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2 years ago

Which expression is equivalent to sin (pi/12)cos(7pi/12) -cos(pi/12)sin(7pi/12) ?

Mathematics

1 answer:

DerKrebs [107]2 years ago

3 0

Answer:

-1

Step-by-step explanation:

We see the given expression is equal to sin(pi/12 - 7pi/12), which is equal to sin(-pi/2), or just -1.

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A survey of 32 different gas stations in Texas found the average price of gasoline to be $3.19 a gallon with a sample standard d

Leni [432]

Answer:

The value of test statistic is -4.1247

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = $3.26 a gallon

Sample mean, $\bar{x}$ = $3.19 a gallon

Sample size, n = 32

Sample standard deviation, σ = $0.096

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 3.26\text{ dollars a gallon}\\H_A: \mu < 3.26\text{ dollars a gallon}$

We use one-tailed t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{3.19 - 3.26}{\frac{0.096}{\sqrt{32}} } = -4.1247$

Thus, the value of test statistic is -4.1247

3 0

3 years ago

Solve for x: 2/3=8/x+6

Tresset [83]

Answer:

x = 6

Step-by-step explanation:

2/3=8/x+6

Using cross products

2 * (x+6) = 3*8

2(x+6) = 24

Divide by 2

x+6 =12

Subtract 6

x = 6

8 0

3 years ago

Read 2 more answers

Which table of ordered pairs represents a proportional relationship?

EleoNora [17]

Answer:

second x -1,-3,-5 y 1 3 5 for proportional relation

8 0

3 years ago

What is the equation of the line that is perpendicular to y= -3x + 1 and passes through (2,3)?

Aleonysh [2.5K]

Answer:

$\large\boxed{y=\dfrac{1}{3}x+2\dfrac{1}{3}}$

Step-by-step explanation:

$\text{Let}\ k:y=_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\============================\\\\\text{We have}\ y=-3x+1\to m_1=-3.\\\\\text{Therefore}\ m_2=-\dfrac{1}{-3}=\dfrac{1}{3}.\\\\\text{The equation of the searched line:}\ y=\dfrac{1}{3}x+b.\\\\\text{The line passes through }(2,\ 3).$

$\text{Put the coordinates of the point to the equation.}\ x=2,\ y=3:\\\\3=\dfrac{1}{3}(2)+b\\\\3=\dfrac{2}{3}+b\qquad\text{subtract}\ \dfrac{2}{3}\ \text{from both sides}\\\\b=2\dfrac{1}{3}$

3 0

3 years ago

Read 2 more answers

For what values (cases) of the variables the expression does not exist: a a 2x−4

Natasha2012 [34]

Step-by-step explanation:

When the denominator is zero, the expression is undefined

2x-4=0

2x=4

x=2

5 0

3 years ago