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3 years ago

17. A baseball trading card is sold for $2, and its

Mathematics

2 answers:

Sidana [21]3 years ago

6 0

Answer:

$4.32

Step-by-step explanation:

8% can be represented as 1.08

2 x 1.08 = 2.16

2 x 1.08 x 1.08 = 2.33

2 x 1.08 x 1.08 x 1.08 = 2.52

etc. all the way up to 10

Sav [38]3 years ago

6 0

Answer:

$1,065.71

Step-by-step explanation:

use the compound interest formula: A = P(1 + r/n)^nt where:

P = principal, $2

r = interest rate, 8% = .08

t = term, in years; 10

n = # of times per year compounding occurs; 1

A = 2(1 + .08/10)^10(1)

A = 2(1 + .008)^10

A = 2(1.008)^10

A = 2.008^10

A = 1065.71

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A small garden measures 9 ft by 13 ft. A uniform border around the garden increases the total area to 192 ft square. What is the

victus00 [196]

The width of border is 1.5 feet

<h3><u>Solution:</u></h3>

Given that small garden measures 9 ft by 13 ft

A uniform border around the garden increases the total area to 192 ft square

To find: width of border

Let the width of border be "x"

Then the new measures of garden are (9 + 2x) feet and (13 + 2x) feet

The total area of garden = 192 square feet

$(9 + 2x)(13 + 2x) =192$

$117 + 18x + 26x + 4x^2 = 192\\\\4x^2 + 44x - 75 = 0$

<em><u>Let us solve the above equation by quadratic formula</u></em>

$\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0\\\\x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Using the above formula,

For $4x^2 + 44x - 75 = 0$ , we have a = 4 ; b = 44 ; c = -75

Substituting the values of a = 4 ; b = 44 ; c = -75 in above quadratic formula we get,

$\begin{aligned}&x=\frac{-44 \pm \sqrt{44^{2}-4(4)(-75)}}{2 \times 4}\\\\&x=\frac{-44 \pm \sqrt{1936-1200}}{8}\\\\&x=\frac{-44 \pm \sqrt{3136}}{8}\\\\&x=\frac{-44 \pm 56}{8}\end{aligned}$

$\begin{aligned}&x=\frac{-44+56}{8} \text { or } x=\frac{-44-56}{8}\\\\&x=\frac{12}{8} \text { or } x=\frac{-100}{8}\\\\&x=1.5 \text { or } x=-12.5\end{aligned}$

Since "x" cannot be negative,

we get x = 1.5

Thus width of border is 1.5 feet

4 0

3 years ago

4. Nine fruit juice bottles contain 4 1/2 litres of fruit juice between them.

brilliants [131]

Answer:

2 $\frac{1}{2}$ litres or 2.5 litres

Step-by-step explanation:

From the question, 9 fruit juice bottles contain 4 $\frac{1}{2}$ litres of fruit juice. Therefore, to find how many litres of fruit juice would be contained in 5 fruit juice bottles, you multiply 5 by 4 $\frac{1}{2}$ litres and you divide the product by 9.

i.e. Let the quantity of the fruit juice for 5 bottles be x.

9 juice bottles ===> 4 $\frac{1}{2}$ litres

5 juice bottles ===> x

∴x = $\frac{5 * 4\frac{1}{2} }{9} litres$