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3 years ago

A radioactive isotope has a half life of 4.51 days. If 12.63 grams are now present, how much will be left after 15

Mathematics

1 answer:

Marizza181 [45]3 years ago

7 0

Answer:

Step-by-step explanation:

$f=ir^t\\ \\ \frac{1}{2}=r^{4.51}\\ \\ ln(0.5)=4.51lnr\\ \\ r=e^{\frac{ln0.5}{4.51}}\\ \\ r\approx 0.8575\\ \\ f(15)=12.63(0.8575^{15}\\ \\ f(15)\approx 1.26g$

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Your hourly salary increased from $14 to $29. What is the percent increase in your salary?

V125BC [204]

Answer:

107%

Step-by-step explanation:

$14 to $29

Original number/start = $14

End number = $29

Increase = $29 - $14 = $15

% increase = Increase ÷ Original Number × 100

Substitute in known values

% increase = 15 ÷ 14 × 100

Divide

% increase = 1.07 × 100

Multiply

% increase = 107%

The percentage increase is 107%

Hope this helps :)

4 0

3 years ago

Read 2 more answers

part 3. Find the value of the trig function indicated, use Pythagorean theorem to find the third side if you need it.

Nat2105 [25]

Answer: $\bold{9)\ \sin \theta=\dfrac{1}{3}\qquad 10)\ \sin \theta = \dfrac{4}{5}\qquad 11)\ \cos \theta = \dfrac{\sqrt{11}}{6}\qquad 12)\ \tan \theta = \dfrac{17\sqrt2}{26}}$

Step-by-step explanation:

Pythagorean Theorem is: a² + b² = c² , where "c" is the hypotenuse

$9)\ \sin \theta=\dfrac{\text{side opposite of}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{4}{12}\quad \rightarrow \large\boxed{\dfrac{1}{3}}$

Note: 4² + (8√2)² = hypotenuse² → hypotenuse = 12

$10)\ \sin \theta=\dfrac{\text{side opposite of}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{16}{20}\quad \rightarrow \large\boxed{\dfrac{4}{5}}$

Note: 12² + opposite² = 20² → opposite = 16

$11)\ \cos \theta=\dfrac{\text{side adjacent to}\ \theta}{\text{hypotenuse of triangle}}=\dfrac{\sqrt{11}}{6}\quad =\large\boxed{\dfrac{\sqrt{11}}{6}}$

Note: adjacent² + 5² = 6² → adjacent = √11

$12)\ \tan \theta=\dfrac{\text{side opposite of}\ \theta}{\text{side adjacent to}\ \theta}=\dfrac{17}{13\sqrt2}\quad =\large\boxed{\dfrac{17\sqrt2}{26}}$

Note: adjacent² + 7² = (13√2)² → adjacent = 17

5 0

3 years ago

Someone help me please

galben [10]

Answer:

∛27 = 3

Step-by-step explanation:

A radical is simply a fractional exponent: $a^{(\frac{m}{n})} = \sqrt[n]{a^{m} }$

Hence, ∛27 = $27^{(\frac{1}{3})}$

Since 27 = 3³, then:

You could rewrite ∛27 as ∛(3)³.

$\sqrt[3]{3^{(3)} } = 3^{[(3)*(\frac{1}{3})]}$

Multiplying the fractional exponents (3 × 1/3) will result in 1 (because 3 is the multiplicative inverse of 1/3). The multiplicative inverse of a number is defined as a number which when multiplied by the original number gives the product as 1.

Therefore, ∛27 = 3.

3 0

3 years ago

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What is the percent of change from 28 to 70

Paul [167]

Your answer will be 150 percent

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3 years ago

A librarian has weekends off and has 10 paid vacation days per year, including holidays that fall on weekdays. If his salary is

Free_Kalibri [48]

5*52=260-10=250 32500/250=130