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2 years ago

What are the amplitude, period, and midline of f(x) = 5 sin(x − π) + 3?

Mathematics

1 answer:

Semmy [17]2 years ago

7 0

Answer:

amplitude: 5; period: 2π; midline: y = 3

Step-by-step explanation:

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1 year ago

Pls can someone help me

eduard

Answer:

x = (h-12y-2)/4

Step-by-step explanation:

Here, we want to make x the subject of the formula

We have this as:

h = 4x + 12y + 2

4x = h-12y-2

x = (h-12y-2)/4

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2 years ago

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3 years ago

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The caffeine content (in mg) was examined for a random sample of 50 cups of black coffee dispensed by a new machine. The mean an

Genrish500 [490]

Answer:

We are 98% confident interval for the mean caffeine content for cups dispensed by the machine between 107.66 and 112.34 mg .

Step-by-step explanation:

Given -

The sample size is large then we can use central limit theorem

n = 50 ,

Standard deviation $(\sigma)$ = 7.1

Mean $\overline{(y)}$ = 110

$\alpha =$ 1 - confidence interval = 1 - .98 = .02

$z_{\frac{\alpha}{2}}$ = 2.33

98% confidence interval for the mean caffeine content for cups dispensed by the machine = $\overline{(y)}\pm z_{\frac{\alpha}{2}}\frac{\sigma}\sqrt{n}$

= $110\pm z_{.01}\frac{7.1}\sqrt{50}$

= $110\pm 2.33\frac{7.1}\sqrt{50}$

First we take + sign

$110 + 2.33\frac{7.1}\sqrt{50}$ = 112.34

now we take - sign

$110 - 2.33\frac{7.1}\sqrt{50}$ = 107.66

We are 98% confident interval for the mean caffeine content for cups dispensed by the machine between 107.66 and 112.34 .

5 0

3 years ago

How to solve this problem step by step. Make brainliest answer if its done. Please

sladkih [1.3K]

D is halfway between A and B

so the coordinates of D are (2,2)

E is halfway between A and C so the coordinates of E are (-1,1)

now you need to find the gradient/slope of DE and BC using the formula:

$\frac{y2 - y1}{x2 - x1}$

<h3>Gradient of DE: </h3>

SUB IN COORDINATES OF D AND E

$\frac{1 - 2}{ - 1 - 2}$

therefore the gradient of DE is 1/3.

<h3>Gradient of BC:</h3>

SUB IN COORDINATES OF B AND C

 $\frac{ - 2 - 0}{ - 3 - 3}$ 

therefore the gradient of BC is -2/-6 which simplifies to 1/3.

<h3>therefore, BC and DE are parallel as they both have a gradient/slope of 1/3 and parallel lines have the same gradient</h3>

6 0

3 years ago