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2 years ago

Pierre deposits $9,000 in a certificate of deposit that pays 1.4% interest, compounded semi-annually.

Mathematics

1 answer:

Elenna [48]2 years ago

5 0

9514 1404 393

Answer:

interest: $63
balance: $9063

Step-by-step explanation:

After 6 months, the interest accrued is ...

I = Prt

I = $9000·0.014·(6/12) = $63

This is added to the principal to get the balance at that point in time.

$9000 +63 = $9063

The interest earned in the first 6 months is $63. The balance after 6 months is $9063.

_____

The compound interest formula will give you the same result for one compounding period. It tells you the balance is ...

A = P(1 +r/n)^(nt)

where n is the number of times interest is compounded in a year (2), and t is the number of years (1/2). For annual rate r = 1.4%, this is ...

A = $9000(1 +0.007)^(2×1/2) = $9000·1.007 = $9063

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Not all visitors to a certain company's website are customers. In fact, the website administrator estimates that about 5% of all

Gnom [1K]

Answer:

0.0135 = 1.35% probability that, in a random sample of 4 visitors to the website, exactly 2 actually are looking for the website.

Step-by-step explanation:

For each visitor of the website, there are only two possible outcomes. Either they are looking for the website, or they are not. The probability of a customer being looking for the website is independent of other customers. This means that the binomial probability distribution is used 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.

5% of all visitors to the website are looking for other websites.

So 100 - 5 = 95% are looking for the website, which means that $p = 0.95$

Find the probability that, in a random sample of 4 visitors to the website, exactly 2 actually are looking for the website.

This is P(X = 2) when n = 4. So

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

$P(X = x) = C_{4,2}.(0.95)^{2}.(0.05)^{2} = 0.0135$

0.0135 = 1.35% probability that, in a random sample of 4 visitors to the website, exactly 2 actually are looking for the website.

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2 years ago

Find the next number in the sequence 1, 1/4, 1/9 , 1/16, 1/25

Umnica [9.8K]

(Add5) 1/9..(add 7) 1/16... (add9) 1/25... (add 11) and get -> 1/36

3 0

3 years ago

Through: (2,2), parallel to y=x+42)

shtirl [24]

Answer:

y=x

Step-by-step explanation:

We want a line parallel to y =x+42

The slope of y =x+42 is 1

Parallel lines have the same slope

We have the slope m=1 and a point (2,2)

We can use point slope form to write a line

y-y1 = m(x-x1)

y-2 = 1(x-2) point slope form

Changing to slope intercept form

y-2 = x-2

Add 2 to each side

y-2+2 = x-2+2

y=x

3 0

3 years ago

I have 10 goats, n of which are male. I need to choose 2 of them to make a casserole.

snow_tiger [21]

Answer: There are 4 male goats.

Step-by-step explanation:

We know that n of the 10 goats are male.

The probability that in a random selection, the selected goat is a male, is equal to the quotient between the number of male goats (n) and the total number of goats (10)

The probability is;

p = n/10

Now the total number of goats is 9, and the number of male goats is n -1

then the probability of selecting a male goat again is:

q = (n-1)/9

The joint probability (the probability that the two selected goats are male) is equal to the product of the individual probabilities, this is

P = p*q = (n/10)*((n-1)/9)

And we know that this probability is equal to 2/15

Then we have:

(n/10)*((n-1)/9) = 2/15

(n*(n-1))/90 = 2/15

n*(n-1) = 90*2/15 = 12

n^2 - n = 12

n^2 - n - 12 = 0

This is a quadratic equation, we can find the solutions if we use Bhaskara's formula:

For an equation:

a*x^2 + b*x + c = 0

The two solutions are given by:

$x = \frac{-b +- \sqrt{b^2 - 4*a*c} }{2*a}$

For our case, the solutions will be:

$n = \frac{1 +- \sqrt{(-1)^2 - 4*1*(-12)} }{2*1 } = \frac{1+- 7}{2}$

The two solutions are:

n = (1 - 7)/2 = -3 (this solution does not make sense, we can not have a negative number of goats)

The other solution is:

n = (1 + 7)/2 = 4

This solution does make sense, this means that we have 4 male goats.

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3 years ago

Which of the following statements describes a correct method for solving this equation?4x+6=8x

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D.its the most logical answer

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3 years ago