Answer:
12
Step-by-step explanation:
1st of all we should let the ration of boys to girls be 2x and 3x.
After that we should make the sum between 2x and3×and the sum of 2numbers is equal to 30
i.e.2x+3x=30
Then ,by solving this eqation we get the value of x=6
After that put the value of x in the number of boys
i.e.
2x=2×6=12
Hence ,the number of boys is 12
Answer:
17.5% per annum
Step-by-step explanation:
<u>Given:</u>
Money invested = $20,000 at the age of 20 years.
Money expected to be $500,000 at the age of 40.
Time = 40 - 20 = 20 years
<em>Interest is compounded annually.</em>
<u>To find:</u>
Rate of growth = ?
<u>Solution:</u>
First of all, let us have a look at the formula for compound interest.

Where A is the amount after T years compounding at a rate of R% per annum. P is the principal amount.
Here, We are given:
P = $20,000
A = $500,000
T = 20 years
R = ?
Putting all the values in the formula:
![500000 = 20000 \times (1+\frac{R}{100})^{20}\\\Rightarrow \dfrac{500000}{20000} =(1+\frac{R}{100})^{20}\\\Rightarrow 25 =(1+\frac{R}{100})^{20}\\\Rightarrow \sqrt[20]{25} =1+\frac{R}{100}\\\Rightarrow 1.175 = 1+0.01R\\\Rightarrow R \approx17.5\%](https://tex.z-dn.net/?f=500000%20%3D%2020000%20%5Ctimes%20%281%2B%5Cfrac%7BR%7D%7B100%7D%29%5E%7B20%7D%5C%5C%5CRightarrow%20%5Cdfrac%7B500000%7D%7B20000%7D%20%3D%281%2B%5Cfrac%7BR%7D%7B100%7D%29%5E%7B20%7D%5C%5C%5CRightarrow%2025%20%3D%281%2B%5Cfrac%7BR%7D%7B100%7D%29%5E%7B20%7D%5C%5C%5CRightarrow%20%5Csqrt%5B20%5D%7B25%7D%20%3D1%2B%5Cfrac%7BR%7D%7B100%7D%5C%5C%5CRightarrow%201.175%20%3D%201%2B0.01R%5C%5C%5CRightarrow%20R%20%5Capprox17.5%5C%25)
So, the correct answer is
<em>17.5% </em>per annum and compounding annually.
ANSWER:
We know that angle fromed by same arc are congruent. so
∠ACB ~ ∠ADB
∠CAD ~ ∠CBD
Therefore, ΔCAF ~ ΔDBF by AA similarity. So, By CPCT
arcAC = arcBD.
Answer:
Ebony need to compare ∠EFG and ∠ONM
Step-by-step explanation:
we know that
If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent by ASA
In this problem
EF ≅ ON ----> the included side
To prove congruence by ASA, of triangles EFG and ONM, the corresponding angles of the included side must be congruent
The corresponding angles of the included side are
∠MON and ∠GEF
and
∠EFG and ∠CNM
so
∠MON ≅ ∠GEF ----> given problem
and
∠EFG ≅ ∠CNM
therefore
Ebony need to compare ∠EFG and ∠ONM
Both angles must be congruent, to prove that triangles EFG and ONM are congruent by ASA
The series is a convergence series and the sum of the series is -8/3
<h3>The type of the series</h3>
The series is given as:

The above series has the following properties:
- First term; a = -4
- Common ratio, r = -1/2
Start by calculating the absolute value of the common ratio
Absolute value = |-1/2|
This gives
Absolute value = 1/2
The above value is less than 1.
It means that the series converges.
<h3>The sum of the series</h3>
This is calculated using:

So, we have:

Evaluate the sum

Evaluate the quotient

Hence, the sum of the series is -8/3
Read more about geometric series at:
brainly.com/question/24643676
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