The weights and heights of six mathematics students are given in the following table: Weight (in pounds)
165 123 212 175 165 147
Height (in centimeters)
172 157 183 178 163 167
State whether weight is a function of height for the six students and explain.
a. Yes, height is a function of weight because two students weigh 165 pounds but have different heights.
b. No, height is not a function of weight because two students weigh 165 pounds but have different heights.
c. Yes, weight is a function of height because for each value of height there is one corresponding value of weight.
d. No, weight is not a function of height because there is not enough data to determine a function.

The solution is the point where the two lines intersect i.e. (-1,-7). The graph for the given system of equations is attached below wherein the blue line represents y=2x-5 and the green line represents y=-x-8.

What is system of equation?

A set or group of equations that are solved collectively is referred to as a system of equations. Both algebraic and visual solutions are possible for these equations. The intersection of two lines represents the system of equations' solution.

For solving the equations graphically, we need to find points for plotting

So, for y = 2x-5,

The y-intercept is -5, so we need to place a point on the graph at (0,-5).  For the another point, put x=1, we get y= -3. So we need to place another point at (1,-3).

Similarly for y = -x-8,

The y-intercept is -8, so we need to place a point on the graph at (0,-8).  For the another point, put x=1, we get y= -9. So we need to place another point at (1,-9).

The solution is the point where the two lines intersect.

When the two lines intersect,

2x-5=-x-8

3x=-3

x=-1

So, y=-7

Hence, the two lines intersect at (-1,-7).

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As per the given volume of cuboid, the length is 4 cm and the surface area of the cuboid is 5.76cm

The general formula to calculate the surface area of cuboid is written as,

SA = 2[lb + bh + hl]

where l refers the length, w refers width and h refers height.

Here we have given that a cube of side length 6 cm and has the same volume as that of a cuboid of height 3 cm and breadth 4 cm.

Now, we have to find the length and the surface area of the cuboid.​

By the given value the Surface Area of Cube is calculated as.

=> 6s sq. =  6 x 4sq.

Then the value is 96 cm square

Then the Surface Area of Cuboid is calculated as,

=> 2(24+10h)=96

When we simplify the equation as

=> 24 + 10h = 48

=> 10h=24

Therefore, the value of h=2.4

Then the volume of Cuboid=6*4*2.4=5.76 cm.

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on solving 6th term in the binomial expansion of (4x + 1)^8 in simplest form is 3584.

A binomial is an algebraic expression with two terms. For example, a + b, x - y, etc are binomials. We have a set of algebraic identities to find the expansion when a binomial is raised to exponents 2 and 3.

A polynomial with just terms is a binomial. An illustration of a binomial is x + 2, where x and 2 are two distinct words. Additionally, in this case, x has a coefficient of 1, an exponent of 1, and a constant of 2. As a result, a binomial is a two-term algebraic statement that comprises a constant, exponents, a variable, and a coefficient.

we know ,

So the 6th term in the equation

is ,8c5 -4x^8-5 = 8c34x^3 is , = 3584

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Lily is making smoothie. Each smoothie 1/2 ​ cup of yogurt. The fraction is   [tex]1\frac{1}{2}[/tex] cup of yogurt does he need to make 3 smoothie.

Fraction:

Fractions represent parts of a whole. This whole thing can be a region or a collection. The word break comes from the Latin word "fraction" which means "to divide". The earliest civilization to study fractions, the Egyptians, used fractions to solve mathematical problems such as the division of food, supplies, and the lack of bullion currency.

In ancient Rome, fractions were written to represent parts of a whole using only words. In India, fractions were originally written with the numbers (numerator and denominator) on top of each other, but without lines. Arabs were the only ones who added the dash used to separate the numerator and the denomination.

According to the question:

Lily on the given conditions, formulate: 1/2 × 3

Write as a single fraction: [tex]\frac{1 * 3}{2}[/tex]

Calculate the product or quotient: 3/2

Convert to mixed fraction: [tex]1\frac{1}{2}[/tex]

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Answer:

x = -60

Step-by-step explanation:

Given the equation:

[tex] \displaystyle{0.1x - 5 = - 11}[/tex]

Add both sides by 5

[tex] \displaystyle{0.1x - 5 + 5= - 11 + 5} \\ \\ \displaystyle{0.1x = - 6}[/tex]

Multiply both sides by 10 to get rid of the decimal

[tex] \displaystyle{0.1x \times 10 = - 6 \times 10} \\ \\ \displaystyle{x= - 60}[/tex]

Therefore, x = -60

Answer:

Step-by-step explanation:

0.1x − 5 = −11

0.1x = -11 + 5

0.1x = -6          multiply by 10 both sides

x = -60

--------------------------

0.1 x (- 60) - 5 = -11

-6 - 5 = -11

-11 = -11

Answer:

a^m + a^n = a^m+n

Step-by-step explanation:

This is true for any value of a and n except 0.

Answer:

2 over 1

Step-by-step explanation:

I'm not really sure what you mean in the question but I've substituted the values in

Answer: 20%

Step-by-step explanation: You can evenly divide 20 by 5, which is four, which makes four 20% of 20. You can subtract 4 from 20 to get 16 to prove this, and keep going all the way back to 0 5 times.

A rectangle is a closed 2-D shape with four sides, four corners, and four right angles (90°).

Four sides, four corners, and four 90° right angles make up the closed, 2-D shape of a rectangle. A rectangle has parallel, equal sides on either side.

A rectangle has four vertices since it has four sides, four angles, and four corners. The intersection of two sides forms the "vertices" of a polygon. They are corners, to put it another way.

Rectangles' basic characteristics include:

Four-sided shapes include rectangles.

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Length of edge of cube = 6.24 unit

A cube is a three-dimensional object that has 6 congruent square faces. Dimensions of all the 6 square faces of the cube are the same. A cube is sometimes also referred to as a regular hexahedron or as a square prism.

Given,

volume of cube = 27×9 cubic units

Length of edge of cube = ∛(27×9)

                                        = ∛243

                                        = 6.24 unit

Hence, 6.24 unit is length of edge of cube.

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Answer:

Point C

Step-by-step explanation:

Lines m and t are on the same plane

We can see that they intersect at Point C

The area of the said triangle is 10 cm²

Here we have been given the right-angled triangle with base 5 cm and altitude 4 cm.

To find the area of a triangle we can either use Heron's formula or the other formula where area of a triangle = 1/2 X base X height

Since we have been given the base and the height we need to use the latter.

Hence area of the said triangle will be

1/2 X 5 X 4 cm²

= 10 cm²

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Answer:

------------------------------

Solve in below steps, using log and exponent rules:

7 is mean Seven is the average of the times shown on the dot plot as the amount of time it takes to get through the obstacle course.

The mean of a dataset, often termed as the arithmetic mean, is the amount of all values divided by the overall number of values (as opposed to the geometric mean). This is the most often used indicator of central tendency and is frequently referred to as the "mean." This is obtained by dividing the number of values in the dataset by the sum of all the values. Calculations can be performed using either raw data or data that has been integrated into frequency tables. A number's average is referred to as its average. Simple math can be used to determine: After simply adding all the digits, divide by the number of digits. the sum divided by the number.

given

three obstacles are overcome by three students.

Total Observations / Sum of Observations = Mean

= 21 / 3

= 7

7 is mean Seven is the average of the times shown on the dot plot as the amount of time it takes to get through the obstacle course.

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The complete question is :- LeveT P × Diane is a camp counselor. She designs a new obstacle course, and tests the course with  friends. The dot plot shows the time it takes them to complete the obstacle course. a What is the mean of the times? Obstacle Course Test mean - mean 7 minutes.

The replacement or substitution approach has the advantage of providing the precise values for the variables (x and y), which correspond to the site of intersection.

The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies.

This makes it easier to solve by combining two linear equations into one equation with a single variable. Learn about the graphical approach and the algebraic method before beginning to solve the linear equations using the substitution method.

By changing the value of another variable in an equation, the variable can be eliminated. Thus, the elimination by substitution method is the name given to this technique.

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Acute angles are the angles that measure less than 90 degrees. Right angles measure 90 degrees and Obtuse angles measure more than 90 degrees.

By adding the squares of the triangle's two smaller sides and comparing the result to the square of the largest side, you can determine whether the triangle is acute, right, or obtuse. The triangle is acute because this sum is higher.

A triangle is said to be acute if the squares of its two shorter sides added together exceed those of its longest side. A triangle is considered obtuse if the sum of the squares of its two shorter sides is less than the square of its longest side.

An overview was given as your information is incomplete.

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Only (i), (ii), (iv) and (v) are Pythagorean triplets. A triplet (a, b, c) is called Pythagorean if the sum of the squares of the two smallest numbers is equal to the square of the biggest number.

Pythagoras, Gauss, Edison, Hawking. The following are the most noted discoveries of each.

Pythagoras, 500 B.C. School Of Mathematics and Pythagorean theorem.Edison, Year 1879 - Invention of incandescent light bulb.Gauss, Year 1801 - Therom of Alegbraic Solution. Stephen Hawking Year1980 - Studies in cosmology particularly contributing to the context of black holes.

you can check by taking largest side square

and adding square of rest two sides

17^2= 15^2+ 8^2

82^2= 18^2+80^2

26^2= 24^2+10^2

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Answer:

24

Step-by-step explanation:

120 x 0.20 = 24

The values of x and y are -1 and 4 respectively.

The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.

Given are two equations, -2x+3y=14 and x+2y=7

Solving equations by using substitution method,

-2x+3y=14..........(i)

x+2y=7

x = 7-2y.......(ii)

Using eq(ii) in eq(i)

-2(7-2y) + 3y = 14

-14+4y+3y = 14

7y = 28

y = 4

Put y = 4 in eq(ii)

x = 7-2(4)

x = -1

Hence, the values of x and y are -1 and 4 respectively.

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Three fundamental ideas provide the foundation for all basic geometry notions. The three are the plane, line, and point.

The father of geometry, Euclid was a brilliant mathematician. Learn more about Euclid and the history of some of the math ideas we use today to see how important they have become.

The terms "ge" and "metria," which both imply "measuring," are the origins of geometry. For more than 2000 years, the Greeks' method of approaching geometry has served as the foundation for geometry.

The study of various mathematical or actual-world forms, figures, and sizes is known as Geometry. We learn about various angles, transformations, and similarities between the forms in geometry. The point, line, and plane are the main building blocks of geometry.

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Three basic ideas form the basis of all basic geometry concepts. The three are planes, lines, and points.

Euclid, the father of geometry, was a brilliant mathematician. Learn about the history of Euclid and some of the mathematical ideas we use today, and see how important they have become. The terms ``ge'' and ``metria'', meaning ``measure,'' are of geometric origin. For over 2000 years, the Greek approach to geometry has served as the foundation of geometry.

Geometry is the study of various mathematical or actual forms, figures, and sizes. In geometry, you will discover the concepts of points, lines, planes, angles, parallel lines, triangles, similarity, trigonometry, quadrilaterals, transformations, circles, and area.

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The graph of the inequality: 3x + y > 7

Can be seen in the image below.

We want to see which graph represents the inequality:

3x + y > 7

We can rewrite the inequality in slope-intercept form as:

y > -3x + 7

So we just need to graph the line:

y = -3x + 7

With a dashed line, and then shade all the region above the line.

To graph the line, you need to find two points that lie on the line.

if we evaluate the line in x = 0 we wll get:

y = -3*0 + 7

y = 7

if x = 1

y = -3*1 + 7

y = -4

Then we have the points (0, -7) and (1, -4), now we can graph these two points and connect them with a dashed line, then shade the region above.

The graph of the inequality is the one below.

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The event with the largest probability is rolling a number higher than 2, so the correct option is B.

First, the fact that a 2 was rolled before does not affect the next rolls of the dice, so that information is extra.

Now we just need to see which option has the largest probability.

A) There are only one number lower than 2, then the probability of this event is p = 1/6

B) There are 3 numbers higher than 2, then the probability is p = 3/6 = 1/2

C) The probability of get another 2 is 1/6

We can see that the event with the largest probability is B, so that one is the most likely to occur.

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In order to respond to the query ,of bar graph we must first comprehend what a compound Tim received 4 emails on Thursday and 8 SMS on Monday, making up 0.52 of all communications.

A blended bar chart is used to display the rates of two connected sets of data. In this investigation, two forms of data—emails and emails used, but they are both grouped together under the term "messages" and are shown as vertical bars in the graph.

Here,

14+16+14+15+14=73 messages in total.

A total of 38 emails were sent: 6 + 10 + 10 + 4 + 8

Email to message ratio is 38/73, or 0.52.

Emails therefore made up 0.52 of the messages.

Tim received 4 emails on Thursday, 8 texts on Monday, and 0.52 of the messages were emails, as shown by an examination of the composite bar chart that we used to come up with the answers to the three questions.

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Chapters on progressions, quadratic equations, linear inequalities, the binomial theorem, permutations and combinations .

A quadratic polynomial in a single variable is x ax2+bx+c=0, which is a quadratic equation. a 0. The fact that this polynomial is of second order guarantees that it has at least one solution according to the Fundamental Theorem of Algebra. Solutions could be straightforward or difficult. A quadratic equation is one that has four variables. This suggests that at least one word in it has to be squared. One of the common formulas for solving quadratic equations is "ax2 + bx + c = 0." where the undefined variable "X" is represented by the numerical coefficients or constants a, b, and c.

given

Chapters on progressions, quadratic equations, linear inequalities, the binomial theorem, permutations and combinations, and mathematical induction can be found in class eleven algebra textbooks.

Students might improve their exam preparation by working through sample papers.

Attempt to answer the test questions from the prior year. Learning about the question format and scoring system will be beneficial.

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The particle size of a solution is 0 point 1 nm – 1 nm, and it is a homogeneous mixture of two or more substances called solution.

The term "solute" refers to the material that is dissolving in the solvent to create a solution. It is less prevalent in the solution than the solvent.

A solvent is a substance found in solutions that helps a solute dissolve. It is more prevalent than the solute in the solution.

A solution has the following characteristics:

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The measure of the interior non-adjacent angle as required in the task content is; 95°.

Recall; It follows from the triangle exterior angle theorem that the measure of exterior angle of a triangle is equal to the sum of the two opposite interiors angles.

On this note, if the sculpture’s opposite interior angle is 32 less than the interior non-adjacent angle, the sum of the two angle measures is therefore;

x + x - 32.

where, x is the measure of the interior non-adjacent angle.

Hence, x + x - 32 = 158

2x = 158 + 32

2x = 190

x = 95°.

Ultimately, the measure of the interior non-adjacent angle is; 95°.

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The additive inverse of 8 /- 15 is -8 /+ 15. This means that the two numbers add up to 0 when combined.

The additive inverse of 8 /- 15 is -8 /+ 15. This means that the two numbers add up to 0 when combined. To find the additive inverse of 8 /- 15, simply change the sign of the number from negative to positive or from positive to negative. In this case, the sign of 15 needs to be changed from negative to positive, giving us 8 /+ 15. This means that when 8 /- 15 is added to 8 /+ 15, the result is 0. The concept of additive inverse is important in mathematics as it helps us to solve equations and understand the properties of numbers. Additive inverse is also referred to as the opposite of a number, as it is the number that needs to be added to the original number to get 0. Therefore, the additive inverse of 8 /- 15 is -8 /+ 15.

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Answer:

Davids Score

Step-by-step explanation: