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3 years ago

What is the median value of the data set shown on the line plot?

Mathematics

1 answer:

Dvinal [7]3 years ago

4 0

Answer:

110

Step-by-step explanation:

it is 110 because it is the number in the middle of the data set.

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A piece of cardboard is 15 inches by 30 inches. A square is to be cut from each corner and the sides folded up to make an open-t

solmaris [256]

Answer:

Maximum volume = 649.519 cubic inches

Step-by-step explanation:

A rectangular piece of cardboard of side 15 inches by 30 inches is cut in such that a square is cut from each corner. Let x be the side of this square cut. When it was folded to make the box the height of box becomes x, length becomes (30-2x) and the width becomes (15-2x).

Volume is given by

V = $V = Length\times Width\times Height\\V = (30 - 2x)(15-2x)x= 4x^3-90x^2+450x\\So,\\V(x) = 4x^3-90x^2+450x$

First, we differentiate V(x) with respect to x, to get,

$\frac{d(V(x))}{dx} = \frac{d(4x^3-12x^2+9x)}{dx} = 12x^2 - 180x +450$

Equating the first derivative to zero, we get,

$\frac{d(V(x))}{dx} = 0\\\\12x^2 - 180x +450 = 0$

Solving, with the help of quadratic formula, we get,

$x = \displaystyle\frac{5(3+\sqrt{3})}{2}, \frac{5(3-\sqrt{3})}{2}$ ,

Again differentiation V(x), with respect to x, we get,

$\frac{d^2(V(x))}{dx^2} = 24x - 180$

At x =

$\displaystyle\frac{5(3-\sqrt{3})}{2}$ ,

$\frac{d^2(V(x))}{dx^2} < 0$

Thus, by double derivative test, the maxima occurs at

x = $\displaystyle\frac{5(3-\sqrt{3})}{2}$ for V(x).

Thus, largest volume the box can have occurs when $x = \displaystyle\frac{5(3-\sqrt{3})}{2}}$ .

Maximum volume =

$V(\displaystyle\frac{5(3-\sqrt{3})}{2}) = (30 - 2x)(15-2x)x = 649.5191\text{ cubic inches}$

8 0

3 years ago

Determine the missing side length

soldier1979 [14.2K]

Answer:

√85

Step-by-step explanation:

The given shape is a right angled triangle.

Let the missing side length be " x ".

By Pythagoras theorem,

x² = 6² + 7²

x² = 36 + 49

x² = 85

x = √85

Therefore, the missing side length be √85.

8 0

3 years ago

A rock is thrown vertically upward from the surface of an airless planet. It reaches a height of s = 120t - 4t2 meters in t seco

12345 [234]

Answer:

Step-by-step explanation:

Given that a rock is thrown vertically upward from the surface of an airless planet. It reaches a height of $s(t) = 120t - 4t^2$

where t is expressed in seconds

The rock goes upto a height where the velocity becomes 0 and then it starts falling down by gravity

Velocity at time t = s'(t) = $120-8t$

This becomes 0 when t =15 seconds

Hence at 15th second the rock starts falling and upto

s(15) = $120(15)-4(15^2)\\= 900$ metres high it goes

The time taken to reach highest point is = 15 seconds.

6 0

4 years ago

60 units and 14 Units per case. How many cases and how many units needed

kozerog [31]

There are 4.29 cases in the units

<h3>How to determine the number of cases?</h3>

The given parameters are:

Units = 60

Rate = 14 units per case

The number of cases is then calculated as:

Case = Unit/Rate

This gives

Case = 60/14

Evaluate

Case = 4.29

Hence, there are 4.29 cases in the units