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3 years ago

Evaluate to one decimal place

Mathematics

1 answer:

ANTONII [103]3 years ago

3 0

Answer:

The correct answer is C. 1.6

Step-by-step explanation:

Let's recall that e or Euler's number is a mathematical constant that is the base of the natural logarithm, in other words, the unique number whose natural logarithm is equal to one. The value of e is approximately 2.71828.

Now, replacing e, we have:

2.71828∧(1/2) = √2.71828 = 1.6 (Rounding to one decimal place)

The correct answer is C. 1.6

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Complete the statements about the key features of the graph of f(x) = x5 – 9x3. As x goes to negative infinity, f(x) goes to neg

Mars2501 [29]

The function is $f(x)= x^{5} -9x ^{3}$

1. let's factorize the expression $x^{5} -9x ^{3}$ :

$f(x)= x^{5} -9x ^{3}= x^{3} ( x^{2} -9)=x^{3}(x-3)(x+3)$

the zeros of f(x) are the values of x which make f(x) = 0.

from the factorized form of the function, we see that the roots are:

-3, multiplicity 1
3, multiplicity 1
0, multiplicity 3

(the multiplicity of the roots is the power of each factor of f(x) )

2.
The end behavior of f(x), whose term of largest degree is $x^{5}$ , is the same as the end behavior of $x^{3}$ , which has a well known graph. Check the picture attached.

(similarly the end behavior of an even degree polynomial, could be compared to the end behavior of $x^{2}$ )

so, like the graph of $x^{3}$ , the graph of $f(x)= x^{5} -9x ^{3}$ :

"As x goes to negative infinity, f(x) goes to negative infinity, and as x goes to positive infinity, f(x) goes to positive infinity. "

7 0

3 years ago

Read 2 more answers

a six sided die is rolled 4 times in a row. What is the probability of getting 4 only on the last trial of this experiment?

hoa [83]

First, start of by saying what the probability of getting a 4 is, which is 1/6.
Now, this means the probability of not getting a 4 is 1-(1/6)=(5/6), since the total probability is 1.

After doing this, you should think about what it means to only get 4 on the last trial, the 4th trial. It means that the probabilities of the 1st, 2nd, and 3rd trial were (5/6) each. The 4th trial had a probability of (1/6). So the probability would be calculated as following: ( $(5/6)^3*(1/6)$ = $5^3/6^4$ . You can use a calculator or your computer to find out that the probability is 125/1296.

I hope this was helpful!

5 0

2 years ago

Which statement is true?

krok68 [10]

Answer:

(B) 1.2 > -6.9

Explanation:

The negative numbers/decimals are always to the left of the 0 on a number line. They are not positive.

The positive numbers are always to the right of the 0 on a number line. They are always greater than negative numbers.

6.9 might be greater than 1.2 if it is a positive number, but if it is a negative number, 1.2 is greater.

5 0

3 years ago

Read 2 more answers

Write the equation of a horizontal line that passes through the point (–2, 2).

Aneli [31]

Answer:

option C

y = 2

Step-by-step explanation:

Given in the question,

a co-ordinate = (-2,2)

x = -2

y = 2

Equation of the straight line

y = mx + c

here m = gradient of the line

c = y - intercept

<h3>we know that gradient of the horizontal line = 0</h3>

plug value in the equation above

y = (0)x + 2

y = 2

7 0

3 years ago

In statistics, what term means "a numerical range around a sample mean accompanied with a statement of how confident one is that

Alex Ar [27]

Answer:

Confidence Interval for the mean

Step-by-step explanation:

Confidence interval is made using the observations of a sample of data obtained from a population, so it is constructed in such a way, that, with a certain level of confidence (this is the statement mentioned in the question), that is, one could have a percentage of probability that the interval, or range around the value obtained, frequently 95%, contains the true value of a population parameter (in this case, the population mean).

It is one way to extract information from a population using a sample of it. This kind of information is what inference statistic is always looking for.

An approximation about how to construct this interval or range:

Select a random sample.
For the specific case of a mean, you need to calculate the mean of the sample (sample mean), and, if standard deviation is unknown or not mentioned, also calculate the sample standard deviation.
With this information, and acknowledged that these values follows a standard normal distribution (a normal distribution with mean 0 and a standard deviation of 1), represented by random variable Z, one can use all this information to calculate a confidence interval for the mean, with a certain confidence previously choosen (for example, 95%), that the population mean must be in this interval or range around this sample mean.

3 0

2 years ago