You collect old coins. today, you have two coins each of which is valued at $100. one coin is expected to increase in value by 5.2 percent annually while the other coin is expected to increase in value by 5 percent annually. what will be the difference in the value of the two coins 25 years from now?

After 3 minutes you both have knitted the same amount of rows.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, You knit 8 rows each minute and have already knitted 10 rows.

Your friend knits 5 rows each minute and has already knitted 19 rows.

Assuming t is the time when will you both have knitted the same amount of rows,

8t + 10 = 5t + 19.

8t - 5t = 19 - 10.

3t = 9.

t = 3 minutes.

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To find the amount of interest earned on a bank account after 4 years, use the compound interest formula. After plugging in the values, the account earns approximately $162.89 in interest.

To calculate the amount of interest earned on a bank account after 4 years, we need to use the formula for compound interest: A = P(1 + r/n)^(nt) - P. In this case, the initial deposit (P) is $3000, the annual interest rate (r) is 1.25%, compounded semi-annually (n = 2), and the time period (t) is 4 years. Plugging in these values, we get:

A = 3000(1 + 0.0125/2)^(2*4) - 3000

Solving this equation, we find that the account earns approximately $162.89 in interest after 4 years.

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Final answer:

The total number of employees working is 54. According to company policy requiring 1 supervisor for every 8 employees, 7 supervisors are needed to comply with this policy.

Explanation:

To find how many supervisors are required, we first need to know the total number of employees working. Since there are 3 teams of 18 employees, the total number of employees is 3 teams * 18 employees per team = 54 employees. Company policy requires 1 supervisor for every 8 employees. Therefore, we divide the total number of employees by the supervisor to employee ratio: 54 employees / 8 employees per supervisor = 6.75. Since we cannot have a fraction of a supervisor, we round up to the next whole number, making it 7 supervisors needed in total.

So, the supervisor would say: "We need 7 supervisors working tonight so we should be OK."

Answer:

The correct answer is: Option: D

D. Maximum: 35°   ;  minimum: −15°  ; Period: 4 hours

Step-by-step explanation:

We are given a function f(t) as:

          [tex]f(t)=25\sin (\dfrac{\pi}{2}t)+10[/tex]

We know that the maximum value of the function is obtained when the sine function is maximum.

i.e. when sine takes the value=1

and the minimum value of the function is obtained when the sine function is minimum.

i.e. when sine takes the value= -1

Hence, the minimum value of the function is:

-25+10= -15

and the maximum value of the function is:

25+10=35

Also the period of the function of the type:

[tex]f(x)=a\sin(bx)+c[/tex]

is:

[tex]Period=\dfrac{2\pi}{b}[/tex]

Hence, here we have: b=π/2

Hence, period is:

[tex]Period=\dfrac{2\pi}{\dfrac{\pi}{2}}\\\\\\Period=4[/tex]

         Hence, option: D is the correct answer.

Answer:B

Step-by-step explanation:

The time at which her lesson start is 9:30 am.

More people to do a task means less time it will take.

Less people to do a task means more time it will take.

Thus, they are inversely related.

If x men take y time for a work,

We can define a constant as "Manpower" needed for doing that specific work.

Let we define:

Manpower needed for a work = y + y + y + .. + y = Time per man × count of men

Manpower needed for a work = xy

We are given that;

Time= 1 hour 20 minutes

Now,

To find the time when Sierra’s lesson started, you need to subtract the duration of her lesson from the time when she finished. You can do this by subtracting the minutes and then the hours.

First, subtract 20 minutes from 10:50 am. To do this, you can take away 10 minutes to get 10:40 am and then take away another 10 minutes to get 10:30 am.

Next, subtract 1 hour from 10:30 am. To do this, you can take away 60 minutes or simply reduce the hour by 1. Either way, you get 9:30 am.

Therefore, by work and time the answer will be 9:30 am.

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Final answer:

The lowest common denominator of the fractions 5/(n-2) and[tex](n+2)/(n^2-4)[/tex] is[tex]n^2 - 4,[/tex] which is the factored form of the denominator of the second fraction.

Explanation:

The question asks to find the lowest common denominator (LCD) of two fractions: 5/(n-2) and (n+2)/[tex]n^2 - 4,[/tex]. To do this, we need to factor each denominator, if possible, and then determine the LCD. The second denominator can be factored into (n+2)(n-2) since it is a difference of squares. For the LCD, we need each factor present at least as many times as it occurs in any one of the denominators. The first fraction is already missing the (n+2) factor, so we multiply the numerator and the denominator of this fraction by (n+2) to have an equivalent fraction with the common denominator.

The common denominator then is (n+2)(n-2), equivalent to[tex]n^2 - 4,[/tex] So the LCD of the two fractions is[tex]n^2 - 4.[/tex] We can use this denominator to combine fractions or compare them. No further steps are necessary because the second fraction already has the LCD. Therefore, the LCD for both fractions is [tex]n^2 - 4.[/tex]

Answer:

120°

Step-by-step explanation:

Final answer:

The proportion of data more than 2.0 standard deviations away from the mean in a normal distribution is less than 5%, consisting of 2.5% in the upper tail and 2.5% in the lower tail.

Explanation:

The proportion of values more than 2.0 standard deviations from the mean in a normal distribution is less than 5% because according to the empirical rule, 95% of the data falls within 2 standard deviations of the mean. Therefore, if you are looking at a normal distribution and you want to know the proportion of data that lies beyond 2 standard deviations from the mean, you would subtract 95% from 100%, which is 5%. This is then split between both tails of the distribution, so you have 2.5% in the upper tail and 2.5% in the lower tail, for a total of 5% more than 2 standard deviations away from the mean.

The answer is 6 inches