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3 years ago

What is this equation x2 – 2x – 6 in vertex form?

Mathematics

1 answer:

Lena [83]3 years ago

7 0

Answer:

In vertex form, the parabola's equation is y=(x−1)^2 +5.

Step-by-step explanation:

You might be interested in

Does someone that knows how to do this??

mezya [45]

Answer:

-1/2

Step-by-step explanation:

rise over run

rise is -2

run is 4

(-2/4)/2=(-1/2)

hope this helps :3

if it did pls mark brainliest

6 0

3 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 $\\ P(Z$ .

Therefore, the probability $\\ P(\overline{x}$ .

Part e

We can follow a similar way than the previous step.

$\\ P(\overline{x} > 23) = P(Z > 1.5)$

For $\\ P(Z > 1.5)$ using the cumulative standard normal table, we can find this probability knowing that

$\\ P(Z1.5) = 1$

$\\ P(Z>1.5) = 1 - P(Z$

Thus

$\\ P(Z>1.5) = 1 - 0.9332$

$\\ P(Z>1.5) = 0.0668$

Therefore, the probability $\\ P(\overline{x}>23) = 1 - P(Z$ .

Part f

This probability is $\\ P(\overline{x} > 16)$ and $\\ P(\overline{x} < 23)$ .

For finding this, we need to subtract the cumulative probabilities for $\\ P(\overline{x} < 16)$ and $\\ P(\overline{x} < 23)$

Using the previous standardized values for them, we have from Part d:

$\\ P(\overline{x}$

We know from Part e that

$\\ P(\overline{x} > 23) = P(Z>1.5) = 1 - P(Z$

$\\ P(\overline{x} < 23) = P(Z1.5)$

$\\ P(\overline{x} < 23) = P(Z$

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

5 0

3 years ago

At big bens bakery 48 chocolate donuts were made,which is 6 times the number of cream filled donuts made.How many more chocolate

ratelena [41]

Answer:

The number of chocolate made donuts is 40 more than cream filed donuts

Step-by-step explanation:

Given as :

The number of chocolate donuts made = 48

The number of chocolate donuts is 6 times the number of cream filled donuts

So, Let the number of cream filled donuts = x

So, number of chocolate donuts made = $6\times x$

∴ $6\times x$ = 48

Or, x = $\frac{48}{6}$ = 8

So, the number of cream filled donuts = 8

Now ,

The number of chocolate donuts made - the number of cream filled donuts = 48 - 8 = 40

So , The number of chocolate made donuts is 40 more than cream filed donuts Answer

7 0

3 years ago

Complete the square to find the vertex of this parabola. x2 - 8x - y - 4 = 0 ([?], [ ]

konstantin123 [22]

Answer:

-20

Step-by-step explanation:

Complete the square to find the vertex of this parablola x^2-8x-y-4=0 {the second one of -20; so 4,-20}

7 0

2 years ago

POSSIBLE POINTS. 7 Two clothing stores are having a sale on all their dress shirts. Store A is charging $15 for each dress shirt

Anon25 [30]

Answer:

The statements are not provided, so i will answer in a general way.

Let's define the variable x as the number of dress shirts brought for some person.

In store A, each one costs $15.

Then the cost of x dress shirts will be:

A(x) = $15*x.

In store B, each one costs $18, but there is a coupon of $9, then we can write the cost in store B as:

B(x) = $18*x - $9.

Now we can find wich store will be cheaper for a given number x, by calculating the difference between A(x) and B(x).

D = A(x) - B(x)

If D is positive, means that B(x) is cheaper.

If D is negative, means that A(x) is cheaper.

If D is equal to zero, means that the cost is the same in both stores.

D = A(x) - B(x) = $15*x - $18*x + $9 = (-$3*x) + $9.

First, let's find for what value of x we have the same cost in both stores:

0 = (-$3*x) + $9.

$9/$3 = 3 = x.

Then for 3 dress shirts, the cost will be the same in each store.

Now, as the coefficient that multiplies x is negative, if we have x > 3, then D will be negative, and if x < 3, D will be positive.

then:

For x = 3, the cost is the same in both stores.

for x > 3, Store A is cheaper.

For x < 2, Store B is cheaper.

6 0

3 years ago