Suppose y varies directly with x. Write a direct variation equation that relates x and y. y=5 and x=2

square side ²= area

s =√81

S = 9

perimeter= 9×4 = 36

3 of them would not be good, 9-6= 3 non-shiny gold rings.

Using two expressions, a mathematical sentence declares two things. The two expressions either employ variables, numbers, or a combination of the two. Symbols or words like equal, greater than, or less than may also be used in a mathematical sentence.

An accurate arrangement of mathematical symbols that expresses a coherent idea constitutes a mathematical sentence, which is equivalent to an English sentence in meaning. Verbs are used in sentences. The verb "=" is used in the mathematical formula "3+4=7 3 + 4 = 7".

The answer is b c 3 9-6=3

3 of them would not be good

9-6= 3 non shiny gold rings

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There are 15 possible sums less than 15 that can be made by taking out one to three balls from the chest.

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Answer:

Parallel Line: [tex]y=-\frac{4}{5}x+\frac{1}{5}[/tex]

Perpendicular Line: [tex]y=\frac{5}{4}x-8[/tex]

Step-by-step explanation:

Perpendicular lines have a slope that is the negative reciprocal of each other. So for example if one line has a slope of: [tex]\frac{a}{b}[/tex], where "a" and "b" are just some constants, then a perpendicular line would have a slope of: [tex]-\frac{b}{a}[/tex], so the slope fraction is just flipped and it's the opposite sign.

Parallel lines never intersect meaning they will have the same slope, since as one goes to the right one and up or down some amount, the only way for the other line to never intersect is to also go up or down by the same amount, which is essentially the slope. The only other condition is that parallel lines must have different y-intercepts, otherwise they have the same slope and y-intercepts meaning they're just the same line and instead of never intersecting they actually intersect at infinitely many points.

The slope-intercept form is especially useful as we can simply look at it and determine the slope and y-intercept, hence the name slope-intercept form. We want to convert into this form to determine the slope of the equation given to us so we can find the perpendicular and parallel lines.

We're given the equation in standard form:

[tex]4x+5y=9[/tex]

We want to convert this into slope-intercept form, which we can do by isolating the y variable. We want to get rid of the 4x term on the left side by subtracting 4x, and we want to do this to both sides to maintain equality:

[tex]4x-4x+5y=9-4x[/tex]

Simplify:
[tex]5y=-4x+9[/tex]

Now we want to get rid of the coefficient of 5 from the left side, and this coefficient is just multiplication so to cancel out multiplication, we divide, specifically by 5 in this case, and on both sides to maintain equality:

[tex]\frac{5y}{5}=\frac{-4x+9}{5}[/tex]

Simplify:
[tex]y=-\frac{4}{5}x+\frac{9}{5}[/tex]

Now we know the slope is: [tex]-\frac{4}{5}[/tex]

For this we simplify find the negative reciprocal so we flip the fraction and "flip" the sign, or in other words if it's negative it becomes positive, if it's positive it becomes negative so: [tex]-\frac{4}{5}\to \frac{5}{4}[/tex]

We can represent the general equation of a perpendicular line in slope-intercept form: [tex]y=\frac{5}{4}x+b[/tex], where "b" is some constant number. We're given that it passes through the point (4, -3) which we can plug in as (x, y) to solve for that value "b"

[tex]-3=\frac{5}{4}(4)+b[/tex]

Simplify on the right side

[tex]-3=5+b[/tex]

Subtract 5 from both sides

[tex]-8=b[/tex]

So now we have the perpendicular line equation: [tex]y=\frac{5}{4}x-8[/tex]

For this we don't have to do anything to the slope, since for parallel lines the slope is the same, so we know the slope is: [tex]-\frac{4}{5}[/tex] and we can plug this into the slope-intercept form to get a general equation for a parallel line: [tex]y=-\frac{4}{5}x+b\text{ where }b\ne\frac{9}{5}[/tex]

Since we're given that it passes through the point (4, -3) we can plug this in as (x, y) to find a definitive equation.

[tex]-3=-\frac{4}{5}(4)+b[/tex]

Simplify on the right side:

[tex]-3=-\frac{16}{5}+b[/tex]

Rewrite the left side to have a denominator of 5:

[tex]-\frac{15}{5}=-\frac{16}{5}+b[/tex]

Add 16/5 to both sides:

[tex]\frac{1}{5}=b[/tex]

So now let's plug this into a general equation we had above to get:
[tex]y=-\frac{4}{5}x+\frac{1}{5}[/tex]

Two events are said to be mutually exclusive in the framework of probability theory if they cannot occur simultaneously or at the same time.

In the context of probability theory, two events are said to be mutually exclusive if they cannot happen simultaneously or at the same time. Alternatively, disjunct occurrences are those that are mutually exclusive. The likelihood that two events will occur simultaneously is 0 if they are deemed to be disconnected events.

Events that cannot exist or occur at the same moment are referred to as mutually exclusive events. There are never two occurrences that can happen at the same moment. The probability of A and B occurring simultaneously is P(A and B)= 0 if A and B are two mathematical events that are mutually exclusive.

a. Being female and preferring basketball are mutually exclusive.

b. Being male and preferring football are mutually exclusive.

c. Being female and preferring hockey are mutually exclusive.

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Reason:

The 4x and -7x are like terms because they involve the same variable x. This allows us to combine the like terms to end up with -3x

4x-7x = -3x

-------

Another example of like terms is 2x and 5x.

Adding them gets us 2x+5x = 7x

We can think of it like saying "2 boxes + 5 boxes = 7 boxes". Replace each word "boxes" with the single letter "x" and we arrive at 2x+5x = 7x.

The amount that Kim Barney spends is $342 for medical expenses.

Given that,

Kim Barney pays a $290.00 yearly premium for a $500.00 deductible insurance plan. 80 percent of the remaining cost is covered by the business. If Kim has medical costs of $2,500.00

To find : The amount that Kim barney spends for the medical expenses.

If the business covers 80% of the remaining balance ($1710), they will be responsible for paying $1368 of it.

10% of 1710 is 171

171x8=1368

The insurance provider covers the $1368.

Kim Barney spends $342.

Consequently, Kim Barney spends the following amount on medical costs $342.

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Answer:

g(f(- 5)) = - 31

Step-by-step explanation:

to calculate g(f(- 5)), evaluate f(- 5) and substitute the value obtained into g(x)

f(- 5) = (- 5)² + (- 5) - 12 = 25 - 5 - 12 = 25 - 17 = 8 , then

g(8) = - 2(8) - 15 = - 16 - 15 = - 31

Answer:

 -31

Step-by-step explanation:

f(x)=x²+x-12

or,f(-5)=(-5)²+(-5)-12

 =25-5-12

 =25-17

 =8

now, g(x)= -2x-15

 = (-2)×8-15

 = -16-15

 =-31

Answer:

The price elasticity of demand measures how responsive the quantity demanded is to a change in price. It can be calculated using the midpoint method, which is (change in quantity demanded / average quantity demanded) / (change in price / average price).

Using the midpoint method to calculate the price elasticity of demand for business travelers and vacationers, you would need more information such as the change in quantity demanded and the average quantity demanded for each group at different prices.

It is not possible to say if the demand is elastic or not for either group based on the information provided.

If the sample size is large (typically n > 30), then it is generally appropriate to use the standard normal distribution (z-distribution) to approximate the sampling distribution of the sample mean.

What are the standard's mean and variance?

Standard deviation is the square root of the number, while variance is equal to the average squared deviations from the mean. Additionally, the variance's square root is the standard deviation.

This is because as the sample size increases, the Central Limit Theorem states that the sample mean will become more normally distributed, regardless of the underlying distribution of the population.

This is due to the fact that the standard error of the sample mean, which is the standard deviation of the sampling distribution of the mean, decreases as the sample size increases. When the sample size is large, the sample mean will be approximately normally distributed with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size.

However, it is important to note that in order to use the z-distribution to approximate the sampling distribution of the sample mean, it is necessary to know the population mean and population standard deviation. If these values are not known, it is appropriate to use the t-distribution, which does not require knowledge of the population parameters.

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The kite is 10 meters high

To calculate how high Ana's kite is, you can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the length of the string is one side of the triangle and the distance Ana needs to move to get under the kite is the other side. The height of the kite is the hypotenuse.

Therefore, the height of the kite can be calculated by:

height =  [tex]\sqrt({string^{2} +distance^{2}) }[/tex]

height =  [tex]\sqrt{(8^{2} + 6^{2} )[/tex]

height = √(64 + 36)

             = √100

height = 10

Hence, the kite is 10 meters high.

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This is an algebraic word problem that is evaluated to give the total pieces of cake Mary distributed to be 35.

In algebraic word problems, we can represent an unknown number using letters and then carry out basic mathematics operations to get the value of the unknown number.

We shall represent the total pieces of cake Mary distributed with the letter x, so that:

x - 4x/5 = 7 {the pieces left that got to the 7}

(5x - 4x)/5 = 7

x/5 = 7

x = 5 × 7 {cross multiplication}

x = 35.

Therefore, the algebraic word problem is solved to give us the total pieces of cake Mary distributed to be 35.

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The expression that represents the length of the rectangle is x + 5

The area of a rectangle is described as follows:

area = lw

where

l = length

w = width

Therefore,

area = x² + 8x + 15

w = x + 3

Therefore,

x² + 8x + 15 = (x + 3)l

divide both sides by x + 3

l =  x² + 8x + 15 / x + 3

l = (x+3)(x+5) / (x + 3)

Finally,

length = x + 5

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The correct option for an adjoining situation in which liquid is flowing through a pipe of variable cross-section representing pressure is  (a) V1>V2 if L1>L2.

This is because, in a pipe of variable cross-section, the velocity of the liquid (V) is directly proportional to the cross-sectional area of the pipe (L). Therefore, if the cross-sectional area of one section of the pipe (L1) is greater than that of another section (L2), then the velocity of the liquid flowing through the first section (V1) will be greater than that of the second section (V2). This is due to the fact that in the area of the pipe where the cross-sectional area is greater, the liquid will have more space to flow and thus will have a higher velocity.

The other options are incorrect because these situations are not possible.

In fluid mechanics, The pressure drop is directly proportional to the fluid velocity, as well as the density of the fluid and the length of the pipe. The pressure drop is inversely proportional to the cross-sectional area of the pipe. So if the cross-sectional area of the pipe is increasing, the pressure is decreasing. And if the cross-sectional area of the pipe is decreasing, the pressure is increasing.

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The complete question is:

Select the correct option for the adjoining situation in which liquid is flowing through a pipe of variable cross-section (P1, P2 represent pressure(a) V1>V2 if L1>L2 (b) V1<V2 for all values of L1 and L2 (c) P1<P2 for all values of L1 and L2 (d) P1>P2 values of L1 and L2

The radioactive substance cesium-137 has a half-life of 30 years.  For the given compound, Initial amount is 647 grams and Amount after 100 years is 64 grams.

A sample's half-life is the amount of time it takes for half of its unstable nuclei to decay, for its activity to halve, or for its count rate to decrease by half. The number of decays that a detector, like the Geiger-Muller tube, records each second is known as the count-rate.

For radioactive compounds, a general exponential function is provided by

Ao(1/2)t/t1/2 = A(t)

Where,

A(t) is the sum that is left after t years.

Ao is the radioactive substance's initial concentration.

The time it takes for a radioactive substance to degrade to A is measured in years.

The radioactive substance's half-life is represented by t1/2.

A(t) = 523(1/2)t/30 in comparison to the general exponential function

A starting point (Ao) of 523 grams

A(t) = 647(1/2)^t/30

t = 100

A(100) equals [647 × (1/2) × 100] /30

=647 × 0.53.333

=647 × 0.0992

=64.182

=64 grams (to the nearest gram)

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The most common level of confidence is 95%, however 90% or 99% have also been used on occasion.

A series of observations that are not reliant on any other samples or data constitute an independent random sample. Random samples selected without regard to sequencing. So, choice C is the proper one.

The essential points that are highlighted below are the followings:

Because the difference between the sample proportions G minus H greater population, according to the question. Due to the interval's all-positive values, it seems expected that district G will have more supporters than district H.

Assurance interval A confidence interval (CI) is a range of estimates for an unknown parameter that is determined by a lower bound and an upper bound. At a certain level of confidence, the interval is calculated.

The most typical level of confidence is 95%, however higher levels, such 90% or 99%, are occasionally employed.

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The area of each of the given shapes is calculated as;

1) 143 sq.in

2) 32 sq.cm

3) 162 sq.yds

4) 150 sq.in

1) The area of a parallelogram is;

Area = base * height

Thus;

Area = 11 * 13

= 143 sq.in

2) Area of a triangle is;

Area = 1/2 * base * height

Area = 1/2 * 8 * 8

Area = 32 sq.cm

3) Area of this will be gotten by the are of the individual triangles;

Area = 2(1/2 * 7 * 8) + 2(1/2 * 12 * 8)

Area = 56 + 96

Area = 162 sq.yds

4) Area = (12 * 12) + (1/2 * 1 * 12)

= 144 + 6

= 150 sq.in

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The height of both trees at the time when they have an equal height will be 48 inches.

Given is that Evelyn planted two trees in her backyard. At the time of planting, Tree A was 32 inches tall and Tree B was 16 inches tall. Each year thereafter, Tree A grew by 4 inches per year and Tree B grew by 8 inches per year.

       Tree {A} : y {A} = 4x + 32

       Tree {B} : y {B} = 8x + 16

Therefore, the height of both trees at the time when they have an equal height will be 48 inches.

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There are 4 quarts in a gallon, and a gallon weighs 8.34 pounds, so a quart weighs 2.085 pounds.

The gallon is a volumetric unit that is used in both imperial and American customary measurements. In use right now are three different variations:

the imperial gallon (imp gal), defined as 4.54609 litres, which is or was used in the United Kingdom, Ireland, Canada, Australia, New Zealand, and some Caribbean countries; the US gallon (US gal), defined as 3.785411784 L,[1] (231 cubic inches), which is used in the US and some Latin American and Caribbean countries; and the US dry gallon ("usdrygal"), defined as 18 US bushel (exactly 4.40488377086 L).

gallon equals 4 quarts

2.1*4 =8.4

gallon of water weigh is 8.4

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Option A) The statement 12 / 3 = 4 can be justified by the equation 4x = 12 as 12 divided by 4 gives 3.

One of the four fundamental arithmetic operations, or how numbers are joined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.

A quotient is the amount that results from dividing two integers. The term "quotient" is used frequently in mathematics and is sometimes known as the integer portion of a division, a fraction, or a ratio.

According to the division property of equality, the quotients of an equation remain equal when both sides are divided by a common real integer that is not equal to 0. The same formula may be expressed in writing as follows: If real numbers a, b, and c are present, with a = b and c 0, then a c = b c.

The statement 12 / 3 = 4 can be justified by the equation 4x = 12 as

12 divided by 4 gives 3.

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Option A) The statement 12 / 3 = 4 can be justified by the equation 4x = 12 as 12 divided by 4 gives 3.

One of the four fundamental arithmetic operations, or how numbers are joined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.

A quotient is the amount that results from dividing two integers. The term "quotient" is used frequently in mathematics and is sometimes known as the integer portion of a division, a fraction, or a ratio.

According to the division property of equality, the quotients of an equation remain equal when both sides are divided by a common real integer that is not equal to 0. The same formula may be expressed in writing as follows: If real numbers a, b, and c are present, with a = b and c 0, then a c = b c.

The statement 12 / 3 = 4 can be justified by the equation 4x = 12 as

12 divided by 4 gives 3.

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Answer:

m = 2/3

Step-by-step explanation:

Take two random points, I personally picked (-2, 0) and (1, 2)

Slope = rise/run = [tex]\frac{2-0}{1-(-2)} = \frac{2}{3}[/tex]

The Minimum for quadratic function f(x) is smaller than g(x)

and it is -5.

What is a quadratic function?

Quadratic function is also a second-degree polynomial function. The graph of a quadratic function is a parabola. The parabola opens upwards if a graph is made for the quadratic formula.

The point at which the function attains maximum or minimum value is the vertex of the quadratic function. When we say second degree, then the variable is raised to the second power like x^2.

A quadratic function is of the form f(x) = ax^2 + bx + c, where a, b, and c are the numbers with a not equal to zero.

Now,

As the we find minimum value by calculating the value for f(x) or g(x)

and from given values f(x) have minimum value of -5 and g(x) have minimum value of 3.

hence,

          Minimum for quadratic function f(x) is smaller than g(x)

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a. -79, -41, -31, 54, 57

b. -56, -55, -54, -43, -39, -37, 18, 22, 43, 44, 52

In both cases, I have put the integers in order from smallest to greatest by comparing each number and placing them in the correct order. Starting with the smallest number and moving to the largest.

the bicycle has a frame size of 22.04 in.

What is unit conversion?

Units of measure are needed in order to measure these values. Sometimes the units of measurement used may not correspond to the standards required for a particular process or application, as well as the measuring choice and convenience. It's crucial to convert these units in a way that makes sense and can be used effectively. Let's use the example of someone who is only familiar with the metric system to better grasp the statement. The person finds it difficult to determine the height of a 25-foot tree. The person will comprehend the height of the tree better if they convert 25 feet to meters. Let's use a unit conversion table to learn about converting between different units.

A bicycle has a 56 cm frame.

As given 1 in = 2.54cm

so 2.54 cm =1 inc

1 cm = 1/2.54

56 cm for the frame = 56*1/2.54 = 22.04 in

Hence the bicycle has a frame size of 22.04 in.

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It is a structured visual representation of simplified thoughts, ideas, structures, relationships, statistical data, anatomy, etc. It can be used in any part of human activity to clarify a topic or provide an example of a topic.

Mind maps, flowcharts, fishbone diagrams, hierarchy/org charts, and SWOT analysis charts are the most common types of diagrams covered in this article. It is a structured visual representation of simplified thoughts, ideas, structures, relationships, statistical data, anatomy, etc. It can be used in any part of human activity to clarify a topic or provide an example of a topic.

A diagram that shows the parts of an object and their interrelationships is called a diagram.

It is a structured visual representation of thoughts, ideas, structures, relationships, statistical data, anatomy, etc. It's a simplification. It can be used in any part of human activity to clarify a topic or provide an example of a topic.

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Here we are interested in finding the slope of the line. From the given graph we can see that that the line passes through points (-6,0) and (0,3) . We know that slope can be calculated by ,

[tex]\longrightarrow slope \ (m)=\dfrac{y_2-y_1}{x_2-x_1} =\tan\theta =\dfrac{rise}{run}[/tex]

[tex]\longrightarrow m =\dfrac{y_2-y_1}{x_2-x_1}\\[/tex]

[tex]\longrightarrow m =\dfrac{0-3}{-6-0}\\[/tex]

[tex]\longrightarrow m =\dfrac{-3}{-6}\\ [/tex]

[tex]\longrightarrow m =\dfrac{1}{2}=0.5[/tex]

And we are done!

A vector is a quantity that has both magnitude, as well as direction. A vector that has a magnitude of 1 is a unit vector. It is also known as Direction Vector.

Unit Vector is represented by the symbol ‘^’, which is called a cap or hat, such as: â. It is given by   â  = a / |a|

Where |a| is for norm or magnitude of vector a.

It can be calculated using a Unit vector formula.

Unit vectors are usually determined to form the base of a vector space. Every vector in the space can be expressed as a linear combination of unit vectors. The dot products of two unit vectors is a scalar quantity whereas the cross product of two arbitrary unit vectors results in third vector orthogonal to both of them. As explained above vectors have both magnitude (Value) and a direction. They are shown with an arrow.

And, â denotes a unit vector. If we want to change any vector in unit vector, divide it by the vector’s magnitude. Usually, xyz coordinates are used to write any vector.

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Answer: The missing value is 81.

Step-by-step explanation: In a square, the formula is [tex]y^2 + 2y + y^2[/tex],

where the first y^2 is staying there. 18/2 is 9, and 9 squared is 81.

The weights (in pounds) of a sample of 13 male eleventh graders ,so the median weight of these students is 159.

Calculate the mean by summing the centre values and dividing them by the number. From there, you may obtain the median.

To arrange the data points in ascending order for a small data set, count the number of data points (n). To get the rank of the data point whose value is the median when the number of data points is unequal, multiply the total by 1 and divide the results by 2.

148, 140, 159, 141, 151, 156, 173, 167, 160, 159, 146, 174, 170

140 , 141 , 146 , 148, 151 ,156,  159 ,159, 160, 167 , 170, 173, 174.

The median weight of these students is 159.

The weights (in pounds) of a sample of 13 male eleventh graders ,so the median weight of these students is 159.

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The length of segment CM is equal to the square root of 10. This is determined by dividing the area of the square ABCD, which has sides of length 3, into three equal parts, resulting in a segment of length √10.

The area of square ABCD can be calculated by squaring the length of one side, which is 3, to get 9. To divide this area into three equal parts, each part must have an area of 3. To find the length of segment CM, the square root of this area, 3, must be taken, resulting in a length of √10.

To find the length of segment CM in square ABCD, the area of the square must first be determined. This can be done by squaring the length of one side, which is 3, resulting in an area of 9. To divide this area into three equal parts, each part must have an area of 3. This means the length of segment CM must be the square root of 3, which is equal to √10. Therefore, the length of segment CM is equal to √10. This is the result of dividing the area of the square ABCD into three equal parts.  This process can be used to determine the length of any segment dividing an area into equal parts

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