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2 years ago

Solve the formula for the specified variable. D=1/2fk for f f=

1 answer:

4 0

We are asked to solve the formula $D=\frac{1}{2}fk$ for $f$ . Starting off, we can divide both sides by $k$ , so we are left with only the variable $f$ on the right-hand side. Next, we need to multiply the reciprocoal of $\frac{1}{2}$ , which is $2$ to both sides. This gives us $2*\frac{D}{k}=f$ , which, when simplified, gives us $\boxed{f=\frac{2D}{k}}$ . Hope this helped and have a phenomenal day!

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Customers are used to evaluate a preliminary product design. In the past, 95% of highly successful products received good review

Sever21 [200]

Answer:

a. 61.5%; b. About 61.8%; c. About 36.4%

Step-by-step explanation:

This is a kind of question that we can solve using the Bayes' Theorem. We have here all the different conditional probabilities we need to solve this problem.

According to that theorem, the probability of a selected product attains a good review is:

$\\ P(G) = P(G|H)*P(H) + P(G|M)*P(M) + P(G|P)*P(P)$ (1)

In words, the probability that a selected product attains a <em>good review</em> is an <em>event </em>that depends upon the sum of the conditional probabilities that the product comes from <em>high successful product</em> P(G|H) by the probability that this product is a <em>highly successful product</em> P(H), plus the same about the rest of the probabilities, that is, P(G|M)*P(M) or the probability that the product has a good review coming from a <em>moderately successful</em> product by the probability of being moderately successful, and a good review coming from a poor successful product by the probability of being poor successful or P(G|P)*P(P).

<h3>The probability that a randomly selected product attains a good review</h3>

In this way, the probability that a randomly selected product attains a good review is the result of the formula (1). Where (from the question):

P(G|H) = 95% or 0.95 (probability of receiving a good review being a highly successful product)

P(G|M) = 60% or 0.60 (probability of receiving a good review being a moderately successful product)

P(G|P) = 10% or 0.10 (probability of receiving a good review being a poorly successful product)

P(H) = 40% or 0.40 (probability of being a highly successful product).

P(M) = 35% or 0.35 (probability of being a moderately successful product).

P(P) = 25% or 0.25 (probability of being a poor successful product).

Then,

$\\ P(G) = P(G|H)*P(H) + P(G|M)*P(M) + P(G|P)*P(P)$

$\\ P(G) = 0.95*0.40 + 0.60*0.35 + 0.10*0.25$

$\\ P(G) = 0.615\;or\; 61.5\%$

That is, <em>the probability that a randomly selected product attains a good review</em> is 61.5%.

<h3>The probability that a new product attains a good review is a highly successful product</h3>

We are looking here for P(H|G). We can express this probability mathematically as follows (another conditional probability):

$\\ P(H|G) = \frac{P(G|H)*P(H)}{P(G)}$

We can notice that the probability represents a fraction from the probability P(G) already calculated. Then,

$\\ P(H|G) = \frac{0.95*0.40}{0.615}$

$\\ P(H|G) =\frac{0.38}{0.615}$

$\\ P(H|G) =0.618$

Then, the probability of a product that attains a good review is indeed a highly successful product is about 0.618 or 61.8%.

<h3>The probability that a product that <em>does not attain </em>a good review is a moderately successful product</h3>

The probability that a product does not attain a good review is given by a similar formula than (1). However, this probability is the complement of P(G). Mathematically:

$\\ P(NG) = P(NG|H)*P(H) + P(NG|M)*P(M) + P(NG|P)*P(P)$

P(NG|H) = 1 - P(G|H) = 1 - 0.95 = 0.05

P(NG|M) = 1 - P(G|M) = 1 - 0.60 = 0.40

P(NG|P) = 1 - P(G|M) = 1 - 0.10 = 0.90

$\\ P(NG) = 0.05*0.40 + 0.40*0.35 + 0.90*0.25$

$\\ P(NG) = 0.385\;or\; 38.5\%$

Which is equal to

P(NG) = 1 - P(G) = 1 - 0.615 = 0.385

Well, having all this information at hand:

$\\ P(M|NG) = \frac{P(NG|M)*P(M)}{P(NG)}$

$\\ P(M|NG) = \frac{0.40*0.35}{0.385}$

$\\ P(M|NG) = \frac{0.14}{0.385}$

$\\ P(M|NG) = 0.363636... \approx 0.364$

Then, the <em>probability that a new product does not attain a good review and it is a moderately successful product is about </em>0.364 or 36.4%.

8 0

1 year ago

the length of the highway is 1500 miles. If 1 inch represents 150 miles, what is the length of the highway on the map?

NeX [460]

Answer:

10 inches.

Step-by-step explanation:

If 1 inch represents 150 miles, and there are 1500 miles covered by the map, then the length of the highway on the map is 10 inches.

4 0

1 year ago

ΔABC is an isosceles triangle with AB = BC= 6 units. D and E are the midpoints or AB and BC, respectively. The length of AC is 8

nydimaria [60]

There are two triangles that exist in this problem. First is the given triangle ABC, witch AB = BC = 6 and AC = 8
Next is the smaller triangle formed by connecting points D and E; triangle EAD, with EA = AD = 3 and the length of DE is unknown.
Because these triangles are similar, a simple ratio may be set up in order to calculate DE.
DE / AC = EA / AB
DE = 3/6 * 8
DE = 4 units

7 0

1 year ago

Read 2 more answers

Definitions and Data Due Sun 02/03/2019 11:59 pm A researcher is interested in attitudes towards releasing prisoners with Alzhei

horrorfan [7]

Answer:

Step-by-step explanation:

Matching each vocabulary word with its corresponding example:

(1). All Americans = f. Population (a group of items, units or subjects under reference of study e.g. inhabitants of a region, numbers of cars in a city, workers in a factory and so on)

(2). The proportion of all Americans who strongly agree that prisoners with life sentences who have Alzheimer's should be released = c. Parameter ( the number that summarizes some characteristic of a population)

(3). The proportion of the 85 Americans surveyed who strongly agree that prisoners with life sentences who have Alzheimer's should be released = d. Statistic (the sample characteristic corresponding to a population parameter used when a sample is used to make statistical inference about a population)

(4). The answer-Strongly Agree' or 'Agree, or Disagree, or Strongly Disagree = b. Variable (any quality, characteristic, quantity or number that can be counted or measured)

(5). The 85 Americans who participated in the survey = e. Sample (a part or fraction of a population selected on some basis)

(6). The list of answers that the 85 Americans gave = a. Data (the pieces of information collected to be used for the analysis)

6 0

1 year ago

The number of airline passengers in 1990 was 466 million. The number of passengers traveling by airplane each year has increased

taurus [48]

Answer:

2010.

Step-by-step explanation:

We have been given an exponential growth formula $P(t)=466\cdot 1.035^t$ , which represents number of passengers traveling by airplane since 1990.