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3 years ago

What are the solutions to the quadratic equation 0=(x−4)(x+2)?

Mathematics

2 answers:

Lena [83]3 years ago

8 0

I agree ^ this perso is correct

Alex777 [14]3 years ago

4 0

Answer:

x = 4,

x = -2

Step-by-step explanation:

( x - 4 ) ( x + 2 ) = 0

Find out when the equation is 0,

When x = 4,

substitute in 4 for x,

( 4 - 4 ) ( 4 + 2 ) = 0

(0) ( 6) = 0 (any number multiplied by 0 is 0).

When x = -2

Substitue in -2 for x,

( -2 - 4 ) ( -2 + 2 ) = 0

(-6) (0) = 0 (again, any number multiplied by 0 is 0).

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The number of people arriving at a ballpark is random, with a Poisson distributed arrival. If the mean number of arrivals is 10,

Stella [2.4K]

Answer:

a) 3.47% probability that there will be exactly 15 arrivals.

b) 58.31% probability that there are no more than 10 arrivals.

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 time interval.

If the mean number of arrivals is 10

This means that $\mu = 10$

(a) that there will be exactly 15 arrivals?

This is P(X = 15). So

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

$P(X = 15) = \frac{e^{-10}*(10)^{15}}{(15)!} = 0.0347$

3.47% probability that there will be exactly 15 arrivals.

(b) no more than 10 arrivals?

This is $P(X \leq 10)$

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

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

$P(X = 0) = \frac{e^{-10}*(10)^{0}}{(0)!} = 0.000045$

$P(X = 1) = \frac{e^{-10}*(10)^{1}}{(1)!} = 0.00045$

$P(X = 2) = \frac{e^{-10}*(10)^{2}}{(2)!} = 0.0023$

$P(X = 3) = \frac{e^{-10}*(10)^{3}}{(3)!} = 0.0076$

$P(X = 4) = \frac{e^{-10}*(10)^{4}}{(4)!} = 0.0189$

$P(X = 5) = \frac{e^{-10}*(10)^{5}}{(5)!} = 0.0378$

$P(X = 6) = \frac{e^{-10}*(10)^{6}}{(6)!} = 0.0631$

$P(X = 7) = \frac{e^{-10}*(10)^{7}}{(7)!} = 0.0901$

$P(X = 8) = \frac{e^{-10}*(10)^{8}}{(8)!} = 0.1126$

$P(X = 9) = \frac{e^{-10}*(10)^{9}}{(9)!} = 0.1251$

$P(X = 10) = \frac{e^{-10}*(10)^{10}}{(10)!} = 0.1251$

$P(X \leq 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.000045 + 0.00045 + 0.0023 + 0.0076 + 0.0189 + 0.0378 + 0.0631 + 0.0901 + 0.1126 + 0.1251 + 0.1251 = 0.5831$

58.31% probability that there are no more than 10 arrivals.

8 0

3 years ago

What is the mean, median and mode of the following data set? Please label each response.

irinina [24]

Answer:

Mean: 21

Median: 23

Mode: 27

Step-by-step explanation:

order from least to greatest:

1, 15, 18, 22, 23, 25, 27, 27, 31

mean: add all the numbers and divide by 9 bc thats how many numbers there are so that means the answer is

Median: to find the median you order the numbers from least to greatest and find out the middle number so in that case the median is 23

Mode: to find the mode you look to see what number is repeated multiple times, so the mode is 27

8 0

4 years ago

A set of n = 15 pairs of X and Y scores has SSX = 10, SSY = 40, and SP = 30. What is the slope for the regression equation for p

Mumz [18]

Answer:

Step-by-step explanation:

We have given $SS_X=10$ , $SS_Y=40$ and SP =30

We have to find the slope for regression on Y from X

The slope on Y from X is given by $b_{yx}=\frac{SP}{SS_X}$

As we have given the value of SP =30 and value of $SS_X=10$

So slope for regression will be $b_{yx}=\frac{30}{10}=3$

3 0

3 years ago

Find the volume of a cylinder with a diameter of 6 inches and a height that is three times the radius. Use pi on your calculator

Virty [35]

ANSWER
$V=254.47in^3$

EXPLANATION

The volume of a cylinder is given by the formula:

$V=\pi \: {r}^{2} h$

The given cylinder has diameter 6. This means that, the radius is

$r = \frac{6}{2}$

$r = 3cm$

The is height is

$h = 3r$

$h = 3(3) = 9cm$

We substitute the values into the formula to obtain;

$V=\pi \: {3}^{2} \times 9$

$V=81\pi$

$V=254.46900494$

The volume is $254.47in^3$ to the nearest hundredth

7 0

3 years ago

Read 2 more answers

Car A, traveling at a constant 10 m/s, crosses the start line 3 seconds before Car B, who is traveling at a constant 15 m/s. At

Margaret [11]

The distance between Car A and car B,When Car A crosses the start line is:
distance =speed car B* time
distance=(15 m/s)(3 s)=45 m

Distance traveled by car A =x, (when the car B is at the same distance from the start line)
time of car A=t

x=10 m/st ⇒ x=10t (1)

Distance traveled by car B=x
time of car B=t-3

x=15(t-3) (2)

With the equations (1) and (2) we make a system of equations:

x=10t
x=15(t-3)

We solve this system of equations:

10t=15(t-3)
10t=15t-45
-5t=-45
t=-45 / -5
t=9

t-3=9-3=6

x=10 t=10 (9)=90

Answer: The time would be 9 seconds for Car A and 6 seconds for car B and the distance would be 90 meters.

8 0

3 years ago