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3 years ago

Which line is parallel to the line y = 3x + 6? A) y = -3x - 6 B) y = 6x + 3 C) y = -1/3x + 6 D) y = 3x - 9

Mathematics

1 answer:

MA_775_DIABLO [31]3 years ago

7 0

Answer:

Step-by-step explanation:

The answer is D

y = 3x + 6 is parallel to y = 3x - 9

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ExtremeBDS [4]

Answer:

The one that wieghs 10 grams

Step-by-step explanation:

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3 years ago

Use the "rule of 72" to estimate the doubling time (in years) for the interest rate, and then calculate it exactly. (Round your

Law Incorporation [45]

Answer:

According to the rule of 72, the doubling time for this interest rate is 8 years.

The exact doubling time of this amount is 8.04 years.

Step-by-step explanation:

Sometimes, the compound interest formula is quite complex to be solved, so the result can be estimated by the rule of 72.

By the rule of 72, we have that the doubling time D is given by:

$D = \frac{72}{Interest Rate}$

The interest rate is in %.

In our exercise, the interest rate is 9%. So, by the rule of 72:

$D = \frac{72}{9} = 8$ .

According to the rule of 72, the doubling time for this interest rate is 8 years.

Exact answer:

The exact answer is going to be found using the compound interest formula.

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

In which A is the amount of money, 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 unit t and t is the time the money is invested or borrowed for.

So, for this exercise, we have:

We want to find the doubling time, that is, the time in which the amount is double the initial amount, double the principal.

is double the initial amount, double the principal.

$A = 2P$

$r = 0.09$

The interest is compounded anually, so $n = 1$

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

$2P = P(1 + \frac{0.09}{1})^{t}$

$2 = (1.09)^{t}$

Now, we apply the following log propriety:

$\log_{a} a^{n} = n$

So:

$\log_{1.09}(1.09)^{t} = \log_{1.09} 2$

$t = 8.04$

The exact doubling time of this amount is 8.04 years.

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4 years ago

In the SuperLottery, three balls are drawn (at random) from ten white balls numbered from $1$ to $10$, and one SuperBall is draw

Verdich [7]

nCr(20, 2) = 190 ways of selecting 2 from 20

nCr(10, 1) = 10 ways of selecting 1 from 10

To find the over all probability of winning,

Calculate the Harmonic Mean (19) and divide by 2

Equivalent to

1/ (1//190 + 1/10) =9.5

So the probability is 1/9.5 = 2/19.

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3 years ago

A company produces fruity drinks that contain a percentage of real fruit juice. Drink A contains 20% real fruit juice and Drink

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Answer:

Therefore the company made 510 liters of Drink A and (510+80)=590 liters of Drink B.

Step-by-step explanation:

Let, the company make x liters of drink A

The company makes drink B of (80+x) liter. Since the company make 80 more liters of Drink B than liters Drink A .

Given drink A contains 20% real fruit.

Therefore x liters of drink A contains $=\frac{20}{100}\times x$ liters $=\frac{x}{5}$ liters real fruit.

Drink B contains 5% real fruit juice.

(80+x) liters of drink B contains $=\frac{5}{100}\times (80+x)$ liters $=\frac{80+x}{20}$ liter real fruit.

The company used 56.5 liters of real fruit juice to make Drink A and Drink B.

According to the problem,

$\frac{80+x}{20}+\frac{x}{5}= 56.5$

$\Rightarrow \frac{80+x+4x}{20}=56.5$

⇒80+5x = 56.5×20

⇒80+5x=1130

⇒5x=1130-80

⇒5x=1050

$\Rightarrow x=\frac{1050}{5}$

⇒x=510

Therefore the company made 510 liters of Drink A and (510+80)=590 liters of Drink B.

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3 years ago

Use the simple interest formula to find the ending balance.

devlian [24]

A = 4000(1 + [0.065 * 5])
A = $5300

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3 years ago