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mr Goodwill [35]
2 years ago
13

Mick paid $2.94 in sales tax on an item that cost $42.00 before tax. At that rate, how much would he paying sales tax before an

item that cost $58 before tax
Mathematics
1 answer:
sergiy2304 [10]2 years ago
5 0
To answer this question you would have two steps involved. The first step would be to find the percentage of $42 that gives us $2.94. Set up an equation 42x=2.94. Divide both sides by 42 to get the decimal 0.07. This equal 7%. Take this percentage multiplied by the $58. You need to change the 7% into 0.07 to be able to calculate it. 0.07 x 58 = $4.06 sales tax.
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A contaminant is leaking into a lake at a rate of R(t) = 1400e0.06t gallons/h. Enzymes have been added to the lake that neutrali
ruslelena [56]

Answer:

Step-by-step explanation:

Rate of leakage, R(t) = 1400 e^0.06t gallons/h

fraction remains , S(t) = e^(-0.32t)

initial contaminant = 1000 gallon

gallons contaminant present after t hour is S(t) R(t)

G(t) = S(t) R(t)

G(t) = 1400 e^{0.06t}\times e^{-0.32t}

G(t) = 1400 e^{- 0.26t}

Put t = 18 hours

G(t) = 1400 e^{- 0.26\times 18}

Taking log on both the sides

ln G = ln 1400 - 0.26 x 18

ln G = 7.244 - 4.68

ln G = 2.564

G = 13 gallons

5 0
2 years ago
A gallon of Moo Milk costs \$5.12$5.12dollar sign, 5, point, 12. What is the price, in dollars, of an 888 ounce glass of Moo Mil
Sladkaya [172]
The correct statement is:
A gallon of Moo Milk costs $5.12 What is the price, in dollars, of an 8 ounce glass of Moo Milk? There are 128 ounces in 1 gallon.

Solution:
Cost of 1 gallon of Moo Milk = $ 5.12

1 gallon = 128 ounces, so we can write:

Cost of 128 ounces of Moo Milk = $ 5.12

Cost of 1 ounce of Moo Milk = $ 5.12/128 = $ 0.04

Cost of 8 ounces of Moo Milk = $ 0.04 x 8 = $ 0.32

Thus, 8 ounces of Moo Milk will cost $ 0.32
3 0
2 years ago
Read 2 more answers
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
1 year ago
Read 2 more answers
−15x+4≤109 OR −6x+70&gt;−2
Xelga [282]

-15x+4\leq109\qquad\text{subtract 4 from both sides}\\\\-15x\leq105\qquad\text{change the signs}\\\\15x\geq-105\qquad\text{divide both sides by 15}\\\\\boxed{x\geq-7}\\or\\-6x+70>-2\qquad\text{subtract 70 from both sides}\\\\-6x>-72\qquad\text{change the signs}\\\\6x

3 0
1 year ago
Read 2 more answers
Solve for x*<br> (17x - 8)
djyliett [7]

Answer:x=4

Step-by-step explanation:

This triangle is an equilateral triangle with all angles equal.

Sum of angles in a triangle=180

17x-8+17x-8+17x-8=180

Collect like terms

17x+17x+17x-8-8-8=180

51x-24=180

51x=180+24

51x=204

Divide both sides by 51

51x/51=204/51

x=4

3 0
1 year ago
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