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MA_775_DIABLO [31]
3 years ago
14

A linear function is given by the equation y=4x. Using the points x and x+1, show that the y-values increase by 4 between any tw

o points separated by x2−x1=1
Mathematics
1 answer:
GrogVix [38]3 years ago
5 0

Answer:

x_2 - x_1 = 1 gives y_2 - y_1 = 4

Step-by-step explanation:

Given

y = 4x

(x_1,x_2) = (x,x+1)

Required

Show that the y values increases by 4 for x_2 - x_1 = 1

We have:

y = 4x

For x_1 = x

y_1 = 4x_1

Substitute x_1 = x

y_1 = 4x

For x_2 = x + 1

y_2 = 4x_2

Substitute x_2 = x + 1

y_2 = 4(x+1)

y_2 = 4x+4

So, we have:

y_2 = 4x+4

y_1 = 4x

Subtract y_1 from y_2

y_2 - y_1 = 4x + 4 - 4x

Collect like terms

y_2 - y_1 = 4x - 4x+ 4

y_2 - y_1 = 4

Hence:

x_2 - x_1 = 1 gives y_2 - y_1 = 4

i.e. an increment of 4

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Answer:

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Step-by-step explanation:

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The distribution of the number of viewers for the American Idol television show follows a normal distribution with a mean of 26
hjlf

Answer:

Probability that next week's show will have between 30 and 37 million viewers is 0.2248.

Step-by-step explanation:

We are given that the distribution of the number of viewers for the American Idol television show follows a normal distribution with a mean of 26 million with a standard deviation of 8 million.

<em>Let X = number of viewers for the American Idol television show</em>

So, X ~ N(\mu=26,\sigma^{2}=8^{2})

Now, the z score probability distribution is given by;

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where, \mu = population mean = 26 million

            \sigma = standard deviation = 8 million

So, probability that next week's show will have between 30 and 37 million viewers is given by = P(30 < X < 37) = P(X < 37) - P(X \leq 30)

    P(X < 37) = P( \frac{X-\mu}{\sigma} < \frac{37-26}{8} ) = P(Z < 1.38) = 0.91621

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<em>Therefore, P(30 < X < 37) = 0.91621 - 0.69146 = 0.2248</em>

Hence, probability that next week's show will have between 30 and 37 million viewers is 0.2248.

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Step by Step Solution:

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Answer:

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As the variable x represents the number of weeks, its coefficient represents the change per week in the amount of money.

Therefore, the change per week in the amount of money in the account is $20.

<u>Initial Balance</u>

The starting amount of money in the account (initial balance) will be the value of y when x = 0:

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Therefore, the starting amount of money in the account is $550.

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