9. Bennett planted four tomato plants in<br> garden, and he recorded their progress<br> a few weeks.

kari74 [83]

The law of an object moving with constant acceleration is

$s(t)=s_0+v_0t+\dfrac{1}{2}at^2$

Where $s$ is space, $t$ is time, $s_0$ is the initial position, $v_0$ is the initial velocity and $a$ is the acceleration.

In this case, if we choose a reference grid with the vertical axis pointing upwards, the acceleration of gravity will point downwards (and thus be negative). The initial position is zero, because the rocket is on the ground, and the initial velocity is 100 (positive because pointing upwards).

So, its law is

$h(t)=100t-\dfrac{1}{2}gt^2$

(I changed $s$ for $h$ since the rocket is moving vertically, so its position is actually its height. Also, g is the acceleration due to gravity).

The rocket hits the ground if its height is zero, so if we set $h=0$ we have

$0=100t-\dfrac{1}{2}gt^2 \iff t(100-\dfrac{1}{2}gt)=0$

Solving for t, we have either t=0, or

$100-\dfrac{1}{2}gt=0 \iff 100=\dfrac{1}{2}gt \iff 200=gt \iff t=\dfrac{200}{g}$

The solution t=0 means that at the beginning the rocket is on the ground. So, we're interested in the other solution. Considering that g is about 32.2 feet/s^2, we have

$t=\dfrac{200}{g}\approx \dfrac{200}{32.2}\approx 6.21$

3 0

3 years ago

The chief chemist for a major oil and gasoline production company claims that the regular unleaded gasoline produced by the comp

Svetradugi [14.3K]

Answer:

The probability of finding an average in excess of 4.3 ounces of this ingredient from 100 randomly inspected 1-gallon samples of regular unleaded gasoline = P(x > 4.3) = 0.00621

Step-by-step explanation:

This is a normal distribution problem

The mean of the sample = The population mean

μₓ = μ = 4 ounces

But the standard deviation of the sample is related to the standard deviation of the population through the relation

σₓ = σ/√n

where n = Sample size = 100

σₓ = 1.2/√100

σₓ = 0.12

The probability of finding an average in excess of 4.3 ounces of this ingredient from 100 randomly inspected 1-gallon samples of regular unleaded gasoline = P(x > 4.3)

To do this, we first normalize/standardize the 4.3 ounces

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (4.3 - 4)/0.12 = 2.5

To determine the probability of finding an average in excess of 4.3 ounces of this ingredient from 100 randomly inspected 1-gallon samples of regular unleaded gasoline = P(x > 4.3) = P(z > 2.5)

We'll use data from the normal probability table for these probabilities

P(x > 4.3) = P(z > 2.5) = 1 - P(z ≤ 2.5) = 1 - 0.99379 = 0.00621

5 0

4 years ago

What is 62 take away 38 =

Allushta [10]

Answer:

the answer is 24

Step-by-step explanation:

68-38 = 24

3 0

4 years ago