Find AuB and AnB for the sets A and B. A={3, 4, 5, 6, 7), B = {4, 6, 8, 10)

In 2010, the population of a town was 8500. The population decreased by 4.5% each year.

Soloha48 [4]

Answer:

This is a problem in exponential decay.

a) If a town's population decreases by 4.5% every year that also means that the town's population decreases by a factor of .955 each year. (1 - .045 = .955)

So, after 5 years, the town's population is:

8,500 * .955^5 which equals 6,752.

So, basically, after t years, the town's population equals

8,500 * .955^t where t is the number of years that have passed since the year 2010.

b) population = 8,500 * .955 ^ (number of years since 2010)

7,000 / 8,500 = .955 ^ (number of years since 2010)

0.8235294118 = .955 ^ (number of years since 2010)

To solve for (number of years since 2010) we take logs of both sides

log (0.8235294118 ) = number of years since 2010 * log(.955)

-0.0843208857 = number of years since 2010 * -0.0199966284

-0.0843208857 / -0.0199966284 = number of years since 2010

4.2167551422 = number of years since 2010

So, population = 7,000 when the year is 2014.2167551422

Or about 2.6 months into 2014

(YES, it's just that "easy") LOL

Step-by-step explanation:

6 0

2 years ago

Find the length BC

Nady [450]

Answer:

The length of BC = 12

Step-by-step explanation:

c^2 = a^2 + b^2

15^2 = 9^2 + b^2

225 = 81 + b^2

b^2 = 225 - 81

b^2 = 144

b = 12

The length of BC is 12

5 0

2 years ago

There are 2504 computer science students at a school. Of these, 1876 have taken a course in Java, 999 have taken a course in Lin

Y_Kistochka [10]

Answer:

492

Step-by-step explanation:

As per the given data of the question:

Total number of students = 2504

Number of students in Java (J) = 1876

Number of students in Linux (L) = 999

Number of students in C = 345

J∩L = 876

L∩C = 231

C∩J = 290

L∩J∩C = 189

Now according to Venn-diagram as drawn below:

Number of students haven taken courses in Java and Linux both only

= J∩L - L∩J∩C

= 876 - 189

= 687

Number of students haven taken courses in Java and C both only

= C∩J - L∩J∩C

= 290 - 189

= 101

Number of students haven taken courses in C and Linux both only

= L∩C - L∩J∩C

= 231 - 189

= 42

Therefore,

Number of students only in Java = 1876 - 687 - 189 - 101 = 899

Number of students only in Linux = 999 - 687 - 189 - 42 = 81

Number of students only in C = 345 - 42 - 189 - 101 = 13

So,

Number of students who have not taken a course in any of these three subjects

= 2504 - 899 - 81 - 13 - 687 - 189 -101 - 42

= 492

Hence, the students who have not taken a course in any of these three subjects = 492.

6 0

2 years ago

Let f(x) = -12-31 +3 and g(x) = 3x - 3. Graph the functions in the same coordinate plane.

castortr0y [4]

Answer:

Zeros of Functions. A zero of a function f is a number a such that f(a) = 0. In other words, a zero of f is a solution for the equation f(x) = 0.

Step-by-step explanation:

5 0

2 years ago

Anthony wants to buy CD for $400 that earns 2.5% APR and is compound quarterly. The CD matures in 3 years. Hi interest earned wi

lukranit [14]

Answer:

The correct option is: B. $30.00

Step-by-step explanation:

The formula for compound interest is.......

$A=P(1+\frac{r}{n})^n^t$ , where A= Final amount, P= Initial amount, r= rate of interest in decimal form, n= number of compounding in a year and t= time duration in years.

Anthony wants to buy CD for $400 that earns 2.5% APR and is compound quarterly and the CD matures in 3 years.

So here, $P= 400, r=2.5\%=0.025, t= 3$

As the CD is compounded quarterly, so here $n= 4$

Plugging these values into the above formula......

$A= 400(1+\frac{0.025}{4})^(^4^*^3^)\\ \\ A= 400(1+0.00625)^1^2\\ \\ A=400(1.00625)^1^2\\ \\ A= 431.053...$

So, the amount of total interest earned $= (\$431.053...-\$400)=\$31.053... \approx \$30.00(Approximately)$

5 0

2 years ago