A shipping container is in the form of a right rectangular prism and it can hold 2640 cubic feet of shipped goods when it is full. Its width is 8 ft and its height is 8 ft 3 inches. Find the length of the container in feet. Round your answer to the nearest tenth if necessary.

Using proportions, it is found that:

A proportion is a fraction of a total amount.

For the perimeter, as it is given in units, the scale factor is the same, hence it is of [tex]\frac{2}{3}[/tex].

For the area, as it is given in units squared, the scale factor is squared, hence:

[tex]\left(\frac{2}{3}\right)^2 = \frac{4}{9}[/tex]

For the volume, as it is given in cubic units, the scale factor is eleveted to the third power, hence:

[tex]\left(\frac{2}{3}\right)^3 = \frac{8}{27}[/tex]

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Answer:

4/5 or 16/20

Step-by-step explanation:

did my best with the info provided

Answer:

4/5

Step-by-step explanation:

8/10 = 80%  1. / the fraction by 2

4/5 = 80%

Answer:

that means he will have 25.2

Answer:

S18 = 288

Step-by-step explanation:

find the first and last term.

n = 1

a1 = 2 x 1 - 3

a18 = 2 x 18 - 3

(simplify the expression)

a1 = -1

a18 = 33

(use the formula for the sum of a finite arithmetic series)

                     a1 + a18

S18 = 18 x ---------------------

                           2

(use the substitute) substitute -1 for a1 and 33 for a18

                       -1 + 33

S18 = 18 x ---------------------

                             2

simplify the expression and ur done hope this helped x

ps. wheres my head :)

Answer:

The correct answer would be option A; Subtraction Property of Equality

Step-by-step explanation:

This is because you are subtracting 3 on both sides of the equation to go from;

x + 3 = 17

to

x = 14

Hope this helps!

Answer:

C:y = 3^x

Step-by-step explanation:

The answer is C because the rate of change is always -6.

Rate of change

Option B

Answer:

C

Step-by-step explanation:

y=0 gives the straight horizontal line passing through (0,0)

y=3 also gives straight horizontal line passing through (0,3)

In order to find out which two lines are parallel, let's find the slope of each line first.

The slope of the line y=3x-2 is 3.

The slope of the line y=1/3x-3 is 1/3

The slope of the line y=x is 1

The slope of the line y=3 is 0

The slope of the line y=0 is 0

Now, if two lines have the same slope, they are parallel to each other.

So if a line's slope is 0, the line parallel to it has a slope of 0.

y=0 and y=3

hope helpful ~

Answer:

60kph

Step-by-step explanation:

Distance = Rate X Time

640 = r x 4+ (r+5) x 7

640 = 4r + 7r + 35

640=11r + 35

640 - 35 = 11r

605 = 11r

r = 605 / 11

r= 55 kph

r=55 =5 =60 kph is the speed of the train

To see if the answer is right: 55 x 4 + 60 x 7 = 220 + 420 = 640 km

Answer:

9560

Step-by-step explanation:

Use a calculator or do long division.

You can also divide by 2 twice.

38240/2 = 19120

19120/2 = 9560

Answer: 9560

Answer:

9560

Step-by-step explanation:

30000÷4=7500

8000÷4=2000

200÷4=50

40÷4=10

0÷4=0

7,500+2,000+50+10+0=9,500+60=9,560

Answer:

Step-by-step explanation:

First, we need to calculate how many years will earn percent.

2010---->2025= 15 years elapsed. Now we have our time, we need to plug it in our compound interest formula=

Principal(rate+1)^time or A=P(1+R)^t

10,000(0.085+1)^15

=$33,997.43

To calculate how much Cam earned, you need to subtract from original amount.

=$33,997.43-10,000=

---->$23997.43

Please mark me brainiest :)

option B.

Calculations ↓

First, let's think of two numbers so that :

These numbers are :

4 and 1

Plug these numbers here :

(x+4) (x+1)

So the correct factored form of this expression is

Option B) (x+4)(x+1)

[tex]\footnotesize\text{hope\:helpful~}}[/tex]

Answer:

144 cm^2

Step-by-step explanation:

A square has equal sides, and so if one side is 12 cm, so are the rest.

So 12 * 12 = 144.

Answer:

c

Step-by-step explanation:

Answer:

[tex]\sf C) \quad 57 \frac34 \:cm^2[/tex]

Step-by-step explanation:

To find the shaded area, subtract the area of the semicircle from the area of the rectangle.

Formulae

[tex]\textsf{Area of a rectangle}=\textsf{width} \times \textsf{length}[/tex]

[tex]\textsf{Area of a semicircle}=\dfrac12 \pi r^2 \quad \textsf{(where r is the radius)}[/tex]

[tex]\textsf{Diameter of a circle}=2r \quad \textsf{(where r is the radius)}[/tex]

Area of rectangle

Given dimensions of the rectangle:

Substituting these values into the formula:

[tex]\implies \textsf{Area}=\textsf{7} \times \textsf{11}=77\: \sf cm^2[/tex]

Area of semicircle

Diameter of semicircle = 11 - 2 - 2 = 7 cm

⇒ Radius (r) = 7 ÷ 2 = 3.5 cm

[tex]\textsf{let}\: \pi=\dfrac{22}{7}[/tex]

[tex]\implies \textsf{Area}=\dfrac12 \left(\dfrac{22}{7}\right) (3.5)^2=19.25\: \sf cm^2[/tex]

Area of shaded region

= area of rectangle - area of semicircle

= 77 - 19.25

= 57.75

[tex]\sf =57 \frac34 \:cm^2[/tex]

Answer:

C

Step-by-step explanation:

Because thats the answer

Answer:

2nd option

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

the centre is at the midpoint of the endpoints of the diameter.

The coordinates of the centre is the average of the coordinates of the endpoints.

centre = ( [tex]\frac{-4+2}{2}[/tex], [tex]\frac{7-1}{2}[/tex] ) = ([tex]\frac{-2}{2}[/tex] , [tex]\frac{6}{2}[/tex] ) = (- 1, 3 )

the radius is the distance from the centre to either of the endpoints

using the distance formula to calculate r

r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2[/tex]

with (x₁, y₁ ) = (- 1, 3 ) and (x₂, y₂ ) = (2, - 1 )

r = [tex]\sqrt{(2-(-1))^2+(-1-3)^2}[/tex]

  = [tex]\sqrt{(2+1)^2+(-4)^2}[/tex]

  = [tex]\sqrt{3^2+16}[/tex]

  = [tex]\sqrt{9+16}[/tex]

  = [tex]\sqrt{25}[/tex]

   = 5

then equation of circle is

(x - (- 1) )² + (y - 3)² = 5² , that is

(x + 1)² + (y - 3)² = 25

Answer:

Unrational

Step-by-step explanation:

Step 1:  Determine what is rational and unrational

"A rational number includes any whole number, fraction, or decimal that ends or repeats. An irrational number is any number that cannot be turned into a fraction, so any number that does not fit the definition of a rational number."

Step 2:  Now determine what our number fits into

Since our decimal isn't a whole number, isn't a fraction, and it is a decimal that continues to either repeat or just continues.  Therefore, our number would fit into the unrational category.  If our number is just 2.67034165508 then it would be a rational number since it ends.  However, since we have the ... at the end that means that it continues and therefore falls into the unrational category.

Answer: Unrational

From rectangle P and Q, the ratio of x to y is 25/18

An equation is an expression used to show the relationship between two or more numbers and variables.

Area of P = 40 * x = 40x cm²

Area of Q = y * (1.25 * 40) = 50y cm²

Given that area of Q = 90% if P = 0.9(40x) = 36x cm²

50y cm² = 36x cm²

x/y = 50/36 = 25/18

From rectangle P and Q, the ratio of x to y is 25/18

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Answer:

See below

Step-by-step explanation:

c will be tha same as the labelled angle = 99 degrees

  then c + b = a straight line = 180

             99 + b   = 180

                    b = 81 degrees

Answer:

$17.5

Step-by-step explanation:

divide 150 by 12 to get 12.5. 12.5 is what they paid per-person with the discount. add 5 to get 17.5 and that is the on-discounted price

The normal cost for an individual is $17.50.

Let's denote the normal cost for an individual as "N."

According to the given information, with the group package, the cost per person is $5 less than the normal cost for an individual. So, the cost for each scout in Tisha's troop is "N - $5."

There are 12 scouts in Tisha's troop, so the total cost for the group is given as $150.

We can set up an equation based on the total cost:

Total Cost = Cost per Person × Number of People

$150 = (N - $5) × 12

Now, let's solve for the normal cost for an individual (N):

$150 = 12N - $60

12N = $150 + $60

12N = $210

N = $210 / 12

N = $17.50

So, the normal cost for an individual is $17.50.

To know more about normal cost:

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Answer:

the answer is D) 300 π

Step-by-step explanation:

Formula for Area of sector is:

θ/360° * π * (r)^2

here,

θ= 30° and radius= 60 in

so, after we substitute, we get:

30/360* π* 60*60       after simplifying we get:

= 1/12* π* 5*60

=300π

Hope it helps.

Answer:

D

Step-by-step explanation:

area of sector=

[tex] \frac{theta}{360} \times \pi \: r {}^{2} \\ \\ \frac{30}{360} \times \pi \: (60) {}^{2} \\ \\ 300\pi[/tex]

360

Answer:

10.34 cm.

Step-by-step explanation:

First we need to calculate the angle between the hour and minute hand

We see that there are 5 *  5-minute intervals between the 2 hands and the clock has 12 * 5-minute intervals, so:

This is 5/12 * 360 = 150 degrees,

So we apply the Cosine Rule to the triangle:

x^2 = 4.5^2 + 6.2^2 - 2*4.5*6.2cos150

= 107.014

x = √107.14 = 10.34.

Missing length is 10.3cm to 1.d.p

The clock is a circle divided into 12

360/12=30 degrees for each part

1) 7 to 8

2) 8 to 9

3) 9 to 10

4) 10 to 11

5) 11 to 12

5 parts

30 x 5 = 150 degrees

We've got an angle between 2 lengths - cosine rule comes to mind for me.

a = root 6.2^2 + 4.5^2 - 2x6.2 4.5 x cos 150

= 10.34476764

length is 10.3cm to 1.d.p

(the others are to 1.d.p too)

Hope this helps!

Answer:

5

Step-by-step explanation:

pythagorean triple is 5-12-14 or use pythagorean theorem

b=[tex]\sqrt{ 13^{2} -12^{2} }=\\\sqrt{169-144} =\\\sqrt{25} =5[/tex]

Answer: 5

Step-by-step explanation: The square root of 13²- 12²

Answer: Choice B and Choice D

Step-by-step explanation:

4^-2 * 7^-2= 16*49=784

Answer:

B & C

Step-by-step explanation:

[tex]4^-^2*7^-^2[/tex] is equal to [tex]\frac{1}{784}[/tex]

[tex]\frac{1}{28^2}[/tex] is also requal to [tex]\frac{1}{784}[/tex]

[tex]\frac{7^-^2}{4^2}[/tex] is also equal to [tex]\frac{1}{784}[/tex]

Answer:

1320 ways

Step-by-step explanation:

an olympic event getting a gold medal is not equal to getting a silver or a bronze medal. Hence, we will use the concept of permutation for this problem as order matters here. Hence, there are 1320 ways in which 8 runners can get these 3 medals

Answer:

2

Step-by-step explanation:

£1 = 100p

3*21p+2*37p+3*86p+x*160p (x is the number of notebooks)

63p+74p+258p+x*160p = 395p+x*160p

He paid £8 so he paid 800p

800p-395p = 405p

405p-85p = 320p

320p:160p = 2

He bought 2 notebooks

Answer:

would you rather, i think