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3 years ago

PLZ HELP ITS DUE TODAY

Mathematics

1 answer:

Nady [450]3 years ago

8 0

9514 1404 393

Answer:

x = {-0.44, 1.69}

Step-by-step explanation:

Multiply by the denominator to eliminate the fraction.

3 = x(4x -5)

4x^2 -5x -3 = 0 . . . . . subtract 3 and put in standard form

Using the quadratic formula with a=4, b=-5, c=-3, we have the solutions as ...

$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(-5)\pm\sqrt{(-5)^2-4(4)(-3)}}{2(4)}\\\\x=\dfrac{5\pm\sqrt{73}}{8}\approx \{-0.443, 1.693\}$

Solutions rounded to hundredths are ...

x = -0.44

x = 1.69

_____

A graphing calculator can show the x-intercepts easily, so it works well to write the equation in the form

f(x) = 0

3/(4x -5) -x = 0

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Read 2 more answers

An orange juice producer buys oranges from a large orange grove that has one variety of orange. The amount of juice squeezed fro

skad [1K]

Answer:

The probability is 70% that the sample mean amount of juice will be contained between 4.9168 ounces and 5.0832 ounces.

Step-by-step explanation:

To solve this question, the Normal probability distribution and the Central Limit Theorem are important.

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 5, \sigma = 0.4, n = 25, s = \frac{0.4}{\sqrt{25}} = 0.08$

The probability is 70% that the sample mean amount of juice will be contained between what two values symmetrically distributed around the population mean?

The lower end of this interval is the value of X when Z has a pvalue of 0.5 - 0.7/2 = 0.15

The upper end of this interval is the value of X when Z has a pvalue of 0.5 + 0.7/2 = 0.85

Lower end

X when Z has a pvalue of 0.15. So X when $Z = -1.04$ .