All categories

4 years ago

-QUICK PLEASE-

Mathematics

1 answer:

Zepler [3.9K]4 years ago

6 0

Answer:

Option B. 0.75 gallons is the right answer.

Step-by-step explanation:

Let the load of dishwasher used in house A = x gallons

Let the load of dishwasher used in house B is = y gallons

and similarly we assume for house C = z gallons

Now from the given question

On Friday amount of water used in all three houses = 17.5 gallons

From the table we will make the equation

x + 2y + 2z = 17.5-----(1)

For Saturday

2x + 3y + 4z = 31.5 ----(2)

For Sunday

2x + 2y + 3z = 24.75 -----(3)

By subtracting equation 3 from 2

y + z = 31.5 - 24.75 = 6.75 ------(4)

Equation (1) multiplied by 2 - equation (2)

2×(x + 2y + 2z) - (2x + 3y + 4z) = 17.5×2 - 31.5

y = 35 - 31.5 = 3.5

By putting y = 3.5 in the equation (4)

z = 6.75 - 3.5 = 3.25

By putting y = 3.5 and z = 3.25 in the equation (1)

x + 7 + 6.5 = 17.5

x = 17.5 - 13.5 = 4

Now the difference between load of dishwasher that uses least water and the most.

x - z = 4 - 3.25 = 0.75 gallons

Option B is the right answer.

You might be interested in

How do you solve 0.25(3x-1)^2=13 for Graphing Parabolas in Vertex Form?

Oksanka [162]

Get the app Socratic and then take a pic, it will explain it better than anybody on here can

4 0

3 years ago

The sum of a number and its ??? equals 0

yarga [219]

Sum of the number and its of inverse equals 0.
$a+(-a)=a-a=0$

6 0

3 years ago

Sophie bought a cylindrical rain barrel to water her garden, but she forgot to ask the seller what the

Assoli18 [71]

The diameter of the cylindrical rain barrel which Sophie bought to water her garden, and want to build a platform for it is 15 in.

<h3>What is of volume of cylinder?</h3>

Volume of cylinder is the amount of quantity, which is obtained by it in the 3 dimensional space.

The volume of the cylinder can be given as,

$V=\pi r^2h$

Here, (r) is the radius of the base of the cylinder and (h) is the height of the cylinder.

Sophie bought a cylindrical rain barrel to water her garden, but she forgot to ask the seller what the diameter of the barrel was.

She needs to know the diameter so that she can build a platform for it to sit on.

The seller told her the volume of the barrel is 6,925pi cubic in and its height is 38 in.

$V=\pi r^2h\\6925=\pi r^2(38)\\\dfrac{6925}{38\pi}= r^2\\r=\sqrt{\dfrac{6925}{38\pi}}\\r\approx7.62 \rm\; in$

The diameter of the cylinder is twice the radius of it. Thus, the diameter of the cylinder is,

$d=7.62\times2\\d=15.23\rm\\d\approx15\rm\; in$

Thus, the diameter of the cylindrical rain barrel which Sophie bought to water her garden, and want to build a platform for it is 15 in.

Learn more about the volume of cylinder here;

brainly.com/question/12748872

#SPJ1

7 0

2 years ago

Consider the differential equation:

Wewaii [24]

(a) Take the Laplace transform of both sides:

$2y''(t)+ty'(t)-2y(t)=14$

$\implies 2(s^2Y(s)-sy(0)-y'(0))-(Y(s)+sY'(s))-2Y(s)=\dfrac{14}s$

where the transform of $ty'(t)$ comes from

$L[ty'(t)]=-(L[y'(t)])'=-(sY(s)-y(0))'=-Y(s)-sY'(s)$

This yields the linear ODE,

$-sY'(s)+(2s^2-3)Y(s)=\dfrac{14}s$

Divides both sides by $-s$ :

$Y'(s)+\dfrac{3-2s^2}sY(s)=-\dfrac{14}{s^2}$

Find the integrating factor:

$\displaystyle\int\frac{3-2s^2}s\,\mathrm ds=3\ln|s|-s^2+C$

Multiply both sides of the ODE by $e^{3\ln|s|-s^2}=s^3e^{-s^2}$ :

$s^3e^{-s^2}Y'(s)+(3s^2-2s^4)e^{-s^2}Y(s)=-14se^{-s^2}$

The left side condenses into the derivative of a product:

$\left(s^3e^{-s^2}Y(s)\right)'=-14se^{-s^2}$

Integrate both sides and solve for $Y(s)$ :

$s^3e^{-s^2}Y(s)=7e^{-s^2}+C$

$Y(s)=\dfrac{7+Ce^{s^2}}{s^3}$

(b) Taking the inverse transform of both sides gives

$y(t)=\dfrac{7t^2}2+C\,L^{-1}\left[\dfrac{e^{s^2}}{s^3}\right]$

I don't know whether the remaining inverse transform can be resolved, but using the principle of superposition, we know that $\frac{7t^2}2$ is one solution to the original ODE.

$y(t)=\dfrac{7t^2}2\implies y'(t)=7t\implies y''(t)=7$

Substitute these into the ODE to see everything checks out:

$2\cdot7+t\cdot7t-2\cdot\dfrac{7t^2}2=14$

5 0

3 years ago

Umm.. Hi there! Can someone please help me out with this? (only for those who know the answer)

nignag [31]

Answer:

The Exterior Angle of triangle LDR is angle d. The Remote Interior Angles are a and b.

The Exterior Angle of triangle PDR is angle 4. The Remote Interior Angles are angles 1 and 2

Explanation:

<u>Interior angles</u> are the angles that are inside the shape. The <u>remote interior angles</u> would be the 2 angles away from the exterior angle.

The <u>exterior angle</u> is the angle, made by the side of the shape and a line drawn out from an adjacent side.

I hope this helps!

6 0

3 years ago

Read 2 more answers