Can someone help me please

If $1000 is invested in an account earning 3% compounded monthly, how long will it take the account to grow in value to $1500? R

My name is Ann [436]

Answer:

14 months

Step-by-step explanation:

1 month) 1.03(1000) = 1030

2 months) 1030(1.03) = 1060.9

3 months) 1060.9(1.03) = 1092.727

4 months) 1092.727(1.03) = 1125.50881

5 months) 1125.50881(1.03) = 1159.2740743

6 months) 1159.2740743(1.03) = 1194.05229653

7 months) 1194.05229653(1.03) = 1229.87386542

8 months) 1229.87386542(1.03) = 1266.77008139

9 months) 1266.77008139(1.03) = 1304.77318383

10 months) 1304.77318383(1.03) = 1370.01184302

11 months) 1370.01184302(1.03) = 1411.11219831

12 months) 1411.11219831(1.03) = 1453.44556426

13 months) 1453.44556426(1.03) = 1497.04893119

14 months) 1497.04893119(1.03) = 1541.96039912

I multiplied them all by 1.03 because 0.03 is 3% but if I multiplied the numbers by 0.03 it would give me 3% of that number instead of increasing it by 3% so by doing 1.03 x the number I am adding the 3% onto the number

3 0

3 years ago

Suppose that 50% of all young adults prefer McDonald's to Burger King when asked to state a preference. A group of 12 young adul

ddd [48]

Answer:

a) 0.194 = 19.4% probability that more than 7 preferred McDonald's

b) 0.787 = 78.7% probability that between 3 and 7 (inclusive) preferred McDonald's

c) 0.787 = 78.7% probability that between 3 and 7 (inclusive) preferred Burger King

Step-by-step explanation:

For each young adult, there are only two possible outcomes. Either they prefer McDonalds, or they prefer burger king. The probability of an adult prefering McDonalds is independent from other adults. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

50% of all young adults prefer McDonald's to Burger King when asked to state a preference.

This means that $p = 0.5$

12 young adults were randomly selected

This means that $n = 12$

(a) What is the probability that more than 7 preferred McDonald's?

$P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 8) = C_{12,8}.(0.5)^{8}.(0.5)^{4} = 0.121$

$P(X = 9) = C_{12,9}.(0.5)^{9}.(0.5)^{3} = 0.054$

$P(X = 10) = C_{12,10}.(0.5)^{10}.(0.5)^{2} = 0.016$

$P(X = 11) = C_{12,11}.(0.5)^{11}.(0.5)^{1} = 0.003$

$P(X = 12) = C_{12,12}.(0.5)^{12}.(0.5)^{0} = 0.000$

$P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) = 0.121 + 0.054 + 0.016 + 0.003 + 0.000 = 0.194$

0.194 = 19.4% probability that more than 7 preferred McDonald's

(b) What is the probability that between 3 and 7 (inclusive) preferred McDonald's?

$P(3 \leq X \leq 7) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 3) = C_{12,3}.(0.5)^{3}.(0.5)^{9} = 0.054$

$P(X = 4) = C_{12,4}.(0.5)^{4}.(0.5)^{8} = 0.121$

$P(X = 5) = C_{12,5}.(0.5)^{5}.(0.5)^{7} = 0.193$

$P(X = 6) = C_{12,6}.(0.5)^{6}.(0.5)^{6} = 0.226$

$P(X = 7) = C_{12,7}.(0.5)^{7}.(0.5)^{5} = 0.193$

$P(3 \leq X \leq 7) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) = 0.054 + 0.121 + 0.193 + 0.226 + 0.193 = 0.787$

0.787 = 78.7% probability that between 3 and 7 (inclusive) preferred McDonald's

(c) What is the probability that between 3 and 7 (inclusive) preferred Burger King?

Since $p = 1-p = 0.5$ , this is the same as b) above.

So

0.787 = 78.7% probability that between 3 and 7 (inclusive) preferred Burger King

7 0

3 years ago

The bakers at Healthy Bakery can make 270 bagels in 10 hours. How many bagels can they bake in 15 hours? What was the rate per h

Tcecarenko [31]

Answer:

405 bagels 27 an hour

Step-by-step explanation:

this is because when you divide 270 by 10 you get 27 which is how much per hour then multiply the # of bagels and the # of hours you get is 405. In other words you first want to know how many bagels it took to get to 270 bagels in 10 hours.Hope it helped.

7 0

3 years ago

I need help quick! <br> what is the coordinate of the midpoint GO

Zolol [24]

0 because the number in the middle is the midpoint.

5 0

3 years ago

Read 2 more answers

Clare travels at a constant speed, as shown on the double number line.

Zanzabum

Answer:

How far does Clare travel in one hour?

A: 36

How far does Clare travel in three hours?

A: 108

How far does Clare travel in 3.5 hours?

A: 126

Step-by-step explanation:

Find the Unit Value

72/2 = 36

Clare travels 36 miles per hour

Therefore, you must multiply the hours by the Unit travel time for the answers.

1 X 36 = 36

3 X 36 = 108

3.5 X 36 = 126

7 0

2 years ago