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3 years ago

3. Diego is attending a college where tuition is $10,600 per year. He

Mathematics

1 answer:

strojnjashka [21]3 years ago

8 0

Let's analyze how much money Diego will have:

He received $3,000 grant;
His parents will another %5,000.

In total, Diego will have $ $3,000+5,000 = 8,000$ . Now, we should find out how much money Diego still need. How $10,600-8,000=2,600$ , we conclude that Diego needs earn $2,600.00 to can pay for the first year's tuition.

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17. Scott cuts his birthday cake into nine equal pieces and eats two of them.

Roman55 [17]

Answer:

A. 0.2222

B. Repeat indefinitely

Step-by-step explanation:

A. We have that Scott has 9 pieces in total and he eats 2 of them. That means he eats 2 out of the 9, so we have 2 ÷ 9. (see attachment)

The decimal form is: 0.2222.

B. Clearly, we can see that throughout the long division, we keep getting 20 - 18 = 2, which makes another 20 and so on. So, this will repeat indefinitely.

7 0

2 years ago

The price of products may increase due to inflation and decrease due to depreciation. Marco is studying the change in the price

likoan [24]

Answer:

A) 3%

B) Product A

Step-by-step explanation:

Exponential Function

General form of an exponential function: $y=ab^x$

where:

a is the initial value (y-intercept)
b is the base (growth/decay factor) in decimal form
x is the independent variable
y is the dependent variable

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

Part A

Product A

Assuming the function for Product A is exponential:

$f(x) = 0.69(1.03)^x$

The base (b) is 1.03. As b > 1 then it is an increasing function.

To calculate the percentage increase/decrease, subtract 1 from the base:

⇒ 1.03 - 1 = 0.03 = 3%

Therefore, product A is increasing by 3% each year.

Part B

$\sf percentage\:change=\dfrac{final\:value-initial\:value}{initial\:value} \times 100$

To calculate the percentage change in Product B, use the percentage change formula with two consecutive values of f(t) from the given table:

$\implies \sf percentage\:change=\dfrac{10201-10100}{10100}\times 100=1\%$

Check using different two consecutive values of f(t):

$\implies \sf percentage\:change=\dfrac{10303.01-10201}{10201}\times 100=1\%$

Therefore, as 3% > 1%, Product A recorded a greater percentage change in price over the previous year.

Although the question has not asked, we can use the given information to easily create an exponential function for Product B.

Given:

a = 10,100
b = 1.01
n = t - 1 (as the initial value is for t = 1 not t = 0)

$\implies f(t) = 10100(1.01)^{t-1}$

To check this, substitute the values of t for 1 through 4 into the found function:

$\implies f(1) = 10100(1.01)^{1-1}=10100$

$\implies f(2) = 10100(1.01)^{2-1}=10201$

$\implies f(3) = 10100(1.01)^{3-1}=10303.01$

$\implies f(4) = 10100(1.01)^{4-1}=10406.04$

As these values match the values in the given table, this confirms that the found function for Product B is correct and that Product B increases by 1% per year.

4 0

2 years ago

The volume of a sphere can be described by the following formula, where V = volume and r = radius of the sphere.

Anika [276]

Option C: $r = \sqrt[3]{\frac{3V}{4\pi} }$ is the right answer