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netineya [11]
3 years ago
13

Here's a graph of a linear function. Write the

Mathematics
1 answer:
Natalija [7]3 years ago
7 0

Answer:

\large\boxed{y=\dfrac{1}{4}x+3}

Step-by-step explanation:

The slope-intercept form of an equation of a line:

y=mx+b

m - slope

b - y-intercept → (0, b)

From the graph we have the points (4, 4) and (0, 3) → b = 3.

We have the equation:

y=mx+3

The formula of a slope:

m=\dfrac{y_2-y_1}{x_2-x_1}

Put the coordinates of the points:

m=\dfrac{3-4}{0-4}=\dfrac{-1}{-4}=\dfrac{1}{4}

Finally we have:

y=\dfrac{1}{4}x+3

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The amount of syrup that people put on their pancakes is normally distributed with mean 63 mL and standard deviation 13 mL. Supp
andreyandreev [35.5K]

Answer:

(a) X ~ N(\mu=63, \sigma^{2} = 13^{2}).

    \bar X ~ N(\mu=63,s^{2} = (\frac{13}{\sqrt{43} } )^{2}).

(b) If a single randomly selected individual is observed, the probability that this person consumes is between 61.4 mL and 62.8 mL is 0.0398.

(c) For the group of 43 pancake eaters, the probability that the average amount of syrup is between 61.4 mL and 62.8 mL is 0.2512.

(d) Yes, for part (d), the assumption that the distribution is normally distributed necessary.

Step-by-step explanation:

We are given that the amount of syrup that people put on their pancakes is normally distributed with mean 63 mL and a standard deviation of 13 mL.

Suppose that 43 randomly selected people are observed pouring syrup on their pancakes.

(a) Let X = <u><em>amount of syrup that people put on their pancakes</em></u>

The z-score probability distribution for the normal distribution is given by;

                      Z  =  \frac{X-\mu}{\sigma}  ~ N(0,1)

where, \mu = mean amount of syrup = 63 mL

            \sigma = standard deviation = 13 mL

So, the distribution of X ~ N(\mu=63, \sigma^{2} = 13^{2}).

Let \bar X = <u><em>sample mean amount of syrup that people put on their pancakes</em></u>

The z-score probability distribution for the sample mean is given by;

                      Z  =  \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \mu = mean amount of syrup = 63 mL

            \sigma = standard deviation = 13 mL

            n = sample of people = 43

So, the distribution of \bar X ~ N(\mu=63,s^{2} = (\frac{13}{\sqrt{43} } )^{2}).

(b) If a single randomly selected individual is observed, the probability that this person consumes is between 61.4 mL and 62.8 mL is given by = P(61.4 mL < X < 62.8 mL)

   P(61.4 mL < X < 62.8 mL) = P(X < 62.8 mL) - P(X \leq 61.4 mL)

  P(X < 62.8 mL) = P( \frac{X-\mu}{\sigma} < \frac{62.8-63}{13} ) = P(Z < -0.02) = 1 - P(Z \leq 0.02)

                                                           = 1 - 0.50798 = 0.49202

  P(X \leq 61.4 mL) = P( \frac{X-\mu}{\sigma} \leq \frac{61.4-63}{13} ) = P(Z \leq -0.12) = 1 - P(Z < 0.12)

                                                           = 1 - 0.54776 = 0.45224

Therefore, P(61.4 mL < X < 62.8 mL) = 0.49202 - 0.45224 = 0.0398.

(c) For the group of 43 pancake eaters, the probability that the average amount of syrup is between 61.4 mL and 62.8 mL is given by = P(61.4 mL < \bar X < 62.8 mL)

   P(61.4 mL < \bar X < 62.8 mL) = P(\bar X < 62.8 mL) - P(\bar X \leq 61.4 mL)

  P(\bar X < 62.8 mL) = P( \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < \frac{62.8-63}{\frac{13}{\sqrt{43} } } ) = P(Z < -0.10) = 1 - P(Z \leq 0.10)

                                                           = 1 - 0.53983 = 0.46017

  P(\bar X \leq 61.4 mL) = P( \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } \leq \frac{61.4-63}{\frac{13}{\sqrt{43} } } ) = P(Z \leq -0.81) = 1 - P(Z < 0.81)

                                                           = 1 - 0.79103 = 0.20897

Therefore, P(61.4 mL < X < 62.8 mL) = 0.46017 - 0.20897 = 0.2512.

(d) Yes, for part (d), the assumption that the distribution is normally distributed necessary.

4 0
3 years ago
Can anyone help me with number 7 a b and c?
Sonbull [250]

Answer:

7a........they are similar because none of the sides are equal

6 0
2 years ago
Find the perimeter of the following triangle. Round your answer to the nearest hundredth.
vladimir2022 [97]

Step-by-step explanation:

step 1. The perimeter (P) is the length around the triangle.

step 2. P = 6 + 5 + L (the length of the hypotenuse)

step 3. L = sqrt(6^2 + 5^2) = sqrt(61) where sqrt is the square root

step 4. P = 11 + sqrt(61) = 18.81.

5 0
2 years ago
HELP WITH THESE QUESTIONS PART 2... 1 Question
Lunna [17]

<u>Step-by-step explanation</u> and Answers:

(\frac{1}{\sqrt{10}},\frac{3}{\sqrt{10}}) is in the format (cos, sin). So, adjacent = 1, opposite = 3, hypotenuse = \sqrt{10}

sin = \frac{opposite}{hypotenuse} = \frac{3}{\sqrt{10}}(\frac{\sqrt{10}}{\sqrt{10}}) = \frac{3\sqrt{10}}{10}

cos =  \frac{adjacent}{hypotenuse} = \frac{1}{\sqrt{10}}(\frac{\sqrt{10}}{\sqrt{10}}) = \frac{\sqrt{10}}{10}

tan = \frac{opposite}{adjacent} = \frac{3}{1} = 3

csc = \frac{hypotenuse}{opposite} = \frac{\sqrt{10}}{3}

sec = \frac{hypotenuse}{adjacent} = \frac{\sqrt{10}}{1} = \sqrt{10}

cot = \frac{adjacent}{opposite} = \frac{1}{3}

7 0
3 years ago
Which of the following is a valid comparison between the possible minimum and maximum values of the function y = -x2 + 4x - 8 an
Arturiano [62]

Answer:

The maximum value of the equation is 1 less than the maximum value of the graph

Step-by-step explanation:

We have the equation y=-x^2+4x-8.

We can know that this graph will have a maximum value as this is a negative parabola.

In order to find the maximum value, we can use the equation x=\frac{-b}{2a}

In our given equation:

a=-1

b=4

c=-8

Now we can plug in these values to the equation

x=\frac{-4}{-2} \\\\x=2

Now we can plug the x value where the maximum occurs to find the max value of the equation

y=-(2)^2+4(2)-8\\\\y=-4+8-8\\\\y=-4

This means that the maximum of this equation is -4.

The maximum of the graph is shown to be -3

This means that the maximum value of the equation is 1 less than the maximum value of the graph

6 0
3 years ago
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