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Westkost [7]
3 years ago
11

Use substitution to solve the system of linear equations. In your final answer, include all of your work.

Mathematics
1 answer:
Fantom [35]3 years ago
4 0
Replace 'y' with -3x+4

x + \frac{1}{3} (-3x+4) = \frac{4}{3} \\  \\ x -x + \frac{4}{3} = \frac{4}{3}  \\  \\ \frac{4}{3} = \frac{4}{3}

The variable 'x' cancels out, leaving the True statement 4/3 = 4/3
This means that the 2 equations are identical regardless of what x and y are.

Answer: System is consistent and dependent, there are an infinite number of solutions.
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Please help i have 2 questions thank you
katrin [286]
1. second option
2. first option
8 0
3 years ago
The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.954 grams and a standard devia
olga_2 [115]

Let <em>X</em> be the random variable representing the amount (in grams) of nicotine contained in a randomly chosen cigarette.

P(<em>X</em> ≤ 0.37) = P((<em>X</em> - 0.954)/0.292 ≤ (0.37 - 0.954)/0.292) = P(<em>Z</em> ≤ -2)

where <em>Z</em> follows the standard normal distribution with mean 0 and standard deviation 1. (We just transform <em>X</em> to <em>Z</em> using the rule <em>Z</em> = (<em>X</em> - mean(<em>X</em>))/sd(<em>X</em>).)

Given the required precision for this probability, you should consult a calculator or appropriate <em>z</em>-score table. You would find that

P(<em>Z</em> ≤ -2) ≈ 0.0228

You can also estimate this probabilty using the empirical or 68-95-99.7 rule, which says that approximately 95% of any normal distribution lies within 2 standard deviations of the mean. This is to say,

P(-2 ≤ <em>Z</em> ≤ 2) ≈ 0.95

which means

P(<em>Z</em> ≤ -2 or <em>Z</em> ≥ 2) ≈ 1 - 0.95 = 0.05

The normal distribution is symmetric, so this means

P(<em>Z</em> ≤ -2) ≈ 1/2 × 0.05 = 0.025

which is indeed pretty close to what we found earlier.

4 0
3 years ago
If y varies inversely as X and Y equals 5 when x equals 3 find X when Y is 15​
omeli [17]

Answer:

x = 1

Step-by-step explanation:

Given that y varies inversely as x then the equation relating them is

y = \frac{k}{x} ← k is the constant of variation

To find k use the condition y = 5 when x = 3

k = yx = 5 × 3 = 15, thus

y = \frac{15}{x} ← equation of variation

When y = 15 then

15 = \frac{15}{x} ( multiply both sides by x )

15x = 15 ( divide both sides by 15 )

x = 1

5 0
3 years ago
A whale costs $14700 and depreciates in value by 8% per year. When will the whale be worth $100
sammy [17]

Answer:

x = 60

Step-by-step explanation:

The question is asking

$14,700 * (1 - 8%)^x = $100

$14,700 * (1 - 0.08)^x = $100

$14,700 * (0.92)^x = $100

(0.92)^x = $100/$14,700

log(0.92^x) = log($100/$14,700)

x * log(0.92) = log(0.0068027)

x = log(0.0068027)/log(0.92)

x = 59.85

Since this question is asking in terms of years, we always round up (in this case to 60), as it won't fully be worth $100 by the beginning of the 59th year.

3 0
3 years ago
Si se invierten $ 500 a una tasa de 5% anual. Hallar el valor futuro a 3 años si el interés es compuesto trimestralmente.
9966 [12]

Answer:

the future value is $5800.38

Step-by-step explanation:

Given that

The invested amount i.e present value is $500

The rate is 5 % per year so quarterly rate is 5% ÷ 4 = 1.25%

The time period is 3 per year so for quartely it is 3 × 4 = 12

We need to find out the future value

So as we know that

Future value = Present value × (1 + rate of interest)^time

= $500 × (1 + 0.0125)^12

= $580.38

hence, the future value is $5800.38

5 0
3 years ago
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