Caleb's car used 8 gallons to travel 144 miles. How far can he travel on 20 gallons

Amina used the quadratic formula to solve an equation. Her result shows two solutions that are complex numbers with imaginary pa

Mama L [17]

A quadratic equation has either two different real roots, one real root, or two conjugate complex roots (this is the case when the discriminant is negative, i.e. when you have no real roots).

Two conjugate complex roots have the same real part and opposite imaginary parts. So, the solutions to Amina's equation will be in this form:

$a+bi,\ \ a-bi$

For some $a,b\in\mathbb{R},\ b\neq 0$

6 0

1 year ago

The monthly salary of Mr. Sachdev gets increased by 5%, thereby his salary becomes Rs. 15,120 per annum, His earlier monthly sal

Elan Coil [88]

1. x = 15120/12 = 1260 (monthly salary)
2. 1200 x 0.05 = 60 (raise)
Check: 1200+60=1260

6 0

1 year ago

If figure 1 is 3 then what is figure 100th

Alexxx [7]

A) 3x100= 300 since figure 1 is 3 then figure 100 is 3x100

8 0

1 year ago

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

So

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

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

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

i will mark as brainiest Jared is using a 100 ft rope to set up a kite-shaped area for food vendors. He has started roping off t

blsea [12.9K]

Sample Response: A kite has two pairs of congruent adjacent sides and opposite sides that are not congruent. Jared has already created one pair of congruent adjacent sides. Since he has used 60 ft of rope, there are 40 ft remaining. This means that he will need 20 ft of rope for each of the other sides, or half of the remaining rope, in order to create another pair of congruent adjacent sides. Since this is a different length than 30 ft, the shape has opposite sides that are not congruent.

4 0

2 years ago

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