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Graph the solution of the inequality: 4/9x - 10 > x/3 - 12

Solnce55 [7]

We are given the inequality. Solving it,
4x/9 - 10 > x/3 - 12
4x/9 - x/3 > -12 + 10
x/9 > -2
x > -18

The graph of the solution would composed of all values greater than -18<span />

3 0

3 years ago

Read 2 more answers

Simplify <br>(sinA +cosA) (sinA-cosA)

kvv77 [185]

Answer:

-cos(2A)

Step-by-step explanation:

We know that (a+b) (a-b) = a^2-b^2

So it means we can simplify to sin^2(A)-cos^2(A) and we know cos^2(A) - sin^2(A) = cos(2A) but we will just multiply by -1 and we get - cos(2A)

5 0

3 years ago

A hot air balloon went from an elevation of 6,039 feet to an elevation of 3,288 feet in 42 minutes. What was its rate of descent

Vikki [24]

Answer:

65.5 feet per second

Step-by-step explanation:

In order to calculate the rate of descent we first need to find the difference in heigh that the hot air balloon descended. We do this by subtracting the initial height from the end height like so...

6,039 - 3,288 = 2,751 ft

Now that we have the difference in height we need to divide this by 42 since that is the amount of time it took for this descent to occur.

2,751 ft / 42s = 65.5 ft/s

Finally we can see that the rate of descent was 65.5 feet per second

8 0

3 years ago

A company manufactures a brand of lightbulb with a lifetime in months that is normally distributed with mean 3 and variance 1. A

Ratling [72]

Answer:

The smallest number of bulbs to be purchased so that the succession of bulbs produces light for at least 40 months with probability at least 0.9772 is 16.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}$

$\Delta = b^{2} - 4ac$

Normal Probability Distribution:

Problems of normal distributions 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.

n values from a normal distribution:

The mean is $\mu n$ and the standard deviation is $s = \sigma\sqrt{n}$

A company manufactures a brand of lightbulb with a lifetime in months that is normally distributed with mean 3 and variance 1.

This means that $\mu = 3, \sigma = \sqrt{1} = 1$

For n bulbs:

The distribution for the sum of n bulds has $\mu = 3n, \sigma = \sqrt{n}$

What is the smallest number of bulbs to be purchased so that the succession of bulbs produces light for at least 40 months with probability at least 0.9772?

We want that: $S_{n} \geq 40 = 0.9772$ .

This means that when X = 40, Z has a pvalue of 1 - 0.9772 = 0.0228, that is, when $X = 40, Z = -2$ . So

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

$-2 = \frac{40 - 3n}{\sqrt{n}}$

$-2\sqrt{n} = 40 - 3n$

$3n - 2\sqrt{n} - 40 = 0$

Using $y = \sqrt{n}$

$3y^2 - 2y - 40 = 0$

Which is a quadratic equation with $a = 3, b = -2, y = -40$

$\Delta = b^{2} - 4ac = (-2)^2 - 4(3)(-40) = 484$

$y_{1} = \frac{-(-2) + \sqrt{484}}{2*3} = 4$

$y_{2} = \frac{-(-2) - \sqrt{484}}{2*3} = -...$

Since y and n have both to be positive:

$y = \sqrt{n}$

$\sqrt{n} = 4$

$(\sqrt{n})^2 = 4^2$

$n = 16$

The smallest number of bulbs to be purchased so that the succession of bulbs produces light for at least 40 months with probability at least 0.9772 is 16.

4 0

3 years ago

The median number of coloring contests won by 4 kids in a certain year is 5. The range of number of contests won by those kids t

Orlov [11]

True
bcause the median number is 5

7 0

3 years ago