An office opens at 9 a.m. and closes at 5 p.m. with a lunch interval of 30 minutes. What is the ratio of lunch interval to the total period in office?

Answer:

-71.4285714286Y

Step-by-step explanation:

-7 1/7*(3 2/5)+ 6 3/5*(-7 1/7) = 71.4285714286Y or shorter 71.42

Answer:

Step-by-step explanation:

If the slope of line d is -7/4, then the slope of a perpendicular is 4/7.

Given a slope, to find the slope of a perpendicular, flip the fraction and change the sign.

Flip -7/4 to get -4/7. Then change the sign of -4/7 to get 4/7.

Answer: 4/7

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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One of the four outcomes chosen at random will happen one out of four times, or 25% of the time. Such a result has a 3 to 1 chance of occurring.

While I am unable to see the image, I presume that it is a straightforward, fair spinner with a value indicator when it stops and can only have the outcomes that are listed.

Given that there are four possible outcomes (pink, purple, blue, and green) and only one desired outcome (green), the probability is one-fourth.

One of the four outcomes chosen at random will happen one out of four times, or 25% of the time. Such a result has a 3 to 1 chance of occurring.

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The question seems wrong, the full question:

You spin the spinner shown below once. The spinner has 4 equal sectors colored pink, purple, blue, and green. What is P(green)? If necessary, round your answer to 2 decimal places.

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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True, The span of {u, v} contains both the line through u and the origin, as well as the line through v and the origin.

The span of a set of vectors is defined as the set of all linear combinations of those vectors. When u and v are nonzero vectors, the span of {u, v} is a two-dimensional subspace of the vector space that contains both u and v, and any linear combination of u and v.

Since u and v are nonzero vectors, the lines through the origin and u, and through the origin and v, are non-degenerate lines in the vector space. Therefore, these lines are contained within the span of {u, v}.

In other words, if we take any scalar multiples of u and v, such as au and bv, where a and b are scalars, the sum au + bv will be a linear combination of u and v and therefore will also be contained within the span of {u, v}.

Therefore, the span of {u, v} contains both the line through u and the origin, as well as the line through v and the origin.

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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 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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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 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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Answer:

         1           3

y = - ----- x + -----

         2           2

Step-by-step explanation:

x + 2y = 3

-x             -x

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

2y = -x + 3

÷2     ÷2  ÷2

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

         1           3

y = - ----- x + -----

         2           2

I hope this helps!

Answer:D

Step-by-step explanation:

the dots are forming a mixed up line going across the plot. D best fits the line.

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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Answer:

C

Step-by-step explanation:

8 : 10 = 18

12 : 15 = 27

36 : 45 = 81

¬ (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 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 net force and magnitude is 54°. The solution has been obtained by using trigonometry.

What is trigonometry?

The primary objective of the branch of mathematics known as "trigonometry" is the study of the sides, angles, and connections of the right-angle triangle.

We are given that three forces are acting on the ring.

So,

A = -128 N + 64 N

A = -64 N

[tex]A_{x}[/tex] = A cos θ[tex]_{A}[/tex]

[tex]A_{x}[/tex] = (-64 N) (cos 180°)

[tex]A_{x}[/tex] = -64 N

[tex]A_{y}[/tex] = A sin θ[tex]_{A}[/tex]

[tex]A_{y}[/tex] = (-64 N) (sin 180°)

[tex]A_{y}[/tex] = 0 N

B[tex]_{x}[/tex] = B cos θ[tex]_{B}[/tex]

B[tex]_{x}[/tex] = (128 N) (cos 30°)

B[tex]_{x}[/tex] = 111 N

B[tex]_{y}[/tex] = B sin θ[tex]_{B}[/tex]

B[tex]_{y}[/tex] = (128 N) (sin 30°)

B[tex]_{y}[/tex] = 64 N

R[tex]_{x}[/tex] = A[tex]_{x}[/tex] + B[tex]_{x}[/tex]

R[tex]_{x}[/tex] = -64 N + 111 N

R[tex]_{x}[/tex] = 47 N

R[tex]_{y}[/tex] = A[tex]_{y}[/tex] + B[tex]_{y}[/tex]

R[tex]_{y}[/tex] = 0 N + 64 N

R[tex]_{y}[/tex] = 64 N

[tex]R = \sqrt{R_{x}^{2} +R_{y}^{2} }[/tex]

[tex]R = \sqrt{(47 N)^{2} +(64 N)^{2} }[/tex]

R = 79 N

θ = [tex]tan^{-1}(\frac{R_{y} }{R_{x}} )[/tex]

θ = [tex]tan^{-1}(\frac{64 }{47} )[/tex]

θ = 54°

Hence, the net force and magnitude is 54°.

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Since, the question is incomplete, the complete question has been attached below

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 derivative of the equation 2y³ + xy - 6x + 3 at the point (1,1) is 0, and the second derivative is 13.

The derivative of y with respect to x can be calculated by differentiating both sides of the equation with respect to x. This gives us:

[tex]\frac{dy}{dx} = \frac{x}{2y^2} - 5[/tex]

We can evaluate dy/dx at the point (1, 1) by substituting x = 1 and y = 1 into the equation for dy/dx and calculating the result. This gives us:

[tex]\frac{dy}{dx} = \frac{1}{2} - 6 = -5.5[/tex]

The second derivative of y with respect to x can be calculated by differentiating both sides of the equation with respect to x twice. This gives us:

[tex]\frac{d^2y}{dx^2} = -\frac{1}{2y^3}[/tex]

We can evaluate d2y/dx2 at the point (1, 1) by substituting x = 1 and y = 1 into the equation for d2y/dx2 and calculating the result. This gives us:

[tex]\frac{d^2y}{dx^2} = -\frac{1}{2} = -0.5[/tex]

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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 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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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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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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Answer:

4 2/3 ÷ 2 1/6 is equal to 2 2/13.

Step-by-step explanation:

When dividing 2 1/6 from 4 2/3, you will get 2 2/13 or 2.15.

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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Answer:

Step-by-step explanation:

Here's a step-by-step explanation to find the three consecutive numbers whose sum is 42:

Let's call the smallest of the three numbers "x".

Since they are consecutive numbers, we can represent the next two numbers as x+1 and x+2.

The sum of these three numbers can be represented as x + (x + 1) + (x + 2) = 42.

Simplifying this equation, we get 3x + 3 = 42.

Subtracting 3 from both sides, we get 3x = 39.

Dividing both sides by 3, we get x = 13.

So, the three consecutive numbers are 13, 14, and 15.

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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Answer:

S

Step-by-step explanation:

the distance formula (Pythagoras on the right-angled triangle of the coordinate differences) says that

sqrt²(130) = 130 = (-5 - x)² + (5 - y)²

let's try Q

130 = (-5 - 5)² + (5 - 2)² = (-10)² + 3² = 100 + 9 = 109

no, wrong.

let's try S

130 = (-5 - 4)² + (5 - -2)² = (-9)² + 7² = 81 + 49 = 130

correct !