the product rule of exponents says that when multiplying two powers that have the same base, you need to

The solution is Option C.

The measures of the legs of the isosceles trapezoid is given by the proportion equation L₂ = 15.5 inches

The Trapezoid is a 4 sided polygon. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.

There are three types of trapezoids , and those are given below:

a) Isosceles Trapezoid

b) Scalene Trapezoid

c) Right Trapezoid

The area of the Trapezoid is given by

Area of Trapezoid = ( ( a + b ) h ) / 2

where , a = shorter base of trapezium

b = longer base of trapezium

h = height of trapezium

Given data ,

Let the measure of legs of PQRS trapezoid be L₂

Let the first trapezoid be represented as T₁ = ABCD

The measure of the legs of T₁ = L₁

And , Let the second trapezoid be represented as T₂ = PQRS

The measure of the legs of T₂ = L₂

The perimeter of T₁ = 72.8 inches

The perimeter of T₂ = 91 inches

The measure of L₁ = 12.4 inches

Now , the two trapezoids are similar

So , measure of L₁ / perimeter of T₁ = measure of L₂ / perimeter of T₂

Substituting the values in the equation , we get

( 12.4 / 72.8 ) = L₂ / 91

Multiply by 91 on both sides of the equation , we get

The measure of L₂ = ( 12.4 x 91 ) / 72.8

The measure of L₂ = 15.5 inches

Hence , the measure of legs of trapezoid is 15.5 inches

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Answer:

Below

Step-by-step explanation:

The maximum area of land that can be enclosed is a SQUARE

  using the river as one side of the square means there are 3 sides that total 800 ft     800 / 3 = 266 2/3 ft per side

  area would then be L x W =    266 2/3  * 266 2/3 = 71111  1/9 ft^2

An octagon is a two-dimensional shape with eight sides, the degree measure of the largest interior angle of the octagon.

Each pair of opposite sides of the octagon are parallel. We can use the formula to determine the degree measure of the largest interior angle of the octagon.

The formula used is: 180(n-2)/n, where n represents the number of sides in the shape. In this case, n is 8, so the equation would be: 180(8-2)/8, which would give us the result of 160.

Therefore, the degree measure of the largest interior angle of the octagon is 160 degrees. This can also be calculated by adding up the internal angles of the octagon, as each interior angle is equal to 360 divided by the number of sides, in this case 8. 360/8 = 45, so 8x45 = 360. If we add all the angles together (4x45 + 3x45 + 3x45) we get 360, which is equal to the degree measure of the largest interior angle of the octagon.

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The y intercept is $25000, the percentage loss is 10% and the decay factor is 0.9

An equation is a mathematical expression that contains two or more numbers and variables linked together by mathematical operations such as exponents, multiplication, division, addition, subtraction and so on.

The standard form of an exponential function is:

y = abˣ

where a is the initial value and b is the multiplication factor.

Let y represent the cost of a van after x years. It is given by:

y = 25000(0.9)ˣ

hence, comparing gives a = 25000, b = 0.9

a) The y intercept is $25000

b) Percentage loss = 1 - 0.9 = 0.1 = 10%

b) Decay factor = b = 0.9

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No, it is average  that Neymar and Luis would have the same tastes and rank a given set of bundles equally. Everyone has unique preferences and tastes that are shaped by their individual experiences.

It is unlikely that Neymar and Luis would have the same tastes and rank a given set of bundles equally. This is because everyone's preferences and tastes are shaped by their individual experiences. Even though Neymar and Luis may have similar backgrounds, they may have had different experiences that have shaped their tastes. For example, Neymar may have had a different upbringing than Luis, which may have resulted in different tastes and preferences. Additionally, Neymar and Luis may have had different life experiences that have shaped their individual tastes. Therefore, it is unlikely that Neymar and Luis would have the same tastes and rank a given set of bundles equally.

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Answer:

p = 975

Step-by-step explanation:

Divide both sides by 25

 25 (p - 949)

-------------------- = 650/25

         25

Then Simplify

p - 949 = 26

Move 949 to the right side

And For your answer you will get:

p = 975 (sorry if i got it wrong)

The inequality to model the situation will be 24b ≤ 250

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

Based on the information, the inequality to model the situation will be 24b ≤ 250. The number of baseball will be:

24b ≤ 250

b ≤ 250 / 24

b ≤ 10

The number of baseball will be 10 or less.

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A correlation coefficient of -0.9 means that there is a strong negative linear relationship between two variables, while a correlation coefficient of 0 means that there is no linear relationship between the two variables.

When two variables have a strong negative linear connection, the values of one variable grow while the values of the other variable fall, and vice versa. When there is no linear relationship, the values of the two variables are more densely packed around the line of best fit, resulting in a smaller standard deviation.

When there is no linear relationship between two variables, the values of the variables are randomly distributed, and there is no consistent link between them. The standard deviation is bigger in this case because the values of the two variables are more spaced apart.

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Therefore , the solution of the given problem of percentage comes out to be $239.6 price he will pay on first store and $419.3 on second store.

In mathematics, a percentage is any value that can be written as a fraction of 100. There are also sporadic uses of the abbreviations "pct.," "pct," or "pc." However, it is commonly indicated by the "%" mark. The proportional amount is flat and lacks any dimensions. Since percentages have a numerator of 100, they can be thought of as fractions. The percent symbol (%) must come after a number to denote that it is a percentage.

Here,
Given :

Price of television is $599

a)

First store is :

=> 50/100 * 599

=> 299.5

and

additional 20% discount :

=> 20/100 * 299.5

=> 59.9

current price =299.5 -59.9 =  $239.6

b)

=> 30/100 * 599

=> 179.7

=> 599 - 179.7

=> $419.3

Therefore , the solution of the given problem of percentage comes out to be $239.6 price he will pay on first store and $419.3 on second store.

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The density of benzene in English units is 9.69 lb/ft³.

Mass per unit volume is measured using density. It can be calculated by dividing an object's mass by its volume. A crucial physical characteristic of matter is density, which has an impact on how objects behave in various settings. A valuable tool for determining the concentration of a specific object or material is density. The more mass an object has for a particular volume, the higher its density. The unit of measurement for density is kilograms per cubic meter (kg/m³).

Benzene has a specific gravity of 0.97, making it 0.97 times heavier than water. The weight of water, which is 62.427 lb/ft³, must be multiplied by the specific gravity to determine the specific weight of benzene.

Benzene has a specific gravity of 0.97, making it 0.97 times heavier than water. The weight of water, which is 62.427 lb/ft³, must be multiplied by the specific gravity to determine the specific weight of benzene. As a result, benzene has a specific gravity of 60.7 lb/ft³.

We must divide the specific weight of benzene by the weight of 1 cubic foot of benzene, which is 6.24lb, in order to determine the density of benzene in English units. As a result, benzene has a density of 9.69 lb/ft³ in English units.

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The solution to the system of Inequalities is gotten as;  (1, 1)

The system of inequalities given for which we are to graph are;

y ≤ x + 2

y < -2x - 1

Now, to find the solution of the system of Inequalities, we will graph both of them on the same graph and the solution will be the point at which both lines intersect each other.

The graph attached shows that the solution of the inequalities is (1, 1)

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The entries in the matrix correspond to whether or not the two elements in the set are related or not related according to the complement of the original relation.

To find the matrix for the complement of a relation, r, given the matrix representing r on a finite set a, you first need to determine the size of the matrix, which is equal to the number of elements in the set. The matrix for the complement of r is simply the matrix for r with all of its entries negated. In other words, you switch all of the 1's to 0's and all of the 0's to 1's.

For example, if the matrix for r is:

[tex]\left[\begin{array}{ccc}1&0&1\\0&1&0\\1&0&1\end{array}\right][/tex]

The matrix for the complement of r would be:

[tex]\left[\begin{array}{ccc}0&1&0\\1&0&1\\0&1&0\end{array}\right][/tex]

This gives us a matrix that represents the complement of the original relation. The entries in the matrix correspond to whether or not the two elements in the set are related or not related according to the complement of the original relation.

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Answer:

The Isosceles Base Angles Theorem states that if two sides of a triangle are equal, then the angles opposite to those sides are equal.

Given: GB = GD

Since GB = GD, triangle ZDGB is isosceles.

By definition of bisects, GU bisects ZDGB.

By the Angle Bisector Theorem, ZG/ZU = GD/GU.

Because GB = GD, ZG = ZU.

By substitution, ZG/ZU = ZG/ZU. Hence, ZB = ZD.

Therefore, ZB ZD, which proves the Isosceles Base Angles Theorem.

Answer:

6j+6

Step-by-step explanation:

I think it would be 6j+6 unless you didn't add the full problem.

The gross pay for the given service is $343.2.

Gross pay is what employees earn before taxes, benefits and other payroll deductions are withheld from their wages.

Given that, the regular salary of some service is $7.80 per hour, we need to calculate the gross payment with over time hour, which is 4 hours and regular hour of work is 40 hours.

Therefore,

To find, gross payment, we will multiply by 7.80 by 4 and 40, and add both to get the regular salary,

Gross payment = 7.80 × 4 + 7.80 × 40  

= 7.80(4+40)

= 7.80 × 44

= 343.2

Hence, the gross pay is $343.2

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Answer:

x = 0.37686455

Step-by-step explanation:

Answer: x≈0.37686455

Step-by-step explanation:

$20,000 due in 50 years would be worth approximately $6,307.51 today, if the discount rate were 7.5%.

The present value of $20,000 due in 50 years, discounted at 7.5%, can be calculated using the formula:

PV = FV / (1 + r)^t

Where:

PV = present value

FV = future value ($20,000)

r = discount rate (7.5%)

t = number of years (50)

Plugging in the numbers, we get:

PV = $20,000 / (1 + 0.075)^50

PV = $20,000 / (1.075)^50

PV = $20,000 / 3.16907

PV = $6,307.51

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Answer:

The distance around the edge of a circular pool is equal to its circumference. If the circumference is 24 meters, then we can use the formula for circumference of a circle, C = 2πr, to find the radius, r.

C = 2πr

24 = 2πr

12 = πr

r = 12/π

The distance from the edge of the pool to the center is equal to the radius of the pool. So, the distance from the edge of the pool to the center is:

r = 12/π = 12/3.14 = 3.83 meters (rounded to 1 decimal place)

Answer:

60

explanation

divide 39 by 65%,

you will get

39 / ( 65/ 100)

= 39 * (100/65)

= 39 * (20 /13)

= 3*20

= 60

To form a solid hypothesis, Darius needs to have defined parameters for concentration, problem-solving, and creativity, a designed measurable methodology, and a control group for comparison. An example of a hypothesis could be that individuals who use the brain-building website will display significant improvement compared to those who don't. Darius could test his hypothesis by measuring the changes in the parameters in two groups of participants at different time intervals.

Darius needs to focus on three primary aspects to construct a hypothesis that can test the claims of the brain-building website. These include clearly defining parameters for concentration, problem-solving skills, and creativity, designing a measurable methodology to observe any potential changes in these parameters, and determining a control group for comparison with the group using the website.

An example of a hypothesis might be, 'Individuals who regularly engage with the brain-building website for a period of six weeks will display a statistically significant improvement in validated measures of concentration, problem-solving skills, and creativity compared to a control group of similar individuals not using the website.'

Darius could then design a study where one group of participants regularly use the website over a period of time while another group does not, measuring changes in the defined parameters in both groups at the start, middle, and end of the study period.

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Therefore , the solution of the given problem of expression comes out to be the 8 expressions are given below.

Addition, multiplication, division, and other mathematical operations are required. When combined, they produce the following: A mathematical operator, some data, and an equation A statement of fact contains values, parameters, and operations like additions, subtractions, multiplications, and divisions. It is possible to contrast and compare various phrases and words.

Here,

Given :

Original expression of eight terms including 3 operations are:

=> 10*2-10 =10

=> 100 * 2 -100 = 100

=> 50/2 - 10 = 15

=> 400/2 - 100 + 100 = 200

=> 500 - 100 + 200 = 600

=> 10/2 - 5=0

=> 6 * 10 - 8 = 52

=> 10*8 - 8 =72

Therefore , the solution of the given problem of expression comes out to be the 8 expressions are given below.

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The cumulative frequency of the third class is 73. This means that 73 out of the 86 mid-level managers surveyed spent between 14 and 20 days traveling each year.

The cumulative frequency of the third class is the sum of the frequencies of all the classes up to and including the third class. In this case, the frequency of the third class is 35, and the frequencies of the first two classes are 13 and 25, respectively. So, the cumulative frequency of the third class is:

13 + 25 + 35 = 73

This means that 73 out of the 86 mid-level managers surveyed spent between 14 and 20 days traveling each year.

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16 × 40 = 640

Therefore, 40 miles is 640 kilometers.

Answer:

$0.36

Step-by-step explanation:

[tex]\frac{\$2.88}{8}=\$0.36[/tex]

The dimensions of the sides DH, VW, and WX are, respectively, 14, 12, and 30.

Two figures are known to be similar if the ratio of their similar sides is equal to a constant.

From the polygons given, the following expressions are true;

DH/12 = 21/18

18DH = 12 × 21

18DH = 252

DH = 14

Similarly:

VW/14 = 18/21

21VW = 14 * 18

21VW = 252

VW = 12

Also;

35/WX = 21/18

21WX = 35 * 18

21WX = 630

WX = 30

Therefore the measure of the sides DH, VW and WX are 14, 12 and 30 respectively.

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The process to graph a line is described below, and the graph of the linear equation is on the image at the end.

I will help you to graph the first line step-by-step.

The linear equation we want to graph is:y = (3/2)*x + 3

First, we need to find two points on the line.

We can do that by evaluating the equation in two different values of x.

If x = 0:

y = (3/2)*0 + 3 = 3

We have the point (0, 3)

if x = 2:

We wil get:y = (3/2)*2 + 3 = 6

We have the point (2, 6)

Now you just need to graph these two points on a coordinate axis and then draw a line that connects them.

That line is the graph of the linear equation.

The graph can be seen on the image at the end.

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The probability of the sum of the upturned faces equal to 7 is Decimal answer is 0.1666667  and rounding to the hundredths place is 16.6%.

There are 66=36 potential pairs of die rolls because the two are independent of one another. Only the following pairs of rolls total seven out of those. (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). The probability of our two die rolls adding up to 7 would then obviously be: 6 ÷ 36 = 1 ÷ 6 = 0.1666667  rounding to the hundredths place = 16.6%. Probability is simply the possibility that something will happen. When we don't know how something will turn out, we can talk about the possibility of one outcome or the likelihood of several.

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Since <1 and <2 are vertical angles, they are equal, so m<2 = 8x - 15 = 8(6) - 15 = 39°  , Since <2 is supplementary to <3,  m<3 = 180° - 39° m<3 = 141°

Vertical angles are angles that are opposite each other when two lines cross. They always have the same measure and are supplementary angles (add up to 180°). Vertical angles are also known as opposite angles or vertically opposite angles. When two lines intersect, four angles are formed. The two pairs of angles opposite each other are known as vertical angles. This is because the lines that they share are vertical to each other, which is why they are also known as vertically opposite angles. Vertical angles can be found in a variety of shapes and figures, including parallelograms, triangles, and quadrilaterals. They can be used to solve many mathematical problems and are an important concept to learn in geometry.

4x + 9 = 8x - 15

4x - 8x = -15 - 9

-4x = -24

x = 6

Therefore, m<2 = 8x - 15 = 8(6) - 15 = 39°

Since <2 is supplementary to <3,

m<3 = 180° - 39°

m<3 = 141°

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The perimeter and area of triangle ABC are 22.15 units and 15 square units

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

A (-5, 2), B (-3, 5), C (5, 2), and D (-3, 2).

For the perimeter, we calculate the side lengths using the distance formula

So, we have

AB = √[(-5 + 3)² + (2 - 5)²] = √13

AC = √[(-5 - 5)² + (2 - 2)²] = 10

BC = √[(-3 - 5)² + (5 - 2)²] = √73

So, we have

Perimeter = √13 + 10 + √73

Evaluate

Perimeter = 22.15 units

For the area, we have

Area = 0.5 * | (x1 * y2 + x2 * y3 + x3 * y1) - (x2 * y1 + x3 * y2 + x1 * y3) |

Area = 0.5 * | (-5 * 5 + -3 * 2 + 5 * 2) - (-3 * 2 + 5 * 5 + -5 * 2) |

Area  = 15 square units

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When 3 is the input, the output is 10. When 10 is the input, the output is 15.

It should be noted that the input for the function is time, measured in hours. The output of the function is energy usage, measured in kilo watts.

From the information, the energy usage of a light bulb is a function. The input for the function is time measured in hours. The output of the function is energy usage, measured in Kilo watts. E (energy) is a function of t (time).

The graph of the function will show energy usage on the y axis and time on the x axis.

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