<img src="https://tex.z-dn.net/?f=f%28x%29%20%3D%20%E2%88%923x2%E2%88%9211x%2B7" id="TexFormula1" title="f(x) = −3x2&minus

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Vilka [71]

2 years ago

;11x+7" alt="f(x) = −3x2−11x+7" align="absmiddle" class="latex-formula">

Mathematics

1 answer:

bixtya [17]2 years ago

4 0

Answer:

$x= \frac{ - 11 + \sqrt{205} }{6} \: \: \: \: \: or \: \: \: \: \\x = \frac{ - 11 - \sqrt{205} }{6}$

Step-by-step explanation:

$- 3x {}^{2} - 11x + 7 = 0 \\ 3x {}^{2} + 11x - 7 = 0$

here,

$a = 3 \\ b = 11 \\ c = - 7$

now,

$D = b {}^{2} - 4ac \\ = (11) {}^{2} - 4(3)( - 7) \\ = 121 + 84 \\ = 205 > 0 \\$

so,

$x = \frac{ - b + - \sqrt{b {}^{2} - 4ac} }{2a} \\ \\ = \frac{ - 11 + - \sqrt{205} }{2(3)} \\ = \frac{ - 11 + - \sqrt{205} }{6} \\ \\ = \frac{ - 11 + \sqrt{205} }{6} \: \: \: \: \: or \: \: \: \: = \frac{ - 11 - \sqrt{205} }{6}$

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What is the area of a regular 16-gon with a radius of 15 feet? Round your answer to the nearest tenth.

Sedbober [7]

Split up the 16-gon into 16 congruent isosceles triangles. Cut each of these isosceles triangles in half to get a right triangle.

The radius of the 16-gon corresponds to the hypotenuse of any of these 32 right triangles. As you probably know, the area of a triangle is half the product of its base and height. For a right triangle, the base and height can be taken to be the two legs. So you need to find their lengths.

Recall that the exterior angles of any convex polygon sum to 360º in measure. For a regular polygon, these angles are all congruent. There are 16 of them in this case, so they each have measure (360/16)º = 22.5º.

Interior angles are supplementary to exterior angles, which means each interior angle of the 16-gon has measure (180 - 22.5)º = 157.5º.

When we split up the 16-gon into isosceles triangles, the "base angles" are equal in measure to half the measure of the interior angles, since each hypotenuse bisects the interior angle. So each base angle has measure 78.75º.

In each right triangle, we then have base b and height h such that

sin(78.75º) = h/15

cos(78.75º) = b/15

Solve for h and b to get

b = 15 cos(78.75º)

h = 15 sin(78.75º)

Then the area of each right triangle is

1/2 b h = 225/2 sin(78.75º) cos(78.75º) = 225/4 sin(157.5º)

and so the area of the 16-gon is

32(1/2 b h) = 1800 sin(157.5º) ≈ 688.8 sq. ft.

4 0

3 years ago

Let X denote the number of flaws along a 100-m reel of magnetic tape (an integer-valued variable). Suppose Zdenote the number of

Lemur [1.5K]

Answer:

a) $P(20 \leq X \leq 30) = P(20-0.5 \leq X \leq 30+0.5)$

$P(19.5 \leq X \leq 30.5) = P(\frac{19.5-25}{5} \leq Z \leq \frac{30.5 -25}{5})=P(-1.1 \leq Z \leq 1.1)$

And we can find this probability like this:

$P(-1.1 \leq Z \leq 1.1)= P(Z\leq 1.1) -P(Z\leq -1.1) = 0.864-0.136= 0.728$

b) $P(X \leq 30)= P(X$

And using the z score we got:

$P(X$

c) $P(X$

And if we use the continuity correction we got:

$P(X$

Step-by-step explanation:

Previous concepts

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".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Continuity correction means that we need to add and subtract 0.5 before standardizing the value specified.

Part a

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

$X \sim N(25,5)$