All categories

3 years ago

Bases are squares with sides that measure 27 inches. The height is 12 inches.

Mathematics

1 answer:

Elan Coil [88]3 years ago

3 0

Answer:

Part 1) $V=8,748\ in^3$

Part 2) $SA=2,754\ in^2$

Step-by-step explanation:

The correct question is

Find the volume and the surface area of a rectangular prism. Bases are squares with sides that measure 27 inches. The height is 12 inches.

Part 1) Find the volume of the prism

The volume of the prism is equal to

$V=Bh$

where

B is the area of the base

h is the height of the prism

Find the area of the base B

$B=27^2=729\ in^2$ ---> the base is a square

we have

$h=12\ in$

substitute

$V=(729)(12)=8,748\ in^3$

Part 2) Find the surface area of the prism

The surface area of the prism is equal to

$SA=2B+Ph$

where

B is the area of the base

P is the perimeter of the base

h is the height of the prism

Find the perimeter of the base P

$P=4(27)=108\ in$

substitute the values in the formula

$SA=2(729)+108(12)=2,754\ in^2$

You might be interested in

^!!Howdy howdy!!^

serious [3.7K]

Answer:

1. >; 2. >

Step-by-step explanation:

⅜ (?) 0.295 Convert ⅜ to a decimal fraction

0.375 (?) 0.295

We can use a number line to decide which number is greater.

In Fig. 1 below, when we go from 0.295 to 0.375, we are moving to the RIGHT, so 0.375 is greater than 0.295.

0.375 > 0.295

-0.770 (?) -4/5 Convert ⅘ to a decimal fraction

-0.770 (?) -0.800

In Fig. 2 below, when we go from -0.80 to -0.77, we are moving to the RIGHT, so -0.770 is greater than -0.800.

-0.770 > -0.800

3 0

3 years ago

Which situation could be represented by the graph?

Ymorist [56]

The correct option which resembles with the given graph is $\fbox{\begin\\\ optionA and optionC\\\end{minispace}}$ .

Further explanation:

From the given graph the it is observed that the interval is $[8,11)$ which is a half open interval or it can be said that it is a half closed interval.

A half closed or a half open interval is an interval in which one end point of the interval is included but the other point is not included.

For example:

In an interval of the form $[a,b)$ the point $a$ is included in the set but the point $b$ is not included in the set.

Similarly, in the interval $[8,11)$ the point $8$ is included in the set but the point $11$ is not included in the set.

In order to determine the correct option which resembles with given graph form interval for each option.

Option A:

As per the statement in option A the age of the student must be at least $8$ years and not more than $11$ years that is the age of the student is either $8$ years or greater than $8$ years and less than $11$ years.

As per the above statement the interval formed is $\fbox{\begin\\\ [8,11)\\\end{minispace}}$ in which $8$ is included in the set and $11$ is not included which means it is a half closed or half opoen interval.

Therefore, $\fbox{\begin\\\ optionA\\\end{minispace}}$ is a correct option.

Option B:

As per the statement in option B the amount of money the babysitter can earn is between $\$8$ and $\$11$ per hour.

As per the above statement the interval formed is $\fbox{\begin\\\ (8,11)\\\end{minispace}}$ in which both of the end points are not included in the set which means that it is an open interval.

Therefore, $\fbox{\begin\\\ optionB\\\end{minispace}}$ is an incorrect option.

Option C:

As per the statement in option C the time required to complete a program in college cannot be less than $8$ hours and the time must be less than $11$ hours.

From the above statement it is concluded that the time required can be $8$ hours or more than $8$ hours but it has to be less than $11$ hours.

So, as per the above the statement the interval formed is $\fbox{\begin\\\ [8,11)\\\end{minispace}}$ .

Therefore, $\fbox{\begin\\\ optionC\\\end{minispace}}$ is a correct option.

Option D:

As per the statement in option D the age of the dogs is either $8$ years old or below $8$ years and age of the dog must be greater than $11$ tears.

As per the above statement the interval formed is $\fbox{\begin\\\ (-\infty,8) \bigcup(11,\infty)\\\end{minispace}}$ .

Therefore, the $\fbox{\begin\\\ optionD\\\end{minispace}}$ is an incorrect option.

So, $\fbox{\begin\\\ optionA and optionC\\\end{minispace}}$ are the correct options which resembles with the given graph.

Learn more:

A problem on composite function brainly.com/question/2723982
A problem to find radius and center of circle brainly.com/question/9510228
A problem to determine intercepts of a line brainly.com/question/1332667

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Sets

Keywords: Interval, set, open interval, closed interval, half open interval, half closed interval, set theory, program, community college, babysitters, veterinary clinic, ages, students.

5 0

3 years ago

Read 2 more answers

How to put this in $799.73 in numeric please help thank you

AlekseyPX

The answer is 800$...

6 0

3 years ago

Find the angles of 22 and 24 thanks

netineya [11]

Answer:

22) 119

24) 15

Step-by-step explanation:

22) 61 + b = 180 <-- supplementary because on the same line

b = 119 <-- subtracted 61 from both sides

24) 87 + (6x + 3) = 180 <-- supplementary because on the same line

87 + 6x + 3 = 180 <-- take out parantheses

90 + 6x = 180 <-- add like terms

6x = 90 <-- subtracted 90 from both sides

x = 15 <-- solve for x by dividing 6 from both sides

6 0

3 years ago

Helpppppppppppppppppppppppppppppppppppp

Alexxandr [17]

To take out terms outside the radical we need to divide the power of the term by the index of the radical; the quotient will be the power of the term outside the radical, and the remainder will be the power of the term inside the radical.
First, lets factor 8:
$8=2 ^{3}$
Now we can divide the power of the term, 3, by the index of the radical 2:
$\frac{3}{2}$ = 1 with a remainder of 1
Next, lets do the same for our second term $x^{7}$ :
$\frac{7}{2}$ = 3 with a remainder of 1
Again, lets do the same for our third term $y^{8}$ :
$\frac{8}{2} =4$ with no remainder, so this term will come out completely.

Finally, lets take our terms out of the radical:
$\sqrt{8x^{7} y^{8} }= \sqrt{ 2^{3} x^{7} y^{8} } =2 x^{3} y^{4} \sqrt{2x}$

We can conclude that the correct answer is the third one.

4 0

3 years ago

Read 2 more answers