In 2011, the winner of the Peachtree Road Race ran the 7-kilometer event in 28 minutes. What is the runner's unit rate? If the runner completed ina 14-kilometer race, what would be the expected time?

Answer:

7/12x+5

Step-by-step explanation:

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:

x = -8

Step-by-step explanation:

I hope this helps!

[tex]→-6x =48[/tex]

[tex] \implies{- 6x = 48}[/tex]

[tex]\implies \: x = \frac{48}{ - 6 } [/tex]

[tex] \blue{\implies \: x = - 8}[/tex]

Answer:

Range is (-5,5)

Step-by-step explanation:

It is the range of y values for the graph

the answer to your question is 4

Answer:

yeah it is 4 i got it right

Step-by-step explanation:

Answer:

f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)f(x) = x2 – p(x + 1) – c, then (α + 1)(β + 1)

Step-by-step explanation:

Answer:

$13.43

Step-by-step explanation:

Given that :

Price of dinner wholesale = $2.20

Markup % = 40%

Hence, selling price = (100 + 40)% * $2.20

Selling price = 140% * $2.20

Selling price = 1.4 * $2. 20 = $3. 08

Hence, price of 4 frozen dinner :

$3. 08 * 4 = $12.32

9% sales tax:

9% * $12.32

0.09 * $12.32 = 1.1088

Total amount paid :

$(12.32 +. 1.1088)

= $13.4288

= $13.43

Answer:

The answer is $13.43

Step-by-step explanation:

I just answered that question, and got it right

Answer:

The answer is 81/100.

Step-by-step explanation:

Multiply the denominator of the second fraction by 10 to get 100, then the numerator as well to get 60. Now that you have 21/100+60/100, all you have to do is add.

$598 basically 11.50•52

its just asking j the total amount of all of them together so add al of them together which is 28

Answer:

28.45

Step-by-step explanation:

*Mark me as brainliest

Answer:

The equivalent to one over five m − 20 is one over five (m − 100) ⇒ B

Step-by-step explanation:

Let us solve the question

∵ One over five means [tex]\frac{1}{5}[/tex]

∴ One over five m - 20 = [tex]\frac{1}{5}[/tex] m - 20

→ By using the distributive property, take one over five as a common factor

  from both terms

∴ [tex]\frac{1}{5}[/tex] m - 20 = [tex]\frac{1}{5}[/tex] [tex](\frac{\frac{1}{5}m}{\frac{1}{5}}[/tex] - [tex]\frac{20}{\frac{1}{5}})[/tex]

→ Simplify the bracket

∵  [tex]\frac{1}{5}[/tex] m ÷ [tex]\frac{1}{5}[/tex] = [tex]\frac{1}{5}[/tex] m × 5 = m

∵ 20 ÷  [tex]\frac{1}{5}[/tex]  = 20 × 5 = 100

∴  [tex]\frac{1}{5}[/tex] [tex](\frac{\frac{1}{5}m}{\frac{1}{5}}[/tex] - [tex]\frac{20}{\frac{1}{5}})[/tex] = [tex]\frac{1}{5}[/tex] (m - 100)

∴ [tex]\frac{1}{5}[/tex] m - 20 = [tex]\frac{1}{5}[/tex] (m - 100)

The equivalent to one over five m − 20 is one over five (m − 100)

Answer:

3(z+3) = 3z + 9 if thats what your asking

Step-by-step explanation:

Answer:

1,5 is your answer

Y=5 and X=1

Insert it in the equation

5=3(1)+2

5=3+2

5=5

Hence proved!

Answer:

Step-by-step explanation:

Let the complement = x

Let the angle = 5*x

x + 5x = 90

6x = 90

x = 90/6

x = 15

So the complement = 15

The angle itself is 5*15 = 75

Answer:

C

Step-by-step explanation:

hope this helps

Answer:it is d because on the chart it is 5 and 2 and your round

Step-by-step explanation:7 times 5 28 equal 30 hope helped correct if wrong

Answer:

m=d*v

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Given the following :

Number of sugar cookies = 42

Number of Oatmeal = 30

To package the cookies into identical containers so that each container has the same number of cookies with no left over ;

We find the greatest common factor of 42 and 30

Factors of 42 : 1, 2, 3, 6, 7, 14, 21, 42

Factors of 30 : 1, 2, 3, 5, 6, 10, 15, 30

The greatest common factor = 6

Answer: the first one is a matrix. the second one is functional.

Step-by-step explanation:

Answer:

If a company has departments such as Video Game Marketing, Movie Marketing, and Toy Marketing, it probably has a  

✔ matrix

organizational structure.

If a company has departments such as Sales, Marketing, Operations, and Human Resources, it probably has a  

✔ functional

organizational structure.

If a company has departments such as Northwest, South, and Northeast, it probably has a  

✔ divisional

organizational structure.

Answer:

$0.50

Step-by-step explanation:

Answer:

0.20

Step-by-step explanation:

5.00 divided by 25

Answer:

ok I did this construction about a year ago but I think I can remember something so if it's not correct I hope you won't be mad with me ok so the first step draw a straight line measure the length then make an AC on both sides then stand on one side make an arc upstand on the other side make an arc upthen stand on one AC and make another ARK on top of the other one then stand on the other AC and make another ark on top of the other one then join the lines yeah I think that's the procedure

Answer:

=10.6x104

Step-by-step explanation:

=8.1x104+2.5x104

=(8.1x104+2.5x104)

=10.6x104

(8.1 x104)+(2.5 x 104)

Multiply the numbers

842.4 + (2.5 x 104)

Multiply the numbers

842.4 +260

Now we do the same thing only different way

        2

       2.5

    x 104

________

           100

            000

             2 50 0

______________

            260

Multiply the digits

4 x 5 =20

Take the last digit and write it in the answer line

Carry the next digit and save it for the next calculation

Multiply the digits

4 x 2=8

Add the carried digit for the previous result

8+2 =10

Write the result in the answer line

Move the next digit and write it the next result below

Every digit multiplied by zero equals zero

Move to the next digit an write the next result below

Every digit multiplied by one stays the same

Add the numbers

Move the decimal sign as many times as there are decimal places in both factors combined.

Remove the unnecessary zeros

The result is 260

842.4+260

Add the numbers

1102.4

  842.4

+   260.0

_________

   1102.4

Write zeros to get the same number of decimal places.

Add the digits in the column

4+0=4

Write the result under the column

Add the digits in the column

2+0=2

Solution: 1102 .4

Alternate form : 5512/5 , 1102 2/5

PLEASE MARK ME AS BRAINLIEST

Domain = [tex]-\infty < x < +\infty[/tex]

Range = [tex]y \le -4[/tex]

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

Explanation:

The arrows on the graph indicate it goes on forever in both left and right directions. So the domain is the set of all real numbers and as an inequality, we write [tex]-\infty < x < +\infty[/tex] which is the same as saying [tex]-\infty < x < \infty[/tex]

This says x is between negative infinity and positive infinity.

In set builder notation, we would say [tex]\{x | x \in \mathbb{R}\}[/tex] and in interval notation, we would write [tex](-\infty, \infty)[/tex]

As you can probably see, the domain is the set of all possible x inputs of a function.

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

The range is the set of all possible y outputs of a function.

The largest output is y = -4 which is where the vertex is located.

There is no smallest y value as the arrows point down, and the graph goes forever in that direction.

So we say the range is [tex]-\infty < y \le -4[/tex] which shortens to [tex]y \le -4[/tex]

The range in set builder notation is [tex]\{y | y \in \mathbb{R}, \ y \le -4\}[/tex]

The range in interval notation is [tex](-\infty, -4][/tex] The square bracket says to include the endpoint, while the parenthesis excludes the endpoint.

Answer:

-176.........................

Answer: There are 27 trees he can plant in one row. There is one pine tree and 2 oak trees in each row

Step-by-step explanation: