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Alex_Xolod [135]
3 years ago
6

Evaluating a piecewise defined function

Mathematics
1 answer:
Dafna11 [192]3 years ago
4 0

Given : if x belongs to the interval -2 ≤ x < -1, then f(x) = -2

As x = -2 belongs to the interval -2 ≤ x < -1 ⇒ f(-2) = -2

As x = -1.5 belongs to the interval -2 ≤ x < -1 ⇒ f(-1.5) = -2

Given : if x belongs to the interval 1 ≤ x < 2, then f(x) = 1

As x = 1 belongs to the interval 1 ≤ x < 2 ⇒ f(1) = 1

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You consider yourself a bit of an expert at playing rock-paper-scissors and estimate that the probability that you win any given
cestrela7 [59]

Answer:

a) 0.37

b) 0.421

c) 0.25

Step-by-step explanation:

Since the probability of winning a game is binomial (P = 0.5) the expected value for number of winning when you play 60 games is

\mu = 60*0.5 = 30

And the standard deviation:

\sigma = 60*0.5*0.5 = 15

a) the cumulative probability of winning at least 35 games is

P(X \geq 35) = 1 - P(X < 35) = 1 - 0.631 = 0.37

b)P(X < 27) = 0.421

c)P(30 \leq X \leq 40) = P(X \leq 40) - P(X \leq 30) = 0.75 - 0.5 = 0.25

7 0
3 years ago
The length of the base of a right triangle is 32 centimeters, and the height is 10 centimeters. What is the area of the triangle
Bas_tet [7]
10(32)=320, 320/2 Area=160
4 0
3 years ago
Read 2 more answers
An environmental science teacher at a high school with a large population of students wanted to estimate the proportion of stude
AnnZ [28]

Answer:

60 students

Step-by-step explanation:

The confidence interval of a proportion is given by:

p\pm z*\sqrt{\frac{p*(1-p)}{n} }

Where 'p' is the proportion of students who responded 'yes', 'z' is the z-score for a 95% confidence interval (which is known to be 1.960), and 'n' is the number of students in the sample.

If the confidence interval is from 0.584 to 0.816, then:

p=\frac{0.584+0.816}{2}=0.7 \\0.816-0.584=2*(1.96*\sqrt{\frac{p*(1-p)}{n}}) \\0.116=1.96*\sqrt{\frac{0.7*(1-0.7)}{n}}\\n=16.8966^2*(0.7*0.3)\\n=60\ students

60 students were in the sample.

8 0
3 years ago
In the diagram EF is the bisector of &lt;DEF = m &lt; D' EF.
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hii! i just wanted to say hope you're having a fantastic day and hope that things are going well (: stay strong and stay safe!

4 0
2 years ago
Simplify the following expression completely using distribution and combining like terms
LiRa [457]

\huge \boxed{\mathbb{QUESTION} \downarrow}

  • Simplify ⇨ 19m + 14 - 3 (3m + 7)

\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}

\sf \: 19 m - 14 - 3 ( 3 m + 7 )

Use the distributive property to multiply -3 by 3m+7.

\sf \: 19m-14-9m-21

Combine 19m and -9m to get 10m.

\sf \: 10m-14-21

Subtract 21 from -14 to get -35.

\boxed{\boxed{\bf \: 10m-35 }}

5 0
2 years ago
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