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The equation of a parabola is given.y=−14x2+4x−19

What are the coordinates of the vertex of the parabola?

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Answers

Answer 1

Answer:

Answer:

vertex ( $(1)/(7)$ , $(131)/(7)$ ).

Step-by-step explanation:

Given : The equation of a parabola is given.

y=−14x²+4x−19

To find : What are the coordinates of the vertex of the parabola.

Solution : We have given that

y = −14x²+4x−19

we will be "completing the square" .

Factor out -14 to make leading coefficient 1

y = -14 ( $x^(2) -(2x)/(7) +(19)/(14)$ )

Add and subtract $((-1)/(7)) ^(2)$

y = -14 ( $x^(2) -(2x)/(7) +(19)/(14)+(-1)/(7)) ^(2) - ((-1)/(7))^(2))$ .

Complete the square

y = -14 ( $(x -(1)/(7)) ^(2) +(19)/(14)- ((-1)/(7))^(2))$ .

y = -14 ( $(x-(1)/(7)) ^(2) -(131)/(7)$

Standard form of parabola vertex form y = a(x - h)²+ k,

Where, ( h, k) are vertex

On comparing a = -14 , h= $(1)/(7)$ , k = $(131)/(7)$

Therefore, vertex ( $(1)/(7)$ , $(131)/(7)$ ).

Answer 2

Answer: The coordinates are 8, -3.

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Help D: An object is dropped from a small plane. As the object falls, its distance, d, above the ground after t seconds, is given by the formula d = –16t2 + 1,000. Which inequality can be used to find the interval of time taken by the object to reach the height greater than 300 feet above the ground?A.-16t^2+1000<300

B. -16t^2+1000<_ 300

C. -16t^2+1000>_300

D.-16t^2+1000>300

Answers

Answer:

D. $-16t^2+1000>300$ is the correct answer.

Step-by-step explanation:

It is given that Distance, d above ground with time 't' is given by the formula:

$d = -16t^2+1000$

The negative sign with $16t^2$ indicates that the distance is decreasing with square of time. i.e. value is getting subtracted from a value 1000.

For example, if t = 0, d = 1000 feet

If t = 2, d = -16 $*$ 4 + 1000 = 936 feet

We can clearly see that when 't' is increasing, the distance 'd' is decreasing.

And at a certain time, the object will be on ground when d = 0 feet.

Inequality for the distance greater than 300 feet i.e.

d > 300 feet

Hence, the inequality will be:

$-16t^2+1000 >300$ is the correct answer.

Let the number of chocolate chips in a certain type of cookie have a Poisson distribution. We want the probability that a cookie of this type contains at least two chocolate chips to be greater than 0.99. Find the smallest value of the mean that the distribution can take.

Answers

Answer:

$\lambda \geq 6.63835$

Step-by-step explanation:

The Poisson Distribution is "a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event".

Let X the random variable that represent the number of chocolate chips in a certain type of cookie. We know that $X \sim Poisson(\lambda)$

The probability mass function for the random variable is given by:

$f(x)=(e^(-\lambda) \lambda^x)/(x!) , x=0,1,2,3,4,...$

And f(x)=0 for other case.

For this distribution the expected value is the same parameter $\lambda$

$E(X)=\mu =\lambda$

On this case we are interested on the probability of having at least two chocolate chips, and using the complement rule we have this:

$P(X\geq 2)=1-P(X<2)=1-P(X\leq 1)=1-[P(X=0)+P(X=1)]$

Using the pmf we can find the individual probabilities like this:

$P(X=0)=(e^(-\lambda) \lambda^0)/(0!)=e^(-\lambda)$

$P(X=1)=(e^(-\lambda) \lambda^1)/(1!)=\lambda e^(-\lambda)$

And replacing we have this:

$P(X\geq 2)=1-[P(X=0)+P(X=1)]=1-[e^(-\lambda) +\lambda e^(-\lambda)[]$

$P(X\geq 2)=1-e^(-\lambda)(1+\lambda)$

And we want this probability that at least of 99%, so we can set upt the following inequality:

$P(X\geq 2)=1-e^(-\lambda)(1+\lambda)\geq 0.99$

And now we can solve for $\lambda$

$0.01 \geq e^(-\lambda)(1+\lambda)$

Applying natural log on both sides we have:

$ln(0.01) \geq ln(e^(-\lambda)+ln(1+\lambda)$

$ln(0.01) \geq -\lambda+ln(1+\lambda)$

$\lambda-ln(1+\lambda)+ln(0.01) \geq 0$

Thats a no linear equation but if we use a numerical method like the Newthon raphson Method or the Jacobi method we find a good point of estimate for the solution.

Using the Newthon Raphson method, we apply this formula:

$x_(n+1)=x_n -(f(x_n))/(f'(x_n))$

Where :

$f(x_n)=\lambda -ln(1+\lambda)+ln(0.01)$

$f'(x_n)=1-(1)/(1+\lambda)$

Iterating as shown on the figure attached we find a final solution given by:

$\lambda \geq 6.63835$

Final answer:

The problem pertains to Poisson Distribution in probability theory, focusing on finding the smallest mean (λ) such that the probability of having at least two chocolate chips in a cookie is more than 0.99. This involves solving an inequality using the formula for Poisson Distribution.

Explanation:

This problem pertains to the Poisson Distribution, often used in probability theory. In particular, we're looking at the number of events (in this case, the number of chocolate chips) that occur within a fixed interval. Here, the interval under study is a single cookie. The question requires us to find the smallest value of λ (the mean value of the distribution) such that the probability of getting at least two chocolate chips in a cookie is more than 0.99.

Using the formula for Poisson Distribution, the probability of finding k copies of an event is given by:

P(X=k) = λ^k * exp(-λ) / k!

The condition here is that the probability of finding at least 2 copies is more than 0.99. Therefore, you formally need to solve the inequality:

P(X>=2) = 1 - P(X=0) - P(X=1) > 0.99

Substituting the values of P(X=0) and P(X=1) from our standard formula, you will need to calculate and find the smallest value of λ that satisfies this inequality.

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Rebecca Clarke's Nursery sells border plants for home gardeners at a discounted price of$12.99. Rebecca Clarke's has 335 plants it needs to sell. Fixed costs for all these plants were
$1,675 and variable costs per plant are $3.65. What is the maximum profit Rebecca Clarke's
will make if it sells all the plants at the discounted price?

Answers

Answer:

$1,540.70

Step-by-step explanation:

1675/335 = 5

3.65 * 335 = 1222.75

Cost of $8.65 per plant, or $2,897.75 for every plant.

12.99 - 8.65 = 4.34

Profit of $4.34 per plant, or $1,540.70 total.

6th grade math, help me please

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

$(42)/(100) * 350 = 147$

The short run is defined as a period of time whereSelect one:
a. some of a firm's inputs are fixed
b. only a small number of firms can enter or exit the industry.
c. the firm always breaks even (earns zero profit).
d. all inputs can be changed, but only for a little while and then must be changed back to their original levels.

Answers

Answer:

Step-by-step explanation:

a q q q q q q q q q q qq q qq q q q q q qa q q q q q q q q q q q

Final answer:

The short run in economics is a period in which some of a firm's inputs are fixed. These fixed inputs can include capital, such as the factory building, which cannot be adjusted quickly in response to changes in economic circumstances. Meanwhile, in the long run, all of a firm's inputs can be changed.

Explanation:

In economics, the short run is referred to as a period wherein some of a firm's inputs are fixed. Notable examples of these fixed inputs can be capital or the factory building, which cannot be increased or decreased instantaneously in response to economic circumstances. This distinguishing characteristicseparates the short run from the long run where, in contrast, firms have the flexibility to change all inputs.

Examples

For instance, consider a bakery production. In the short run, the bakery cannot immediately expand its premises or decrease the size of its building if the demand changes. The equipment can't be heightened, the building is fixed and it can't be altered. Here, the bakery can increase production by hiring more employees or extending their hours which are known as variable inputs but cannot change its fixed inputs like the size of the building or equipment.

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Is the answer a, b, c, or d.

Answers

The correct answer is D.

$-2 \leq y\ \textless \ 3$

The graph shows the set of values that y takes, so you can see that the thick black line goes from -2 to 3 and the black point at -2 represents a closed interval at this point and the empty point at 3 represents an open interval at that point.

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