tasha fnished a job in 3/4 hour. megan finished it in 4/5 of the time tasha took. how long did megan take to finish the job?

Final answer:

To solve the equation 1 - sin θ = 1/2 on the interval 0 ≤ θ < 2π, isolate the sine function and find the values of θ that satisfy the equation by taking the inverse sine of both sides. The solutions are θ = -π/6 and θ = 5π/6.

Explanation:

To solve the equation 1 - sin θ = 1/2 on the interval 0 ≤ θ < 2π, we can start by isolating the sine function. Subtracting 1/2 from both sides of the equation, we get -sin θ = -1/2. Next, we can find the values of θ that satisfy this equation on the given interval by taking the inverse sine (sin⁻¹) of both sides. This gives us θ = sin⁻¹(-1/2).

Using the unit circle or a calculator, we can find the values of θ that satisfy this equation. Let's first find the value of θ in the first quadrant. Here, sin θ = -1/2, so θ = sin⁻¹(-1/2) = -π/6.

Since we are looking for solutions on the interval 0 ≤ θ < 2π, we need to find the other solution that lies in the second quadrant. In the second quadrant, sin θ is also negative, but the angle is measured from the positive x-axis in the clockwise direction. Therefore, θ = -π + π/6 = 5π/6 is the other solution.

Final answer:

To solve the equation 1 - sin θ = 1/2 on the interval 0 ≤ θ < 2π, you can isolate the sine function and apply the inverse sine function to find the solutions.

Explanation:

To solve the equation 1 - sin θ = 1/2 on the interval 0 ≤ θ < 2π, we can start by isolating the sine function. Subtracting 1/2 from both sides of the equation, we get -sin θ = -1/2.

Next, we can apply the inverse sine function to both sides. This will give us two possible values for θ within the given interval: θ = π/6 and θ = 5π/6.

Therefore, the solutions to the equation 1 - sin θ = 1/2 on the interval 0 ≤ θ < 2π are θ = π/6 and θ = 5π/6.

Answer:

Correct answers of Logan is 19.

Step-by-step explanation:

Since, Logan didn't answered one problem.

Thus, total problem he attempt is 24.

Let the number of correct answer = x

and, Number of wrong answer = y

Then x + y = 24

And since it is given that,

He earned 4 points for correct answer and deduct 2 points for wrong answer. and he got score 66.

Thus we get equation,

4x - 2y = 66

Solving these two equation we get,

x = 19 and y = 6

Thus, Correct answers of Logan is 19.

Corresponding sides are congruent is not the correct answer here.

Similar triangles has same corresponding angles and the corresponding sides are in proportion and for the congruent triangles the corresponding angles and the corresponding sides are same.

Two triangles is similar if their corresponding angles are congruent and their corresponding sides are in equal proportion.

We can can think of a triangle having x°,  y°,  z° as it's interior angle and for the other triangle to be similar it must also have x°,  y°,  z° as it's interior angle and the first triangle has length of the 3 sides equal to some values the other triangle to be similar it's side must have values in the same multiples of the previous values of the first triangle.

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3^4 = 3x3x3x3 = 81

 Answer is D) 81

To find the number of student and adult tickets sold at a baseball game, we can set up a system of equations using the given information. Solving the system of equations will give us the values of the variables. In this case, 150 student tickets and 250 adult tickets were sold.

Let's assume that the number of student tickets sold is 'x' and the number of adult tickets sold is 'y'.

According to the information given, the total attendance was 400 people, so we can write the equation: x + y = 400.

The total ticket sales were $1050, so we can write another equation: 2x + 3y = 1050.

Now we have a system of equations that we can solve to find the values of x and y.

Using substitution or elimination method, we find that x = 150 and y = 250.

Therefore, 150 student tickets and 250 adult tickets were sold.

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Answer: It’s C

Step-by-step explanation:

Lynn's method of multiplying 4 by 305 and doubling the result will not give her the correct answer to 44 x 305. This method is equivalent to multiplying by 8, not 44.

Lynn's method will not give her the correct answer. When Lynn multiplies 4 by 305 and then doubles the product, she is effectively multiplying 305 by 8, not by 44. To show this, consider the mathematical operations: when we multiply 4 by 305 we get 1220, and when we then double 1220 we get 2440. This is different from the result of multiplying 44 by 305, which is 13420. Therefore, the correct answer is C. Lynn's method will not be correct. Therefore, multiplying by 4 and then doubling the product is the same as multiplying by 8, not 44.

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Answer: 100 rides are needed to break even.

Step-by-step explanation:

We have given the cost function

C(x)=15x+2000 where x is the number of rides.

And rides cost 35$

⇒ revenue function would be 35 times x

i.e.R(x)=35 x , where x is the number of rides.

Break even point of a firm occurs when at a certain point x the total cost equals to the total revenue.

i.e. at break even point

total revenue=total cost

⇒35x=15x+2000

⇒35-15x=2000[subtract 15x from both sides]

⇒20x=2000 [simplify]

⇒x=2000/20[dividing both sides with 20]

⇒x=100

∴ 100  rides are needed to break even.

The revenue function will be 35x and the breakeven point will be 100 rides.

From the information given, the revenue function will be calculated by multiplying the price by the quantity. This will be:

= 35 × x

= 35x

The breakeven point will be the point where total revenue equals the total cost. This will be:

35x = 15x + 2000

35x - 15x = 2000

20x = 2000

x = 2000/20

x = 100

Therefore, the revenue function will be 35x and the breakeven point will be 100 rides.

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To evaluate (rs)(4) and (r/s)(3) for the given functions, substitute the value of x into the functions and calculate the product and quotient, respectively.

To find (rs)(4), we need to substitute the value of x into the functions r(x) and s(x) and then find their product. r(x) = 2√x, so r(4) = 2√4 = 2√2 = 2(2) = 4. s(x) = √x, so s(4) = √4 = 2. Therefore, (rs)(4) = 4(2) = 8.

To find (r/s)(3), we need to substitute the value of x into the functions r(x) and s(x) and then find their quotient. r(3) = 2√3 and s(3) = √3. Therefore, (r/s)(3) = (2√3) / √3 = 2.

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Answer:

Step-by-step explanation:

The distributive property: a(b + c) = ab + ac

To factor out -1/3 from 1/3y - 3/2, distribute the negative sign to both terms resulting in -1/9y + 1/2.

To factor out -1/3 from the expression 1/3y - 3/2, we can distribute the negative sign to both terms. This results in -1/3(1/3y) + (-1/3)(-3/2). Simplifying this further, we get -1/9y + 1/2.

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a^2 + b^2 = c^2

3^2 +b^2 = 5^2

9 + b^2 = 25

b^2 = 16

b = sqrt(16)

b=4