How many different ways can Kevin set the switches

The demand for a daily newspaper at a newsstand at a busy intersection is known to be normally distributed with a mean of 150 an

AURORKA [14]

Answer:

171 newspapers.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 150, \sigma = 25$

How many newspapers should the newsstand operator order to ensure that he runs short on no more than 20% of days

The number of newspapers must be on the 100-20 = 80th percentile. So this value if X when Z has a pvalue of 0.8. So X when Z = 0.84.

$Z = \frac{X - \mu}{\sigma}$

$0.84 = \frac{X - 150}{25}$

$X - 150 = 0.84*25$

$X = 171$

So 171 newspapers.

4 0

3 years ago

Can any kind soul help me please

bezimeni [28]

Answer:

p-q= -4

p=q-4

x^2 + px + q=0

=> x^2 + (q-4)x + q = 0

d= b^2-4ac

=(q-4)^2 - 4(1)(q)

= q^2 + 16 -8q - 4q

=q^2 -12q+16

given that D=16

q^2 -12q+16 = 16

=> q^2 -12q = 0

=> q^2 = 12q

=> q = 12q/q

=> q= 12

Therefore the value of q is 12 and the value of p is q-4 = 12-4= 8

Hope you understood............

6 0

3 years ago

Rework problem 35 from the Chapter 2 review exercises in your text, involving auditioning for a play. For this problem, assume 9

sweet-ann [11.9K]

Answer: 1) 6300 ways

2) 2520 ways

3) 0.067

Step-by-step explanation:

For this problem, assume 9 males audition, one of them being Winston, 5 females audition, one of them being Julia, and 6 children audition. The casting director has 3 male roles available, 1 female role available, and 2 child roles available.

How many different ways can these roles be filled from these auditioners?

Available: 9M and 5F and 6C

Cast: 3M and 1F and 2C

As it is not ordered: C₉,₃ * C₅,₁ * C₆,₂

C₉,₃ = 9!/3!.6! = 84

C₅,₁ = 5!/1!.4! = 5

C₆,₂ = 6!/2!.4! = 15

C₉,₃ * C₅,₁ * C₆,₂ = 84.5.15 = 6300

How many different ways can these roles be filled if exactly one of Winston and Julia gets a part?

2 options Winston gets or Julia gets it:

1) Winston gets it but Julia no:

8 male for 2 spots

4 females for 1 spot

6 children for 2 spots

C₈,₂ * C₄,₁ * C₆,₂

C₈,₂ = = 8!/2!.6! = 28

C₄,₁ = 4!/1!.3! = 4

C₆,₂ = 6!/2!.4! = 15

C₈,₂ * C₄,₁ * C₆,₂ = 28.4.15 = 1680

2) Julia gets it but Winston does not

8 male for 3 spots

1 female for 1 spot

6 children for 2 spots

C₈,₃ * C₆,₂

C₈,₃ = 8!/3!.5! = 56

C₆,₂ = 6!/2!.4! = 15

C₉,₃ * C₆,₂ = 56.15 = 840

1) or 2) = 1) + 2) = 1680 + 840 = 2520

What is the probability (if the roles are filled at random) of both Winston and Julia getting a part?

8 male for 2 spots

1 female for 1 spot

6 children for 2 spots

C₈,₂ * C₆,₂

C₈,₂ = = 8!/2!.6! = 28

C₆,₂ = 6!/2!.4! = 15

C₈,₂ * C₆,₂ = 28.15 = 420

p = 420/6300 = 0.067

6 0

3 years ago

Write 4–6 sentences explaining why it is important to have precise definitions in mathematics.

dimaraw [331]

Mathematics can be tricky so precise definitions are important. Without them there can be confusion which more often then not will generate a wrong answer. With clear precise definitions it is easier to understand the topic. Therefore, it is easier to get the correct answer.

4 0

4 years ago

David has 16 skate wheels, which he is putting on 4 boards to go with the 3 boards he has. How many boards does he have altogeth

Aleksandr-060686 [28]

He has a total of 7 Boards. he has 3 boards of his own and then you add the 4 additional boards that he has

4 0

3 years ago