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3 years ago

..............................answer

Mathematics

2 answers:

LenKa [72]3 years ago

8 0

Answer: I think B

Step-by-step explanation:

Grace [21]3 years ago

6 0

Answer:

*****************the answer is B************************

Step-by-step explanation:

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in the unted states, the height of men are normally distributed with the mean 69 inches and standard deviation 2.8 inches. If 16

yaroslaw [1]

Answer:

Probability that their mean height is less than 68 inches is 0.0764.

Step-by-step explanation:

We are given that in the united states, the height of men are normally distributed with the mean 69 inches and standard deviation 2.8 inches.

Also, 16 men are randomly selected.

<em>Let </em> $\bar X$ <em> = sample mean height</em>

The z-score probability distribution for sample mean is given by;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean height = 69 inches

$\sigma$ = population standard deviation = 2.8 inches

n = sample of men = 16

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

So, probability that the mean height of 16 randomly selected men is less than 68 inches is given by = P( $\bar X$ < 68 inches)

P( $\bar X$ < 68 inches) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{68-69}{\frac{2.8}{\sqrt{16} } }$ ) = P(Z < -1.43) = 1 - P(Z $\leq$ 1.43)

= 1 - 0.9236 = 0.0764

<em>Now, in the z table the P(Z x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.43 in the z table which has an area of 0.92364.</em>

Therefore, probability that their mean height is less than 68 inches is 0.0764.

3 0

4 years ago

CONSTRUCTION You are asked to copy a segment CD, construct a segment bisector by paper folding, and label the

lilavasa [31]

The steps on the construction of a segment bisector by paper folding, and label the midpoint M is given below.

<h3>What are the steps of this construction?</h3>

1. First, one need to open a Compass so that it is said to be more than half the length of the said segment.

2. Without altering it, with the aid of the compass, do draw an art above and also below the said line segment from one of the segment endpoints.

3. Also without altering it and with use the compass, do draw another pair of arts from the other and points. One arc will be seen above the segment and the other or the second arc will be seen below.

4. Then do draw the point of intersection that is said to exist between the pair of arts below the line segment and also in-between the pair of arts as seen below the line segment

5. Lastly, do make use of a straight edge to link the intersection points between the both pair of arts.

Learn more about segment bisector from

brainly.com/question/24736149

#SPJ1

5 0

2 years ago

Find the value of d.<br> 1/2d - 5 -1/4d = 10

Ksenya-84 [330]

D=60. multiply both sides of the equation by 4 since it’s a factor, giving you 2d-20-d=40. since there are like terms with d, collect them to get d-20=40 and move 20 to the right and change it’s sign. that will give you d=40+20, then calculate to get d=60. hope this helped! :)

6 0

3 years ago

Caleb earns points on his credit card that he can use towards future purchases. He earns four points per dollar spent on flights

Doss [256]

Given:
Flights: 4 points per dollar
Hotels: 2 points per dollar
Other: 1 point per dollar.
Total spent = $9,480
Points earned = 14,660

Let
x = money spent on flights
y = money spent on hotels
z = money spent on other purchases.

Because the money spent on flights was $140 more than twice the money spent on hotels, therefore
x = 2y + 140 (1)

Total charges were $9,480, therefore
x + y + z = 9480 (2)

Total points earned was 14,660. Therefore
4x + 2y + z = 14660 (3)

Subtract (2) from (3).
4x + 2y + z - (x + y + z) = 14660 - 9480
3x + y = 5180 (4)
Substitute (1) into (4).
3(2y + 140) + y = 5180
7y + 420 = 5180
7y = 4760
y = 680
From (1), obtain
x = 2y + 140 = 2*680 + 140 = 1500
From (2), obtain
z = 9480 - (x + y) = 9480 - (1500 + 680) = 7300

Answer:
$1,500 was spent on flights,
$680 was spent on hotels,
$7,300 was spent on other purchases.

8 0

4 years ago

Prove that dx/x^4 +4=π/8

insens350 [35]

$\displaystyle\int_0^\infty\frac{\mathrm dx}{x^4+4}$

Consider the complex-valued function

$f(z)=\dfrac1{z^4+4}$

which has simple poles at each of the fourth roots of -4. If $\omega^4=-4$ , then

$\omega^4=4e^{i\pi}\implies\omega=\sqrt2e^{i(\pi+2\pi k)/4}$ where $k=0,1,2,3$

Now consider a semicircular contour centered at the origin with radius $R$ , where the diameter is affixed to the real axis. Let $C$ denote the perimeter of the contour, with $\gamma_R$ denoting the semicircular part of the contour and $\gamma$ denoting the part of the contour that lies in the real axis.

$\displaystyle\int_Cf(z)\,\mathrm dz=\left\{\int_{\gamma_R}+\int_\gamma\right\}f(z)\,\mathrm dz$

and we'll be considering what happens as $R\to\infty$ . Clearly, the latter integral will be correspond exactly to the integral of $\dfrac1{x^4+4}$ over the entire real line. Meanwhile, taking $z=Re^{it}$ , we have

$\displaystyle\left|\int_{\gamma_R}\frac{\mathrm dz}{z^4+4}\right|=\left|\int_0^{2\pi}\frac{iRe^{it}}{R^4e^{4it}+4}\,\mathrm dt\right|\le\frac{2\pi R}{R^4+4}$

and as $R\to\infty$ , we see that the above integral must approach 0.

Now, by the residue theorem, the value of the contour integral over the entirety of $C$ is given by $2\pi i$ times the sum of the residues at the poles within the region; in this case, there are only two simple poles to consider when $k=0,1$ .

$\mathrm{Res}\left(f(z),\sqrt2e^{i\pi/4}\right)=\displaystyle\lim_{z\to\sqrt2e^{i\pi/4}}f(z)(z-\sqrt2e^{i\pi/4})=-\frac1{16}(1+i)$
$\mathrm{Res}\left(f(z),\sqrt2e^{i3\pi/4}\right)=\displaystyle\lim_{z\to\sqrt2e^{i3\pi/4}}f(z)(z-\sqrt2e^{i3\pi/4})=\dfrac1{16}(1-i)$

So we have

$\displaystyle\int_Cf(z)\,\mathrm dz=\int_{\gamma_R}f(z)\,\mathrm dz+\int_\gamma f(z)\,\mathrm dz$
$\displaystyle=0+2\pi i\sum_{z=z_k}\mathrm{Res}(f(z),z_k)$ (where $z_k$ are the poles surrounded by $C$ )
$=2\pi i\left(-\dfrac1{16}(1+i)+\dfrac1{16}(1-i)\right)$
$=\dfrac\pi4$

Presumably, we wanted to show that

$\displaystyle\int_0^\infty\frac{\mathrm dx}{x^4+4}=\frac\pi8$

This integrand is even, so

$\displaystyle\int_0^\infty\frac{\mathrm dx}{x^4+4}=\frac12\int_{-\infty}^\infty\frac{\mathrm dx}{x^4+4}=\frac12\frac\pi4=\frac\pi8$

as required.

6 0

4 years ago