A rectangular prism is a three-dimensional geometric figure, hollow or solid, contained by six rectangular sides that meet at right angles to form eight vertices. The maximum capacity of a rectangular prism is calculated with the formula,, where Volume and length, width, and height.

For a rectangular shaped box with a maximum capacity of 2.25 · 104 cubic meters, a length of 25 meters, a width of 2x meters and height of 1.5·102 meters, x =
meters.

Answer:

See Explanation

Step-by-step explanation:

Required

Write three equivalent ratios

To solve these questions, we do the following:

Whatever is being applied to a part of the ratio must be done on the other part

Solving (9):

[tex]Ratio = \frac{2}{7}[/tex]

Multiply through by 2

[tex]Ratio = \frac{2*2}{7*2} = \frac{4}{14}[/tex]

Multiply through by 3

[tex]Ratio = \frac{2*3}{7*3} = \frac{6}{21}[/tex]

Multiply through by 5

[tex]Ratio = \frac{2*5}{7*5} = \frac{10}{35}[/tex]

Hence, the equivalents are: [tex]\frac{4}{14}, \frac{6}{21}, \frac{10}{35}[/tex]

Solving (10):

Ratio = 1.5 to 3.5

Multiply by 2

[tex]Ratio = 1.5 * 2\ to\ 3.5 * 2[/tex]

[tex]Ratio = 3\ to\ 7[/tex]

Multiply by 3

[tex]Ratio = 1.5 * 3\ to\ 3.5 * 3[/tex]

[tex]Ratio = 4.5\ to\ 10.5[/tex]

Multiply by 4

[tex]Ratio = 1.5 * 4\ to\ 3.5 * 4[/tex]

[tex]Ratio = 6\ to\ 14[/tex]

Hence, the equivalents are:  3 to 7, 4.5 to 10.5 and 6 to 14

Solving (11):

Ratio = 6.25 to 1.25

Divide by 5

[tex]Ratio = 6.25/5\ to\ 1.25/5[/tex]

[tex]Ratio = 1.25\ to\ 0.25[/tex]

Multiply by 2

[tex]Ratio = 6.25*2\ to\ 1.25*2[/tex]

[tex]Ratio = 12.5\ to\ 2.5[/tex]

Multiply by 4

[tex]Ratio = 6.25*4\ to\ 1.25*4[/tex]

[tex]Ratio = 25\ to\ 5[/tex]

Hence, the equivalents are:  1.25 to 0.25, 12.5 to 2.5 and 25 to 5

Solving (12):

[tex]Ratio = 3 : 3\frac{1}{2}[/tex]

Multiply by 2

[tex]Ratio = 3 *2: 3\frac{1}{2}*2[/tex]

[tex]Ratio = 6: 7[/tex]

Multiply by 4

[tex]Ratio = 3 *4: 3\frac{1}{2}*4[/tex]

[tex]Ratio = 12: 14[/tex]

Multiply by 6

[tex]Ratio = 3 *6: 3\frac{1}{2}*6[/tex]

[tex]Ratio = 18: 21[/tex]

Hence, the equivalents are: 6:7, 12:14 and 18:21

Solving (13)

[tex]Ratio = 1\frac{2}{3} : \frac{5}{4}[/tex]

Convert mixed fraction to improper fraction

[tex]Ratio = \frac{5}{3} : \frac{5}{4}[/tex]

Multiply by 2

[tex]Ratio = \frac{5}{3}*2 : \frac{5}{4}*2[/tex]

[tex]Ratio = \frac{10}{3} : \frac{5}{2}[/tex]

Multiply by 3

[tex]Ratio = \frac{5}{3}*3 : \frac{5}{4}*3[/tex]

[tex]Ratio = 5 : \frac{15}{4}[/tex]

Multiply by 12

[tex]Ratio = \frac{5}{3}*12 : \frac{5}{4}*12[/tex]

[tex]Ratio = 20 : 15[/tex]

Hence, the equivalents are: 10/3:5/2, 5 : 15/4, and 20:15

Answer:

b is 42

hope that helpssss

Answer:

x = 5

Step-by-step explanation:

[tex]\frac{x}{2x - 3} = \frac{10}{14}[/tex] --> Triangle Proportionality Theorem

10(2x - 3) = 14(x) --> Cross Multiplying

20x - 30 = 14x --> Distributing 10 and 14 to the parentheses

20x -30 - 14x + 30 = 14x - 14x + 30 --> Subtracting 14x and adding 30 on both sides

6x = 30 --> Simplifying

6x/6 = 30/6 --> Dividing 6 on both sides

x = 5 --> Simplifying

Hope this helped!

By the way, I'm not so sure you understand the concept of "Triangle Proportionality Theorem" since you asked a similar one before that. So I'll post an image that I found on the internet that explains it. :D

Answer:

4.625

Step-by-step explanation:

that is the answer

Answer:

x=30

Step-by-step explanation:

-8/5 - 6 = -54

-8x/5 - 6 = -54

-8x/5 −  6 +6 = -54 plus 6

Then Add the numbers and simplify

so then the answer would be x=30

Answer: x=30

Step-by-step explanation:

Answer:

It might be b

Step-by-step explanation:

I think it is B

Answer:

x = 90

Step-by-step explanation:

The 90-degree angle and "x" form a straight line. The degree measurement of a straight line is 180. That means that if one adds 90 and "x", they will get 180, and therefore, x equals 90.

Answer:

7

Step-by-step explanation:

3x8-3x3+2

24-3x3+2

24-9+2

15+2

=17

Answer: the awnser is B

Answer:

In 25 years, Tina will have $354,452.86

Step-by-step explanation:

Monthly Contribution - $366.69 (Tina & Employer)

Length of Time in Years - 25

Estimated Interest Rate - 8.1%

Compound Frequency - Monthly

Given:

The objective function, [tex]C=2x+3y[/tex],

Constraints,

[tex]2x+3y\leq 24[/tex]

[tex]3x+y\leq 15[/tex]

[tex]x\geq 2[/tex]

[tex]y\geq 3[/tex]

To find:

The minimum value of the given objective function.

Solution:

We have,

Objective function, [tex]C=2x+3y[/tex]            ....(i)

The related equations of given constraints are

[tex]2x+3y=24[/tex]       ...(ii)

[tex]3x+y=15[/tex]              ...(iii)

[tex]x=2[/tex], it is a vertical line parallel to y-axis and 2 units left from y-axis.

[tex]y=3[/tex], it is a horizontal line parallel to x-axis and 4 units above from y-axis.

Table of value for (i),

x :   0     12

y :   8     0

Table of value for (ii),

x :   0      5

y :   15     0

Plot these points on a coordinate plane and draw these 4 related lines.

The sign of inequality of [tex]2x+3y\leq 24[/tex] and [tex]3x+y\leq 15[/tex] is ≤, it means the related lines are solid lines and the shaded region lie below the related line.

For [tex]x\geq 2[/tex], left side of the line [tex]x=2[/tex] is shaded.

For [tex]y\geq 3[/tex], shaded region is above the line [tex]y=3[/tex].

From the below graph it is clear that the vertices of the feasible (common shaded region) are (2,3), (4,3), (3,6) and (2,6.667).

Points                     [tex]C=2x+3y[/tex]    

(2,3)                        [tex]C=2(2)+3(3)=4+9=13[/tex]    (Minimum)

(4,3)                        [tex]C=2(4)+3(3)=8+9=17[/tex]    

(3,6)                        [tex]C=2(3)+3(6)=6+18=24[/tex]    

(2,6.667)                 [tex]C=2(2)+3(6.667)=4+20=24[/tex]

Therefore, the objective function is minimum at point (2,3).

Answer:

I believe its 3.75

Step-by-step explanation:

Answer:

$10

Step-by-step explanation:

6.25×60% = 3.75

3.75+6.25 = 10

$10

Answer:

30x-6-6x-30

30x-30x-6-6

0-12

-12

Answer:

yes

Step-by-step explanation:

yes

Answer:

c) a and e

Step-by-step explanation:

literally look at it b is just highest point, c is decreasing, d is lowest point... a is rising and e is also rising

Answer:

its is a geometric sequence not arithmetic

Answer:

It's equal to two "ones" ;v;

Step-by-step explanation:

The 8 is 80 "Tens", the 2 is 2 "ones" and the 6 is 6 tenths

Answer:

Answer:Since the expression on each side of the equation has the same denominator, the numerators must be equal.

x

2

=

16

Take the square root of both sides of the equation to eliminate the exponent on the left side.

x

=

±

√

16

The complete solution is the result of both the positive and negative portions of the solution.

Tap for more steps...

x

=

4

,

−

4

Exclude the solutions that do not make

x

2

x

−

4

=

16

x

−

4

true.

x

=

−

4

Step-by-step explanation:

Step-by-step explanation:

First one on the left = Second one on the right

Second one on the left = First one on the right

Third one on the left = Third one on the right

Answer: $8.60

Step-by-step explanation:

Let the price of a bread = x

Let the price of a tarts = x - 1

If 3 times the price of a loaf of bread is $29.5 more than half of the price of a box of tarts. This can be represented as:

3 × x = 1/2 × (1 - x) + 29.5

3x = 0.5 - 0.5x + 29.5

3x + 0.5x = 29.5 + 0.5

3.5x = 30

x = 30/3.5

x = 8.6

Question:

You play tennis against a player that you have a 20% chance of winning. What is the probability that you win no game out of 6 games?

Answer:

[tex]Probability = 0.262144[/tex]

Step-by-step explanation:

Represent the probability of winning with P(Win)

[tex]P(Win) = 20\%[/tex]

Required

Determine the probability of not winning 6 games

First, we calculate the probability of not winning a game.

Opposite probability add up to 1.

So, we have:

[tex]P(Win) + P(Lose) = 1[/tex]

[tex]P(Lose) = 1 - P(Win)[/tex]

[tex]P(Lose) = 1 - 20\%[/tex]

[tex]P(Lose) = 100\% - 20\%[/tex]

[tex]P(Lose) = 80\%[/tex]

The sample space of losing 6 games is:

Lose Lose Lose Lose Lose Lose

Therefore, the probability is:

[tex]Probability = 80\% *80\% *80\% *80\% *80\% *80\%[/tex]

[tex]Probability = 0.80*0.80*0.80*0.80*0.80*0.80[/tex]

[tex]Probability = 0.262144[/tex]

Answer:

maybe 9

Step-by-step explanation:

Answer:

Step-by-step explanation:

A = P + I

Putting values in the equation

4500 = 3750 + I

4500 / 3750 = I

1.2 = I

Answer:

I=750

Step-by-step explanation:

soln ,

here ,

A=4500

P=3750

I=?

Now,

A=P+I

or,4500=3750+I

or,I=4500-3750

•°•I=750

hope this helps^-^

Answer:

3.66666666667

Step-by-step explanatio