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11Alexandr11 [23.1K]
3 years ago
11

The 1985 Mexico City earthquake measured a magnitude 8.0 on the Richter scale. The Richter scale uses the function M (I) = log (

StartFraction I Over I Subscript 0 Baseline EndFraction). Which equation relates the intensity of the 1985 earthquake, I, with the intensity of the threshold quake, Io?
A.) I = 810(Io)

B.) Io = 810(I)

C.) I = 108(Io)

D.) Io = 108(I)
Mathematics
1 answer:
Travka [436]3 years ago
7 0

Answer:

The correct option is C: I = 10⁸I₀.   

Step-by-step explanation:

The function of the Richter scale is:

M_{(I)} = log(\frac{I}{I_{0}})

Since the magnitude of the earthquake is 8.0, the relation between the intensity, I, with the intensity of the threshold quake, Io, is:

8.0 = log(\frac{I}{I_{0}})

10^{8} = \frac{I}{I_{0}}

I = 10^{8}I_{0}

Therefore, the correct option is C: I = 10⁸I₀.                

I hope it helps you!                    

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Caroline is making some table decorations.
jolli1 [7]

Answer:

Caroline buys 3 packs of candles and 5 packs of holders.

Step-by-step explanation:

1.) You need to add numbers of candle packs together until they both reach the same number, for example, multiples of 30 are 30, 60, 90.

2.) Then you add multiples of the holders. 18, 36, 54, 72, 90.

3.) You find that Caroline buys 3 pakcs of candles and 5 packs of holders to have the same number of both.

6 0
3 years ago
4sinθ – 1 = - 3 for 0<θ< 360
EastWind [94]

Answer:

\theta = 210^\circ or \theta = 330^\circ

Step-by-step explanation:

4 \sin \theta - 1 = -3

4 \sin \theta = -2

\sin \theta = \dfrac{-2}{4}

\sin \theta = -0.5

For sin θ = 0.5, the reference angle is θ = 30 deg.

\sin 30^\circ = 0.5

\theta = 210^\circ or \theta = 330^\circ

7 0
3 years ago
When a number is divided by 5 the answer is 3 remainder 4, what is that number?
skelet666 [1.2K]

We know that 5 fits entirely into our number three times, and then there's a remainder of 4.

If 5 fits three times exactly, it means that our number is at least 15 (5x3).

From here, we have a remainder of 4, which leads to 15+4=19

5 0
2 years ago
A researcher thinks that a person's mood has an effect on how helpful that person is likely to be. To test this, the researcher
eimsori [14]

Answer:

One possible confound for the experiment is the attitude of the research assistants.

Step-by-step explanation:

A confounder simply means a variable that has impact in influencing both the dependent variable and independent variable, causing a spurious association.

So, we can conclude that the attitudes of the research assistants have positive and negative impacts in determining the reactions of both participants in the experiment.

The rudeness of a research assistant will negatively impact the response of the participant allocated to him/her.

The calmness of the other research assistant will positively impact the response of the participant allocated to him/her.

5 0
2 years ago
A child lets go of a balloon that rises at a constant rate. 5 seconds after it was released, the balloon is at a height of 16 fe
Mama L [17]

Answer:

1. h = 2.4t + 4

2. 4 feet

3. 220 feet

Step-by-step explanation:

1. Write a linear model for the height, h, of the balloon as a function of the number of seconds, s that it has been raising.

Since the balloon rises at a constant rate, we find this rate by using the initial and final values of height and time at 5 seconds and 20 seconds respectively which are 12 feet and 52 feet respectively.

So, rate = gradient of line

= change in height/change  in time

= (52 ft - 16 ft)/(20 s - 5 s)

= 36 ft/15 s

= 2.4 ft/s

Now the equation of the line which shows the height is gotten from

(h - h')/(t - t') = rate

Using h'= 16 feet and t' = 5 s, we have

(h - 16)/(t - 5) = 2.4

h - 16 = 2.4(t - 5)

h - 16 = 2.4t - 12

h = 2.4t - 12 + 16

h = 2.4t + 4

where h is the height of the balloon above the ground and t is the time spent in the air in seconds.

2. What was the height of the balloon initially before the child let it go?

We obtain the initial height of the balloon before the child let go at time, t = 0 the time before the child let go.

So, substituting t = 0 into the equation for h, we have

h = 2.4t + 4

h = 2.4(0) + 4

h = 0 + 4

h = 4 feet

So, the height of the balloon before the child let go is 4 feet above the ground.

3. Use your model to predict the height of the balloon after 90 seconds.

We insert t = 90 s into the equation for h. So,

h = 2.4t + 4

h = 2.4(90) + 4

h = 216 + 4

h = 220 feet

So, the height of the balloon after 90 s is 220 feet above the ground.

8 0
2 years ago
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