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Leya [2.2K]
2 years ago
9

How do you simplify without using a calculator (-5)(7)+4×5​

Mathematics
1 answer:
Evgesh-ka [11]2 years ago
7 0

Answer:

-15 Is the answer

Step-by-step explanation:

(-5)(7)+4×5​

= -15

(-5)(7) + 4×5 = -15/1 = -15

Multiple: -5 * 7 = -35

Multiple: 4 * 5 = 20

Add: the result of step No. 1 + the result of step No. 2 = -35 + 20 = -15

Hope this helps.

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Use the power series for 1 1−x to find a power series representation of f(x) = ln(1−x). What is the radius of convergence? (Note
Viktor [21]

a. Recall that

\displaystyle\int\frac{\mathrm dx}{1-x}=-\ln|1-x|+C

For |x|, we have

\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n

By integrating both sides, we get

\displaystyle-\ln(1-x)=C+\sum_{n=0}^\infty\frac{x^{n+1}}{n+1}

If x=0, then

\displaystyle-\ln1=C+\sum_{n=0}^\infty\frac{0^{n+1}}{n+1}\implies 0=C+0\implies C=0

so that

\displaystyle\ln(1-x)=-\sum_{n=0}^\infty\frac{x^{n+1}}{n+1}

We can shift the index to simplify the sum slightly.

\displaystyle\ln(1-x)=-\sum_{n=1}^\infty\frac{x^n}n

b. The power series for x\ln(1-x) can be obtained simply by multiplying both sides of the series above by x.

\displaystyle x\ln(1-x)=-\sum_{n=1}^\infty\frac{x^{n+1}}n

c. We have

\ln2=-\dfrac\ln12=-\ln\left(1-\dfrac12\right)

\displaystyle\implies\ln2=\sum_{n=1}^\infty\frac1{n2^n}

4 0
3 years ago
Ten experts rated a newly developed chocolate chip cookie on a scale of 1 to 50. Their ratings were:
Sunny_sXe [5.5K]

Answer:

Option B.

Step-by-step explanation:

The given data set is

34, 35, 41, 28, 26, 29, 32, 36, 38, 40

We need to find the mean deviation of the given data.

Number of observations, n = 10

Mean of the data is

Mean=\dfrac{\sum x}{n}

Mean=\dfrac{34+35+41+28+26+29+32+36+38+40}{10}

Mean=\dfrac{339}{10}

Mean=33.9

Formula for mean deviation is

\text{Mean deviation}=\dfrac{\sum |x-mean|}{n}

\sum |x-mean|=|34-33.9|+|35-33.9|+|41-33.9|+|28-33.9|+|26-33.9|+|29-33.9|+ |32-33.9|+|36-33.9|+|38-33.9|+|40-33.9|=41.2

\text{Mean deviation}=\dfrac{41.2}{10}

\text{Mean deviation}=4.12

The mean deviation of the ratings is 4.12.

Therefore, the correct option is B.

8 0
3 years ago
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slavikrds [6]

(the scale shows that 1 inch = 8 ft)

a) 56 ft [ (7 ×8) ft ]

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If you roll a six-sided die, what is the probability you will obtain greater than a 2?
Delvig [45]

If we will roll a fair die then the outcomes wil be 1,2,3,4,5,6.

Hence, the total number of events= 6

3,4,5 and 6 are greater than 2.

So, there's 4 events which are greater than 2.

Now the formula to find the probability is:

probability=\frac{Number of events more than 2}{Total number of events.}

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So, the probability of getting greater than a 2 is 2/3.

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Acute it is an Acute
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