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prisoha [69]
2 years ago
11

Find the length of the second base of a trapezoid with one base measuring 18 feet, a height of 5.3 feet, and an area of 125.4 sq

uare feet.​
Mathematics
1 answer:
faltersainse [42]2 years ago
6 0

Answer:

29.32 feet

Step-by-step explanation:

area of a trapezoid = height/2 * (first base + second base)

125.4 = 5.3 / 2 * (18 + second base)

125.4 = 2.65 * (18 + second base)

We want to solve for the second base. To do this, we can start by isolating the (18+second base) by dividing each side by 2.65

47.32 = 18 + second base

subtract 18 from both sides to solve for the second base

29.32 = second base

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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!

                 

                 

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Answer:

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Step-by-step explanation:

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3 years ago
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Leah and Ashley go to the movie theater and purchase refreshments for their friends
klasskru [66]

Answer:

The required system of equations is:

5 m+   7  n = 113.75  

6 m +   14  n  =  185.50

The price of 1 bag of popcorn  = $10.5

The price of 1 drink   = $8.75

Step-by-step explanation:

Let us assume the cost of 1 bag of popcorn = $ m

And, the cost of 1 drink = $ n

Now, Leah spends a total of 113.75 on 5 bags of popcorn and 7 drinks.

Cost of 5 bags + 7 drinks = 5 m +   7  n  =  $ 113.75

⇒ 5 m+   7  n = 113.75   .. (1)

Also, Ashley spends a total of 185.50 on 6 bags of popcorn and 14 drinks

Cost of 6 bags + 14 drinks = 6 m +   14  n  =  $185.50

⇒  6 m +   14  n  =  185.50   .. (2)

So, here the system of equations that can be used to find the price of one bag of popcorn (m) and the price of one drink (n) are

5 m+   7  n = 113.75   .. (1)

6 m +   14  n  =  185.50   .. (2)

Now, to solve this, Multiply (1) with -2 and add with 2, we get:

-10m + 6m - 14 n + 14 n = 185.5 - 227.5

or, - 4  m = -42 , or m = 42/4 = 10.5

Putting the value of m = 10.5 in 5 m+   7  n = 113.75 , we get n = 8.75

Hence,  the price of 1 bag of popcorn  = m = $10.5

And the price of 1 drink  = n = $8.75

6 0
3 years ago
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