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Ray Of Light [21]
2 years ago
5

) Final averages are typically normally distributed with a mean of 72 and a standard deviation of 12.5. Your professor states th

at the top 8% of the class will receive an A; the next 20% will receive a B; the next 42% will receive a C; the next 18% will receive a D; and the bottom 12% will receive an F. What grade must you exceed in order to receive a grade of C or better
Mathematics
1 answer:
Bad White [126]2 years ago
6 0

Answer:

65.45

Step-by-step explanation:

Zscore = (x - mean) / standard deviation

x = score

Percentage below C :

D = 18% ; F = 12%

Sum = 30%

Obtain the Zscore for the proportion below D

P(Z < 0.30) = -0.524

Hence, Zscore = -0.524

Put Zscore = -0.524 in the equation :

-0.524 = (x - 72) / 12.5

-0.524 * 12.5 = x - 72

-6.55 = x - 72

-6.55 + 72 = x

x = 65.45

To receive a grade of C or better, score must be atleast 65.45

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Find the shortest distance, d, from the point (5, 0, −6) to the plane x + y + z = 6.
DENIUS [597]

Answer:

\frac{7}{\sqrt{3}}

Step-by-step explanation:

The shortest distance d, of a point (a, b, c) from a plane mx + ny + tz = r is given by:

d = |\frac{(ma + nb + tc - r)}{\sqrt{m^2 + n^2 + t^2}} |                   --------------------(i)

From the question,

the point is (5, 0, -6)

the plane is x + y + z = 6

Therefore,

a = 5

b = 0

c = -6

m = 1

n = 1

t = 1

r = 6

Substitute these values into equation (i) as follows;

d = |\frac{((1*5) + (1*0) + (1 * (-6)) - 6)}{\sqrt{1^2 + 1^2 + 1^2}} |

d = |\frac{((5) + (0) + (-6) - 6)}{\sqrt{1 + 1 + 1}} |

d = |\frac{(-7)}{\sqrt{3}} |

d = \frac{7}{\sqrt{3}}

Therefore, the shortest distance from the point to the plane is  d = \frac{7}{\sqrt{3}}

5 0
3 years ago
What is trometry? helpp plz
SVEN [57.7K]

it is the measurement of the positions, motions, and magnitudes of stars.

7 0
3 years ago
X x 2 divided by 4 equals
fiasKO [112]

Answer:

I think it's 2x/4 (1x/2 if simplified). if it's multiple choice that's what I'd go with and if that answer is wrong then sorry

Step-by-step explanation:

x•2 is 2x because you don't know the value x and you still have to divide by four. when simplified, 2/4 is 1/2 so it'd be 1x/2

8 0
3 years ago
The data shown in the table below can be
kvv77 [185]

Answer:

6: 12

7: 14

8: 16

Step-by-step explanation:

You do the last (y) term given [18] minus the first (y) term [10] given divided by how many terms it takes to get from the last (y) term given minus the first (y) term given [4]. So the equation looks like this:

(18 - 10)/4= 8/4 = 2

4 0
3 years ago
Find the standard form of the equation for the conic section represented by x^2 + 10x + 6y = 47.
Levart [38]

Answer:

The standard form of the equation for the conic section represented by x^2\:+\:10x\:+\:6y\:=\:47 is:

4\left(-\frac{3}{2}\right)\left(y-12\right)=\left(x-\left(-5\right)\right)^2

Step-by-step explanation:

We know that:

4p\left(y-k\right)=\left(x-h\right)^2 is the standard equation for an up-down facing Parabola with vertex at (h, k), and focal length |p|.

Given the equation

x^2\:+\:10x\:+\:6y\:=\:47

Rewriting the equation in the standard form

4\left(-\frac{3}{2}\right)\left(y-12\right)=\left(x-\left(-5\right)\right)^2

Thus,

The vertex (h, k) = (-5, 12)

Please also check the attached graph.

Therefore, the standard form of the equation for the conic section represented by x^2\:+\:10x\:+\:6y\:=\:47 is:

4\left(-\frac{3}{2}\right)\left(y-12\right)=\left(x-\left(-5\right)\right)^2

where

vertex (h, k) = (-5, 12)

7 0
2 years ago
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