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Nat2105 [25]
3 years ago
7

David rolls a fair dice 240 times. How many times would David expect to roll a three?

Mathematics
1 answer:
jolli1 [7]3 years ago
4 0

Answer:

40

Step-by-step explanation:

There are 6 numbers on an dice (1-6) Divide 240 by 6 and the reasonable amount of times to roll a 3 is 40 time

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A cone-shaped paper drinking cup is to be made to hold 27 cm of water. Find the height h and radius r of the cup that will use t
andreyandreev [35.5K]

Answer:

  • r = 2.632 cm
  • h = 3.722 cm

Step-by-step explanation:

The formula for the volume of a cone of radius r and height h is ...

  V = (1/3)πr²h

Then r² can be found in terms of h and V as ...

  r² = 3V/(πh)

The lateral surface area of the cone is ...

  A = (1/2)(2πr)√(r² +h²) = πr√(r² +h²)

The square of the area is ...

  T = A² = π²r²(r² +h²)

Substituting for r² using the expression above, we have ...

  T = π²(3V/(πh))((3V/(πh) +h²) = 9V²/h² +3πVh

We want to find the minimum, which we can do by setting the derivative to zero.

  dT/dh = -18V²/h³ +3πV

This will be zero when ...

  3πV = 18V²/h³

  h³ = 6V/π . . . . . multiply by h³/(3πV)

For V = 27 cm³, the value of h that minimizes paper area is ...

  h = 3∛(6/π) ≈ 3.7221029

The corresponding value of r is ...

  r = √(3V/(πh)) = 9/√(π·h) ≈ 2.6319242

The optimal radius is 2.632 cm; the optimal height is 3.722 cm.

_____

The second derivative test applied to T finds that T is always concave upward, so the value we found is a minimum.

__

Interestingly, the ratio of h to r is √2.

8 0
3 years ago
Find the perimeter of the rectangle 3x length 5 width ​
crimeas [40]

Answer:

2(2x+5)

Step-by-step explanation:

Length of the rectangle=l= 3x

Breadth of the rectangle=b= 5

Perimeter= 2(l+b)

= 2(3x+5)

3 0
3 years ago
Find the domain and range of the exponential function h(x) = –343x.
Amanda [17]

The function is supposed to be;

h(x) = -343^(x)

Answer:

The domain will be a set of real numbers while the range will be y ≤ 0 and on the interval (-∞, 1)

As x is increasing, h is decreasing and as x is decreasing, h is increasing

Step-by-step explanation:

We are given the function as;

h(x) = -343^(x)

The formula is;

y = a^(x) since it's symmetrical to the x-axis

However in this case;

y = -a^(x)

Now, the domain is y and the range is a set of values of x.

I've attached a graph of this function drawn on desmos.

From the graph we can see that The domain will be a set of real numbers while the range will be on the interval (-∞, 1)

For a value of x = 0,we have;

h(0) = -343^(0)

h(0) = -343

When we increase the value of x to 3,we have;

h(3) = -343^(3)

h(3) = -40353607

When we decrease the value of x to -3, we have;

h(-3) = -343^(-3)

h(-3) = 0.00000002478

Thus, we can conclude that;

As x is increasing, h is decreasing and as x is decreasing, h is increasing

4 0
2 years ago
How can the decimal 0.57 be written as a fraction
Akimi4 [234]
If you want to convert 0.57 into a fraction, you can do it like this:
<span>
<span>0.57 equals to 57/100 </span></span><span>(you can't do anything else because 57 and 100 don't have common factors).

</span><span><span /><span>The result is 57/100.</span>
</span>
7 0
3 years ago
Read 2 more answers
1 27 points from 35 points.
pishuonlain [190]

Answer:

127 from 35

127 - 35

92

Step-by-step explanation:

6 0
3 years ago
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