3/9 a rational number

The given expression can be simplified by using the rule of negative exponent.

In the expression, there are two terms with negative exponent. The second base term y has a negative exponent -2/3. The second negative exponent -6 is applied to both base terms.

The rule states that the negative exponent can be solved by reciprocating the base term i.e. a^-x=1/a^x.

Solving the negative exponent for y,

Hence, x^1/2y^-2/3=x^1/2/y^2/3.

Solving the second negative exponent -6 that applies to both terms, applying the same rule i.e. a^-x=1/a^x.

(x^1/2/y^2/3)^-6=(y^2/3/x^1/2)^6

Multiplying the powers and simplifying,

y^2/3*6/x^1/2*6=y^4/x^3

The simplest form of the expression (x^¹/₂y^⁻²/₃)^-6 is y^4/x^3.

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Answer:

Toyota

Step-by-step explanation:

im not sure im a 5th grder that just guessed

Answer:

a) 33/50         b) 17/50

Step-by-step explanation:

total cars = 250

toyotas = 165

The probablity of the first car to leave being a toyota is

165/250

Simplify it to 33/50

The probability of the first car to leave not being a toyota is

(250 - 165)/250

= 85/250

= 17/50

=======================================================

Explanation:

Define the following three events:

Notation like P(A) = 12/20 means the probability of event A (aka picking the plain biscuit) is 12/20 since there are 12 plain biscuits out of 20 total. I'll leave the fraction un-reduced so we can see where the 12 and 20 come from. Going from 12/20 to 3/5 has us lose vital information about the original values.

Notation like AB means a plain biscuit was selected first and then a chocolate biscuit is selected second in that exact order. I'm assuming the first selection is not replaced. This makes the probability of the second selection dependent on the first.

So,

P(AB) = P(A)*P(B given A) = (12/20)*(5/19) = 3/19

P(AC) = P(A)*P(C given A) = (12/20)*(3/19) = 9/95

P(BC) = P(B)*P(C given B) = (5/20)*(3/19) = 3/76

The last step is to add those results to get the probability of event AB, event BC or event AC of occurring. Addition is possible since the events are mutually exclusive.

P(AB)+P(AC)+P(BC) = 3/19 + 9/95 + 3/76 = 111/380

I've skipped a few steps, so let me know if you need to see the finer details. Also feel free to ask about any questions in general if they come up.

The percentage increase from the boat price of 2600 to 4100 is 57.69%

The given parametes are

Cost price = 2600

Selling price = 4100

The percentage increase in the price of the boat is calculated as

Percentage increase = (Selling price - Cost price)/Cost price * 100%

Substitute the known values in the above equation

So, we have

Percentage increase = (4100 - 2600)/2600 * 100%

Evaluate the difference in the above equation

So, we have

Percentage increase = 1500/2600 * 100%

Evaluate the quotient in the above equation

So, we have

Percentage increase = 0.5769 * 100%

Evaluate the product in the above equation

So, we have

Percentage increase = 57.69%

Hence, the percentage increase from the boat price of 2600 to 4100 is 57.69%

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Answer:

60% (Rounded to the first decimal)

Step-by-step explanation:

How many times does 2600 go in 4100:

4100/2600 = 1.6

The height of the pine tree shaped like a cone is 58.03 feet.

The curved surface of a cone is when we only consider the surface area of the sides.

We know the general formula for the volume of a cone is (1/3)πr²h.

Given, the volume of a pine tree shaped like a cone is 3887.2 cubic feet also given that it has a radius of 8 feet,

∴ We can obtain the height of the pine tree by equating given volume with the formula and substituting the value of radius.

So, (1/3)π(8)²h = 3887.2.

(1/3).(3.14).(64)h = 3887.2.

(200.96/3)h = 3887.2.

h = (3887.2×3)/200.96.

h = 11661.6/200.96.

h = 58.03 feet.

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A linear equation that relates the cost of c in dollars of renting a truck to the number x of miles driven is c = 0.09x + 39, and the cost of renting the truck if the truck is driven 187 miles and 319 miles is equal to $55.83 and $67.71 respectively.

If the rental company rents a truck by charging $34 and 0.09$ per mile, the liner equation can be given as

c = 0.09x + 39

where c represents the cost in dollars of renting the truck and x represents the number of miles

If the truck is driven 187 miles, it can be calculated using the linear equations as follows,

c = 0.09x + 39

As x = 187

c = 0.09 (187) + 39

c = 16.83 + 39

c = 55.83

If the truck is driven 319 miles, it can be calculated using the linear equations as follows,

c = 0.09x + 39

As x = 319

c = 0.09 (319) + 39

c = 28.71 + 39

c = 67.71

Hence the cost in dollars of renting the truck if the truck is driven 187 miles and 319 miles is calculated to be 55.83 and 67.71 respectively.

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The child that will have a greater percentage of increasing amounts is; The child with original amount of $500

The amount that has increased from the initial number to the final number in terms of 100 parts of the original is essentially what the concept of percentage increase refers.

We are given that the original amount found in their savings account are;

First child; A = $500

Second child; B = $300

Thus the first child denoted by A has greater amount in savings compared to the second child and as such child A will have a greater percentage of increasing amounts.

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Answer: The older child.

Step-by-step explanation: The original amounts in their savings accounts

were $500 and $300, respectively.

The width of the rectangle with a perimeter of 220 inches is 38 inches.

A rectangle is a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.

The perimeter of a rectangle is expressed as;

P = 2( length + width )

Given the data in the question;

Let x represent the width of the rectangle.

To solve for the width ( x ), plug the given values into the perimeter formula above and solve for x.

P = 2( length + width )

220 = 2( (2x - 4 ) + x )

220 = 2( 2x - 4 + x )

220 = 2( 3x - 4 )

220 = 6x - 8

6x = 220 + 8

6x = 228

x = 228/6

x = 38

Therefore, the width of the rectangle x is 38 inches.

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Answer:

x=7 -2x+4=-10

-2x+4-4=-10-4

Step-by-step explanation:

this should be right pick me brainliest

Confirmed Solution:

[tex]x=7[/tex]

Further Explanation:

Displayed Above

Hope this helps!

points of discontinuity are x = -4&x = +4.

x = +4 is removable discontinuity

The x- intercept is x = 0The y- intercept is y= -(1/16).

points of discontinuity:

In rational functions, points of discontinuity are defined as fractions with undefined or zero as their denominator. When the denominator of a fraction is 0, the fraction is no longer defined and shows up as a hole or break in the graph.

points of discontinuity removable:

A point on the graph that is removable discontinuity is one that may be filled in with a single value despite not existing.If an is zero for a factor in the denominator that shares a factor with a factor in the numerator, a removable discontinuity at x=a in the graph of a rational function occurs.

points of discontinuity non removable:

A function's break that cannot be repaired with a single point is referred to as a non-removable discontinuity. It cannot be filled in with a single point, a vertical asymptote (a vertical line that the graph approaches but never crosses because the function is undefined at that x-value) is non removable.

given that y=1/x²-16

write 16 as a 4²

[tex]y = \frac{1}{ {x}^{2} - {4}^{2} } [/tex]

[tex]y = \frac{1}{(x + 4)(x - 4)} [/tex]

now,

domain : x !=4.

points of discontinuity are

(x+4) = 0 (x-4) = 0

x = -4 x = +4

Here x = +4 is removable discontinuity.

The x- intercept is

if x = 0, then

[tex]y = \frac{ 1}{ - 16} [/tex]

The y- intercept is

if y = 0

x = 0.

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Using a system of equations, it is found that the number of votes that he received for each place is given as follows:

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are given as follows:

He received 892 total votes, hence:

x + y + z = 892.

Total of 2029 points, hence:

3x + 2y + z = 2029.

He had 4 fewer than twice as many second-place votes as first-place votes, hence:

x = 2y - 4.

Replacing in each of the first two equations:

x + y + z = 892.

2y - 4 + y + z = 892

3y + z = 896.

3x + 2y + z = 2029

3(2y - 4) + 2y + z = 2029

8y + z = 2041.

Multiplying the first equation by -1, and subtracting the second equation from the first, we have that:

5y = 1145

y = 1145/5

y = 229.

The other amounts are given as follows:

Hence the number of votes that he received for each place is given as follows:

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Answer:

Step-by-step explanation:

90-degree rotation

Let me explain, you see point B? Yeah, okay. 90 degrees is a right angle, so you see how the replica blue B is on the line a right angle from it?

That's how you figure that out, if the point is on a line 90 degrees from it it's a 90-degree rotation

If you remain confused please don't hesitate to ask :))

The equation is a quadratic equation.

Linear equation is a equation whose degree is 1. Degree is defined as the highest power of the variable in a polynomial function.

Quadratic equation is a equation whose degree is 2.

Exponential equation is a equation in which the variable appear a exponents.

Now we have been the equation that is,

                  [tex]y=3(x + 1)^{2}[/tex]

Expanding this we would get

                  y = 3([tex]x^{2}[/tex] + 1 + 2x)

                  y = 3[tex]x^{2}[/tex] + 2x + 3

Here the highest power is 2 that is the degree is 2 . Thus this equation is a quadratic equation.

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The pounds of apple left after 1 week is 2.1 pounds.

The pounds of apple would decline each day that Sandy eats it.

An exponential function is a function that is used in mathematics with the form: f ( x ) = [tex]a^{x}[/tex]

Where:

The pounds of apple left = initial pounds of apple x (1 - rate at which she eats it)^number of days

10 x (1 - 0.2)^number of days

10 x 0.8^7 = 2.1 pounds

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When written as a fraction, 0.116 can be found to be the equivalent of 29 / 250

The value of 0.116 has 3 decimals after the decimal point. This means that it is a thousandth decimal.

The fraction form is therefore:
= 116/1,000

You can then take this to be simplest form:
= (116 / 2) / (1,000 / 2)

= 58 / 500

= (58 / 2) / (500 / 2)

= 29 / 250

In conclusion, 0.116 = 29/250

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Answer:

9.5

Step-by-step explanation:

[tex]\frac{KQ}{BK} = \frac{?}{?}\\ KQ = \frac{BK}{2}\\KQ = \frac{19}{2}\\KQ = 9.5[/tex]

3 log (x) - log (6) + log (2.4) = 9 => x = 1357.28, by properties of logarithm.

Now,

3 log (x) - log (6) + log (2.4) = 9

=> 3 log (x) - 0.778 + 0.38 = 9

=> 3 log (x) = 9 - 0.38 + 0.778 = 9.398

=> log (x) = 3.13267

Since, generally the base of log is 10, raising them to 10.

=> [tex]10^{log_{10}(x)} = 10 ^{3.13267}[/tex]

=> x = 1357.28

Hence, 3 log (x) - log (6) + log (2.4) = 9 => x = 1357.28, by properties of logarithm.

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The maximum value of the periodic function will be 2.5 if the amplitude of a periodic function is 2.5 and its minimum value is 0 option (H) 2.5 is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that:

The amplitude of a periodic function = 2.5

The minimum value = 0

The maximum value = the amplitude = 2.5

Thus, the maximum value of the periodic function will be 2.5 if the amplitude of a periodic function is 2.5 and its minimum value is 0 option (H) 2.5 is correct.

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Answer:

3.19 or 3.2 if round

Step-by-step explanation:

160^2 = 25600

81826 / 25600= 3.19

The angle measures for this problem are given as follows:

15. m<2 = 18º.

16. m<1 = 79º.

17. m<UPS = 151º.

18. m<W = 131º.

19. m<1 = 34º.

20. m<1 = 147º.

Using the angle addition postulate, we have that an angle of 90º is split into two angles, angle 1 and angle 2, hence:

m<1 + m<2 = 90º.

We use this equation to solve for x as follows:

7x - 19 + x + 5 = 90

8x - 14 = 90

8x = 104

x = 104/8

x = 13º.

Hence the measure of angle 2 is given as follows:

m<2 = x + 15 = 18º.

1 and 4 are vertical angles, meaning that they are congruent, hence we can solve for x as follows:

6x + 25 = 10x - 11

4x = 36

x = 9º.

Hence the measure of angle 1 is given as follows:

m<1 = 6(9) + 25 = 79º.

Angles 4 and 5 are supplementary, meaning that the sum of their measures is of 180º, hence we solve for x as follows:

3x + 7 + 9x - 43 = 180

12x = 216

x = 216/12

x = 18.

The measure of angle UPS is:

m<UPS = m<4 + 90º = 3(18) + 7 + 90 = 151º.

From the explanation of supplementary angles in item 17, we have that:

m<W + 49º = 180º

m<W = 131º.

Complementary angles are angles whose sum of the measures is of 90º, hence:

m<2 + m<3 = 90º

m<2 + 56 = 90

m<2 = 34º.

Vertical angles are congruent, hence:

m<2 = m<1 = 34º.

The measures of the angles are:

Angles that form a linear pair are supplementary, hence:

m<1 + m<2 = 180

5x - 18 + x = 180

6x = 198

x = 198/6

x = 33.

Then the measure of angle 1 is given by:

m<1 = 5(33) - 18 = 147º.

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the easiest way to solve division is to first use calculator if you don't have it you can count the number by dividing them

[tex]ln(e^x) \geq 1[/tex] is sometimes true, by seen by operations on logarithm.

Now,

For example, let x = 0.1

Then, [tex]ln(e^{(0.1)}) = 0.1 < 1[/tex]

For example, let x = 2

Then, [tex]ln(e^2) = 2 > 1[/tex]

Hence, [tex]ln(e^x) \geq 1[/tex] is sometimes true, by seen by operations on logarithm.

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Explanation:

Central angle AOC is 144 degrees. This means arc ABC is 144 degrees because the central angle subtends this arc.

The remaining bit of the circle is 360-144 = 216 degrees. If we placed point E somewhere on the edge of the circle, toward the bottom, then major arc AEC is 216 degrees in measure.

Notice how inscribed angle ADC subtends this 216 degree arc. So according to the inscribed angle theorem, angle ADC is half of the 216 degree arc at 216/2 = 108 degrees.

Angle APD = 180 - (angle APC) = 180 - 145 = 35 degrees

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

Focus solely on triangle ADP. We have these interior angles

The three interior angles must add to 180

A+D+P = 180

A+108+35 = 180

A+143 = 180

A = 180-143

A = 37 which is the measure of angle BAD.

Step-by-step explanation:

I hope this helped you

The AC in Rhombus ABCD is 16 cm.

In question it is not given that what is E, so, let suppose that E is intersecting point of diagonals AC and BD of rhombus with side AB, BC, CD and DA.

Rhombus is a parallelogram with four equal sides and sometimes one with no right angles.

As it is given that AE =8 cm.  

And, we know that AC is diagonal rhombus,

so, as E is middle point of diagonal AC

Then,    AC  = 2 × AE

            AC  = 2 × 8

Hence,  AC  = 16 cm.

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Answer:

j

Step-by-step explanation:

kl

-15_, -9, -3_, 3, 9...

First of all we understand about what is sequence ?

A sequence is an ordered list of numbers (or other elements like geometric objects), that often follow a specific pattern or function. Sequences can be both finite and infinite.

Now we know that

Arithmetic = each new term differs from the previous term by a fixed amount.

an = a1 + d (n − 1)

Geometric = each element after the first is obtained by multiplying the previous number by a constant factor

an = a1 (r)^(n − 1)

Given pattern is

_,-9,_,3,9

find out the blanks by following a pattern ..

The term to term rule of a sequence describes how to get from one term to the next.

There is the difference of +6

hence The common different is +6.

-15_, -9, -3_, 3, 9...

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Answer:

she got 30 dollars.

Step-by-step explanation:

2x3x=50

5x=50

5x/5=50/5

=10

10*3=30 dollars

All the ways of sampling the students that would produce a representative sample are Simple random sampling, Strafied random sampling, Systematic sampling, Cluster sampling, Convenience sampling.

Sampling : In statistics, quality assurance, and survey methodology, sampling is the selection of a subset of individuals from within a statistical population to estimate characteristics of the whole population.

Given that Clayton wonders what types of sports the students at his school like to play. So, he plans to ask a small sample of them.

Explanation:

Let us assume that there are 3000 students in Clayton's school and he has to choose a sample of 20 students.

1) Simple random sampling - Pick 20 of the students of the school from the 3000 students there are in his school.

2) Strafied random sampling - Divide all the students of the school into 4 grades and randomly pick 5 students from each of the grades.

3) Systematic sampling - Pick evert 7th student who enters the school premises until 20 students are picked.

4) Cluster sampling - Pick several 1st period classes of the school then randomly pick students from those classes.

5) Convenience sampling - Ask 20 students from all the 3000 students in the school recess.

Therefore, All the ways of sampling the students that would produce a representative sample are Simple random sampling, Strafied random sampling, Systematic sampling, Cluster sampling, Convenience sampling.

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The three consecutive odd integers are 17, 19 and 21 respectively.

Linear equations are equations that has a leading degree of 1. Given the three consecutive odd numbers to be

2x+1, 2x+3 and 2x+5

If the sum of the smallest number and middle number is 27 less than three times the largest number, then;

2x + 1 + 2x + 3 = 3(2x+5) - 27

Simplify

4x + 4 = 3(2x) + 3(5) - 27

4x + 4 = 6x + 15 - 27

4x - 6x = 15 - 27 - 4

-2x = -16

x = 16/2

x = 8

Determine the numbers

Smallest number = 2x + 1

Smallest number = 2(8) + 1 = 17

Middle number = 2x + 3

Middle number = 2(8) + 3

Middle number = 19

Largest number = 2(8) + 5

Largest number = 21

Hence the three consecutive odd integers are 17, 19 and 21 respectively.

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