1. Simplify using only positive exponents:
(2t)^-6

Using the scale given, the actual length of each side is: 21 feet.

The scale of a drawing or a map is a ratio or a fraction that represents the relationship between the size of an object on the drawing or map and its actual size in the real world. The scale is used to convert the dimensions of objects on a drawing or map to their real-world dimensions.

Given the scale of 1 unit = 3.5 feet, and also the image which gives the blueprint shows that every side of the house is equal to each other.

Each side = 6 units.

Therefore, 6 * 3.5 feet = 21 feet.

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The result of this operation can then be used to calculate the maximum discount available for each product.

The formula to find the maximum discount product in SQL is:

MAX(Discount) = MAX(Price)-MIN(Price);

This formula calculates the maximum discount available on a product by subtracting the minimum price of the product from the maximum price. This can be used to determine the best value for money for a product by comparing the discount with the prices of other products.

For example, if the minimum price of a product is $100 and the maximum price is $200, the maximum discount available for that would be $100. This could be used to compare the discount of this  The result of this operation can then be used to calculate the maximum discount available for each product. to the discounts of other products and find out which one gives the best value for money.

This formula can be implemented in SQL by using the MAX() and MIN() aggregate functions to find the maximum and minimum prices for each product. The result of this operation can then be used to calculate the maximum discount available for each product.

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The height of the Public Park entreence in smaller scale is 7.9 inches

The actual height of the Park entrence is 7.9*48 = 379.2 inches = 31 feet 7.2 inches

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Direct Variation

When there is a direct variation, an increase or decrease in one quantity will result in an equivalent rise or fall in the other. For instance, a rise in the quantity of commodities will result in higher costs.

Indirect Variation

A change in one quantity will directly affect a change in another, known as a direct variation. A rise in the quantity of goods, for instance, will result in higher costs.

In the scale 1 inch = 4 feet= 4*12 = 48 inches

The height of the Public Park entreence in smaller scale is 7.9 inches

The actual height of the Park entrence is 7.9*48 = 379.2 inches = 31 feet 7.2 inches

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Given:-

[tex] \: [/tex]

To find:-

[tex] \: [/tex]

By using formula:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

hope it helps!:)

The graph of two functions: (a) f(2)+g(2) = 0 (b) f(6) - 9 = 0 (c) f(2)•g(2) = -9 (d) f(2) = 5 (e) g(2) = -5 (f) f(6) = 1

(a) To solve f(2)+g(2)=0, use the graph to find the value of f(2) and g(2). From the graph, f(2) is equal to 5 and g(2) is equal to -5. When these values are added together, the result is 0. Therefore, f(2)+g(2)=0.

(b) To solve f(6)-9=0, use the graph to find the value of f(6). From the graph, f(6) is equal to 1. When the value of f(6) is subtracted from 9, the result is 0. Therefore, f(6)-9=0.

(c) To solve f(2)•g(2)=-9, use the graph to find the value of f(2) and g(2). From the graph, f(2) is equal to 5 and g(2) is equal to -5. When these values are multiplied together, the result is -9. Therefore, f(2)•g(2)=-9.

(d) To solve f(2)=5, use the graph to find the value of f(2). From the graph, f(2) is equal to 5. Therefore, f(2)=5.

(e) To solve g(2)=-5, use the graph to find the value of g(2). From the graph, g(2) is equal to -5. Therefore, g(2)=-5.

(f) To solve f(6)=1, use the graph to find the value of f(6). From the graph, f(6) is equal to 1. Therefore, f(6)=1.

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The call center received a number of calls between 3:00 PM and 4:00 PM is 350.

A call center (Commonwealth spelling) or call center (American spelling; see spelling differences) is a managed capability that can be centralized or remote that is used for receiving or transmitting a large volume of inquiries by telephone. An inbound call center is operated by a company to administer incoming product or service support or information inquiries from consumers. According to this question,

The call center received 40% more inquiries between 3:00 PM and 4:00 PM than the 250 inquiries received between 2:00 PM and 3:00 PM.

So, if 250 inquiries were received between 2:00 PM and 3:00 PM, 40% of that is 250 * 40% = 100.

And the total number of inquiries received between 3:00 PM and 4:00 PM is 250 + 100 = 350.

Therefore, the call center received a number of calls between 3:00 PM and 4:00 PM is 350.

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Answer:

Step-by-step explanation:

A regular polygon with 3 sides is an equilateral/equiangular triangle. All the interior angles measure 60 degrees. The exterior angles are supplementary to that (add up to 180) so an exterior angle is 180 - 60 = 120

The probability of rolling a die 2 times and then rolling 2 odd numbers in a row is 1/4

When rolling a fair six-sided die, each outcome has an equal chance of happening, so the probability of rolling an odd number is 1/2 i.e. 3 out of 6

The probability of rolling two odd numbers in a row is then

(1/2) * (1/2) = 1/4.

This means that, the probability of rolling a die two times and then rolling 2 odd numbers in a row is 1/4

Therefore, the probability of rolling a die 2 times and then rolling 2 odd numbers in a row is 1/4

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The missing side of the first triangle is 125' and the angle is 20.61°.

the missing side of the second triangle is 117' and the angle is 69.39°.

Having three edges and three vertices, a triangle is a three-sided polygon. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.

Given the two triangles are congruent,

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. These triangles can be turned, flipped, rotated, and slid to create an identical appearance.

we can compare both the triangles and the remaining dimensions of triangle 1 are side = 125' and angle = 20.61°

and dimensions of second triangle are,

side = 117' and angle = 69.39°

Hence the dimensions of the first triangle, side = 125' and angle = 20.61°,

and for the second triangle, side = 117' and angle = 69.39°.

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¬ (p ↔ q) and p ↔¬q are proved to be logically equivalent.

The given statement are-

¬ (p ↔ q) and p ↔¬q

To prove these are logically equivalent, use contrapositive law

¬(p↔q) = ¬[(p∧q) ∨ (¬p∧¬q)]

¬(p↔q) = (p∧¬q) ∨ (¬p∧q)

And,

p↔¬q = (p∧¬q) ∨(¬p∧¬(¬q))

p↔¬q = (p∧¬q) ∨(¬p∧ q)

Thus,  ¬ (p ↔ q) and p ↔¬q are proved to be logically equivalent.

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The first translation T (10, 2) means 10 units to the right that is 10 blocks to the east, and 2 units up that is 2 blocks to the north.  The second translation T (-23, -3) 23 units to the west and 3 units to the south.

In mathematics, a translation is the up, down, left, or right movement of a shape. Because the translated shapes appear to be exactly the same size as the original ones, they are consistent with one another. Just one or more directions have been altered. There is no change in the shape because it is simply being moved from one location to another.

The given translations are T (10, 2)° T (-23, -3).

The first translation T (10, 2) means 10 units to the right that is 10 blocks to the east, and 2 units up that is 2 blocks to the north.

The second translation T (-23, -3) means 23 units to the left or 23 units to the west and 3 units down that is 3 units to the south.

Hence, the first translation T (10, 2) means 10 units to the right that is 10 blocks to the east, and 2 units up that is 2 blocks to the north.

The second translation T (-23, -3) means 23 units to the left or 23 units to the west and 3 units down that is 3 units to the south.

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Given:-

[tex] \: [/tex]

To find:-

[tex] \: [/tex]

By using formula:-

[tex] \: [/tex]

Solution:-

[tex] \rm{C = 2πr} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm{ = 2×3.14×7} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm{=2×21.98 } \\ \: \: \: \: \: \: \: \: \underline{ \boxed{\rm{ \bold{\red{=43.96}}}}}[/tex]

[tex] \: [/tex]

hope it helps!:)

When conducting a chi-square test for a 2 by 2 contingency table, the null hypothesis tested is the two variables are independent of each other.

The chi-square test is a statistical method used to analyze the relationship between two categorical variables.

Here we need to determine whether the null hypothesis can be rejected, the chi-square test compares the observed frequencies of the two variables with the expected frequencies.

If the difference between the observed and expected frequencies is large enough, it can be concluded that the two variables are not independent, and the null hypothesis can be rejected.

It's important to note that the chi-square test is only appropriate for 2 by 2 contingency tables, where both variables being studied are categorical and have only two categories each. Additionally, the sample size must be large enough to allow for valid statistical inference.

In the chi-square test for a 2 by 2 contingency table is used to determine if there is a significant relationship between two categorical variables, with the null hypothesis being that the two variables are independent of each other.

Therefore option (d) is correct.

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The resulting angle of 4 π / 3 is positive and coterminal with - 2π / 3

What are coterminal angles ?

Coterminal angles are the angles that have the identical initial facet and share the terminal aspects. these angles occupy the usual function, though their values are one of a kind. they are at the same sides, within the identical quadrant and their vertices are same. while the angles are moved clockwise or anticlockwise the terminal aspects coincide at the identical attitude.

Given angles measure of -2 pi / 3

So we have to add 2π to - 2 π / 3

- 2π / 3 + 2 π

 = 2π - 2π / 3

= 6 π - 2 π / 3

= 4π / 3

The resulting angle of 4 π / 3 is positive and coterminal with - 2π / 3

Therefore, The resulting angle of 4 π / 3 is positive and coterminal with

- 2π / 3

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Answer: 29x64=1856

Step-by-step explanation:

Answer:

29 x 64 = 1856

Step-by-step explanation:

Step 1: First we set up our equation like this:

  6 4

x 2 9

Step 2: Multiply

4 x 9 = 36. Put 6 below the line and 3 as a reminder on top:

  3  

  6 4

x 2 9

_______

      6

Step 3: Multiply again...

9 x 6 = 54. Take 54 and add 3 from the previous step to get 57. Enter 57 at the bottom:

  6 4

x 2 9

________

5 7 6

Step 4: Add 0

Enter a 0 at the bottom right as a place holder, because you now move over one digit:

  6 4

x 2 9

________

 5 7 6

+       0

Step 5: Multiply again. (Sheesh)

2 x 4 = 8. Put 8 below the line and 0 as a reminder on top:

  0

  6 4

x 2 9

________

 5 7 6

+   8  0

Step 6: Multiply (Last time)

2 x 6 = 12. Take 12 and add 0 from the previous step to get 12. Enter 12 at the bottom:

  6 4

x 2 9

________

    5 7 6

+ 1 2  8  0

Step 7: Add to get answer

Add up the bottom two numbers (576 + 1280 = 1856) to get the answer:

  6 4

x 2 9

________

    5 7 6

+ 1 2 8  0

________

= 1 8 5 6

The bottom line is the answer. Therefore, 64 times 29 equals:

1856

The value of x from pythagoras theorem we get as 32.45

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Let the length of the perpendicular be y , the length of the 3rd side be z

Using Pythagoras Theorem :

x² - y² = 27² , ............(i)

x² + z² = (27 +9)² = 36² .......(ii)

y² - z² = 9²   ................(iii)

Adding equation (i), (ii) and (iii) we get ,

2x² = 27²+36² + 9²

⇒x = 32.45

The value of x from pythagoras theorem we get as 32.45.

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An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides.

Completed question :

Please answer fast The vertices of a rectangle are located at the coordinates (1, 4), (1, 5), (6, 5),

1

,

4

,

1

,

5

,

6

,

5

,

and (6, 4)

6

,

4

.

Find the length of the sides of the rectangle and its perimeter.

Given data :

Horizontal sides

There are two x-values present : 1 and 6

Find the difference

6 - 1 = 5

The horizontal sides of the rectangle are 5 units long

Vertical sides

Two y-values are present : 4 and 5

Find the difference

5 - 4 = 1

The vertical sides of the rectangle are 1 unit long

Perimeter

2(Horizontal side + Vertical side)

2(5 + 1)

2(6)

12

The perimeter of the rectangle is 12 units

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The solution to the system is (x, y) = (7, 5).

What is the linear equation?

A linear equation is an equation of a straight line. It is an equation of the form y = mx + b, where m is the slope of the line and b is the y-intercept.

The system has one solution (7,5).

One method to solve the system of linear equations is substitution. From the first equation, x = y + 2. Substituting this into the second equation, we get -3(y + 2) + 3y = 6, which simplifies to -3y - 6 + 3y = 6.

Combining like terms, we get -3y = -6, or y = 2.

Finally, substituting y = 2 back into x = y + 2, we get x = 2 + 2, or x = 4. So, the solution to the system is (x, y) = (7, 5).

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The percentage change in GDP over the time period from 2010 to 2011 was 4.14%. This means that the nominal GDP increased by 4.14% during this time period.

To calculate the percentage change in Gross Domestic Product (GDP) over the time period from 2010 to 2011, we can use the following formula:

Percentage change = (GDP in 2011 - GDP in 2010) / GDP in 2010 * 100%

Substituting the values, we get:

Percentage change = ($15.1 trillion - $14.5 trillion) / $14.5 trillion * 100% = $0.6 trillion / $14.5 trillion * 100% = 4.14%

So, the percentage change in GDP over the time period from 2010 to 2011 was 4.14%. This means that the nominal GDP increased by 4.14% during this time period.

In conclusion, the percentage change in Gross Domestic Product (GDP) over the time period from 2010 to 2011 was 4.14%, which means that the nominal GDP increased by 4.14% during this time period.

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Approximately 68% of data lies between 0 and 1 standard deviation in the standard normal curve.

The area under the standard normal curve is equal to 1. It is divided into four sections: below 0 standard deviation, between 0 and 1 standard deviation, between 1 and 2 standard deviations, and above 2 standard deviations. Each of these sections has an area of 0.25, or 25%. The area between 0 and 1 standard deviation is 0.25, or 25%, of the entire area under the curve, so 68% of the data lies within it.

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Answer: (3, 7) (7, 4)

Step-by-step explanation:

The line fits better in predicting the points in the data. Also I got the right answer on the same test. The first time I did the test, I did (1,10) (10,10) which is INCORRECT. I reset the test and picked (3,7) (7,4) and it was CORRECT.

So let me be clear, (1,10) (10,1) IS THE WRONG ANSWER

(3,7) (7,4) IS THE RIGHT ANSWER

PROOF:

The fraction of the original action figures will Natasha and her 3 friends each receive is (1/15).

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Total number of action figures = x

Number of action figures left = (1/5)x

The number of action figures received by each friend.

= (1/5)x ÷ 3

= (1/15)x

Thus,

Each friend received (1/15) of the original action figures.

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Answer:

m = 50kg

Step-by-step explanation:

First, you  have to know that mass is an indicator of the amount of matter that makes up a body. Its unit in the International System is the kilogram (kg).

The mass of an object will always be the same, no matter where it is located.

On the other side, bodies are subjected to the action of forces, such as the force of gravity or electromagnetic forces.

So, weight is the action exerted by the force of gravity on the body. That is, weight is a measure of how much force gravity exerts on the mass of an object.

The weight of an object is measured in Newton (N) and will vary according to the force of gravity that acts on it.

The expression for the calculation of the weight is:

P= m×g

where:

In this case, you know that:

P= 980 N

m= ?

g= 19.6 [tex]\frac{m}{s^{2} }[/tex]

Replacing in the expression for the calculation of the weight:

980 N= m× 19.6 [tex]\frac{m}{s^{2} }[/tex]

Solving:

[tex]\frac{980N}{19.6\frac{m}{s^{2} } }[/tex]

m=50 kg

The probability of event A is  [tex]P(A)=\frac{7}{18}\\[/tex],

The probability of event B is [tex]\\P(B)=\frac{1}{2}[/tex]

What is Probability?

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

The sample space of rolling two dice has 36 possible outcomes.  Remember that the "sample space" is a set which contains all possible outcomes.  

(1,1) (2,1) (3,1) (4,1) (5,1) (6,1)

(1,2) (2,2) (3,2) (4,2) (5,2) (6,2)

(1,3) (2,3) (3,3) (4,3) (5,3) (6,3)

(1,4) (2,4) (3,4) (4,4) (5,4) (6,4)

(1,5) (2,5) (3,5) (4,5) (5,5) (6,5)

(1,6) (2,6) (3,6) (4,6) (5,6) (6,6)

Using these probabilities, you can answer your questions:

A:  The  probability of getting sum of greater number than 7

A={(6,2),(2,6),(3,5),(3,6),(4,4)(4,5)(4,6),(5,3)(5,4)(5,6)(6,3)(6,4)(6,5)(6,6)}

n(A)=14

P(A)=14/36.

P(A)=7/18.

B:Getting Sum of odd numbers.

B={(1,2)(1,4)(1,6)(2,1)(2,3)(2,5)(3,2)(3,4)(3,6)(4,1)(4,3)(4,5)(5,2)(5,4)(5,6)(6,1)(6,3)(6,5)}

n(B)=18

P(B)=18/36.

P(B)=1/2

[tex]P(A)=\frac{7}{18}\\\\P(B)=\frac{1}{2}[/tex]

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Answer:

C

Step-by-step explanation:

8 : 10 = 18

12 : 15 = 27

36 : 45 = 81

The dynamic range for a 9-bit magnitude PCM code is 3072 dB.

The dynamic range for a 9-bit magnitude PCM code is the difference between the maximum and minimum representable amplitude levels, which is calculated using the formula:

Dynamic range = (2^n - 1) * 6dB

where n is the number of bits used to represent each sample in the PCM code.

For a 9-bit magnitude PCM code, n = 9, so the dynamic range is:

Dynamic range = (2^9 - 1) * 6dB = (512 - 1) * 6dB = 3072dB

So, a 9-bit magnitude PCM code has a dynamic range of 3072dB.

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The constant rate at which the water is filling the bucket is: 2/5 gallon per minute.

The constant rate of a proportional relationship is the ratio of the change in the dependent variable to the change in the independent variable.

It is also called the slope of the line in a graph representing the relationship. It is given as, k = y/x.

From the given graph, we can pick the point on the line, (5, 2), and find the constant rate, which is the rate the water is filling the bucket.

Constant rate = y/x = 2/5 gallon per minute.

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The pi is a ratio and is obtained from a circle. If the diameter and the circumference of a circle are known, the value of pi will be as π = Circumference/ Diameter.

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