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2 years ago

What is the equation of the line that passes through (1, 2) and is parallel to the line whose equation is 2x + y - 1=0?

Mathematics

1 answer:

elixir [45]2 years ago

7 0

Answer:

y=-2x+4

Step-by-step explanation:

2x+y-1=0

2x+y=0+1

2x+y=1

y=1-2x

y=-2x+1

y=mx+b where m=slope and b=y-intercept

parallel means same slope,

so the slope would still be -2.

--------------

y-y1=m(x-x1)

y-2=-2(x-1)

y=-2x+2+2

y=-2x+4

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A particular variety of watermelon weighs on average 20.4 pounds with a standard deviation of 1.23 pounds. Consider the sample m

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Answer:

a) The expected value of the sample mean weight is 20.4 pounds.

b)The standard deviation of the sample mean weight is 0.123.

c) There is a 14.46% probability the sample mean weight will be less than 20.27.

d) This value is $c = 20.6153$ .

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$ .

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

A particular variety of watermelon weighs on average 20.4 pounds with a standard deviation of 1.23 pounds. This means that $\mu = 20.4, \sigma = 1.23$

Consider the sample mean weight of 100 watermelons of this variety. This means that $n = 100$ .

a. What is the expected value of the sample mean weight? Give an exact answer.

By the Central Limit Theorem, it is the same as the mean of the population. So the expected value of the sample mean weight is 20.4 pounds.

b. What is the standard deviation of the sample mean weight? Give your answer to four decimal places.

By the Central Limit Theorem, that is:

$s = \frac{\sigma}{\sqrt{n}} = \frac{1.23}{\sqrt{100}} = 0.123$

The standard deviation of the sample mean weight is 0.123.

c. What is the approximate probability the sample mean weight will be less than 20.27?

This is the pvalue of Z when $X = 20.27$ .

Since we are working with the sample mean, we use $s$ instead of $\sigma$ in the Z score formula

$Z = \frac{X - \mu}{s}$

$Z = \frac{20.27 - 20.4}{0.123}$

$Z = -1.06$

$Z = -1.06$ has a pvalue of 0.1446.

This means that there is a 14.46% probability the sample mean weight will be less than 20.27.

d. What is the value c such that the approximate probability the sample mean will be less than c is 0.96?

This is the value of $X = c$ that is in the 96th percentile, that is, it's Z score has a pvalue 0.96.

So we use $Z = 1.75$

$Z = \frac{X - \mu}{s}$

$1.75 = \frac{c - 20.4}{0.123}$

$c - 20.4 = 0.123*1.75$

$c = 20.6153$

This value is $c = 20.6153$ .

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2 years ago

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3 years ago

What is the y intercept of the line?

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Answer:

The Y-Intercept of a line is the point where a line's graph intersects (crosses) the Y-axis.

A y-intercept of 3 means that a line's graph intersects the Y-axis at the point (0,3).

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Step-by-step explanation:

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Answer:

Step-by-step explanation:

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2 years ago

Select the correct answer from each drop-down menu.

Xelga [282]

Answer:

a) Option A: r = 5

b) Option C: y = x

Step-by-step explanation:

a) First, we know that a circle centered at the origin of radius R is written as:

x^2 + y^2 = R^2

Then x^2+y^2=25 can be rewritten as:

x^2 + y^2 = 5^2

This is a circle of radius 5.

Then in polar form, this can be written as:

r = 5

b) Now we have the angle 225°

For rectangular coordinates (x, y)

The correspondent value of θ is given by:

Tan(θ) = y/x

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This can be rewritten as x = y

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2 years ago

What is the equation of the line that passes through (1, 2) and is parallel to the line whose equation is 2x + y - 1=0?​

What is the equation of the line that passes through (1, 2) and is parallel to the line whose equation is 2x + y - 1=0?