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Ahat [919]
3 years ago
5

Which equation best represents a trend line for the scatter plot?

Mathematics
2 answers:
alukav5142 [94]3 years ago
4 0

Answer:

Option A ic orrect.

y=-\frac{3}{7}x+ 4

Step-by-step explanation:

Point slope form:

The equation of line is given by:

y-y_1=m(x-x_1)      .....[1]

where m is the slope of line and a point (x_1,y_1) lies on the line in the coordinate plane.

As per the statement:

You can see from the graph of line

We have two points i.e,

(0, 4) and (7, 1)

First calculate the slope:

\text{Slope} = \frac{y_2-y_1}{x_2-x_1}

then;

\text{Slope}(m) = \frac{1-4}{7-0} = -\frac{3}{7}

Now, substitute the value of m and (0,4) in [1] we have;

y-4=-\frac{3}{7}(x-0)  

Simplify:

y-4=-\frac{3}{7}x

Add 4 to both sides we get;

y=-\frac{3}{7}x+ 4

Therefore, the equation best represents the trend line for the scatter plot is y=-\frac{3}{7}x+ 4

kvasek [131]3 years ago
3 0
Y = (-3/7)x + 4

Looking at the graph, you can see the trend line plotted. And conveniently, there are a couple of points on the trend line that are indicated. Those points being (0,4) and (7,1). The equation of a line in slope intercept form is:y = ax+b

Looking at the points available, the point (0,4) already gives us the y intercept since x is equal to 0. So our equation becomes:
y = ax + 4

Now we need to determine a which is the slope. The slope is the change in y divided by the change in x. So let's do that
(1-4)/(7-0) = -3/7

And now our equation becomes:
y = (-3/7)x + 4

And given formatting issues, the first option available is the correct one.
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there are 3 seniors for every 2 juniors in the concert choir. if there are 21 seniors in all, how many jurors are in the concert
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The ratio ...

... seniors : juniors = 3 : 2

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3 0
3 years ago
Of the total population of American households, including older Americans and perhaps some not so old, 17.3% receive retirement
Alex Ar [27]

Answer:

47.54% probability that more than 20 households but fewer than 35 households receive a retirement income

Step-by-step explanation:

We use the binomial aproxiation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

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.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

p = 0.173, n = 120. So

\mu = E(X) = np = 120*0.173 = 20.76

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{120*0.173*0.827} = 4.14

In a random sample of 120 households, what is the probability that more than 20 households but fewer than 35 households receive a retirement income?

We are working with discrete values, so this is the pvalue of Z when X = 35-1 = 34 subtracted by the pvalue of Z when X = 20 + 1 = 21.

X = 34

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

Z = \frac{34 - 20.76}{4.14}

Z = 3.2

Z = 3.2 has a pvalue of 0.9993

X = 21

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

Z = \frac{21 - 20.76}{4.14}

Z = 0.06

Z = 0.06 has a pvalue of 0.5239

0.9993 - 0.5239 = 0.4754

47.54% probability that more than 20 households but fewer than 35 households receive a retirement income

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