MEMO

To: All businesses in Simpsons Square Mall

From: Louise Pembrooke, Simpsons Square Mall Manager

Re: New garbage collection rules

Simpsons Square Mall has hired a new waste collection company. Quick Clean, Inc., will be collecting garbage and recycling from all businesses starting next Monday. Collection days will not change, nor will the types of garbage and recycling that are acceptable to dispose of. The pickup time will be two hours later, so please adjust your schedules accordingly.

Each business will be given one blue garbage can and one green recycling bin. Full garbage cans must weigh no more than 40 pounds. Recycling bins must weigh no more than 20 pounds. Do not overfill the garbage cans. Debris that is not in cans must weigh no more than 10 pounds. Items put in the compactor should weigh no more than 60 pounds, except in December when it may weigh up to 70 pounds. Put your garbage in the alley behind your business’s back door.

You own a store in Simpsons Square Mall. Each garbage can must weigh no more than:

10 pounds.
20 pounds.
40 pounds.
60 pounds.
70 pounds.

Answer:

3.56 cm.

Step-by-step explanation:

1/3 π r^2 h = V

1/3 π (5.13)^2 h  = 98

h = 98 / (1/3 π (5.13)^2)

=  98 / 27.55899

= 3.556.

Cone is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.

If the volume and radius of a cone are 98 cm and 5.13 cm.

The height of the cone is 3.56 cm.

It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.

The volume of a cone is 1/3πr²h.

Example:

The cone has a radius of 2 cm and a height of 3cm.

The volume of a cone:

= 1/3 x 3.14 x 4 x 3

= 12.56 cm³

We have,

Cone:

Volume = 98 cm

Radius = 5.13 cm

Height of the cone = h

The volume of a cone:

V = 1/3πr²h

98 = 1/3 x π x (5.13)² x h

[ Take π = 3.14 ]

98 = 1/3 x 3.14 x 26.31 x h

Multiply 3 on both sides.

98 x 3 = 3.14 x 26.31 x h

Divide both sides by (3.14 x 26.31).

h = (98 x 3) / (3.14 x 26.31)

h = 294 / 82.61

h = 3.56 cm

Thus,

If the volume and radius of a cone are 98 cm and 5.13 cm.

The height of the cone is 3.56 cm.

Learn more about cones here:

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Answer:

no idea

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

This is because alternate exterior angles are congruent when we have parallel lines like this.

Angle 2 and angle 8 are both outside the parallel lines, so that's what makes them exterior angles. Also, they are on alternating sides of the transversal line (angle 2 on the left, angle 8 on the right). So that's where the "alternating" comes from. The other pair of alternate exterior angles is angle 1 and angle 7.

Answer:

1/4 of them were rotten

rotten ones = 1/4 × 12 = 3

ones that weren't rotten = 12 - 3 = 9

Answer:

the answer is b

Step-by-step explanation:

you have to divide 6.50 by 5 to see how much 1 bar will cot

6.50 divided by 5 is 1.3

Answer:

(At least) 10 centimeters.

Step-by-step explanation:

The radius of the ice cream scoop is 2.5 cm and the radius of the cone is also 2.5 cm.

We want to determine the height of the cone such that it will fit all of the ice cream when it melts without any spilling.

First, we will find the volume of the ice cream scoop. The volume for a sphere is given by:

[tex]\displaystyle V=\frac{4}{3}\pi r^3[/tex]

Since the radius is 2.5 cm, the volume of the full ice cream scoop is:

[tex]\displaystyle V=\frac{4}{3}\pi (2.5)^3[/tex]

Use a calculator:

[tex]V\approx 65.4498\text{ cm}^3[/tex]

The volume of a cone is given by:

[tex]\displaystyle V=\frac{1}{3}\pi r^2h[/tex]

The radius of the cone is 2.5 cm. Therefore:

[tex]\displaystyle V=\frac{1}{3}\pi(2.5)^2h=\frac{1}{3}\pi(6.25 h)=\frac{6.25\pi}{3}h[/tex]

The volume of the cone should be equal to the volume of the scoop. So:

[tex]\displaystyle 65.4498=\frac{6.25\pi}{3}h[/tex]

Solve for h:

[tex]\displaystyle h\approx 65.4498\Big(\frac{3}{6.25\pi}\Big)=10\text{ cm}[/tex]

The height of the cone should be (at least) 10 cm.

Answer:

13 ingredients

Step-by-step explanation:

The number of different recipes that can be made from 2 ingredients = 78

Since there are no two recipes that share the exact same two ingredients ;

The number of recipes in Mark's kitchen is:

nCk = 78

k = Number of ingredients per recipe = 2

n = total number of ingredients in kitchen

Total recipes made = 78

n! / (n-r)!r! = 78

n! / (n - 2)!2! = 78

n(n-1)(n-2)! / (n-2)! * 2 * 1 = 78

n(n - 1) / 2 = 78

n(n-1) = 156

n² - n = 156

n² - n - 156 = 0

Factorize :

n² - 13n + 12n - 156 = 0

n(n - 13) +12(n-13) = 0

(n-13) = 0 ; (n+12) = 0

n = 13 or n = - 12

n cannot be negative

Hence, n = 13

Number of ingredients is 13

Answer:

14. x=30, y=15, z=165

15. x=10, y=25

Step-by-step explanation:

Answer:

1)

x= 30

y=15

z=150

2)

x= 10

y=25

Step-by-step explanation:

1)

2x+90+x=180

3x+90=180

x= 90/3=30

2y= x

2y=30

y= 30/2=15

2y+z= 180

30+z= 180

z= 150  

2)

3x= 5x-20

5x-3x=20

x=20/2=10

2y+4y+ (5x-20) = 180

6y+30= 180

y= 150/6= 25

I hope im right!!

Answer:

The answer is 7

Step-by-step explanation:

5x+2x=49-2x+2x

7x=49+0

7x/7=49/7

x=7

The number is 7 if five times a number is 49 greater than the product of 2 and the opposite of the number.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Five times a number is 49 greater than the product of 2 and the opposite of the number.

Let the number is x:

From the statement "Five times a number is 49 greater than the product of 2 and the opposite of the number" we can frame a linear equation in one variable:

5x + 2x = 49 - 2x + 2x

After solving the above equation:

7x = 49

x = 49/7

x = 7

Thus, the number is 7 if five times a number is 49 greater than the product of 2 and the opposite of the number.

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Answer:

214

Step-by-step explanation:

Answer:

Step-by-step explanation: potential energy Ep = mgh

And g = 9.81 m/s². Ep = 0.0008 kg·9.81 m/s²· 22 m , unit is J

Answer:

V= l x b x h

= 9cm x 6cm x 12cm

=648

Answer:

ΔFGH≅ΔYZX

Step-by-step explanation:

Answer:

Step-by-step explanation:

The area of a triangle is half the product of the base and the height

A=hb/2

A=(8 1/2)(14 1/6)(1/2)

A=(17/2)(85/6)(1/2)

A=1445/24 ft^2

A=60.21 ft^2 (approximately)

Answer:

I'm just going to answer so the "Genius" answerer can get Brainliest or something...

Step-by-step explanation:

9514 1404 393

Answer:

  3. $6000 at 8%; $5000 at 5%

  4. 66 2/3 gallons of 9%; 133 1/3 gallons of 6%

Step-by-step explanation:

For many mixture problems, it works well to let a variable represent the amount of the largest contributor used in the mix.

3. Let x represent the amount invested at 8%. Then the total interest is ...

  8%x +5%(11000-x) = 730

  3%x = 730 -550

  x = 180/0.03 = 6000

$6000 was invested at 8%; $5000 was invested at 5%.

__

4. Let x represent the number of gallons of 9% content. Then the alcohol content of the mix is ...

  9%x +6%(200 -x) = 7%(200)

  3%x = 1%(200) . . . . . subtract 6%(200)

  x = 200/3 = 66 2/3 . . . . . divide by 3%

  200 -x = 133 1/3

66 2/3 gallons of 9% wine and 133 1/3 gallons of 6% wine should be used.

Answer:

2

Step-by-step explanation:

First you find what is in the parentheses

2+7 =9

9-1 = 8

Then find the exponent because on PEMDAS

2 * 2 = 4

Then divide

8 divided by 4 = 2

2 is your answer

Answer:

4.375 sq. in.

Step-by-step explanation:

multiply 1.25 by 3.5 and you get 4.375

Answer:

Step-by-step explanation:

1. cotx = 0

2. cosx = 1

So the solution set is:

Answer:

45mm

Step-by-step explanation:

First, find the whole area of the square, which is 225 mm squared.

Then, we have to find the area of the shaded trapezoid. Remember, the area of the trapezoid is [tex]\frac{h(b^{1}+b^{2} }{2}[/tex]

We get the area of the trapezoid to be 180 mm.

We subtract 180 from 225 mm to get 45 mm as our answer.

Answer:

Step-by-step explanation:

y=4x-1

y-1=4(x-7)

y-1=4x-28

y=4x-27

Answer:

Step-by-step explanation:

y - x = -5

y =  x-5

y = 2x² - 3x - 5

x-5 = 2x² - 3x - 5

2x² - 4x = 0

x² - 2x  = 0

x(x - 2) = 0

x = 2, 0

(x,y) = (2,-3), (0,-5)