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kobusy [5.1K]
3 years ago
11

Find the equation for the trend line through the points (0, 11) and (100, 33). Then use it to predict the number of baskets Romy

would make after practicing for 80 minutes.
Mathematics
1 answer:
sleet_krkn [62]3 years ago
5 0

Answer:

28 baskets

Step-by-step explanation:

The equation for a linear trend line is given by:

y = mx + b, where y and x are variables, m is the slope of the line and b is the y intercept (that is value of y when x is zero).

The equation of a line passing through two points (x_1,y_1)\ and\ (x_2,y_2) is:

y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)

y represent the number of baskets made and x represents the time take. Given that the line passes through the points  (0, 11) and (100, 33), hence:

y-11=\frac{33-11}{100-0}(x-0)\\\\y-11=\frac{11}{50}x\\\\y=  \frac{11}{50}x+11

The number of baskets Romy would make after practicing for 80 minutes (x = 80) is:

y=\frac{11}{50}x+11\\\\y=\frac{11}{50}(80)+11  \\\\y=17.6+11\\\\y=28.6\\\\Therefore\ y\ =\ 28\ baskets

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Step-by-step explanation:

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3 years ago
A small business owner estimates his mean daily profit as $970 with a standard deviation of $129. His shop is open 102 days a ye
Katena32 [7]

Answer:

The probability that the shopkeeper's annual profit will not exceed $100,000 is 0.2090.

Step-by-step explanation:

According to the Central Limit Theorem if we have a population with mean <em>μ</em> and standard deviation <em>σ</em> and we select appropriately huge random samples (<em>n</em> ≥ 30) from the population with replacement, then the distribution of the sum of values of <em>X</em>, i.e ∑<em>X</em>, will be approximately normally distributed.  

Then, the mean of the distribution of the sum of values of X is given by,  

 \mu_{x}=n\mu

And the standard deviation of the distribution of the sum of values of X is given by,  

 \sigma_{x}=\sqrt{n}\sigma

The information provided is:

<em>μ</em> = $970

<em>σ</em> = $129

<em>n</em> = 102

Since the sample size is quite large, i.e. <em>n</em> = 102 > 30, the Central Limit Theorem can be used to approximate the distribution of the shopkeeper's annual profit.

Then,

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Compute the probability that the shopkeeper's annual profit will not exceed $100,000 as follows:

P (\sum X \leq  100,000) =P(\frac{\sum X-\mu_{x}}{\sigma_{x}}

                              =P(Z

*Use a <em>z</em>-table for the probability.

Thus, the probability that the shopkeeper's annual profit will not exceed $100,000 is 0.2090.

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A box contains 9 pounds of sand the entire box of sand will be poured in equal amounts into 6 small bags how many bags of sand w
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