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mr_godi [17]
3 years ago
15

Factor completely 3x^2− x − 4.

Mathematics
2 answers:
Mamont248 [21]3 years ago
3 0
(x+1) x (3x-4) is the answer
vichka [17]3 years ago
3 0

Answer:

( x + 1 ) ( 3 x − 4 )

Step-by-step explanation:

3x^2− x − 4

Factor − 1 out of − x .

3 x^2 − ( x ) − 4

Rewrite − 1 as 3 plus − 4

3 x^2 + ( 3 − 4 ) x − 4

Apply the distributive property.

3 x^2 + 3 x − 4 x − 4

Group the first two terms and the last two terms.

( 3 x 2 + 3 x ) − 4 x − 4

Factor out the greatest common factor (GCF) from each group.

3 x ( x + 1 ) − 4 ( x + 1 )

Factor the polynomial by factoring out the greatest common factor, x + 1 .

( x + 1 ) ( 3 x − 4 )

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Cars arrive at the Wendy's drive-through at a rate of 1 car every 5 minutes between the hours of 11:00 PM and 1:00 AM. on Saturd
mestny [16]

Answer:

1) P(X = 8) = 0.1033

P(X = 9) = 0.0688

2) Expected number of 200 restaurants in which exactly 8 customers use the drive-through: 20.66

Expected number of 200 restaurants in which exactly 9 customers use the drive-through: 13.76

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.

Question 1. Use the Poisson distribution to calculate the probability that exactly 8 cars will use the drive-through between 12:00 midnight and 12:30 AM on a Saturday night at Wendy's. Do the same for exactly 9 cars.

Cars arrive at the Wendy's drive-through at a rate of 1 car every 5 minutes between the hours of 11:00 PM and 1:00 AM. on Saturday nights. This means that during 30 minutes, 6 cars expected to arrive. So \mu = 6.

P(X = 8)

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

P(X = 8) = \frac{e^{-6}*(6)^{8}}{(8)!} = 0.1033

P(X = 9)

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

P(X = 9) = \frac{e^{-6}*(6)^{9}}{(9)!} = 0.0688

Question 2. At how many of the 200 restaurants in the survey would you expect exactly 8 customers to use the drive-through? exactly 9 customers?

There is a 10.33 probability that 8 customers would use the drive through for each restaurant.

So of 200, the expected number is

E(X) = 200*0.1033 = 20.66

There is a 6.88 probability that 9 customers would use the drive through for each restaurant.

So of 200, the expected number is

E(X) = 200*0.0688 = 13.76

8 0
3 years ago
A cafeteria used 5 gallons of milk and preparing like how many 1 quart containers of milk did the cafeteria use
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The cafeteria used 20, 1 quart containers. <span />
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3 years ago
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Also this question tooo pleease, PS: what topic is this <br> Solve for x.
MrRissso [65]

This falls under geometry. The two labeled angles are congruent, which means the line segment between them (AD in the image) is a bisector of the angle at vertex A. Use the angle bisector theorem, which says that

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8 0
3 years ago
How much Zn and how much HCl should be used to produce 1.5 g ZnCl2
tatuchka [14]

Answer:

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  • 0.80256 g of HCl

Step-by-step explanation:

The required mass of reactants can be computed from the number of moles of product.

  moles of ZnCl₂ = (1.5 g)/(136.282 g) ≈ 0.0110066 moles

Then the mass of Zn required is ...

  mass of Zn = (0.0110066 mol)(65.382 g/mol) = 0.71963 g

Two moles of HCl are used in the reaction with each mole of Zn, so the mass of HCl required is ...

  mass of HCl = 2(0.0110066 mol)(36.458 g/mol) = 0.80256 g

_____

<em>Comment</em>

The discrepancy in the last two decimal places of the weights above versus the calculator output below comes from rounding of moles of Zn to 4 significant digits, instead of 5 or more. The number of moles of ZnCl₂ is closer to 0.0110066.

4 0
3 years ago
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