99 POINTS
suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 12 gallons of fuel, the airplane weighs 2176 pounds. when carrying 46 gallons of fuel, it weighs 2399 pounds. how much does the airplane weigh if it is carrying 54 gallons of fuel?

Answers

Answer 1
find the difference in gallons and the difference in the weights

46 - 12 = 34 gallons

2399 - 2176 = 223 pounds
 so 34 gallons of gas weighs 223 pounds

find weight per pound: 223 pounds / 34 gallons = 6.5588 pounds per gallon
 round to 6.6 pounds per gallon

54 gallons - 46 gallons = 8 gallons

 8 gallons x 6.6 pounds per gallon = 52.8 pounds, round to 53 pounds

2399 + 53 = 2452 weight of plane with 54 gallons





Related Questions

When rounding to.the nearest hundred are you to add or subtract?

Answers

basically you don't really do either, mostly because when your rounding you mostly just look at the number your rounding to. okay so say your number is like 127 you would round to 100 because your number would've been below 150. And we know that five is the middle of every thing. 10 and the whole number system is made up of tens. So when you have to choose to round you have to go up to the next ten so say your number is 27 since it's above 5 you would round to 30. So if you have 127 it's below the 5 mark (which would be 150) so you would round to 100 because it's below that mark. 

Answer:

When you round to the nearest hundred:

150 or higher turns into 200, so you'd do add.

But when it's 149 or lower, you simply subtract it by 49.

Step-by-step explanation:


the right rectangular prism will be sliced perpendicular to its base along the dashed line. Select from the drop-down menus to correctly describe the cross section formed by the slice.

Answers

The cross section (slice) would be a rectangle.

A rectangular prism is the shape of a box with 6 rectangular sides. If you slice down perpendicular to the base, you would still have another rectangle.

A flagpole stands on a concrete region, as shown. What is the approximate perimeter of the concrete region? Use 3.14 for π.
Thanks!

Answers

The approximate perimeter is 25.12 feet.

The outer edges of the concrete region form semicircles.  The perimeter of a circle is called the circumference, and is given by the formula
C=πd

Since these are semicircles, the circumference is given by C=1/2πd.

There are 4 of these semicircles, so the total would be
C=4(1/2)πd

The diameter of each one is 4 feet:
C=4(1/2)(3.14)(4) = 25.12

Seven subtracted from the quotient of a number and 2 is -6

Answers

n/2 -7 = -6

add 7 to both sides;
n/2 -7+7 = -6+7

n/2 = 1
multiply both sides by 2 (  or divide by 1/2 ) in order to get n by itself.

n/2 * 2/1 = 1 * 2/1

n = 2

18 / n - 7 = 2  

18 / n =9  

18 = 9n  

2 = n  


18 / 2 - 7 = 2  

9 - 7 = 2  

2 = 2

There are 80 marbles in a bag. You randomly choose 20 marbles from the bag. The results are shown in the table. Predict the total number of yellow marbles.

Color
Blue 6
Red 9
Yellow 5

There are about ___ yellow marbles.

Answers

There are about 20 yellow marbles.

The experimental probability is 5/20, since 5 yellow marbles were drawn out of 20 in the sample.

5/20(80) = 400/20 = 20

Due tomorrow please help

Answers

For some of these, a calculator is helpul.

The sum is 294903.

_____
This is the sum of 15 terms of a geometric sequence with first term 9 and common ratio 2. That sum is given by the formula
[tex]S_{n}=a\dfrac{r^{n}-1}{r-1}[/tex]
[tex]S_{15}=9\dfrac{2^{15}-1}{2-1}=9\cdot(32768-1)=294903[/tex]

How many two-digit positive integers can be formed from the digits 1, 5, 6, and 8 if no digit is repeated?

Answers

Total Number of digits = 4

We have to fill two places using the 4 digits without repeating the digits.

The first place digit can be filled in 4 ways. When first place is filled, one number is already taken, so now we can fill the second place using remaining 3 digits (3 ways)

So, the total number of ways of forming 2 digit numbers = 4 x 3 = 12 ways

All at once, pandemonium broke loose. ______________ the marching band came around the corner, dogs began barking, and the horses pulling the mayor's carriage began to run!

Which word best completes the passage above? (5 points)


Anyway

Because

Following

Simultaneously

Answers

Answer:

The answer is word SIMULTANEOUSLY.

Step-by-step explanation:

The alternative that fits best is " d.Simultaneously"

All at once, pandemonium broke loose. Simultaneously, the marching band came around the corner, dogs began barking, the horses pulling the Mayors carriage began to run.

This word maintains the coherence and cohesion of the given text.

Answer:

The alternative that fits best is  " d. Simultaneously"

Step-by-step explanation:

Thus, the complete sentence would read:  "All at once, pandemonium broke loose. Simultaneously the marching band came around the corner, dogs began barking, and the horses pulling the mayor's carriage began to run!"

The explanation for this is that the word "Simultaneously" is the only one that fits the phrase, and maintains the coherence and cohesion of the text.  The words "anyway", "because", and "following", when embedded in the phrase, change the meaning of what the author wanted to go through.

A lab worker monitors the growth of a bacteria colony starting at 9:00 a.m. At that time, there are 100 bacteria. According to the exponential function f(x) = 100(4)x, the bacteria quadruple every hour. Which equation could you use to determine the number of bacteria in the colony after 6 hours?

Answers

We know that the exponential growth of the Bacteria's population is model by the function [tex]f(x)=100(4)^x[/tex], so to find the number of bacteria after 6 hours, we just need to evaluate our function at [tex]x=6[/tex]. In other words, we are going to replace [tex]x[/tex] with 6 in our function:
[tex]f(x)=100(4)^x[/tex]
[tex]f(6)=100(4)^6[/tex]
[tex]f(6)=409600[/tex]

We can conclude that the we should use the equation: [tex]f(6)=100(4)^6[/tex] to find the number of bacteria in the colony after 6 hours. Evaluating the function we get that the number is 409,600.

The equation to determine the number of bacteria in the colony after 6 hours is [tex]f(x) = 100(4)^x[/tex] and after 6 hours, there will be 409,600 bacteria in the colony.

To find the number of bacteria after 6 hours, one would substitute x with 6 in the exponential function [tex]f(x) = 100(4)^x[/tex].

This function models the growth of the bacteria colony, where the initial number of bacteria is 100 and they quadruple every hour.

The variable x represents the number of hours that have passed since the initial measurement at 9:00 a.m.

By substituting x = 6 into the function, we get:

[tex]f(6) = 100(4)^6[/tex]

Now, calculate the value of [tex](4)^6[/tex]:

[tex](4)^6 = 4 \times 4 \times 4 \times 4 \times 4 \times 4 = 4096[/tex]

Then, multiply this by the initial number of bacteria, which is 100:

f(6) = 100 [tex]\times[/tex] 4096

Finally, calculate the total number of bacteria after 6 hours:

f(6) = 409600

What is the simplified form of the following expression? 10abc^2 sqrt 49a^2b^2c^2


Answers

Answer: [tex]70a^2b^2c^3[/tex] will be the answer.

Explanation:

Since Given expression is [tex]10abc^2\sqrt{49a^2b^2c^2}[/tex]

We can write, [tex]10abc^2\sqrt{49a^2b^2c^2}= 10abc^2\sqrt{7^2a^2b^2c^2}[/tex]

[tex]\Rightarrow 10abc^2\sqrt{49a^2b^2c^2}= 10abc^2\sqrt{(7abc)^2}[/tex]

[tex]\Rightarrow 10abc^2\sqrt{49a^2b^2c^2}= 10abc^27abc[/tex]

[tex]\Rightarrow 10abc^2\sqrt{49a^2b^2c^2}= 10\times7abc^2abc[/tex]

[tex]\Rightarrow 10abc^2\sqrt{49a^2b^2c^2}= 70abc^2abc[/tex]

[tex]\Rightarrow 10abc^2\sqrt{49a^2b^2c^2}= 70a^2b^2c^3[/tex]

1. The simplified form of the expression [tex]10abc^2[/tex] is simply [tex]10abc^2[/tex] itself.

2. The simplified form of the expression [tex]\sqrt{49a^2b^2c^2}[/tex] is 7abc.

1. Since there are no like terms to combine, and no operations to perform, the expression remains unchanged.

2. The expression [tex]\sqrt{49a^2b^2c^2}[/tex] represents the square root of [tex]49a^2b^2c^2[/tex]. To simplify this, we need to find the square root of each term under the radical.

[tex]\sqrt{49a^2b^2c^2} = \sqrt{49} * \sqrt{a^2} * \sqrt{b^2} * \sqrt{c^2}[/tex]

The square root of 49 is 7, and the square root of any variable raised to the power of 2 is simply the variable itself. So, we have: [tex]\sqrt{49a^2b^2c^2} = 7 * a * b * c[/tex]

To know more about expression:

https://brainly.com/question/34132400

#SPJ6

Anyone know the answer to this geometry problem?

Answers

Let's talk about the choices
◯  ∠4 and ∠5 . . . . . . . . these are complementary angles whose sum is 90°
◯  ∠7 and ∠9 . . . . . . . . these are vertical angles, equal to each other
◯  ∠2 and ∠3 . . . . . . . . these are supplementary angles that together form a straight line. They are a linear pair.
◯  ∠1 and ∠2 . . . . . . . . these are "adjacent" angles in the quadrilateral that also includes ∠9 and ∠10.

The appropriate choice is ...
  ◉  ∠2 and ∠3

PLEASE HELP I NEED SOMEBODY TO PARAPHRASE THIS FOR ME! I'LL MARK BRAINLIEST!! 50 POINTS!!!


if the variables cancel out leaving u with an untrue statement, like 0 = 4 or 2 = 6, then u will have no solutions
if the variables cancel out leaving u with a true statement, like 2 = 2 or 4 = 4, then u will have infinite solutions
if u end up with a variable equaling a number, then u have 1 solution

Answers

3x + 4 = 2x + 2
3x - 2x = 2 - 4
x = -2
one solution
3x+4=2x+2
3x-2x=2x+2-2x
1x=2

The other person is wrong

The relationship between the monthly fee for Brandon’s phone and the price per minute for long distance is modeled by the linear function f (x) = 0.05x + 3, where x is the number of minutes used for long distance. What is the total bill if Brandon used 20 minutes of his long distance service in a month?

Answers

If you use 0.05x+3 (x equal to the number of minutes) it would be 0.05(20) + 3 = 4. Pretty sure this is correct, but you might want to check it.

the linear function f (x) = 0.05x + 3,

f(x) is the monthly fee and x is the price per minute

Brandon used 20 minutes of his long distance

So x is 20 minutes

We plug in 20 for x

f(x) = 0.05x + 3

f(20) = 0.05(20) + 3 = 4

So total bill is  $4 if Brandon used 20 minutes of his long distance service in a month

What is the difference for this question?

Answers

removing the parentheses gives
5x^2 + 2x + 11 - 7 - 4x  + 2x^2
= 7x^2 - 2x + 4
For this case we have the following polynomials:
 (5x2 + 2x + 11) - (7 + 4x - 2x2)
 Rewriting we have:
 5x2 + 2x + 11 - 7 - 4x + 2x2
 By grouping terms of the same degree we have:
 x2 (5 + 2) + x (2-4) + (11-7)
 Rewriting:
 7x2 - 2x + 4
 Answer: the difference is
 7x2 - 2x + 4

Which number is irrational? A. square root of 64 B. square root of 256 C. square root of 100 D. square root of 80

Answers

the square foot is 100 that is the number that is irrational ur welcome.
D its 80 square root of 80 is 8.94427191

The variable z varies jointly with x and y. also, z = -75 when x = 3 and y = -5. what equation describes this variation?

Answers

The equation describing variation will be found as follows:
zαxy
z=kxy
where k is the proportionality constant
k=z/xy
when x=3, y=-5 then z=-75
k=-75/(-5*3)=5
hence the formula will be:
z=5xy


Answer:

c

5

-10

Step-by-step explanation:

Anyone know the answer?

Answers

21x - 19 = 3x + 17   |add 19 to both sides
21x = 3x + 36    |substract 3x from both sides
18x = 36     |divide both sides by 18
x = 2

Susan has a rectangular garden that measures 20 feet by 10 feet. what is the least amount of fencing that she needs to buy in order to enclose the garden?

Answers

To find the amount of feet of fencing she will need, you will calculate the perimeter of the rectangle or space.

To find the perimeter you add the links of all sides.

20 feet + 10 feet + 20 feet + 10 feet= 60 feet

Susan will need a minimum of 60 feet of fencing.

What is the IMA of the doorknob shown?

1.5
3
6
15

Answers

To solve this problem you must apply the proccedure shown below:

 1. You must apply the following formula for calculate the IMA of the doorknob shown in the figure attached of the problem above:

 IMA=outer radius/inner radius

 outer radius=3 cm
 inner radius=0.5 cm

 2. When you substitute these values into the formula, you obtain:

 IMA=3 cm/0.5 cm
 IMA=6

Therefore, the answer is: 6

Answer:

6

Step-by-step explanation:

18. you work a part-time job earning $6.80/hr with tips that average $2.30/hr. you work 20 hr/wk and your deductions are FICA (7.65%), federal tax withholding (8.95%), and state tax withholding (6.1%). how much are you allowed in housing expenses per month?

Im asking for help not for you to do it.

Answers

Total housing expenses per month allowed will be $168.81.

To calculate how much you are allowed in housing expenses per month, we need to first determine your after-tax income.

You earn $6.80/hr plus tips averaging $2.30/hr, resulting in an hourly wage of

$6.80 + $2.30 = $9.10

Working 20 hours a week gives you a weekly income of

20 hours × $9.10/hr = $182

Monthly, this equates

$182  4 weeks = $728

The deductions are as follows: FICA (7.65%), federal tax withholding (8.95%), and state tax withholding (6.1%). These deductions total to

7.65% + 8.95% + 6.1% = 22.7%

To get the after-tax income, we calculate

$728 - (22.7% × $728)

≈ $562.69

This is your monthly take-home pay.

Financial experts often recommend spending no more than 30% of your take-home pay on housing. Therefore

$562.69 × 30%

= $168.81 houses expenses per month

Solve the open sentence.

–2 ≤ n + 4 ≤ 7



A. n ≤ 2 and n ≤ 7


B. n ≥ –6 and n ≤ 3

C. n ≥ 6 and n ≤ –4


D. n ≤ –6 and n ≤ 4

Answers

–2 ≤ n + 4 ≤ 7    |-4

–6 ≤ n ≤ 3

Answer: B. n ≥ –6 and n ≤ 3

explain one of the theorems that you would use to find the zero of higher degree polynomial

Answers

Rational Root Theorem:


If the rational number [tex]x=\frac{b}{c}[/tex] is a zero of a higher degree polynomial:

[tex]P(x)=kx^{n}+...+m[/tex]


where all the coefficients are integers. Then [tex]b[/tex] will be a factor of [tex]m[/tex] and [tex]c[/tex] will be a factor of [tex]k[/tex]


1. Use the rational root theorem to enumerate all possible rational zeroes of the polynomial [tex]P(x)[/tex]


2. Evaluate the polynomial from the first step until you can find a zero. Let’s suppose the zero is [tex]x=r[/tex]. It will be a zero if [tex]P(r)=0[/tex]. Then if this is true, write the polynomial as:

[tex]P(x)=(x-r)Q(x)[/tex]


3. Repeat this process using [tex]Q(x)[/tex] this time rather than [tex]P(x)[/tex]. The process finishes until we reach a second degree polynomial, then solve as it is widely known for a quadratic equation.


Prove and show your work
cos t (sect -cos t)= sin^2 t
sin 0 cot 0= cos 0

Answers

1) Manipulating the Left side
cost · sect - cos²t (Note: sect= 1/cost, cos²t = 1-sin²t)
cost · (1/cost) - (1 - sin²t)
       1            - 1 + sin²t
               0          + sin²t
                             sin²t

2) Manipulating the Left side
sinФ · cotФ (Note: cotФ = cosФ/sinФ)
sinФ · (cosФ/sinФ)
(sinФ · cosФ)/sinФ
cosФ 

A professor uses a video camera to record the motion of an object falling from a height of 250 meters. The function f(x) = –5x2 + 250 can be used to represent the approximate height of the object off the ground after x seconds. Which is the best estimate for the amount of time elapsed when the object is 120 meters off the ground? 4 seconds 5 seconds 6 seconds 7 seconds
(The answer is 5 seconds)

Answers

did you answer your own question?

Answer:

B is the answer

Step-by-step explanation:

i just took the test

Which of these ordered pairs is a solution to the linear inequality?

Answers

the answer to the question is (0,5)

The volume of a cuboid is 1404cm3. The length is 9cm and the width is 130mm. Work out the height of the cuboid in cm.

Answers

Convert mm to cm:
130mm = 13cm

Formula:
Volume = Length x Width x Height

Substitute known values into the variables:
1404 = 9 x 13 x height

1404 = 117 x height

height = 1404 ÷ 117 = 12 cm

Answer : Height = 12 cm

To calculate the height of the cuboid, we convert the width to centimeters and use the volume formula. After conversion, we find the height by dividing the volume (1404cm³) by the product of the length (9cm) and width (13cm), resulting in a height of 12cm.

To find the height of the cuboid, we can use the formula for calculating volume, which is volume = length x width x height. The question gives us the volume of the cuboid as 1404cm³, the length as 9cm, and the width as 130mm. However, we need to ensure all units are the same, so let's convert the width from millimeters to centimeters: 130mm = 13cm (since 1cm = 10mm).

Now, using the formula for volume:

Volume = length x width x height1404cm³ = 9cm x 13cm x height

To find the height, we divide the volume by the product of the length and width:

height = Volume / (length x width)height = 1404cm³ / (9cm x 13cm)height = 1404cm³ / 117cm²height = 12cm

Therefore, the height of the cuboid is 12cm.

Ginger wanna join a gym.she goes to the local gym and is told that there is a one-time fee of $100 to join and then a monthly fee of $30.if she belongs to the gym for one year then the 12th month is free.how much will a one year membership cost her?

Answers

100+30m from the last problem
100+30(11)
100+330
430 dollars, which is highway robbery..

Park rangers released 12 fish into a pond in year 0. Each year, there were twice as many fish as the year before. How many fish were there after x years? Write a function to represent this scenario.

Answers

y = 12 + 2x

This is probably right. I'm 99% sure. :)

Answer: The function would be,

[tex]f(x)=12(2)^x[/tex]

Step-by-step explanation:

Given,

Park rangers released 12 fish into a pond in year 0,

Thus, the initial number of fish = 12,

Also, there were twice as many fish as the year before,

⇒ After 1 year the number of fishes = 2(12) = 12(2),

Similarly,

After 2 years = 2(12(2))= 12(2)²,

After 3 years = 2(12(2)²) = 12(2)³,

................, so on,....

Thus, the number of fishes after x years would be,

[tex]12(2)^x[/tex]

Let f(x) represents the number of fish after x years,

[tex]\implies f(x) = 12(2)^x[/tex]

Which is the required function that the given scenario.

Given the three vertices F(-5, 0), G(3, -3), and H(-2, 8), what are the coordinates of I that make quadrilateral FGIH a square

Answers

The coordinates are: (6,5)

PLEASE HELP URGENT!!!
The price of the land is $2300 per acre ( 1 acre = 4840) how much does the land cost?

Answers

Two of the three side lengths are given.  To find the area of the triangular piece of land, we'll need to calculate the length of the third side, the side opposite the 100 degree angle.  Use the Law of Cosines for this task.

a^2 = b^2 + c^2 - 2ac*cosA

Here, a^2 = 500^2 + 750^2 - 2(500)(750)cos 100 deg, or

          a^2 = 250000 + 572500 - 750000(-0.1736), or
                 = 692264

Then a = +sqrt(692264) = 832 yds

Use Heron's Formula to find the area of the land.

First, calculate s=(a+b+c)/2:  (500+750+832)/2 = 1041=s

According to Heron's Formula, A = sqrt( s(s-a)(s-b)(s-c) )

Here, A = sqrt( 1041*(1041-500)*(1041-750)*(1041-832) )

I will leave this calculation to you to complete.

Suppose the area of the land is A square yards.  Convert this to acres, using the fact that 1 acre = 4840 yd^2.

In acres, the area is 

          1 acre
A* ---------------- = (A/4840) acres
        4840 yd^2

How much will this cost?  Recall that the unit cost of the land is $2300/acre.

Then the total cost will be:
                             $2300
(A/4840) acres * ------------- = 0.475*A dollars.  (Substitute your value for A)
                              1 acre

Two of the three side lengths are given.  To find the area of the triangular piece of land, we'll need to calculate the length of the third side, the side opposite the 100 degree angle.  Use the Law of Cosines for this task.


a^2 = b^2 + c^2 - 2ac*cosA


Here, a^2 = 500^2 + 750^2 - 2(500)(750)cos 100 deg, or


         a^2 = 250000 + 572500 - 750000(-0.1736), or

                = 692264


Then a = +sqrt(692264) = 832 yds


Use Heron's Formula to find the area of the land.


First, calculate s=(a+b+c)/2:  (500+750+832)/2 = 1041=s


According to Heron's Formula, A = sqrt( s(s-a)(s-b)(s-c) )


Here, A = sqrt( 1041*(1041-500)*(1041-750)*(1041-832) )


I will leave this calculation to you to complete.


Suppose the area of the land is A square yards.  Convert this to acres, using the fact that 1 acre = 4840 yd^2.


In acres, the area is 


         1 acre

A* ---------------- = (A/4840) acres

       4840 yd^2


How much will this cost?  Recall that the unit cost of the land is $2300/acre.


Then the total cost will be:

                            $2300

(A/4840) acres * ------------- = 0.475*A dollars.  (Substitute your value for A)

                             1 acre


1

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