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3 years ago

If you deposit $5000 into an account paying 6% annual interest compounded monthly, how long until

Mathematics

2 answers:

Anna35 [415]3 years ago

7 0

Answer:

3,000

Step-by-step explanation:

mafiozo [28]3 years ago

5 0

Answer:

7.85 years which I think rounds to about 7 years and 11 months

Step-by-step explanation:

The formula for compound interest is

$AV=PV*(1+\frac{i}{n})^{t*n}$

Where AV = Accumulated Value (or Future value)

PV= Present value

i= nominal interest rate

n= number of times compunded in a period (here a period is a year)

t= number of periods (years in this case)

We can plug this numbers in to get

8000=5000*(1+(.06/12))^12x

First we divide by 5000 to get

1.6=(1.005)^12x

We can rewrite this into a logarithim

log₁.₀₀₅1.6=12x

The formatting here is kind of weird but I'm trying to say that log base 1.005 1.6 = 12x

We can compute this and get

94.2355=12x

divide by 12 to get that

x=7.85 Years

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Your next math test is worth 111 points and contains 32 problems. Each problem is worth either 4 points or 3 points. How many 3

AysviL [449]

There are a total of 32 problems.

Assumed all 32 problems are 3 points questions ⇒ 32 x 3 = 96 points.

The test is worth 111 points, so there is an extra of 111-96 points = 15 points.

The difference in points in the 2 type of questions is 4 - 3 = 1 points.

Number of 4 points questions = 15 ÷ 1 = 15.

Number of 3 points questions = 32 - 15 = 17.

Answer: There are 17 3-points questions and 15 4-points questions.

6 0

3 years ago

Simplify 4a^3 b^2 x 6a^6b^9

Ket [755]

Answer:

24a^9 b^11

Step-by-step explanation:

$4a ^{3} b ^{2} \times 6a ^{6} b ^{9} \\ = (4 \times 6)a ^{3 + 6}b ^{2 + 9} \\ = 24a^{9} b^{11}$

5 0

3 years ago

The Skittles jar has a radius of 3.5 cm and a height of 11.5 cm. Using the two given boxes for reference what would be a good es

nevsk [136]

Answer:

1052

Step-by-step explanation:

The two given boxes for reference are presented below.

Since we know the dimensions of the first container, we can calculate its volume.

$V_1= 5 \text{cm} \cdot 4 \text{cm} \cdot 4 \text{cm} = 80 \text{cm}^3$

The first container held 192 skittles. Using that fact, now that we know the volume of the first box, we can calculate the volume of a single skittle.

$v = \frac{80}{192} = 0.416 \approx 0.42 \text{cm}^3$

The second container held 258 skittles.

The volume of the second box is:

$V_2 = 12 \text{cm}\cdot 3 \text{cm} \cdot 3 \text{cm} = 108 \text{cm}^3$

Using this facts, the volume of a single skittle would be

$v = \frac{108}{258} = 0.418 \approx 0.42 \text{cm}^3$

Therefore, the volume of single skittle is around to 0.42 cm³.

A skittle jar is a cylinder. Its volume is calculated by the formula

$V = r^2h \pi$ ,

where $r$ is the radius and $h$ is the height. From the given data, we have $r = 3.15 \text{cm}$ and $h = 11.5 \text{cm}$ . Hence, the volume of the jar is