If sin α=(12/13), and cos α=(5/13), then tan α = ?

Answers

Answer 1

Answer: sin α = 12/13 opposite/hypothenue
cos α = 5/13 adjacent/hypothenue
tan α = 12/5 opposite/adjacent

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Question:In the equation P = 2x + 7, P represents the price, in dollars, of tickets to a concert x hours after they go on sale. When will the price exceed $20.00?

1. Describe in words how the equation can be used to solve the problem.

2. Draw a graphical representation of the price equation, and illustrate how a solution could be found that way.

Answers

Let

P-------> the price in dollars of tickets

x------> the number of hours

we know that

$P=2x+7$ -------> equation A

When will the price exceed $20.00?

Part 1) Describe in words how the equation can be used to solve the problem

Substitute the value of P equal to $\$20.00$ in the equation A and find the value of x

For $P=\$20.00$

substitute in equation A

$20=2x+7$

$2x=20-7$

$2x=13$

$x=6.5\ hours$

therefore

the answer Part 1) is

the price exceed $\$20.00$ when the time exceed $6.5\ hours$

Part 2) Draw a graphical representation of the price equation, and illustrate how a solution could be found that way.

using a graphing tool

Draw the equation of the lines

$P=2x+7$

$P=20$

the solution is the intersection both graphs

see the attached figure

the solution is the point $(6.5, 20)$

that means

for $x=6.5\ hours$

$P=\$20.00$

1. This equation can be used to help solve the problem by plugging in numbers for x. Whatever answer for x gives a price that is more than $20.00 is the answer for the number of tickets that have to be sold in order to exeed $20.00.

2. This equation has the same format as an equation in slope intercept form. This makes it easy to graph.The y intercept will be 7 and the slope is 2. Using this information, it is easy to graph the equation and find a solution. The graph should look like the image I attached to this answer.

Multiply ($728.00) * (6.2%) and round to the nearest cent. (Include the correct units.)

Answers

6.2% = 0.062, % means divide by 100.

$728.00 * 0.062 = $45.136
If the next digit is 5 or higher, round up. (4 or lower, round down)
$45.14

For a standard normal distribution, which of the following expressions must always be equal to 1?A) P(z≤-a)-P(-a≤z≤a)+P(z≥a)
B) P(z≤-a)-P(-a≤z≤a)+P(z≥a)
C) P(z≤-a)+P(-a≤z≤a)-P(z≥a)
D) P(z≤-a)+P(-a≤z≤a)+P(Z≥a)

Answers

P(z ≤ -a) + P(-a ≤ z ≤ a) + P(z ≥ a) = 1 - P(z ≤ a) + [P(z ≤ a) - P(z ≤ -a)] + 1 - P(z ≤ a) = 2 - 2P(z ≤ a) + P(z ≤ a) - [1 - P(z ≤ a)] = 2 - P(z ≤ a) - 1 + P(z ≤ a) = 1

Therefore, option D is the correct answer.

Answer:

D. $P(z\le -a)+P(-a\le z\le a)+P(z\ge a)$

Step-by-step explanation:

Properties of normal distribution-

The normal curve is symmetrical about the mean (μ).
The mean is at the middle of the graph and it divides the area into two equal halves.
The total area under the curve is equal to 1.

The total area under the curve can be divided into parts like,