MATHEMATICS COLLEGE

Apply the laws of exponents, calculate the result and express the result in scientific notation, and as a decimal: (8.110^-4)^2Format your answer like this: The result of the scientific notation is __10^--. The result as a decimal is _.

Answers

Answer 1

Answer:

the result in scientific notation is 6.561×10⁻⁷
the result as a decimal is 0.000 000 656 1

Explanation:

The rules of exponents say the exponent outside parentheses applies to each factor inside parentheses.

... (8.1*10^-4)^2 = 8.1^2 × (10^-4)^2

... = 65.61 × 10^-8

... = 6.561 × 10^-7 . . . . adjust to scientific notation with one digit left of the decimal point

The exponent of -7 means the decimal point in the decimal number is 7 places to the left of where it is in scientific notation. That is ...

... 6.561 × 10^-7 = 0.0000006561

Related Questions

A certain analytical method for the determination of lead yields masses for lead that are low by 0.5 g. Calculate the percent relative error caused by this deviation for each measured mass of lead. Report the percent relative error with the correct number of significant figures.
Determine the ration of the geometric sequence 1/10, -1/2, 5/2
Data was collected for 300 fish from the North Atlantic. The length of the fish (in mm) is summarized in the GFDT below. Lengths (mm) Frequency 140 - 143 1 144 - 147 16 148 - 151 71 152 - 155 108 156 - 159 83 160 - 163 18 164 - 167 3 What is the class boundary between the sixth and seventh classes?
Misu sheet owner of the bedspread shop knows his customers will pay no more than $135 for a comforter misu wants a 20% makeup on cost roundup instead of a selling price what is misus price
A deck of cards contains RED cards numbered 1,2,3, BLUE cards numbered 1,2,3,4,5,6, and GREEN cards numbered 1,2. If a single card is picked at random, what is the probability that the card is GREEN AND has an ODD number? Provide the final answer as a fraction.

Rock concert tickets are sold at a ticket counter. Femalesandmalesarriveat times of independent Poisson processes with rates 30 and 20 customers per hour. (a) What is the probability the first three customers are female

Answers

Answer: The probability that the first three customers are female is 0.216

Step-by-step explanation:

The attachment below shows the calculations clearly.

Two lines in the plane of a floor are

Answers

Answer:

never skew

Step-by-step explanation:

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.2 inches. What is the probability that a sheet selected at random will be less than 29.75 inches long

Answers

Answer:

6.68% or 0.0668

Step-by-step explanation:

Mean sheet length (μ) = 30.05 inches

Standard deviation (σ) = 0.2 inches

In a normal distribution, for any length X, the z-score is determined by the following expression:

$z=(X-\mu)/(\sigma)$

For X = 29.75, the z-score is:

$z=(29.75-30.05)/(0.2)\nz=-1.5$

A z-score of -1.5 corresponds to the 6.68th percentile of a normal distribution.

Therefore, the probability that a sheet selected at random will be less than 29.75 inches long is 6.68%.

A population of bacteria is initially 2,000. After three hours the population is 1,000. Assuming this rate of decay continues, find the exponential function that represents the size of the bacteria population after t hours. Write your answer in the form f(t).

Answers

Final answer:

The exponential function representing the bacteria population after t hours is f(t) = 2000 * e^(ln(0.5)/3 * t).

Explanation:

To find the exponential function that represents the size of the bacteria population after t hours, we can use the formula N = N0 * e^(kt), where N0 is the initial population, e is Euler's number (approximately 2.71828), k is the growth/decay constant, and t is the time in hours.

In this case, the initial population N0 is 2,000 and the population after 3 hours is 1,000. Plugging these values into the formula, we get:

N = 2000 * e^(3k) = 1000

Solving for k, we find k = ln(0.5)/3. Therefore, the exponential function representing the bacteria population after t hours is f(t) = 2000 * e^(ln(0.5)/3 * t).

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Final answer:

The exponential decay function representing the bacteria population after t hours is f(t) = 2000 × 0.5^(t/3), where t is the number of hours passed.

Explanation:

The student has observed a population of bacteria decreasing from 2,000 to 1,000 over three hours and seeks an exponential function to model the decay of the population over time, expressed as f(t). Since the population is halving every three hours, we can represent this with the function f(t) = 2000 × 0.5^(t/3), where 2000 is the initial population, 0.5 represents the halving, and t is the time in hours. The exponent (t/3) is used because the halving occurs every three hours.

Learn more about Exponential Decay here:

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Consider △LNM.
Which statements are true for triangle LNM? Check all that apply.

Answers

Answer:

The correct options are 1, 2 and 4.

Step-by-step explanation:

In a triangle, the side which does not make an angle is called opposite side of that angle.

From the given graph it is clear that

Opposite side of ∠L is NM.

Option 1 is correct.

Opposite side of ∠M is NL.

Opposite side of ∠N is ML.

Option 2 is correct.

The side next to an angle is called adjacent side.

Adjacent sides of ∠L is LM and LN.

Adjacent sides of ∠M is LM and MN.

Adjacent sides of ∠N is LN and MN.

In a right angled triangle, the opposite sides of a right angle is called hypotenuse.

Angle M is a right angled, so the side NM is hypotenuse. Option 4 is correct.

Therefore the correct options are 1, 2 and 4.

1 2 and 4 are correct. the others arent

Use induction to prove the following formula is true for all integers n where n greaterthanorequalto 1. 1 + 4 + 9 + .. + n^2 = n(n + 1)(2n + 1)/6

Answers

Answer with Step-by-step explanation:

Since we have given that

1+4+9+........................+n² = $(n(n+1)(2n+1))/(6)$

We will show it using induction on n:

Let n = 1

L.H.S. :1 = R.H.S. : $(1* 2* 3)/(6)=(6)/(6)=1$

So, P(n) is true for n = 1

Now, we suppose that P(n) is true for n = k.

$1+4+9+...................+k^2=(k(k+1)(2k+1))/(6)$

Now, we will show that P(n) is true for n = k+1.

So, it L.H.S. becomes,

$1+4+9+......................+(k+1)^2$

and R.H.S. becomes,

$((k+1)(k+2)(2k+3))/(6)$

Consider, L.H.S.,

$1+4+9+..+k^2+(k+1)^2\n\n=(k(k+1)(2k+1))/(6)+(k+1)^2\n\n=k+1[(k(2k+1))/(6)+(k+1)]\n\n=(k+1)[(2k^2+k+6k+6)/(6)]\n\n=(k+1)(2k^2+7k+6)/(6)]\n\n=(k+1)(2k^2+4k+3k+6)/(6)]\n\n=(k+1)[(2k(k+2)+3(k+2))/(6)]\n\n=((k+1)(2k+3)(k+2))/(6)$