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Answer:

a. 43,200 drips

b. 4 gallons (approximately, actual value is 3.8)

c. 61 cups(approximately, actual value is 60.8, using 3.8 gallons and not 4 gallons)

Step-by-step explanation:

Here, we have a faucet wasting water at a rate of 15 drips per 30 seconds, now we want to calculate the number of drips wasted in a day

To find this, what we need to do is fund the number of seconds in a day first

There are 24 hours with 60 minutes, with each minute having 60 seconds

So the number of seconds in a day = 24 * 60 * 60 = 86,400 seconds

Now 15 drips is wasted in 30 seconds

x will be wasted in 86,400 seconds

x = (15 * 86400)/30 = 43,200 drips are wasted in a day

b. Mathematically , there are about 3,000 drips in a liter of water

So;

3,000 drips = 1 liter

43,200 drips = x liter

x = 43200/3000 = 14.4 liters of water

Mathematically,

1 liter = 0.264 gallons

So 14.4 liters = 14.4 * 0.264 = 3.8 gallon

which is equal to 4 gallons of water approximately

c. Mathematically;

1 gallon = 16 cups of water

So 3.8 gallons of water will measure 3.8 * 16 = 60.8 which is approximately 61 gallons of water

Answer:

m∠DEA = 62° and m∠ADB = 318°

Step-by-step explanation:

[tex]AB\left | \right |DC[/tex], - (Given)

m∠CB = 62° (Given)

we have;

m∠CB ≅ m∠DA (parallel lines congruent arc theorem)

m∠DA = 62° = m∠DEA

m∠DAB = 104° Given

Therefore, m∠AB = 104° - 62° = 42° (sum of angle)

m∠DC = 360 - 62 - 62 - 42 = 194°  (sum of angles around a circle)

m∠ADB = 360° - m∠AB (sum of angles around a circle)

Therefore, m∠ADB = 360° - 42° = 318°

The required angles are;

m∠DEA = 62° and m∠ADB = 318°

Answer:

[tex]\large \boxed{\sf \ \ 70\% \ \ }[/tex]

Step-by-step explanation:

Hello,

We assume that the year is 52 weeks, and we note r the interest rate we are looking for. The rate is expressed in percent and is annually, meaning that the investment is, after the first week :

   [tex]1000\cdot (1+\dfrac{r\%}{52})=1000\cdot (1+\dfrac{r}{5200})[/tex]

For the second week

   [tex]1000\cdot (1+\dfrac{r}{5200})^2[/tex]

After 52 weeks

   [tex]1000\cdot (1+\dfrac{r}{5200})^{52}[/tex]

and we want to be equal to 2000 so we need to solve:

[tex]1000\cdot (1+\dfrac{r}{5200})^{52}=2000\\\\\text{*** divide by 1000 both sides ***}\\\\(1+\dfrac{r}{5200})^{52}=\dfrac{2000}{1000}=2\\\\\text{*** take the ln **}\\\\52\cdot ln(1+\dfrac{r}{5200})=ln(2)\\\\\text{*** divide by 52 ***}\\\\ln(1+\dfrac{r}{5200})=\dfrac{ln(2)}{52}\\\\\text{*** take the exp ***}\\\\\displaystyle 1+\dfrac{r}{5200}=exp(\dfrac{ln(2)}{52})=2^{(\dfrac{1}{52})}=\sqrt[52]{2}\\\\r = 5200\cdot (\sqrt[52]{2}-1)=69.77875...[/tex]

Rounded to the nearest percent, the solution is 70%.

If you want to double your capital in one year with weekly compounding you need an interest rate of 70% !!

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

4%

Step-by-step explanation:

Answer:

arc KL=minor arc

arc LJK=major arc

Step-by-step explanation:

so minor arc is a arc which is larger than a semicircle .

a major arc is a circle having measure less than radians.

Answer        

6B+7X-9Y+19

Step-by-step explanation:

Answer:

58 square units.

Step-by-step explanation:

From the graph attached,

Area of the figure = Area of the rectangle A + Area of two squares B and C

Area of rectangle A = Length × width

                                 = 10 × 5

                                 = 50 square units

Area of the square B = (Side)²

                                   = (2)²

                                   = 4 square units

Similarly area of the square C = 2² = 4 square units

Area of the total figure = 50 + 4 + 4

                                      = 58 square units

Therefore, 58 square units will be the answer.

Answer:

Step-by-step explanation:

3y + 10= 5y-25

Group like terms

Send the constants to the right side of the equation and those with variables to the left side

that's

3y - 5y = - 25 - 10

Simplify

- 2y = - 35

Divide both sides by - 2

Hope this helps you

Answer:

y=35/2 or 17.5

Step-by-step explanation:

1) 3y + 10= 5y-25

-3y          -3y

2) 10 = 2y - 25

3) 10 = 2y - 25

  +25        +25

35= 2y

4)Divide both sides by 2

y=35/2 or 17.5

Answer:

[tex] csc (R) = \frac{13}{12} [/tex]

Step-by-step explanation:

Formula for any given angle (Ѳ) is given as csc Ѳ = length of hypotenuse side//length of opposite side. It is the inverse of sin Ѳ.

In the right triangle given above, the opposite length = 24, while the length of the hypotenuse = 26

Thus,

[tex] csc (R) = \frac{hypotenuse}{opposite} [/tex]

[tex] csc (R) = \frac{26}{24} [/tex]

[tex] csc (R) = \frac{26}{24} [/tex]

[tex] csc (R) = \frac{13}{12} [/tex]

Answer:

(x*(1+a))*0.8 = 400; x = 500/1+a

Step-by-step explanation:

First, increase the number (which we will call x) by a%

x*(1+a) -> You do 1 + a because if you wanted to increase let's say 5 by 20% you would do 5 + 5*0.2 and if you factor that out it becomes 5(1+0.2)

Next, decrease it by 80%.

(x*(1+a))*0.8

Finally, make it into an equation.

(x*(1+a))*0.8 = 400

If you solve it, you get:

x(1+a) = 500

x = 500/1+a

Answer:

Step-by-step explanation:

a = 8

b  = 10

a^3 =8^3 = 512

b^3= 10^3 =1000

a^3 + b^3 = 1512

a^2 = 64

-ab = - 80

b^2 = 100

a + b=18

(a + b) (64 -  80+ 100)

18 * (84)

1512'

Answer:

The best fit is A. Linear model

Step-by-step explanation:

Given:

Monthly Rate = $20, Number of customers = 5000

If there is a decrease of $1 in the monthly rate, the number of customers increase by 500.

To find:

The type of model that best fits the given situation?

Solution:

Monthly Rate = $20, Number of customers = 5000

Let us decrease the monthly rate by $1.

Monthly Rate = $20 - $1  = $19, Number of customers = 5000 + 500 = 5500

Let us decrease the monthly rate by $1 more.

Monthly Rate = $19 - $1  = $18, Number of customers = 5500 + 500 = 6000

Here, we can see that there is a linear change in the number of customers whenever there is decrease in the monthly rate.

We have 2 pair of values here,

x = 20, y = 5000

x = 19, y = 5500

Let us write the equation in slope intercept form:

[tex]y =mx+c[/tex]

Slope of a function:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\dfrac{5500-5000}{19-20}\\\Rightarrow -500[/tex]

So, the equation is:

[tex]y =-500x+c[/tex]

Putting x = 20, y = 5000:

[tex]5000 =-500\times 20+c\\\Rightarrow c = 5000 +10000 = 15000[/tex]

[tex]\Rightarrow \bold{y =-500x+15000}[/tex]

Let us check whether (18, 6000) satisfies it.

Putting x = 18:

[tex]-500 \times 18 +15000 = -9000+15000 = 6000[/tex] so, it is true.

So, the answer is:

The best fit is A. Linear model

Answer:

A

Step-by-step explanation:

Kenny scored 13 points, and Micheal scored p points.  They scored a total of 27 points.  This means that 27 is the sum of their scores.  The answer is A.

13 + p = 27

Answer:

It’s b or it’s 13+p=27

Step-by-step explanation:

Answer:

Step-by-step explanation:

When we talk about the transformation of functions, we can mention stretching, rotating, dilating, shifting. However, when we want to transform linear functions, there are only two transformations that are worthy in that case, those are vertical stretch or compression and vertical shift.

Now, you may ask, why only vertical transformation? the reason behind that is because horizontal transformation would give the exact same result because it's only a straight line which we are transforming.

Another common question would be, why only two transformations? it's because with these two you can get all the results because it's a straight line.

The image attached shows examples of this.

Answer: 69

Step-by-step explanation:

Answer:

Hey there!

The surface area of the triangular pyramid can be expressed as: 4 times the area of one triangle.

The area of one triangle is 17.32, so the total surface area is 69.28.

Hope this helps :)

The surface area of the triangular pyramid will be equal to 692.8 square inches.

The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.

Given that:-

The formula for the surface area of the pyramid is given as follows;-

SA =  Base area + (1/2) [ Perimeter  x  Slant height ]

SA =  [ (1/2) x  20  x 17.32)]  + (1/2) [ 60   x   17.32 ) ]

SA=  [  173.2   +  519.6 ]

SA = 692.8 squarer inches

Therefore the surface area of the triangular pyramid will be equal to 692.8 square inches.

To know more about a surface area follow

https://brainly.com/question/25292087

#SPJ5

Answer:

$192

Step-by-step explanation:

The cost function is given as:

C(x)=18x+240

The price function is given as:

p(x)= 90 - 3x

The revenue R(x) is the product of the price and the number of products. It is given by:

R(x) = xp(x) =  x(90 - 3x) = 90x - 3x²

The profit P(x) is the difference between the revenue and the cost of production. Therefore:

P(x) = R(x) - C(x) = 90x - 3x² - (18x + 240) = 90x - 3x² - 18x - 240

P(x) = -3x² + 72x - 240

The standard equation of a quadratic equation is ax² + bx + c. The function has a maximum value at x = -b/2a

Since  P(x) = -3x² + 72x - 240, the maximum profit is at:

x = -72/2(-3) = 12

at x = 12, the profit is:

P(12) = -3(12)² + 72(12) - 240 = -432 + 864 - 240 = $192

Answer:

N = 82

Step-by-step explanation:

(N - 49)/11 = 3

N - 49 = 33

N = 82

This question is incomplete

Complete Question

Mr. Conner is placing stone tiles to make a patio. Each tile is 1 square foot. The drawing shows the dimensions of his patio. A quadrilateral is broken into a triangle and rectangle. The triangle has a base of 20 feet and a height of 6 feet. The rectangle has a base of 20 feet and a height of 12 feet. How many total stone tiles will Mr. Connor need for the patio?

Answer:

300 tiles

Step-by-step explanation:

From the above question, we know that the patio is a combination of a triangle and a rectangle.

Step 1

Find the area of the shape

a) Area of the Triangle = 1/2 × Base × Height

Base = 20 feet

Height = 6 feet

Area = 1/2 × 20 × 6

Area = 60 square feet

b) Area of the rectangle

= Length × Breadth.

The rectangle has a

Base = Breadth = 20 feet

Height = Length = 12 feet

Area = 20 × 12 = 240 square feet.

Total Area of the patio

= Area of Triangle + Area of square

= 60 square feet + 240 square feet

= 300 square feet

Step 2

We are told that each stone tile = 1 square foot.

Hence, if the total area of the patio = 300 square feet, the number of stone tiles that would be used is

1 square foot = 1 stone tile

300 square feet = 300 stone tiles.

Therefore,the total stone tiles that Mr. Connor will need for the patio is 300 stone tiles.

Answer:

The answer is 300

Step-by-step explanation:

Answer:

a) (-4). (-7/8) = 28/8

b) (-4). (-7/8)= 28/8

c) (-4).(+ 3/5) = -12/5

d) (-2).(-3/4). (-1/7) = (6/4)(-1/7)= -6/28

Step-by-step explanation:

a) (-4). (-7/8) = 28/8

b) (-4). (-7/8)= 28/8

c) (-4).(+ 3/5) = -12/5

d) (-2).(-3/4). (-1/7) = (6/4)(-1/7)= -6/28

É repetido talvez com sinal alterado para mostrar a diferença na resposta. Se o sinal for alterado, a resposta também se tornará negativa. Seria - 28/8.

Quando um número negativo é multiplicado por um número negativo, obtém um número positivo. Mas quando um número positivo é multiplicado por um número negativo, dá uma resposta negativa.

Sempre se lembre

negativo * negativo = positivo

positivo * negativo = negativo

negativo * positivo = negativo

positivo * positivo = positivo

Em palavras simples, dois sinais diferentes dão um sinal negativo e dois sinais semelhantes dão um sinal positivo na multiplicação.

English

a) (-4). (-7/8) = 28/8

b) (-4). (-7/8)= 28/8

c) (-4).(+ 3/5) = -12/5

d) (-2).(-3/4). (-1/7) = (6/4)(-1/7)= -6/28

Its repeated maybe with a changed sign to show the difference in the answer. If the sign is changed the answer would also become negative . It would become - 28/8.

When a negative number is multiplied with a negative number it gives a positive number. But when a positive number is multiplied with a negative number it gives a negative answer.

Always remember  

negative * negative= positive  

positive *negative=negative

negative *positive =negative

positive * positive =  positive

In simple words two unlike signs give a negative sign and two similar signs give a positive sign in multiplication.

Answer:

total rotation = 90 clockwise.

Step-by-step explanation:

Rotation from B to negative y-axis = 45 degrees because B(-3,-3)

Rotation from negative y-axis to B' = 45 degrees because B(-3,3)

Therefore total rotation = 45+45 = 90 clockwise.

Answer:

A is the correct answer

Yes, 50% is within the bounds of the interval

Step-by-step explanation:

Here, we want to know if the interval support that a majority of the voters favored the mileage increase.

Our correct selected answer is yes.

To be able to select that out of all the options, we must look at the interval of the proportion of the voters that support the mileage. The proportion is noticeable from the question and we can see that within the given interval, we have 50% of the proportion lying within it.

Since we have 50% lying within our interval, then we can confidently confirm at 90% confidence interval for p that the interval support that a majority of voters favored a mileage increase

Answer:

{-0.5, 0.1}

Step-by-step explanation:

[tex]x = \frac{8 \pm \sqrt{(-8)^2 - 4 \cdot -20 \cdot 1}}{-40} = \frac{8 \pm 12}{-40}[/tex]

so x is 20/-40 = -0.5 or x = -4/-40 = 0.1

Answer:

(x+6) / 6

Step-by-step explanation:

(3x+18) /18

Factor out 3 from the numerator

3(x+6) /18

Cancel a 3 from the numerator and denominator

(x+6) / 6

Answer:

exact form: n=378/13

decimal form: n=29.0769....

mixed number form: n=[tex]29\frac{1}{13}[/tex]

Step-by-step explanation:

Answer:

n = 21

Step-by-step explanation:

[tex]\frac{n}{2}-\frac{3n}{9}+\frac{5n}{9}=21\\\\\frac{9n}{18}-\frac{6n}{18}+\frac{10n}{18}=21\\\\\frac{3n}{18}+\frac{10n}{18}=21\\\\\frac{13n}{18}=21\\\\13n=273\\\\n=21[/tex]

Steps:

1. Write as fractions

2. Make the fractions have the same denominator

3. Collect like terms

4. Collect like terms

5. Multiply both sides by 18

6. Divide both sides by 13.

Answer:

32 degrees (rounded to nearest angle)

Step-by-step explanation:

Using trigonometric ratios:

Please refer to the picture of my explanation below.

tan^-1 means inverse, so on calculator remember to use the inverse function, by shifting.

Answer:

3

1/5

3/4

3/4

Step-by-step explanation:

Coefficient is a number that is always written in front of a term.

3xy^3=3

xy/5=1/5

3/4xy=3/4

3/4x^2y=3/4

Hope this helps ;) ❤❤❤

Answer: ITS B

Step-by-step explanation:

(2)(2)(2)(2)(2)

=32

2^5

=32

Hey there! I'm happy to help!

We are talking about exponents here, which is the power to which a number is raised. What does it mean to raise a number to a power? It means to multiply it a certain number times.

For example, 3 to the the 3rd power is 27 because you multiply 3 three times (3×3×3), giving you 27.

We have 2×2×2×2×2. We see that we have the number 2 and need to raise it to a certain power. Since there are 5 2s, we are raising to the 5th power.

Therefore, the answer is B.) 2 to the 5 power.

Have a wonderful day! :D

Answer:

First question: last option

The triangle inequality states that the sum of he two shortest sides of a triangle must be greater than the longest side, therefore the answer is 14, 6, and 9 because 6 + 9  > 14 is a true statement.

Second question: I'm not sure, sorry

Third question: second option

He never specified if 85° was the base angle or not so he could draw 2 triangles: one with 85° as the base angles and one with 85° as the other angle.

Answer:

Step-by-step explanation:

first : Side = 13 cm, side = 6 cm,  side =6  

second : Side = 13 cm and 5 and 8

third: Side = 14 cm, side = 7 cm and 6

forth : 14 cm, side = 6 cm, side = 9 cm

to form a triangle the theory is: a+b>c and b+c>a and a+c>b

first one : a=13 b=6 and c=6 ( not a triangle)

second: a=13 b=5 and c=8 ( not a triangle)

third : a=14,b=7,c=6 (not a triangle)

forth : a=14,b=6,c=9 ( a triangle 14+6>9,6+9>14, and 9+14>6)

Wendy description :Triangle A: All sides have length 9 cm.

Triangle B: Two sides have length 10 cm, and the included angle measures 60°

Triangle C: Two angles measure 50°.

Triangle D: Base has length 8 cm, and base angles measure 45°

triangle A is equilateral triangle all sides are equal it is a special triangle because it has three sides and angles equal.

Triangle C: is not unique because you can not specify triangles by given angles only

Victor is incorrect, because more than one triangle can be drawn with the given information because only two sides are given and the third con be different.

Answer:

commutative property of multiplication

Step-by-step explanation:

Answer:

see attached diagram

Step-by-step explanation:

1.  1 and 70 are angles on a line (supplementary)

2. vertical angles with 70

3. angles on a line are supplementary

4. 2 and 4 are supplementary interior angles between parallel lines m & n

5. corresponding angle with 70