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3 years ago

Name:

Mathematics

1 answer:

baherus [9]3 years ago

7 0

Step-by-step explanation:

(Explanation is above)

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What is the difference between the value of your stocks at the end of the second year and your initial investment?

Brrunno [24]

Given:

$\begin{gathered} Investment=3,150.00 \\ First-year=loss-5\% \\ Second-year=gain-9\% \end{gathered}$

To Determine: The value of the stocks in the second year compared to the initial investment

Solution

$\begin{gathered} First-year=5\%-loss \\ End-of-first-year=(100-5)\%\times3150 \\ =95\%\times3150 \\ =2992.50 \end{gathered}$ $\begin{gathered} Second-year=9\%-gain \\ End-of-second-year=(100+9)\%\times2992.50 \\ =109\%\times2992.50 \\ =1.09\times2992.50 \\ =3261.83 \end{gathered}$

Therefore, the difference between the value of your stocks at the end of the second year and the initial investment is

$\begin{gathered} Difference=3261.83-3150 \\ =111.83 \end{gathered}$

Hence, the difference is $111.83

5 0

1 year ago

During a checker game there are 16 pieces left. the ratio of black to red is 3:5. How many black pieces are left on the board?

olganol [36]

We know that there are 16 pieces left and that the ratio is 3 : 5. The ratio teels us there are 8 "parts" inside (because 3 + 5 = 8), so now we may just divide 16 by 8 to find out how much is one such "part":

16 ÷ 8 = 2

Now we can see that one "part" of the ratio is for 2 pieces. So if the ratio of black to red pieces is 3 : 5, then there are 3 * 2 = 6 red pieces and <u>5 * 2 = 10 black bieces</u>.

6 0

2 years ago

Prove the identity with steps.

Sav [38]

Remember that a double angle formula for cosine is
$\cos(2x)=\cos^{2}x-\sin^{2}x$

So
$\cos^{2}(2x)-\sin^{2}(2x)=\cos(4x)$
$\rightarrow \cos^{2}(2x)-\sin^{2}(2x)=\cos(2*2x)$
$\rightarrow \cos^{2}(2x)-\sin^{2}(2x)=\cos^{2}(2x)-\sin^{2}(2x)$

4 0

2 years ago

Because Helen was prepared to pay cash for a yellow car with a marked price of $9200 she was given a discount of $1012 what perc

Liula [17]

Answer:

11%

Step-by-step explanation:

The percentage of the discount is 1012/9200 x 100 = 11%

3 0

2 years ago

Para festeja su cumpleaños,Nancy compró 15 paquetes de pizzetas. Si cocinó 288 pizzetas, cuántos paquetes completos le quedaron?

Lorico [155]

Answer:

Nancy consumió 12 paquetes de pizzetas y le quedaron 3 paquetes completos.

Step-by-step explanation:

En primer lugar, debemos descomponer el número total de pizzas como una multiplicación de números primos. Al realizar la descomposición factorial tenemos que:

$288 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3$

Entonces, los familia de divisores de 288 es el siguiente conjunto:

$D_{288} = \{2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144 \}$

Si tanto la cantidad de paquetes de pizzetas y la cantidad cocinada de pizzetas son números enteros y positivos, siendo la última mucho mayor. Entonces, la cantidad de pizzetas debe ser un número entero y la cantidad de paquetes gastados menor a la cantidad de paquetes comprados y el número entero más cercano a esa cantidad. Entonces, concluimos que Nancy se gastó 12 paquetes de pizzetas, quedándole 3 paquetes completos.

6 0

2 years ago