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3 years ago

How do you know that 21 over 30 is greater than 2 over 3

1 answer:

7 0

The problem deals with fractions comparison, lets do it:
21/30 > 2/3
we begin solving:
21 > (2/3)*30
21 > 2*10
21 > 20
therefore the proposed inequality is true, 21/30 > 2/3

You can solve as well getting same denominator for both fractions and comparing directly, in this case we need to get 2/3 to be divided by 30:
2/3 = (10/10)(2/3) = 20/30
So we have:
21/30 > 2/3
which is equal to:
21/30 > 20/30
and we compare directly because both fractions are divided by the same number, and we can see that the inequality is true.

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A student in Greece discovers a pottery bowl

finlep [7]

Answer:

The age of the pottery bowl to the nearest year is 15606 years.

Step-by-step explanation:

Let the initial amount of C-14 in the bowl i.e. $N_{0} = 100$ and today (say after t years) the amount of C-14 in the bowl i.e. N = 21.

Therefore, from the given equation we can write

$21 = 100 e^{- 0.0001t}$ {Since, k is give to be 0.0001}

⇒ $0.21 = e^{- 0.0001t}$

Now, taking ln on both sides we get

ln 0.21 = - 0.0001t (ln e) {Since, $\ln a^{b} = b \ln a$ }

⇒ - 1.560647 = - 0.0001t {We have ln e = 1}

⇒ t = 15606.47 years ≈ 15606 years

Therefore, the age of the pottery bowl to the nearest year is 15606 years.(Answer)

3 0

3 years ago

Please help me with just the first two questions

katovenus [111]

Fyfvnjg der hung dssecbyvb nnnhrtjnkinb

4 0

3 years ago

Abby needs 8.75 bags of carrots two times a month to feed the horses. How many bags will she need to feed the horses for 7 month

8090 [49]

Answer:

122.5

Step-by-step explanation:

take 8.75 multiply it by 2 then multiply it by 7 to get your answer 122.5

5 0

3 years ago

Kabul’s bookshop marks up all books by 40 percent of their cost. The overhead rate is 16 percent of the selling price. What is t

morpeh [17]

Answer:

The net profit rate on the book is 5.41

Step-by-step explanation:

Given as :

The marks up percentage of book = m = 40%

The overhead rate is 16% of selling price

The cost price of book = c.p = $18.10

Let The profit = $p

Let The selling price = s.p

Now, According to question

mark up percentage = $\dfrac{s.p - c.p}{c.p}$

I.e 40% = $\dfrac{s.p - 18.10}{18.10}$

Or, $\dfrac{40}{100}$ + 1 = $\dfrac{s.p}{18.10}$

Or, $\dfrac{140}{100}$ = $\dfrac{s.p}{18.10}$

Or, s. p = $\dfrac{140\times 18.10}{100}$

∴ s.p = $25.34

So, selling price of book = s.p = $25.34

Now, The overhead percentage = 16%

i.e overhead rate = $\dfrac{\textrm estimated cost}{\textrm estimated total base unit}$

Or, estimated cost = 16% × 25.34

I,e estimated cost = 0.16 × 25.34

∴ estimated cost = $4.05

Now,

Profit = selling price of book - estimated book cost

I.e p = $25.34 - $4.05

∴ p = $21.29

So, The profit rate% = $\dfrac{\textrm profit}{\textrm estimated cost}$

I.e The profit rate% = $\dfrac{21.29}{4.05}$

∴ profit rate %= 5.41

So, The profit rate = p = 5.41

Hence, The net profit rate on the book is 5.41 Answer

4 0

3 years ago

In a group of 42 students, 9 study both Art and Biology.

LUCKY_DIMON [66]

Answer:
The probability the student studies Art and
Biology is 0.2143.
Step-by-step explanation:
Denote the events as follows:
A = a students studies Art
B= a students studies Biology
The information provided is:
N = 42
n (An B) = 9
n (A' n B) = 10
n (A' n B') =7
Then the number of students who study Art
but not Biology is:
n(An B') = N -n (An B) -n (A' nB) - n (A'n B')
= 42 - 10 - 7 - 9
= 16
The number of students who study Art but
not Biology is 16.
Compute the probability the student studies
Art and Biology as follows:
P(ANB)
n(ANB)
= 0.2143
Thus, the probability the student studies Art
and Biology is 0.2143.

3 0

2 years ago