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A scientist digs near an ancient city.She finds a cup buried at -7 feet. She finds a plate buried at -4 feet.
Use absolute value to show which was buried farther from the surface.
A. The cup is farther from the surface, because |-7 is less than 1-4).
B. The cup is farther from the surface, because |-71 is greater than |-
4.
C. The plate is farther from the surface, because (-71 is greater than
1-41.
D. The plate is farther from the surface, because -7 is greater than -
4.
My

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

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If a 5 ft tall man cast an 8 ft long shadow at the same time a tree cast a 24 ft long shadow, how tall is the tree?

Answers

Answer:

15 feet

Step-by-step explanation:

We have 2 similar right triangles with legs height and length of shadows.

height of men : length of shadows of the man = height of tree : length of shadows of the tree

5 : 8 = x : 24

8x = 5* 24

x = 5*24/8 = 15 (feet)

Answer:

15ft

Step-by-step explanation:

5 ft is to 8 ft

A ft is to 24 ft

A = 24*5/8

A = 15ft

15ft

Solve the following equation: 3x - 7 = 9 + 2x.
A)12
B)16
c)20
d)24

Answers

answer:
B

the equation:
3x-7=9+2x

step 1: subtract 2x from both sides
x-7=9

step 2: add 7 to both sides
x=16

Answer:

Option B

Step-by-step explanation:

$3x - 7 = 9 + 2x\n\n3x-7+7=9+2x+7\n\n3x = 9 + 7 + 2x\n\n3x=16+2x\n\n3x-2x=16+2x-2x\n\n\boxed{x=16}$

Hope this helps!

The lifetime of a certain type of battery is normally distributed with a mean value of 10 hours and standard deviation of 2 hours. Find the probability that a randomly selected battery has a lifetime greater than 12 hou g

Answers

Answer:

$P(X>12)=P((X-\mu)/(\sigma)>(12-\mu)/(\sigma))=P(Z>(12-10)/(2))=P(z>1)$

And we can find this probability using the complement rule:

$P(z>1)=1-P(z<1)$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(z>1)=1-P(z<1)=1-0.841=0.159$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the lifetime of a certain type of battery of a population, and for this case we know the distribution for X is given by:

$X \sim N(10,2)$

Where $\mu=10$ and $\sigma=2$

We are interested on this probability

$P(X>12)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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

If we apply this formula to our probability we got this:

$P(X>12)=P((X-\mu)/(\sigma)>(12-\mu)/(\sigma))=P(Z>(12-10)/(2))=P(z>1)$

And we can find this probability using the complement rule:

$P(z>1)=1-P(z<1)$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(z>1)=1-P(z<1)=1-0.841=0.159$

Can someone help me out with this

Answers

Answer:

This is correct.

Step-by-step explanation:

What is the result of adding these two equations?
5x-y=6
-2x+y=8

Answers

3x=14 I am pretty sure

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).

Learn more about exponential function here:

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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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