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Dovator [93]
4 years ago
7

Solve the inequality for x. Show each step of the solution. 12X>9(2X-3)-15

Mathematics
2 answers:
agasfer [191]4 years ago
6 0
12x > 18x - 27 - 15
12x > 18x - 42
12x - 18x > -42
-6x > -42
x < -42/-6
two negatives make a positive so now its x < 42/6
Lastly divide 42/6 so it can equal 7

Answer: X < 7.
Igoryamba4 years ago
3 0
12x>9(2x-3)-15
12x>18x-27-15
12x-18x>-27-15
-6x>-42
"x" must be always positive, therefore we have to change the sign on both sides of the inequality, and we have to change "<" by ">".

6x<42
x<42/6
x<7


Answer: x<7

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158

Step-by-step explanation:

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Find the lateral area of the cylinder.<br><br>Give your answer in the terms of pi.
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Hi there! 

The formula for the lateral area of a cylinder is LA = 2 x pi x r x h. (two times pi times radius times height) Using this formula, we can plug in the values and solve for the lateral area.

Plugging in the values: LA = 2 x pi x 7 x 9
Simplifying: LA = 2pi x 63
LA = 126pi yd^2

ANSWER:
The 4th option - 126pi yd^2

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6 0
3 years ago
1. Find the value of 8.3 x 24.2 x 0.03. Round your answer to the nearest hundredth.
MrMuchimi

The rounded value is option B) 6.03 which is rounded to the nearest hundredth.

<u>Step-by-step explanation:</u>

  • To find the value of 8.3 x 24.2 x 0.03, we need to multiply the given numbers to get a decimal value.
  • And then, after getting the value of 8.3 x 24.2 x 0.03 it should be rounded to the nearest hundredth.

<u>So, let's multiply the numbers first :</u>

8.3 × 24.2 × 0.03 = 6.0258

The value is 6.0258

<u>To round the value 6.0258 to the nearest hundredth :</u>

  • The first number next to the decimal point represents the tenth.
  • The second number next to the decimal point is the hundredth.
  • The third number next to the decimal point is thousandth.

Therefore, to round the value to the nearest hundredth, look for the thousandth number is either less than 5 or greater and or equal to 5.

If, thousandth place is greater or equal to 5, then the hundredth number should be increased by 1.

The hundredth is 6.02 and the number in the thousandth place is 5. So add 1 to the hundredth place.

The value is rounded to 6.03 to the nearest hundredth.

5 0
3 years ago
The manager wants to advertise that anybody who isn't served within a certain number of minutes gets a free hamburger. But she d
aksik [14]

Answer:

The number of minutes advertisement should use is found.

x ≅ 12 mins

Step-by-step explanation:

(MISSING PART OF THE QUESTION: AVERAGE WAITING TIME = 2.5 MINUTES)

<h3 /><h3>Step 1</h3>

For such problems, we can use probability density function, in which probability is found out by taking integral of a function across an interval.

Probability Density Function is given by:

f(t)=\left \{ {{0 ,\-t

Consider the second function:

f(t)=\frac{e^{-t/\mu}}{\mu}\\

Where Average waiting time = μ = 2.5

The function f(t) becomes

f(t)=0.4e^{-0.4t}

<h3>Step 2</h3>

The manager wants to give free hamburgers to only 1% of her costumers, which means that probability of a costumer getting a free hamburger is 0.01

The probability that a costumer has to wait for more than x minutes is:

\int\limits^\infty_x {f(t)} \, dt= \int\limits^\infty_x {}0.4e^{-0.4t}dt

which is equal to 0.01

<h3>Step 3</h3>

Solve the equation for x

\int\limits^{\infty}_x {0.4e^{-0.4t}} \, dt =0.01\\\\\frac{0.4e^{-0.4t}}{-0.4}=0.01\\\\-e^{-0.4t} |^\infty_x =0.01\\\\e^{-0.4x}=0.01

Take natural log on both sides

ln (e^{-0.4x})=ln(0.01)\\-0.4x=ln(0.01)\\-0.4x=-4.61\\x= 11.53

<h3>Results</h3>

The costumer has to wait x = 11.53 mins ≅ 12 mins to get a free hamburger

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