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2 years ago

Explain when it would be more useful to use the Counting Principle than a tree diagram to count possible outcomes of an event.

Mathematics

1 answer:

Kipish [7]2 years ago

8 0

Because a tree diagram is mostly for finding how many possibilities or choices one has.

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Find the volume of the cylinder. Use 3.14 for T. Round to the nearest tenth.

AleksandrR [38]

It will be 5 cm and use 3.14 to multiply

4 0

1 year ago

Watch help video

ollegr [7]

Answer: 15309

hope this helps, the nth term calulation is (7/3) times 3^n

6 0

2 years ago

Use the definition of a Taylor series to find the first three non zero terms of the Taylor series for the given function centere

Ket [755]

Answer:

$e^{4x}=e^4+4e^4(x-1)+8e^4(x-1)^2+...$

$\displaystyle e^{4x}=\sum^{\infty}_{n=0} \dfrac{4^ne^4}{n!}(x-1)^n$

Step-by-step explanation:

<u>Taylor series</u> expansions of f(x) at the point x = a

$\text{f}(x)=\text{f}(a)+\text{f}\:'(a)(x-a)+\dfrac{\text{f}\:''(a)}{2!}(x-a)^2+\dfrac{\text{f}\:'''(a)}{3!}(x-a)^3+...+\dfrac{\text{f}\:^{(r)}(a)}{r!}(x-a)^r+...$

This expansion is valid only if $\text{f}\:^{(n)}(a)$ exists and is finite for all $n \in \mathbb{N}$ , and for values of x for which the infinite series converges.

$\textsf{Let }\text{f}(x)=e^{4x} \textsf{ and }a=1$

$\text{f}(x)=\text{f}(1)+\text{f}\:'(1)(x-1)+\dfrac{\text{f}\:''(1)}{2!}(x-1)^2+...$

$\boxed{\begin{minipage}{5.5 cm}\underline{Differentiating $e^{f(x)}$}\\\\If $y=e^{f(x)}$, then $\dfrac{\text{d}y}{\text{d}x}=f\:'(x)e^{f(x)}$\\\end{minipage}}$

$\text{f}(x)=e^{4x} \implies \text{f}(1)=e^4$

$\text{f}\:'(x)=4e^{4x} \implies \text{f}\:'(1)=4e^4$

$\text{f}\:''(x)=16e^{4x} \implies \text{f}\:''(1)=16e^4$

Substituting the values in the series expansion gives:

$e^{4x}=e^4+4e^4(x-1)+\dfrac{16e^4}{2}(x-1)^2+...$

Factoring out e⁴:

$e^{4x}=e^4\left[1+4(x-1)+8}(x-1)^2+...\right]$

<u>Taylor Series summation notation</u>:

$\displaystyle \text{f}(x)=\sum^{\infty}_{n=0} \dfrac{\text{f}\:^{(n)}(a)}{n!}(x-a)^n$

Therefore:

$\displaystyle e^{4x}=\sum^{\infty}_{n=0} \dfrac{4^ne^4}{n!}(x-1)^n$

7 0

1 year ago

a coin is tossed 3 times. what is the probability of getting heads on the first toss, heads on the second toss, and tails on the

Salsk061 [2.6K]

Answer:

There are 2^3 = 8 possible outcomes after tossing a fair coin fairly 3 times. The 8 possible outcomes are: TTT, HTT, THT, TTH, HHT, HTH, THH, HHH. Exactly 2 of 8 possible outcomes result in 3 of the same faces showing up.

Step-by-step explanation:

3 0

2 years ago

A parking lot is 75 feet wide and 90 feet long. What is the cost of paving the lot with concrete at $3.50 per square yard?

g100num [7]

This question is super simple when you sit down and think about what it's asking. What is the cost of the whole paving lot?

We know that the paving lot is 90 ft by 75 ft, we need to start by finding the area of the whole paving lot.

Area of a rectangle is Length multiplied by Width.

90 × 75 = 6,750

The area of the paving lot is 6,750 feet squared.

Now we need to find the cost of the paving lot, we know that one square yard costs $3.50 to pave.

We can solve this by first taking the step to finding how many yards are in the paving lot.

A yard is 3 feet so we'll divide the area of the paving lot by 3.

6,750 ÷ 3 = 2,250

With the paving lot having 2,250 square yards we can now multiply this by the $3.5 cost per square yard.

2,250 × 3.5 = 7,875

It should cost $7,875 dollars to pave the entire lot.

3 0

2 years ago