A leaky faucet wastes 2,400 gallons of water per year. How many quarts of water are wasted per month? [1 gallon = 4 quarts]

Answer:

2700

Step-by-step explanation:

Answer:

Based off of the given information I believe the answer is 8,000,000 hydrogen atoms because it appears that the ratio between hydrogen and oxygen atoms in 2:1.

Step-by-step explanation:

Using the 2:1 ratio of hydrogen to oxygen atoms in water (H2O), a volume of water with 4,000,000 oxygen atoms would contain 8,000,000 hydrogen atoms.

We know that water, with the chemical formula H2O, consists of two hydrogen atoms for every oxygen atom. Using this information, for every oxygen atom in water, we need to account for two hydrogen atoms.

Given that a certain volume of water contains 100,000 hydrogen atoms and 50,000 oxygen atoms, we have a 2:1 ratio of hydrogen to oxygen atoms. If we want to determine how many hydrogen atoms are in a volume of water containing 4,000,000 oxygen atoms, we must apply the same 2:1 ratio.

To do so, we multiply the number of oxygen atoms by 2 (since there are two hydrogen atoms for every one oxygen atom), obtaining: 4,000,000 oxygen atoms  times 2 = 8,000,000 hydrogen atoms.

Answer:

if i don't doubt then 1/4

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

Just did test

Answer:

= 32√3 ft²

Step-by-step explanation:

Area of the trapezoid will be equal to the area of the square and that of the triangle.

Considering the triangle part;

Cos 60 = x/8

x = 8 × sin  60

   = 4

Base of the triangle part = 4 ft

Therefore, top of the trapezoid = 6 ft

Height = 8 × sin 60

            = 8 × √3/2

           = 4 √3

Area of the trapezoid

Area = ((a+b)/2) × h

        = ((6 + 10 )/2 )× 4√3

        = 16/2 × 4√3

        = 32√3 ft²

Answer:

4th option is correct

Step-by-step explanation:

Here in the triangle we have angle = 60

hypotenuse= 8

opposite and adjacent can be solved using trigonometric ratios

cos 60  = [tex]\frac{adjacent}{hupotenuse} \\\frac{adjacent}{8} \\\frac{1}{2}=\frac{adjacent}{8}[/tex]

which gives adjacent = 4  on solving

likewise using sine we can find opposite side to the angle which is height of

trapezium.

sin60[tex]\frac{opposite}{hypotenuse}=\frac{x}{8} \\\frac{\sqrt{3} }{2}=\frac{x}{8}\\x=4\sqrt{3}[/tex]

therefore height =[tex]4\sqrt{3}[/tex] and adjacent = 4  ft

therefore opposite sides of Trapezium are 10 ft and 6 ft  

Formula for area of Trapezium =[tex]\frac{1}{2}[/tex](sum of parallel sides)x height

=      [tex]\frac{1}{2}[/tex](10+6)x [tex]4\sqrt{3}[/tex]

on solving it ,we get  [tex]32\sqrt{3}[/tex]

Answer:   [tex]\bold{\dfrac{11}{18}}[/tex]

Step-by-step explanation:

Think of the products row by row:

11  12  13  14  15  16  - 0 products greater than 6

21 22 23 24 25 26  - 3 products greater than 6

31 32 33 34 35 36  - 4 products greater than 6

41 42 43 44 45 46   - 5 products greater than 6

51 52 53 54 55 56  - 5 products greater than 6

61 62 63 64 65 66  - 5 products greater than 6

[tex]\dfrac{\text{number greater than 6}}{\text{total possible outcomes}}=\dfrac{22}{36}=\dfrac{11}{18}\ when\ reduced[/tex]

Answer:

11/18.

Step by.step explanation:

There are 36 possible outcomes when 2 dice are rolled.

Outcomes for a product greater than six are:

2,4  2,5  2,6  3,3  3,4  3,5  3,6  4,2  4,3  4,4  4,5  4,6  5.2 ......5.6 , 6.2 .......6.6.

=  22 ways.

required Probability is 22/36 = 11/18 (answer).

Answer:

  x = 11.5

Step-by-step explanation:

Taking the logarithm base 2 will transform this to a linear equation.

  2(2x+7) = 3(2x -3)

  0 = 3(2x -3) -2(2x +7) . . . . subtract the left side

  0 = 2x -23 . . . . . . . . . . . . . simplify

  0 = x - 23/2 . . . . . . . . . . . . divide by 2

  11.5 = x . . . . . . . . . . . . . . . . add 11.5

The solution is x = 23/2 = 11.5.

_____

Check

This value of x makes the equation become ...

  4^(2·23/2 +7) = 8^(2·23/2 -3)

  4^30 = 8^20 . . . . . true

Answer:

Geometric

Step-by-step explanation:

Does multiplying the same number with each term give the next term?

If so, then it is Geometric Sequence.

Does adding the same number with each term give the next term?

If so, then it is Arithmetic Sequence.

We see that multiplying by 3 gives us each successive term. 2 times 3 is 6 and 6 times 3 is 18. So it is geometric sequence.

It is NOT arithmetic sequence since we add 4 to 2 to get next number 6, but we have 12 to get next number, which is 18. So not an arithmetic sequence.

Answer is "Geometric"

$10.75 x 8 = $86 x 4(weeks) = $344

Multiply his hourly rate by the number of hours per week:

$10.75 x 8 hours = $86.00 per week.

An average month has 4 weeks, so in a 4 week month, multiply his weekly pay by the number of weeks in a month. ( Some months have 5 weeks, so you would need to multiply the weekly amount by 5 weeks).

$86 x 4 weeks = $344

20% as a fraction is 1/5

25% is 1/4

40% is 2/5

and 70% is 7/10

Depending on what your fraction is, you can find the answer in the fraction itself-

20%, you can take 20, 5 times to get to 100. Hence 1/5.

25 can go into 100 4 times (1/4)

40 is just 20 twice, so its 2/5.

Take 10 7 times and get 7/10.

Hope this helps a bit :)

Answer:

Popcorn costs: $5.75, and drink costs: $2.25.

Step-by-step explanation:

Answer:

44.50 = 3 x + 4 y

84= 4x +8 y

each popcorn bag costs $2.5

Step-by-step explanation:

Hi, to answer this question we have to write a system of equations:

The total cost for Kevin (44.50) is equal to the product of the number of popcorn bags bought (x ) and the price of each bag, plus the product of the number of drinks purchased (y) and the price of each drink (y).

Mathematically speaking

Kevin : 44.50 = 3 x + 4 y

Using the same process for Levi:

Levi : 84= 4x +8 y

The system is  

44.50 = 3 x + 4 y (k)

84= 4x +8 y (L)

If we multiply Kevin's equation by 2 and subtract it to Levi's equation:

89 = 6x +8y

          -

( 84= 4x +8 y)

----------------------

5 = 2x

solving for x

5/2= x

2.5 =x

each popcorn  costs $2.5

Answer:

Step-by-step explanation:

________

Good evening ,

________________

“”There are 9 pages in the album ,Farah puts the same number of photos on each page ,for a total of 63 photos “”

We can explain the last sentence this way : “ 9p = 63” then p=7

__

:)

Answer:

Step-by-step explanation:

-4x∧2  -1

-4x squared minus one

Answer:

True

Step-by-step explanation:

The given inequality is

[tex]5\le x\le 8[/tex]

The boundaries of the inequality are inclusive.

We use the square brackets to indicate closed interval.

[tex]5\le x\le 8[/tex] is therefore written in interval notation as;

[5,8]

The correct choice is true

[tex] \frac{27 \: miles \div 2}{2 \: hours \div 2} = \frac{13.5 \: miles}{1 \: hour} [/tex]

[tex] \frac{13.5 \: miles \div 2}{1 \: hour \div 2} = \frac{6.75 \: miles}{0.5 \: hour} [/tex]

The boat will travel 6.75 or

[tex]6 \frac{3}{4} [/tex]

miles in 1/2 hour.

Your Answer: 2 1/2 (The integer two, and the proper fraction one all over two.)

Explanation: If Brooke gave her dog two whole biscuits and then a half, it would sum up to the improper fraction 5/2 (Five all over two.) When you divide 5 by 2, you get 2.5, which is equivalent to 2 1/2.

Hope this helps ya :D

Answer:

The draw in the attached figure

Step-by-step explanation:

Let

L-----> the length of the rectangle

W----> the width of the rectangle

we know that

The perimeter of a rectangle is equal to

[tex]P=2(L+W)[/tex]

we have

[tex]W=23\ ft[/tex]

so

[tex]P=2L+46[/tex] -----> equation A

[tex]P\leq 236\ ft[/tex]  ----> inequality B

substitute equation A in the inequality B and solve for L

[tex]2L+46\leq 236[/tex]

[tex]2L\leq 236-46[/tex]

[tex]2L\leq 190[/tex]

[tex]L\leq 95\ ft[/tex]

The maximum possible  value of L is 95 ft

therefore

The rectangle could be

Length 95 ft

Width 23 ft

see the attached figure to see the draw

Answer:

[tex]\large\boxed{A\subset B}[/tex]

Step-by-step explanation:

[tex]A=\{1,\ 2\},\ B=\{1,\ 2,\ 3,\ 4\}\\\\A\subset B,\ \text{because all elements of the set A are the elements of the set B.}[/tex]

Answer:

See explanation

Step-by-step explanation:

If MA is tangent to the circle k(O), then radius OA is perpendicular to segment MA.

If MB is tangent to the circle k(O), then radius OB is perpendicular to segment MB.

Consider two right triangles MOA and MOB. In these triangles:

Thus, triangles MOA and MOB are congruent by HL theorem. So

∠AMO=∠BMO.

If point C is symmetric to point O with respect to point B, then OC⊥MB. Consider two right triangles MOB and MCB. In these triangles:

Thus, triangles MOB and MCB are congruent by HL theorem. So

∠BMO=∠BMC.

Hence,

∠AMC=∠AMO+∠BMO+∠BMC=3∠BMC.

Answer:

Step-by-step explanation:

15 less than twice a number g is 19

2g - 15 = 19      add 15 to both sides

2g - 15 + 15 = 19 + 15

2g = 34       divdie both sides by 2

2g : 2 = 34 : 2

g = 17

Since an 100% chance is all possibilities, then it must add up to 100. If we take away that 14 from 100 by subtracting, you just get 86. Therefore, there is an 86% chance that it will not rain tomorrow.

Answer:

5 minutes

Step-by-step explanation:

300 seconds / x minutes = 60 seconds / 1 minute

300 = 60x; divide both sides by 60 to get x; 5 = x

Answer:

[tex]103\ seconds[/tex]

Step-by-step explanation:

Let

x-----> the length of the smaller section in seconds

y----> the length of the longer section in seconds

we know that

[tex]x+y=180[/tex] ----> equation A

[tex]\frac{x}{y}=\frac{3}{4}[/tex]

[tex]x=\frac{3}{4}y[/tex] -----> equation B

substitute equation B in equation A and solve for y

[tex]\frac{3}{4}y+y=180[/tex]

[tex]\frac{7}{4}y=180[/tex]

[tex]y=180*4/7[/tex]

[tex]y=103\ seconds[/tex]

Answer:

(4,10) is the solution

Step-by-step explanation:

2x + y = 18

x – y = –6

Using elimination

2x + y = 18

x – y = –6

----------------------

3x    = 12

Dividing each side by 3

3x/3 = 12/3

x =4

Now we can find y

2x+y = 18

2(4) +y =18

8+y = 18

Subtracting 8 from each side

8-8+y = 18-8

y=10

(4,10) is the solution

Answer:

Choice D is correct

Step-by-step explanation:

We are given the exponential function;

[tex]y=7^{-x}[/tex]

Using the law of exponents the function can be re-written as;

[tex]y=(\frac{1}{7})^{x}[/tex]

The base 1/7 is less than 1 hence this represents an exponential decay function.

For any exponential decay function y;

as x approaches infinity, y will always tend to 0

as x approaches negative infinity, y will always tend to infinity

See the attachment;

Answer:

1/2 or 0.5

Step-by-step explanation:

First think: How many numbers are there between 5 and ten that are odd?

5,7 and 9 are all odd (that makes 3 numbers)

Then you take that and divide it by the total number of numbers between 5 and 10

5,6,7,8,9,10 (that makes 6 numbers)

You then get 3/6, simplified to 1/2 or 0.5

Answer:

The answer is d = √[(p - m)² + (q - n)²] ⇒ first answer

Step-by-step explanation:

* The distance between any to points (x1 , y1) , (x2 , y2) is

- d = √[square the difference of x- coordinates plus

        square the difference of y-coordinates]

∴ d = √[(x2 - x1)² + (y2 - y1)²] or

∴ d² = (x2 - x1)² + (y2 - y1)²

* x2 - x1 is the horizontal distance (h) and y2 - y1

 is the vertical distance (v)

- By using Pythagoras theorem

∴ d = √[h² + v²]

∵ The two points are (p , q) and (m , n)

- Put x1 = m and y1 = n

- Put x2 = p and y2 = q

∴ d² = (p - m)² + (q - n)²

∴ d = √[(p - m)² + (q - n)²]

∴ The answer is d = √[(p - m)² + (q - n)²] ⇒ first answer

Answer:

The answer is d = √[(p - m)² + (q - n)²] ⇒ first answer

Step-by-step explanation:

The pumping stations will deliver approximately 8.188 gallons of oil during the 4-hour period from t = 0 to t = 4.

To find the amount of oil delivered by the pumping stations during the 4-hour period from t = 0 to t = 4, we need to evaluate the definite integral of the function D(t) over that interval. The function D(t) is given by D(t) = 5t / (1 + 3t). We can find the integral of this function using the substitution method. Let u = 1 + 3t, then du = 3dt. Rearranging this equation, we have dt = du / 3.

Substituting this in the integral, we get:

∫ D(t) dt = ∫ (5t / u) * (1/3) du = (5/3) * ∫ (t / u) du

Integrating the above expression, we get:

∫ D(t) dt = (5/3) * ∫ (t / u) du = (5/3) * ∫ (t / (1 + 3t)) du

To evaluate this integral, we can use the natural logarithm function. We know that ∫ (1/u) du = ln|u| + C, where C is the constant of integration. Substituting back for u, we have:

(5/3) * ∫ (t / (1 + 3t)) du = (5/3) * ∫ (t / u) du = (5/3) * ln|1 + 3t| + C

Now, we can use the definite integral to find the amount of oil delivered during the 4-hour period:

∫04 D(t) dt = (5/3) * ∫04 (t / (1 + 3t)) dt = (5/3) * [ln|1 + 3(4)| - ln|1 + 3(0)|] = (5/3) * [ln|13| - ln|1|] = (5/3) * ln|13| = 8.188

Therefore, the pumping stations will deliver approximately 8.188 gallons of oil during the 4-hour period from t = 0 to t = 4.

https://brainly.com/question/32465992

#SPJ12

Answer:

  f(x) = -4/3x² -2/3x +10

Step-by-step explanation:

The quadratic regression function of a graphing calculator or spreadsheet can determine the equation for you.

___

Or, you can determine it yourself.

The equation can be written in the form ...

   f(x) = a(x +3)(x -5/2) . . . . . . . using the given x-intercepts

for some value of "a"

For x = 0, this must match the y-intercept.

  f(0) = a(0 +3)(0 -5/2) = 10

  -15/2·a = 10

  a = -20/15 = -4/3

So, the function can be written as ...

  f(x) = (-4/3)(x +3)(x -5/2)

or

  f(x) = -4/3x² -2/3x +10

-2/3( 2x^2 + x - 15) is the answer.

From the given x-intercepts, 2 factors of the equation will be (x + 3) and

(2x - 5):- So we can write:

At the y-intercept x = 0 so we have the equation a(0+3)(2(0) - 5) = 10  where a is a constant.

a * -15 = 10

a = -2/3  so the function is  (-2/3)(x  + 3)(2x - 5)

= -2/3( 2x^2 + x - 15).