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klemol [59]
1 year ago
14

Caleb bought groceries and paid $1.60 in sales tax.the sales tax rate is 2.5% What was the price of Caleb’s groceries,before tax

Mathematics
1 answer:
Goryan [66]1 year ago
7 0

Let price of the Caleb's groceries was $x.

Given that tax rate is 2.5% or 0.025

Then sales tax is given by product of 0.025 and x.

which is 0.025x.

Given that tax paid is $1.60 so both must be equal

0.025x=1.6

divide both side by 0.025

x=1.6/0.025

x=64

Hence final answer is $64.

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bonufazy [111]

Answer:

The probability that the inhabitant spoke thruthfully given than the other one says so is 1/4.

Step-by-step explanation:

Let A be the event 'the first inhabitant speaks the truth' and B the event the person you asked speaks the truth'

We have that

P(A) = P(B) = 1/3

The second person will say that the first person speaks the truth if:

- Both are lying

- Both are saying the truth

The probability that both inhabitants lies is 2/3 * 2/3 = 4/9

The probability that both inhabitants speaks the truth is 1/3² = 1/9

Therefore, in this problem, we want to know P(A ∩ B | (A∩ B) ∪ (A^c ∩ B^c) )

(note that, since the second persons says that A didnt lie, then in order for it to be true then the second person have to also say the truth).

We know that P(A ∩ B) = 1/9 and P((A∩ B) ∪ (A^c ∩ B^c)) = 4/9 + 1/9 = 5/9. Using the bayes formula we have

P(A ∩B | (A∩ B) ∪ (A^c ∩ B^c) ) = P((A∩ B) ∪ (A^c ∩ B^c) | A ∩ B) * P(A∩ B)/ P((A∩ B) ∪ (A^c ∩ B^c))

Note that P((A∩ B) ∪ (A^c ∩ B^c) | A∩B) = 1 because the condition is more restrictive than the probability we are asking for, therefore

P(A ∩B | (A∩ B) ∪ (A^c ∩ B^c) )  = P(A∩ B)/P((A∩ B) ∪ (A^c ∩ B^c))  = (1/9) / (4/9) = 1/4.

The probability that the inhabitant spoke thruthfully given than the other one says so is 1/4.

7 0
2 years ago
A computer uses 239 watts per hour. How many watts would it use if it is on for 8 days?
Serjik [45]
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4 0
2 years ago
Adam lived a quarter of his life as a boy as fifth as a young man, a third in middle-age and 13 years in retirement. How old was
Anika [276]

ANSWER

Find out the how old was we when he died.

To proof

Let us assume that the age of the Adam be x

As given

Adam lived a quarter of his life as a boy as fifth as a young man, a third in middle-age and 13 years in retirement.

x =\frac{x}{4} +\frac{x}{5} +\frac{x}{3} + 13

L.C.M of denominator i.e ( 4,5,3) =60

than the equation becomes

60x = 15x + 12x +20x +780

60x - 47x = 780

13x = 780

x =\frac{780}{13}

x = 60 years

therefore the Adam age  when he died is 60 years.

Hence proved




5 0
2 years ago
a scientist wants to study 24 stars he studies 1/3 of them one week and 1/4 of them next week how many of them are left to study
zvonat [6]
6 because 1/3 of 24 is 8 and 1/4 of 8 is 6
4 0
2 years ago
Mr. Woo wants to ship a fishing rod to his son that is 42 inches long. He has a box that measures 10 inches by 10 inches by 40 i
chubhunter [2.5K]

Answer:

The 42 inches long fishing rod will fit in the box.

Step-by-step explanation:

The diagonal of a cuboidal box is the largest measurement inside the box.

Now, the dimensions of the box are 10 inches by 10 inches by 40 inches.

Therefore, the diagonal length of the box is \sqrt{10^{2} + 10^{2} + 40^{2}} = 42.42 inches which is greater than 42 inches.

Hence, the 42 inches long fishing rod will fit in the box. (Answer)

8 0
2 years ago
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