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2 years ago

12

You want to see if your dog will respond when you open the front door. After many attempts, you found that the dog barked 75% of

the time when you opened the door. Suppose you open the door 8 times. How many times do you expect your dog to bark?

1 answer:

KatRina [158]2 years ago

4 0

The dog barked 6 times

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I NEED HELP ASAP!!!!!!!!!!! One day, the temperature started at 14 degrees at 6:00 a.m., then climbed 5 degrees by noon, and the

ANTONII [103]

B.12 degrees I did this before

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3 years ago

Write an equation in point-slope form for the line that has a slope of 5 and contains the point (-1,2)

Cloud [144]

Answer:

y - 2 = 5(x+1)

Step-by-step explanation:

Point slope form is

y-y1 = m(x-x1) where m is the slope and ( x1,y1) is a point on the line

y - 2 = 5(x- -1)

y - 2 = 5(x+1)

4 0

2 years ago

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Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do n

aliya0001 [1]

Answer:

$f(x)=\sum_{n=1}^{\infty}(-1)^{(n-1)}2^{n}\dfrac{x^n}{n}$

Step-by-step explanation:

The Maclaurin series of a function f(x) is the Taylor series of the function of the series around zero which is given by

$f(x)=f(0)+f^{\prime}(0)x+f^{\prime \prime}(0)\dfrac{x^2}{2!}+ ...+f^{(n)}(0)\dfrac{x^n}{n!}+...$

We first compute the n-th derivative of $f(x)=\ln(1+2x)$ , note that

$f^{\prime}(x)= 2 \cdot (1+2x)^{-1}\\f^{\prime \prime}(x)= 2^2\cdot (-1) \cdot (1+2x)^{-2}\\f^{\prime \prime}(x)= 2^3\cdot (-1)^2\cdot 2 \cdot (1+2x)^{-3}\\...\\\\f^{n}(x)= 2^n\cdot (-1)^{(n-1)}\cdot (n-1)! \cdot (1+2x)^{-n}\\$

Now, if we compute the n-th derivative at 0 we get

$f(0)=\ln(1+2\cdot 0)=\ln(1)=0\\\\f^{\prime}(0)=2 \cdot 1 =2\\\\f^{(2)}(0)=2^{2}\cdot(-1)\\\\f^{(3)}(0)=2^{3}\cdot (-1)^2\cdot 2\\\\...\\\\f^{(n)}(0)=2^n\cdot(-1)^{(n-1)}\cdot (n-1)!$

and so the Maclaurin series for f(x)=ln(1+2x) is given by

$f(x)=0+2x-2^2\dfrac{x^2}{2!}+2^3\cdot 2! \dfrac{x^3}{3!}+...+(-1)^{(n-1)}(n-1)!\cdot 2^n\dfrac{x^n}{n!}+...\\\\= 0 + 2x -2^2 \dfrac{x^2}{2!}+2^3\dfrac{x^3}{3!}+...+(-1)^{(n-1)}2^{n}\dfrac{x^n}{n}+...\\\\=\sum_{n=1}^{\infty}(-1)^{(n-1)}2^n\dfrac{x^n}{n}$

3 0

2 years ago

Four times a number added to 7 times the number equals 44.

zysi [14]

If you're looking for the value of the number, then here's how:
Let's call the number x
4x + 7x = 44
11x = 44
÷ 11
x = 4
So the number you're looking for is 4, if you wanted to know something else then let me know!

8 0

3 years ago

Solve the equation and check the solution 16+x=42

tigry1 [53]

The answer would be: X=26

6 0

3 years ago

Read 2 more answers