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3 years ago

The Pythagorean theorem is true for all similar triangles. A. True B. False

2 answers:

5 0

False. It only relates to the sides of a right triangle in a simple way, so that if the lengths of any two sides are known, the length of the third side can be found.

Scorpion4ik [409]3 years ago

3 0

Answer: False

Step-by-step explanation:

The Pythagorean theorem is true for all right triangles.

In geometry, the Pythagorean theorem which is also known as Pythagoras' theorem, tells a fundamental relation among the three sides of a right triangle. It states that in right triangle the square of the hypotenuse which is the side opposite the right angle is equal to the sum of the squares of the other two sides.

Therefore, the given statement is false.

The Pythagorean theorem is true for all right triangles.

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You can walk 1.5 miles in a half hour. What is your average speed?

Alexandra [31]

3 miles per hour. you multiply 1.5 by 2

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3 years ago

A hotel charges $225 per night to rent a suite. The hotel charges $75 per day for full room service . If Jessica and Ashley purc

Mrrafil [7]

A) 3
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2 years ago

Suppose a geyser has a mean time between eruptions of 72 minutes. Let the interval of time between the eruptions be normally dis

nikitadnepr [17]

Answer:

(a) The probability that a randomly selected time interval between eruptions is longer than 82 minutes is 0.3336.

(b) The probability that a random sample of 13-time intervals between eruptions has a mean longer than 82 minutes is 0.0582.

(c) The probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 minutes is 0.0055.

(d) Due to an increase in the sample size, the probability that the sample mean of the time between eruptions is greater than 82 minutes decreases because the variability in the sample mean decreases as the sample size increases.

(e) The population mean must be more than 72, since the probability is so low.

Step-by-step explanation:

We are given that a geyser has a mean time between eruptions of 72 minutes.

Also, the interval of time between the eruptions be normally distributed with a standard deviation of 23 minutes.

(a) Let X = the interval of time between the eruptions

So, X ~ N( $\mu=72, \sigma^{2} =23^{2}$ )

The z-score probability distribution for the normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = population mean time = 72 minutes

$\sigma$ = standard deviation = 23 minutes

Now, the probability that a randomly selected time interval between eruptions is longer than 82 minutes is given by = P(X > 82 min)

P(X > 82 min) = P( $\frac{X-\mu}{\sigma}$ > $\frac{82-72}{23}$ ) = P(Z > 0.43) = 1 - P(Z $\leq$ 0.43)

= 1 - 0.6664 = 0.3336

The above probability is calculated by looking at the value of x = 0.43 in the z table which has an area of 0.6664.

(b) Let $\bar X$ = sample mean time between the eruptions

The z-score probability distribution for the sample mean is given by;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean time = 72 minutes

$\sigma$ = standard deviation = 23 minutes

n = sample of time intervals = 13

Now, the probability that a random sample of 13 time intervals between eruptions has a mean longer than 82 minutes is given by = P( $\bar X$ > 82 min)

P( $\bar X$ > 82 min) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ > $\frac{82-72}{\frac{23}{\sqrt{13} } }$ ) = P(Z > 1.57) = 1 - P(Z $\leq$ 1.57)

= 1 - 0.9418 = 0.0582

The above probability is calculated by looking at the value of x = 1.57 in the z table which has an area of 0.9418.

(c) Let $\bar X$ = sample mean time between the eruptions

The z-score probability distribution for the sample mean is given by;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean time = 72 minutes

$\sigma$ = standard deviation = 23 minutes

n = sample of time intervals = 34

Now, the probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 minutes is given by = P( $\bar X$ > 82 min)

P( $\bar X$ > 82 min) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ > $\frac{82-72}{\frac{23}{\sqrt{34} } }$ ) = P(Z > 2.54) = 1 - P(Z $\leq$ 2.54)

= 1 - 0.9945 = 0.0055

The above probability is calculated by looking at the value of x = 2.54 in the z table which has an area of 0.9945.

(d) Due to an increase in the sample size, the probability that the sample mean of the time between eruptions is greater than 82 minutes decreases because the variability in the sample mean decreases as the sample size increases.

(e) If a random sample of 34-time intervals between eruptions has a mean longer than 82 minutes, then we conclude that the population mean must be more than 72, since the probability is so low.

6 0

3 years ago

Seven less than the product of 24 and Jose’s savings

Liono4ka [1.6K]

Answer:

$24j -7$

Step-by-step explanation:

Given

$Savings \to$ j

Required

Express 7 less than 24 * j

First, we have:

$24 * j = 24j$

7 less is then expressed as:

$24j -7$

6 0

3 years ago

A portfolio is efficient if which of the following is true?

fgiga [73]

Answer:

In economics, a portfolio is a term for a specific set of stocks, bonds, shares, and other securities owned by an investor. In general, the investor seeks to compile and diversify a portfolio of securities that offers maximum profitability and at the same time is diverse, in order to minimize possible risks. In general, these types of portfolios are considered efficient, as they do not leave the investment risk tied to a single factor. However, these two goals often go against each other, so the composition of the portfolio means a certain compromise.

8 0

2 years ago