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2 years ago

Which of the following are possible equations of a parabola that has no real solutions and opens downward?

Mathematics

2 answers:

bekas [8.4K]2 years ago

6 0

Answer:

$y = - {(x - 4)}^{2} - 2$

$y = - {(x + 4)}^{2} - 2$

Step-by-step explanation:

The vertex form of a parabola is given as

$y = a {(x - h)}^{2} + k$

If this parabola opens downward, then a<0.

This means for a function opening downward not to have a solution, the k value must also be negative and taking a square root of a negative number will not give real solution.

From the given options, examples of such functions are:

$y = - {(x + 4)}^{2} - 2$

and

$y = - {(x - 4)}^{2} - 2$

icang [17]2 years ago

5 0

Answer:it’s y>=-(x+4)^2-2

Step-by-step explanation:

I checked it in my graphing calculator and it works. I’m also doing the program sooo

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I am planning to attend a company-paid conference. My charges will include $412.00 for airfare, $378.00 for conference registrat

Anna007 [38]

Answer:

$1000.00

Step-by-step explanation:

The supervisor is asking for an expense form of a <u>total (?) </u>when you return.

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2 years ago

400 students were randomly sampled from a large university, and 289 said they did not get enough sleep. Conduct a hypothesis tes

melomori [17]

Answer:

The sample proportion represents a statistically significant difference from 50%

Step-by-step explanation:

Null hypothesis: The sample proportion is the same as 50%

Alternate hypothesis: The sample proportion is not the same as 50%

z = (p' - p) ÷ sqrt[p(1 - p) ÷ n]

p' is sample proportion = 289/400 = 0.7225

p is population proportion = 50% = 0.5

n is number of students sampled = 400

z = (0.7225 - 0.5) ÷ sqrt[0.5(1 - 0.5) ÷ 400] = 0.2225 ÷ 0.025 = 8.9

The test is a two-tailed test. Using a 0.01 significance level, critical value is 2.576. The region of no rejection of the null hypothesis is -2.576 and 2.576.

Conclusion:

Reject the null hypothesis because the test statistic 8.9 falls outside the region bounded by the critical values -2.576 and 2.576.

There is sufficient evidence to conclude that the sample proportion represents a statistically significant difference from 50%.

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2 years ago

A fisherman catches fish according to a Poisson process with rate lambda = 0.6 per hour. The fisherman will keep fishing for two

spayn [35]

Answer:

Step-by-step explanation:

Given that a fisherman catches fish according to a Poisson process with rate lambda = 0.6 per hour.

The fisherman will keep fishing for two hours.

Since he continues till he gets atleast one fish, we can calculate probability as follows:

(a) Find the probability that he stays for more than two hours.

= Prob (x=0) in I two hours and P(X≥1) in 3rd hour

=P(x=0)*P(X=0)*P(X≥1) (since each hour is independent of the other)

= $0.5488^2*(1-0.8781)\\\\=0.2645$

(b) Find the probability that the total time he spends fishing is between two and five hours.

Prob that he does not get fish in I two hours * prob he gets fish between 3 and 5 hours

= $P(0)^2 *F(1)^3\\=0.5488^2*0.2645^3\\=0.00557$

Expected value in Geometric distribution = $\frac{1-p}{p}$ , where p = prob of getting 1 fish in one hour

= $\frac{0.6}{1-0.6} \\=3$

(d) Find the expected total fishing time, given that he has been fishing for four hours.

= Expected fishing time total/expected fishing time for 4 hours

=3/0.6*4

= 1.25 hours

4 0

2 years ago

Ahmad just put some money into a cd that pays 11.3% interest compounded semiannually according to the rule of 72 in approximatel

lilavasa [31]

The "rule of 72" says that the doubling time in years is approximately 72 divided by the interest rate in percent. To make the money grow by a factor of 4 requires that it double twice, so will take twice as long as the period to double once.
2×72/11.3 ≈ 12.7 . . . . years

_____
The "rule of 72" is an approximation. The actual quadrupling time for this interest rate and compounding is about 12.6 years. (The actual product of doubling time and nominal interest rate is about 71.25.)

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2 years ago

The students at Barton academy are planning a fundraiser to give money to an organization in their community. They voted for whi

Aneli [31]

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2 years ago