Pls help! Step by step

Pls Help! Step By Step

Answers

Answer 1

Answer:

x = 6[tex]\sqrt{2}[/tex]

Step-by-step explanation:

using the cosine ratio in the right triangle and the exact value

cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then

cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{6}{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

x = 6[tex]\sqrt{2}[/tex]

This is the exact value for x. It may be rounded if you wish

Answer 2

Answer:

[tex]x=6\sqrt{2}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

From inspection of the given right triangle:

θ = 45°A = 6H = x

Substitute the given values into the cosine trigonometric ratio and solve for x:

[tex]\implies \cos(45^{\circ})=\dfrac{6}{x}[/tex]

[tex]\implies \dfrac{\sqrt{2}}{2}=\dfrac{6}{x}[/tex]

[tex]\implies x\sqrt{2}=6 \cdot 2[/tex]

[tex]\implies x\sqrt{2}=12[/tex]

[tex]\implies x=\dfrac{12}{\sqrt{2}}[/tex]

[tex]\implies x=\dfrac{12}{\sqrt{2}}\cdot \dfrac{\sqrt{2}}{\sqrt{2}}[/tex]

[tex]\implies x=\dfrac{12\sqrt{2}}{2}[/tex]

[tex]\implies x=6\sqrt{2}[/tex]


Related Questions

Write the expression as a number in scientific notation.

the quantity 4.2 times ten to the fifth power end quantity times the quantity 1.5 times ten to the negative eighth power end quantity all divided by the quantity 2.5 times ten to the negative fourth power end quantity

2.52 × 10−1
2.52 × 101
3.2 × 10−7
3.2 × 107

Answers

On solving the provided question, we can say that - the answer of the following equation is = [tex](4.2 X 10^5)(1.5 X 10^3) / 2.5 X 10^4[/tex] = 25.2

What is equation?

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

[tex](4.2 X 10^5)(1.5 X 10^3) / 2.5 X 10^4[/tex]

630000/25000

25.2

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

Which object has the largest resultant force?
10N-
10N-
30 N-
A
C
30 N
5N
-5N
10N-
5N-
5N-
5N-
B
D
10N
10 N

Answers

Answer:

To find the resultant force of an object, we need to add up all the forces acting on it. The resultant force is the overall force that the object experiences, taking into account all the individual forces.

In this case, we are given four objects, A, B, C, and D, and the forces acting on them. To find the object with the largest resultant force, we need to calculate the resultant force for each object by adding up all the forces acting on it.

For object A, the forces acting on it are: 10 N, 10 N, and 10 N, for a total of 10 N + 10 N + 10 N = 30 N.

For object B, the forces acting on it are: 5 N, 5 N, 5 N, and 5 N, for a total of 5 N + 5 N + 5 N + 5 N = 20 N.

For object C, the forces acting on it are: 30 N and -5 N, for a total of 30 N + (-5 N) = 25 N.

For object D, the forces acting on it are: 10 N and -5 N, for a total of 10 N + (-5 N) = 5 N.

Therefore, the object with the largest resultant force is object C, with a resultant force of 25 N.

Help me

Like just draw on it

Answers

Answer:

Step-by-step explanation:

if a Relation is a Function
in the
1) ((−1, 8), (0, 15), (1, –4), (2, 0)) 2) {(-5, 2), (5, 2), (0, -3), (3,-8)) 3) ((-2, 7), (6, 2), (−2, −3), (0, 9))
is a function
because there is not any
Points which have the
X-Coordinate and differen
y-Coordinates.
4) {(7,2), (4,-6), (2,-2). (4,-9)} 5) {(2, 3), (2, 4), (2, 5), (2,6)}
6) {(1,4), (2,4), (3, 4), (4-4)}

Answers

1). The relation given; { (−1, 8), (0, 15), (1, –4), (2, 0) } as given is a function.

2). The relation given; { (-5, 2), (5, 2), (0, -3), (3,-8) } as given is a function.

3). The relation given; { (-2, 7), (6, 2), (−2, −3), (0, 9) } as given is not a function.

4). The relation given; { (7,2), (4,-6), (2,-2). (4,-9) } as given is not a function.

5). The relation given; { (2, 3), (2, 4), (2, 5), (2,6) } as given is not a function.

6). The relation given; { (1,4), (2, 4), (3, 4), (4, -4) } as given is a function.

What is a function?

It is important to know that a function is a special kind of relation in which case no one input value, x is assigned more than one output value.

On this note, when a relation is such that one of its input values is assigned two or more output values; such relation is not a function.

Read more on function;

https://brainly.com/question/10439235

#SPJ1

The four approved methods of document destruction are

Answers

Answer:

1area

2 water

3 food

4 house

Answer:

shredding, incineration, pulping, and pulverization.

Step-by-step explanation:

Shredding: This involves cutting paper into small pieces using a shredding machine. The shreds are usually too small to be reconstructed, making it an effective method for destroying sensitive documents.

Incineration: This involves burning paper to ash using high heat. Incineration is a fast and efficient way to destroy large volumes of documents, but it is not always practical or environmentally friendly.

Pulping: This involves breaking down paper using water and chemicals to create a slurry that can be recycled or disposed of. This method is effective for destroying large volumes of paper, but it is not suitable for destroying documents with sensitive information.

Pulverization: This involves grinding paper into a fine powder using a pulverization machine. The powder is then disposed of or recycled. This method is effective for destroying documents with sensitive information, but it is not practical for destroying large volumes of paper.

There are a total of 32 books and calculators on a table. The ratio of the number of books to the
number of calculators is 5: 3. How many calculators are on the table?
A. 3
B. 12
C. 20
D. 24

Answers

Answer:

B. 12

Step-by-step explanation:

Your ratio of 5:3 means that the ratio includes 8 objects (5+3). If you multiply the whole ratio by 4, then you have 32 objects on your table. Multiplying your ratio by 4 gives you 5*4 : 3*4 which is 20:12. and since 20 is your amount of books and 12 is your amount of calculators, you have 12 calculators on your table.

A cylindrical tank has a diameter of 30m and height 20m.
a) Find its volume in m³, correct to two decimal places.
b) What is the capacity of the tank in litres?​

Answers

Step-by-step explanation:

d = 30m, so r = 15m

h = 20m

We know,

V = πr^2h

= (22×15×15×20)/7 [Taking π = 22/7]

= 14142.86m^3

= 14142875.14 litres

4 3/5+ 2 2/3= l need someone to help me out

Answers

Here’s the answer I hope it helps

Your parents allow you to borrow a car to get to your part-time job, but you have to pay for a tank of gas each month. Gasoline costs $2.76/gallon and the tank takes 15 gallons. You have 2 coworkers who are each willing to pay for a quarter of a tank each month to carpool with you to work. How much do you save each month?


$16.46


$20.70


$15.91


$18.55

Answers

20.70 is your answer

determine if each liners function is a direct variation. If it is state the constant of variation.

Answers

The liners function are not direct variation

What is a direct variation?

The relationship between two variables in which one is a constant multiple of the other is referred to as direct variation.

For instance, two variables are said to be in proportion when one affects the other. b = ka is the equation

If b is directly proportional to a, then k is the constant of variation and the value of k = b/a for all value of b and a

In the problem, the variables are compared as follows

feet = k * sec

k = feet / sec

For the first values, k = 33 / 3 = 11

For the second values, k = 36 / 6 = 6

since 11 ≠ 6 the function is not a direct variation

Learn more about direct variation at:

https://brainly.com/question/25215474

#SPJ1

12 divided by four
plus 2 x 6+4

Answers

Answer:

19

Step-by-step explanation:

12 divided by four plus 2 x 6+4

assuming that the question is:

12 : 4 + 2 x 6 + 4 =

3 + 12 + 4 =                     (remember PEMDAS)

19

Marissa and Kyle own a total of 66 dvds. Kyle owns 3 more than twice as many dvds as marissa. how many dvds does marissa own?

Answers

The number of Dvds owned by Maarissa is 45

How to find the number of dvds?

The given parameters that will guide us in finding the number  of dvds owned by marissa are

Marissa and Kyle own a total of 66 dvds. Kyle owns 3 more than twice as many dvds as marissa.

Let the number of dvds owned by Marissa be x

Nymber of dvds owned by Kyle be y

This implies that  x+y = 66 ............................1

also, 2y + 3 = x ..................................................2

Substitute x = 2y + 3 in equation 1

= 2y + 3+y =66 Collecting like terms

⇒ 3y = 63

Making y the subject of the relation we have y=21

Recall that  2y + 3 = x

That means x = 2(21) + 3

x=45

Therefore Marrissa owns 45 dvds

Learn more about word problems on https://brainly.com/question/29027588

#SPJ1

If the probability of s1 = .6 and the probability of F = .40 what is the value at node 4.
Group of answer choices

320

280

310

260

200

Answers

If the probability of s1 = .6 the value above node degree 4 will be 320, as determined by the solution.

What does a node's degree mean?

The area of mathematics known as probability deals with numerical descriptions about how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

According to the given information:

S1 probability = 0.6

F's likelihood is 0.40.

If the probability of S1 is given a value of 0.6, then

Probability of S2 then equals 0.4.

Using the table equation's payoff values as an exception.

EV=Σ

Each decision's expected value is calculated.

EV(Node 8) = 0.6 * 100 + 0.4 * 300

= 180

EV(Node 9) = 0.6 * 400 + 0.4 * 200= 320

We chose the best value for node 4 from nodes 8 and 9.

The ideal option for node 9 is the line complicated branch with EV(node 8) = 180.

The ideal anticipated value is determined to be 320.

Node 4's EV is 320.

To know more about probability visit:

https://brainly.com/question/30034780

#SPJ1

(7/8 x 14) / (3/8 x 6) + 2 1/5

Answers

Answer:

7/8 x 14= 12.25 or 49/4 or 12 1/4

(3/8 x 6) + 2 1/5= 4.45

(hope this helps I probably wasn't fully understanding)

a doughnut factory can make 1980 doughnuts in 1.5 hr how long would it take to make 6600 doughnuts

Answers

Answer: 5 Hours

Step-by-step explanation:

Divide 6600 by the amount per 1.5 hours.

6600 / 1980 = 3.333

Multiply the answer by the 1.5 hours.

1.5 x 3.333 = 5

Six families went to the food festival. Each family has 2 adults and 4 children. The entry fee for each child ticket costs $4, and an adult ticket costs $8. What would be the total cost of the festival tickets?

Answers

By solving an expression we will see that the total cost for the tickets is $192.

What would be the total cost of the festival tickets?

We know that six families went to the food festival, each family has 2 adults and 4 children, then there are:

6*2 = 12 adults in total.

6*4 = 24 children in total.

We know that each child ticket costs $4, and an adult ticket costs $8, then the total cost of all the tickets is what we get when we solve the expression below:

12*$8 + 24*$4

That is, the number of adults times the cost of an adult ticket plus the number of children times the cost of a children ticket.

The total cost is then:

12*$8 + 24*$4 = $192

Learn more about solving expressions:

https://brainly.com/question/723406

#SPJ1

is 50 tens x 4 hundreds =40 tens x 5 hundreds true or false

Answers

Answer:

True, 50 tens times hundreds equal 40 tens times 5 hundreds

Step-by-step explanation:

50 tens times 4 hundreds equals to 40 ten times 5

hundreds because if you multiply 50 by 4 hundreds

you'll get 20,000 and if you multiply 40 tens by

hundred it will still give you 20,000

Therefore:

50 × 400 = 40 × 500

20,000 = 20,000

Elaina bought 4.6 pounds of sliced ham at a price of $6.15 per pound. How much did she spend in total? quick

Answers

Answer:

$28.29

Step-by-step explanation:

1 pound: $6.15
4.6 pounds: 6.15 x 4.6 = $28.29

Ryan spots an airplane on radar that is currently approaching in a straight line, and
that will fly directly overhead. The plane maintains a constant altitude of 6300 feet.
Ryan initially measures an angle of elevation of 15 to the plane at point A. At some
later time, he measures an angle of elevation of 31 to the plane at point B. Find the
distance the plane traveled from point A to point B. Round your answer to the
nearest foot if necessary.

Answers

If Ryan spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The  distance the plane traveled from point A to point B is: 13,027ft .

How to find the distance?

Constant altitude =6300 feet

Angle of elevation =15 to the plane at point A

An angle of elevation =31 to the plane at point B.

So,

Tan 15° = 6300/ON

ON =23,511.92

Tan 31° =6300/OB

OB = 10,484.96

So,

AB =23,511.92 - 10,484.06

AB = 13,026.96

AB = 13,027ft (Approximately)

Therefore the distance is 13,027ft.

Learn more about distance here:https://brainly.com/question/26550516

#SPJ1

A builder buys a 21.5 acres of land to develop a new community of homes and parks.The builder plans to use 0.75 of the land for a park.How many acres will he use for the park?

Answers

He will use 9.375 acres of the land for the park

How to determine how many acres he will use for the park?

A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole.

Since the land is 21.5 acres and 0.75 of the land  was used for a park. we can write:

acres used for the park = 0.75 × 12.5 = 9.375 acres

Thus, he will use 9.375 acres for the park

Learn more about fractions on:

brainly.com/question/11562149

#SPJ1

What is 507 less than 607

Answers

Yes 607 is a greater number which makes 507 LESS! Please mark brainliest

find an equation for the line that passes through the points (-6,-3) and (4,5).

Answers

The equation of the line that passes through the points (- 6, - 3) and (4, 5) is y = (4 / 5) · x.

How to determine the equation of the line from two points

In this question we have the knowledge of two points, of which we must derive the equation of a line, whose definition is shown below:

y = m · x + b

Where:

x - Independent variable.y - Dependent variable.m - Slopeb - y-Intercept

The slope of the line can be determined by secant line formula:

m = Δy / Δx

Where:

Δx - Change in independent variable.Δy - Change in dependent variable.

First, determine the slope of the line:

m = [5 - (- 3)] / [4 - (- 6)]

m = 8 / 10

m = 4 / 5

Second, determine the intercept of the line:

b = y - m · x

b = 5 - (4 / 5) · 4

b = 5 - 5

b = 0

Third, write the equation of the line:

y = (4 / 5) · x

To learn more on equation of the line: https://brainly.com/question/2564656

#SPJ1

The Singh family ordered a large pizza with a diameter of 16 inches for dinner. If one of the members of the family ate one eighth of the pizza, how many square inches of pizza are remaining? Use 3.14 for π.

200.96 square inches
175.84 square inches
100.48 square inches
25.12 square inches

Answers

Answer: D

Step-by-step explanation: 25.12

Answer: The actual answer is (175.84 square inches)

Step-by-step explanation:

First, find the area of the pizza.

You need to use the formula for area of a circle: A = πr^2

or in words, the area of a circle is equal to pi times radius to the second power.

So find the radius which is half the diameter.

The diameter is 16 inches, so the radius is 8 inches.

Now raise 8 to the second power, meaning that you need to times 8 by 8

(8 * 8 = 64) Now you times 64 by pi or 3.14. (64 * 3.14 = 200.96)

That is the area of the entire pizza.

But you still need to find how many square inches are left after 1/8 is eaten.

If 1/8 is eaten, then that means the pizza is divided into eighths.

Take 200.96 and divided that by 8 to find how much the individual pieces are.

200.96/8 = 25.12

But you need to find what is left is the pizza, so times 25.12 by 7 because that is how many pieces are left. 25.12 * 7 = 175.84

Sorry for the long explanation, but here is proof that the answer is correct. I took the same test and got the answer right

Here is a photo from my test:

Have a good day

Make 4 equal warehouses out of a fence 300 m long. What is the width and length of the sv part if we want them to be the largest possible areas

Answers

The width and the length that gives the largest possible areas are 75 meters by 37.5 meters

How to determine the width and the length that gives the largest possible areas

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

Number of warehouses = 4

Perimeter of fence = 300 meters

Represent the width with x and the length with y

So, we have the following equations

Area = 4xy

Perimeter = 2(4x + y)

Substitute the known values in the above equation, so, we have the following representation

2(4x + y) = 300

Divide both sides by 2

2x + y = 150

Make y the subject

y = 150 - 2x

Substitute y = 150 - 2x in Area = 4xy

A = 4x(150 - 2x)

This gives

A = 600x - 8x²

Differentiate and set to 0

600 - 16x = 0

So, we have

16x = 600

Divide by 16

x = 37.5

Recall that

y = 150 - 2x

So, we have

y = 150 - 2 x 37.5

Evaluate

y = 75

Hence, the dimensions are 75 meters by 37.5 meters

Read more about area at

https://brainly.com/question/24487155

#SPJ1

16. Find the length of x.

Answers

Answer: 4.8

Step-by-step explanation: By using the intersecting chords theorem, we know that 10 * x = 6 * 8

This simplifies to 10x = 48

After dividing both sides by 10 we get x = 4.8

A system of linear equations with an infinite number of solutions is a(n) __________ system.

Answers

A system of linear equations with an infinite number of solutions is a(n) equivalent equations system.

What is the equation?

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

here,
When a system of linear equations consists of an infinite number of solutions then this equation should be dependent and consistent as well, and this system is said to be a system of equivalent equations.

Thus, A system of linear equations with an infinite number of solutions is a(n) equivalent equations system.

Learn more about equations here:

brainly.com/question/10413253

#SPJ1

help please!!!!!!!!!!!!!!!!!!!!1

Answers

Answer:

Not a function

Step-by-step explanation:

A function is when every input(x) has only one output (y).  The input 1 has two outputs (0 and 1) so it is not a function.

If you shift the cubic parent function, F(x)=x^3, down 9 units, what is the equation of the new function

Answers

Therefore the table values of which represents a linear function are table 2 and table 3

What is linear equation?

A linear equation is a first-order (linear) term and a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. A "linear equation of two variables" is what is sometimes referred to here, where y and x are the variables.

Here,

The values shown in table 2 have same constant rate of change of 3 units.

where as,

The values shown in table 3 have same constant rate of change of 5 units.

Therefore the table values of which represents a linear function are table 2 and table 3

To know more about linear equation , visit

brainly.com/question/12974594

#SPJ1

You are given 2 parallel lines on the coordinate plane. You are told to translate x + 3,y-2, rotate 180° clockwise about the origin, then reflect over the y-axis. After the transformations you will have what type of lines?

A Intersecting lines
B. The Same Line
C. Parallel Lines

Answers

Since matching angles are formed and the equal corners are congruent when a line joins two parallel lines, one of the choices isc=d.

Parallel lines are what?

Geometry refers to parallel lines as beams, straight lines that never overlap. Parallel planes are those that never cross each other while occupying the same three-dimensional space. Curves which are equal with each other and keep a predetermined minimum separation from one another must not overlap or intersect. Parallel lines on a plane are those that always have the same distance between them. A parallel line cannot be crossed. Perpendicular lines are those that intersect directly at a 90 degree angle.

Here,

Given :  vertical angles, A = d also represents a solution.

B+d=180 as a result of b+c=180 therefore

B+d=180 as a result of b+c=180 therefore Since a=d, c=d, and b+d=180, the answer is B,C,E.

To know more about parallel lines visit:

brainly.com/question/16701300

#SPJ1

Does the table below represent a proportional relationship?

A. Yes, because all the ratios of y to x are equal to 2.

B. Yes, because all the ratios of y to x are equal to 3.

C. No, because all the ratios of y to x are not equal.

D. No, because all the numbers are positive.

Answers

The table represents a proportional relationship because all the ratios of y to x are equal to 3. (option B)

What is a proportional relationship?

Two variables exhibit a proportional relationship if the constant of proportionality remains constant for all the given values in the table.

The equation that is used to represent a proportional relationship is:

y = kx

Where:

k = constant of proportionality

Value of k when x is 1:

3 = k

Value of k when x is 2:

6 = 2k

k = 6 / 2

k = 3

Value of k when x is 3:

9 = 3k

k = 9 / 3

k = 3

Value of k when x is 4:

12 = 4k

k = 12 / 4

k = 3

To learn more about proportional relationships, please check: https://brainly.com/question/20048815

#SPJ1

Other Questions
11c+ 8) (-9c - 1)Help plssss Write an equation Y=|x| 10 units down A sound wave generated by a musical note has the characteristics presented in the table. What is the missing value?Air 346 55 6. 3Glass 5,640 55 102Brass 4,700 55 ?A. 112B. 100C. 85D. 98 The question states "The amplitude of a body undergoing simple harmonic motion is doubled. Which of the following is also doubled?a) maximum speedb) frequencyc) total energyd) period You have $50,000 in savings for retirement in an investment earning a stated annual rate of 7% compounded monthly. You aspire to have $1,000,000 in savings when you retire. Assuming you add no more to your savings, how many years will it take to reach your goal Other parts of a web page that a search engine robot may examine include: a. The title, meta tag descriptions and some text within the web page. b. The background page color c. The types of fonts used within the web paged. The operating system it was developed on. A team of scientists is developing a computer model to predict the change in average global temperatures over the next 100 years. The model accounts for a wide variety of variables that could affect temperature during this time. Which variable would most likely affect the temperatures that the model predicts The dedication of citizens to the common welfare of their community or country, even at the cost of his or her individual interests. Both citizens and leaders are willing to set aside what they want for the common good. P4(s) + Cl(g) PCI3(l) + energy 4. Calculate the gram-formula mass of the product. Show all work. g/mol In the six weeks, Shapera mowed 7 lawns, worked 36 hours at the pet store, and delivered newspapers 7 days. Did she make enough to buy the computer? Explain your answer which of these actions would most likely decrease a persons net worth for at least the next 6 months? 5. A study conducted in North Carolina on weight gain during pregnancy. According to data from the entire registry (population), the number of pounds gained during pregnancy was approximately normally distributed with a mean of 0.23 pounds and a standard deviation of 13.84 pounds. Calculate the probability that a randomly selected mother in North Carolina gained weight Question content area topPart 1Which of the following expressions is equivalent to 12x32x13?Question content area bottomPart 1Select all that apply.A.10x16B.2(7x5)C.17x13D.14x16E.14x10 Tell whether each system of equations has no solution, one solution, or infinitely many solutions. Show how you arrived at your conclusion for each. a. y = 5x + 11 and y = 5x b. y = 6x + 3 and y = 3x c. x + 4y = 8 and y = -1/4x + 2 The emergence of a protected, extended stage of childhood in the 1800s occurred as a result ofA. legal restrictions on how children were treated.B. a growing population of elderly (and therefore grandparents).C. greater economic resources of parents.D. the spread of schooling and a decline in child deaths. how does producing various goods make a country stronger in Ancient China?Plsssss help meeeee What is the reason for some people being opposed to capital punishment? They believe it violates the Eight Amendment regarding cruel and unusual punishment. All of these people believe that life is sacred and that individuals should never die. People against capital punishment see all inmates as responsible citizens that must be returned to society. Capital punishment opponents all believe that probation will solve all of the problems of overcrowding What is the value of 5 by 2? Individuals who have been crime victims maintain a significantly higher chance of future victimization than people who have remained nonvictims. A. True B. False A sentence that specifies a given amount of time to be served in custody and allows little or no variation from the time specified is called a(n):