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3 years ago

Find the vertex of the graph of the function. f(x) = (x + 4)2 - 1

Mathematics

1 answer:

Elanso [62]3 years ago

5 0

Answer:

The vertex of the function is at point (-4,-1).

Step-by-step explanation:

Given function:

$f(x)=(x+4)^2-1$

Solution:

The vertex form of a function is given by:

$f(x)=a(x-h)^2+k$

where $(h,k)$ is the vertex of the function. At this point the function has the maximum or minimum value.

Writing the given function in the vertex form.

$f(x)=(x-(-4))^2+(-1)$

On comparing the above function with the standard form we find that:

$a=1\\h=-4\\k=-1$

Thus, the vertex of the function is at point (-4,-1)

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What's the value of X?

elena-14-01-66 [18.8K]

Answer:

a) x=93

Step-by-step explanation:

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3 years ago

Read 2 more answers

A self proclaimed psychic was tested for ESP. The psychic was presented with 200 cards face down and asked to determine if the c

swat32

Answer:

The 95% confidence interval would be given (0.172;0.288).

We are confident at 95% that the true probability that the psychic correctly identifies the symbol on the card in a random trial is between (0.172;0.288).

We can conclude that her random guessing would have got her correct 20% of the time. Since the confidence interval contains 0.2, she has no psychic powers, rather she just guessed it like normal people. Any person could have got it correct this many times.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Description in words of the parameter p

$p$ represent the probability that the psychic correctly identifies the symbol on the card in a random trial

$\hat p$ represent the estimated probability that the psychic correctly identifies the symbol on the card in a random trial

n=200 is the sample size required

$z_{\alpha/2}$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Numerical estimate for p

In order to estimate a proportion we use this formula:

$\hat p =\frac{X}{n}$ where X represent the cases successful

$\hat p=\frac{46}{200}=0.23$ represent the estimated probability that the psychic correctly identifies the symbol on the card in a random trial

Confidence interval

The confidence interval for a proportion is given by this formula:

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$0.23 - 1.96 \sqrt{\frac{0.23(1-0.23)}{200}}=0.172$

$0.23 + 1.96 \sqrt{\frac{0.23(1-0.23)}{200}}=0.288$

And the 95% confidence interval would be given (0.172;0.288).

We are confident at 95% that the true probability that the psychic correctly identifies the symbol on the card in a random trial is between (0.172;0.288).

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3 years ago

Carol is going to buy a purse she found. It is originally $120.00, but has been marked down 25%. When Carol goes to buy the purs

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3 years ago

Given a geometric sequence with a1 = 6 and r= 2/3 write an explicit formula for an the nth term of the sequence.

fomenos

the explicit formula for aₙ the nth term of the sequence will be: $a_{n}=6\times (\frac{2}{3})^{n-1}\\$

Step-by-step explanation:

The explicit formula of geometric sequence is of the form:

$a_{n}=a_{1}r^{n-1}$

where a₁ is the first term and r is the common ratio.

We are given:

a₁ = 6

r = 2/3

Putting values in the formula:

$a_{n}=a_{1}r^{r-1}\\a_{n}=6\times (\frac{2}{3})^{n-1}\\$

So, the explicit formula for aₙ the nth term of the sequence will be: $a_{n}=6\times (\frac{2}{3})^{n-1}\\$

Keywords: Explicit formula for geometric sequence

Learn more about Explicit formula for geometric sequence at:

#learnwithBrainly

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2 years ago

Floyd is an aspiring music artist. He has a record contract that pays him a base rate of \$200$200dollar sign, 200 a month and a

Thepotemich [5.8K]

Floyd's contract consists of
(i) $200 per month fixed.
(i) $12 per album sold.

Let x = number of albums sold last month.
Because total earnings is $644, therefore
200 + 12x = 644

To find x, do the following:
Subtract 200 from each side.
12x = 644 - 200 = 444
Divide each side by 12.
x = 444/12 = 37

Answer:
The equation is 12x + 200 = 644.
The solution for x (number of albums sold) is 37.

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3 years ago