For three lengths to be able to form a triangle, it suffices that every one of those lengths is shorter than the sum and longer than the difference of the other two.

It is enough to check just one side.

So,

3 + 4 > 5

4 - 3 < 5

Your triangle is constructible.

6 0

3 years ago

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The number of accidents per week at a hazardous intersection varies with mean 2.2 and standard deviation 1.4. This distribution

ankoles [38]

Answer:

a) Normal Distribution

b) 0.146

c) 0.070

Step-by-step explanation:

We are given the following information in the question:

The number of accidents per week at a hazardous intersection varies with mean 2.2 and standard deviation 1.4

a) $\bar{x}$ : mean number of accidents per week at the intersection during a year (52 weeks)

According to central limit theorem, as the sample size becomes larger, the distribution of mean approaches a normal distribution.

Since we have a large sample, the approximate distribution of $\bar{x}$ is a normal distribution with

$\text{Mean} = 2.2\\\text{Standard Deviation} = \displaystyle\frac{\sigma}{\sqrt{n}} = \frac{1.4}{\sqrt{52}} = 0.19$

b) P(mean is less than 2)

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

P(x > 610)

$P( \bar{x} < 2) = P( z < \displaystyle\frac{2 - 2.2}{0.19}) = P(z < -1.052)$

Calculation the value from standard normal z table, we have,

$P(\bar{x} < 2) = 0.146$

c) P(fewer than 100 accidents at the intersection in a year)

P(x < 100)

$P( \bar{x} < \frac{100}{52}) =P(\bar{x} < 1.92) =P(z < \displaystyle\frac{1.92 - 2.2}{0.19}) = P(z < -1.473)$

Calculation the value from standard normal z table, we have,

$P(x$

7 0

3 years ago

Which of the following are possible rational roots of the polynomial function f(x)=5x^2-3x+3

yanalaym [24]

You didn't post any option, but the ration roots theorem states that all possible rational roots of a polynomial come in the form

$\pm\dfrac{p}{q}$

where p divides the constant term and q divides the leading term of the polynomial. So, in your case, p divides 3 (i.e. it is 1 or 3), and q divides 5 (i.e. it is 1 or 5).

So, the possible roots are

$\pm 1,\quad \pm 3,\quad \pm\dfrac{1}{5},\quad \pm\dfrac{3}{5}$

For the record, this parabola has no real roots.

7 0

3 years ago

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A science teacher has a supply of 50% sugar solution and a supply of 80% sugar solution. How much of each solution should the te

mash [69]

How much of each solution should the teacher mix together to get 105 ML of 60% sugar solution for an experiment?

1. Look at how 60% is closer to the solution of lower concentration (50%). You can deduce that you will be mixing a higher volume of the 50% solution.

2. All 4 answers add up to 105ml.

3. The intuitive answer is the first option:
70 ML of the 50% solution and 35 ML of the 80% solution

4. Let's check whether point 3 is true.
70ml/105ml X 0.5 + 35ml/105ml X 0.8 = (35 + 28)/105= 63/105= 60% / 105 ml = 105ml of 60% sugar solution

3 0

3 years ago