What is the volume of a rectangular prism with length 9 ft, height 5 ft, and width 6 ft?

Write the equation of the trigonometric graph.

prisoha [69]

Answer:

$f(x)= \sin(6x)+3$

Step-by-step explanation:

The parent function of this graph is: y = sin(x)

The sine function is periodic, meaning it repeats forever.

Standard form of a sine function:

$f(x) = \sf A \sin (B(x + C)) + D$

A = amplitude (height from the mid-line to the peak)
2π/B = period (horizontal distance between consecutive peaks)
C = phase shift (horizontal shift - positive is to the left)
D = vertical shift

The parent function y = sin(x) has the following:

Amplitude (A) = 1
Period = 2π
Phase shift (C) = 0
Vertical shift (D) = 0
Mid-line: y = 0

From inspection of the given graph:

Amplitude (A) = 1
$\sf Period=\dfrac{\pi}{12}-\dfrac{-\pi}{4}=\dfrac{\pi}{3}$
Phase shift (C) = 0
Vertical shift (D) = +3 (as mid-line is y = 3)

$\sf If\:Period=\dfrac{\pi}{3} \implies \dfrac{2 \pi}{B}=\dfrac{\pi}{3}\implies B=6$

Substituting the values into the standard form:

$\implies f(x) =1 \sin (6(x + 0)) + 3$

$\implies f(x) = \sin (6x) + 3$

Therefore, the equation of the given trigonometric graph is:

$f(x)= \sin(6x)+3$

6 0

2 years ago

Sonya plays a game where she moves forward or backward on a game board. Positive numbers represent forward moves. Negative numbe

umka21 [38]

Answer:

This means sonya moves 3 units backward 4 times

Step-by-step explanation:

4(-3) ;

4 represents the number of times a (-3) movement is executed.

-3 means a backward movement due to the presence of negative sign.

Hence, we can conclude that Sonya moves 3 units backward 4 times or can infer a direct multiplication of 4(-3) = - 12 ;

A backward movement of - 12 units.

3 0

3 years ago

Is of 12 equal to 9? no

Vesnalui [34]

Answer:

12=9

Obviously

.................

4 0

3 years ago

7.21 as a percentage

kirill115 [55]

721% is the right answer.

5 0

3 years ago

The personnel department of a large corporation wants to estimate the family dental expenses of its employees to determine the f

Verizon [17]

Answer:

CI(95%): [205,5;400.8]dolars

Step-by-step explanation:

Hello!

So you need to construct a confidence interval for the average family dental expenses (μ) using the sample given in the problem. To estimate it you need to first choose a statistic. For this small sample, considering that the variable has a normal distribution (I made a quick Shapiro Wilks test, with p-value 0.3234, you can assume normality) the best statistic to use is the Student's t-test.

t= [x(bar)-μ]/S/√n ≈ t₍ₙ₋₁₎

The formula for the confidence interval to estimate the mean is

x(bar)± $t_{n-1; 1-\alpha/2}$ * (S/√n)

The critical value is from a t-distribution with 11 degrees of freedom

± $t_{n-1; 1-\alpha/2} = t_{11; 0.975} = 2.201$

>remember since it's two-tailed, to get the right critical value you have to divide α by 2. So in the text, you received a confidence level of 1-α=0.95 so α=0.05 then α/2=0.025 and 1-α/2=0.975

To construct the interval, you need to first calculate the sample mean and the standard derivation.

Sample

115; 370; 250; 593; 540; 225; 117; 425; 318; 182; 275; 228

n= 12

∑xi = 3638 ∑xi² = 1362670

Sample mean

x(bar): (∑xi)/n = 3638/12 = 303.17 dolars

Standard derivation

S²= 1/n-1*[∑xi²- (∑xi)²/n] = 1/11 * [1362670-((3638)²/12)] = 23614.47 dolars²

S= 153.67 dolars

Confidence interval (95%)

303.17± 2.201* (153.67/√12)

[205,5;400.8]dolars

I hope you have a SUPER day!

3 0

4 years ago