A rectangular prism has a length of 312 inches, a width of 5 inches, and a height of 112 inches. What is the volume of the prism? Enter your answer as a simplified mixed number or a decimal

Answer:

The distance between them in 2.5 min will be 320 ft

Step-by-step explanation:

Let

x--------------> Bill distance after 2.5  min------- > speed  45 ft/min

y--------------> Greg distance after 2.5  min------> speed 75 ft/min

z-------------> distance between them in 2.5 min

we Know that

z=x+y+20

Remember that

To find the distance multiply the speed by the time

so

x=45*2.5=112.5 ft

y=75*2.5=187.5 ft

therefore

z=x+y+20-----------> 112.5+187.5+20=320 ft

Final answer:

Bill and Greg's total distance apart after 2.5 minutes is 320 feet, calculated by adding their initial distance of 20 feet to the distance they covered in 2.5 minutes at their combined speed of 120 feet per minute.

Explanation:

Bill and Greg are walking away from each other with speeds of 45 and 75 feet per minute, respectively.

Since they are moving in opposite directions, their relative speed is the sum of their individual speeds, which is 45 + 75 feet per minute, or 120 feet per minute.

To find the distance between them after 2.5 minutes, we multiply their relative speed by the time elapsed. Therefore, the distance is:

Distance = Speed × Time = 120 feet/minute × 2.5 minutes = 300 feet.

We must also include the initial distance between them, which was 20 feet, so the total distance after 2.5 minutes is:

Total distance = Initial distance + Distance covered in 2.5 minutes = 20 feet + 300 feet = 320 feet.

Answer:  the correct option is (D) [tex]x=\dfrac{k-11}{3}.[/tex]

Step-by-step explanation:  We are given to solve the following equation for the value of x :

[tex]3x+11=k~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To solve the given equation for x, we need to take x on one side and all other terms on the other side of the equality.

The solution of equation (i) is as follows :

[tex]3x+11=k\\\\\Rightarrow 3x=k-11\\\\\Rightarrow x=\dfrac{k-11}{3}.[/tex]

Thus, the required value of x is [tex]x=\dfrac{k-11}{3}.[/tex]

Option (D) is CORRECT.

Answer:

Robin is 9 years old and Batman is 36 years old

Step-by-step explanation:

Batman: 4x

Robin: x

4x + x = 45

5x = 45

x= 9

Answer: 56.25

Step-by-step explanation:

Since there are four sides to a square and the area is 225 yards you would -

225 yards/ 4 sides

= 56.25 yards per side

The sperm whale's underwater duration is seven times that of the sea cow, showcasing remarkable breath-holding abilities, likely adapted for deep-sea foraging and hunting.

The relationship between the underwater durations of a sperm whale and a sea cow suggests that the sperm whale's capability is sevenfold that of the sea cow. Let's denote the sea cow's duration as "x." Accordingly, the sperm whale's underwater duration would be 7 times x.

In practical terms, if we assume the sea cow can stay submerged for 10 minutes (x = 10), then the sperm whale, being seven times more proficient, can stay underwater for 7 times 10, which is 70 minutes (7x = 7 * 10 = 70). This sevenfold difference implies a significant contrast in their breath-holding abilities.

The numerical representation extends universally; if the sea cow can endure underwater for "x" units of time, the sperm whale can endure for 7 times "x" units of time. This relationship showcases the remarkable adaptation of the sperm whale to extended submersion, likely linked to its deep-sea foraging behavior and hunting strategies.

In essence, the sperm whale can stay underwater for a duration that is seven times longer than that of the sea cow, highlighting its remarkable breath-holding capacity.

A sperm whale can stay underwater for 7 times longer than a sea cow, so it can stay underwater for 7 times the duration of a sea cow.

If a sperm whale can stay underwater 7 times longer than a sea cow, we can express this relationship as:

Time a sperm whale can stay underwater = 7 * Time a sea cow can stay underwater

So, if we let the time a sea cow can stay underwater be represented by 'x', then the time a sperm whale can stay underwater is:

7 * x

Therefore, a sperm whale can stay underwater for 7 times longer than a sea cow, which means it can stay underwater for 7x.

Answer: The correct option is 4.

Explanation:

The formula of law of cosine is,

[tex]a^2=b^2+c^2-2bc\cos(A)[/tex]

Where a,b,c are sides of the triangle and A is the interior angle of vertex A.

Reason for correct option:

From the above formula we can easily conclude that to find an unknown angle measure we need the length of all sides of the triangle.

In figure 4 all sides are given, so the correct option is 4.

Reason for incorrect option:

In figure 1,2 and three all sides are not known, so we can apply the cosine rule to mind the unknown angle measure.

Therefore option 1,2 and 3 are incorrect.

Answer:

There are infinitely many solutions.

Step-by-step explanation:

While solving a system of equations, if we get a true statement like 1=1, then there will be "infinitely many solutions" and if we get a false statement like 1=2, then there will be "no solution".

Here the statement is 4=4, which is a true statement.

So, there are infinitely many solutions.

Answer:3,4.b

Step-by-step explanation: Took the test.

Answer: d.) The area of the new circle is 16 times larger.

Step-by-step explanation:

Let the radius of the original circle be r.

Then the area of the original circle will be :-

[tex]\text{A}_1=\pi r^2[/tex]

When she multiplies her original radius by four and repaints the circle.

The new radius = [tex]R=4r[/tex]

Then the area of the new circle will be :-

[tex]\text{Area}=\pi R^2\\\\\Rightarrow\ \text{Area}=\pi (4r)^2\\\\\Rightarrow\ \text{Area}=\pi (16r^2)\\\\\Rightarrow\ \text{Area}=16\pi r^2\\\\\Rightarrow\ \text{Area}=16(\pi r^2)\\\\\Rightarrow\ \text{Area}=16A_1[/tex]

Hence, The area of the new circle is 16 times larger.

Answer:  The required result is [tex]40\dfrac{3}{8}.[/tex]

Step-by-step explanation:  We are given to perform the following indicated operation :

[tex]E=7\dfrac{1}{8}\times5\dfrac{2}{3}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To perform the given multiplication, first we need to convert the mixed fraction to improper fraction.

The simplification of the given operation is as follows :

[tex]E\\\\\\=7\dfrac{1}{8}\times5\dfrac{2}{3}\\\\\\=\dfrac{57}{8}\times\dfrac{17}{3}\\\\\\=\dfrac{19\times17}{8}\\\\\\=\dfrac{323}{8}\\\\\\=40\dfrac{3}{8}[/tex]

Thus, the required result is [tex]40\dfrac{3}{8}.[/tex]

Answer:

The correct answer is pilot. I took the test

Step-by-step explanation:

Final answer:

The slope of the skateboard ramp, calculated using the rise over run formula, is 0.3. This is found by dividing the rise of 1.2 meters by the run of 4 meters.

Explanation:

The slope of a ramp is calculated as the rise divided by the run. To find the slope of the skateboard ramp, which rises 1.2 meters above the ground and runs 4 meters horizontally at the base, you would use the formula:

Slope (m) = Rise / Run

Here, the rise is the height the ramp rises above the ground, which is 1.2 meters, and the run is the distance along the ground, which is 4 meters horizontally. By substituting the given rise and run into the formula, you obtain:

Slope (m) = 1.2 m / 4 m = 0.3

So, the slope of the skateboard ramp is 0.3.

Answer:  The description is mentioned in the below explanation.

Step-by-step explanation:

Since  greatest integer function rounds down a real number to the nearest integer. for example, if f(x)=[x] and for x =1.3 f(x)= [1.3]= 1

or x= 0.9 f(0.9)= [0.9]= 0

Here, The given function, y=4[x+2]

Which is a greatest integer function and it is described on  [0,3)

So, For the values of  [tex]1 >x\geq 0[/tex],we take  x=0 ⇒ y= 4(0+2)= 8

For,  [tex]2>x\geq 1[/tex] , we take x=1, ⇒ y = 4(1+2)= 12

For,  [tex]3>x\geq 2[/tex] we take x=2, ⇒ y = 4(2+2)=16

The graph description for the open or close interval, is mean describe values of variable for the interval. The graph [tex]y=4[x+2][/tex] is described and the values of y we get are 8,12, and 16 for the values of x as 0,1 and 2.

Integer keeps the values as positive or the negative and graphed at the number line.

Given information-

The function of the graph given in the problem is,

[tex]y=4[x+2][/tex]

This function need to be describe on the points [0,3).

The close bracket is used in left side means the value 0 is included and the  open bracket is used in right side means the value 3 is excluded.

Thus find the value of variable y for the different intervals o x,

The interval is,

[tex]0\leq x<3[/tex]

         [tex]y=4(0+2)\\y=4\times2\\y=8[/tex]

         [tex]y=4(1+2)\\y=4\times3\\y=12[/tex]

         [tex]y=4(2+2)\\y=4\times4\\y=16[/tex]

The graph of the given point is attached below.

Thus the graph [tex]y=4[x+2][/tex] is described and the values of y we get are 8,12, and 16 for the values of x as 0,1 and 2.

Learn more about the graph integer on a number line here;

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