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Kisachek [45]
2 years ago
12

Nick starts with 20 milligrams of a radioactive substance. The amount of the substance decreases by 12 each week for a number of

weeks, w. He writes the expression 20(12)w to find the amount of radioactive substance remaining after w weeks. Autumn starts with 1 milligram of a radioactive substance. The amount of the substance decreases by 50% each week for a number of weeks, w. She writes the expression (1−0.5)w to find the amount of radioactive substance remaining after w weeks. Use the drop-down menus to explain what each part of Nick's and Autumn's expressions mean.
Mathematics
1 answer:
Gre4nikov [31]2 years ago
6 0

Answer:

what the answer

Step-by-step explanation:

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At the beginning of year 1, paolo invests $500
suter [353]
\bf ~~~~~~ \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\to &\$500\\
r=rate\to 4\%\to \frac{4}{100}\to &0.04\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{annuall, thus once}
\end{array}\to &1\\
t=years\to &t
\end{cases}
\\\\\\
A=500\left(1+\frac{0.04}{1}\right)^{1\cdot t}\implies A=500(1+0.04)^t
\\\\\\
\textit{after 5 years }t=5\qquad A=500(1.04)^5

the example on your picture uses A(n) and n = years, but is pretty much the same, in this case is t = years.
3 0
1 year ago
Read 2 more answers
If r=[x,y,z] and r0=[x0,y0,z0], describe the set of all points (x,y,z) such that Ir-r0I =1.
sdas [7]

Answer:

The points (x,y,z) that respond to Ir-r0I =1, are all that describes the form (x-x_0)^2+(y-y_0)^2+(z-z_0)^2=1 with:

-1+x₀<x<1+x₀

-1+y₀<y<1+y₀

-1+z₀<z<1+z₀

Step-by-step explanation:

All points required in this problem came from applying the definition of modulus of a vector:

Ir-r0I =1.

|(x,y,z)-(x_{0},y_{0},z_{0})|=|(x-x_{0},y-y_{0},z-z_{0})|=\sqrt{(x-x_{0})^2+(y-y_{0})^2+(z-z_{0})^2}=1\\(x-x_{0})^2+(y-y_{0})^2+(z-z_{0})^2=1^2=1

5 0
2 years ago
Which phrase describes the perpendicular distance between two bases of a cylinder
Flura [38]

Answer:

The height of the cylinder

Step-by-step explanation:

The perpendicular distance between two bases of a cylinder is not going to be the radius or diameter of the bases (because it is BETWEEN the bases, not ON them) and it is not the area of the bases because the area of a shape cannot be a distance.

So, the only option left is the height of the cylinder, which is the correct answer.

5 0
1 year ago
Recent homebuyers from a local developer allege that 30% of the houses this developer constructs have some major defect that wil
umka21 [38]

Answer:

3.54% probability of observing at most two defective homes out of a random sample of 20

Step-by-step explanation:

For each house that this developer constructs, there are only two possible outcomes. Either there are some major defect that will require substantial repairs, or there is not. The probability of a house having some major defect that will require substantial repairs is independent of other houses. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

30% of the houses this developer constructs have some major defect that will require substantial repairs.

This means that p = 0.3

If the allegation is correct, what is the probability of observing at most two defective homes out of a random sample of 20

This is P(X \leq 2) when n = 20. So

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{20,0}.(0.3)^{0}.(0.7)^{20} = 0.0008

P(X = 1) = C_{20,1}.(0.3)^{1}.(0.7)^{19} = 0.0068

P(X = 2) = C_{20,2}.(0.3)^{2}.(0.7)^{18} = 0.0278

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0008 + 0.0068 + 0.0278 = 0.0354

3.54% probability of observing at most two defective homes out of a random sample of 20

5 0
1 year ago
What additional information could be used to prove that △ABC ~ △NML? Check all that apply. ∠B ≅ ∠M △ABC is a right triangle. △AB
Elena L [17]

Answer:

1,3,5

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
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