Assume that the cheetah travels an average of 40 mph to go from its resting place to a rock near a river. On the return trip to

(1 3/4) divided by (1/5) =
(7/4) ÷ (1/5) =
7/4 multiplied by 5/1 =
35/4 or 8 3/4 <===

The options you provided are unclear to me, so I will respond in general terms: to determine if a point (ordered pair) lies on a line, you need to substitute the x-value from that pair into the line's equation and check if the resulting y-value matches the y-value of the ordered pair. For example, if your line is y = 4/3x + 1/3, we can check if (0, 0) and (2, 3) fit this line. We find that y = 4/3·0 + 1/3 gives us 1/3, which does not equal 0, indicating (0, 0) is not on the line. For (2, 3), substituting yields y = 4/3·2 + 1/3 = 3, meaning (2, 3) is on the line.

Answer:

a) The likelihood that none of the sampled employees are from the Hawaii plant is 1.74%.

b) The chance that exactly 1 employee from the sample is found working in the Hawaii plant is 8.70%.

c) There is an 89.56% chance that 2 or more employees in the sample are from the Hawaii plant.

d) The probability that 9 employees from the sample are working at the Texas plant is 8.70%.

Step-by-step explanation:

Each employee has two potential employment locations: either Texas or Hawaii. Thus, the binomial probability distribution can be utilized to solve this scenario.

Binomial probability distribution

This distribution defines the probability of achieving exactly x successes in n trials where there are only two outcomes.

Here, denotes the number of ways to choose x objects from a set of n, represented by the subsequent formula.

And p is the probability of success occurring.

In this context, we know:

The sample comprises 10 employees, therefore .

a. Calculate the probability that none of the sampled employees are from the Hawaii plant (to 4 decimals)?

Given that 20 out of 60 employees are based in Hawaii:

We aim to find P(X = 0).

Thus, the likelihood that none in the sample are from Hawaii stands at 1.74%.

b. Calculate the probability that 1 employee from the sample is from the Hawaii plant?

This is represented as P(X = 1).

Therefore, there is an 8.70% possibility that 1 employee in the sample comes from Hawaii.

c. Calculate the probability that 2 or more employees in the sample are from the Hawaii plant?

We can observe two scenarios: either fewer than 2 employees are from Hawaii or 2 and beyond. The combined probabilities equal decimal 1. So:

We seek to find .

From problems a and b, we possess values for both probabilities.

Accordingly, the chance that 2 or more employees in this sample operate at the Hawaii plant is 89.56%.

d. Calculate the likelihood that 9 employees in the sample are working at the Texas plant?

This corresponds to the probability found in part b for 1 employee working in Hawaii.

Consequently, there is an 8.70% chance that 9 employees belong to the Texas plant.

Answer:

The equation 0 = 3x² + 17x - 160 might be useful in determining the length.

Step-by-step explanation:

The area of the vegetable garden is specified as 170 ft².

Now, regarding the provided equations;

1) For 0 = 3x² + 2x + 180, applying the quadratic formula results in:

x = [-2 ± √(3² - 4(3 × 180)]/(2 × 3)

x = [-2 ± √(-2151)]/6

The square root value is negative, indicating no real solution for x.

Thus, this equation does not help find the length.

2) For the equation 0 = 3x² + 10x + 180, employing the quadratic formula, the square root value is also negative, hence there's no natural root for x. This means this equation can't be used to determine the length.

3) For 0 = 3x² + 17x - 160, the roots when using the quadratic formula yield -10.67 or 5. The value 5 is viable since it is a whole number. Considering the area is also a whole number, this equation can be applied to ascertain the length.

4) For 0 = 3x² - 160, simplifying gives;

3x² = 160

x² = 160/3

x = ±√(160/3)

x = ±7.303

Since the area is a whole number but this length isn't, this equation may not accurately determine the length.