8meters long 4 meters wide and 2 meters deep.What is the volume of the pond.

Answers

Answer 1

Volume of a 3 dimensional object is Length x Width x Height. The length is 8 meters, the width is 4 meters, and the height (the depth rather) is 2 meters. Therefore, the volume of the pond is equal to 8 x 4 x 2

8 x 4=32 x 2=64

The volume of the pond is 64 meters

Related Questions

What is the line of symmetry for the parabola whose equation is y = x2 + 10x + 25

Answers

In order to do this, use the simple formula x = -b/2a, where a and b are taken directly from the equation for the parabola. a = 1 and b = 10, so your line of symmetry equation is x = -10/2(1) or x = -5, which is also the x coordinate of the vertex. The long way that will tell you that y coordinate of the vertex would be to put it into vertex form by completing the square. But not necessary here as you are only being asked for the line of symmetry. If you are told to find the coordinates of the vertex this simplified equation will not work.

Answer:

x= -5

Step-by-step explanation:

What is the place value for 5 in the number 12354897

Answers

It would be in the ten thousands place.

Write down all elements of ({9, 10, 11} ∩ {10, 11, 12, 13}) ∪ {14, 15}. (enter your answer in set notation.)

Answers

What we have so far:
Let set A = {9, 10, 11}
Let set B = {10, 11, 12, 13}
Let set C = A∩B. This means: the intersection of A & B.
Let set D = {14, 15}
Let set Universal = C∪D. This means: the union of C & D where C is the intersection of A & B.

Solution:
Let us first solve for set C.
C = A∩B
C = {9, 10, 11} ∩ {10, 11, 12, 13}
C = {10, 11} <--- New value for set C

Let us now solve for set Universal.
Universal = C∪D
Unviversal = {10, 11} ∪ {14, 15}
∴ Universal = {10, 11, 14, 15} <--- What we are looking for.

Therefore, the answer is Universal = {10, 11, 14, 15}.

A pallet stacked with bags of cement weighing a total of 5501 N must be pushed up a 2.30-m incline to a 75.0-cm high platform. What force, in Newtons, must be applied to get the job done?

Answers

Assume that the incline is frictionless.
Refer to the diagram shown below.

Note that 75 cm = 0.75 m.
Therefore the angle of the incline is given by
sin(x) = 0.75/2.3 = 0.3261.

The weight pushed up the incline is W = 5501 N.
The component of the weight acting down the incline is
W*sin(x) = 5501*0.3261 = 1793.9 N

The force, F, should overcome this weight acting along the incline, therefore
F = 1794 N (nearest integer)

Answer: 1794 N

Prove the identity

cos(-x)/[1+sin(-x)]=secx+tanx

Answers

↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓↓

I thought of a number, doubled it, then decreased by 17. Then I divided the result by 3. I got 15. What was my number?

Answers

is your answer 31 .. i might be wrong but i tried

The number person thinking about is 14.

Given that, I thought of a number, doubled it, and then decreased it by 17. Then I divided the result by 3. I got 15.

What is the equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number be x.

Double it=2x

Decreased it by 17=2x+17

Divided the result by 3=(2x+17)/3

The result is equal to 15.

(2x+17)/3=15

⇒2x+17=45

⇒2x=28

⇒x=14

Therefore, the number person thinking about is 14.

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True or false The coefficient of (x^(k)) (y^(n-k)) in the expansion of (x+y)^n equals (n choose k)

Answers

This is under the binomial theorem. A binomial theorem is an equation that predicts the sequence when a binomial is raised to certain power. The general form of the equation is (a+b)^n. The equation for the binomial theorem would be

nCk a^(n-k) b^k, where k is the kth term of the expanded form, n is the nth power. The coefficient of the term in the binomial expansion is nCk or n!/k!(n-k)!.

Find an implicit and an explicit solution of the given initial-value problem. (use x for x(t).) dx dt = 2(x2 + 1), x(π/4) = 1

Answers

[tex]\displaystyle \dfrac{dx}{dt}=2(x^2+1)\\\\ \int_{t_0}^t dt=\int_{x_0}^x\dfrac{dx}{2(x^2+1)}\\\\ t-t_0=\dfrac{1}{2}\int_{x_0}^x\dfrac{dx}{(x^2+1)}\\\\ t-t_0=\dfrac{1}{2}\left[\arctan(x)\right]_{x_0}^x\\\\ t-t_0=\dfrac{1}{2}\left[\arctan(x)-\arctan(x_0)\right][/tex]

We'll use [tex]x(\pi/4)=1[/tex], considering that [tex]x_0=1, t_0=\dfrac{\pi}{4}[/tex]:

[tex]t-t_0=\dfrac{1}{2}\left[\arctan(x)-\arctan(x_0)\right]\\\\ t-\dfrac{\pi}{4}=\dfrac{1}{2}\left[\arctan(x)-\arctan(1)\right]\\\\ t-\dfrac{\pi}{4}=\dfrac{1}{2}\left[\arctan(x)-\dfrac{\pi}{4}\right]\\\\ t-\dfrac{\pi}{4}=\dfrac{1}{2}\arctan(x)-\dfrac{\pi}{8}\\\\ t-\dfrac{\pi}{8}=\dfrac{1}{2}\arctan(x)\\\\ \boxed{\arctan(x)=2t-\dfrac{\pi}{4}}[/tex]

Applying tan in the both sides:

[tex]\arctan(x)=2t-\dfrac{\pi}{4}\\\\ \tan(\arctan(x))=\tan\left(2t-\dfrac{\pi}{4}\right)\\\\ \boxed{x(t)=\tan\left(2t-\dfrac{\pi}{4}\right)}[/tex]

if I'm going to the lake that is 60 miles away and I'm driving 40 miles per hour how long would it take for me to get there

Answers

About 1.5 hours since you would do distance divided by the rate to get the time.

Select true and false for each question.

a.) LN(x^a) = a + LN x
b.) LN sqrt of 3(xy) = 1/3 (ln x + ln y)
c.) (ln a)^3b = 3b ln a
d.) log_a b^2 = (log_a b)^2

Answers

Select true and false for each question.

a.) LN(x^a) = a + LN x
b.) LN sqrt of 3(xy) = 1/3 (ln x + ln y)
c.) (ln a)^3b = 3b ln a
d.) log_a b^2 = (log_a b)^2 = True

The total cost for playing paintball is Php 100 per gun for rent and Php 1000 per 2000 paintballs. Assuming only 2000 paintballs is allowed for team who will play, which of the following function notation matches the situation?

Answers

For problems involving algebra, you have to formulate algebraic equations to be able to solve the problem. Algebraic equations are mathematical terms which include variables to denote the unknown numbers.

For this problem, you are to find the total cost which consists of cost for the gun rent and cost for the paintballs. Hence, your equationmust consist of two terms. The equation must be:

Total cost = 100x + 1000

The term x denotes the number of guns. Hence, it must be multiplied with 100 to determine the cost. On the otherhand, the constant 1000 is for the paintballs. Since it was given that each team must have 2000 paintballs, then it follows that they must pay 1000 Php.

Alfredo delivers the daily newspaper to every even numbered house in his block. If he starts at number 68 and finishes at number 512, how many papers does he deliver every day.

Answers

he delivers 224 papers every day

Answer:

Alfredo delivers the daily newspaper to every even numbered house in his block. If he starts at number 68 and finishes at number 512, how many papers does he deliver every day.

Step-by-step explanation:

From 512 to 68, there are a total of 444 houses, of which 222 are pairs, which is half, if it is even with the previous two, would be 224, otherwise, 222, if one yes and the other does not, 223.

What related number sentence shows the commutative property addition 3+9=12

Answers

The related number sentence that shows the commutative property addition for the equation 3+ 9 + 12 is 9 + 3 = 12

Please take note, the commutative property of addition is
a + b = c
b + a = c
a + b = b + a

Commutative originates from the word move around or commute, therefore, commutative property refers to the act of moving stuff around. In addition, the rule is a + b = b + a; wherein from the example above, means 9 + 3 = 3 + 9. They want to say that the computation uses the Commutative Property, if at any time, a computation depends on moving stuff around

A computer repairman makes $25 per hour. Which equation models the situation? Let h represent the hours worked. Let d represent the total amount earned.

Answers

The total amount earned, d, with respect to the number of hours, h, worked is:

d(h)=25h

Rotating Light A searchlight rotates through one complete revolution every 4 seconds. How long does it take the light to rotate through 90°?

Answers

it takes 1 second. beep beep

Using the formula in model 1, choose the correct answers for the total amount and amount of interest earned in the following compound interest problem. $500 at 4% for 5 years, compounded annually. Total Amount = $ Interest Amount =$

Answers

The formula to find the total amount is
A=p (1+r)^t
A total amount?
P present value 500
R interest rate 0.04
T time 5years
A=500×(1+0.04)^(5)=608.33

To find the interest amount just subtract the amount of the present value from the total amount
interest amount
608.33−500=108.33

Answer:

608.33

108.33

Step-by-step explanation:

Found answer in above answer.

Suppose you buy a 1.25-pound package of ham at $5.20 per pound.What fraction of a pound did you buy

Answers

You bought [tex]$ \frac{25}{104} $[/tex]of a pound of ham, which is approximately 0.2404 pounds.

To find the fraction of a pound you bought, divide the total weight by the price per pound.

Given:

Total weight = 1.25 pounds

Price per pound = $5.20

[tex]\[ \text{Fraction of a pound} = \frac{\text{Total weight}}{\text{Price per pound}} \]\[ \text{Fraction of a pound} = \frac{1.25}{5.20} \]\[ \text{Fraction of a pound} \approx \frac{125}{520} \][/tex]

Now, simplify the fraction:

[tex]\[ \text{Fraction of a pound} \approx \frac{25 \times 5}{104 \times 5} \]\[ \text{Fraction of a pound} = \frac{25}{104} \][/tex]

So, you bought [tex]$ \frac{25}{104} $[/tex] of a pound of ham.

A football is punted from a height of 2.5 feet above the ground with an initial vertical velocity of 45 feet per second. Write an equation to model the height h in feet of the ball t seconds after it has been punted. The football is caught at 5.5 feet above the ground. How long was the football in the air?

Answers

First assume that the football is going straight up, that is important. next you have a good rate problem here. So you have y = mx + b, where m is the rate and b is the starting point. Now plug in data m is 45 ft/s and b = 2.5ft, so the equation is y = 45x + 2.5. Now the ball was caught at 5.5 so put that in for y. 5.5 = 45x + 2.5. Solve to get 1/9 of a sec.

The equation for the height of a football punted with initial conditions is calculated, and the time the football spent in the air is determined.

Given: Initial height = 2.5 feet

Initial vertical velocity = 45 ft/s

The height at which the ball is caught = is 5.5 feet

Equation to model height: h(t) = -16t² + 45t + 2.5 where h(t) is the height at time t seconds.

Time in the air: To find how long the ball is in the air, solve for t when h(t) = 5.5 feet.

Final answer: The football was in the air for approximately 1.9 seconds.

A plane travel from California and back it took one hour long on the way out than it did on the way back the planes average speed was 300 miles an hour the average speed on the way back with 350 miles an hour how many hours did the trip take

Answers

recall your d = rt, distance = rate * time

the distance the plane travelled over and back was the same distance, say "d", since it simply went over to that city and then it came back from it.

if it took say "t" hours to come back, on the way over, it took then " t + 1 ", because it took longer on the way out by 1 hour.

and we know the speed rates.... ok

[tex]\bf \begin{array}{lccclll} &distance&rate&time\\ &-----&-----&-----\\ \textit{going out}&d&300&t+1\\ \textit{coming back}&d&350&t \end{array} \\\\\\ \begin{cases} \boxed{d}=300(t+1)\\ d=350t\\ ----------\\ \boxed{300(t+1)}=350t \end{cases}[/tex]

solve for "t" to see how many hours it took on the way back.

the whole trip took then (t + 1) + t

A local grocer wants to find out whether how many mixed flower bouquets in his inventory everyday. To that end, kept records of the daily bouquet sales for the last 27 days. The average number of bouquets sold every day was 11.8 and the sample standard deviation is 2.3. Construct a 99% confidence interval for the number of bouquets sold on a given day..

Answers

Given:
n = 27, sample size
df = n-1 = 26, degrees of freedom
xb = 11.8, sample mean
s = 2.3, sample standard deviation.

Because population statistics are not known, we should use the Student's t-distribution.
At 99% confidence interval, the t-value = 2.779 (from tables).
The confidence interval is
11.8 +/- 2.779*(2.3/√(27)) = 11.8 +/- 1.23 = (10.57, 13.03)

Answer: (10.6, 13.0) to the nearest tenth

under which of the following operations are the polynomials 3x+2 and 4y-11 not closed

Answers

Lets check all the choices:

A. subtraction:

(3x+2)-(4y-11)=3x+2-4y+11=3x-4y+13

similarly, (4y-11)-(3x+2)=-3x+4y-13

both are polynomials (of 2 variables)

B. (3x+2)(4y-11)=12xy-33x+8y-22, which is a polynomial

C. (3x+2)+(4y-11)=3x+2+4y-11=3x+4y-9, which is a polynomial

D.
both [tex] \frac{3x+2}{4y-11} [/tex] and [tex] \frac{4y-1}{3x+2} [/tex] are rational expressions in 2 variables, not polynomials

Answer: D

Tina is placing 30 roses and 42 tulips in vase for table decorations in her restaurant each vase will hold the same number of flowers each vase will have only one type of flower what is the greatest number of flowers She can place it each vase

Answers

6 flowers... for a total of 12 vases: 5 of roses and 7 of tulips

Answer: 6

Step-by-step explanation:

Given : Tina is placing 30 roses and 42 tulips in vase for table decorations in her restaurant .

Each vase will hold the same number of flowers and each vase will have only one type of flower .

Then, the greatest number of flowers she can place it each vase will be the greatest common factor of 30 and 42.

Prime factorization of 30 and 42 :

[tex]30=2\times3\times5\\\\42=2\times3\times7[/tex]

We can see that greatest common factor of 30 and 42 = [tex]2\times3=6[/tex]

Hence, the greatest number of flowers she can place it each vase =6

whats the solution of the equation

Answers

3x+9-7x=2(x+6)

3x-7x = -4x

-4x+9 =2x+12

9=6x+12

-3 = 6x

x=-3/6 = - 1/2

x = - 1/2

How to simplify?
2a - 4b - 16 + (3a + 7 ) - 8

Answers

2a + 3a -4b -16+7-8 group terms
= 5a -4b -17

an architectural drawing lists the scale as 1/4"=1'. if a bedroom measures 2 1/2" by 3 3/4" on the drawing, how large is the bedroom?

Answers

One way to solve this type of problem is to use proportions.

1/4" equals 1 ft
2 1/4" corresponds to how many feet? Call this "x."

Then 1
--
4 1 ft
------------------ = -----------
9
--- x
4

Solve this for x. First, reduce the first set of fractions. That boils down to (1/9).

Equate (1/9) to 1/x. It's obvious that x = 9 (feet).

Use the same method to find the length of the bedroom.

Answer:

The answer is 10 ft by 15 ft

Step-by-step explanation:

2 1/2 is also 2 2/4

Since 1/4 = 1

2/4 = 2 feet

Plus the whole number being 2 from 2 2/4 equates to 8 feet

because 2 is the same as 8/4.

2 2/4 = 10 feet

Do the same with 3 3/4 and you get 15 feet total.

Resulting in 10 ft by 15ft

Tim is employed at an annual salary of $23999.04.his regular workweek is 36 hours and he is paid semi monthly. What is caseys remineration of gross per pay period ? What is his hourly rate of pay ? What is his gross pay for a period in a which he worked

Answers

$23999.04/24=$999.96 = bi-weekly = 72 hrs 999.96/72 =$13.88833333333333

Final answer:

Tim's gross pay per pay period is $999.96. His hourly rate is approximately $12.82. This was calculated by dividing his annual salary by the number of pay periods and dividing his pay per period by the number of work hours per period respectively.

Explanation:First, we start by finding Tim's pay per pay period. Since he is paid semi-monthly, this means he is paid twice a month and since there are 12 months in a year, he will have 24 pay periods in a year. To calculate his gross pay per pay period, we divide his annual salary by the number of pay periods: $23999.04 ÷ 24 = $999.96 per pay period. Next, we calculate Tim's hourly rate. Since he works 36 hours in a week, and there are roughly 4.33 weeks in a month (52 weeks in a year / 12 months = 4.33), his monthly work hours would be 36 hours * 4.33 = roughly 156 hours. Since he's paid twice a month, his total work hours per pay period would be 156 / 2 = 78 hours. If we divide his pay per period by the number of work hours per period, we get his hourly rate: $999.96 ÷ 78 hours = roughly $12.82 per hour.

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Ed ate 3/8 of the pizza and jen ate 1/4 of the pizza. How much of the pizza is left

Answers

one third is left, i think. Sorry, I might be off.

First of all, Ed ate 3/8 of the pizza and jen ate 1/4 of the pizza which means that they are total 3/8+1/4=3/8+2/8=5/8 of the pizzas. Also, we know the pizza has portion of 1 or 8/8 in this case, so 8/8-5/8=3/8 represent the portion of pizza is left. As a result, the pizza is 3/8 left. Hope it help!

The equation of a given circle in general form is x2+ y2 − 8x + 12y + 27 = 0. Write the equation in standard form, (x − h)2 + (y - k)2 = r2, by completing the squares in the equation. Show your work in a table.

Answers

The equation of the circle is [tex] x^{2} + y^{2} +8x+12y+27=0[/tex]

we take x-es and y-s 'close' to each other, and complete the square:

[tex]x^{2}+8x + y^{2} +12y+27=0[/tex]

write the coefficients of the linear terms (the x and y with degree 1) as 2*'something', to see how to complete the square:

[tex]x^{2}+2*4*x + y^{2} +2*6*y+27=0[/tex]

which means that [tex]x^{2}+2*4*x[/tex] needs [tex] 4^{2} [/tex]

and [tex]y^{2} +2*6*y[/tex] needs [tex] 6^{2} [/tex] to become perfect square trinomials:

[tex](x^{2}+2*4*x + 4^{2})-4^{2} + (y^{2} +2*6*y+ 6^{2})-6^{2} +27=0[/tex]

[tex] (x+4)^{2}+ (y+6)^{2}=16+36-27 [/tex]
[tex] (x+4)^{2}+ (y+6)^{2}=25 [/tex]

[tex](x-(-4))^{2}+ (y-(-6))^{2}= 5^{2} [/tex]

Answer: [tex](x-(-4))^{2}+ (y-(-6))^{2}= 5^{2} [/tex]

Answer:

Step Reason

x2 + y2 - 8x + 12y + 27 = 0 given

x2 - 8x + y2 + 12y = -27 Isolate the constant term

x2 - 8x + 16 + y2 + 12y + 36 = -27 + 16 + 36 Complete the square by adding . 16 and 36 to both sides.

(x2 - 2∙4∙x + 42) + y2 + 12y + 36 = 25 Group and rearrange terms in x.

(x - 4)2 + y2 + 12y + 36 = 25 (a - b)2 = a2 - 2ab + b2

(x - 4)2 + (y2 + 2∙6∙y + 62) = 25 Group and rearrange terms in y.

(x - 4)2 + (y + 6)2 = 25 (a + b)2 = a2 + 2ab + b2

(x - 4)2 + (y + 6)2 = 52 Take the square root to find r = 5.

Step-by-step explanation:

this is the exact answer from plato

hope this helps a little bit :))

let log P/N=8 and log M/N=5

What is the relationship between P and M?

Answers

Want to use some of the algebra rules of log's:

log(a)-log(b)= log(a/b),

so log(P/N) - log(M/N) = log( P/N:M/N) = log(P/M),

Then: 8-5 = log(P/M), log(P/M)=3.

If log here means natural logarithm (base e), then P/M = e^3,

If log here means basis 10, decimal logarithm, then P/M = 10^3 = 1000.

Translate the sentence into an equation. Nine more than the quotient of a number and 7 is equal to 3 . Use the variable y for the unknown number.

Answers

Hi!

Nine more = 9 +
Quotient of a number and 7 = y/7
Equal to three = = 3

Put it together:

9 + y/7 = 3
^ the answer

Bonus points if you can tell me what y equals ;)

Hope this helps! :)

The equation is 9+ y/7 = 3

What is equation?

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S

Given statement:

Nine more than the quotient of a number and 7 is equal to 3.

let the number be y

The 9+ y/7 = 3

quotient of a number and 7 is y/7

and, nine more than= 9+ y/7

So, 9+ y/7 = 3

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