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vampirchik [111]
2 years ago
11

After the price of petroleum oil went up by 10%, a consumer reduced his oil consumption by the same percent. By what percent wou

ld his petroleum bill be changed? THE ANSWER IS NOT 10%.
Mathematics
1 answer:
IgorLugansk [536]2 years ago
7 0
Let's assign some random values to it, and say 1 unit of petroleum costs 100 bitcoins, because we all know bitcoins are the best currency :P

If the price goes up by 10%, it is now 100*1.1 = 110bitcoins for 1 unit.

However he's only getting 0.9 units now, so multiplying 110 by 0.9 gives us 99 bitcoins. His petroleum bill used to be 100 (which is why I picked 100 as it's easier), and now it is 99. Therefore his petroleum bill has reduced by 1%
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Tems11 [23]

Answer:

<em>96π units²</em>

Step-by-step explanation:

Find the diagram attached

Area of a sector is expressed as;

Area of a sector = θ/2π * πr²

Given

θ = 3π/4

r = 16

Substitute into the formula

area of the sector = (3π/4)/2π * π(16)²

area of the sector = 3π/8π * 256π

area of the sector = 3/8 * 256π

area of the sector = 3 * 32π

<em>area of the sector =96π units²</em>

5 0
2 years ago
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Write an arithmetic series for which S5 = 10.
Ludmilka [50]
S5=10 means the 5th number is 10. 
So the arithmetic sequence is s1, s2,s3, s4, 10
3 0
2 years ago
The solid graph is a translation of RootIndex 3 StartRoot x EndRoot. On a coordinate plane, 2 cube root functions are shown. The
serious [3.7K]

Answer: 2 units up.

Step-by-step explanation:

If you take a look at the graph, it shows that it is 2 units up from where it initially started, therefore it is moved 2 units up. It says the SOLID graph is the translation, therefore it would be moving 2 units up.

6 0
2 years ago
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Nathan had an infection, and his doctor wanted him to take penicillin. Because Nathan’s father and paternal grandfather were all
Sergio039 [100]
Let events
A=Nathan has allergy
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T=Nathan tests positive
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We are given
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We want to calculate probability that Nathan is allergic AND tests positive
P(T n A)

From definition of conditional probability,
P(T|A)=P(T n A)/P(A)
substitute known values,
0.98 = P(T n A) / 0.75
solving for P(T n A)
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Hope this helps!!
3 0
2 years ago
A boat tour guide expects his tour to travel at a rate of x mph on the first leg of the trip. On the return route, the boat trav
Georgia [21]

<em><u>The intervals included in solution are:</u></em>

\frac{1}{x} + \frac{1}{x}-10\ge \frac{2}{24}\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:0

<em><u>Solution:</u></em>

Given that,

A boat tour guide expects his tour to travel at a rate of x mph on the first leg of the trip

On the return route, the boat travels against the current, decreasing the boat's rate by 10 mph

The group needs to travel an average of at least 24 mph

<em><u>Given inequality is:</u></em>

\frac{1}{x} + \frac{1}{x} - 10\geq \frac{2}{24}

<em><u>We have to solve the inequality</u></em>

\frac{1}{x} + \frac{1}{x} - 10\geq \frac{2}{24}\\\\\frac{2}{x}  - 10\geq \frac{2}{24}

\mathrm{Subtract\:}\frac{2}{24}\mathrm{\:from\:both\:sides}\\\\\frac{2}{x}-10-\frac{2}{24}\ge \frac{2}{24}-\frac{2}{24}\\\\Simplify\\\\\frac{2}{x}-10-\frac{2}{24}\ge \:0

\frac{2}{x}-\frac{10}{1}-\frac{2}{24} \geq 0\\\\\frac{ 2 \times 24}{x \times 24} -\frac{10 \times 24}{1 \times 24} - \frac{2 \times x }{24 \times x}\geq 0\\\\\frac{48}{24x}-\frac{240x}{24x}-\frac{2x}{24x}\geq 0\\\\Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions\\\\\frac{48-240x-2x}{24x}\geq 0\\\\Add\:similar\:elements\\\\\frac{48-242x}{24x}\ge \:0

\mathrm{Multiply\:both\:sides\:by\:}24\\\\\frac{24\left(48-242x\right)}{24x}\ge \:0\cdot \:24\\\\Simplify\\\\\frac{48-242x}{x}\ge \:0\\\\Factor\ common\ terms\\\\\frac{-2\left(121x-24\right)}{x}\ge \:0\\\\\mathrm{Multiply\:both\:sides\:by\:}-1\mathrm{\:\left(reverse\:the\:inequality\right)}

When we multiply or divide both sides by negative number, then we must flip the inequality sign

\frac{\left(-2\left(121x-24\right)\right)\left(-1\right)}{x}\le \:0\cdot \left(-1\right)\\\\\frac{2\left(121x-24\right)}{x}\le \:0\\\\\mathrm{Divide\:both\:sides\:by\:}2\\\\\frac{\frac{2\left(121x-24\right)}{x}}{2}\le \frac{0}{2}\\\\Simplify\\\\\frac{121x-24}{x}\le \:0

\mathrm{Find\:the\:signs\:of\:the\:factors\:of\:}\frac{121x-24}{x}\\

This is attached as figure below

From the attached table,

\mathrm{Identify\:the\:intervals\:that\:satisfy\:the\:required\:condition:}\:\le \:\:0\\\\0

<em><u>Therefore, solution set is given as</u></em>:

\frac{1}{x} + \frac{1}{x}-10\ge \frac{2}{24}\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:0

8 0
2 years ago
Read 2 more answers
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