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3 years ago

A

1 answer:

8 0

Alright, lets say the measure of the 3rd angle (the smallest one) is x degree, then measure of the 1st angle will be (x + 25) degree, and 2nd one: 3x degree. The sum of all the angles in any triangles is 180 degrees.

(x + 25) + 3x + x = 180

5x + 25 = 180 ---> 5x = 180 - 25 ---> 5x = 155 ---> x = 155/5 ---> x = 31o (third angle)

31 + 25 = 56o (first angle)

3 × 31 = 93o (second angle)

56 + 93 + 31 = 180

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What interest rate, to the nearest tenth of a percent, that is required for an investment subject to continuous compounding to i

Sunny_sXe [5.5K]

Answer:

It will take an interest rate of 8.1% to get 150% of the initial investment in just 5 years.

Step-by-step explanation:

Use the formula for continuous compounding

$X(t) = Pe^{rt}$

where r stands for the (annual) interest rate, t for time in years, P for the initial principal (investment) and X is the amount after t years.

(this formula can be beautifully derived from just basic considerations, btw)

We are given t=5, and percent increase on the initial P, so we can solve for r

$X(5) = 1.5P=Pe^{r\cdot5}\\1.5=e^{r\cdot5}\\\ln 1.5=\ln e ^{5r}\\\ln 1.5=5r\\r = \frac{\ln 1.5}{5}=0.081\rightarrow 8.1\%$

It will take an interest rate of 8.1% to get 150% of the initial investment in just 5 years.

5 0

3 years ago

Can anyone help me in explaining subtraction of polynomials please help I’m desperate and I’m pretty much on my own when it come

Sidana [21]

Answer:

Think of combining like terms when subtracting polynomials. For example, 3x² and -2x². They both have x² in common. So, if you were to combine 3x² and -2x², it would be like 3x² + (-2x²). Think of this like 3 + (-2), which equals 1. In this case, it would equal 1x² or x².

Let's take this problem for example: 6x² - 3x + 4 - (-2x² +2x - 2)

Parentheses are super important; The first thing you want to do is distribute the negative sign out to everything inside the parentheses!

So,

6x² - 3x + 4 - (-2x² +2x - 2) *multiply the neg. to -2x², 2x, and -2

Now, if you do that, the equation would now look like:

6x² - 3x + 4 + 2x² - 2x + 2

Now think of combining like terms. Here are the like terms:

6x² - 3x + 4 + 2x² - 2x + 2 (Let's rewrite it to look like this...)

6x² + 2x² - 3x - 2x + 4 + 2

Let's combine the x²'s first, so... 6x² + 2x² = 8x²

Let's combine the x's, so... -3x - 2x = -5x

Let's combine the constants (numbers with no variable), so... 4 + 2 = 6

Your solution should be 8x² - 5x + 6

4 0

2 years ago

35 2/9 divided 5 8/9

weqwewe [10]

Answer:

53/405

Step-by-step explanation:

5 0

3 years ago

How to Become a Millionaire Upon graduating from col- lege, Donna has no initial capital. However, during each year she makes de

lesantik [10]

Answer:

amount is 1000 × $e^{0.08t}$

$40762.20 balance of Donna's account will be 1 million dollars when she retires in 40 years

rate 14.97 % when Donna's account will have a balance of 1 million dollars in 40 years when principal is $2500

Step-by-step explanation:

principal = $1000

rate = 8 % = 0.08

to find out

the future value, S(t)

principal when Donna's account will be 1 million dollars when she retires in 40 year

at what rate Donna's account will have a balance of 1 million dollars in 40 years

solution

we know compounded continuously formula i.e.

amount = principal × $e^{rt}$ ..................1

put the value principal and rate in equation 1 to find amount any time

amount = principal × $e^{rt}$

amount = 1000 × $e^{0.08t}$

in 2nd part we have time 40 year and amount 1 million so put rate amount and time in equation 1 to find principal

rt = 0.08 × 40 = 3.2

amount = principal × $e^{rt}$

1000000 = principal × $e^{3.2}$

principal = 1000000 / $e^{3.2}$

principal = 1000000 / 24.5325302

principal = 40762.20397

so $40762.20 balance of Donna's account will be 1 million dollars when she retires in 40 years

in 3rd part we have amount 1 million and principal $2500 and time 40 year put all these in equation 1 to find rate

amount = principal × $e^{rt}$

1000000 = 2500 × $e^{40r}$

take ln both side

ln $e^{40r}$ = ln (1000000 / 2500 )

40 r = ln 400

r = ln (400) / 40

r = 0.149787

so rate 14.97 % when Donna's account will have a balance of 1 million dollars in 40 years when principal is $2500

5 0

3 years ago

A number cube with the numbers 1 through 6 is rolled. What is the probability of the number cube showing a 4 or a number less th

Sonja [21]

Answer:

Step-by-step explanation:

The probability is

(

)

Explanation:

To calculate the probability you have to count the number of all possible results

and the number of results that fulfill the given condition

In this case

{

}

Thereare 6 possible result of a dice toss. So

The given condition is "the result is divisible by

", so

{

}

- those are the only numbers divisible by

, so

Finally to calculate the probability we have to divide

(

)

Note The probability is never larger than

, so if you get such result then there must be a mistake in calculations.

4 0

3 years ago

Read 2 more answers