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3 years ago

The standard form of the equation of a parabola is y = 5x2 + 20x + 14.

2 answers:

8 0

The vertex form of quadratic equation is expressed as:

y = a (x - h)² + k

We manipulate the given equation to be the same as the vertex form. First we transpose the constants to the left-hand side.

y - 14 = 5x² + 20x

Then, we factor out in right hand side the coefficient of the x² term.

y- 14 = 5 (x² + 4x)

We divide the coefficient of the x term with 2 and take its square. We add this value to both sides of the equation but we should remember that in the left-hand side we should multiply this value with five to keep it balanced.

y - 14 + 20 = 5 (x² + 4x +4)

We simplify the right-hand side as:

y + 6 = 5 (x + 2)²

We can now manipulate further the equation above in the vertex form. Thus,

y= 5 [ x- (-2)]² - 6

Ber [7]3 years ago

7 0

Answer:

y = 5(x+2)^2 - 6

Step-by-step explanation:

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2 years ago

Jonah calculates that the perimeter of the rectangle below is 6 1/4x - 3. Explain his error and include the correct expression.

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2 years ago

The MagicSoft software company has a proposal to the city council of Alva, Florida, to relocate there. The proposal claims that

EleoNora [17]

Answer:

The correct estimate of the amount generated to the local economy is $3,333,333. $\bar3$

Step-by-step explanation:

The amount the expected to be generated for the local economy = $3.3 million

The amount of salaries that will generate $3.3 million = $1 million

The percentage of the amount of the salaries and the subsequent earnings expected to be spent on the local community = 70%

Therefore, we have;

For a first amount of 1 million into the economy, the next amount to into the economy is 70/100 × 1 million = 700,000, then we have 70/100 × 700,000 and so on, which is a geometric sequence, with first term, a = $1 million, the common ratio, r = 70/100 = 0.7, the number of terms = Infinity = ∞

The sum of a geometric sequence to infinity is given as follows;

$\sum\limits_{k = 0}^{\infty }a \cdot r^k = S_{\infty} = \dfrac{a}{1 - r}$

Substituting the known values gives;

$\sum\limits_{k = 0}^{\infty }1,000,000 \times 0.7 ^k = \dfrac{1,000,000}{1 - 0.7}= 3,333,333.\bar 3$

Therefore, the correct estimate of the amount generated to the local economy by the $1 million salaries that will be paid = $3,333,333. $\bar3$ .

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2 years ago

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1 year ago

Customers arrivals at a checkout counter in a department store per hour have a Poisson distribution with parameter λ = 7. Calcul

IgorLugansk [536]

Answer:

(1)14.9% (2) 2.96% (3) 97.04%

Step-by-step explanation:

Formula for Poisson distribution: $P(k) = \frac{\lambda^ke^{-k}}{k!}$ where k is a number of guests coming in at a particular hour period.

(1) We can substitute k = 7 and $\lambda = 7$ into the formula:

$P(k=7) = \frac{7^7e^{-7}}{7!}$

$P(k=7) = \frac{823543*0.000911882}{5040} = 0.149 = 14.9\%$

(2)To calculate the probability of maximum 2 customers, we can add up the probability of 0, 1, and 2 customers coming in at a random hours

$P(k\leq2) = P(k=0)+P(k=1)+P(k=2)$

$P(k\leq2) = \frac{7^0e^{-7}}{0!} + \frac{7^1e^{-7}}{1!} + \frac{7^2e^{-7}}{2!}$

$P(k \leq 2) = \frac{0.000911882}{1} + \frac{7*0.000911882}{1} + \frac{49*0.000911882}{2}$

$P(k\leq2) = 0.000911882+0.006383174+0.022341108 \approx 0.0296=2.96\%$

(3) The probability of having at least 3 customers arriving at a random hour would be the probability of having more than 2 customers, which is the invert of probability of having no more than 2 customers. Therefore:

$P(k\geq 3) = P(k>2) = 1 - P(k\leq2) = 1 - 0.0296 = 0.9704 = 97.04\%$

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2 years ago