A bag contains 10 3/4cups of almonds. A serving of almonds is 1/4 cup. How many servings of almonds does the bag contain?

Answer:

Katherine will create at least 8 playlists. Each of these will feature 4 pop songs and 9 rock songs.

Detailed Explanation:

Katherine has a library of 32 pop songs and 72 rock songs on her mp3 player. She intends to distribute these into playlists, ensuring an equal count of pop and rock songs in each.

To determine the minimum number of playlists, we find the GCF of the two numbers provided.

For 32, we can express it as 2^5, and 72 can be described as 2^3*3^2

Thus, the GCF for the two figures is 2^3, equaling 8.

Consequently, she will generate 8 playlists, with each containing 4 pop songs and 9 rock songs.

To identify the most sensible savings goal for Kirk and his family, follow these calculations:

a. $225 per month over 2 years equals $5400 (calculated as 225 * 2 * 12)
b. $200 per month for 3 years totals $7200 (calculated as 200 * 3 * 12)
c. $100 per month across 4 years will give $4800 (calculated as 100 * 4 * 12)
d. $75 saved monthly for 5 years amounts to $4500 (calculated as 75 * 5 * 12)

The optimal savings target would be option b, since $7200 exceeds <span>$6845.</span>

Options

• Counting rule for permutations
• Counting rule for multiple-step experiments
• Counting rule for combinations
• Counting rule for independent events

Answer:

(C) Counting rule for combinations

Step-by-step explanation:

To find the number of outcomes when selecting n objects from N objects, we apply either permutation or combination.

• If the order of selection matters, we utilize permutation.

• On the other hand, if the order of selection does not matter, we opt for combination.

Thus, the counting method employed for determining experimental outcomes when selecting n objects from N objects without regard to selection order is referred to as the counting rule for combinations.

Answer:

The inequality used to calculate the number of articles written by Mustafa for his school paper is .

Mustafa has authored over 8 articles.

Step-by-step explanation:

Details given:

Total combined number of articles = 22

Let 'x' represent the articles written by Mustafa.

Now stated:

Heloise has authored as many articles as Mustafa.

Heloise's articles number =

Gia has penned as many articles as Mustafa.

Gia's article count =

It follows that;

The total of articles from Mustafa, Heloise, and Gia must be more than or equal to the total combined articles.

Expressing it in an equation gives us;

Thus the inequality for finding the number of articles penned by Mustafa for his school project is .

Now simplifying the inequality:

By taking the LCM to standardize the denominator, we get:

Thus, Mustafa has written in excess of 8 articles.

Answer:

Parallel

corresponding angles theorem

NYM

AA

Step-by-step explanation:  I DID IT ON EDGE!: )

We know that side NM is  _________________

✔ parallel

to side XZ. If we consider side NY as the transversal, angle pairs are formed. According to the  _____________

✔ corresponding angles theorem

, it follows that ∠YXZ is congruent to ∠YNM. Also, angle XYZ is congruent to angle  _____________

✔ NYM

due to the reflexive property. Hence, triangle XYZ is similar to triangle NYM by the  _____________

✔ AA

 similarity theorem.