Answer:
Option 2 50 ≤ s ≤ 100
Option 5 She could deposit $50
Option 6 She could deposit $75
Step-by-step explanation:
Let
s -----> amount of money Layla deposit into a saving account
we know that
25%=25/100=0.25
50%=50/100=0.50
so
-----> 
-----> 
The compound inequality is
<em>Verify each case</em>
case 1) 25 ≤ s ≤ 50
The statement is false
see the procedure
case 2) 50 ≤ s ≤ 100
<u>The statement is True</u>
see the procedure
case 3) s ≤ 25 or s ≥ 50
The statement is false
Because is s ≤ 100 and s ≥ 50
case 4) s ≤ 50 or s ≥ 100
The statement is false
Because is s ≤ 100 and s ≥ 50
case 5) She could deposit $50
<u>The statement is true</u>
Because the value of s satisfy the compound inequality
case 6) She could deposit $75
<u>The statement is true</u>
Because the value of s satisfy the compound inequality
So 1st consider that it's a square! That's very important. So for a square, all 4 sides are equal.
And now considering that the given information is the diameter. So any angle made at the circle extended from the 2 points of diameter gives an angle of 90°
Now consider one triangle. So we already know that 2 sides of the triangle are equal (because they are 2 sides of a square) , has a side of 10 (diameter) and and angle of 90°. So remaining 2 angles are 45°
Now solve it by applying
<h2>
Hello!</h2>
The answers are:
The possible values for x in the equation, are:
First option, ![5\sqrt[3]{3}](https://tex.z-dn.net/?f=5%5Csqrt%5B3%5D%7B3%7D)
Second option, ![\sqrt[3]{375}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B375%7D)
<h2>
Why?</h2>
To solve the problem, we need to remember the following properties of the exponents and roots:
![a\sqrt[n]{b}=\sqrt[n]{a^{n}*b} \\\\\sqrt[n]{a^{m} }=a^{\frac{m}{n}}\\\\(a^{b})^{c}=a^{b*c}](https://tex.z-dn.net/?f=a%5Csqrt%5Bn%5D%7Bb%7D%3D%5Csqrt%5Bn%5D%7Ba%5E%7Bn%7D%2Ab%7D%20%5C%5C%5C%5C%5Csqrt%5Bn%5D%7Ba%5E%7Bm%7D%20%7D%3Da%5E%7B%5Cfrac%7Bm%7D%7Bn%7D%7D%5C%5C%5C%5C%28a%5E%7Bb%7D%29%5E%7Bc%7D%3Da%5E%7Bb%2Ac%7D)
Then, we are given the expression:
So, finding "x", we have:
![x^{3}=375\\\\(x^{3})^{\frac{1}{3} } =(375)^{\frac{1}{3}}\\\\x=\sqrt[3]{375}=\sqrt[3]{125*3}=\sqrt[3]{125}*\sqrt[3]{3}=5\sqrt[3]{3}](https://tex.z-dn.net/?f=x%5E%7B3%7D%3D375%5C%5C%5C%5C%28x%5E%7B3%7D%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%20%7D%20%3D%28375%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%5C%5C%5C%5Cx%3D%5Csqrt%5B3%5D%7B375%7D%3D%5Csqrt%5B3%5D%7B125%2A3%7D%3D%5Csqrt%5B3%5D%7B125%7D%2A%5Csqrt%5B3%5D%7B3%7D%3D5%5Csqrt%5B3%5D%7B3%7D)
Hence, the possible values for x in the equation, are:
First option,
Second option,
Have a nice day!
Answer: 41.5 min
Step-by-step explanation:
This problem can be solved with the Radioactive Half Life Formula:
(1)
Where:
is the final amount of the radioactive element
is the initial amount of the radioactive element
is the time elapsed
is the half life of the radioactive element
So, we need to substitute the given values and find from (1):
(2)
(3)
(4)
Applying natural logarithm in both sides:
(5)
(6)
Clearing :
This is the time elapsed
