Write an equation of the line with a slope of 2 and y-intercept of 9

Those 2 questions I need help with . find sec θ and tanθ

Zielflug [23.3K]

STEP - BY - STEP EXPLANATION

What to find?

The the value of secθ.

Given:

(4, 3)

⇒(x, y) = (4, 3)

Step 1

Draw a sketch.

Step 2

Substitute the values into the trig. ratio formula below.

$tan\theta=\frac{opposite}{adjacent}$

From the sketch above, opposite = 3 and adjacent = 4

$tan\theta=\frac{3}{4}$

Step 3

Find the value of the hypotenuse side using Pythagoras theorem.

let h be the hypotenuse side.

$\begin{gathered} h^2=4^2+3^2 \\ \\ =16+9 \\ \\ =25 \\ \\ h=5 \end{gathered}$

Hence, hypotenuse = 5

Step 4

Substitute the values into the formula below:

$\begin{gathered} cos\theta=\frac{adjacent}{hypotenuse} \\ \\ =\frac{4}{5} \end{gathered}$

But,

$sec\theta=\frac{1}{cos\theta}=\frac{1}{\frac{4}{5}}=\frac{5}{4}$

ANSWER

secθ= 5/4

tanθ=3/4

7 0

1 year ago

According to a survey, 18% of the car owners said that they get the maintenance service done on their cars according to the sche

Annette [7]

Answer:

a) For this case we define the random variable X="number of car owners in a random sample of 12 who get the maintenance service done on their cars according to the schedule recommended by the auto company". And for this case the distribution for X is:

$X \sim Binom (n =12, p=0.18)$

And the possible values for the random variable are X=0,1,2,3,4,5,6,7,8,9,10,11,12

b) Using the probability mass function we got:

$P(X=3)=(12C3)(0.18)^3 (1-0.18)^{12-3}=0.21506$

Step-by-step explanation:

Previous concepts

A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

Solution to the problem

Part a

For this case we define the random variable X="number of car owners in a random sample of 12 who get the maintenance service done on their cars according to the schedule recommended by the auto company". And for this case the distribution for X is:

$X \sim Binom (n =12, p=0.18)$

And the possible values for the random variable are X=0,1,2,3,4,5,6,7,8,9,10,11,12

Part b

Find to 3 decimal places the probability that exactly 3 car owners in a random sample of 12 get the maintenance service done on their cars according to the schedule recommended by the auto company.

Using the probability mass function we got:

$P(X=3)=(12C3)(0.18)^3 (1-0.18)^{12-3}=0.21506$

6 0

3 years ago

Atmospheric pressure at Earth's surface is approximately 14.7 pounds per square inch. Atmospheric pressure decreases by approxim

chubhunter [2.5K]

Answer:

The standard, or near-average, atmospheric pressure at sea level on the Earth is 1013.25 millibars, or about 14.7 pounds per square inch.

The gauge pressure in my automobile tires is a little more than twice that value. If you live at a higher altitude, the pressure will be lower since there is less air above weighing down upon you. The pressure also varies by relatively small amounts as high and low pressure systems move past.

Step-by-step explanation:

3 0

3 years ago

What is the constant of proportionality

melisa1 [442]

Step-by-step explanation:

“The constant of proportionality is the ratio between two directly proportional quantities. Two quantities are directly proportional when they increase and decrease at the same rate.”

5 0

2 years ago

Read 2 more answers

Please help <br> Can someone answer and tell me how to do this <br> (Will mark brainliest)

Gre4nikov [31]

Answer:

57 degrees

Step-by-step explanation:

Total measurement of any triangle is 180 degrees.

/_V=180-53.8-69.2=57 degrees

8 0

3 years ago