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Vladimir [108]
3 years ago
8

Ten people stand in line. The first goes to the back of the line and the next person sits down, so that the person who was third

is now first in line. Now that person goes to the back of the line and the next person sits down. This process is repeated until only one person remains. What was the original position in line of the only remaining person?
Mathematics
1 answer:
Lelu [443]3 years ago
7 0
I
right?
don't rely in me i'm in elementary school
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Thomas needs to buy a cardboard sheet that will allow him to make his 224 in 3 box. To help construct the box, he decided to cut
Slav-nsk [51]

Answer:

Part 1; The volume of the box Thomas wants to make is 224 = 2·w² + 12·w

Part 2; The zeros for the equation of the function, are w = -14, or w = 8

Part 3

The width of the box is 8 inch

The length of the box, is 14 inches

The height of the box, is given as 2 inches

Part 4

Please find attached the graph of the function

Step-by-step explanation:

Part 1

The volume of the box Thomas wants to make, V = 224 in.³

The dimensions he cuts out from the length and width = 2 in² each

The length of the box = 6 inches + The width of the box

Let <em>l</em> represent the length of the box and let <em>w</em> represent the width of the box, we have;

l = 6 + w

The height of the box, h = The length of the cut out square = 2 inches

The volume of the box, V = Length, l × Width, w × Height, h

∴ V = l × w × h

l = 6 + w, h = 2

∴ V = (6 + w) × w × 2

V = 2·w² + 12·w,

The equation of the volume of the box, V = 2·w² + 12·w, where, V = 224

∴ 224 = 2·w² + 12·w

Part 2

The zeros of the equation for the volume of the box, V = 2·w² + 12·w, where, V = 224 are found as follows;

V = 224 = 2·w² + 12·w

∴ 2·w² + 12·w - 224 = 0

Dividing by 2 gives;

(2·w² + 12·w - 224)/2 = w² + 6·w - 112 = 0

∴ (w + 14) × (w - 8) = 0

The zeros for the equation of the function, are w = -14, or w = 8

Part 3

We reject the value, w = -14, therefore, the width of the box, w = 8 inch

The length of the box, l = 6 + w

∴ l = 6 + 8 = 14

The length of the box, l = 8 inches

The height of the box, <em>h</em>, is given as h = 2 inches

Part 4

The graph of the function created with MS Excel is attached

4 0
3 years ago
One store has carrots on sale for $1.1 for 3 pounds, while another store has carrots on sale for $0.78 for two pounds. Which sto
irina1246 [14]

Answer:

1) The store selling for 1.1 per 3 lbs

2) $6.24

Step-by-step explanation:

1)

1.1/3 = 0.37

0.78/2 = 0.39

0.37 is cheaper so it's a better deal

2)

\frac{0.78}{3} =\frac{x}{24} \\\\3x=18.72\\x=6.24

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What is the standard form of function f?
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Answer:

A = 4; B = -1 ; C = -29

Step-by-step explanation:

y = 4(x + 6) + 5

y = 4x + 24 +5

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If you place a 10-foot ladder against the top of a 6-foot building, how many feet will the bottom of the ladder be from the bott
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Draw a right triangle and label the sides using the given information. (Drawing below) Use pythagorean theorem to find the missing length:

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6^2 + x^2 = 10^2

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x^2 = 64. square root of both sides

x = 8

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How do I find the arc length with given radius &amp; central angel?
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The length of an arc subtended by a central angle is proportional to the circle's circumference. If the given central angle has measure \theta and the circle has radius r, then the arc has length \ell such that

\dfrac{\ell}\theta=\dfrac{2\pi r}{2\pi}=r

where \theta is given in radians. Then

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If \theta is given in degrees, then

\dfrac{\ell}\theta=\dfrac{2\pi r}{360}\implies\ell=\dfrac{\theta\pi r}{180}

8 0
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