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adelina 88 [10]
3 years ago
9

Spartan Stadium at San Jose State University in California has a seating capacity of about 30,000. A newspaper article states th

at the Spartans get four times as many tickets as the visiting team. Suppose S represents the number of tickets for the Spartans and V represents the number of tickets for the visiting team’s fans. Which system could be used by a newspaper reader to determine how many tickets each team gets? a. 4S + 4V = 30,000 S = 4V c. S + V = 30,000 V - 4S = 0 b. S - 4V = 0 S + V = 30,000
Mathematics
1 answer:
torisob [31]3 years ago
7 0

The answer is the option b: b. \left \{ {{S-4V=0} \atop {S+V=30,000}} \right. \\

The explanation is shown below:

1. You have that <em>S</em> represents the number of tickets for the Spartans and <em>V</em> represents the number of tickets for the visiting team's fans, and the seating capacity of the Spartan Stadium is 30,000. Therefore, the total number of tickets is 30,0000:

S+V=30,000

2. If the Spartans get four times as many tickets as the visiting team, you have:

S=4V

S-4V=0

3. If you solve the system of equations by the method of substitution, you obtain:

S+V=30,000

4V+V=30,000

V=6,000

4. Calculate <em>S:</em>

S+6,000=30,000

S=24,000

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Answer:

(a) P(X > $57,000) = 0.0643

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Step-by-step explanation:

We are given that U.S. Bureau of Economic Statistics reports that the average annual salary in the metropolitan Boston area is $50,542.

Suppose annual salaries in the metropolitan Boston area are normally distributed with a standard deviation of $4,246.

<em>Let X = annual salaries in the metropolitan Boston area</em>

SO, X ~ Normal(\mu=$50,542,\sigma^{2} = $4,246^{2})

The z-score probability distribution for normal distribution is given by;

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

where, \mu = average annual salary in the Boston area = $50,542

            \sigma = standard deviation = $4,246

(a) Probability that the worker’s annual salary is more than $57,000 is given by = P(X > $57,000)

    P(X > $57,000) = P( \frac{X-\mu}{\sigma } > \frac{57,000-50,542}{4,246 } ) = P(Z > 1.52) = 1 - P(Z \leq 1.52)

                                                                     = 1 - 0.93574 = <u>0.0643</u>

<em>The above probability is calculated by looking at the value of x = 1.52 in the z table which gave an area of 0.93574</em>.

(b) Probability that the worker’s annual salary is less than $46,000 is given by = P(X < $46,000)

    P(X < $46,000) = P( \frac{X-\mu}{\sigma } < \frac{46,000-50,542}{4,246 } ) = P(Z < -1.07) = 1 - P(Z \leq 1.07)

                                                                     = 1 - 0.85769 = <u>0.1423</u>

<em>The above probability is calculated by looking at the value of x = 1.07 in the z table which gave an area of 0.85769</em>.

(c) Probability that the worker’s annual salary is more than $40,000 is given by = P(X > $40,000)

    P(X > $40,000) = P( \frac{X-\mu}{\sigma } > \frac{40,000-50,542}{4,246 } ) = P(Z > -2.48) = P(Z < 2.48)

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<em>The above probability is calculated by looking at the value of x = 2.48 in the z table which gave an area of 0.99343</em>.

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                                                                      = 1 - 0.90490 = 0.0951

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