The option that explains Sarita's mistake is Sarita’s solution is correct. She made an error in her verification.
<h3>What was Sarita's mistake?</h3>
The given equation is: 5(x - 3) + 7(x + 4) = 73
In order to determine the value of x, take the following steps:
1. Apply the Distributive property:
5x - 15 + 7x + 28 = 73
2. Add similar terms together:
12x + 13 = 73
3. Combine similar terms:
12x = 73 - 13
4. Add similar terms
12x = 60
5. Divide both sides of the equation by 12
x = 60 / 12
x = 5
In order to verify the answer, substitute for x in the given equation :
5(5 - 3) + 7(5 + 4) = 73
5(2) + 7(9) = 73
10 + 63 = 73
73 = 73
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If all were dimes, the value would be $3.30. Brendan has $2.85 more than that. Each quarter that replaces a dime increases the value by $0.15, so Brendan must have $2.85/$0.15 = 19 quarters.
Brendan has 14 dimes and 19 quarters.
D. The economy of the Soviet Union was falling behind that of other major industrialized nations.
Answer:
b=4
Step-by-step explanation:
P.T.c^2=a^2 +b^2
5^2=3^2 +b^2
25=9+b^2
b^2 =25-9
b^2 =16
b=sqrt(16)
b=4
A function m(t)= m₀e^(-rt) that models the mass remaining after t years is; m(t) = 27e^(-0.00043t)
The amount of sample that will remain after 4000 years is; 4.8357 mg
The number of years that it will take for only 17 mg of the sample to remain is; 1076 years
<h3>How to solve exponential decay function?</h3>
A) Using the model for radioactive decay;
m(t)= m₀e^(-rt)
where;
m₀ is initial mass
r is rate of growth
t is time
Thus, we are given;
m₀ = 27 mg
r = (In 2)/1600 = -0.00043 which shows a decrease by 0.00043
and so we have;
m(t) = 27e^(-0.00043t)
c) The amount that will remain after 4000 years is;
m(4000) = 27e^(-0.00043 * 4000)
m(4000) = 27 * 0.1791
m(4000) = 4.8357 mg
d) For 17 mg to remain;
17 = 27e^(-0.00043 * t)
17/27 = e^(-0.00043 * t)
In(17/27) = -0.00043 * t
-0.4626/-0.00043 = t
t = 1076 years
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