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2 years ago

Solve the system of linear equations. 3x−2y=1 9x−6y=3

1 answer:

8 0

Get the y by itself

-2y= -3x + 1

Divide -2 to everything

y= 3/2x - 1/2

Other equation (get y by itself)

-6y= -9x + 3
y=3/2x - 1/2

Use substitution

3/2x-1/2=3/2-1/2

0=0

All real numbers (any value of x makes the equation true)

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How is 1.35 x 10–5 written in standard notation?

natka813 [3]

Answer:

13.5x - 5

Step-by-step explanation:

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2 years ago

Find the circumference and the area of the circle with a diameter of 15ft

guapka [62]

Answer:

Circumference is pi times diameter so that would equal 15 pi. The formula to find the area of a circle is A=pi * r^2 So you divide 15 by 2 to find the radius. r=7.5 Then you square it and multiply it by pi and get 56.25pi which is about equal to 176.715

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2 years ago

Help pls i need this luv you guys ,<333

bagirrra123 [75]

Answer:

x ≈ 3.1 ft

Step-by-step explanation:

The segment from the centre to the chord is a perpendicular bisector, thus

The triangle is right with base = $\frac{1}{2}$ x

Applying Pythagoras' identity to the right triangle, then

( $\frac{1}{2}$ x )² + 1.4² = 2.1²

$\frac{1}{4}$ x² + 1.96 = 4.41 ( subtract 1.96 from both sides )

$\frac{1}{4}$ x² = 2.45 ( multiply both sides by 4 )

x² = 9.8 ( take the square root of both sides )

x = $\sqrt{9.8}$ ≈ 3.1 ft ( to the nearest tenth )

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3 years ago

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2 years ago

Suppose that administrators at a large urban high school want to gain a better understanding of the prevalence of bullying withi

boyakko [2]

Answer:

lower limit =0.261

upper limit =0.369

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Description in words of the parameter p

$p$ represent the real population proportion of people that have experienced bullying

X= 63 people in the random sample that have experienced bullying

n=200 is the sample size required

$\hat p=\frac{63}{200}=0.315$ represent the estimated proportion of people that have experienced bullying

$z_{\alpha/2}$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Numerical estimate for p

In order to estimate a proportion we use this formula:

$\hat p =\frac{X}{n}$ where X represent the number of people with a characteristic and n the total sample size selected.

$\hat p=\frac{63}{200}=0.315$ represent the estimated proportion of people that they were planning to pursue a graduate degree

Confidence interval

The confidence interval for a proportion is given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 90% confidence interval the value of $\alpha=1-0.90=0.1$ and $\alpha/2=0.05$ , with that value we can find the quantile required for the interval in the normal standard distribution.