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3 years ago

What expression is equal to6 e + 3 (e-1)

Mathematics

2 answers:

eimsori [14]3 years ago

6 0

Answer:

9e -3

Step-by-step explanation:

Perform the indicated multiplication:

6 e + 3 (e-1) = 6e + 3e - 3

This, in turn, simplifies to

9e -3, or 3(3e - 1).

olga2289 [7]3 years ago

6 0

Answer:

ANSWER: 9e-3

Step-by-step explanation:

6e+3(e−1)

As we need to simplify the above expression:

First we open the brackets :

3(e-1)=3e-33(e−1)=3e−3

Now, add it to 6e.

So, it becomes,

$$\begin{lgathered}6e+3e-3\\\\=9e-3\end{lgathered}$$

Hence, equivalent expression would be 9e-3.

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True or false the expression 24 - 2x + 3y has three terms

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I believe the answer is false

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3 years ago

Which of the following equations correctly shows the relationship between the values of x and the values of y?

Firdavs [7]

Every time the x goes up 1 the y goes up by 3

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2 years ago

Read 2 more answers

Show how to find the roots (zeros) of the function in the picture below.

Vikki [24]

Answer:

The roots (zeros) of the function are:

$x=5,\:x=-8$

Step-by-step explanation:

Given the function

$f\left(x\right)=x^2+3x-40$

substitute f(x) = 0 to determine the zeros of the function

$0=x^2+3x-40$

First break the expression x² + 3x - 40 into groups

x² + 3x - 40 = (x² - 5x) + (8x - 40)

Factor out x from x² - 5x: x(x - 5)

Factor out 8 from 8x - 40: 8(x - 5)

Thus, the expression becomes

$0=x\left(x-5\right)+8\left(x-5\right)$

switch the sides

$x\left(x-5\right)+8\left(x-5\right)=0$

Factor out common term x - 5

$(x - 5) (x + 8) = 0$

Using the zero factor principle

if ab=0, then a=0 or b=0 (or both a=0 and b=0)

$x-5=0\quad \mathrm{or}\quad \:x+8=0$

Solve x - 5 = 0

x - 5 = 0

adding 5 to both sides

x - 5 + 5 = 0 + 5

x = 5

solve x + 8 = 0

x + 8 = 0

subtracting 8 from both sides

x + 8 - 8 = 0 - 8

x = -8

Therefore, the roots (zeros) of the function are:

$x=5,\:x=-8$

6 0

2 years ago

A random sample of n = 64 observations is drawn from a population with a mean equal to 20 and standard deviation equal to 16. (G

dezoksy [38]

Answer:

a) The mean of a sampling distribution of $\\ \overline{x}$ is $\\ \mu_{\overline{x}} = \mu = 20$ . The standard deviation is $\\ \frac{\sigma}{\sqrt{n}} = \frac{16}{\sqrt{64}}=2$ .

b) The standard normal z-score corresponding to a value of $\\ \overline{x} = 16$ is $\\ Z = -2$ .

c) The standard normal z-score corresponding to a value of $\\ \overline{x} = 23$ is $\\ Z = 1.5$ .

d) The probability $\\ P(\overline{x}$ .

e) The probability $\\ P(\overline{x}>23) = 1 - P(Z$ .

f) $\\ P(16 < \overline{x} < 23) = P(-2 < Z < 1.5) = P(Z$ .

Step-by-step explanation:

We are dealing here with the concept of a sampling distribution, that is, the distribution of the sample means $\\ \overline{x}$ .

We know that for this kind of distribution we need, at least, that the sample size must be $\\ n \geq 30$ observations, to establish that:

$\\ \overline{x} \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

In words, the distribution of the sample means follows, approximately, a normal distribution with mean, $\mu$ , and standard deviation (called standard error), $\\ \frac{\sigma}{\sqrt{n}}$ .

The number of observations is n = 64.

We need also to remember that the random variable Z follows a standard normal distribution with $\\ \mu = 0$ and $\\ \sigma = 1$ .

$\\ Z \sim N(0, 1)$

The variable Z is

$\\ Z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$ [1]

With all this information, we can solve the questions.

Part a

The mean of a sampling distribution of $\\ \overline{x}$ is the population mean $\\ \mu = 20$ or $\\ \mu_{\overline{x}} = \mu = 20$ .

The standard deviation is the population standard deviation $\\ \sigma = 16$ divided by the root square of n, that is, the number of observations of the sample. Thus, $\\ \frac{\sigma}{\sqrt{n}} = \frac{16}{\sqrt{64}}=2$ .

Part b

We are dealing here with a random sample. The z-score for the sampling distribution of $\\ \overline{x}$ is given by [1]. Then

$\\ Z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

$\\ Z = \frac{16 - 20}{\frac{16}{\sqrt{64}}}$

$\\ Z = \frac{-4}{\frac{16}{8}}$

$\\ Z = \frac{-4}{2}$

$\\ Z = -2$

Then, the standard normal z-score corresponding to a value of $\\ \overline{x} = 16$ is $\\ Z = -2$ .

Part c

We can follow the same procedure as before. Then

$\\ Z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

$\\ Z = \frac{23 - 20}{\frac{16}{\sqrt{64}}}$

$\\ Z = \frac{3}{\frac{16}{8}}$

$\\ Z = \frac{3}{2}$

$\\ Z = 1.5$

As a result, the standard normal z-score corresponding to a value of $\\ \overline{x} = 23$ is $\\ Z = 1.5$ .

Part d

Since we know from [1] that the random variable follows a standard normal distribution, we can consult the cumulative standard normal table for the corresponding $\\ \overline{x}$ already calculated. This table is available in Statistics textbooks and on the Internet. We can also use statistical packages and even spreadsheets or calculators to find this probability.

The corresponding value is Z = -2, that is, it is two standard units below the mean (because of the negative value). Then, consulting the mentioned table, the corresponding cumulative probability for Z = -2 is $\\ P(Z$ .