Help me I’ll mark brainliest please

A motorboat travels 165 kilometers in 3 hours going upstream and 510 kilometers in 6 hours going downstream. What is the rate of

nikitadnepr [17]

<h3>Rate of the boat in still water is 70 km/hr and rate of the current is 15 km/hr</h3><h3><u>Solution:</u></h3>

Given that,

A motorboat travels 165 kilometers in 3 hours going upstream and 510 kilometers in 6 hours going downstream

Therefore,

Upstream distance = 165 km

Upstream time = 3 hours

<h3><u>Find upstream speed:</u></h3>

$speed = \frac{distance}{time}\\\\speed = \frac{165}{3}\\\\speed = 55$

Thus upstream speed is 55 km per hour

Downstream distance = 510 km

Downstream time = 6 hours

<h3><u>Find downstream speed:</u></h3>

$speed = \frac{510}{6}\\\\speed = 85$

Thus downstream speed is 85 km per hour

<em><u>If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then</u></em>

Speed downstream = u + v km/hr

Speed upstream = u - v km/hr

Therefore,

u + v = 85 ----- eqn 1

u - v = 55 ----- eqn 2

Solve both

Add them

u + v + u - v = 85 + 55

2u = 140

u = 70

<em><u>Substitute u = 70 in eqn 1</u></em>

70 + v = 85

v = 85 - 70

v = 15

Thus rate of the boat in still water is 70 km/hr and rate of the current is 15 km/hr

3 0

3 years ago

Dan was thinking of a number. Dan doubles it and adds 0.8 to get an answer of 58.9. Form an equation with

chubhunter [2.5K]

Answer:

2x + .8 = 58.9

His number, x, is 29.05

Step-by-step explanation:

2x + .8 = 58.9

2x = 58.1

x = 29.05

6 0

2 years ago

g A population is infected with a certain infectious disease. It is known that 95% of the population has not contracted the dise

trasher [3.6K]

Answer:

There is approximately 17% chance of a person not having a disease if he or she has tested positive.

Step-by-step explanation:

Denote the events as follows:

<em>D</em> = a person has contracted the disease.

+ = a person tests positive

- = a person tests negative

The information provided is:

$P(D^{c})=0.95\\P(+|D) = 0.98\\P(+|D^{c})=0.01$

Compute the missing probabilities as follows:

$P(D) = 1- P(D^{c})=1-0.95=0.05\\\\P(-|D)=1-P(+|D)=1-0.98=0.02\\\\P(-|D^{c})=1-P(+|D^{c})=1-0.01=0.99$

The Bayes' theorem states that the conditional probability of an event, say <em>A</em> provided that another event <em>B</em> has already occurred is:

$P(A|B)=\frac{P(B|A)P(A)}{P(B|A)P(A)+P(B|A^{c})P(A^{c})}$

Compute the probability that a random selected person does not have the infection if he or she has tested positive as follows:

$P(D^{c}|+)=\frac{P(+|D^{c})P(D^{c})}{P(+|D^{c})P(D^{c})+P(+|D)P(D)}$

$=\frac{(0.01\times 0.95)}{(0.01\times 0.95)+(0.98\times 0.05)}\\\\=\frac{0.0095}{0.0095+0.0475}\\\\=0.1666667\\\\\approx 0.1667$

So, there is approximately 17% chance of a person not having a disease if he or she has tested positive.

As the false negative rate of the test is 1%, this probability is not unusual considering the huge number of test done.

7 0

3 years ago

An ion has a charge of +7. How far is it from being neutral?

jeka57 [31]

We are given that

An ion has a charge of +7

and a neutral has charge always 0

so, change is charge = ion charge - neutral change

so, we can plug values

change is charge = +7 -0

change is charge = 7

so, option-C..................Answer

8 0

3 years ago

Helping a friend E e e e e

OLga [1]

Answer:sorry that’s math not art

Step-by-step explanation: math is not art therefore I can’t help u

6 0

2 years ago