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3 years ago

Calculate the mean,median and mode.(3 points each)

Mathematics

1 answer:

Marizza181 [45]3 years ago

5 0

Answer:

1. The first set of number is

1,2,3,4,5

Mean= 1+2+3+4+5/5

= 15/5

= 3

Median= 3

Mode= N/A

The next set of numbers is

2,3,4,5,6,6

Mean= 2+3+4+5+6+6/6

= 26/6

= 4.3

Median=4+5/2

= 9/2

= 4.5

Mode= 6

The next set of number is

6,7,5,4,5,6,2,5

Mean= 2+4+5+5+5+6+6+7/8

= 40/8

= 5

Median= 5+5/2

= 10/2

= 5

Mode= 5

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3 years ago

Harold bought 20 toys for his nieces and nephews. The least expensive toy cost $6.19, and the most expensive toy cost $9.81. Whi

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3 years ago

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

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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

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

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3 years ago

Solve for x: 10(x + 1) = 2x - 7

Lisa [10]

Answer:Simplifying

x = -2.125

Step-by-step explanation:Add '-10' to each side of the equation.

10 + -10 + 8x = -7 + -10

Combine like terms: 10 + -10 = 0

0 + 8x = -7 + -10

8x = -7 + -10

Combine like terms: -7 + -10 = -17

8x = -17

Divide each side by '8'.

x = -2.125

Simplifying

x = -2.125

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