Mathematics, 29.05.2021 08:00 mmoore36

Sara is planning on fully renovating her kitchen. She figures that this will cost a total of $25,750. If Sandra already has $21,400 saved up, what annual interest rate compounded semiannually would Sara need to earn in order to have the required
funds if she invests her money for 2.5 years?

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Answer from: chem1014

She needs an annual interest rate of 7.54%.

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.

She figures that this will cost a total of $25,750.

This means that A = 25750 .

Sandra already has $21,400 saved up

This means that P = 21400 .

Semianually compunding, 2.5 years.

This means that n = 2, t = 2.5

What interest rate?

We have to find r. So

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

$25750 = 21400(1 + \frac{r}{2})^{2*2.5}$

$(1 + 0.5r)^5 = \frac{25750}{21400}$

$\sqrt[5]{(1 + 0.5r)^5} = \sqrt[5]{\frac{25750}{21400}}$

$1 + 0.5r = (\frac{25750}{21400})^{\frac{1}{5}}$

1 + 0.5r = 1.0377

0.5r = 0.0377

$r = \frac{0.0377}{0.5}$

r = 0.0754

0.0754*100% = 7.54%

She needs an annual interest rate of 7.54%.

Answer from: Quest

The answer for this is 9/1253decimal form 0.007

Answer from: Quest

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range:

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