What’s 27/162 reduced to lowest terms?

You spend 480 minutes per day at school. We will assume that you go to school for 5 days per week.

480 minutes × 5 days = 2,400 minutes per week

There are 4 weeks in a month, so we will multiply the minutes per week by 4 weeks to get the monthly time spent in school.

2,400 minutes per week × 4 weeks = 9,600 minutes per month

You are in school for 10 months, so we will multiply the minutes per month by 10.

9,600 minutes per month × 10 months = 96,000 minutes in school

Now, we will divide the time in school by the number of minutes in school per day.

96,000 minutes in school ÷ 480 minutes per day = 200 days in school

Answer: 96,000 hours or 200 days

The area of the shaded region is [ (36 * √3)/4 - 3 * (9 * √3)/4 ] square units = (36 * √3)/4 - 27 * √3/4 square units = 9 * √3/4 square units.

The area of a triangle can be found using the following formula:

Area = (base * height) / 2

The area of the shaded region can be found by subtracting the sum of the areas of three small equilateral triangles from the area of the original equilateral triangle.

Each of the small equilateral triangles has side length 3, since it is half the length of the original triangle's sides. The area of each small triangle is (3^2 * √3)/4 = (9 * √3)/4 square units.

The area of the original equilateral triangle is (6^2 * √3)/4 = (36 * √3)/4 square units.

Hence, the area of the shaded region is [ (36 * √3)/4 - 3 * (9 * √3)/4 ] square units = (36 * √3)/4 - 27 * √3/4 square units = 9 * √3/4 square units.

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Answer:

D

Step-by-step explanation:

diff y / diff x = slope

so -6/2 = -3

Y intercept is where x= 0, so it's 6

D

The monomial is 6² completes it and makes it (6p - 7q)².

A polynomial is an algebraic expression.

A polynomial of degree n in variable x can be written as,

a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.

We know a monomial is a polynomial that consists of a single term.

Given, __ - 42pq + 49q².

= ___ - 42pq + 7²q².

Now, 6×7 = 42,

Therefore,  ___ - 42pq + 7²q²,

= 6²p² - 42pq + 7²q².

= (6p)² - 42pq + (7q)².

= (6p - 7q)².

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Answer:

a)  32° Celsius

b)  C = m/3 + 4

c) 30 chirps

d) m = 3C - 12

This would be the equation needed to find the number of chirps as a function of temperature

Step-by-step explanation:

Part a.

Since there are 84 chirps in 25 seconds
we get temperature, C = 84/3 + 4 = 28 + 4 = 32° Celsius

part b.
Equation is
C = m/3 + 4

Part c.

We have C = 14

Therefore

14 = m/3 + 4

Multiply throughout by 3

==> 3 x 14 = 3 x m/3 + 3 x 4

==> 42 = m + 12

Subtract 12:

42 - 12 = m30 = m

or m = 30 chirps

part d.

Inverse of the function C = m/3 + 4 is m expresses as a function of C

C = m/3 + 4

Multiply by 3 both sides:
3C = m + 12

3C - 12 = m

or m = 3C - 12

This would be the equation needed to find the number of chirps as a function of temperature

[tex]\qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ \stackrel{\stackrel{a}{\downarrow }}{9}x^2\stackrel{\stackrel{b}{\downarrow }}{-2}x\stackrel{\stackrel{c}{\downarrow }}{-9}=0 ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases} \\\\\\ (-2)^2-4(9)(-9)\implies \text{\LARGE 328}[/tex]

Answer:

183

365/2

you get 182.5 but you round up because you don't have half a person in the room.

Step-by-step explanation:

(a). There is a 57.16 Mbps difference. (b). There is a 2.74 standard deviation difference. (c). 2.74 is the z-score (d). The maximum data rate offered by the carrier is more than 2.

When something is careful and purposeful, you use the word measured to describe it. The men's voices were measured and quiet. Voters will be attracted to her more considered reaction. These are a couple of those illustrations. using a thermometer to measure body temperature using a measuring cylinder to determine the weight of produce in a store. Measuring the stature of an infant to retain his/her growth record.

(a). (74.5 - 17.34) = 57.16

(b). 57.16/20.79

= 2.74

(c). z = (X - μ)/sd

= (74.5 - 17.34)/20.79

= 2.74

(d). Because it is higher than 2, the carrier's greatest data speed is noteworthy.

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The Sine Function is y =  4 sin(π /2 x ) + 1

In trigonometry, the sine function can be defined as the ratio of the length of the opposite side to that of the hypotenuse in a right-angled triangle.

Given:

Period = 4

Amplitude = 4

Midline: y = 1

y-intercept: (0, 1)

We know that

y = Asin (Bx + C) + D

A = the amplitude = 4

So, B =  2pi / period

         = 2π / 4

         = π /2

and, C = phase shift  

C = 0

Also, D = midline  =  1

So, the sine Function is

y =  4 sin(π /2 x ) + 1

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The short piece is 28 cm and the other piece is 43 cm longer or (28+15 = 43 cm).

Based on the question, One piece will be length x and the other piece will be 15 cm longer, so it will be x + 15 cm long.

Added together the length of these two boards will equal 71 cm. So the equation will be:

x + (x + 15) = 71

2x+15=71

2x=71-15

2x=56

x=28 cm

The short piece is 28 cm and the other piece is 43 cm longer or 28+15 = 43 cm.

Mathematical modeling can be done by taking the following steps, namely:

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The amount of petrol left remaining in the car after Tuesday journey is (x/2) - 2

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

A car has x litres of petrol in its tank. One half is used on Monday. Therefore:

Amount of petrol remaining = x - (1/2) of x = x - x/2 = x/2

A further 2 litres on Tuesday, hence:

Amount of petrol left = (x/2) - 2

The amount of petrol left is (x/2) - 2

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The fraction of the entire space jenny use for pink roses is 1/8 of the whole garden

A word problem in math is a math question written as one sentence or more that requires children to apply their math knowledge to a 'real-life' scenario.

These word problem are translated into mathematical equations.

Represent the total garden by x

Jenny uses 1/2 of the garden to plant roses

= 1/2×x = x/2

She uses 1/4 of the space to plant pink roses

= 1/4 × ×/2

= x/8

Therefore she uses 1/8 of the whole garden to plant pink roses.

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The equation for the given scenario is y=50/57x-3.16.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

From the given figure, the coordinate points are (129, 110) and (300, 260).

Substitute (x₁, y₁)=(129, 110) and (x₂, y₂=(300, 260) is slope formula, we get

Slope (m) =(260-110)/(300-129)

= 150/171

= 50/57

Substitute, m=50/57 and (x, y)=(129, 110) in y=mx+c, we get

110=50/57 (129)+c

110=113.16+c

c= -3.16

Substitute, m=50/57 and c= -3.16 in y=mx+c, we get

y=50/57x-3.16

Therefore, the equation for the given scenario is y=50/57x-3.16.

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The first truck did 62% of all the job.

First, from the problem we know that the first truck does its job at a rate per hour:

And, the second truck has a rate per hour of:

So, the rate per hour with both trucks working together will be the sum:

Now, we have to find the time it will take to do the whole job with both trucks, the whole job done will be represented by 100% or 1:

Where t is the unknown time that it takes to do all the job. Solving this we have:

This means that the whole job will be done after 3.08 hours using both trucks. However, the problem is asking just about the first truck. To find that answer we just have to multiply its rate with the time:

This decimal number represents the portion that the first truck finished to have the job done. 0.62 means that it did 62% of all the job.

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correct question:

The city just assigned a second garbage truck to empty the bins in Kat’s neighborhood on trash day. The crew from the first garbage truck used to empty all the bins by themselves in 5 hours. In their training, it took the crew from the second garbage truck 8 hours to empty all the bins. When the two crews start working together, what part of all the garbage bins will the first garbage truck empty? To the nearest tenth, the first garbage truck will empty about of all the bins.

Answer:

Step-by-step explanation:

When the two crews start working together, the part of all the garbage bins that the first garbage truck will empty is; A: 0.6

We are told that the first truck empties all bins in 5 hours. Thus;

Rate of first truck per hour = ¹/₅

Second truck empties all bins in 8 hours. Thus;

Rate of second truck per hour = ¹/₈

If both trucks work together, their rate per hour is;

Combined rate per hour = ¹/₅ + ¹/₈

Combined rate per hour = ¹³/₄₀

Thus, number of hours it will take for both of them to do the whole job, we will solve as;

¹³/₄₀t = 1

where t is the time it will take both of them combined to finish the whole job.

Thus;

t = ⁴⁰/₁₃

The part that the first garbage truck will empty when they both work together = ¹/₅t = ¹/₅ * ⁴⁰/₁₃

⇒ Approximately 0.6

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In Pavlov's experiments, he paired the presentation of food with a buzzer and measured salivation to each. In this (b) conditioned stimulus (CS)

Like many great scientific advances, Pavlovian conditioning (aka classical conditioning) was discovered accidentally. Ivan Petrovich Pavlov (1849–1936) was a physiologist, not a psychologist.

During the 1890s, Russian physiologist, Ivan Pavlov was researching salivation in dogs in response to being fed. He inserted a small test tube into the cheek of each dog to measure saliva when the dogs were fed (with a powder made from meat).

Pavlov predicted the dogs would salivate in response to the food placed in front of them, but he noticed that his dogs would begin to salivate whenever they heard the footsteps of his assistant who was bringing them the food.

The complete question is-

In Pavlov's experiments, he paired the presentation of food with a buzzer and measured salivation to each. In this

experiment the buzzer was the ___.

A. unconditioned stimulus (US)

B. conditioned stimulus (CS)

C. unconditioned response (UR)

D. conditioned response (CR)

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As a result, the coordinate of the picture of point B (4, 9) under dilation with the origin as the center and a scale factor of 2 is (8, 18).

Coordinates are a pair of integers that are used to locate a point or object in a two-dimensional plane. A point's location on a 2D plane is defined by two integers called the x-coordinate and the y-coordinate. The distance between two points is known as the x-coordinate, or abscissa, while the distance between two points is known as the y-coordinate, or ordinate. Point (3, 2), for example, is three units distant from the positive y-axis and two units away from the positive x-axis.

Here,

A dilation with center at the origin and scale factor of 2 will stretch or shrink the distances from the origin by a factor of 2. If the given point B is (4,9), its image under the dilation will be:

(2 * 4, 2 * 9) = (8, 18)

So the coordinate of the image of point B (4, 9) under the dilation with center at the origin and scale factor of 2 is (8, 18).

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Correct Answer is c. Phyllis has a comparative advantage in producing cakes.

What is comparative advantage?

Comparative advantage is an economic concept that refers to the ability of an individual, firm, or country to produce a particular good or service more efficiently compared to others.

The opportunity cost of producing one cake for John is (20 loaves of bread) / (18 cakes) = 1.11 loaves of bread per cake.

The opportunity cost of producing one cake for Phyllis is (30 loaves of bread) / (15 cakes) = 2 loaves of bread per cake.

Since Phyllis has a lower opportunity cost of producing cakes (2 loaves of bread per cake) compared to John (1.11 loaves of bread per cake), Hence, Phyllis has a comparative advantage in producing cakes.

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(22 x 12) x 9 or 22 x 12 x 9. In both cases, the product is obtained by multiplying 22 by 12, and then multiplying that result by 9, which gives us 3024.

The associative law of multiplication states that the way in which the numbers are grouped within an expression does not change the product. In other words, you can change the grouping of the factors and still obtain the same result. For example, the expression 22 x (12 x 9) can be rewritten as (22 x 12) x 9 or 22 x 12 x 9, and the product will be the same in all cases.

In the expression 22 x (12 x 9),

the associative law can be used to rearrange the factors into

(22 x 12) x 9 or

22 x 12 x 9.

In both cases, the product is obtained by multiplying 22 by 12, and then multiplying that result by 9, which gives us 3024.

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Answer:

  36 square units

Step-by-step explanation:

You want the area of the parallelogram with vertex coordinates (-6, 6), (-9, -3), (-5, -3), (-2, 6).

The area of a parallelogram is the product of the base length and the height perpendicular to that base.

Here, the base is a horizontal line, so its length is the difference of the x-coordinates of the end points:

  -5 -(-9) = 4 . . . . base

The height is the difference of y-coordinates between the top edge and the bottom edge:

  6 -(-3) = 9 . . . . height

Then the area is ...

  A = bh = 4·9 = 36 . . . . square units

The solution of the inequality are shown in figure.

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequalities are,

⇒ x + 1 < 9

⇒ 4x ≤ 8

Now, We can simplify as;

⇒ x + 1 < 9

Subtract 1 both side;

⇒ x < 9 - 1

⇒ x < 8

⇒ 4x ≤ 8

Divide by 4;

⇒ x ≤ 4

Thus, The solution of the inequality are shown in figure.

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It should be noted that r = [(s - a)(s - b) (s - c)/s]1/2, dimensionally consistent.

The radius a of a circle inscribed by an isosceles triangle whose sides are A, B and C is given.

r = [(s - a)(s - b) (s - c)/s]1/2, where s = (a + b + c)/2.

a, b , c actual lengths of the sides,

s = average length of the sides

So that we can write

L = [(L - L)(L - L) (L - L)/L]^1/2

= [(L)(L) (L)/L]^1/2

= [L^2]^1/2

= L

Therefore r = [(s - a)(s - b) (s - c)/s]1/2, dimensionally consistent.

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Answer:

6.5

Step-by-step explanation:

C = 2πr

40.841/2π = r

6.5 = r

Answer:

○ [tex]\displaystyle 6,5\:ft.[/tex]

Step-by-step explanation:

[tex]\displaystyle {\pi}d = C \\ 13,000094062…{\pi} = 40,841 \\ \\ \boxed{6,5000470308…} = \frac{13,000094062…}{2} \\ \\ \\ \boxed{\boxed{6,5 \approx r}}[/tex]

I am joyous to assist you at any time.

We would give 4.78 mg of Gentamicin to baby Nathaniel.

Unit conversion means the conversion between different units and measurements of the same quantity done by the process of multiplication or division.

Given,

Dosage of Gentamicin per kg = 1.3 mg/kg

Weight of the baby = 8.1pounds

1 pound = 0.4536 kg

8.1 pounds = 3.674 kg

Weight of the baby in kilograms = 3.674 kg

Then dosage to the baby = 3.674 × 1.3

                                          = 4.7762 ≈ 4.78mg

Hence, 4.78 mg of Gentamicin, baby Nathaniel would receive.

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Each builder will be paid £32.55 for work on tuesday.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that on Monday it took 5 people, three and half hours to build a wall. An identical wall needs to be built on Tuesday but only 2 people are available. Each person is paid £9.30 for each hour or part of an hour they work.

5 people take 3.5 hours to build a wall.

1 person will take (3.5/5) hours to build a wall.

2 persons will take (3.5/5 x 2) hours to build a wall.

1 person is paid £9.30 for each hour. So 2 persons will get -

£{9.30 x 3.5/5 x 2}

£32.55

Therefore, each builder will be paid £32.55 for work on tuesday.

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The Supreme Court's interpretation of numerous constitutional amendments did not result in the creation of the right to privacy or any of the other three privacy rights. The average freedom against arbitrary searches and seizures, the right to due process, and the right to free speech are the three privacy rights.

The Supreme Court's interpretation of numerous constitutional amendments did not result in the creation of the right to privacy or any of the other three privacy rights. The freedom against arbitrary searches and seizures, the right to due process, and the right to free speech are the three privacy rights. The Fourth, Fifth, and First Amendments of the Constitution, respectively, gave rise to these rights. The right to privacy has been developed and is safeguarded by the Supreme Court through its interpretation of the various amendments, despite the fact that it is not expressly stated in the Constitution. Individuals are protected by the right to privacy from having their private information or activities revealed without their permission.  Additionally, it gives people the freedom to decide how they want to live their life, including the right to marry, the right to access contraception, and the right to help getting an abortion. Despite not being one of the three privacy rights established by the Supreme Court, the right to privacy is still a crucial kind of protection for people. It guarantees that people have control over the information they share, the choices they make, and the respect for their privacy.

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The complete question is

which of the following is not one of the three privacy rights created by the supreme court through its interpretation of various constitutional amendments right to privacy or any of the other three privacy rights.

To find points on a Cartesian plane, you need to know the x and y coordinates of the point. The Cartesian plane has two axes, the x-axis and the y-axis, which intersect at the origin (0, 0).

The x-coordinate of a point tells you how far the point is from the y-axis, either to the right (if the coordinate is positive) or to the left (if the coordinate is negative).

The y-coordinate of a point tells you how far the point is from the x-axis, either up (if the coordinate is positive) or down (if the coordinate is negative).

So, to find a point on the Cartesian plane, you need to know both its x and y coordinates. For example, the point (3, 4) is located 3 units to the right of the y-axis and 4 units up from the x-axis.

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Since z is directly proportional to the product of x and y, then x, y, and z are related by this equation: z = xy/2.

Mathematically, a proportional relationship or direct variation can be represented by the following equation:

y = kx

Where:

Based on the information provided, we have the following:

z ∝ xy

z = kxy

In order to have a proportional relationship and equivalent ratios, the variables z, x, and y must have the same constant of proportionality:

Constant of proportionality (k) = z/xy

Constant of proportionality (k) = 15/(5 × 6)

Constant of proportionality (k) = 15/30

Constant of proportionality (k) = 1/2.

For the equation, we have:

z = kxy

z = 1/2 × xy

z = xy/2

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By adding improper fractions 5/12 + 1/4, we get 8/12 or 2/3.

What is the least common multiple?

The LCM is multiple which is useful if fractions need to be expressed in the same name, and the further discussion can be defined as follows: When the other number is multiple, LCM will have the larger number: Example: So, the 2 and 4 LCM.

1/4 and 5/12 do not have a common denominator, so we first take LCM of the denominators.

LCM = 12

Therefore, we make 1/4 with denominator 12,

i.e, 1x3/4x3 = 3/12

Now, we can add the two fractions which have a common denominator.

3+5/12 = 8/12 which can be simplified to 2/3 (after cutting the numerator and denominator with 4.)

Hence, by adding improper fractions 5/12 + 1/4, we get 8/12 or 2/3.

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The average T2, T7, T6, T4, and T10 in Processor 1

T8, T9, T3, T1, and T5 on Processor 2.

Work on tasks t2, t7, t6, t4, and t10 will be done by processor 1. The first task to be finished is task t2, followed by tasks t7, t6, t4, and lastly t10. Work on tasks t8, t9, t3, t1, and t5 will be done by processor 2. The first work to be finished is task t8, followed by t9, t3, t1, and ultimately t5. In order to finish the job quickly, both processors will cooperate, with Processor 1 concentrating on the early tasks and Processor 2 concentrating on the later duties. This guarantees that the project is finished on schedule and that all the tasks are carried out in the proper order.

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