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valentina_108 [34]
3 years ago
11

When Colton commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of 41 minutes and a

standard deviation of 3.5 minutes. Using the empirical rule, determine the interval that represents the middle 95% of his commute times
Mathematics
1 answer:
N76 [4]3 years ago
6 0

Answer:

(34, 48)

Step-by-step explanation:

According to the Empirical Rule, 95% of normally distributed data lie within two standard deviations of the mean.  That, in turn, means 95% of the data in this problem lie within 2(3.5 min), or 7 min, of the mean:

41 - 7 < mean < 41 + 7, or

34 < mean < 48, or simply (34, 48)

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Given the parabola below, find the endpoints of the latus rectum. (x-2)^2=-20(y+2)
Shtirlitz [24]

Answer:

The endpoints of the latus rectum are (12, -7) and (-8, -7).

Step-by-step explanation:

A parabola with vertex at point C(x, y) = (h,k) and whose axis of symmetry is parallel to the y-axis is defined by the following formula:

(x-h)^{2} = 4\cdot p \cdot (y-k) (1)

Where:

y - Independent variable.

x - Dependent variable.

p - Distance from vertex to the focus.

h, k - Coordinates of the vertex.

The coordinates of the focus are represented by:

F(x,y) = (h, k+p) (2)

The <em>latus rectum</em> is a line segment parallel to the x-axis which contains the focus. If we know that h = 2, k = -2 and p = -5, then the latus rectum is between the following endpoints:

By (2):

F(x,y) = (2, -2-5)

F(x,y) = (2,-7)

By (1):

(x-2)^{2} = -20\cdot (-7+2)

(x-2)^{2} = 100

x - 2 = \pm 10

There are two solutions:

x_{1} = 2 + 10

x_{1} = 12

x_{2} = 2-10

x_{2} = -8

Hence, the endpoints of the latus rectum are (12, -7) and (-8, -7).

4 0
3 years ago
Count back write the difference = 11 - 3
sergey [27]

Answer:

11-3=8

Step-by-step explanation:

so your answer is going to equal 8

4 0
3 years ago
Read 2 more answers
Idek what to do, help
stepladder [879]
Distribute the 5 to the (2+y). Parenthisis always come first. after that combine the 5y and the -y. you should end up with 2-(+4y) +2. add the -2 and +2. you should be left with 4y

8 0
3 years ago
Select All That Apply .
makvit [3.9K]

Answer:

the 4th one ,hoped this help

7 0
3 years ago
Which is equivalent to (-4)3
sveticcg [70]

Answer(-6)2

Step-by-step explanation:

6 0
3 years ago
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