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kiruha [24]
3 years ago
9

The following points are rotated about the origin through 90° in clockwise direction. Find the new coordinates,

Mathematics
1 answer:
Natasha_Volkova [10]3 years ago
8 0

Answer:

C

Maybe it is B or A as the answer.

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Use the IVT to prove that one solution to <img src="https://tex.z-dn.net/?f=x%5E%7B3%7D%20%2Bx-5%3D0" id="TexFormula1" title="x^
Dafna11 [192]

Let <em>f(x)</em> = <em>x</em>³ + <em>x</em> - 5. <em>f(x)</em> is a polynomial so it's continuous everywhere on its domain (all real numbers). Since

<em>f</em> (1) = 1³ + 1 - 5 = -3 < 0

and

<em>f</em> (2) = 2³ + 2 - 5 = 5 > 0

it follows by the intermediate value theorem that there at least one number <em>x</em> = <em>c</em> between 1 and 2 for which <em>f(c)</em> = 0.

7 0
3 years ago
10|x+8| - 13 = -2|x+8|+11
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3 years ago
An airport limousine can accommodate up to four passengers on any one trip. The company will accept a maximum of six reservation
miss Akunina [59]

Answer:

a) 0.109375 = 0.109 to 3 d.p

b) 1.00 to 3 d.p

Step-by-step explanation:

Probability of someone that made a reservation not showing up = 50% = 0.5

Probability of someone that made a reservation showing up = 1 - 0.5 = 0.5

a) If six reservations are made, what is the probability that at least one individual with a reservation cannot be accommodated on the trip?

For this to happen, 5 or 6 people have to show up since the limousine can accommodate a maximum of 4 people

Let P(X=x) represent x people showing up

probability that at least one individual with a reservation cannot be accommodated on the trip = P(X = 5) + P(X = 6)

P(X = x) can be evaluated using binomial distribution formula

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = 6

x = Number of successes required = 5 or 6

p = probability of success = 0.5

q = probability of failure = 0.5

P(X = 5) = ⁶C₅ (0.5)⁵ (0.5)⁶⁻⁵ = 6(0.5)⁶ = 0.09375

P(X = 6) = ⁶C₆ (0.5)⁶ (0.5)⁶⁻⁶ = 1(0.5)⁶ = 0.015625

P(X=5) + P(X=6) = 0.09375 + 0.015625 = 0.109375

b) If six reservations are made, what is the expected number of available places when the limousine departs?

Probability of one person not showing up after reservation of a seat = 0.5

Expected number of people that do not show up = E(X) = Σ xᵢpᵢ

where xᵢ = each independent person,

pᵢ = probability of each independent person not showing up.

E(X) = 6(1×0.5) = 3

If 3 people do not show up, it means 3 people show up and the number of unoccupied seats in a 4-seater limousine = 4 - 3 = 1

So, expected number of unoccupied seats = 1

5 0
3 years ago
The total number of miles Jeremy walked on a hike can be represented by using the formula. If and n represents the total number
KatRina [158]

Answer:

A) 2 miles, 5 miles, 8 miles

Step-by-step explanation:

Let's get some details cleared.

We're interested in finding how many miles he walked at the end of each hour in a period of 3 hours.

We know what  is, so we can use that as our starting point.

Your answer is A.

7 0
3 years ago
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Find the radius of a circle given that the area is three times its circumference
lbvjy [14]

Answer:

Radius of the circle = 6 units

Step-by-step explanation:

Let the radius of the circle be r

According to the given condition:

Area of the circle = 3 times the circumference of the circle

\therefore \pi r^2 =3\times 2\pi r\\\therefore r^2 = \frac{3\times 2\pi r}{\pi}\\\therefore r^2 = 3\times 2r\\\therefore r = 6\: units\\

5 0
3 years ago
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