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Dafna11 [192]
3 years ago
11

an unopened can of iced tea contains 350 cubic centimeters of liquid. if the van is 5 inches long and has a .8 inch diameter, wh

ich is the best estimate of the volume of iced tea contained in the top 3 inches of the can
Mathematics
1 answer:
MariettaO [177]3 years ago
3 0

the can is 5 inches tall, so its height is 5 inches, so 3 inches off 5 inches that'd be 3/5.

the can has a diameter of 0.8 inches, meaning it has a radius of half that, or 0.4 inches.

if say the volume of iced-tea is V, how much is 3/5 of V?  well, is just their product.


\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=0.4\\ h=5 \end{cases}\implies V=\pi (0.4)^2(5)\implies V=0.8\pi \\\\\\ \stackrel{\textit{and 3/5 of that will be}}{\cfrac{3}{5}\cdot 0.8\pi }\implies V\approx \stackrel{in^3}{1.51}

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What is the probability that a random person who tests positive for a certain blood disease actually has the disease, if we know
xeze [42]

Answer:

Step-by-step explanation:

Hello!

Any medical test used to detect certain sicknesses have several probabilities associated with their results.

Positive (test is +) ⇒ P(+)

True positive (test is + and the patient is sick) ⇒ P(+ ∩ S)

False-positive (test is + but the patient is healthy) ⇒P(+ ∩ H)

Negative (test is -) ⇒ P(-)

True negative (test is - and the patient is healthy) ⇒ P(- ∩ H)

False-negative (test is - but the patient is sick) ⇒ P(- ∩ S)

The sensibility of the test is defined as the capacity of the test to detect the sickness in sick patients (true  positive rate).

⇒ P(+/S) =<u> P(+ ∩ S)  </u>

                    P(S)

The specificity of the test is the capacity of the test to have a negative result when the patients are truly  healthy (true negative rate)

⇒ P(-/H) =<u> P(- ∩ H)  </u>

                   P(H)

For this particular blood disease the following probabilities are known:

1% of the population has the disease: P(S)= 0.01

95% of those who are sick, test positive for it: P(+/S)= 0.95 (sensibility of the test)

2% of those who don't have the disease, test positive for it: P(+/H)= 0.02

The probability of a person having the blood sickness given that the test was positive is:

P(S/+)= <u> P(+ ∩ S)  </u>

                P(+)

The first step you need to calculate the intersection between both events + and S, for that you will use the information about the sickness prevalence in the population and the sensibility of the test:

P(+/S) =<u> P(+ ∩ S) </u>

                 P(S)

P(+/S)* P(S)  = P(+ ∩ S)  

P(+ ∩ S) = 0.95*0.01= 0.0095

The second step is to calculate the probability of the test being positive:

P(+)=  P(+ ∩ S) +  P(+ ∩ H)

Now we know that 1% of the population has the blood sickness, wich means that 99% of the population doesn't have it, symbolically: P(H)= 0.99

Then you can clear the value of P(+ ∩ H):

P(+/H) =<u> P(+ ∩ H) </u>

                 P(H)

P(+/H)*P(H)  = P(+ ∩ H)

P(+ ∩ H) = 0.02*0.99= 0.0198

Next you can calculate P(+):

P(+)=  P(+ ∩ S) +  P(+ ∩ H)= 0.0095 + 0.0198= 0.0293

Now you can calculate the asked probability:

P(S/+)= <u> P(+ ∩ S)  </u> =<u> 0.0095 </u>= 0.32

                P(+)        0.0293

I hope it helps!

                 

                 

6 0
2 years ago
I don’t understand this
Inessa05 [86]

Answer:

54

Step-by-step explanation:

18 inches per year * 3 years = 54 inches

5 0
3 years ago
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9x+y=28<br> 3x+3y=(-12)<br> Solve using elimination
Rzqust [24]

Answer:

(x, y)=(4,-8)

Step-by-step explanation:

9x+y=28

3x+3y=-12 /:(-3)

9x+y=28.......(1)

-x-y=4......(2)

9x+y=28

(1)+(2): 8x=32

9x+y=28

x=32/8

9x+y=28

x=4

9*4+y=28

x=4

36+y=28

x=4

y=28-36

x=4

y=-8

x=4

(x, y) =(4,-8)

5 0
2 years ago
Factoring<br>factor: 80n^2+56n​
Zinaida [17]

Answer:

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Step-by-step explanation:

just multiply 80n x 56n and get 4480n but since 80n is to the 2nd and 56n is to the first add them to get to the power of 3 and put that on 4480n

5 0
3 years ago
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Subtract seven more than twice a number from the square of one-third of the number to get zero?
andreev551 [17]
Let us assume the unknown number = x
Now we have to follow the details given in the question to bring out the actual equation. In this case there will be only one equation.
(x/3)^2 - (2x + 7) = 0
(x/3)^2 = 2x + 7
x^2/9 = 2x + 7
x^2 = 9(2x + 7)
x^2 = 18x + 63
x^2 - 18x = 63
This would be the final equation for the given problem. his problem needs any solver to understand the words very minutely.
5 0
3 years ago
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