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3 years ago

The length of one side of a square is (x + 2 1/4). If the perimeter is 14 units, what is the area?

Mathematics

1 answer:

Stels [109]3 years ago

7 0

The perimeter is the total of adding all of the side lengths together.

A square has 4 equal side lengths.

So the perimeter of a square is:

P = s + s + s + s or P = 4s

[P = perimeter s = side lengths of the square]

Since you know the side length of the square is (x + 2 1/4), you can replace s with (x + 2 1/4)

P = 4s

P = 4(x + 2 1/4) Multiply 4 into (x + 2 1/4)

P = 4x + 8 4/4

P = 4x + 9

Since you know the perimeter, you can plug it in.(you could have also plugged it in in the beginning)

P = 4x + 9

14 = 4x + 9 Subtract 9 on both sides

5 = 4x Divide 4 on both sides

5/4 = x

Now that you know x, find the side length of the square.

(x + 2 1/4)

(5/4 + 2 1/4)

2 6/4 = 3 2/4 = 3 1/2 units or 3.5 units

To find the area of a square, you multiply 2 of the sides together:

A = s · s

A = 3.5 · 3.5

A = 12.25 units²

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3 years ago

How do you work out the rate, time and principal from the compound interest formula?

wlad13 [49]

Answer:

Part 1) $P=A/(1+\frac{r}{n})^{nt}$ (see the explanation)

Part 2) $r=n[\frac{A}{P}^{1/(nt)}-1]$ (see the explanation)

Part 3) $t=log(\frac{A}{P})/[(n)log(1+\frac{r}{n})]$ (see the explanation)

Step-by-step explanation:

we know that

The compound interest formula is equal to

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

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

Part 1) Find the Principal P

The values of A,r,n and t are given

Isolate the variable P

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

Divide both side by $(1+\frac{r}{n})^{nt}$

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

Part 2) Find the rate r

The values of A,P,n and t are given

Isolate the variable r

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

Divide both sides by P

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

Elevated both sides to 1/(nt)

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

subtract 1 both sides

$\frac{A}{P}^{1/(nt)}-1 =\frac{r}{n}$

Multiply by n both sides

$r=n[\frac{A}{P}^{1/(nt)}-1]$

Part 3) Find the time t

The values of A,P,r and n are given

Isolate the variable t

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

Divide both sides by P

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

Apply log both sides

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

Apply property of exponents

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

Divide both side by $(n)log(1+\frac{r}{n})$

$t=log(\frac{A}{P})/[(n)log(1+\frac{r}{n})]$

3 0

3 years ago

We draw a random sample of size 25 from a normal population with variance 2.4. If the sample mean is 12.5, what is a 99% confide

Helen [10]

Answer:

Step-by-step explanation:

Confidence interval for the population mean is expressed by the formula;

CI = xbar ± Z(S/√n) where;

xbar is the sample mean = 12.5

Z is the z score at 99% confidence = 2.576

S is the standard deviation = √variance

S = √2.4 = 1.5492

n is the sample size = 25

Substituting the given values into the formula given above,

CI = 12.5 ± 2.576(1.5492/√25)

CI = 12.5 ± 2.576(0.30984)

CI = 12.5 ± 0.7981

CI = (12.5-0.7981, 12.5+0.7981)

CI = (11.2019, 12.7981)

Hence the 99% confidence interval for the population mean is 11.2≤ $\mu$ 12.8 (to 1 decimal place)

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