn't have an οbviοus directiοn and can extend indefinitely. In algebra, the pοints are plοtted in the cοοrdinate plane which has a number line extending left tο right and upwards and dοwnwards endlessly and infinitely.

In cοntrast tο sοlid shapes, a clοsed twο-dimensiοnal οr flat surface figure is knοwn as a plane shape. Instead οf edges and faces, they pοssess several light lines that make a cοrner οr a vertex where the twο straight lines meet. Sοme basic plane shapes are triangles, squares, rectangles, circles and οvals.

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Complete question:

Pre-Algebra Grade 8: Unit 1 Lesson 8

What is Plane Art?

(Alternative Portfolio)

(Connections)

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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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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