Water drips from a faucet at a rate of 41 drops/minute. Assuming there are 15,000 drops in a gallon, how many minutes would it take for the dripping faucet to fill a 1‑gallon bucket? Round your answer to the nearest whole number.

Answer:

See Below

Step-by-step explanation:

Taking Right Hand Side to verify the identity:

tan ( 2π - x)

Resolving Parenthesis

tan 2π + tan (-x)

We know that tan 2π = 0

0 + tan (-x)

=> tan(-x) = Left Hand Side

Hence Proved

Answer:

[tex]\boxed{ \sf {view \: explanation}}[/tex]

Step-by-step explanation:

[tex]\Rightarrow \sf tan ( 2\pi - x)=tan(-x)[/tex]

[tex]\sf Apply \ distributive \ law.[/tex]

[tex]\Rightarrow \sf tan (2\pi) + tan (-x) =tan(-x)[/tex]

[tex]\sf Apply : tan(2\pi) =0[/tex]

[tex]\Rightarrow \sf 0 + tan (-x) =tan(-x)[/tex]

[tex]\Rightarrow \sf tan (-x) =tan(-x)[/tex]

[tex]\sf Hence \ verified.[/tex]

Answer:

Quota Sampling

Step-by-step explanation:

Quota Sampling is a non-probability sampling method in research, where the researcher forms subgroups of individuals who are representative of the entire population through random selection. Quota sampling is often used by researchers who want to get an accurate representation of the entire population. It saves time and money especially if accurate samples are used.

In the example given above, where the research creates subgroups of 30 pre-school children by dividing them into 10 two-year-old children, 10 three-year-old, and 10 four-year-old children, he has applied the quota sampling.  These subgroups would give a proper representation of the preschool children in local daycare centers.

Answer:

5 is the answer..

Step-by-step explanation:

simply by calculating

Answer:

-x+3

Step-by-step explanation:

2x^2-5x+3 Square 2x

4x-5x+3 combine like terms

-x+3

Hope this helps

Answer:

Factoring answer: (x-1)(2x-3)

Quadratic Formula: x = 3/2, 1

Complete the square: 2(x - 5/4)^2 - 1/8

Find the x and y intercept: X - (1,0), (3/2,0) Y - (0,3)

Hope this helps :)

Answer:

49191

Step-by-step explanation:

kakaj=122£91¥1

+££1£188282

2828282

+82882

182828

818192÷

ans=40

A cuboid is a three-dimensional shape where the volume is given by Length x width x height.

The rectangular box is a cuboid.

The book is also a cuboid

The number of box that can fit inside the box is 12.

A cuboid is a three-dimensional shape where the volume is given by Length x width x height.

Example:

The volume of a cuboid with a height of 2 cm, 3cm wide, and 4 cm length is 24 cm³.

We have,

Book:

Height = 6 cm

Wide = 15 cm

Length = 20 cm

Rectangular box:

Height = 20 cm

Wide = 30 cm

Length = 36 cm

Tha area of the box.

Area = 20 x 30 x 36 = 21600 cm³

The area of the book.

Area = 6 x 15 x 20 = 1800 cm³

The number of books that can fit in the box.

= Area of the box / Area of the book

= 21600 / 1800

= 12

Thus,

The number of box that can fit inside the box is 12.

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Answer:

Step-by-step explanation:

Let the points be A and B

A ( 3 , 7 ) --------> (x1 , y1 )

B ( 2 , -1 ) --------> ( x2 , y2 )

Finding the midpoint:

[tex]( \frac{x1 + x2}{2} , \frac{y1 + y2}{2} )[/tex]

[tex] = ( \frac{3 + 2}{2} , \: \frac{7 + ( - 1)}{2} )[/tex]

[tex] = ( \frac{5}{2} , \: \frac{7 - 1}{2} )[/tex]

[tex] = ( \frac{5}{2} ,\: \frac{6}{2} )[/tex]

[tex] = (2.5 ,\: 3)[/tex]

Hope this helps...

Good luck on your assignment ....

Answer:

(2,-1)

Step-by-step explanation:

Welol to find the line of (3,7) and (2,-1) we need to use the following formula,

[tex]\frac{y^2-y^1}{x^2-x^1}[/tex]

So -1 is y2 7 is y1 so -1 - 7 = -8

2-3 = -1

Hence, the slope of the line is 8.

And graphing more points on the graph using the slope we can see the y intercept is -17.

So the equation is y = 8x - 17

And the mid point is at (2, -1)

Answer:

no

Step-by-step explanation:

The 5x+30 is the supplementary angle of the interior one:

180 - 5x - 30 = -5x + 150

Then they have to add up to 180:

4x-9 + 2x+3 -5x + 150 = 180

which simplifies to x = 36

So the angles would be 135, 75 and -30, which is impossible!

Note: The figure in the problem is NOT drawn to scale.

Because the figure is a rhombus, its diagonal bisects the intersecting angle AND opposite angles are congruent (this was hard to notice since the figure wasn't drawn to scale)

If you look at the image I attached to my answer, we now have an isosceles triangle with angles [tex]\angle 1[/tex], [tex]\angle 1[/tex], and 32

The property of a triangle is that all angles must add to 180 degrees

[tex]\angle 1+\angle 1+32=180[/tex]

[tex]2\angle1=148[/tex]

[tex]\angle1=74[/tex]

Thus, the measurement of angle 1 is 74 degrees. Let me know if you need any clarifications, thanks!

To solve this system of equations by addition, our first goal is to cancel

out one of the variables by adding the two equations together.

However, if we add these two equations together right away, nothing

will cancel so we need to set things up so a variable will cancel.

Notice that we have an 2x in our second equation.

If we had a -2x in our first equation, then the x's would cancel out.

In order to create a -2x in the first equation, we simply

multiply both sides of the first equation by -2.

So we have (-2)(x - 2y) = (-4)(-2) which can be rewritten as -2x + 4y = 8.

Now rewrite both equations, as shown below.

Now when we add the equations together, the x terms

will cancel out and we're left with 5y = 15.

Dividing both sides by 5, y = 3.

To solve for x, plug a 3 in for y in either one of our 2 original equations.

So let's go with our second equation.

Plugging a 3 in for y, we get 2x + (3) = 7.

Now subtract 4 from both sides to get 2x = 4.

Dividing both sides by 2, we fid that x = 2.

Since x = 2 and y = 3, our answer is the ordered pair (2, 3).

Answer:

  about 325

Step-by-step explanation:

On average, the mileage is about 21.7 miles per gallon, so 15 gallons would be good for about 325 miles.

If we look at the table for fills that total 15 gallons, we see the first and last total 330 miles, and the 3rd and 4th total 314 miles. So, we expect somewhere between these values, on average.

A formal average adds the miles driven and divides by the total of gallons used. That result is shown below. While we might estimate that we could drive 325 miles on 15 gallons, we have found that our mileage actually varies.

Answer:

x1 = -5

x2 = 3

Step-by-step explanation:

You have the following equation:

[tex]\frac{6}{x}-\frac{4}{5}=\frac{2x}{5}[/tex]        (1)

To find the solutions of the equation (1) you first eliminate the denominators of the equation, by multiplying the m.c.m, which is 5x, as follow:

[tex]30-4x=2x^2[/tex]

Next, you write the previous equation in the general form ax^2 +bx+c=0, as follow:

[tex]2x^2+4x-30=0[/tex]

Next, you use the quadratic formula to find the solutions:

[tex]x_{1,2}=\frac{-b\pm \sqrt{b^2-4(a)(c)}}{2a}\\\\a=2;\ \ b=4;\ \ c=-30\\\\x_{1,2}=\frac{-4\pm \sqrt{4^2-4(2)(-30)}}{2(2)}\\\\x_{1,2}=\frac{-4\pm16}{4}\\\\x_1=-5\\\\x_2=3[/tex]

Then, the solutions for the given equation are x1=-5 and x2=3

Answer:Let PQRS to be the rhombus where PQ=12cm and RS = 16cm

step 1:let,PQ and RS intersect each other at O.Now, diagonals of rhombus bisect each other at right angles.

STEP 2:Since POQ is a right angled triangle, by pythagoras theoram.

STEP 3:After applying formula , PQ =10cm .length of each side of rhombus is 10cm.

Step-by-step explanation:

Answer:

10cm

Step-by-step explanation:

As you can see in the first image is a rhombus with its diagonals 12cm and 16cm

You can see that the diagonals divide the rhombus into four right triangles and that the hypotenuse of each triangle is one side of the rhombus.

In the second image I picked out one triangle from the rhombus and slashed the length of the diagonals of the rhombus in half to get the sides of the triangle.

Now all you have to do is use the Pythagorean theorem to find the hypotenuse of the triangle which will give you the length of side of rhombus

6² + 8² = hypotenuse²

36 + 64 = h²

100 = h²

h = √100

h = 10

All the side of the rhombus are equal so all the sides of the rhombus are 10cm

Answer: <CED is the right angle, which measures 90 degrees. Since the measure of a straight angle is 180 degrees. <CEA must also be 90 degrees by the Definition of Right Angle. A bisector cuts the angle measure in half. m<AEB is 45 degrees.

Answer:

False

Step-by-step explanation:

Given

A = [tex]\frac{1}{2}[/tex] bh ( multiply both sides by 2 to clear the fraction )

2A = bh ( divide both sides by b )

[tex]\frac{2A}{b}[/tex] = h

Answer:

A: -3

Step-by-step explanation:

I got it right on my quiz!

If  equation of the graphed line is 2x – y = –6 then the x-intercept of the graph is -3.

To find the x-intercept of the graph, we need to determine the x-coordinate where the line intersects the x-axis.

At the x-intercept, the y-coordinate is zero.

Given the equation of the line as 2x - y = -6.

we can substitute y = 0 since it is the y-coordinate at the x-intercept.

2x - 0 = -6

2x = -6

Divide both sides by 2:

x = -6/2

x = -3

Therefore, the x-intercept of the graph is -3.

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Answer:

72

Step-by-step explanation:

First find the discount

10% of 80

.10 * 80

8

Subtract this amount from the bill

80 -8 = 72

The customer will pay 72

Answer:

Step-by-step explanation:

The door is shape is a combination of a rectangle and a semicircle with a square window.

Area of the door = Area of rectangle + area of a semi circle

Area of a rectangle = Length * Width (LW)

area of a semicircle = πr²/2 where r is the radius of the semi circle.

Given the length of the rectangle = 2m and its width = 1m

Area of rectangle = 2*1 = 2m²

Given the radius of the semicircle = 1/2 m

Area of the semi circle = π(0.5)²/2

= 0.25π/2

= 0.785/2

Area of the semicircle= 0.3925m²

Area of the door = 2+0.3925

Area of the door = 2.3925m²

Since we are not to paint the window, we will subtract the area of the window from the total area.

Area of the window = area of a square = 0.2*0.2

= 0.04m²

Area to be painted = Area of door - Area of the square

Area to be painted = 2.3925m² - 0.04m²

Area to be painted  = 2.3535m²

Note that there was no enough information for us to calculate the amount of paint needed but knowing the area of the part to be painted can guide us.

Answer:

The coordinates of point B are (-2, 2).

Step-by-step explanation:

Given:

Point A (2,−8)

Point C (−4,7)

Point B divides the line AB such that the ratio AB:BC is 2:1.

To find: The coordinates of point B.

Solution:

We can use the segment formula here to find the coordinates of point B which divides line AC in ratio 2:1

[tex]x = \dfrac{mx_{2}+nx_{1}}{m+n}\\y = \dfrac{my_{2}+ny_{1}}{m+n}[/tex]

Where [tex](x,y)[/tex] is the co-ordinate of the point which  

divides the line segment joining the points [tex](x_{1}, y_{1})[/tex] and [tex](x_{2}, y_{2})[/tex] in the ratio [tex]m:n[/tex].

m = 2

n = 1

As per the given values  

[tex]x_{1} = 2\\x_{2} = -4\\y_{1} = 8\\y_{2} = 7[/tex]

Putting the values in the formula:

[tex]x = \dfrac{2 \times (-4)+1\times 2}{2+1}=\dfrac{-8+2}{3} =-2\\y = \dfrac{2\times 7+1 \times (-8)}{2+1} = \dfrac{6}{3} =2[/tex]

So, the coordinates of point B are (-2, 2).

Ms. Logrieco's door: 35 students per 10 minutes

Mr. Riley's door: 22 students per 8 minutes

Time Frame: 24 minutes

35 x 2 = 70

35 x 2/5 = 14

70 + 14 = 84

22 x 3 = 66

84 + 66 = 150

Thus, we can expect for 150 students to be in the cafeteria after 24 minutes.

Answer:

64 is the answer

hope you like tjis

stay at home stay safe

Answer:

Each angles measures 64 degrees

Step-by-step explanation:

Bisect means divide in half

128/2 = 64

Each angles measures 64 degrees

Answer:

Half ans is in pic...

now, the circumference of the smaller wheel, will just be C = 2πr, with a radius of "r".

we also know that the large wheel has a circumference that is 9 feet larger than the small one, so, since the small one has a circumference of 2πr, then the large one will have a circumference of 2πr + 9.

after Thomas cycled for a while, the large did 500 revolutions, or times around, whilst the small one did 1400, since it's smaller.  On that time, they covered however, the same amount of ground, since they're on the same bike.

The amount covered by the small one in 1400 cycles, is 1400(2πr), that's how much ground it covered.

The amount covered by the large one in 500 cycles, is 500(2πr + 9).

And we know that ground covered, is the same for both, therefore, we also know that   1400(2πr)  =  500(2πr + 9).

Refer to the pic for rest...

Hope it helped

Mark BRAINLIEST!

Answer:  see below

Step-by-step explanation:

I used a coordinate graph and placed the Ticket Booth at the origin (0, 0)

Then I chose a distance of 4 (you can choose any distance) and placed the three events equidistant from the origin by using the x- and y- axis to easily determine a distance of 4 from the origin.

(0 - 4, 0) = (-4, 0)

(0 + 4, 0) = (4, 0)

(0, 0 + 4) = (0, 4)

If the booths are placed first you would need to find the equation of a circle that contains all three points and place the booth at the center.

You do this by creating a system of three equations inputting the x,y coordinates of each booth and solving for h, k, r.

Equation of a circle is: (x - h)² + (y - k)² = r²

Answer:

28

Step-by-step explanation:

All angle measures must add up to 180. x + 85 + 67 = 180; x = 28

For any triangle, the three angles always add to 180 degrees

85+67+x = 180

x+152 = 180

x = 180-152

x = 28

Answer:

x = 138

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the opposite interior angles

x = B+ C

x = 68+ 70

x =138

Answer:

138 degrees

Step-by-step explanation:

A triangle is made up of 180 degrees, it lists 2 values already, 68&70. when added that equals 138.

So 180-138 is 42 degrees, which would be the last angle within the triangle.

Since a line is also 180 degrees, its 180-42, which makes x 138 degrees

Answer:

3

Step-by-step explanation:

2y+4=10  

10-4=2y

6=2y

2y=6

y=3

Answer:

3 is the value of y because 2*3=6and 6+4=10 that's why valueof y is =3

Step-by-step explanation:

Its a simple..

=4^2×5^12×6^8

=16×244140625×1679616

= 6.561×10^15

Hope it helps...

Answer:

24m^3

Step-by-step explanation:

Volume is L x W x H which is base times width times height. So you take the Length (3), the width (4) and the height (2) you multiply them together to get 24m. but your not done. you have to add the exponent

Answer:

20

Step-by-step explanation:

Since 30 and 3x are complementary we can write:

30 + 3x = 90

3x = 60 so x = 20°.

Answer:

20

Step-by-step explanation:

30 + 3x = 90

=> 3x = 90 - 30

=> 3x = 60

=> x = 60/3

=> x = 20

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Answer:

k = 1

Step-by-step explanation:

The equation of a parabola in vertex form is

f(x) = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (4, 1 ), thus k = 1