What is an example of exponential form?

The probability that three segments were chosen could form a triangle [tex]\frac{7}{20}[/tex] .

Using the probability concept, it is found that there is a  probability that the three segments selected could form a triangle.

The number of desired outcomes divided by the number of total outcomes is called probability.

In this problem, the order in which the sides of the segments are selected is not important, hence, the combination formula is used to find the number of total outcomes.

Combination formula:

[tex]C_{n.x}[/tex] is the number of different combinations of x objects from the set of n elements, given by:

            [tex]C_{n,x} = \frac{n !}{x ! ( n - x) !}[/tex]

Total outcomes:

Three segments from a set of six lengths, hence:

[tex]C_{6,3} = \frac{6 !}{3 ! 3 !} = 20[/tex]

Desired outcomes:

Then :

p = [tex]\frac{D}{T} = \frac{7}{20}[/tex]

 [tex]\frac{7}{20}[/tex] -the probability that the three segments selected could form a triangle.

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Explanation:

The segment (4x-9) units long is the midsegment of the triangle. This is because each endpoint is a midpoint of the slanted sides.

One property of midsegments is that it is half as long as the side parallel to it.

The (4x-9) side is half as long compared to the 6x side.

Rephrased another way: The 6x is twice as long compared to (4x-9)

We'll use this to set up the equation to solve for x.

6x = 2*(4x-9)

6x = 8x-18

6x-8x = -18

-2x = -18

x = -18/(-2)

x = 9 is the final answer

From the give expressions, the rational one are numbers 1 and 3 and the irrational ones are numbers 2 and 4 respectively

Rational numbers are numbers that can be expressed as a ratio or whole number while the irrational numbers cannot be expressed as ratios or whole numbers

The given expressions are

1)  2√9 + 8

= 2*3+8

6+8

=14     This a Rational number because it shows a whole number

2)   2√7 +8

This is irrational hence it cannot be expressed to lowest term

3)    3√18√2

= 3*√18*2

=3*√36

=3*6

=1 8

This is rational because it can be expressed to its lowers term and forms a whole number

4) 2√15√3

= 2*√45

= 2*√9√3

=2*3*√3

=6√3

This is irrational because it does not form a whole number

In conclusion, the rational numbers show whole numbers while the irrational numbers show none whole numbers

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Graph A represents the relation as a function. Then the correct option is A.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

If the number of values of the dependent variables is one for a single value of the independent. Then the relation is known as function.

If the number of values of the dependent variables is more than one for a single value of the independent. Then the relation is not function.

In graph A, for each value of 'x' the number of the value 'y' is one. Then graph A represents the relation as a function.

Then the correct option is A.

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The measure of each of the angle of a rectangle is 90 degrees.

A rectangle is a four-sided shape with four right angles. Each angle measures 90 degrees, meaning that the sum of the angles of a rectangle is 360 degrees. This is true regardless of the size or proportions of the rectangle.

Each angle of a rectangle can also be referred to as a right angle.

A rectangle is a four-sided shape with four right angles, making each of its angles 90 degrees. This is the measure of each of the angles of a rectangle - 90 degrees.

The four angles fit together perfectly to form a rectangle, making it a very useful shape for construction and design.

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An equation that is parallel to the line 32x-y=15 is y = 32x - 47.

y' = 4x³

m = slope of tangent line =slope of the given line = 32

y' = 32 at the tangent point

4x³ = 32

x = 2

y = 2⁴+ 1 = 17

The tangent point is (2,17)

Tangent line:

y = 32x + b

17 = 32(2) + b

b = -47

y = 32x - 47

The straight line that "just touches" the curve at a particular location is known as the tangent line (or simply tangent) to a plane curve in geometry. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.

A straight line has a slope of f'(c), where f' is the derivative of f, and is said to be tangent to a curve at a point x = c if it passes through the point (c, f(c)) on the curve. Space curves and curves in n-dimensional Euclidean space have a similar definition.

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Answer:

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John types at a rate of 16 words per minute.

With the stable rate, in 4 minutes he types:

To solve this we must be knowing each and every concept related to arithmetic sequence and its calculations. Therefore, arithmetic sequence can be defined as below.

An arithmetic sequence is a collection of integers that follow a specific pattern. It's an arithmetic sequence if you pick any number inside the sequence and subtract it from the preceding one, and the outcome remains the same or constant.

an = a₁ + (n-1) d

The common difference, indicated by the letter d, is the constant difference between all pairs of subsequent or succeeding integers in a series. To transition from one phrase to another, we employ the common difference.

Therefore, arithmetic sequence can be defined as above.

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Answer:

1) The mistake is not following order of operations, the multiplication between the 3 and (2a - 4) in the brackets is a priority. You should of added the 8 after you resolve the bracket.

2) We can remember the order using PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

The side length of one side of the square is 8n¹⁸

From the question, we have the following parameters that can be used in our computation:

Area = 64 n Superscript 36square units

Express the area expression properly

So, we have the following representation

Area = 64n³⁶ square units

Take the square roots of both sides to calculate the side length

This gives

Side length = 8n¹⁸

Hence, the side length is 8n¹⁸

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Answer:

Slope= 3/4

y intercept= (0,-3)

Step-by-step explanation:

hope it helps :)

if the diameter is 8 meters, then its radius is half that, or 4 meters.

[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=4\\ h=12 \end{cases}\implies V=\pi (4)^2(12)\implies V=192\pi[/tex]

The volume of a right circular cylinder with a diameter of 8 meters and a height of 12 meters is,

⇒ V = 96π m³

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Diameter of a right circular cylinder = 8 meters

And, Height of a right circular cylinder = 12 meters

Now, We know that;

The volume of a right circular cylinder is,

⇒ V = πr²h

Here, Diameter of a right circular cylinder = 8 meters

Radius = 8 / 2 = 4 m

Thus, We get;

⇒ V = πr²h

⇒ V = π × 4² × 12

⇒ V = 96π m³

Thus, The volume of a right circular cylinder with a diameter of 8 meters and a height of 12 meters is,

⇒ V = 96π m³

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Based on the information provided, a) if X has a binomial distribution, n = 5 and p = 0.256. b) X can take values in the range of 0 to 5. c) The values of P(x) for x = 0, 1, 2, 3, 4 , 5 are 0.228, 0.392, 0.269, 0.093, 0.016, and  0.011 respectively. d) mean = 1.28 and standard deviation = 0.995.

a) If X has a binomial distribution n represents the number of tickets bought which is 5 and p represents the probability of winning a prize after taking a single ticket which is 0.256.

b) X can take values in the range of 0 to 5, which indicates the possible number of won tickets. Hence, x = 0, 1, 2, 3, 4, 5. c)

Using the binomial distribution formula, P (x) = nCx*p^x*(1 – p)^(n-x). Hence,

P(0) = 5C0*(0.256)^0*(1 – 0.256)^)(5-0) = 0.228

P(1) = 5C1*(0.256)^1*(1 – 0.256)^)(5-1) = 0.392

P(2) = 5C2*(0.256)^2*(1 – 0.256)^)(5-2) = 0.269

P(3) = 5C3*(0.256)^3*(1 – 0.256)^)(5-3) = 0.093

P(4) = 5C4*(0.256)^4*(1 – 0.256)^)(5-4) = 0.016

P(5) = 5C5*(0.256)^5*(1 – 0.256)^)(5-5) = 0.011

d) The mean and standard deviation of the distribution is given by:

mean = n*p = 5*0.256 = 1.28

standard deviation = √np(1 – p) = √5(0.256)(1 – 0.256) = 0.995

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Answer:

(-1,-1)

Step-by-step explanation:

First thing to consider: the expression is y<-2+3 not y<-2x+3

When plotting this on a graph a possible answer is (-1,-1)

Answer:

x=6−3y

Step-by-step explanation:

5(x+3y)=30

x+3y=6

x=6−3y

Have great day♡

Answer: x = 6 - 3y

Step-by-step explanation: 5x+15y=30

Subtract 15y from both sides.

5x=30−15y

Divide both sides by 5.

5x/5 = 30-15y/5

Dividing by 5 undoes the multiplication by 5.

x = 30-15y/5

Divide 30−15y by 5.

x=6−3y

Answer: 8 Miles is the answer

Step-by-step explanation: this is because if you pay a $5 tip that leaves you at $20 then you divide 20 by 2.50 which equals 8

8 is the answer

Answer:

you have given wrong answer bro\sis correct it

If you purchase a reciprocal membership from the two museums, you can visit both at no charge.

Mathematical expressions with variables, constants, coefficients, and algebraic operations are called algebraic expressions.

As a similar matter, the adjective reciprocal can also be used to denote something that is opposite or inversely connected (which is just about the opposite of what reciprocal is generally used to mean). A reciprocal membership is available from the two museums, allowing you access to both for free.

This fraction, turned upside down, is the reciprocal of a number. The reciprocal, then, has the top number, or numerator, on top and the bottom number, or denominator, of the original fraction on the bottom. Due to the fact that 1/6 is the inverse of 6/1 and 6 = 6/1, the reciprocal of 6 is 1/6.

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You can dilate a line centered at the origin by using its coordinates of origin.

Dilating a line centered at the origin is a useful tool in geometry. To do this, you need to first identify the coordinates of the origin, or (0,0). Then, you need to identify the equation of the line.

Once you have these two points, you can calculate the coordinates of the line when you multiply the equation by a certain number, which is known as the scale factor.

This scale factor will determine the amount of dilation that needs to be applied to the line. Finally, you can plot the new points on a graph and draw the line to see the new shape.

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The increase in their bill when they switch from their current phone plan to the unlimited plan will be $13.99.

The cost of the current phone plan is calculated as follows:

The cost of the current phone plan = $55 + $19 + $9.50

The cost of the current phone plan = $83.50

The cost of the unlimited plan will be:

The cost of the new unlimited plan = $85 + $12.49

The cost of the new unlimited plan = $97.49

The increase in their bill will be:

The increase in their bill = $97.49 - $83.50

The increase in their bill = $13.99

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When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.

According to me , independent is the word which is associated with multiplication when computing probabilities . Because when the events are independent then we multiply the probabilities .

According to the multiplication rule of probability, the probability of occurrence of both the events A and B is equal to the product of the probability of B occurring and the conditional probability that event A occurring given that event B occurs.

The probability of the union of two events is equal to the sum of individual probabilities. The union of two set contains all the elements of previous sets. The union is denoted by ∪. The equation for the students earnings will be expressed as P(A∪B). The occurrence of event A changes the probability of B then the events are dependent. If the probability of two events happening together is zero then the events are mutually exclusive.

Therefore,

When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.

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The unit rate that corresponds to the proportional relationship shown in the graph is: 4/3 cm/s.

A proportional relationship is a mathematical relationship in which two variables are directly proportional to each other, meaning that the ratio of their values is always constant. The unit rate of a proportional relationship is the constant of proportionality, also known as the coefficient of proportionality. It is a number that relates the two variables in the relationship and it is also the slope of the line in the graph representation of the relationship.

For example, in a proportional relationship of y = kx, where y and x are the two variables and k is the constant of proportionality, the unit rate is k. It tells us how much y changes for each unit change in x. For example, if k=2, then for each increase of 1 in x, y will increase by 2.

Using a point on the graph, (12, 16):

Unit rate = y/x = 16/12 = 4/3 cm/s.

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The radius of the sphere, given the volume of the sphere and the formula for the volume, is  15. 64 mm

We are told that to find the volume of a sphere, we can use the formula :

Volume of sphere = 4 / 3 x π x r³

We are then given that volume in this instance to be 5, 100π mm³ which means that we can equate the formula to this volume to be able to find the radius.

We can therefore find the radius to be:

5, 100 π = 4 / 3 x π x r³

r ³ = 5, 100 π / ( 4 / 3 x π )

r ³ = 5, 100 / ( 4 / 3 )

r ³ = 3, 825

r = ∛ 3, 825

r = 15. 64 mm

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Answer:

200%

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8 cm}\underline{Percent change formula}\\\\$\rm Percent\:change=\dfrac{final\:value-initial\:value}{initial\:value} \times 100$\\ \end{minipage}}[/tex]

Given values:

Substitute the values into the percent change formula to find the percent increase in car sales:

[tex]\begin{aligned} \implies \textsf{percent change}&=\dfrac{450000-150000}{150000}\times 100\\\\&=\dfrac{300000}{150000}\times 100\\\\ &=2\times 100\\\\&=200\%\end{aligned}[/tex]

Therefore, the percent increase in car sales was 200%.

The equation representing the data is N=12×3ⁿ Where n is the number of months.

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here, A population of mice has a growth factor of 3. after one month, there are 36 mines. after 2 months, there are 108 mice.

let n be the number of months and N be the number of mice after n months

thus , N=36

⇒ 36=12×3¹

N=108

⇒108=12×3²

Therefore for any n the Number of mice is N=12×3ⁿ

Hence, The equation representing the data is N=12×3ⁿ Where n is the number of months.

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Answer: y= -2x+8

Step-by-step explanation: