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chubhunter [2.5K]
3 years ago
6

In what direction and by how many units is the graph of f(x) = −3 cos(2x − π) + 2 vertically and horizontally shifted

Mathematics
1 answer:
MakcuM [25]3 years ago
8 0

Answer:

Vertical shift is 2 units top and horizontal shift is \frac{\pi }{2} units to the right

Step-by-step explanation:

Consider the function f(x) = a cos(bx + c) + d.

In this graph, the horizontal shift is -c/b and the vertical shift is d.

Let's compare our graph, f(x) = -3 cos(2x - π) + 2 with this graph.

Here, a = -3, b = 2, c = -π and d = 2.

So, vertical shift = d = 2 units top and

horizontal shift = -\frac{c}{b} =-\frac{-\pi }{2} =\frac{\pi}{2} units to the right.


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Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

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Now, we have to find a value of T, which is found looking at the t table, with 49 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.9}{2} = 0.95. So we have T = 1.6766

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The 90% confidence interval for the true mean lifespan of this product is between 13.1 and 16.9 years.

8 0
2 years ago
Susan’s red notebook cover is 20 centimeters by 30 centimeters. She has a sticker for each letter in her name. Each sticker is a
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Answer:

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100 - 56 = 44

So 44 centimeters of the notebook cover will still be showing.

Step-by-step explanation:

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A​ scratch-off lottery ticket has 14 concealed spaces among which are 4 symbols saying​ "Win!". The person who bought the ticket
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Step-by-step explanation:

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Answer:

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