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2 years ago

Given the trinomial 5x^2-2x-3, predict the type of solutions.

Mathematics

2 answers:

pishuonlain [190]2 years ago

3 0

Consider the trinomial $5x^2-2x-3.$

1. Find the discriminant:

$D=b^2-4ac=(-2)^2-4\cdot 5\cdot (-3)=4+60=64,\\ \\\sqrt{D}=8>0.$

2. Find the roots of given trinomial:

$x_{1,2}=\dfrac{-b\pm \sqrt{D}}{2a}=\dfrac{2\pm 8}{2\cdot 5}=1,-0.6.$

3. Conclusion: given trinomial has two different real roots.

Mnenie [13.5K]2 years ago

3 0

Given: 5x^2 - 2x - 3

Using a calculator to obtain the solutions to the given trinomial, the solutions obtained are 1 and -3/5. The values 1 and -3/5 are rational and real numbers. Therefore, the type of solutions obtained are rational and real.

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The newest invention of the 6.431x staff is a three-sided die. On any roll of this die, the result is 1 with probability 1/2, 2

Gwar [14]

Answer:

<h2>The answer is 0.23(approx).</h2>

Step-by-step explanation:

The given die is a three sided die, hence, there are only three possibilities of getting the outcomes.

We need to find the probability of getting exactly 3s as the result.

From the sequence of 6 independent rolls, 2 rolls can be chosen in $^6C_2 = \frac{6!}{2!\times4!} = \frac{30}{2} = 15$ ways.

The probability of getting two 3 as outcome is $\frac{1}{4} \times\frac{1}{4} = \frac{1}{16}$ .

In the rest of the 4 sequences, will not be any 3 as outcome.

Probability of not getting a outcome rather than 3 is $1 - \frac{1}{4} = \frac{3}{4}$ .

Hence, the required probability is $15\times\frac{1}{16}(\frac{3}{4})^4 = \frac{1215}{4096}$ ≅0.2966 or, 0.23.

4 0

2 years ago

Nico and Albert are finishing up a science project. They measured the length in inches of three insects. They also found the ave

atroni [7]

Answer:

Step-by-step explanation:

Given the length of the bugs as shown;

Lady bug = 3/8

Ant = 1/4

Firefly = 7/8

Honey bee = 0.8

Deer tick = 0.2

Before we arrange the length in ascending order (shortest to longest), we will have to represent them in percentage.

Lady bug = 3/8×100

= 300/8

= 37.5%

Ant = 1/4×100

Ant = 25%

Firefly = 7/8 × 100

Firefly = 87.5%

Honey bee = 0.8×100

Honey bee = 80%

Deer tick = 0.2×100

Deer tick = 20%

On rearranging in ascending order:

20%, 25%, 37.5%, 80%, 87.5%

Based on the insect

Deer tick, Ant, ladybug, honey bee, Firefly

Based on their length:

0.2, 1/4, 3/8, 0.8, 7/8

5 0

2 years ago

Read 2 more answers

A man has 28 coins in his pocket, all of which are dimes and quarters. if the total value of his change is 520 cents, how many d

nordsb [41]

Assuming x = dimes, y = quarters

$x + y = 28 \\ 0.1x + 0.25y = 5.20$

$x + y = 28 \\ x = 28 - y$

Substitute that into,
$0.1(28 - y) + 0.25y = 5.20 \\ 2.8 - 0.1y + 0.25y = 5.20 \\0.15y = 2.4 \\ y = 16$

Answer : He has 16 quarters.

Hope this helps. - M

5 0

2 years ago

A university warehouse has received a shipment of 25 printers, of which 10 are laser printers and 15 are inkjet models. If 6 of

Tanya [424]

Answer:

The probability is 0.31

Step-by-step explanation:

To find the probability, we will consider the following approach. Given a particular outcome, and considering that each outcome is equally likely, we can calculate the probability by simply counting the number of ways we get the desired outcome and divide it by the total number of outcomes.

In this case, the event of interest is choosing 3 laser printers and 3 inkjets. At first, we have a total of 25 printers and we will be choosing 6 printers at random. The total number of ways in which we can choose 6 elements out of 25 is $\binom{25}{6}$ , where $\binom{n}{k} = \frac{n!}{(n-k)!k!}$ . We have that $\binom{25}{6} = 177100$

Now, we will calculate the number of ways to which we obtain the desired event. We will be choosing 3 laser printers and 3 inkjets. So the total number of ways this can happen is the multiplication of the number of ways we can choose 3 printers out of 10 (for the laser printers) times the number of ways of choosing 3 printers out of 15 (for the inkjets). So, in this case, the event can be obtained in $\binom{10}{3}\cdot \binom{15}{3} = 54600$

So the probability of having 3 laser printers and 3 inkjets is given by

$\frac{54600}{177100} = \frac{78}{253} = 0.31$

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2 years ago

Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. The foundation chair for a hosp

slavikrds [6]

Answer:

For this case we want to test if the mean number of filled overnight beds is over 523. If X represent our random variable "number of filled overnight beds", the system of hypothesis are:

Null Hypothesis: $\mu \leq 523$

Alternative hypothesis: $\mu > 523$

And for this case after conduct the test is FAIL to reject the null hypothesis. So then we can conclude that the claim that the number of filled overnight beds is over 523 is not statistically supported

Step-by-step explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

Solution to the problem

For this case we want to test if the mean number of filled overnight beds is over 523. If X represent our random variable "number of filled overnight beds", the system of hypothesis are:

Null Hypothesis: $\mu \leq 523$

Alternative hypothesis: $\mu > 523$

6 0

2 years ago