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3 years ago

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1/2x - 3/4y=-2 Solve for Y

1 answer:

sertanlavr [38]3 years ago

5 0

$\frac{1}{2}x-\frac{3}{4}y=-2\ \ \ |Add\ \frac{3}{4}y\\\\
\frac{1}{2}x=-2+\frac{3}{4}y\ \ \ |Add\ 2\\\\
\frac{1}{2}x+2=\frac{3}{4}y\ \ |*\frac{4}{3}\\\\
y=\frac{4}{3}(\frac{1}{2}x+2)\\\\
\boxed{y=\frac{2}{3}x+\frac{8}{3}}$

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Question Help Scores of an IQ test have a bell-shaped distribution with a mean of 100100 and a standard deviation of 1010. Use

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Answer:

a) 95% percentage of people has an IQ score between 80 and 120.

b) 68% percentage of people has an IQ score between 90 and 110.

c) 2.5% percentage of people has an IQ score greater than 120.

Step-by-step explanation:

The empirical formula states that:

The empirical rule is known as the three-sigma rule or 68-95-99.7 rule.
It is a rule which states that for a normal distribution, almost all data falls within three standard deviations of the mean.
68% of data falls within the first standard deviation that is $\mu \pm \sigma$

95% of data falls within the second standard deviation that is $\mu \pm 2\sigma$

99.7% of data falls within the third standard deviation that is $\mu \pm 3\sigma$

a) percentage of people has an IQ score between 80 and 120

(80, 120) can be written as:

$(80, 120) = (100-2(10), 100 + 2(10))\\= (\mu \pm 2\sigma)$

Thus, it is the interval within two standard deviation from the mean.

Thus, by empirical formula, 95% percentage of people has an IQ score between 80 and 120.

b) percentage of people has an IQ score between 90 and 110

(90, 110) can be written as:

$(90, 110) = (100-1(10), 100 + 1(10))\\= (\mu \pm 1\sigma)$

Thus, it is the interval within one standard deviation from the mean.

Thus, by empirical formula, 68% percentage of people has an IQ score between 90 and 110.

c) P(score greater than 120)

= 1 - percentage of score less than 80 - percentage of score between 80 and 120

$= 1 - (95\% + 2.5\%) = 2.5\%$

From empirical formula,

2.5% percentage of people has an IQ score greater than 120.

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Write an exponential function in the form y=ab^xy=ab x that goes through points (0, 20)(0,20) and (6, 1280)(6,1280).

Phoenix [80]

Answer:

$y=20(2)^x$

Step-by-step explanation:

We want to write an exponential function that goes through the points (0, 20) and (6, 1280).

The standard exponential function is given by:

$y=ab^x$

The point (0, 20) tells us that <em>y</em> = 20 when <em>x</em> = 0. Hence:

$20=a(b)^0$

Simplify:

$20=a(1)\Rightarrow a=20$

So, our exponential function is now:

$y=20(b)^x$

Next, the point (6, 1280) tells us that <em>y</em> = 1280 when <em>x</em> = 6. Thus:

$1280=20(b)^6$

Solve for <em>b</em>. Divide both sides by 20:

$64=b^6$

Therefore:

$b=\sqrt[6]{64}=2$

Hence, our function is:

$y=20(2)^x$

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