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3 years ago

Solve the equation. 44 – 1 + 7q = 106

Mathematics

1 answer:

PolarNik [594]3 years ago

3 0

Let's solve your equation step-by-step. 44−1+7q=106

Step 1: Simplify both sides of the equation. 44−1+7q=106
Simplify: (Show steps) 44+−1+7q=106(7q)+(44+−1)=106 (Combine Like Terms)7q+43=1067q+43=106

Step 2: Subtract 43 from both sides.7q+43−43=106−437q=63

Step 3: Divide both sides by 7.‌7q7‌=‌637‌

q=9

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An open-top box with a square base is to have a volume of 4 cubic feet. Find the dimensions of the box (in ft) that can be made

Lemur [1.5K]

Answer:

The dimension of box= $2ft\times 2ft\times 1ft$

Step-by-step explanation:

We are given that

Volume of box=4 cubic feet

Let x be the side of square base and h be the height of box

Volume of box= $lbh=x^2h$

$4=x^2h$

$h=\frac{4}{x^2}$

Now, surface area of box,A= $x^2+4xh$

$A=x^2+4x(\frac{4}{x^2})=x^2+\frac{16}{x}$

$\frac{dA}{dx}=2x-\frac{16}{x^2}$

$\frac{dA}{dx}=0$

$2x-\frac{16}{x^2}=0$

$2x=\frac{16}{x^2}$

$x^3=8$

$x=2$

$\frac{d^2A}{dx^2}=2+\frac{32}{x^3}$

Substitute x=2

$\frac{d^2A}{dx^2}=2+\frac{32}{2^3}=2+4=6>0$

Hence, the area of box is minimum at x=2

Therefore, side of square base,x=2 ft

Height of box,h= $\frac{4}{2^2}=1 ft$

Hence, the dimension of box= $2ft\times 2ft\times 1ft$

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3 years ago

25 - 4x = 15 - 3x + 1 - x

kenny6666 [7]

Hello!

To solve algebraic equations, we need to first, simplify the common terms, and secondly use SADMEP. SADMEP is strictly used to solve algebraic equations, and is used like PEMDAS. SADMEP is an acronym for subtract, addition, division, multiplication, exponents, and parentheses.

25 - 4x = 15 - 3x + 1 - x (simplify the common terms)

25 - 4x = 16 - 4x (subtract 16 from both sides)

9 - 4x = -4x (add 4x to both sides)

9 = 0 → This means that there is no solutions.

Therefore, this equation has no solutions, which are contradictions because those are the equations with no solution.

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3 years ago

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Answer:

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Step-by-step explanation:

Calculation for the expected profit for one spin of the roulette wheel with this bet

Based on the information given you bet $50 on 00 while the standard roulette has 38 possible outcomes which means that the probability or likelihood of getting 00 will be 1/38.

Therefore when we get an 00, we would get the amount of $1,750 with a probability of 1/38 and in a situation where were we get something other than 00 this means we would lose $50 with a probability of 37/38.

Now let find the Expected profit using this formula

Expected profit = sum(probability*value) -sum(probability*value)

Let plug in the formula

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