Two ballpoint pens are selected at random from a box that contains 3 blue pens, 2 red pens, and 3 green pens. If X is the number

<span>P(black socks): 24/42 or 12/21
P(black socks without replacement): 23/41. Consequently, the chance of randomly selecting 2 black socks, without replacement, from the basket is 12/21×23/41=276/861, equivalent to 32%. Hope this helps!</span>

Answer:

Hence, utilizing linear depreciation gives us 17222.22.

Step-by-step explanation:

The boat's initial value is noted to be $250,000.

The straight-line depreciation method for calculating a boat is as follows:

Cost of the boat is $250,000.

Deep Blue anticipates selling it for $95,000 after 9 years.

Employing the formula, we calculate:

(250000-95000)/9=155000/9=17222.22

Thus, the outcome using linear depreciation is 17222.22.

Answer:

Step-by-step explanation:

<pGreetings!

a. The variable X represents the height of a Goomba, which follows a normal distribution with a mean of μ= 12 inches and a standard deviation of δ= 6 inches.

To find the probability that a Goomba picked at random has a height between 13 and 15 inches, you express it as:

P(13≤X≤15)

Considering that standard normal probability tables provide cumulative values, you can express this range as the cumulative probability up to 15 minus the cumulative probability up to 13. You'll first need to standardize these variable heights to obtain corresponding Z values:

P(X≤15) - P(X≤13)

P(Z≤(15-12)/6) - P(Z≤(13-12)/6)

P(Z≤0.33) - P(Z≤0.17)= 0.62930 - 0.56749= 0.06181

b. Now we have Y as the variable indicating the height of a Koopa Troopa. This variable also follows a normal distribution, with a mean μ= 15 inches and a standard deviation δ=3 inches.

The query concerns the probability that a Koopa Troopa stands taller than 75% of Goombas.

First step:

You need to determine the height of a randomly chosen Koopa Troopa that exceeds 75% of the Goomba population.

This entails determining the value of X corresponding to the limit below which 75% of the population falls, denoted by:

P(X ≤ b)= 0.75

Step 2:

Search the standard normal distribution for the Z value that has 0.75 beneath it:

Next, you will reverse the standardization to solve for "b"

Z= (b - μ)/δ

b= (Z*δ)+μ

b= (0.674*6)+12

b= 16.044 inches

Step 3:

With the height that identifies a Koopa Troopa taller than 75% of the Goomba population determined, compute the probability of selecting that Koopa Troopa:

P(Y≤16.044)

This time, utilize the Koopa’s average height and standard deviation to find the probability:

P(Z≤(16.044-15)/3)

P(Z≤0.348)= 0.636

The likelihood of randomly selecting a Koopa Troopa that is taller than 75% of Goombas is 63.6%

I hope this information is useful!

Let’s tackle the problem. We know the formula for <span>the height of the ball is as follows:

</span>
<span>
Here, x represents </span><span>the horizontal distance in yards that the ball has traveled in the air. Given that distance is always a positive value, we conclude that x must be greater than or equal to 0. Thus:

</span><span>

The horizontal plane indicates the function's zero point, and since the ball cannot have negative height values, must also remain positive. Ultimately, the graph reveals that the suitable domain is:

</span><span>
</span><span>
</span>

Answer:

Steven is mistaken.

Step-by-step explanation:

Steven has

• 9 unique shirts
• 5 unique hats
• 4 unique scarves.

He selects only two out of the three types of clothing. The combinations can be calculated as

• options to select a shirt and a hat;
• options to select a hat and a scarf;
• options to select a shirt and a scarf.

In total, there are

different methods to choose just two out of the three clothing items.

As a result, Steven is not correct.