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3 years ago

Order of Operations

Mathematics

1 answer:

emmasim [6.3K]3 years ago

6 0

Given:

$4 + 9 + 16 \div 4 - 8 -3 \times 5$

To find:

The number of possible solutions, if the Order of Operations did not exist.

Solution:

We have,

$4 + 9 + 16 \div 4 - 8 -3 \times 5$

Now,

Case 1:

$[4 + 9 + 16] \div [4 - 8 -(3 \times 5)]=29\div (4 - 8 -15)$

$4 + 9 + 16 \div 4 - 8 -(3 \times 5)=-\dfrac{29}{19}$

Case 2:

$[4 + 9 + 16] \div (4 - 8 -3) \times 5=29\div (-7\times 5)$

$4 + 9 + 16 \div (4 - 8 -3) \times 5=-\dfrac{29}{35}$

Case 3:

$4 + 9 + (16 \div 4) - 8 -(3 \times 5)=4+9+4-8-15$

$4 + 9 + (16 \div 4) - 8 -(3 \times 5)=-6$

Many more possibilities are there.

Therefore, there are more than 3 possible solutions.

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3 years ago

Which expression is equivalent to (2^3)^-5

Ostrovityanka [42]

Hi!

You didn't list the options, but I think I know the answer. Let me know if my answer isn't listed! :)

$(x^{3} )^{-5}$
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3 years ago

Read 2 more answers

Help please:))

Blababa [14]

Answer:

a) Because this asks about the radius and height, I assume that we are talking about a cylinder shape.

Remember that for a cylinder of radius R and height H the volume is:

V = pi*R^2*H

And the surface will be:

S = 2*pi*R*H + pi*R^2

where pi = 3.14

Here we know that the volume is 1000cm^3, then:

1000cm^3 = pi*R^2*H

We can rewrite this as:

(1000cm^3)/pi = R^2*H

Now we can isolate H to get:

H = (1000cm^3)/(pi*R^2)

Replacing that in the surface equation, we get:

S = 2*pi*R*H + pi*R^2

S = 2*pi*R*(1000cm^3)/(pi*R^2) + pi*R^2

S = 2*(1000cm^3)/R + pi*R^2

So we want to minimize this.

Then we need to find the zeros of S'

S' = dS/dR = -(2000cm^3)/R^2 + 2*pi*R = 0

So we want to find R such that:

2*pi*R = (2000cm^3)/R^2

2*pi*R^3 = 2000cm^3

R^3 = (2000cm^3/2*3.14)

R = ∛(2000cm^3/2*3.14) = 6.83 cm

The radius that minimizes the surface is R = 6.83 cm

With the equation:

H = (1000cm^3)/(pi*R^2)

We can find the height:

H = (1000cm^3)/(3.14*(6.83 cm)^2) = 6.83 cm

(so the height is equal to the radius)

b) The surface equation is:

S = 2*pi*R*H + pi*R^2

replacing the values of H and R we get:

S = 2*3.14*(6.83 cm)*(6.83 cm) + 3.14*(6.83 cm)^2 = 439.43 cm^2

c) Because if we pack cylinders, there is a lot of space between the cylinders, so when you store it, there will be a lot of space that is not used and that can't be used for other things.

Similarly for transport problems, for that dead space, you would need more trucks to transport your ice cream packages.

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2 years ago

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nalin [4]

Answer: B

Explanation:

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18 red marbles

4 blue marbles

10 green marbles.

You are asked what part of Osteen's marbles are red?

Probability = number of possible outcomes/total number of out outcomes.

P(Red) = 18/32 = 9/16

Both, 18 and 32 are divisible by 2 which gives 9/16. Since 9/16 cannot be reduced any further, we live it as it is. If you wanted to plug this into a calculator that would give 0.5625 which is 56.25% of Osteen's marbles are red.

P(Blue) = 4/32 = 1/8. 1/8 = 0.125 which 12.5% of his marbles are blue.

P(Green) = 10/32 = 5/16. 5/16= 0.3125 which 31.25 of his marbles are green. When you add 0.5625 + 0.125 + 0.3125 = 1 which is 100%. All probabilities add up to 1.

Hope this elaborate explanation helps.

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2 years ago

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ohaa [14]

Given:

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To find:

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