Madame Pickney has a rather extensive art collection and the overall value of her collection has been increasing each year. Three years ago, her collection was worth $400,000. Two years ago, the value of the collection was $440,000 and last year, the collection was valued at $484,000. Assume that the rate at which Madame Pickney’s art collection’s value increase remains the same as it has been for the last three years. The value of the art collection can be represented by a geometric sequence. The value of the collection three years ago is considered the first term in the sequence. What explicit rule can be used to determine the value of her art collection n years after that?

Mixed number form is 3 7/10

Don’t know if you needed that, just though I’d put it out there, though.

The correct answer is [tex]L = \frac{5}{p}[/tex]

To write an equation that models the length (in yards) of each piece of yarn if Marcus cuts a 5-yard length into p pieces, we need to express the length of each piece as a function of the number of pieces (p).

Given information:

- The total length of yarn is 5 yards.

- Marcus needs to cut the yarn into p equal pieces.

Let L be the length of each piece of yarn in yards.

[tex]\text{Total length} = \text{Sum of the lengths of all pieces}[/tex]

[tex]5 = L \times p[/tex]

[tex]L = \frac{5}{p}[/tex]

Therefore, the equation that models the length (in yards) of each piece of yarn if Marcus cuts it into p pieces is:

[tex]L = \frac{5}{p}[/tex]

In comparing distances, Lynne lives closer to the playground than Jorge. This is determined by comparing the fractions representing their distances from the playground, with Lynne's being smaller.

In this situation, we need to compare the distances each person lives from the playground. Jorge lives 5/6 mile from the playground and Lynne lives 4/6 mile from the playground. Since a smaller fraction represents a smaller distance, we can say that Lynne lives closer to the playground than Jorge does.

To understand this better, consider fractions as a way to divide a whole into parts. The larger the denominator, the more parts the whole is divided into and the smaller each part is. But in this case, the denominators are the same (6), so we look at the numerators. The numerators tell us how many of these parts we have. Since 4 is smaller than 5, Lynne who lives 4/6 mile away lives closer than Jorge who lives 5/6 mile away.

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Ricardo incorrectly determined he needed 1/4 cup of olive oil for one loaf of bread. The correct amount is 1/6 cup when the 2/3 cup required for four loaves is divided by four.

Ricardo has a recipe for four loaves of bread that requires 2/3 cup of olive oil. To adjust the recipe to make one loaf, he needs to divide the amount of olive oil by four. If Ricardo shades two parts of a paper folded into three parts to represent 2/3, and then folds this paper into four parts and shades one of those, he is effectively calculating one fourth of 2/3. The calculation for the correct amount of olive oil for one loaf is as follows:

(2/3) × (1/4) = 2/12

= 1/6

So, the correct amount of olive oil needed for one loaf is 1/6 cup, not 1/4 cup, which means Ricardo's model does not give him the correct amount.

Final answer:

Sophie waits for Rana after finishing a biking trip of 20 miles, accounting for their different speeds. The answer is calculated based on the difference in distances covered by Sophie and Rana.

Explanation:
Sophie bikes at a speed of s miles per hour, and Rana bikes at a speed of r miles per hour. They went for a 20 miles trip each at their usual speeds. After Sophie finishes, Rana still has to cover a distance of 20 - 20*(r/s) miles. Therefore, the time Sophie waits for Rana is (20 - 20*(r/s))/s hours.

Answer: CO≅HZ

Step-by-step explanation:

The two chords are congrunt so the intercepted arcs are congruent  CO≅HZ

Since segment CO is congruent to segment HZ, a congruence statement that is true include the following: C. CO ≅ HZ.

In Mathematics and Euclidean Geometry, two geometric figures are considered to be congruent only when their corresponding side lengths are equal and the magnitude of their angles are congruent.

Since we know that rigid motions preserve both the side length and angle measure, this ultimately implies that congruent segments have the same (equal) length.

In this context, we can reasonably infer and logically deduce that arc CO is congruent with arc HZ because chord CO is congruent to chord HZ;

arc CO ≅ arc HZ (intercepted arcs).

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Answer:2/9

Step-by-step explanation:

Final answer:

To solve 7x6, visualize a table with 7 rows of 6 columns each. Multiplying these numbers means counting all the cells in this table, which equals 42, since 7 times 6 is 42.

Explanation:

To find the product of 7x6, imagine you have 7 rows of a chart and each row has 6 columns. This means you'll fill the chart with numbers so that there are six numbers in each of the seven rows. Multiplying 7 by 6 means you're essentially counting how many numbers you'll have if you filled all the rows and columns.

To find the result, you just need to do a simple multiplication of the two numbers (7 and 6).
Here's how it's done step-by-step:

Understand that 7x6 is the same as adding the number 6 together, 7 times.

6 + 6 + 6 + 6 + 6 + 6 + 6

When you add them up, you get 42.

Therefore, the product of 7x6 is 42, meaning if you had a table with 7 rows and 6 columns, it would contain 42 cells.

The minimum number of complete revolutions that the wheel must make it to roll at least a 1,000 feet is 32.

The circumference of a circle is the perimeter of the circle. It is the total length of the boundary of the circle. The circumference of a circle is the product of the constant π and the diameter of the circle.

Given that, a wheel has a radius of 5 ft.

We know that, the formula to calculate circumference of a circle is 2πr.

So, circumference of wheel is 2×3.14×5

= 31.4 feet

Number revolutions to roll at least a 1,000 feet is

1000/31.4

= 31.84

≈ 32

Therefore, the minimum number of complete revolutions that the wheel must make it to roll at least a 1,000 feet is 32.

Learn more about the circumference here:

brainly.com/question/28757341.

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