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3 years ago

An object is launched at 29.4 meters per

Mathematics

1 answer:

Lerok [7]3 years ago

4 0

Answer:

The reasonable domain for the scenario is option 'a';

a) [0, 7]

Step-by-step explanation:

For the projectile motion of the object, we are given;

The speed at which the object is launched, v = 29.4 meters per second

The height of the platform from which the object is launched, h = 34.3 meter

The equation for the height of the object as a function of time 'x' is given as follows;

f(x) = -4.9·x² + 29.4·x + 34.3

The domain for the scenario, is given by the possible values of 'x' for the function, which is found as follows;

At the height from which the object is launched, x = 0, and f(x) = 34.3

At the ground level to which the object can drop, f(x) = 0

∴ f(x) = -4.9·x² + 29.4·x + 34.3 = 0

-4.9·x² + 29.4·x + 34.3 = 0

By the quadratic formula, we have;

x = (-29.4 ± √(29.4² - 4 × (-4.9) × 34.3))/(2 × (-4.9)

∴ x = -1, or 7

Given that time is a natural number, we have the reasonable domain for the scenario as the start time when the object is launched, t = 0 to the time the object reaches the ground, t = 7

Therefore, the reasonable domain for the scenario is; 0 ≤ x ≤ 7 or [0, 7].

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Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.3. (Round your ans

Maurinko [17]

Answer:

0.0039 is the probability that the sample mean hardness for a random sample of 12 pins is at least 51.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 50

Standard Deviation, σ = 1.3

Sample size, n = 12

We are given that the distribution of hardness of pins is a bell shaped distribution that is a normal distribution.

Formula:

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

Standard error due to sampling =

$=\dfrac{\sigma}{\sqrt{n}} = \dfrac{1.3}{\sqrt{12}} = 0.3753$

P(sample mean hardness for a random sample of 12 pins is at least 51)

$P( x \geq 51) = P( z \geq \displaystyle\frac{51 - 50}{0.3753}) = P(z \geq 2.6645)$

$= 1 - P(z < 2.6645)$

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

$P(x \geq 51) = 1 - 0.9961= 0.0039$

0.0039 is the probability that the sample mean hardness for a random sample of 12 pins is at least 51.

3 0

3 years ago

Determine whether the triangles are similar. or not.

mr Goodwill [35]

Answer:

Step-by-step explanation:

We know that ∠ $ABE$ ≅ ∠ $DBC$ because they are vertical angles, so that's one pair of congruent angles. However, we can't compare ∠ $BAE$ and ∠ $DCB$ as they have different measures, so we'll have to find the measure of either ∠ $AEB$ or ∠ $BDC$ . Let's go with the former. Using the fact that the sum of the measures of the interior angles of a triangle is $180$ °, we know that $m$ ∠ $AEB=180-(53+42)=180-95=85$ °. Now, we know that ∠ $AEB$ ≅ ∠ $DCB$ because their measures are equal. That's another pair of congruent angles. Therefore, the angles are similar by $AA$ . Hope this helps!