1. Mrs.vega brought a new aquarium for her turtles. How much space will the turtles have in the aquarium if the length is 3.2 ft, the width is 1.5 ft and the height is 27 ft?

2. What is the volume of a cylinder that has a radius of 6 inches and height of 8 inches?

Answers

Answer 1

1. 4.5 square feet of surface area, 129.6 cubic feet of swimming volume. 2. 288 pi cubic inches or approximately 904.8 cubic inches. For the turtles, since they're in a rectangular prism, the volume will be the product of the length, width, and height. So 3.2 ft * 1.5 ft * 27 ft = 4.5 ft^2 * 27 ft = 129.6 ft^3 Therefore the turtles have 4.5 square feet of surface area to get to in order to breath and 129.6 cubic feet in which to swim. The volume of the cylinder will be the area of it's cross section which is pi r^2 multiplied by the height. So pi * 6^2 * 8 = pi * 36 * 8 = pi * 288 = approximately 904.8 cubic inches.

Related Questions

Solve, kara's store experienced fixed costs of $200 and variable costs of $4 a shirt. write an equation that can be used to determine the total expenses encountered by kara's

Answers

Since the variable cost would be 4, you would multiply the variable of which is given, in this case, x, with 4. 4x
Since it's a fixed cost, you wouldn't touch the 200 and just add it to the 4x to get the total.

f(x)=4x+200

Find the equation perpendicular to the line y=−3x+5 that passes through point (2, 6).

Answers

Attached the solution and work.

Hey there! :)

Perpendicular to y = -3x + 5 ; passes through (2, 6).

Our slope is -3. We know this because it is in the "m" position from slope-intercept form. However, since our equation we're looking for is perpendicular to our given one, we must find the negative reciprocal of -3.

A negative reciprocal is simply a number that is flipped and either given a negative or gets a negative removed.

So the negative reciprocal of -3 is 1/3. This means that our new slope is 1/3.

Now, using point-slope form ( y-y₁=m(x-x₁) ), our new slope (1/3) & (2, 6) , let's find our new equation!

y-y₁=m(x-x₁) y - (6) = 1/3(x - 2)

Simplify.

y - 6 = 1/3x - 2/3

~Hope I helped!~

There are 11 books on a shelf. 5 of these books are new. (a) What is the ratio of new books to used books? (b) What is the ratio of used books to all books?

Answers

a)
Since 5 of the books are new, that means that the other books are used. So, there are 11-5=6. The ratio would be 5:6.

b)
The ratio is 6:11. You get the 6 from the above problem.

Hope this helps!

a) The ratio of new books to used books 5:6.

b) The ratio of used books to all books is 6:11.

What is the ratio?

The ratio is defined as the representation of one number with respect to the other number or one number is how many times the other number.

The ratio will be calculated as follows:-

a) Since 5 of the books are new, that means that the other books are used. So, there are 11-5=6. The ratio would be 5:6.

b) We know that the number of used books is 6. The ratio is 6:11.

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you can find the ______ parts of two congruent triangles by aligning them perfectly on top of each other.

A. corresponding

B. similar

C. complementary

D. supplementary

Answers

It is A. Corresponding.

You can find the corresponding parts of two congruent triangles by aligning them perfectly on top of each other.

What are Congruent Triangles?

Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape

The three sides are equal (SSS: side, side, side)

Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)

Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)

Given data ,

Let the first triangle be ΔABC

Let the second triangle be ΔDEF

Now , when the triangles are aligned perfectly on top of each other ,

They are corresponding and the and the measures of the angles are same

And , the measure of the legs of the triangles will also be congruent

Hence , the corresponding parts are same

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Which is NOT equivalent to 6/8? A.3/4 B.18/24 C.9/12 D.18/16

Answers

d d d d d d d d d d d d

D 18/16 because its over a whole number its 1.2 6/8 isnt a whole number

For the data shown in the scatter plot, which is the best estimate of r? -0.95, -0.55, 0.55, 0.95

Answers

From the data shown in the scater plots, the points are scattered apart which means that r is not close to 1.

Also the data points increase to the right which means that r is positive.

Therefore, the estimate for r in the data shown in the scatter plot is 0.55

Sarah has a $2000 bond with a 5% coupon. How much interest will Sarah received for this bond every 6 months?

Answers

Sarah has = $2000 5% coupon

n= interest in 6 months

$2000 x 5% = $100 interest in month

$100 x 6 months = $600 interest in 6 months

A normal probability/quantile plot is used to see if the distribution of a quantitative variable follows a __________ distribution.

Answers

The normal distribution has a mean of 0 and a standard deviation of 1.

Standard

I hoped this helped!

Suppose a college student pays $700 for tuition fees. However, she also has to pay $400 for her textbooks (ouch!). What percent of her total education costs does she pay for her books? Write your answer to the nearest tenth of a percent, but in decimal form.

Answers

400+700=1100

400/1100=0.36363636...

The books cost about 36 percent of her education costs

Final answer:

The student spends approximately 40% of her total education costs on her books, represented as 0.4 in decimal form.

Explanation:

The student's total education costs are the sum of the tuition fees ($700) and the cost of her books ($400). This comes to a total of $700 + $400 = $1100. The percent of the total education cost that is spent on books is then given by the cost of the books divided by the total cost, or $400 / $1100. When expressed as a decimal, this works out to be approximately 0.36 or 36%, but since we want to the nearest tenth of a percent in decimal form, it becomes 0.4 or 40% to the nearest tenth. Therefore, the student spends 40% of her total education costs on her books.

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The sales tax rate for a local county is 8.4%. If an item costs $391 (before tax), how much sales tax will be due?

Answers

For every 100 dollars, the sales tax would be around 8 dollars and 4 cents. Since there is still 91 dollars you would have to add around 7 dollars and 68 cents. You would go 8 x 3 for 24 plus 7 dollars for 31 dollars and then deal with the change. 4 times 3 is 12 cents plus 68 cents for 80 cents.

The total would be 31 dollars and 80 cents.

Yeah the answer would be 31 dollars and 80 cents :)

An angle is 5 times the measure of its complement. find the measure of the larger angle

Answers

Answer:

75°

Step-by-step explanation:

The angle is our unknown, so we will call it x. If x is the angle, then its complement is 90 - x (complementary angles add up to 90). The word "is" means "equals", and "5 times" is multiplying the complementary by 5:

x = 5(90 - x) so

x = 450 - 5x

Combine like terms to get

6x = 450 so

x = 75

The other angle, the complement to that angle, is 90 - 75 = 15

The larger angle is 75°

Angle bisectors of the angles ∠A and ∠B of a triangle ∆ABC intersect each other at point M. Find m∠AMB, if m∠A = 58°, m∠B = 96°.

Answers

measure angle A is 58 degrees, this means that, the angle bisector divides the angle into two equal angles each of measure 58/2 = 29 degrees

measure angle B is 96 degrees, this means that the angle bisector divides the angle into two equal angles each of measure 96/2 = 48 degrees

In triangle AMB, we know that the sum of all measure of a triangle is 180 degrees and we have measure angle MAB = 29 degrees and measure angle MBA = 48 degrees
Therefore,
measure angle AMB = 180 - (29+48) = 103 degrees

Answer:

103 degrees

Step-by-step explanation:

Bisectors means you make a line in the middle splitting the angle in half. So you divide A by 2 to get 29 and B to get 48. Then you add them to get 77. And now you only need point m's angle. 180-77 is 103 so the answer they are looking for is 103.

Which method of the math object rounds a value to the next lowest integer??

Answers

In Javascript, the math object that rounds a value to the next lowest integer is the math.floor(number);

The floor function. For example floor(1.75)=1

Omar makes 8 dollars for each hour of work. write an equation to represent his total pay p after working h hours.

Answers

Final answer:

The equation for Omar's total pay after working h hours at $8 per hour is p = 8h. This linear equation indicates a direct proportion between hours worked and total pay, reflecting a total of $64 for an 8-hour day.

Explanation:

The equation to represent Omar's total pay, p, after working h hours, at the rate of $8 per hour, is given by p = 8h. This linear equation shows that the total pay is directly proportional to the number of hours worked. Therefore, if Omar works for a standard 8-hour day, he would earn 8 hours times $8 per hour, which equals $64 for that day.

There is no answer choices. I really need help with this! prime factorize (expand) the expression 12a^3bd^5

Answers

[tex]\bf 12a^3bd^5\qquad \begin{cases} 12=2\cdot 2\cdot 3\\ a^3=a\cdot a\cdot a\\ d^5=d\cdot d\cdot d\cdot d\cdot d \end{cases}\implies (2)(2)(3)aaabddddd[/tex]

is all I can see, I mean, you can't kill a dead horse, you can hit it, it won't make it deader, just flatter.

A probability experiment consists of rolling a fair 12-sided die. Find the probability of the event below. rolling a 5

Answers

it is one out of twelve, if the twelve sides have all numbers from 1-12

Christa went shopping for back-to-school clothes. Before the tax was added on, her total was $176. If the sales tax is 6%, what was the total amount she paid?

Answers

First, you multiply 176 by the discount 6% or 0.06

176 * 0.06= 10.56
$10.56 represents the number that needs to be added to get the total

176+10.56= 186.56

So Christ spent $186.56 on back to school clothes

Answer:

$176·1.06 = $186.56

Therefore, the total amount that Christa paid was $186.56.

If p is a prime number, for how many values of p is p^2 +21p - 1 also prime?

Answers

ugherw;guih4g;/mr5t;
./erbgjkwehjbf.aeh bnjlnbwef erl,jh

Solve the inequality (show your work):

-5/2(3x + 4) < 6 - 3x

Answers

-5/2(3x+4)<6-3x Multiply through parenthesis by -5/2

-15/2x-10<6-3x Multiply both sides by 2

-15x-20<12-6x Move terms

-15x+6x<12+20 Combine like terms

-9x<32 Divide both sides by -9

x>-32/9 Answer

The value of the x is greater than negative of 32 over 9.

What is inequality?

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality is given as,

–5/2(3x + 4) < 6 – 3x

Simplifying the equation,

–5(3x + 4) < 2(6 – 3x)

5(3x + 4) > 2(3x – 6)

15x + 20 > 6x – 12

9x > –12 – 20

x > –32 / 9

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Decide which of the two points on the graph of the line
X=0
A. 0,7
B. -4,0

Answers

When x = 0

A. 0, 7 is your answer

hope this helps

Which number should replace the question mark in the number grid below?

Answers

B. 5

Each row across (left to right) adds up to 43

In 1995, 57.5% of students at gardiner university graduated in 4 or fewer years of study. in 2009, that number had fallen to 52.8%. what was the rate of change for percent of students graduating within 4 years from 1995 to 2009

Answers

-0.3357% per year The rate of change is given by change/time The change found by finding the difference in the two percentages: 52.8 - 57.5 = -4.7% The time that passed is found in a similar way 2009 - 1995 = 14 Now plugging in to the for

A worker currently receives a yearly salary of $20,000.

a)Find the dollar values of a 3%, 4%, and 6% raise for this worker

Answers

Take 20,000*1.03
do the same for 4% and 6%
And round to the nearest dollar

Hey!

Hope this helps...

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Because we are finding DOLLAR amounts, and not a total, we are simply going to do this:

Salary * (percent /100) = $Value

20,000 * 3% [or 0.03] = $600

20,000 * 4% [or 0.04] = $800

20,000 * 6% [or 0.06] = $1,200

Now to find his new salary if he were to get a raise, we will add the individual amounts to 20,000 is he were to only get a SINGLE percent raise increase...

If his salary (currently) is $20,000 and gets a 3% raise, his new salary is:

$20,600

If his salary (currently) is $20,000 and gets a 4% raise, his new salary is:

$20,800

If his salary (currently) is $20,000 and gets a 6% raise, his new salary is:

$21,200

If he were to get all THREE raises at the same time (per say) [or one after the other going off of a $20,000 salary], his new salary is:

$22,600

What is the area of a triangle with vertices at (−2, 1) , (2, 1) , and (3, 4) ?

Answers

Steps:

1. Let the three points be as follows:

A(-2,1), B(2,1), C(3,4)

2. Use the distance formula for points to find the lengths AB, BC, and AC. You will need to use the formula 3 times.

3. Use Heron's formula

A = sqrt{s(s-AB)(s-BC)(A-AC)}

Note s = (AB + BC + AC)/2

GET STARTED NOW.

check the picture below.

you can pretty much count the lengths off the grid.

recall that A = 1/2 bh.

Writing equation in slope intercept form

Answers

I will do B only. You do the rest. The idea is to isolate y for all equations.

using multiplication property of equality solve x/2=6

Answers

[tex] \frac{x}{2} [/tex] = 6
[tex] \frac{x}{2} [/tex] (2) = 6(2)
x=12

Answer:

x=12

Step-by-step explanation:

↓↓↓↓↓↓↓↓↓↓↓↓

Multiplication property of equality is multiply both sides of an equation by the same number does not change the equation.

[tex]\frac{x}{2}=6[/tex]

multiply two both sides

[tex]\frac{2x}{2}=6*2[/tex]

simplify

[tex]6*2=12[/tex]

[tex]12/2=6[/tex]

[tex]12/6=2[/tex]

[tex]2*6=12[/tex]

[tex]x=12[/tex]

Hope this helps!

Describe how to draw a line that passes through the origin and has a slope of 3/5

Answers

The "origin" of a line is simply the points (0, 0)

To draw a line that passes through the origin (0, 0) & has a slope of 3/5, we simply start by drawing a point at (0, 0).

Then, from there, you use the slope to find your next points.

Slope = rise/run

So, 3 is the rise, and 5 is the run.

So, starting from (0, 0), you go up 3 times, and go to the right 5 times. So, (3, 5) is your next point. Just continue doing that and you'll get a line.

~Hope I helped!~

PLEASE ANSWER
1. Simplify the following expression:

a + 2c − 5b − c + a − b

2a − 6b + 2c
2a − 6b + c
a − 6b + c
a − 5b + 2c

2. Evaluate the following expression using the values given:

Find 3x^2 − y^3 − y^3 − z if x = 3, y = −2, and z = −5.

Numerical Answers Expected!

Answer for Blank 1:

Answers

#1 2a - 6b + c

#2 48 ( i think this is right )

The expression is simplified as 2a − 6b + c. Then the correct option is B. The value of the expression 3x² - y³ - y³ - z will be 48.

What is the value of the expression?

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

The expression is given below.

⇒ a + 2c − 5b − c + a − b

Simplify the expression, then we have

⇒ 2a − 6b + c

Then the correct option is B.

The expression is given below.

⇒ 3x² - y³ - y³ - z

If x = 3, y = −2, and z = −5. Then the value of the expression will be

⇒ 3(3)² - (-2)³ - (-2)³ - (-5)

⇒ 3 x 9 + 8 + 8 + 5

⇒ 27 + 21

⇒ 48

The value of the expression 3x² - y³ - y³ - z will be 48.

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Order numbers least to greatest, -1.6, 5/2, -7/8, 0.9, -6/5

Answers

-1.6 , -6/5 , -0.875, 0.9, 2.5

The negative number many seem high but since the greatest negative number is closer to zero it is higher than the other negative numbers.

a piggy bank contains $2.40 in nickels and dimes. if there are 33 coins in all, how many nickels are there

Answers

There are 18 nickels and 15 dimes.

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1. Mrs.vega brought a new aquarium for her turtles. How much space will the turtles have in the aquarium if the length is 3.2 ft, the width is 1.5 ft and the height is 27 ft? 2. What is the volume of a cylinder that has a radius of 6 inches and height of 8 inches?

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1. Mrs.vega brought a new aquarium for her turtles. How much space will the turtles have in the aquarium if the length is 3.2 ft, the width is 1.5 ft and the height is 27 ft?

2. What is the volume of a cylinder that has a radius of 6 inches and height of 8 inches?