the quotient of n and 3 is less than 5

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:

7/6x3/7===21/42=== 1/2

Step-by-step explanation:

Answer:

The answer is

[tex] \huge y = 4x - 22[/tex]

Step-by-step explanation:

To find an equation of a line given the slope and a point we use the formula

[tex]y - y_1 = m(x - x_1)[/tex]

where

m is the slope

( x1 , y1) is the point

From the question the point is (3, -10) and the slope 4

We have

[tex]y + 10 = 4(x - 3) \\ y + 10 = 4x - 12 \\ y = 4x - 12 - 10[/tex]

We have the final answer as

[tex]y = 4x - 22[/tex]

Hope this helps you

Answer:

y+10=4(x-3) in point-slope form

Step-by-step explanation:

In point-slope form, this is how you will write out the equation. Point slope form is y-y1=m(x-x1). You substitute the values in order to get this equation.

Answer:

jkl

Step-by-step explanation:

jkl

Answer:

x=2

Step-by-step explanation:

Answer:

The inverse of the function is

P^-1(t) = Log5 t - Log5 19,300

or P^-1(t) = Log5 (t/19,300)

Step-by-step explanation:

Here, we want to find the inverse of the function.

Make t the subject of the formula, then solve the equation for P(t)

P(t) = 19,300(5)^t

Replace P(t) with t and t with P(t)

So we have

t = 19,300(5)^P(t)

Now make P(t) subject of formula

divide both sides by 19,300

t/19,300 = 5^p(t)

By logarithmic law:

Log5 (t/19,300) = P(t)

Hence P(t) = Log5 t - Log5 19,300

Now replace P(t) with P^-1(t)

So the inverse is;

P^-1(t) = Log5 t - Log5 19,300

Answer:

C)

Step-by-step explanation:

got it right on edge :)

Answer:

The answer is 26 is after 34.

The pattern is x - 8 = y.

Step-by-step explanation:

Good luck! <3

Answer:

x ≥ 15

Step-by-step explanation:

5x + 3 ≥ 48

Group like terms

5x ≥ 48 – 3

5x ≥ 45

divide both sides by 5

5x/5 ≥ 45/5

x ≥ 15

Answer:

1.34 times the length of Noah's bike ride

Step-by-step explanation:

634/472

1.34322033898

1.34

1.34 times the length of Noah's bike ride

Answer:

No

Step-by-step explanation:

Answer:

Why... Um... ok

Step-by-step explanation:

Answer:

The overall change is 116points gained

Step-by-step explanation:

Points gained = 12points

Points lost  = 114points

Points gained  = 218points

Unknown:

Overall change in its value  = ?

Solution:

 The overall change  = Total points gained  - Total points lost

                                    = (218 + 12) - 114

                                     = 116points

The overall change is 116points gained

Answer:

its 116

Step-by-step explanation:

12 - 114

-102 + 218 = 116

Answer:

49

Step-by-step explanation:

so let explain

you first have to make the fractions into whole numbers the way you do that is by

1) multiply the 3 times -3

2) then add 2

3) = -7

The next one you do the same

4 times -2

plus 1 =-7

so then this what the equation would look like

-7(-7)

so you multiply the 7 and get

49

Answer:

10. you're welcome, good Luckk!

Answer:

Town C.

Step-by-step explanation:

Average change of population with time for town A = [tex] \frac{24,500 - 22,000}{4} = \frac{2,500}{4} = 625 [/tex]

Average change of population with time for town B = [tex] \frac{34,770 - 31,200}{6} = \frac{3,570}{6} = 595 [/tex]

Average change of population with time for town C = [tex] \frac{22,000 - 18,000}{5} = \frac{4,000}{5} = 800 [/tex]

Average change of population with time for town D = [tex] \frac{34,100 - 32,000}{3} = \frac{2,100}{3} = 700 [/tex]

Town C had the greatest average change in population over time (800/yr).

Answer:

its c

Step-by-step explanation:

Answer:

There were 16 ounces of Cat Food after 24 days.

Step-by-step explanation:

From the graph attached,

For an ordered pair (x, y) lying on the graph,

x-coordinate represents the number of days since bag was bought and y- coordinate represents the ounces of cat food required.

Now the value x = 24 on x-axis shows the number of days since the bag was bought.

For x = 24, ounces of cat food in the bag ( y ) = 16 ounce

Therefore, 16 ounces of Cat Food were in the bag after 24 days since it was bought.

16 ounces of cat food was in the bag, on 24th day

Given : The y axis represents dependent variable ie the 'ounces of cat food' , and x axis represents independent variable ie 'days since bag was bought'

To find : Value of y ie ounces of food - on a particular value of x ie days since bag bought , we draw a straight vertical line from value of x to the curve & correspond it to y axis.

From x = 24, if we draw a straight vertical line to the graph - it touches the point ( x,y ) = (24, 16). Extending it further to y axis, we get value of y ie 'ounces of food' = 16

To learn more, refer https://brainly.com/question/18385183?referrer=searchResults

Answer:

well the numbers are 58 60 62 64 and 66

Step-by-step explanation:

it's because when u add these 5 numbers u get 310 hope this helps

Answer: 62

Step-by-step explanation:

Answer:

After 88 seconds, they will blink together.

Step-by-step explanation:

Time after which the first light blinks = 8 seconds

Time after which the second light blinks = 22 seconds

Initially, both the lights blink together.

To find:

The time at which they will blink together again.

Solution:

Let us have a look at the time after which each light will blink.

First light will blink after:

8 s, 16 s, 24 s, 32 s, 40 s, 48 s, 56 s, 64 s, 72 s, 80 s, 88 s, 96 s, 104 s, ......

Second light will blink after:

22 s, 44 s, 66 s, 88 s, 110 s, .....

It can be seen that common time is 88 second, at which the both will blink together.

So, the answer is 88 s.

This answer can also be computed by taking the LCM (Least Common Multiple) of both the numbers i.e. 8 and 22.

Using the factorization method:

[tex]8=\underline{2}\times 2\times 2[/tex]

[tex]22=\underline{2}\times 11[/tex]

Common is 2.

Therefore the LCM will be:

[tex]2\times 2\times2\times 11 = \bold{88}[/tex]

So, the answer is 88 s.

Answer:

The instantaneous velocity of the eagle at the given time is  7.5 m/s.

Step-by-step explanation:

Given;

height of the cliff, h = 125 m

the height at which the eagle is flying, h(t) = 125 + 1.25t²

The velocity of the eagle is given by;

v = dh/dt

v = 2.5t

The instantaneous velocity of the eagle at t = 3 seconds is given by;

v = 2.5(3)

v = 7.5 m/s

Theerefore, the instantaneous velocity of the eagle at t = 3 seconds is  7.5 m/s.

Answer:

4:9 is the ratio

Step-by-step explanation:

4 in Texas and 9 in Michigan

Answer:

i do i am right noww lol

Step-by-step explanation:

Answer:

x=-2x+5

Step-by-step explanation:

Answer:

A,B,C

Step-by-step explanation:

When you divide 16 by 12 you  get 1.3 repeating. When you divide A , B , C by their numbers you get 1.3 repeating also. But D and E equal 1.5 so that's how you know those to answers are incorrect:)

glad to help!

The equivalent ratio are 8:6, 32:24 and 4:3

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

Ratio = 16 : 12

Simplifying the ratio

= 16/12

= 4/3

So, first 8:6

= 4: 3

and, second 32:24

= 4:3

and, third = 4:3

and, fourth 12 : 8

= 3:2

Hence, the equivalent ratio are 8:6, 32:24 and 4:3

Learn more about ratio here:

https://brainly.com/question/13419413

#SPJ5

Answer:

[tex]12x+10y-5[/tex]

Step-by-step explanation:

[tex]4y+13x-5+6y-x[/tex]

Combine the like terms

[tex]12x+10y-5[/tex]

Answer:

I going to say this should be easy because there must be a f(x) in a function so I think the answer is A.

Step-by-step explanation:

I think that functions must have f(x) in the equation.

Answer:

B.2≤x≤5

Step-by-step explanation:

Answer:

Option B is the correct answer

Step-by-step explanation:

[tex] 2 \leqslant x \leqslant 5[/tex] is the domain of the given problem.