Airlines limit the size of carry-on luggage, so that the sum of the length, width, and height of a piece of luggage cannot exceed 55 inches. A passenger has a box with a base which measures 15 inches by 20 inches. Which inequality represents the possible height (h) of the box, so that the airline will allow it to be carried on the plane?

Answers

Answer 1

The inequality that represents the possible height (h) of the box is h ≤ 20

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Let h represent the height of the box. The base measures 15 inches by 20 inches and the height cannot exceed 55 inches. Hence:

height + length + width ≤ 55

h + 20 + 15 ≤ 55

h ≤ 20

The inequality that represents the possible height (h) of the box is h ≤ 20

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Related Questions

Help Please!! If cos theta = - square root 2/2 and pie/2 < theta < pie, what are the values of sin theta and tan theta? What is theta in degrees and radians?

Answers

The values of the sine and tangent of the angle are √2 / 2 and - 1. By using inverse trigonometric functions, the value of angle is 135° (3π / 4).

How to find the values of other trigonometric functions and the angle behind them

According to the statement, the cosine of the angle is in the second quadrant and therefore the value of the sine must be positive and the value of the tangent must be negative. Then, the value of the sine is found by the fundamental formula:

sin θ = √(1 - cos² θ)

sin θ = √[1 - (- √2 / 2)²]

sin θ = √(1 - 1 / 2)

sin θ = √(1 / 2)

sin θ = √2 / 2

And the value of the tangent:

tan θ = sin θ / cos θ

tan θ = (√2 / 2) / (- √2 / 2)

tan θ = - 1

By using inverse trigonometric functions, we find that the value of angle is 135° (3π / 4).

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12 divided by 3 - 6(2) -8 divided by 4

Answers

The answer is -10 because division and multiplication must be done first. Subtraction and addition is done after.

First make a substitution, and then use integration by parts to evaluate the integral.

Answers

Answer: 1/2 ([tex]\pi[/tex]) sin [tex]\pi[/tex] + ∫ x cos [tex]\pi ^{2}[/tex] dx + c

1/2 ([tex]\frac{\pi }{2}[/tex]) sin [tex]\frac{\pi }{2}[/tex] + ∫ x cos [tex]\frac{\pi }{2} ^{2}[/tex] dx + c

Step-by-step explanation:

We can't just integrate straight away, so we try substitution.

While trying substitution, we observe that we could integrate cos([tex]x^{2}[/tex]) x dx

by substitution.

So, let's split the integrand and use integration by parts.

we can represent θ = x,

so, we can write,

= ∫[tex]x^{3} cos x^{2} dx[/tex]

= ∫ [tex]x^{2} cos (x^{2} )xdx[/tex]

We notice that we could rewrite this as ∫ u cos(u) 1/2 du, but we don't see how to integrate that, so we'll continue with parts for now.)

= ∫ [tex]x^{2} cos (x^{2} )xdx[/tex]

Let u=[tex]x^{2}[/tex] and dv = [tex]cos(x^{2} )xdx[/tex]

Clearly du= 2x dx, and

we can integrate dv by substitution to get.

= 1/2 sin [tex]x^{2}[/tex]

uv - ∫ vdu = 1/2 [tex]x^{2}[/tex] sin([tex]x^{2}[/tex]) - ∫ x sin ([tex]x^{2}[/tex]) dx

Integrate by substitution again to finish.

∫ [tex]x^{3} cos (x^{2}) dx[/tex] = 1/2 [tex]x^{2} sin x^{2}[/tex] + ∫ x cos [tex]x^{2}[/tex] dx + c

Then,

x = √[tex]\pi[/tex] and √[tex]\frac{\pi }{2}[/tex]

∫ [tex]x^{3}[/tex] cos [tex]x^{2}[/tex] dx = 1/2 (√[tex]\pi ^{2}[/tex]) sin √[tex]\pi ^{2}[/tex] + ∫ x cos [tex]\pi ^{2}[/tex] dx + c

= 1/2 ([tex]\pi[/tex]) sin [tex]\pi[/tex] + ∫ x cos [tex]\pi ^{2}[/tex] dx + c

∫ [tex]x^{3}[/tex] cos [tex]x^{2}[/tex] dx = 1/2 ([tex]\frac{\pi }{2}[/tex]) sin [tex]\frac{\pi }{2}[/tex] + ∫ x cos [tex]\frac{\pi }{2} ^{2}[/tex] dx + c

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Write the slope-intercept form of the equation for each line.

Answers

Answer: y=4/5x-1.5

Step-by-step explanation: slope intercept form is y=mx+b

m is going to be the slope of the line which in this case is 4/5 (rise over run)

b is going to be where the line intercepts the y-axis, in this case it looks to be at -1.5. Since the y-intercept is in the negatives, we subtract b.

x is an just a variable to be added in for if/when this equation is used.

Compare -2.3 and -8/3 using symbols <, >, or =.

Answers

₋2.3 < ₋8/3 is the correct answer.

Given, we need to compare the terms.

₋8/3 = ₋2.67

therefore, 2.3 is less than 2.667

hence we form it as ₋2.3 < ₋2.67

we form: ₋2.3 < ₋8/3

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Match the equivalent expressions

Answers

Answer: The first one is 36. The second one is 0. The third one is 1/216 and the last on is 1/1,296.

Step-by-step explanation:

-5x+3y=-30
Find x interception

Answers

The x-intercept of given equation is x=6 and point is (6,0).

Given the equation is -5x+3y=-30.

Here, we will find the x-intercept of the given equation.

The x-intercept is the point at which a line intersects the x-axis and the y-intersection is the point where a line intersects the y-axis.

We will find the x-intercept by substituting y=0 and applying the inverse operations.

Firstly we will substitute y=0 in equation, we get

-5x+3(0)=-30

Now, we will simplify this, we get

-5x+0=-30

-5x=-30

Further, we will divide both sides with -5, we get

-5x/-5=-30/-5

x=-6

Hence, the x-intercept of the given equation -5x+3y=-30 is x=6.

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please help

please hurry

Answers

The value indicated of the function indicated on the graph of the function is 2

How to determine the value indicate on the graph of the function?

The graph represents the given parameter

The given graph is a linear function

This is so because the graph is represented by a straight line

A linear function is represented as

f(x) = mx + c

Where the vertex is

m represents the slope

c represents the y-intercept

From the given graph of the equation, we have

f(1) = 2

This means that

When x = 1, the value of f(x) is 2

Hence, the value indicated of the function indicated on the graph of the function is 2

Answers

The remainder and factor of the given algebraic expression [tex]\frac{5x^{5} -4x^{3} -11x^{2} +12}{x+1}[/tex] is [tex](5x^{4} -5x^{3} +x^{2} -12x+12)(x+1)[/tex] and [tex]0[/tex]

As per the given question, we are supposed to find out the factor and remainder of the given algebraic expression [tex]\frac{5x^{5} -4x^{3} -11x^{2} +12}{x+1}[/tex] using remainder theorem concept.

Before solving this, we need to know the concept of remainder theorem.

According to which "When a polynomial is divided by a linear polynomial, the remainder theorem is used to get the remaining. We are aware that long division of polynomials can be used to find the remainder after dividing one polynomial by another. The remainder can instead be discovered using the remainder theorem."

Hence using the same concept we can conclude that the factors are [tex](5x^{4} -5x^{3} +x^{2} -12x+12)(x+1)[/tex] and remainder is [tex]0[/tex]

Algebraic Expression: An algebraic symbol or set of symbols that includes one or more integers, variables, and arithmetic operations.Remainder Theorem: When a polynomial is divided by a linear polynomial, the remainder theorem is used to get the remaining. We are aware that long division of polynomials can be used to find the remainder after dividing one polynomial by another. The remainder can instead be discovered using the remainder theorem.

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Which library has more volumes, Baton Rouge or El Paso? What number sentence shows the comparison? A. Baton Rouge; 1,232,185 < 1,277,003 B. El Paso; 1,232,185 > 1,277,003 C. Baton Rouge; 1,232,185 > 1,277,003 D. El Paso; 1,232,185 < 1,277,003

Answers

The library has more volumes in El Paso.

The number sentence that shows the comparison is 1,232,185 < 1,277,003

Hence, El Paso; 1,232,185 < 1,277,003. Option D

This is further explained below.

What is a library?

Generally, A library is a collection of resources, such as books or other forms of media, that are made available for use rather than being kept only for the purpose of the show.

A library is a facility that makes resources available for physical or digital access, and it may exist either as a real place or as a virtual area, or both.

In conclusion, The library has more volumes in El Paso.

The number sentence that shows the comparison is 1,232,185 < 1,277,003

Hence, El Paso; 1,232,185 < 1,277,003.

Answers

Answer:

x=90, y= 130

Step-by-step explanation:

PLEASE HELP WITH THIS QUESTION! ILL GIVE BRAINLYEST

Answers

A equals to 24
B equals to 96
C equals to 48

Francisco earns seven dollars an hour at his part-time job last week he worked 16 hours what was his gross pay for the week what was his salary for the year if he works 16 hours a week all year

Answers

Answer:

he works 7 dollars an hour so 16 x 7 = 112 that's for a whole week a year would be 356 x 7 = 2,555 that's 1 whole year

Step-by-step explanation:

sorry if i got this wrong

Andy got a loan of $120000 from a bank at a rate of 9% per annum calculate the i for the loan at the end of the first year

Answers

Answer:

I=$10800

Step-by-step explanation:

I=($120000×9×1)÷100

I=$1200×9=$10800

Solve for x.

4x^2 - 10 = 90

Answers

Hope this helps :)

4x^2-10=90
Add 10 to each side
4x^2=100
Divide by 4
X^2=25
Get rid of the square
x=5

X = 5

4x^2 - 10 = 90

4x^2 = 90 + 10

4x^2 = 100

X^2 = 100/4

X^2 = 25

Square root of 25 X= 5

Jill won 55 pieces of gum playing the bean
bag toss at her school's game night. Later,
she gave one to each of her friends. She
only has 40 remaining. How many did
she give away

Answers

She gave 15 always because she started with 55 and she ended with 40. 55-40=15.

Answer =15

Hope it helps

Answer:

15 gum

Step-by-step explanation:

55-40 = 15

Brett works for the local farmer, delivering feed and produce to the local community. He uses his own truck for the deliveries. He
gets paid a travel allowance of 64 cents per kilometer travelled. How much car travel allowance would Brett get paid for
travelling a total of 87km?
Select one:
O $55.68
O $67.24
O $54.86
O $45.90
If there is currently $139.50 petty cash in the tin how much do I need to withdraw from the bank to make $200.00 in the tin?

Answers

Brett will get paid $55.68 for travelling a total of 87 kilometers at an allowance of 54 cents per kilometer.

According to the International System of Units (SI), one kilometer is equal to 1,000 meters in American English. The United States and the United Kingdom are significant outliers, where the statute mile is the unit of measurement used to express distances between geographical locations on land.

One Kilometer is roughly equivalent to 0.621 miles.

Brett delivers produce for the farmer using his truck.

He gets paid a travel allowance of 64 cents per kilometer.

So to calculate his total allowance we multiply the allowance with the distance travelled.

Brett gets paid: $0.64×87=$55.68

Hence Brett gets paid $55.68. So the first option is correct.

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Two trains leave the same station at the same time but are headed in opposite directions. One train travels at 80 mph and the other train travels at 65 mph. How much time passes until the trains are 580 miles apart?

__Hours.

Answers

38.7 hours would have passed until the trains are 580 miles apart

How much time passes until the trains are 580 miles apart?

The given parameters are

Train 1 = 80 mph

Train 2 = 65 mph

The difference in the speeds of the trains is

d = 80mph - 65mph

Evaluate

d = 15mph

The distance moved is

Distance = 15 * t

At 580 miles apart, we have

15 * t = 580

Divide by 15

t = 38.7 hours

Hence, 38.7 hours would have passed until the trains are 580 miles apart

Answers

the second option is one of them. the 5th option is also one. and the 4th one

What company has the absolute advantage when it comes to producing phones?
a. Gonzalez and Bros. Inc
b. The G company Inc
c. they both do
d. neither

Answers

(Option a) Gonzalez and Bros . Inc has the absolute advantage when it comes to producing phones.

Absolute advantage theory

In his book The Wealth of Nations, the 18th-century economist Adam Smith proposed the concept of absolute advantage to describe how countries could benefit from trade by specializing in producing and exporting the goods that they can make more successfully than other countries.

On the other hand, China, Thailand, and Vietnam create and export low-cost manufactured goods. These three countries benefit greatly from their much lower unit labor costs.

Here, option a Gonzales and Bros. Inc has the absolute advantage when it comes to producing phones.

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Alex is thinking of a number that is multiplied by 7 and the added with 27. The result is
equal to 111.
44) What is the equation that you can write to solve for the number if the unknown
number is x.c

Answers

The equation that can be used to solve for the unknown number that Alex is thinking is 7x + 27 = 111

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the unknown number. The number is multiplied by 7 and the added with 27. The result is equal to 111. Hence:

7x + 27 = 111

The equation that can be used to solve for the unknown number that Alex is thinking is 7x + 27 = 111

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Michael rented a truck for one day. There was a base fee of $16.95, and there was an additional charge of 97 cents for each mile driven. Michael had to pay $277.88 when he returned the truck.

For how many miles did he drive the truck?

Answers

Answer: 286.474227

Step-by-step explanation: The answer is correct if doing division, if not then this is wrong. I divided 277.88 with 0.97 and got 286.474227

Is y=10•0.93^x exponential decay, exponential growth or neither

Answers

Answer: Exponential decay

Explanation: The base of the actual exponential function, [tex]0.93^{x}[/tex], is less than 1, which means that the output will become smaller.

the distribution of lengths of rainbow trout from a certain river are normally distributed with a standard deviation of 2.4 inches. it 15% of the rainbow trout are longer than 15 inches, which of the following is closest to the mean of the distribution?

Answers

Based on the calculations, the value which closest to the mean of the distribution is equal to: B. 18 inches.

What is a z-value?

A z-value is also referred to as a z-score or standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.

In Statistics, z-values can either be positive or negative and it can be calculated by using this formula:

Z = (x - μ)/δ

Where:

x represents the sample mean or observed data.μ represents the mean.δ represents the standard deviation.

If 15 percent of the rainbow trout are longer than 15 inches, then we have:

P(x > 15) = 0.15

From the z-table, the z-value which corresponds to a mean of 0.15 is given by:

z-value = -1.036

Substituting the given parameters into the formula, we have;

Z = (x - μ)/δ

-1.036 = (15 - μ)/2.4

-1.036 × 2.4 = 15 - μ

-2.4864 = 15 - μ

μ = 15 + 2.4864

Mean, μ = 17.4864

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Complete Question:

The distribution of lengths of rainbow trout from a certain river are normally distributed with a standard deviation of 2.4 inches. it 15% of the rainbow trout are longer than 15 inches, which of the following is closest to the mean of the distribution?

A. 26 inches

B. 18 inches

C. 30 inches

D. 33 inches

E. 34 inches

In the figure to the right, if AC=16 and BC=13, what is the radius?

Answers

Answer:

Radius AB = 9.3 units

Step-by-step explanation:

BC (tangent) make right angle with radius AB.

AC = 16 units

BC = 13 units

Find:

Radius AB = ?

Computation:

Using Pythagoras theorem:

Radius AB = 9.3 units

On Monday, Mia spent 3 1/2 hours studying. On Tuesday she spent another 1 3/5 hours studying. What is the total time she spent studying?

pls help me, srry not college

Answers

Answer:

5 1/10

Step-by-step explanation:

let me know if you need an explanation

Working alone, Rob can mop a warehouse
in six hours. Molly can mop the same
warehouse in nine hours. How long would
it take them if they worked together?l

Answers

It will take Molly and Rob 54/15 hours to mop the warehouse.

What is defined as the concept of work and time?Work is described as anything that has an impact or has an outcome. When it is stated somebody has done a certain work, it means that he or she has completed all of the work. As a result, if Manu accomplishes his work in 5 days, he will complete 100% of the work in 5 days.As a result, we could indeed say that he completes 20% of a work in one day. Similarly, he completes 40% of a work in two days and 60% of a work in three days.

For the given question;

Rob takes 6 hours for cleaning the ware house.

Let 'R' be the work done by rob.

Then, work done by Rob in 6 hours is 1/R = 1/6.

Similarly;

Let work by Molly is 'R'.

The, work done by Molly in 1 hour is 1/M = 1/9.

The total work done by both is 1 hour is;

1/R + 1/M = 1/6 + 1/9

Om simplification;

1/R + 1/M = 15/54.

Thus, the total time taken by doing the work is; 54/15 hours.

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Borrowed money for 4 years at 9%. Total interest paid was 2520. How much was borrowed

Answers

The required amount that was borrowed is 7000.

Given that,
Borrowed money for 4 years at 9%.
The total interest paid was 2520.
To determine how much money was borrowed.

What is simple interest?

Simple interest is defined as the percentage of earnings on the lending for a period of time

Here,
interest = [principal * rate * time ] / 100
2520 = [principal * 9* 4] / 100
Principal = 2520 * 100 / 9*4
Principal = 7000
So, the principal amount or initial amount is $7000.

Thus, the required amount that was borrowed is 7000.

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A deck of cards contains RED cards numbered 1,2,3 and BLUE cards numbered 1,2. Let R be the event of drawing a red card, B the event of drawing a blue card, E the event of drawing an even numbered card, and O the event of drawing an odd card.

Drawing the Blue 2 is an outcome of which of the following events? Select all correct answers

Answers

Answer: E & B

Step-by-step explanation:

Among fatal plane crashes that occurred during the past 65 years, 260 were due to pilot error, 62 were due to other human error, 315
were due to weather, 682 were due to mechanical problems, and 313 were due to sabotage.
Fill in the relative frequency for each category. Write answers in percentage form and round to one decimal place as needed. Do not include the percent symbol.

Answers

Answer: Pilot Error: 15.9%

Human Error: 3.8%

Weather: 19.3%

Mechanical Problems: 41.8%

Sabotage: 19.2%

Step-by-step explanation:

260+62+315+682+313=

322+997+313=

1319+313=1632 total crashes

Pilot error: 260/1632=

0.159=

0.159*1=

0.159*100%=15.9%

Human error: 62/1632=

0.03799=

0.038=

0.038*100%=3.8%

Weather: 315/1632=

0.193=

0.193*100%=19.3%

Mechanical Problems: 682/1632=

0.41789=

0.418=41.8%

Sabotage: 313/1632=

0.191789=

0.192=19.2%

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