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FromTheMoon [43]
3 years ago
10

Starting at sea level, a submarine descended at a constant rate to a depth of − 4/5 mile relative to sea level in 3 minutes.

Mathematics
2 answers:
Jobisdone [24]3 years ago
5 0
If it were 4 then it would be 1 1/3 for one minute
igomit [66]3 years ago
4 0

Answer:

\texttt{Submarine's depth relative to sea level after the first minute = }-\frac{4}{15} miles

Step-by-step explanation:

Starting at sea level, a submarine descended at a constant rate to a depth of −4/5 mile relative to sea level in 3 minutes.

Total time = 3 minutes

[tex]\texttt{Total depth descended in 3 minutes = }-\frac{4}{5}miles[/tex]

We need to find what was the submarine's depth relative to sea level after the first minute,

\texttt{Depth descended in per minute = }-\frac{\frac{4}{5}}{3}=-\frac{4}{15}miles

\texttt{Submarine's depth relative to sea level after the first minute = }-\frac{4}{15}\times 1=-\frac{4}{15} miles\\\\\texttt{Submarine's depth relative to sea level after the first minute = }-\frac{4}{15} miles

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Write each ratio in its simplest form 8: 10 show working​
Sloan [31]

Answer:

Simple solution for that!

4 : 5

Step-by-step explanation:

both 8 and 10 are divided by 2

8 ÷ 2 : 10 ÷2

4 : 5

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3 years ago
A=(2 3)<br> (-1 4)<br><br> Calculate A^2-6A+11I
disa [49]

Answer:

A² - 6A + 11 I = \left[\begin{array}{ccc}0&0\\0&0\end{array}\right]

Step-by-step explanation:

Given the matrix

A=\left[\begin{array}{ccc}2&3\\-1&4\end{array}\right]

Calculate A² - 6A + 11 I

A^2 = A*A= \left[\begin{array}{ccc}2&3\\-1&4\end{array}\right] *\left[\begin{array}{ccc}2&3\\-1&4\end{array}\right] = \left[\begin{array}{ccc}2*2-3*1&2*3+3*4\\-1*2-4*1&-1*3+4*4\end{array}\right] =\left[\begin{array}{ccc}1&18\\-6&13\end{array}\right]

6A=6*\left[\begin{array}{ccc}2&3\\-1&4\end{array}\right] =\left[\begin{array}{ccc}12&18\\-6&24\end{array}\right]

11 I = 11 * \left[\begin{array}{ccc}1&0\\0&1\end{array}\right] =\left[\begin{array}{ccc}11&0\\0&11\end{array}\right]

∴ A² - 6A + 11 I = \left[\begin{array}{ccc}1&18\\-6&13\end{array}\right] -\left[\begin{array}{ccc}12&18\\-6&24\end{array}\right] +\left[\begin{array}{ccc}11&0\\0&11\end{array}\right] =\left[\begin{array}{ccc}0&0\\0&0\end{array}\right]

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3 years ago
Explain two different waysto find the difference for 12-3
sergey [27]
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3 years ago
A certain type of automobile battery is known to last an average of 1,150 days with a standard deviation of 40 days. If 100 of t
sergejj [24]

Answer:

a) 0.4772 = 47.72% probability that the average is between 1,142 and 1,150.

b) 0.0228 = 2.28% probability that the average is greater than 1,158.

c) 0 = 0% probability that the average is less than 950.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

A certain type of automobile battery is known to last an average of 1,150 days with a standard deviation of 40 days.

This means that \mu = 1150, \sigma = 40

Sample of 100:

This means that n = 100, s = \frac{40}{\sqrt{100}} = 4

(a) The average is between 1,142 and 1,150.

This is the pvalue of Z when X = 1150 subtracted by the pvalue of Z when X = 1142. So

X = 1150

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{1150 - 1150}{4}

Z = 0

Z = 0 has a pvalue of 0.5

X = 1142

Z = \frac{X - \mu}{s}

Z = \frac{1142 - 1150}{4}

Z = -2

Z = -2 has a pvalue of 0.0228

0.5 - 0.0228 = 0.4772

0.4772 = 47.72% probability that the average is between 1,142 and 1,150.

(b) The average is greater than 1,158.

This is 1 subtracted by the pvalue of Z when X = 1158. So

Z = \frac{X - \mu}{s}

Z = \frac{1158 - 1150}{4}

Z = 2

Z = 2 has a pvalue of 0.9772

1 - 0.9772 = 0.0228

0.0228 = 2.28% probability that the average is greater than 1,158.

(c) The average is less than 950.

This is the pvalue of Z when X = 950. So

Z = \frac{X - \mu}{s}

Z = \frac{950 - 1150}{4}

Z = -50

Z = -50 has a pvalue of 0

0 = 0% probability that the average is less than 950.

4 0
3 years ago
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