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3 years ago

Solve the following compound

Mathematics

1 answer:

hammer [34]3 years ago

5 0

Answer:

b<-12 or b>-12

(-∞,-12]U[-12,∞)

Step-by-step explanation:

0.5b > -6 or 3b + 16 <-8 + b

I solve these separately

0.5b > -6

Divide by .5 on each side

0.5b/.5 > -6/.5

b >-12

3b + 16 <-8 + b

subtract b from each side

3b-b + 16 <-8 + b -b

2b+16<-8

Subtract 16 from each side

2b+16-16<-8-16

2b< -24

Divide each side by 2

2b/2 <-24/2

b<-12

b<-12 or b>-12

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Howard invested $5,000 in Certificate of Deposit (CD) that pays 3.75% interest. compounded weekly. What is the value of the CD a

blsea [12.9K]

Answer:

The value of the CD at the end of the 4 years is $5,808.86.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

$A(t) = P(1 + \frac{r}{n})^{nt}$

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

Howard invested $5,000 in Certificate of Deposit (CD) that pays 3.75% interest.

This means that $P = 5000, r = 0.0375$

Compounded weekly

An year has 52 weeks, so $n = 52$

Then

$A(t) = P(1 + \frac{r}{n})^{nt}$

$A(t) = 5000(1 + \frac{0.0375}{52})^{52t}$

What is the value of the CD at the end of the 4 years?

This is A(4). So

$A(4) = 5000(1 + \frac{0.0375}{52})^{52*4} = 5808.86$

The value of the CD at the end of the 4 years is $5,808.86.

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3 years ago

Can y'all help me with my math problem please

kolezko [41]

Answer:

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Step-by-step explanation:

Option D

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3 years ago

Read 2 more answers

Mitch jarred 12 liters of jam 2 days. How many days does Mitch need to spend making jam if he want to jar 18 jam in all

grigory [225]

Answer:

3 days

Step-by-step explanation:

well, in 2 days mitch can jar 12 liters of jam right? but 12 is divisible by 2. so let’s just do that to help us out later, 12 / 2 = 6

now that we have that, let’s make sure. in 1 day he can jar 6, in 2 he can jar 12.

that seems right! so now, can we add 6 to 12 to make 18? yep! how many more times do we need to add 6? 1 time. so 12 + 6 = 18. every 6 liters is 1 day. so 1 day + 1 day + 1 day (18 liters) is 3 days total!

hope this helped you!

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3 years ago

Richard had just been given a 6-question multiple-choice quiz in his history class. Each question has four answer, of which only

In-s [12.5K]

Answer:

a) 0.02% probability that he will answer all questions correctly.

b) 82.20% probability that he will answer at least one questions correctly

c) 16.94% probability that he will answer at least half questions correctly

Step-by-step explanation:

For each question, there are only two possible outcomes. Either Richard answer it correctly, or he answers it wrong. The probability of answering a question correctly is independent from other questions. So we use the binomial probability distribution to solve this problem.

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.

Richard had just been given a 6-question multiple-choice quiz in his history class.

This means that $n = 6$

Each question has four answer, of which only one is correct. Since Richard had not attend not attended class recently, he doesn't any of the answer.

This means that $p = \frac{1}{4} = 0.25$

a. What is the probability that he will answer all questions correctly?

This is $P(X = 6)$ .

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

$P(X = 6) = C_{6,6}.(0.25)^{6}.(0.75)^{0} = 0.0002$

0.02% probability that he will answer all questions correctly.

b. What is the probability that he will answer at least one questions correctly?

Either he does not answer any of the questions correctly, or he does answer at least one correctly. The sum of the probabilities of these events is decimal 1. So

$P(X = 0) + P(X \geq 1) = 1$

We want $P(X \geq 1)$

$P(X \geq 1) = 1 - P(X = 0)$

In which

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

$P(X = 0) = C_{6,0}.(0.25)^{0}.(0.75)^{6} = 0.1780$

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.1780 = 0.8220$

82.20% probability that he will answer at least one questions correctly

c. What is the probability that he will answer at least half questions correctly?

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

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

$P(X = 3) = C_{6,3}.(0.25)^{3}.(0.75)^{3} = 0.1318$

$P(X = 4) = C_{6,4}.(0.25)^{4}.(0.75)^{2} = 0.0330$

$P(X = 5) = C_{6,5}.(0.25)^{5}.(0.75)^{1} = 0.0044$

$P(X = 6) = C_{6,6}.(0.25)^{6}.(0.75)^{0} = 0.0002$

$P(X \geq 3) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) = 0.1318 + 0.0330 + 0.0044 + 0.0002 = 0.1694$

16.94% probability that he will answer at least half questions correctly

4 0

3 years ago

Set up the equation you would use to solve the problem.Do not actually solve the equation.

Cloud [144]

Answer: B

Explanation

I believe it’s B because it says when the plane fly with the wind it’s 390miles so if we want to know the speed of the plane In still air it should be 390/x + 10 because we need to consider that the speed of the plane + the speed of wind. While the plane fly at 325 against the wind so it should be 325/x - 10 cuz this time it goes against the wind.

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3 years ago