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mixas84 [53]
3 years ago
15

Steph,andra,emily,and becca are planning a road trip from their hometown to san antonio

Mathematics
1 answer:
morpeh [17]3 years ago
7 0

Answer:

a. Emily should begin her turn as the third driver at point (1, -0.5).

b. Emily's turn to drive end at point (-2.5, -3.75).

Step-by-step explanation:

Let assume that the group of girls travels from their hometown to San Antonio in a straight line. We know that each location is, respectively:

Hometown

H(x,y) = (8,6)

San Antonio

T(x,y) = (-6,-7)

Then, we can determine the end of each girl's turn to drive by the following vectorial expression based on the vectorial equation of the line:

Steph

S(x,y) = H(x,y) + \frac{1}{4}\cdot [T(x,y)-H(x,y)] (1)

S(x,y) = (8,6) + \frac{1}{4}\cdot [(-6,-7)-(8,6)]

S(x,y) = (8,6) +\frac{1}{4}\cdot (-14,-13)

S(x,y) = (4.5,2.75)

Andra

A(x,y) = H(x,y) + \frac{2}{4}\cdot [T(x,y)-H(x,y)] (2)

A(x,y) = (8,6) + \frac{2}{4}\cdot [(-6,-7)-(8,6)]

A(x,y) = (8,6)+\frac{2}{4}\cdot (-14,-13)

A(x,y) =(1, -0.5)

Emily

E(x,y) = H(x,y) + \frac{3}{4}\cdot [T(x,y)-H(x,y)] (3)

E(x,y) = (8,6) + \frac{3}{4}\cdot [(-6,-7)-(8,6)]

E(x,y) = (8,6)+\frac{3}{4}\cdot (-14,-13)

E(x,y) = (-2.5, -3.75)

a. <em>If the girls take turns driving and each girl drives the same distance, at what point should they stop from Emily to begin her turn as the third driver? </em>

Emily's beginning point is the Andra's stop point, that is, A(x,y) =(1, -0.5).

Emily should begin her turn as the third driver at point (1, -0.5).

b. <em>At what point does Emily's turn to drive end?</em>

Emily's turn to drive end at point (-2.5, -3.75).

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a) Mean of X = 0.40

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Step-by-step explanation:

a) The probability that play is successful is 0.40. Hence, the probability that play isn't successful is then 1 - 0.40 = 0.60.

Random variable X represents when play is successful or not, X = 1 when play is successful and X = 0 when play isn't successful.

The probability mass function of X is then

X | Probability of X

0 | 0.60

1 | 0.40

The mean is given in terms of the expected value, which is expressed as

E(X) = Σ xᵢpᵢ

xᵢ = each variable

pᵢ = probability of each variable

Mean = E(X) = (0 × 0.60) + (1 × 0.40) = 0.40

Variance = Var(X) = Σx²p − μ²

μ = mean = E(X) = 0.40

Σx²p = (0² × 0.60) + (1² × 0.40) = 0.40

Variance = Var(X) = 0.40 - 0.40² = 0.24

b) If the conversion is successful, the team scores 2 points; if not the team scores 0 points. If Y ia the number of points that team scores.Y can take on values of 2 and 0 only.

A Bernoulli distribution is a discrete distribution with only two possible outcomes in which success occurs with probability of p and failure occurs with probability of (1 - p).

Since the probability of a successful conversion and subsequent 2 points is 0.40 and the probability of failure and subsequent 0 point is 0.60, it is evident that Y is a Bernoulli's distribution.

The probability mass function for Y is then

Y | Probability of Y

0 | 0.60

2 | 0.40

c) Mean and Variance of Y

Mean = E(Y)

E(Y) = Σ yᵢpᵢ

yᵢ = each variable

pᵢ = probability of each variable

E(Y) = (0 × 0.60) + (2 × 0.40) = 0.80 points

Variance = Var(Y) = Σy²p − μ²

μ = mean = E(Y) = 0.80

Σy²p = (0² × 0.60) + (2² × 0.40) = 1.60

Variance = Var(Y) = 1.60 - 0.80² = 0.96

Hope this Helps!!!

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