Graph the solutions to I-2 on a number line.

The given dimensions of the base of the box are 2 x 3 units.

Let h be the height of the box.

So, the volume of the box = 2 x 3 x h ...(i)

The shape of baseball is spherical and one baseball fits in a cubical box having the minimum dimensions equal to the diameter of the spherical ball.

Assuming the diameter of the baseball is d units.

So, the volume occupied by one baseball= volume of the cubical box having the side [tex]d[/tex] units.

[tex]=d^3[/tex] cubic units

So, the volume required to pack 48 baseballs

[tex]= 48 d^3 \cdots(ii)[/tex]

Assuming that all the baseballs fit in the box, i.e peripheral balls in every horizontal and vertical layer touched the box as shown in the figure.

So, the length, 3 units and the width, 2 units, must be the integral multiple of the diameter, [tex]d[/tex] units, of the baseball. i.e

The length, [tex]3 = ad\cdots(iii)[/tex]

The width, [tex]2=bd\cdots(iv)[/tex]

The height, [tex]h=cd\cdots(iv)[/tex]

where [tex]a,b[/tex] and [tex]c[/tex]  belong to the natural number.

This required volume must be equals to the volume of the box.

From equations (i) and (ii),

[tex]2\times 3\times h=48d^3[/tex]

 [from (iii) and (iv)]

[tex]\Rightarrow abhd^2=48d^3[/tex]

[tex]\Rightarrow h=\frac{48d^3}{6abd^2}[/tex]

[tex]\Rightarrow h=\frac{48}{ab}d[/tex]

On comparing with the equation (iv)

[tex]c=\frac{48}{ab}\cdots(v)[/tex]

Now, if the diameter of the baseball is unity,i.e, d=1 unit

( integer) and (integer) [from (iii) and (iv)]

(also an integer)  [from (v)]

Now, the height of the box,

[tex]h=8 \times 1= 8[/tex] unit.

Hence, the other dimension of the box, is 8 units corrosponding to the unity diameter of the baseball.

Note the height of the box depends on the diameter of the baseball, so it will have infinite possible value for different value of the diameter.

For example, the value of height for d=1 unit has been shown.

and another example may be if units, then (integer) and (integer)

(also an integer)  [from (v)]

Now, the height of the box,

[tex]h=2 \times 0.5= 1[/tex] unit. [from (iv)]

Here, the height of the box is 2 units corrosponding to 0.5 unit diameter of the baseball.

The possivle values of d can be taken for which [tex]a,b[/tex] and [tex]c[/tex] must be integers.

Answer:

equivalent

Step-by-step explanation:

equivalent because they have to be the same and not intersecting with eachother♡ Hope it helps ;)

Answer:

x=11/9 hope this helped <3

Step-by-step explanation:

Let's solve your equation step-by-step.

34x+2x=44

Step 1: Simplify both sides of the equation.

34x+2x=44

(34x+2x)=44(Combine Like Terms)

36x=44

36x=44

Step 2: Divide both sides by 36.

Answer:

for 31/34 is the answer for eye color

Step-by-step explanation:

2 + 1 =3

34-3=31

31 out of the 34 students have neither blue or brown eyes.

31/34

Answer:

X=-4

Step-by-step explanation:

the first thing you do is add 1 to both sides to make the variable be alone

-6x=24

now divide 6 on both sides the variable cancels out and your left with 24/-6

so your answer is -4

Answer:

hey do you want to do a zoom

Step-by-step explanation:

i am done with my basketball game

Answer:

22

Step-by-step explanation:

66 ÷3=22

3= one third

Answer:

let x and be the two integers

x+y=-112

if one of them is -109

let x be one of the that is substitute-109 to the above equation

-109+y=-112

collect like terms to the left hand side.

-109+112=-y

3=-y

move the sigh to the constant

y=-3

Step-by-step explanation:

hope this helps, good night!!!!

If something is written in its simplest radical form, that means that you have already found all possible roots and eliminated any radicals from the denominator of a fraction. ... For example, if your fraction is 2/√7, multiply by √7/√7 to get 2√7/√49. This will simplify to 2√7/7.  hope this helps

Answer:

Square roots are the opposite of “squaring” a number, or multiplying it by itself. For example, three squared is nine (3 2 = 9), so the square root of nine is three. In symbols, this is √9 = 3. The “√” symbol tells you to take the square root of a number, and you can find this on most calculators.

Step-by-step explanation:

hope it helps

Answer:

What is the least number of plates and cups she can buy?

The least number of cups of plates and cups she can buy is 24

How many packs of plates?

3 packs of plates

How many packs of cups?

2 packs of cups

Step-by-step explanation:

What is the least number of plates and cups she can buy?

We solve this using the Lowest Common Multiple method

The L.C.M of 8 and 12

Multiples of 8: 8, 16, 24, 32, 40

Multiples of 12: 12, 24, 36, 48

Therefore,

LCM(8, 12) = 24

Hence, the least number of cups and plates she can buy is 24

How many packs of plates?

Plates are sold in packs of eight

Hence: 24 ÷ 8 = 3 packs of plates

How many packs of cups?

Cups are sold in packs of 12

Hence: 24 ÷ 12 = 2 packs of cups

Answer:

Step-by-step explanation:

-42

Answer:

7.01

7.02

7.03

7.04

and on and on till

7.99

or 7 1/100 7 2/100 and on and on

Step-by-step explanation:

Answer: d) acute isoceles

Step-by-step explanation:

it has 2 acute angles and it's isoceles because it has 2 sides of equal length

Answer:

d. acute isosceles

Step-by-step explanation:

ABC had two sides that are equal so it is an isosceles triangle

<B = 90-44 = 46

A and C must be equal

A + B + C = 180

A + 46 + B = 180

2A = 180- 46

2A = 134

A = 67  so C = 67

All angles are acute

Answer:

mr martin was a hero in my eyes he saved many lives and was one of the strongest people to ever live (who is mr martin?)

Step-by-step explanation:

Answer:

-19 degrees

Step-by-step explanation:

13+6=19

you would need to add the negative since it said dropped in temperature and the temperature was already negative.

Answer:

The top line is a pure gross sales number showing how much revenue the company brought in for a given period.

Answer:

42.85% or 6/14

Step-by-step explanation:

6 / 14 = 0.428571428571

0.428571428571 * 100 ~ 42.85%                

Can I get Brainliest?                    

Answer: G=7.12

Step-by-step explanation: 25g-175=3 add 175 to both side which makes the equation 25g=178 and divide 178 by 25 which gives you 7.12

Answer:

g=178/25

Step-by-step explanation:

Step 1: 25(g-7)/25=3/25

Step2: g-7=3/25

Step 3: g-7+7=3/25 + 7

Answer: g=178/25

Decimal form would be g=7.12

Answer:

3.90993025975

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept)

y = 2x + 7 ← is in slope- intercept form

with slope m = 2

Parallel lines have equal slopes, thus

y = 2x + c ← is the partial equation

To find c substitute (- 2, 4) into the partial equation

4 = - 4 + c ⇒ c = 4 + 4 = 8

y = 2x + 8 → D

Answer:

20 containers

Step-by-step explanation:

Given:

D = 0.07N

Where,

D = Amount of deposits

N = Number of containers

If D = $1.40 find N

D = 0.07N

1.40 = 0.07N

Divide both sides by 0.07

N = 1.40 / 0.07

= 20

N = 20 containers

if you deposit $1.40, you will buy a total of 20 containers.

Answers:

=====================================================

Work Shown:

List out the perfect squares

{1,4,9,16,25,36,49,64,81,100,121}

We stop once we reach 117 or just a bit higher.

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

Then notice that

[tex]16 < 19 < 25 \ ... \ \text{19 between the squares 16 and 25}\\\\\sqrt{16} < \sqrt{19} < \sqrt{25} \ ... \ \text{ apply square root to all sides}\\\\4 < \sqrt{19} < 5[/tex]

Which shows [tex]\sqrt{19}[/tex] is between 4 and 5. Therefore, the two closest integers to [tex]\sqrt{19}[/tex] are 4 and 5.

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

We follow the same steps for [tex]\sqrt{50}[/tex]

So,

[tex]49 < 50 < 64\\\\\sqrt{49} < \sqrt{50} < \sqrt{64}\\\\7 < \sqrt{50} < 8[/tex]

So the square root of 50 is between 7 and 8.

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

And finally,

[tex]100 < 117 < 121\\\\\sqrt{100} < \sqrt{117} < \sqrt{121}\\\\10 < \sqrt{117} < 11[/tex]

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

Using a calculator, we find that

[tex]\sqrt{19} \approx 4.36[/tex]

[tex]\sqrt{50} \approx 7.07[/tex]

[tex]\sqrt{117} \approx 10.82[/tex]

which helps confirm our answers.

Answer:

Chicken: 500g

Peppers: 1kg

Onions: 10g

Tortillas: 14

Step-by-step explanation:

hope this helps

Answer:

its a

Step-by-step explanation:

Answer:

D. 75

Step-by-step explanation:

Bc they are congruent that means that DAY has angles 60 and 45 so you add them together to get 105 and bc triangles are 180 deg, the last angle is 75 (180-105 = 75)

Answer:

$62.95 (meal) + $5.03 (sales tax) +$.75 (sales tax tip) + $9.44 (meal tip)

Total: $78.17

Answer:

$78.19

Step-by-step explanation:

To find the total after the sales tax is charged you have to do

$62.95 x 1.08 (1 = to the total and .08 to add sales tax value) =$67.986  round*

Now you take $67.99 (has been rounded) and multiply but .15 to find out what is 15% of $67.99 , it comes out to be 10.1979 (Round)

Now to finish you add $67.99 +$10.20 = $78.19

Answer:

1.4

Step-by-step explanation:

Answer:

6 times

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

add me on discord fun54658#0871