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2 years ago

-3x+4y=7 y=3x-5 I NEED HELP PL Z HELP ME

Mathematics

1 answer:

andrew-mc [135]2 years ago

3 0

$- 3x + 4y = 7 \\ y = 3x - 5$

[Substitute the given value of y into the first equation]

$- 3x + 4 \times (3x - 5) = 7$

[Distribute 4 through the parentheses]

$- 3x + 12x - 20 = 7$

[Collect like terms]

$9x - 20 = 7$

[Move the constant to the right-hand side and change its sign]

$9x = 7 + 20$

[Add the numbers]

$9x = 27$

[Divide both sides of the equation by 9]

$x = 3$

[Substitute the given value of x into the second equation]

$y = 3 \times 3 - 5$

[Multiply the numbers]

$y = 9 - 5$

[Subtract the numbers]

$y = 4$

[The possible solution of the system is the ordered pair (x,y)]

$(x,y)=(3,4)$

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Answer:

(a) See Explanation

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Step-by-step explanation:

Given

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$\sigma = \$20$ --- standard deviation

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Solving (a): The reason we can't determine the probability that an amount to access internet by a household will exceed $55.

The question says that a lot of households pay low rates, but the percentage of the households in this category is not given. This means that it is impossible to determine the shape of the distribution.

Hence, the probability cannot be calculated.

Solving (b): Sample mean and Sample standard deviation

The sample mean estimates the population mean

So:

$\bar x =\mu$

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The sample standard deviation is calculated as thus:

$\sigma_x = \frac{\sigma}{\sqrt n}$

$\sigma_x = \frac{20}{\sqrt{500}}$

$\sigma_x = \frac{20}{22.36}$

$\sigma_x = 0.8944$

Solving (c): The shape of the distribution.

We have:

$n = 500$ --- The sample size

According to Central limit theorem, When the sample size is greater than 30, then the shape of the distribution is normal.

Hence, the shape is normal

Solving (d): $P(\bar x \ge 55)$

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$t = \frac{\bar x - \mu}{\sigma}$

$t = \frac{55 - 50}{0.8945}$

$t = \frac{5}{0.8945}$

$t = 5.590$

So:

$P(\bar x > 55) = P(t > 5.590)$

Referencing the z table, we have:

$P(t > 5.590) = 0$

Hence:

$P(\bar x > 55) = 0$

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