What ratio is equivalent to 2:1

The graph below shows two polynomial functions, f(x) and g(x):

UNO [17]

With the f(x) = x^2 - 2x + 1 there is an even degree polynomial as the highest degree here is 2 and there is a positive leading coefficient as the coefficient for the highest degree is considered to be 1. Therefore all statements for f(x) is false.

With g(x) = x^3 +1 there is an odd degree polynomial as x is raised to 3 and there is a positive leading coefficient as x^3 is multiplied to 1. Therefore only the fourth statement holds to be true

6 0

3 years ago

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Please help Convert 82% to a fraction. Show your work.

aleksklad [387]

82 percent turns into 82/100

That then becomes 41/50 when simplified

Answer = 41/50

6 0

3 years ago

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Suppose an article reported that 16% of unmarried couples in the United States are mixed racially or ethnically. Consider the po

makkiz [27]

Answer:

39.36% probability that the proportion of couples in the sample who are racially or ethnically mixed will be greater than 0.17.

Step-by-step explanation:

For each couple, there are only two possible outcomes. Either they are mixed racially or ethnically, or they are not. This means that the binomial probability distribution is used to solve this problem.

However, we are working with samples that are considerably big. So i am going to aproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$n = 100, p = 0.16$

So

$E(X) = 100*0.16 = 16$

$\sqrt{Var(X)} = \sqrt{100*0.16*0.84} = 3.67$

When n = 100, what is the probability that the proportion of couples in the sample who are racially or ethnically mixed will be greater than 0.17?

This is 1 subtracted by the pvalue of Z when $X = 100*0.17 = 17$ . So:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{17 - 16}{3.67}$

$Z = 0.27$

$Z = 0.27$ has a pvalue of 0.6064.

So there is a 1-0.6064 = 0.3936 = 39.36% probability that the proportion of couples in the sample who are racially or ethnically mixed will be greater than 0.17.

4 0

3 years ago

What polynomial expressions equal 8x^3+64?

Natali5045456 [20]

Answer:

$\displaystyle \boxed{8[x + 2][x^2 - 2x + 4]}$

Step-by-step explanation:

Use the Difference of Cubes [(a³ - b³)(a² + 2ab + b²)] to figure this out:

$\displaystyle 8x^3 + 64 \\ 8[x^3 + 8] \\ \\ x + 2 = \sqrt[3]{x^3 + 8}$

Then, since the divisor\factor is in the form of x - c, use what is called Synthetic Division. Remember, in this formula, −c gives you the OPPOSITE terms of what they really are, so do not forget it. Anyway, here is how it is done:

−2| 1 0 0 8

↓ −2 4 −8

___________

1 −2 4 0 → ${x}^{2} - 2x + 4$

You start by placing the c in the top left corner, then list all the coefficients of your dividend [x³ + 8]. You bring down the original term closest to c then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have no remainder. Finally, your quotient is one degree less than your dividend, so that 1 in your quotient can be an x², the −2x follows right behind it, then 4, giving you the other factor of $x^2 - 2x + 4$ , attaching this to the first two factors you started out your work on:

$\displaystyle \boxed{8[x + 2][x^2 - 2x + 4]}$

I am joyous to assist you anytime.

6 0

4 years ago

How do i put -8-3x=y in slope intercept form?

masha68 [24]

Slope intercept form : y = mx + b

-8-3x=y
y = -3x - 8

Answer would the be : y = -3x - 8

6 0

3 years ago