Csc theta * cos^2 theta +sin theta= csc theta

Answers

Answer 1
Answer:

Step-by-step explanation:

\csc \theta \cos^(2)\theta +  \sin \theta = \csc \theta(1 - \sin^(2)\theta) +  \sin \theta

=   (\csc \theta -  \sin \theta) +  \sin \theta

=  \csc \theta


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A bicycle wheel has a circumference of 75 inches. What is the approximate radius of the wheel?

Answers

Answer:

23.87

Step-by-step explanation:

The half-life of a radioactive substance is 200 years. There are 8000 grams of the substance initially. How many grams of the substance are left after 300 years?

Answers

Answer:

There are 2,000 grams left after 300 years.

Step-by-step explanation:

Giving the following information:

The half-life of a radioactive substance is 200 years. There are 8000 grams of the substance initially.

First, we need to calculate the reduction of the substance each year:

Yearly reduction= 8,000/400= 20 grams per year

Now, for 300 years:

300 year reduction= 20*300= 6,000

There are 2,000 grams left after 300 years.

2. Customers who purchase a certain model of car can order an engine in any of three sizes. Of all cars of this type sold, 45% have a small engine, 35% have a medium-sized engine, and 20% have a large engine. Of cars with the small engine, 10% fail an emission test within two years of purchase, while 12% of those with the medium size and 15% of those with the large engine fail. If a randomly chosen car of this model fails an emission test within two years, what is the probability it is a car with a small engine

Answers

Answer: 0.1397 ; 0.385

Step-by-step explanation:

Given the following :

Small engine population = 45% ; 10% fail

Medium engine population = 35% ; 12% fail

Large engine population = 20% ; 15% fail

Probability that a randomly chosen car fails emission test :

P(failure) = Σ(population % * failure %)

P(failure) = (45%*10%) + (35%*12%) + (20%*15%)

P(failure) = 0.045 + 0.042 + 0.03 = 0.117

B) what is the probability it is a car with a small engine

P = small engine cars with emission failure / total emission failure

= (0.45 × 0.1) / 0.117 = 0.045 / 0.117 = 0.3846

= 0.385

#7: Twenty-three more than 10 times a number is the same as 5 more than 1 pointthe number. *
Your answer
26 more than twice the

Answers

Answer:

23+10r= 5+r

Step-by-step explanation:

let r be the number

What is the most accurate measurement of 1 mile

Answers

Answer:

there are 5280  feet in a mile

Step-by-step explanation:

Solve the equation9x² – 29x – 28 = 0
Give your answers to 2 decimal places when appropriate

Answers

Final answer:

The roots of the equation 9x² - 29x - 28 = 0 are x = 4 and x = -0.78.

Explanation:

The equation given is a quadratic equation. To solve it, we can use the quadratic formula: x = [-b ± sqrt(b²-4ac)] / (2a), where a, b, and c are coefficients of the quadratic equation. In your equation, a=9, b=-29, and c=-28.

So now, we substitute these values into the quadratic formula:
x = [29 ± sqrt((-29)²-4*9*(-28))] / (2*9)
Solving inside the square root first, we get:
x = [29 ± sqrt(841+1008)] / 18
x = [29 ± sqrt(1849)] / 18
Continue to simplify and you get:
x = [29 ± 43] / 18, which gives us two possible solutions:
x = 72 / 18 = 4
and
x = -14 / 18 = -0.78 (to two decimal places).

Learn more about Quadratic Equation here:

brainly.com/question/26090334

#SPJ3

Answer:

x = 4 or x = 0.78

Step-by-step explanation:

9x² – 29x – 28 = 0

2 roots: x = ((-(-29) ± √(-29)² - 4 x 9 x (-28)) / (2 x 9)

               = (29 ± √841 + 1008) / 18

               = (29 ± 43) /18

x = 72 /18 = 4     or

x = -14 /18 = - 0.78