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goblinko [34]
2 years ago
11

___________probabilities

Mathematics
1 answer:
taurus [48]2 years ago
6 0

Answer:

Determined

Step-by-step explanation:

Determined

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Find a second-degree polynomial (that is, an equation of the form y =a + bx + cx2 d that goes through the three points (0, 1), (
Lostsunrise [7]

Answer:

y = 1 - x^2

Step-by-step explanation:

we're given three points (0,1),(1,0) and (-1,0). and and equation of a parabola

y = a + bx + cx^2

we can plug in each of the coordinates, and 3 equations

(x,y) = (0,1)

1 = a + b(0) + c(0)^2

a=1\quad\quad\Rightarrow A

(x,y) = (1,0)

0 = a + b(1) + c(1)^2

a + b + c=0\quad\quad\Rightarrow B

(x,y) = (-1,0)

0 = a + b(-1) + c(-1)^2

a - b + c=0\quad\quad\Rightarrow C

These are are three equations, well we can simultaneously solve them to find the values of a, b and c.

we already found that, a = 1. so we plug this value in the rest of the equations. we'll use equation B.

a + b + c=0

1 + b + c=0

b=-1-c

we can substitute this value of b and a = 1, equation C

a - b + c=0

1 -(-1-c) + c=0

1 +1+c + c=0

2+2c=0

c=-1

we can use this value of c back in b

b=-1-(-1)

b=0

hence our equation of the 2-degree polynomial will be:

y = a + bx + cx^2

y = 1 + (0)x + (-1)x^2

y = 1 - x^2

and this polynomial indeed passes through all the points (0, 1), (1, 0), and (-1, 0).

And since these are the only solutions to the simultaneous equation we solved (i.e. we have single values of a,b and c). there's no other possibility.

8 0
3 years ago
A circus performer walks on a tightrope 25 feet above the ground. The tightrope is supported by two beams and two support cables
miv72 [106K]
The length of the support cable is about 29 feet.

If you sketch out the question, you will see that it will form a right triangle with the cable as the hypotenuse.

Just set up and use the Pythagorean Theorem.

15^2 + 25^2 = c^2
850 = c^2
29.15 = c
5 0
3 years ago
3/2 times 2/3 in the simplest form
Lostsunrise [7]

Answer:

3/2 x 2/3 = 1

Step-by-step explanation:

3 0
2 years ago
A researcher wants to estimate the percentage of all adults that have used the Internet to seek pre-purchase information in the
Lubov Fominskaja [6]

Answer:

The required sample size for the new study is 801.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

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

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

The margin of error is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

25% of all adults had used the Internet for such a purpose

This means that \pi = 0.25

95% confidence level

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

What is the required sample size for the new study?

This is n for which M = 0.03. So

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.03 = 1.96\sqrt{\frac{0.25*0.75)}{n}}

0.03\sqrt{n} = 1.96\sqrt{0.25*0.75}

\sqrt{n} = \frac{1.96\sqrt{0.25*0.75}}{0.03}

(\sqrt{n})^2 = (\frac{1.96\sqrt{0.25*0.75}}{0.03})^2

n = 800.3

Rounding up:

The required sample size for the new study is 801.

4 0
2 years ago
Please answer number 1? Thank you
Naddik [55]

Answer:

This is a normal distribution and we can use the standard score to compute for probabilities. We compute the standard score of the given.

Explnation:

z = (x - mu)/sd

z = (2625 - 2600)/50 = 25/50 = 0.5.

Consulting the z-table, P(z <= 0.5) = 0.6915.

P(z > 0.5) = 1 - P(z <= 0.5) = 1 - 0.6915 = 0.3085.

I hope this helped! <3

6 0
2 years ago
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