All categories

2 years ago

Find the point of intersection of the lines: y = 4x + 1 and y = – 2x + 4 A. (2 , 9) B. ( 1 2, 3 ) C. (1 , 2) D. ( 1 4, 2)

Mathematics

1 answer:

alekssr [168]2 years ago

3 0

Answer:

B. (1/2, 3)

Step-by-step explanation:

It is perhaps easiest to try the point values in the equations.

A — 4·2+1 = 9; -2·2 +4 ≠9 . . . . not the answer

B — 4·1/2 +1 = 3; -2·(1/2) +4 = 3 . . . . this is the answer

we need go no further since we have the answer

You might be interested in

Jordan Has 9 Blue Balls, 6 Red Balls And 5 Brown Balls In A Box. Two Balls Are Drawn Without Replacement From The Box. What Is T

marshall27 [118]

5/20 .
add up the number of all the balls combined
5 out of the 20 total are brown

5 0

1 year ago

Read 2 more answers

Minato drove 390 miles. Part of the drive was along local roads, where his average speed was 20 mph, and the rest was along a hi

pashok25 [27]

Answer:

45 miles.

Step-by-step explanation:

Given that the:

Total distance covered = 390 miles

Total time = 8 hours

Let the distance covered along the local way = L

And the distance covered along the highway = H

Along with local way,

Speed = distance/ time

20 = L / T

T = L /20 .... (1)

Along the highway,

Distance covered H = 390 - L

Let the time = t

Speed = distance/time

60 = (390 - L)/t

t = ( 390 - L)/60

But total time = T + t

That is

8 = L/20 + (390 - L)/60

The LCM at right hand side will be 60

8 = ( 3L + 390 - L )/60

Cross multiply

480 = 2L + 390

Collect the like terms

2L = 480 - 390

2L = 90

L = 90/2

L = 45 miles.

Therefore, the distance Minato drive along local roads is 45 miles

4 0

2 years 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

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

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

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

Anita can clean a typical pool in 8 hours. Chao can clean a typical pool in 6 hours. How long should it take Anita and Chao work

ivanzaharov [21]

Anita can clean 1/8 portion of the pool in 1 hour

Chao can clean 1/6 portion of the pool in 1 hour

Both of them working together can clean 1/8 + 1/6 = 7/24 portion of the pool in 1 hour

Therefore, it will take both of the working together 1/(7/24) = 24/7 or 3 3/7 hours to clean a typical pool.

3 0

2 years ago

Which measure is the largest? 1.2 km, 120,600 cm, 1,220,000 mm, 120 meters

aalyn [17]

The answer would be 1,220,000mm.

You can do this if you convert all the measures into one unit. Let us convert all into km.

The first one is already in km, so we do not need to covert it.

Let's start with converting 1,220,000mm to km.

There are 1, 000,000 mm in one km.

$1,220,000X \frac{1km}{1,000,000mm} = 1.22km$

So there are 1.22km in 1,220,000mm.

Next, we have 120m. There are 1,000m in 1km.

$120mX \frac{1km}{1,000} =0.12km$

There are 0.12km in 120m

Now you can see that 1,220,000mm is the longest.

4 0

1 year ago