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Mathematics

1 answer:

Eva8 [605]3 years ago

7 0

i hope my answer help you

1st=5x-100

2nd=1/3x-7

3rd=x²×4

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According to records, the amount of precipitation in a certain city on a November day has a mean of 0.10 inches; with a standard

Alecsey [184]

Answer:

Probability that the mean daily precipitation will be 0.09 inches or less for a random sample of 40 November days is 0.103.

Step-by-step explanation:

We are given that according to records, the amount of precipitation in a certain city on a November day has a mean of 0.10 inches; with a standard deviation of 0.05 inches.

A random sample of 40 November days is taken(taken over many years).

Let $\bar X$ = sample mean daily precipitation

The z score probability distribution for sample mean is given by;

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

where, $\mu$ = population mean = 0.10 inches

$\sigma$ = population standard deviation = 0.05 inches

n = sample of days = 40

Now, the probability that the mean daily precipitation will be 0.09 inches or less is given by = P( $\bar X$ $\leq$ 0.09 inches)

P( $\bar X$ $\leq$ 0.09 inches) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ $\leq$ $\frac{0.09-0.10}{\frac{0.05}{\sqrt{40} } }$ ) = P(Z $\leq$ -1.265) = 1 - P(Z < 1.265)

= 1 - 0.8971 = 0.1029

The above probability is calculated by looking at the value of x = 1.265 from the z table which will lie between x = 1.26 and x = 1.27 which has an area of 0.89617 and 0.89796 respectively.

Hence, the probability that the mean daily precipitation will be 0.09 inches or less for a random sample of 40 November days is 0.103.

8 0

3 years ago

The functions f(x) = (x + 1)2 - 5 and g(x) = -(x - 2)2 + 3 have been rewritten using the completing-the-square method. What is t

emmasim [6.3K]

f(x) has vertex = (- 1, - 5 ) and is a minimum

g(x) has vertex = (2, 3 ) and is a maximum

the equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

f(x) = (x + 1)² - 5 is in this form with vertex = (- 1, - 5 ) and minimum

to determine if maximum/ minimum