Select the simplification that accurately explains the following statement. 7 3 = 7 1 3 A.

Hello and Greetings Brainly users.

This is an exercise in "Equation of the line that passes through two points". The equation of a line is a mathematical formula used to describe a straight line in a Cartesian plane.

To find the equation of a line that passes through two points, you must first calculate the slope using the formula: m = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are the given points. Then, the point-slope form of the equation of the line is used to obtain the equation of the line: y - y₁ = m(x - x₁).

By solving this equation, we can obtain the equation of the line that passes through two points. If the slope of the line is zero, as in the case of two points lying on the same horizontal line, then the equation of the line is simply a horizontal line at y = k, where k is the y-coordinate of the points.

Applying the following formula:

m = (y₂ - y₁) / (x₂ - x₁)

where m is the slope of the line.

We find that the points are:

x₁ = 6 ,   y₁ = 4

x₂ = -5 , y₂ = 4

We substitute the data in the formula and solve:

m = (y₂ - y₁) / (x₂ - x₁)

m = (4 - 4)/(-5-6)

m = 0/-11

m = 0

Now, we can use the point-slope form of the equation of the line to obtain the equation of the line:

Where m = 0 and (x₁, y₁) is one of the two given points. We can choose any of the two points, but for this we will choose (6,4).

So, substituting the values we have, we have:

y - 4 = 0(x - 6)

Simplifying, we arrive at:

y - 4 = 0

y = 4

The equation of the line that passes through the points (6,4) and (-5,4) is y = 4 , since it is a horizontal straight line through the values of y = 4.

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Based on the description of the problem,the measure of ∠BTX is 60°.

A circle is a two-dimensional geometric shape made up of all the points that are equally spaced apart from the circle's centre.

The radius of the circle is the distance measured from any point on the circle to its centre.

The circumference is the collection of all the points on the circle.

Based on the description of the problem, we can conclude that triangle BOX is an isosceles triangle with OB = OX. This is because both OB and OX are radii of the same circle centered at O.

Since m/BOX = 120°, we can find the measure of angle B by dividing this angle in half, since angle B is the base angle of the isosceles triangle BOX.

∠BO = (180° - 120°)/2 = 30°

Now, since TX and TB are tangent to the circle at points X and B respectively, we know that angle BTX is equal to the sum of angles BOY and OXT, since angle BOY and OXT are both in the same quadrant and add up to 90°.

∠BTX = ∠BOY + ∠OXT>

Since triangle BOX is an isosceles triangle with angle BOY equal to 30°, we can find the measure of angle OXT as follows:

∠OXT = 180° - ∠BOX - ∠BOY

= 180° - 120° - 30°

= 30°

Therefore,

∠BTX = ∠BOY + ∠OXT

= 30° + 30°

= 60°

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Answer:

The choice that provides the greatest advantage for a career as an art teacher is:

enjoys children, is flexible, competent in a variety of art forms, and is energetic

Here are the key reasons why this is the best choice:

• Enjoys children - Working with students is core to being a teacher. An art teacher needs to enjoy interacting with and assisting children.

• Is flexible - The role of a teacher requires adapting to different students' needs, interests, abilities and challenges. Flexibility is important.

• Competent in a variety of art forms - An art teacher needs to be knowledgeable and skilled across different art mediums, subjects, techniques to support students.

• Is energetic - Teaching requires passion, enthusiasm and energy to keep students engaged and motivated.

In contrast, the other options lack important characteristics for an art teacher:

• Dislikes children, dislikes mess, intolerant of noise, and creates computer graphics - These indicate unsuitable qualities for a teacher.

• Organized, neat, quiet, and likes to paint houses in spare time - While organized and detail-oriented are good, the other traits do not reflect the key responsibilities of art instruction and supporting students.

• Enjoys art museums, reads often, hard worker, is a part-time photographer - An interest in art is relevant but not sufficient. Important teaching qualities like flexibility, working with children, knowledge of art forms are missing.

So in summary, the choice that highlights enjoying children, flexibility, competence across art forms, and energy are the characteristics that would provide the greatest advantage for a career as an art teacher. Art knowledge and skills are prerequisite but a passion for instructing students and learning is essential.

Step-by-step explanation:

The rule that yields the dilation of the figure KLMN centered at the origin is (x, y) → (2x, 2y). So, the correct answer D).

In this question, we are looking for the rule that yields the dilation of the figure KLMN centered at the origin. Option D, (x, y) → (2x, 2y), represents a dilation by a scale factor of 2, which means that the image will be twice as large as the original figure. Thus, option D is the correct answer.

This rule doubles the distance of each point from the origin and results in an image that is twice as large as the original figure. Rule A translates the figure up and to the right, while Rule B halves the coordinates of each point, resulting in an image that is half as large. Rule C translates the figure to the right and up by 2 units.

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The Law of Large Numbers is a fundamental concept in probability theory and statistics stating the number of trials of a random event increases, the average of the outcomes approaches the expected value of the event. It's better to use 500 trials.

In other words, as we repeat an experiment a large number of times, the proportion of times that a certain outcome occurs will converge to its probability of occurrence. This is an important concept in statistical inference, as it helps to ensure that the results of a sample are representative of the population from which it was drawn.

Now, if you were using the relative frequency of an event to estimate the probability of the event, it would be better to use 500 trials rather than 100 trials. The reason is that the larger the number of trials, the more accurate the estimate of the probability is likely to be.

Using a larger sample size reduces the impact of random variation and provides a more precise estimate of the true probability. The Law of Large Numbers tells us that as the sample size increases, the relative frequency of the event should converge to the true probability, so a larger sample size will generally give a more reliable estimate

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Answer:

32.5

Step-by-step explanation:

hope this helps

Answer:

N'(2, 3)

Step-by-step explanation:

my trick is counting how many spaces away it is from the axis it's being reflected over. So for this one N was at (2, -3) so I counted upwards 3 spaces from the 2 and i got to (2,3). i hope that makes sense the way i explained it.

hope this helps ;)

Answer:

  see attached

Step-by-step explanation:

You want the image of point N(2, -3) after reflection in the y-axis, plotted on the graph.

A line of reflection is the perpendicular bisector of the segment between a point and its image. That is, the image point is as far from the line as the original point, but on the opposite side of it.

The attached figure shows the location of image point N'(-2, -3).

__

Additional comment

The coordinate transformation for reflection in the y-axis just changes the sign of the x-coordinate. That puts the image point as far to the left as the original is to the right:

  (x, y) ⇒ (-x, y) . . . . . . reflection in the y-axis

For any value of x, the corresponding value of y will always be 7, and the line will be a horizontal line passing through the point (5,7).

If a straight line is parallel to the x-axis, then it means that the line will have a constant y-value for all values of x. This means that the slope of the line will be zero, because there will be no change in y for any change in x.

To find the equation of a straight line passing through the point (5,7) that is parallel to the x-axis, we need to find the equation in the form of y = mx + b, where m is the slope of the line and b is the y-intercept.

Since the slope of the line is zero, we can write the equation as:

y = 0x + b

where b is the y-intercept.

To find the value of b, we can use the point (5,7) that the line passes through. Substituting x = 5 and y = 7 in the equation, we get:

7 = 0(5) + b

Simplifying, we get:

b = 7

Therefore, the equation of the straight line passing through the point (5,7) that is parallel to the x-axis is:

y = 7

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In this problem, we are given the angle A, and the side lengths a and b of triangle ABC. Using the   Geometry concept of Law of Sines, we can solve for the remaining angles and side lengths of the triangle. We find that sin(B) ≈ ∠B ≈ ° and ∠C ≈ °, and we can calculate that c ≈ 9.69. This gives us one possible triangle that satisfies the given conditions.

However, the problem states that there are two triangles that satisfy these conditions. To find the second triangle, we must first construct a triangle with angle A₁ = 180° - A and sides a₁ and b₁ such that a₁/b₁ = a/b. This is possible because the Law of Sines tells us that this ratio is constant for all three sides of a triangle. We then apply the Law of Sines to this new triangle to solve for its remaining parts. We find that sin(B₁) ≈ ∠B₁ ≈ ° and ∠C₁ ≈ °, and we can calculate that c₁ ≈ 12.02. This gives us the second possible triangle that satisfies the given conditions.

Now, to show that the areas of the two triangles are proportional to the sines of their respective angles C and C₁, we use the area formula for a triangle, which is 1/2 * base * height. The height of each triangle can be calculated using the sine of the angle opposite the base. Therefore, we have:

Area of ΔABC/ Area of ΔA₁B₁C₁ = (1/2 * a * c * sin(C)) / (1/2 * a₁ * c₁ * sin(C₁))

We can simplify this expression by substituting a1/b1 for a/b and simplifying:

Area of ΔABC/ Area of ΔA₁B₁C₁ = (a/b) * (c/c₁) * (sin(C)/sin(C₁))

Using the Law of Sines, we know that a/b = sin(A)/sin(B) and c/c₁ = sin(C)/sin(C₁), so we can substitute these values into our expression:

Area of ΔABC/ Area of ΔA₁B₁C₁ = (sin(A)/sin(B)) * (sin(C)/sin(C₁)) * (sin(C)/sin(C₁))

Using the fact that the angles in a triangle sum to 180°, we can solve for sin(A) and sin(B):

sin(A) = sin(180° - B - C) = sin(B + C)

sin(B) = sin(180° - A - C) = sin(A + C)

Substituting these values into our expression, we get:

Area of ΔABC/ Area of ΔA₁B₁C₁ = (sin(B + C)/sin(B)) * (sin(C)/sin(C₁)) * (sin(C)/sin(C₁))

Simplifying this expression, we get:

Area of ΔABC/ Area of ΔA₁B₁C₁ = sin(C)/sin(C₁)

Therefore, the areas of the two triangles are proportional to the sines of their respective angles C and C₁

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The quadrilateral ABCD has been reflected across the line x=2 to form its image, as can be seen in the provided figure.

A quadrilateral is a closed object with four successive sides that is referred to as a four-sided polygon in geometry. A quadrilateral's internal angles are always added up to 360 degrees. There are numerous varieties of quadrilaterals, such as: A hexagon with two sets of parallel sides is called a parallelogram. A trapezoid with four sharp angles is a rectangle. a rectangles with four equal sides is referred to as square. A parallelogram with one of the parallel sides is called a trapezium (or a trapezoid in American English). A trapezoid with two adjacent sets of equal-length sides is referred to as a kite.

given

The quadrilateral ABCD has been reflected across the line x=2 to form its image, as can be seen in the provided figure.

Thus, the appropriate answer is: Refraction along the line x=2

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The interior angle measures formed at the center of each stage at a music festival from greatest to least are as follow,

Stage A = 126.01° > Stage B =31.33° > Stage C = 22.66°

Shape of the arrangement of three stages at a music festival is triangle.

Distance between the centers of each stage are as follow,

Stage A and Stage B = 100 yards

Stage B and Stage C = 135 yards

Stage C and Stage A = 210 yards

For Interior angles,

Use the Law of Cosines, which states that for a triangle with sides a, b, and c and opposite angles A, B, and C,

c² = a² + b² - 2abcos(C)

Label the sides of the triangle formed by the three stages,

Side AB = 100 yards

Side BC = 135 yards

Side CA = 210 yards

Then,  find the interior angles at each stage as follows,

At Stage A,

a = 210 yards (CA)

b = 100 yards (AB)

c = 135 yards (BC)

cos(A) = (b² + c² - a²) / (2bc)

⇒cos(A) = (100² + 135² - 210²) / (2 × 100 ×135)

⇒cos(A) = -0.5880

⇒A = arccos(-0.5880)

A = 126.01 degrees

At Stage B,

a = 100 yards (AB)

b = 135 yards (BC)

c = 210 yards (CA)

cos(B) = (a² + c² - b²) / (2ac)

⇒cos(B) = (100² + 210² - 135²) / (2 × 100 ×210)

⇒cos(B) = 0.8542

⇒B = arccos(0.8542)

⇒B = 31.33 degrees

At Stage C,

a = 135 yards (BC)

b = 210 yards (CA)

c = 100 yards (AB)

cos(C) = (a²+ b² - c²) / (2ab)

⇒cos(C) = (135² + 210² - 100²) / (2 × 135 × 210)

⇒cos(C) = 0.9228

⇒C = arccos(0.9228)

⇒ C = 22.66 degrees

Therefore, the interior angle measures formed at the center of each stage from greatest to least are,

Stage A = 126.01 degrees

Stage B =31.33 degrees

Stage C = 22.66 degrees

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On solving the provided question we can say that As a result, because the Pythagorean theorem is not met, the presented numbers do not represent the sides of a right triangle.

The Pythagorean Theorem is the fundamental Euclidean geometry relationship between the three sides of a right triangle. According to this rule, the area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides. According to the Pythagorean Theorem, the square that spans the hypotenuse of a right triangle opposite the right angle equals the sum of the squares that span its sides. It is sometimes expressed as a2 + b2 = c2 in general algebraic notation.

The supplied figures reflect the lengths of the three sides of a right triangle, with the hypotenuse (the side opposite the right angle) being 5.47722557505, and the other two sides being 2.2360679775 and 5.

The sum of the squares of the two shorter sides of a right triangle is equal to the square of the hypotenuse, according to the Pythagorean theorem. In this situation, we can write:

2.2360679775² + 5² = 5.47722557505²

When we simplify and solve for one of the variables, we get:

5² = 5.47722557505² - 2.2360679775²

25 = 24.9999999999971

As a result, because the Pythagorean theorem is not met, the presented numbers do not represent the sides of a right triangle. We could round the data to approach the sides of a right triangle, but it would not get accurate solutions.

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Answer:

y=1/2x+4

Step-by-step explanation:

The point of intersection is 4, and it goes up one, right 2 so the rise over run is 1/2

He run on Thursday is 3.75 miles.

Algebra helps in converting a mathematical statement into an equation. We know if we have ‘more’ or ‘sum’ in the given sentence we use addition operation (+) . Similarly If we have ‘less’ or ‘difference’ we use subtraction (−) . If we have a ‘quotient’ we use division operation (÷) . To define more generalized terms; we use algebra. It is a very vast branch of mathematics and is used in all the branches of mathematics like polynomial, linear equations, graphs, etc. and in daily life too.

Now, Gavriel ran 5 miles on Wed

and,  On Thursday, he ran 3/4 as far.

We have to find the how far did he run on Thursday.

On Thursday , The distance will be:

=> 5 × 3/4

=> 15/4

=> 3.75 miles

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Answer:

y=1.6x+3

Step-by-step explanation:

Answer: y=1/2x+3 i don’t know if I’m right, be warned!

Step-by-step explanation:

first find the slope (the m) by doing rise over run or you can find 2 points and find slope by using subtraction. Then get the +b by finding out where the line crosses the y intercept and put that all together leaving the y and x variables the same.

Answer: the population density is approximately 121.75 people/km^2.

Step-by-step explanation: Assuming a scenario whereby the island in question is entirely populated and encompasses a total expanse of 100 square kilometers, it follows that the resulting population density would be as follows:

The formula for population density can be expressed as the ratio of total population to a given geographic area. Mathematically, it is written as Population density = Population / Area.

The metric for measuring population density yields a value of 121.75 individuals per hectare.

The metric expressing the number of individuals residing in a given geographic area is referred to as population density. In this specific instance, the population density is calculated to be 121.75 persons per square kilometer.

Assuming a complete occupancy of the island and a cumulative surface area of 100 square kilometers, it can be posited that...

10% of 2-digit positive integers have a tens digit that is one greater than the ones digit.

To solve this problem, we first need to determine how many 2-digit positive integers there are. Since the smallest 2-digit integer is 10 and the largest is 99, we have a total of 90 integers (99-10+1).

Next, we need to determine how many of these integers have a tens digit that is one greater than the ones digit. To do this, we can create a chart and list out all possible combinations:

10, 21, 32, 43, 54, 65, 76, 87, 98

There are a total of 9 such integers. Therefore, the percentage of 2-digit positive integers that have a tens digit that is one greater than the ones digit is:

9/90 * 100% = 10%

So, 10% of 2-digit positive integers have a tens digit that is one greater than the ones digit.
To answer your question, let's first identify the range of 2-digit positive integers and determine the number of combinations where the tens digit is one greater than the ones digit.

The range of 2-digit positive integers is from 10 to 99. Now, we need to find the pairs of digits where the tens digit is one greater than the ones digit. The possible pairs are:

(1,0), (2,1), (3,2), (4,3), (5,4), (6,5), (7,6), (8,7), and (9,8)

There are 9 pairs that meet the condition. Now we need to find the total number of 2-digit positive integers:

99 (the last 2-digit integer) - 10 (the first 2-digit integer) + 1 = 90

So, there are 90 two-digit positive integers in total.

Now, we can calculate the percentage of the 2-digit positive integers that have a tens digit one greater than the ones digit:

(9 / 90) * 100 = 10%

Therefore, 10% of 2-digit positive integers have a tens digit that is one greater than the ones digit.

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Approximately 4.44% of 2-digit positive integers have a tens digit that is one greater than the ones digit.

Let's consider the possible pairs of tens digit and ones digit that satisfy the condition. There are 4 such pairs: [tex](1, 0)$, $(2, 1)$, $(3, 2)$[/tex], and [tex](4, 3)$.[/tex] For each tens digit, there is exactly one ones digit that satisfies the condition. So, out of the 90 possible two-digit positive integers (ranging from 10 to 99), only 4 of them have a tens digit that is one greater than the ones digit.

Therefore, the percentage of 2-digit positive integers that have a tens digit that is one greater than the ones digit is:

[tex]$\frac{4}{90} \cdot 100% \approx 4.44%$[/tex]

So, approximately 4.44% of 2-digit positive integers have a tens digit that is one greater than the ones digit.

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Answer: 1.2

Step-by-step explanation:

0.2 times 6 is 1.2

Answer:

 D. √3 ; 2

Step-by-step explanation:

 30/60/90 triangles have sides of 1/√3/2 respectfully.

30 pairs with 1, 60 pairs with √3, 90 pairs with 2.

the angles pair with whatever side it is directly diagonal to.

i hope this helped you in some way! let me know if you are confused.

edit: my brainly keeps messing up my text

The factor that does not influence the consumer when deciding to buy a product is Time period. The correct option is C

An identifiable length of time such as a day, week, month, or year is referred to as a time period. Given that it can affect consumer behavior market conditions and the efficacy of various plans and tactic time is a crucial factor in many facets of business and marketing.

Therefore, Note that time is not a factor that influences customer behavior when determining whether to purchase a product in the context of the initial query. The factor that does not influence the consumer when deciding to buy a product is Time period

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Yes, 90 degrees (clockwise) and -270 degrees (counterclockwise) are coterminal angles.

Two angles are coterminal if they share the same terminal side when drawn in standard position. In other words, coterminal angles differ by an integer multiple of 360 degrees.

To see if 90 degrees and -270 degrees are coterminal, we can add 360 degrees to the smaller angle (-270 degrees) and see if we get the other angle:

-270 + 360 = 90

Since we obtain 90 degrees after adding 360 degrees to -270 degrees, these two angles are coterminal. They share the same terminal side in standard position, even though their rotations have different directions (clockwise and counterclockwise).

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The missing factor in the second equation is 1, and the completed equation is: -24y + (-5) = -4(6y + 5/4)

We know that the GCF of -24y and -20 is 4. To find the missing factor in each equation, we can divide both terms by the GCF of 4.

For the first equation, we have:

-24y = 4 * (-6y)

Dividing both sides by 4, we get:

-6y = -24/4

Simplifying, we get:

-6y = -6

Therefore, the missing factor in the first equation is -1, and the completed equation is:

-24y + 20 = -4(6y - 5)

For the second equation, we have:

-20 = 4 * (-5)

Dividing both sides by 4, we get:

-5 = -20/4

Simplifying, we get:

-5 = -5/1

Therefore, the missing factor in the second equation is 1, and the completed equation is:

-24y + (-5) = -4(6y + 5/4)

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Before doing calculations we can predict rectangular prism A has greater surface area to volume ratio than that of rectangular prism B.

The surface area of rectangular prism A is 136 square inches and that of B is 170 square inches. And  the ratio of surface area to volume of rectangular prism A is 1.4167 square inches/ cubic inches (approximately) and that of B is 1.1334 square inches/ cubic inches (approximately).

Rectangular prism A has dimension as,

length = 3 inches , breadth = 4 inches and height = 8 inches

Rectangular prism B has dimension as,

length = 5 inches , breadth = 5 inches and height = 6 inches

The surface area of rectangular prism can be calculated using the formula = 2( length*breadth + length*height + height*breadth)

Therefore, surface area of rectangular prism A = 2{ (3*4) + (3*8) + (4*8)} square inches =136 square inches (that is, 136 [tex]inches^{2}[/tex])

Surface area of rectangular prism B = 2{ (5*5) + (5*6) + (5*6)} square inches =170 square inches (that is, 170 [tex]inches^{2}[/tex])

The volume of rectangular prism can be calculated using the formula = length * breadth * height (in cubic unit)

Therefore, volume of rectangular prism A = (3)(4)(8) cubic inches =96 cubic inches (that is, 96 [tex]inches^{3}[/tex] )

Volume of rectangular prism B = (5)(5)(6) cubic inches =150 cubic inches (that is, 150 [tex]inches^{3}\\[/tex] )

Therefore, ratio of surface area to volume of rectangular prism A = (136/96) square inches/ cubic inches = 1.4167 square inches/ cubic inches (approximately)

Ratio of surface area to volume of rectangular prism B = (170/150) square inches/ cubic inches = 1.1334 square inches/ cubic inches (approximately)

Thus,  ratio of surface area to volume of rectangular prism A is greater than that of rectangular prism B.

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The measurement that is closest to the lateral surface area of the cylinder is 132.15 square centimeters.

To determine the lateral surface area of a cylinder, you can use the formula 2πrh, where "r" represents the radius of the circular base of the cylinder, and "h" represents the height of the cylinder. This formula calculates the total area of the curved part of the cylinder, excluding the top and bottom circular bases.

The height of the cylinder is 5.8 cm and the radius of the circular base is 7.6/2 = 3.8 cm.

So, the lateral surface area of the cylinder is approximately:

2π(3.8)(5.8) ≈ 132.15 cm²

The value that is nearest to the lateral surface area of the cylinder is 132.15 square centimeters.

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The graph shown in the equation y = - 2x - 4 is the graph that corresponds to that equation. The answer is option (B).

A data structure called a graph is used to show the mathematical connection between two or more objects. It is made up of nodes and edges, where nodes stand in for individual things and edges for the connections between them. In computer science, graphs are used to solve a variety of issues, including finding the shortest path between two points and figuring out whether a graph contains cycles. In addition, social networks, transportation networks, and many other kinds of networks can all be represented using graphs.

Option B's graph is the one that corresponds to the equation y = - 2x - 4.

The following is how the equation is written in slope-intercept form:

It is -2 degrees.

-4 is the intercept.

This shows that the slope of the graph is negative and that the trend line crosses the y axis at a negative four-degree angle.

The only graph with a negative slope and a -4 intercept is the one for option B.

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Complete question attached below,

Answer: 10 lego sets

Step-by-step explanation: The equation is 10X, 10 dollars times the amount of legos he is buying,

Answer:

5.25 or 5 1/4

Step-by-step explanation:

-8(0.5x-3)=3

first, just multiply -8 by 0.5x and -8 by -3 and you'll get:

-4x+24=3

next, subtract 24 on both sides, meaning subtract 24 by 24 on the left side and subtract 24 by 3 on the ride side:

-4x=-21

the final thing you have to do is divide -4 on both sides to get the x by itself:

x=5.25 or 5 1/4

The value of the unknown number -12.

Given that: twice a certain number is added to 10 and the result is minus 14.

Let's assume that the number we are trying to find is "x".

We can represent the statement twice this number (2x) is added to 10, and the result is -14 in an algebraic equation.

2x + 10 = -14

We can solve for x by isolating it on one side of the equation. We can start by subtracting 10 from both sides of the equation:

2x + 10 - 10  = -14 - 10

2x = -14 - 10

Simplifying the right side of the equation, we get:

2x = -24

Finally, we can solve for x by dividing both sides of the equation by 2:

2x/2 = -24/2

x = -12

Therefore, the number we are looking for is -12.

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Your friend has only a 10% chance of winning one of the prizes, given that you win one of the prizes. Then the probability that both you and your companion will win a prize in this challenge is 3%. 

Let's begin by calculating the likelihood of you winning a prize, which is given as 30% or 0.3. The likelihood of your companion winning a prize is given as 20% or 0.2. In the event that you win a prize, at that point, the likelihood of your companion winning a prize diminishes to 10% or 0.1. Ready to speak to this conditional likelihood as P.

Presently, ready to utilize the equation for conditional likelihood to discover the likelihood of both you and your companion winning a prize.

P(You and Companion both win a prize)

= P(You win a prize) x P(Friend wins a prize|You win a prize)

= 0.3 x 0.1

= 0.03 or 3%.

thus, the likelihood that both you and your companion will win a prize in this challenge is 3%. 

To learn about probability visit:

https://brainly.com/question/30034780

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