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1 year ago

12

Chris is standing on a cliff that is 3 feet above sea level. He dives into the water and descends to a depth 10 feet below the s

urface of the sea. On a number line, what is the distance between the two elevations?
a:7
b;8
c:13
d:14

1 answer:

grin007 [14]1 year ago

6 0

The answer is 7 I’m pretty sure

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1 point) As reported in "Runner's World" magazine, the times of the finishers in the New York City 10 km run are normally distri

BigorU [14]

Answer:

(a) E (X) = 61 and SD (X) = 9

(b) E (Z) = 0 and SD (Z) = 1

Step-by-step explanation:

The time of the finishers in the New York City 10 km run are normally distributed with a mean,<em>μ</em> = 61 minutes and a standard deviation, <em>σ</em> = 9 minutes.

(a)

The random variable <em>X</em> is defined as the finishing time for the finishers.

Then the expected value of <em>X</em> is:

<em>E </em>(<em>X</em>) = 61 minutes

The variance of the random variable <em>X</em> is:

<em>V</em> (<em>X</em>) = (9 minutes)²

Then the standard deviation of the random variable <em>X</em> is:

<em>SD</em> (<em>X</em>) = 9 minutes

(b)

The random variable <em>Z</em> is the standardized form of the random variable <em>X</em>.

It is defined as: $Z=\frac{X-\mu}{\sigma}$

Compute the expected value of <em>Z</em> as follows:

$E(Z)=E[\frac{X-\mu}{\sigma}]\\=\frac{E(X)-\mu}{\sigma}\\=\frac{61-61}{9}\\=0$

The mean of <em>Z</em> is 0.

Compute the variance of <em>Z</em> as follows:

$V(Z)=V[\frac{X-\mu}{\sigma}]\\=\frac{V(X)+V(\mu)}{\sigma^{2}}\\=\frac{V(X)}{\sigma^{2}}\\=\frac{9^{2}}{9^{2}}\\=1$

The variance of <em>Z</em> is 1.

So the standard deviation is 1.

8 0

1 year ago

Given: The coordinates of triangle PQR are P(0, 0), Q(2a, 0), and R(2b, 2c).

masha68 [24]

Answer:

The line containing the midpoints of two sides of a triangle is parallel to the third side ⇒ proved down

Step-by-step explanation:

* Lets revise the rules of the midpoint and the slope to prove the

problem

- The slope of a line whose endpoints are (x1 , y1) and (x2 , y2) is

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

- The mid-point of a line whose endpoints are (x1 , y1) and (x2 , y2) is

$(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

* Lets solve the problem

- PQR is a triangle of vertices P (0 , 0) , Q (2a , 0) , R (2b , 2c)

- Lets find the mid-poits of PQ called A

∵ Point P is (x1 , y1) and point Q is (x2 , y2)

∴ x1 = 0 , x2 = 2a and y1 = 0 , y2 = 0

∵ A is the mid-point of PQ

∴ $A=(\frac{0+2a}{2},\frac{0+0}{2})=(\frac{2a}{2},\frac{0}{2})=(a,0)$

- Lets find the mid-poits of PR which called B

∵ Point P is (x1 , y1) and point R is (x2 , y2)

∴ x1 = 0 , x2 = 2b and y1 = 0 , y2 = 2c

∵ B is the mid-point of PR

∴ $B=(\frac{0+2b}{2},\frac{0+2c}{2})=(\frac{2b}{2},\frac{2c}{2})=(b,c)$

- The parallel line have equal slopes, so lets find the slopes of AB and

QR to prove that they have same slopes then they are parallel

# Slope of AB

∵ Point A is (x1 , y1) and point B is (x2 , y2)

∵ Point A = (a , 0) and point B = (b , c)

∴ x1 = a , x2 = b and y1 = 0 and y2 = c

∴ The slope of AB is $m=\frac{c-0}{b-a}=\frac{c}{b-a}$

# Slope of QR

∵ Point Q is (x1 , y1) and point R is (x2 , y2)

∵ Point Q = (2a , 0) and point R = (2b , 2c)

∴ x1 = 2a , x2 = 2b and y1 = 0 and y2 = 2c

∴ The slope of AB is $m=\frac{2c-0}{2b-2a}=\frac{2c}{2(b-c)}=\frac{c}{b-a}$

∵ The slopes of AB and QR are equal

∴ AB // QR

∵ AB is the line containing the midpoints of PQ and PR of Δ PQR

∵ QR is the third side of the triangle

∴ The line containing the midpoints of two sides of a triangle is parallel

to the third side

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Sam is designing a fence post for his yard. He will need to construct a perpendicular line through the point above the line to m

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Answer:

Step-by-step explanation:

D is correct. The idea here is to ensure that the point on the post is equidistant from the bottom of the post (where it meets the ground), which in turn ensures that the angle between ground and post is 90° in at least two places on the ground.

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Olivia has a box of 20 colored tiles. There are four types of colors including black, green, white, and yellow. There are 8 blac

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Answer:

SHE CAN EXPECT TO PICK A GREEN TILE ABOUT A 197 TIMES

Step-by-step explanation:

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A table titled Text messages sent has entries 7, 100, 1, 3, 17, 10, 15, 12, 7, 38. What is the mean of this sample, which consis

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Answer:

Step-by-step explanation:

7+100+1+3+7+10+15+12+17+38/10

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