Please help me idk this

An athlete runs 8 miles in 50 minutes on a treadmill. At this rate how far can the athlete run in 1 hour

alexdok [17]

Set it up into ratio or proportion

8/50 :: x/60

3 0

3 years ago

Jorge is asked to build a box in the shape of a rectangular prism. The maximum girth of the box is 20 cm. What is the width of t

MariettaO [177]

Answer:

The width of the box is 6.7 cm

The maximum volume is 148.1 cm³

Step-by-step explanation:

The given parameters of the box Jorge is asked to build are;

The maximum girth of the box = 20 cm

The nature of the sides of the box = 2 square sides and 4 rectangular sides

The side length of square side of the box = w

The length of the rectangular side of the box = l

Therefore, we have;

The girth = 2·w + 2·l = 20 cm

∴ w + l = 20/2 = 10

w + l = 10

l = 10 - w

The volume of the box, V = Area of square side × Length of rectangular side

∴ V = w × w × l = w × w × (10 - w)

V = 10·w² - w³

At the maximum volume, we have;

dV/dw = d(10·w² - w³)/dw = 0

∴ d(10·w² - w³)/dw = 2×10·w - 3·w² = 0

2×10·w - 3·w² = 20·w - 3·w² = 0

20·w - 3·w² = 0 at the maximum volume

w·(20 - 3·w) = 0

∴ w = 0 or w = 20/3 = 6. $\overline 6$

Given that 6. $\overline 6$ > 0, we have;

At the maximum volume, the width of the block, w = 6. $\overline 6$ cm ≈ 6.7 cm

The maximum volume, $V_{max}$ , is therefore given when w = 6. $\overline 6$ cm = 20/3 cm as follows;

V = 10·w² - w³

$V_{max}$ = 10·(20/3)² - (20/3)³ = 4000/27 = 148. $\overline {148}$

The maximum volume, $V_{max}$ = 148. $\overline {148}$ cm³ ≈ 148.1 cm³

Using a graphing calculator, also, we have by finding the extremum of the function V = 10·w² - w³, the coordinate of the maximum point is (20/3, 4000/27)

The width of the box is;

6.7 cm

The maximum volume is;

148.1 cm³

5 0

3 years ago

How do i solve for x if 6x - 6 - 7x =6

Dmitry_Shevchenko [17]

Answer:

X = 12

Step-by-step explanation:

Step 1 :

Pulling out like terms :

1.1 Pull out like factors :

-x - 12 = -1 • (x + 12)

Equation at the end of step 1 :

Step 2 :

Solving a Single Variable Equation :

2.1 Solve : -x-12 = 0

Add 12 to both sides of the equation :

-x = 12

Please said thanks

7 0

3 years ago

Read 2 more answers

1.) A man invested $600 at 8% per annum for 5 years. Calculate: a.) The simple interest payable b.) The total amount of money th

Bezzdna [24]

Answer:

Following are the solution to this question:

Step-by-step explanation:

Using formula:

$\text{Simple Interest} = \frac{P \times R \times T}{100} \\\\\text{ Total amount} = \text{principle}+ \text{Simple Interest}$

In question (1):

$Principle= \$ 600\\Rate = \ 8 \%\\Time= \ 5$

In point a:

$\to \frac{P \times R \times T}{100} \\\\\to \frac{(600 \times 8 \times 5)}{100}\\\\ \to 240$

In point b:

$\to amount = principle \ +\ simple \ interest$

$= 600 + 240 \\\\= 840$

In question (2):

$Principle= \$ 12,450\\Rate = \ 7.25 \%\\Time= \ 6$

In point a:

$\to \frac{P \times R \times T}{100} \\\\\to \frac{(12,450 \times 7.25 \times 6)}{100}\\\\ \to 5,415.75$

In point b:

$\to amount = principle \ +\ simple \ interest$

$= 12,450 + 5,415.75 \\\\= 17,865.75$

The 3 question is incomplete, that's why it can't be solved.

7 0

3 years ago

Please help! Correct answer only!

Tcecarenko [31]

Answer:

<em>" Expected Payoff " ⇒ $ 1.56 ; Type in 1.56</em>

Step-by-step explanation:

Consider the steps below;

$Tickets That Can Be Entered - 1 Ticket,\\Total Tickets Entered - 1000 Tickets,\\\\Proportion - 1 / 1000,\\Money One ( First Ticket ) = 820 Dollars,\\Money One ( Second Ticket ) = 740 Dollars,\\\\Proportionality ( First ) - 1 / 1000 = x / 820,\\Proportionality ( Second ) - 1 / 1000 = x / 740\\\\1 / 1000 = x / 820,\\1000 * x = 820,\\x = 820 / 1000,\\x = 0.82,\\\\1 / 1000 = x / 740,\\1000 * x = 740,\\x = 740 / 1000,\\x = 0.74\\\\Conclusion ; " Expected Payoff " = 0.82 + 0.74 = 1.56$

<em>Solution; " Expected Payoff " ⇒ $ 1.56</em>

4 0

3 years ago