URGENT!!
A tap is dripping.
It takes 1 hour 40 minutes to fill a litre container.
a) What is the rate of flow, in litres per hour (litres/h)?
b) How long does it take for the tap to drip 100 ml of water?

Answer:

Step-by-step explanation:

One clue about where to start is this: the sentence describes the length by referring to the width. "The LENGTH is blah, blah, blah, the WIDTH. When that happens, choose a variable to represent the width (the quantity being referred to).

Width = w

Length IS three more than (added to) 4 times (multiplied by) the width

Length = 4w + 3

Area of a rectangle is the width multiplied by the length.

Equation: w(4w + 3) = 24

Solve.

Multiply out the left side.

4w^2 + 3w = 24

Subtract 24.

4w^2 + 3w -24 =0

This equation does not factor. Use the Quadratic Formula. One of the solutions is a negative number, so that should be rejected (width can't be a negative number).

[tex]w=\frac{-3+\sqrt{393}}{8}[/tex]

Substitute this into the expression 4w + 3 to find the length. A calculator can give you decimals for both dimensions.

Answer:

[tex] \displaystyle \rm x \cos(a) + \sin(a) \ln\left( | \sin(x) | \right) + C[/tex]

Step-by-step explanation:

we would like to integrate the following integration:

[tex] \displaystyle \int \frac{ \sin(x + a) }{ \sin(x) } dx[/tex]

we can rewrite the denominator by using algebraic identity given by:

[tex] \displaystyle \rm\sin( \alpha \pm \beta ) = \sin( \alpha ) \cos( \beta ) \pm \cos( \alpha ) \sin( \beta ) [/tex]

thus substitute:

[tex] \displaystyle \int \frac{ \sin(x ) \cos(a) + \cos(x) \sin(a) } { \sin(x) } dx[/tex]

we should rewrite integrand as sum therefore we can use sum integration formula

[tex] \displaystyle \rm\int \frac{ \sin(x ) \cos(a) } { \sin(x) } + \frac{ \cos(x) \sin( \alpha ) } { \sin(x) } dx[/tex]

use sum integration formula:

[tex] \displaystyle \rm\int \frac{ \sin(x ) \cos(a) } { \sin(x) } dx + \int \frac{ \cos(x) \sin( \alpha ) } { \sin(x) } dx[/tex]

reduce fraction:

[tex] \displaystyle \rm\int \cos(a) dx + \int \frac{ \cos(x) \sin( \alpha ) } { \sin(x) } dx[/tex]

rewrite:

[tex] \displaystyle \rm\int \cos(a) dx + \int \frac{ \cos(x) } { \sin(x) } \cdot \sin( a) dx[/tex]

use trigonometric indentity:

[tex] \displaystyle \rm\int \cos(a) dx + \int \cot(x) \cdot \sin( a) dx[/tex]

use constant integration formula

[tex] \displaystyle \rm\int \cos(a) dx + \sin(a) \int \cot(x) dx[/tex]

use integration rules:

[tex] \displaystyle \rm x \cos(a) + \sin(a) \ln\left( | \sin(x) | \right)[/tex]

and finally we of course have to add constant of integration

[tex] \displaystyle \rm x \cos(a) + \sin(a) \ln\left( | \sin(x) | \right) + C[/tex]

And we are done!

[tex]\text{Note:I used integration by substitution to figure out }\\\displaystyle \int \cot(x)dx \:\text{part}[/tex]

Answer:

C. The standard deviation decreases from 5.63 to 1.85, which means a graph of the values is less spread out without the outlier.

Step-by-step explanation:

I just took the test and got it right! I hope this helps <3

Answer:

47.1 ft

Step-by-step explanation:

C = πd

C = 3.14 · 15

C = 47.1

C ≈ 47.1 ft

Answer:

(1, 6) is the solution

Step-by-step explanation:

-2x + 6y = 34

2x + 2y = 14;     divide by 2

x + y = 7;        subtract x

y = 7 - x

let's substitute y with 7 - x in first equation

-2x + 6*(7 - x) = 34;    expand multiplication

-2x + 6*7 - 6*x = 34;    group

-8x + 42 = 34;         subtract 42

-8x = 34 - 42 = -8;      divide by -8

x = 1

y = 7 - 1 = 6

It is the only solution, as we've arrived at exact numbers.

Answer:

1.) x = 10

2.) x = 5

3.) x = 3

4.) x = 27

5.) x = 30

6.) x = 29

7.) x = 7

8.) x = 32

9.) x = –4

10.) x = 60

Answer:

x = 2.

Step-by-step explanation:

First convert to vertex form:

f(x) = 5x^2 - 20x + 3

= 5(x^2 - 4x) + 3

= 5 [(x - 2)^2 - 4] + 3

= 5(x - 2)^2 -20 + 3

= 5(x - 2)^2 - 17.

The line of symmetry  is x = 2.

Answer:

The length of the sides of the square is approximately 11.239 centimeters.

Step-by-step explanation:

Since the circle is inscribed in the square, the length of each side of the square ([tex]l[/tex]), in centimeters, is equal to the length of the diameter of the circle ([tex]D[/tex]), in centimeters. The area of the circle ([tex]A_{c}[/tex]), in square centimeters:

[tex]A_{c} = \frac{\pi\cdot D^{2}}{4}[/tex] (1)

Where [tex]D[/tex] is the diameter of the circle, in centimeters.

If we know that [tex]A_{c} = 99.2\,cm^{2}[/tex], then the length of the sides of the square is:

[tex]D = \sqrt{\frac{4\cdot A_{c}}{\pi} }[/tex]

[tex]l = D \approx 11.239\,cm[/tex]

The length of the sides of the square is approximately 11.239 centimeters.

There are 360 cubic inches of cheese would you have eaten.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

This wedge of cheese is shaped like a triangular prism.

And, The wedge of cheese is 10 inches tall. The base of the cheese is shaped like a triangle with a base of 9 and a height of 8 inches.

Hence, The value of volume of cheese is,

⇒ (1/2 × 9 × 8) × 10

⇒ 36 × 10

⇒ 360 inches³

Thus, There are 360 cubic inches of cheese would you have eaten.

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ2

Answer:

(x − 10)(x + 2)

Step-by-step explanation:

i just took the test and thats the right answer:)

you would have to deposit approximately $22,807 quarterly into the account to reach your goal of saving $26,000 over the next 3 years at an interest rate of 4.4%.

Use the concept of compound interest defined as:

The interest that is computed using both the principal and the interest that has accrued during the previous period is called compound interest.

The compound interest formula is:

[tex]A = P(1 + r/n)^{(nt)}[/tex]

Where,

A is compounded amount

P is the principal amount

r is the rate of interest

n is the number of times compounding

t is time.

Given that,

Goal: Save enough money to pay cash for the next car.

Target amount: $26,000.

Timeframe: Over the next 3 years.

Interest rate: 4.4%.

Deposit frequency: Quarterly.

To calculate the amount you need to deposit quarterly to reach $26,000 over the next 3 years with an interest rate of 4.4%,

Use the formula of compound interest described above:

Where,

A = $26000

P =?

r = 4.4% or 0.044 as a decimal

n = 4

t = 3 years

Substituting the given values, we get:

[tex]26,000 = P(1 + 0.044/4)^{4\times3}[/tex]

Simplifying further:

[tex]26,000 = P(1 + 0.011)^{12 }[/tex]

[tex]26,000 = P(1.011)^{12}\\\\26,000 = P(1.1402)[/tex]

To solve for P, divide both sides of the equation by 1.1402:

P = 26,000 / 1.1402

P ≈ 22,807

Hence, you would have to deposit approximately $22,807 quarterly into the account.

To learn more about simple and compound interests visit:

https://brainly.com/question/30964674

#SPJ12

Answer:

first, x and x that will be 2x  then x and 5 in the green box u get 5x and then pink you get 4x and orange you get 20.

Step-by-step explanation:

Answer:

[tex](4,3)[/tex]

Step-by-step explanation:

Given

See attachment for complete question

Required

Identify the unexplored point

Since the shaded region has been explored, an unexplored point will be located in the white region.

The given points are:

[tex](-5,2)\ (0,0)\ (4,3)\ (-2,4)[/tex]

Plot each of the above points on the grid (See attachment 2)

In attachment 2, only (4,3) lies on the white region.

Hence, (4,3) has not been explored

Question is incomplete :

It costs $4 to go to the swimming pool

The cost of n visits =

Membership at the pool costs $21. Members pay $3 each time. WHAT is The cost for a member to swim including membership fee?

What is the difference between the cost of 15 visits with and without a membership?

Answer:

Kindly check explanation

Step-by-step explanation:

Given that:

Swimming cost = $4

Cost of swimming n Times = cost per swim * number of swims

= $4 * n

= $4n

Membership cost = $21

Cost per swim for members = $3

Swimming cost including membership fee :

21 + 3n ; n = number of visits

For 15 visits ; n = 15

Amount paid :

Members = 21 + 3(15) = 21 + 45 = $66

Non - Member = 4(15) = 60

Difference :

$66 - 60 = 6

Members incur $6 more than non - members

The required value of the missing sides with the help of trig ratios we have x = 19.9.

If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.

Here,
To find the missing side in the given right triangle, we can use trigonometric ratios. Specifically, we can use the tangent ratio:

Cosine of an angle = opposite side / adjacent side

In this case, we know the measure of one acute angle (19 degrees) and the length of the adjacent side (21). We want to find the length of the opposite side, which we can represent as x.

cos(19°) = x / 21

Multiplying both sides by 21, we get:

x = 21 cos(19°)

Using a calculator, we can evaluate the right-hand side to get:

x ≈ 19.85

Rounding to the nearest tenth, the missing side is approximately 19.9 units long.

Learn more about trig ratios here:

https://brainly.com/question/14977354

#SPJ7

Answer:

b.

[tex] {4}^{15} \times {5}^{10} [/tex]

Step-by-step explanation:

In the given expression u can bring the 5^-2 in the neumerator making it 5^2.

Then multiply both powers by 5.

Answer:

12 nickels

11 dimes

Step-by-step explanation:

Let n = no. of nickels

     d = no. of dimes

   5n = value of nickels in cents

   10d = value of dimes in cents

    170 = total value in cents

(1)   n + d = 23             (2)   5n + 10d = 170

           d = 23 - n                5n + 10(23 - n) = 170

                                           5n + 230 - 10n = 170

                                                     - 5n = - 60

                                                          n = 12 nickels

           d = 23 - 12 = 11 dimes

Check:  12(5) + 11(10) = 60 + 110 = 170 cents or $1.70

Answer:

The height of the taller building is: 51.345m

Step-by-step explanation:

Given

The question has missing details (See attachment for the illustration of the complete question)

Required

The height of the tall building

The height, a, is calculated as:

[tex]a = b +c[/tex]

To solve for b, we consider the upper half of the attached image

The upper half is a right triangle.

Using tan formula, we have:

[tex]tan(31) = \frac{b}{30}[/tex]

Solve for b

[tex]b = 30 * tan(31)[/tex]

To solve for c, we consider the lower half of the attached image

Using tan formula, we have:

[tex]tan(48) = \frac{c}{30}[/tex]

Solve for c

[tex]c = 30 * tan(48)[/tex]

Recall that: [tex]a = b +c[/tex]

So:

[tex]a = 30 * tan(31) + 30 * tan(48)[/tex]

[tex]a = 30 * 0.6009 + 30 * 1.1106[/tex]

[tex]a = 18.027 + 33.318[/tex]

[tex]a = 51.345[/tex]

Answer:

[tex] x = 45 \ \& \ y = 5 [/tex]

Step-by-step explanation:

The system of linear equations in two variables is ,

[tex]\begin{cases} x = 9y \cdots (i)\\ x - 5y = 20\cdots (ii) \end{cases}[/tex]

We can easily solve out this Question using substitution method . For that , substituting x = 9y from equation (i) to equation (ii) , we have ,

[tex]\implies x - 5y = 20 \\\\\implies 9y - 5y = 20 \\\\\implies 4y = 20 \\\\\implies y =\dfrac{20}{4}\\\\\implies\boxed{\boxed{ y = 5 }}[/tex]

Substituting this value in (i) ,

[tex]\implies x = 9y \\\\\implies x = 9\times 5 \\\\\implies \boxed{\boxed{ x = 45 }}[/tex]

Answer: (45,5)

Step-by-step explanation:

You're given what x equals: 9y. Substitute that into the equation x - 5y = 20. Your equation should look like this: 9y - 5y = 20. From there, solve for y. 9y subtracted by 5y is 4y. Then, solve 4y = 20. Divide both sides of the equation by 4. The result is y = 5. We now know the y-coordinate in the ordered pair. Substitute this y-value into the first equation: x = 9y. 9(5) = 45. x = 45.

Plug these two values into the ordered pair (x,y).

Answer:

[tex]AB = 5[/tex]

Step-by-step explanation:

Given

[tex]A =(1,-1)[/tex]

[tex]B = (1,4)[/tex]

[tex]C = (8,4)[/tex]

Required

Distance between vertices A and B

To do this, we simply calculate distance AB using distance formula.

[tex]d = \sqrt{(x_1-x_2)^2 + (y_1 - y_2)^2}[/tex]

So, we have:

[tex]AB = \sqrt{(1-1)^2 + (4 - -1)^2}[/tex]

Simplify the expression the bracket

[tex]AB = \sqrt{0^2 + 5^2}[/tex]

Evaluate all squares

[tex]AB = \sqrt{0 + 25}[/tex]

[tex]AB = \sqrt{25}[/tex]

Take positive square root

[tex]AB = 5[/tex]

Hence, the line segment that connects A and B is 5 units long.

Answer:

She was paid $1,200 this month

Step-by-step explanation:

Ratios:

[tex]\frac{15}{100} =\frac{180}{x} \\\\15x=18000\\x=1200[/tex]

Double checking:

1200(15%) = 180

Answer:

circumference = π2r = (3.14)(2)(21) = 131.88 miles

Step-by-step explanation:

Answer:

131.9

Step-by-step explanation:

[tex]3.14 \times 21 \times 2[/tex]

Answer:

144

Step-by-step explanation:

sorry if im wrong its been awhile since ive done this

Answer:

The answer should be (x + 9, y + 9)

Step-by-step explanation:

Answer:

The 12'' one.

Step-by-step explanation:

The crust is at the perimeter of the pizza, and the pizza is a circle, so we just need to calculate the perimeter of the different pizza sizes, and see which one has a perimeter of 37.68 in.

First, you should remember that for a circle of radius R, the perimeter is:

P = 2*3.14*R

(notice that the measures in the image are the diameters of the pizzas, and the radius is half of the diameter)

The radius that we need to have if we want a perimeter of 37.68 in is given by:

P = 37.68 in = 2*3.14*R

   (37.68 in)/(2*3.14) = R = 6 inches.

Then we need a pizza of 6 inches (or a diameter of 2*6 inches = 12 inches)

Then the pizza that Ms. Van Rock should get is the 12 inch one.

Answer:

7:00pm

Step-by-step explanation:

Answer:

A)The composite figure consists of two rectangular pyramids.

D)The total volume is 45 units³.

Step-by-step explanation:

Hope it helps...

Have a great day!!

statements about the composite figure are true

A)The composite figure consists of two rectangular pyramids.

D)The total volume is 45 units³.

The volume of a pyramid is found using the formula V = (1/3) Bh, where 'B' is the base area and 'h' is the height of the pyramid.

As, we can see the two figure shared same rectangular base .

So, the composite figure consists of two rectangular pyramids.

Now, Volume of pyramid,

=5*9*1.5/3

= 22.5

So, the total volume is 22.5+22.5

=45 units³.

Hence, correct statement are:

A)The composite figure consists of two rectangular pyramids.

D)The total volume is 45 units³.

Learn more about volume of pyramid here:

https://brainly.com/question/17615619

#SPJ2

Answer:

I think it is 38+11i not sure but try it