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Leona [35]
3 years ago
6

What is the factorization???

Mathematics
1 answer:
Sav [38]3 years ago
6 0

we can see that

the above curve is parabola

so, firstly , we can find vertex

vertex is (4,0)

(h,k)=(4,0)

now, we can use vertex formula of parabola

y=(x-h)^2+k

we can plug h and k

and we get

y=(x-4)^2+0

so, we can factor it as

y=(x-4)(x-4)............Answer

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Marvin wants to purchase a rectangular rug. It has an area represented by the expression 4x^2+64x+256. what is the length and wi
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Answer: the length and width are

(x + 8) and (x + 8)

Step-by-step explanation:

The rug has an area represented by the expression

Area = 4x² + 64x + 256.

The factors in the factored expressions represent the length and width of the rug.

Dividing the the equation by 4, it becomes

x² + 16x + 64 = 0

We would find two numbers such that their sum or difference is 16x and their product is 64x^2.

The two numbers are 8x and 8x. Therefore,

x² + 8x + 8x + 64 = 0

x(x + 8) + 8(x + 8) = 0

The factors are

(x + 8)(x + 8)

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3 years ago
For tax purposes, a car rental company assumes each car in their fleet depreciates by 6% per year. If the initial value of a car
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The value of a car after 10 years be $20898.27 if the car rental company assumes each car in their fleet depreciates by 6% per year option (a) $20898.27 is correct.

<h3>What is an exponential function?</h3>

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent \rm y = a^x

where a is a constant and a>1

We can solve this problem by exponential function:

The word  depreciate means the price is decreasing.

We can find the value be when the car is 10 years old:

p = 38800(1 - 0.06)¹⁰

p = 38800(0.94)¹⁰

p = 20898.266 ≈ $20898.27

Thus, the value of a car after 10 years be $20898.27 if the car rental company assumes each car in their fleet depreciates by 6% per year option (a) $20898.27 is correct.

Learn more about the exponential function here:

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There are 30 businesses with 4 executives each for the new office building. Each business needs one office for each of its execu
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1 executive to 360 offices

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Suppose a random variable, x, arises from a binomial experiment. If n = 6, and p = 0.30, find the following probabilities using
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Answer:

<u></u>

  • <u>a) P(X=1) = 0.302526</u>
  • <u>b) P(X=5) = 0.010206</u>
  • <u>c) P(X=3) = 0.18522</u>
  • <u>d) P(X≤3) = 0.92953</u>
  • <u>e) P(X≥5) = 0.010935</u>
  • <u>f) P(X≤4) = 0.989065</u>

Explanation:

Binomial experiments are modeled by the formula:

       P(X=x)=C(n,x)\cdot p^x\cdot (1-p)^{(n-x)}

Where

  • P(X=x) is the probability of exactly x successes

  • C(n,x)=\dfrac{n!}{x!\cdot (n-x)!}

  • p is the probability of one success, which must be the same for every trial, and every trial must be independent of other trial.
  • n is the number of trials
  • 1 - p is the probability of fail
  • there are only two possible outcomes for each trial: success or fail.

<u>a.) P (x=1)</u>

<u></u>

       P(X=1)=\dfrac{6!}{1!\cdot (6-1)!}\times (0.3)^1\times(1-0.3)^{(6-1)}=0.302526

<u>b.) P (x=5)</u>

     P(X=5)=\dfrac{5!}{5!\cdot (6-5)!}\times (0.3)^5\times (1-0.3)^{(6-5)}=0.010206

<u>c.) P (x=3)</u>

Using the same formula:

    P(X=3)=0.18522

<u>d.) P (x less than or equal to 3)</u>

  • P(X≤3)= P(X=3) + P(X=2) + P(X=1) + P(X=0)

Also,

  • P(X≤3) = 1 - P(X≥4) = 1 - P(X=4) - P(X=5) - P(X=6)

You can use either of those approaches. The result is the same.

Using the second one:

  • P(X=4) = 0.059335
  • P(X=5) = 0.010206
  • P(X=6) = 0.000729

  • P(X≤3) = 1 - 0.05935 - 0.010206 - 0.000729 = 0.92953

<u>e.) P(x greather than or equal to 5)</u>

  • P(X≥5) = P(X=5) + P(X=6)
  • P(X≥5) = 0.010206 + 0.000729 =  0.010935

<u>f.) P(x less than or equal 4)</u>

  • P(X≤4) = 1 - P(X≥5) = 1 - P(X=5) - P(X=6)
  • P(X≤4) = 1 - 0.010206 - 0.000729 = 0.989065
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