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1 year ago

Rounded 6,289,002 to the nearest 1,000,000

1 answer:

8 0

<span>6,289,002 rounded to the nearest 1,000,000 is 6,000,000. This is because the number in the hundred thousands column, the one to the right of the first digit, is less than five, so it gets rounded down.</span>

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∆ABC and ∆PQR are similar. ∆ABC is dilated by a scale factor of 1.25 and rotated 45° counterclockwise about point B to form ∆PQR

Andrej [43]

This is the concept of transformation of figures, given that ΔABC is similar to ΔPQR, the sides of ABC are 5 units, 4.2 units and 4 units. Since the two triangles are similar and PQR is the image of ABC under the dilation 1.25, the sides of PQR will be:
(5*1.25),(4.2*1.25),(4*1.25)
this will give us:
6.25, 5.25, 5
The length of the sides of PQR are 6.25 units, 5.25 units and 5 units

7 0

1 year ago

A bank gets an average of 12 customers per hour. Assume the variable follows a Poisson distribution. Find the probability that t

Alina [70]

Answer:

75.76% probability that there will be 10 or more customers at this bank in one hour.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

A bank gets an average of 12 customers per hour.

This means that $\mu = 12$

Find the probability that there will be 10 or more customers at this bank in one hour.

Either there are less than 10 customers, or there are 10 or more. The sum of the probabilities of these events is 1. Then

$P(X < 10) + P(X \geq 10) = 1$

We want $P(X \geq 10)$

Then

$P(X \geq 10) = 1 - P(X < 10)$

In which

$P(X < 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)$

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-12}*12^{0}}{(0)!} \approx 0$

$P(X = 1) = \frac{e^{-12}*12^{1}}{(1)!} = 0.0001$

$P(X = 2) = \frac{e^{-12}*12^{2}}{(2)!} = 0.0004$

$P(X = 3) = \frac{e^{-12}*12^{3}}{(3)!} = 0.0018$

$P(X = 4) = \frac{e^{-12}*12^{4}}{(4)!} = 0.0053$

$P(X = 5) = \frac{e^{-12}*12^{5}}{(5)!} = 0.0127$

$P(X = 6) = \frac{e^{-12}*12^{6}}{(6)!} = 0.0255$

$P(X = 7) = \frac{e^{-12}*12^{7}}{(7)!} = 0.0437$

$P(X = 8) = \frac{e^{-12}*12^{8}}{(8)!} = 0.0655$

$P(X = 9) = \frac{e^{-12}*12^{9}}{(9)!} = 0.0874$

$P(X < 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) = 0 + 0.0001 + 0.0004 + 0.0018 + 0.0053 + 0.0127 + 0.0255 + 0.0437 + 0.0655 + 0.0874 = 0.2424$

Then

$P(X \geq 10) = 1 - P(X < 10) = 1 - 0.2424 = 0.7576$

75.76% probability that there will be 10 or more customers at this bank in one hour.

3 0

2 years ago

A clock gains 4 minutes every hour. One day it is set to the correct time, 9:00 AM. What is the correct time when the clock show

Serhud [2]

First we have to figure out how many hours have passed. Since 1PM also means 1300 hours, we'll subtract 9 from 13. 13-9=4. therefore, 4 hours have passed. if it gains 4 minutes every hour, we'll multiply the amount of hours that have passed by the amount the clock gains every hour. 4x4=16. now we subtract 16 from 1300 because the clock is ahead of the real time, but remember and hour only has 60 minutes! 1300-16=1244. Therefore, the correct time is 12:44PM.

4 0

1 year ago

A circus ring is the arena where much of the action takes place at a circus. The figure below shows a circus ring with the cente

Goshia [24]

Answer:

Step-by-step explanation:

a) A diameter is a line that cuts a circle through at the centre. Line AD is a diameter.

Radius is half of a diameter i.e AD/2 = AO or OD

Chord is a straight line that touches the circumference of a circle. It doesn't pass through the centre like the diameter but cuts through the segments of a circle. Example of a chord is line FH

A tangent is a line that touches the circumference of a circle at just a point. It can touch any point on the circle. Example of a tangent line are AB and DE.

b) We must know that angle at a point or in a circle is 360°.

<EOH + <ECH = 360°

If <EOH = 131°

<ECH = 360° - 131°

<ECH = 229°

- <EFH falls in the circumference of the circle. Also know that, angle at the centre of a circle is twice angle at the circumference. Since <EOH is at the centre of the circle. <EFH = <EOH/2

<EFH = 131/2

<EFH = 65.5°

c) Given AB = DE, then <AB = <DE (oppositely directed angle).

Given <AOB = 20° then <DE = 20°

d) According to the diagram, <GFD = <GLD

If <GFD = 126°, then <GLD = 126°

e) Given HK = x+4, FK = x+14, GK = x, CK = x+32

From the diagram, CG = CK + KG

CG = x+32+x

CG = 2x+32

Also, FH = FK+HK

FH = x+14+x+4

FH = 2x+18

4 0

1 year ago

The probability that Evan purchases a comic book from the bookstore (event A) is 0.67, and the probability that Glen purchases a

Sveta_85 [38]

The question is asking to choose among the following choices that states the statement that is true about the said information and base on the given data, I would say the answer among them is <span>Events A and B are dependent because P(A and B) do not equal P(A) x P(B). I hope you are satisfied with my answer and feel free to ask for more</span>

7 0

2 years ago

Read 2 more answers