solve the equation 6sin(2 theta)=5 for a value of theta in the first quadrant. give your answer in radians and degrees.

Step-by-step explanation:

"t t hours" ????

you mean 11 hours ?

13 gallons now.

2 gallons are used (and therefore disappear from the tank) per hour.

so, in 5 hours 5×2 = 10 gallons will be used.

that leaves 13 - 10 = 3 gallons in the tank.

in 11 hours 11×2 = 22 gallons would have been used.

but there are only 13 gallons in the tank.

so, if he does not fill up, he will have 0 gallons left after 11 hours. in fact, already after 13/2 = 6.5 hours.

the point :

when you use 2 gallons per hour, that means in t hours you are using t × 2 or 2t gallons.

circumference of the mirror = 175.84 cm

area of the mirror = 2461.76 cm²

The measure needed to find the amount of wire round the mirror is the circumference.

The measure needed to find the amount of glass needed is the area.

The circumference and area of a circle can be found as follows:

circumference of the mirror = 2πr

circumference of the mirror = 2 × 3.14 × 28 = 175.84 cm

area of the mirror = πr²

area of the mirror = 3.14 × 28²

area of the mirror = 2461.76 cm²

The measure needed to find the amount of wire round the mirror is the circumference.

The measure needed to find the amount of glass needed is the area.

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Answer:

2n^3 + 6n^2 + 8n

Answer: It's 2n^3 + 6n^2 + 8n

Step-by-step explanation:

Answer:

10 unit^2.

Step-by-step explanation:

The base of the triangle (CE)

= 6 - 2 = 4 units

The height = 5

Area = 1/2 * 4 * 5

= 10 unit^2.

Answer:

10

Step-by-step explanation:

area = hight ×base÷2

hight = 5-0

= 5

base = 6-2

= 4

area = 4×5÷2

=10

The value of the quantity after 1.2 minutes, to the nearest hundredth, is 313.56

A quantity is a measurable attribute of a particular thing or group of objects. One quantity might be more than, less than, or equal to another quantity when comparing them. Quantity is a notion that is used frequently in both mathematics and the sciences.

A quantity cannot be a property that cannot be compared. The conventional format for presenting a quantity is as the product of a magnitude and a unit.

According to the question,

Initial value of the quantity=310

Rate of growth= 8.5% per second

Value of the quantity after 1.2 minutes,

=[tex]310(1+\frac{8.5}{100}) ^{1.2*60}[/tex]

=[tex]310(\frac{108.5}{100})^{72}[/tex]

=313.56

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Answer:

141008.06

Step-by-step explanation:

Answer:

[tex]y = -\frac{1}{2} x+4[/tex]

Step-by-step explanation:

Standard form for equation of line: y = mx + c

where m = gradient or slope

c = y-intercept

From the question we know that,

x = 2

y = 3

m = - 0.5

We will substitute these values into the equation to find c.

3 = (-0.5)(2) + c

3 = - 1 + c

c = 3 + 1 = 4

Therefore the equation of this line is [tex]y = -\frac{1}{2} x+4[/tex]

The logarithmic form of 13^2=169 is [tex]\log_{13}(169) = 2[/tex]

The equation is given as

13^2=169

Take the logarithm of both sides

log(13^2) = log(169)

This gives

2log(13) = log(169)

Divide both sides by log(13)

[tex]\log_{13}(169) = 2[/tex]

Hence, the logarithmic form of 13^2=169 is [tex]\log_{13}(169) = 2[/tex]

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it is a relatively easy way to draw a sample while ensuring randomness is the answer.

Systematic sampling is a probabilistic sampling method in which a researcher selects members of a population at regular intervals. For example, select every 15 people from the list of populations. If the population is in random order, this can mimic the benefits of a simple random sample.

These are generally preferred by researchers because they are easy to implement and understand. The important assumption that the results represent the majority of the normal population ensures that the entire population is sampled equally. The process also provides a higher level of control for systematic sampling compared to other sampling methods. systematic sampling also has a lower risk factor because the data is unlikely to be contaminated.

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Using the binomial distribution, it is found that there is a 0.0012 = 0.12% probability at least two of them make it inside the recycling bin.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

With 5 shoots, the probability of making at least one is [tex]\frac{211}{243}[/tex], hence the probability of making none, P(X = 0), is [tex]\frac{232}{243}[/tex], hence:

[tex](1 - p)^5 = \frac{232}{243}[/tex]

[tex]\sqrt[5]{(1 - p)^5} = \sqrt[5]{\frac{232}{243}}[/tex]

1 - p = 0.9908

p = 0.0092

Then, with 6 shoots, the parameters are:

n = 6, p = 0.0092.

The probability that at least two of them make it inside the recycling bin is:

[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]

In which:

[P(X < 2) = P(X = 0) + P(X = 1)

Then:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{6,0}.(0.0092)^{0}.(0.9908)^{6} = 0.9461[/tex]

[tex]P(X = 1) = C_{6,1}.(0.0092)^{1}.(0.9908)^{5} = 0.0527[/tex]

Then:

P(X < 2) = P(X = 0) + P(X = 1) = 0.9461 + 0.0527 = 0.9988

[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.9988 = 0.0012[/tex]

0.0012 = 0.12% probability at least two of them make it inside the recycling bin.

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Step-by-step explanation:

[tex] - 32 + 45 = 13 \\ t_{n} = ( a_{1} + (n - 1)d) \\ \\ d = 13 \: \: a_{1} = - 45[/tex]

[tex] t_{n} = - 45 + (n - 1)13 = = = > \\ - 45 + 13n - 13 = = = > \\ t_{n} = 13n - 58[/tex]

and now

[tex]124 = 13n - 58 = = = > \\ 182 = 13n = = = > n = 14[/tex]

The number of terms in the sequence: –45, –32, –19, –6, ..., 124 = 9.

The common difference is -45 - (-32)= 13

                                                  d = 13.

AP is a sequence of numbers in order, in which the difference among any two consecutive numbers is a constant cost. it's also referred to as mathematics series.

using arithmetic progress:-

last term = (n-1)d

first term(a) = –45

    term = a + (n-1)d

there is a difference of 13, so the sequence will be

–45, –32, –19, –6,7, 20, 33, 46, 59, 72, 85, 98, 111, 124.

∴ number of terms = 9

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The function that has a domain of all real numbers is:

A. [tex]y = 2x^{\frac{1}{3}} - 7[/tex].

The domain of a function is the set that contains all possible input values for the function.

If a function has an even root, equivalent to an exponent of [tex]\frac{1}{n}[/tex] with n even, the domain is only positive values, while if the exponent is odd, the domain is all real values.

Researching the problem on the internet, the function with odd exponent is:

A. [tex]y = 2x^{\frac{1}{3}} - 7[/tex].

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Answer:

The prime factors of 13195 are 5, 7, 13 and 29. The largest prime factor of the number 600851475143 is 6857

Answer: 5

Step-by-step explanation:

11/2-x = 1/3 + 1/6

-x+11/2 = 1/2

   - 11/2   - 11/2

-x = -5

Divide -1 by both sides

And it gives you the answer 5.

The blue marble is predicted to be picked 120 times, in the experiment of picking a marble from a bag containing 3 red and 2 blue marbles and performing this experiment 300 times, using the theoretical probability.

The theoretical probability of any event is the ratio of the number of favorable outcomes to the event, to the total number of possible outcomes in the experiment.

If we have an event A, the number of favorable outcomes to event A as n, and the total number of possible outcomes in the experiment as S, then the theoretical probability of event A is given as:

P(A) = n/S.

In the question, we are given that Ellen has a bag with 3 red marbles and 2 blue marbles in it. She is going to randomly draw a marble from the bag 300 times, putting the marble back in the bag after each draw.

We are asked the predict the number of times that the marble picked will be blue using the theoretical probability.

Let the event of picking a blue marble be A.

The number of favorable outcomes to event A (n) = 2 {The total number of blue marbles in the bag}.

The total number of possible outcomes in the experiment of picking a ball (S) = 5 {The total number of marbles in the bag}.

Thus, the theoretical probability of event A is,

P(A) = n/S = 2/5 = 0.4.

To predict the number of times marble picked was blue, we multiply the time's the experiment was performed by the theoretical probability of picking a blue ball.

Thus, the predicted number of times = 300 * 0.4 = 120.

Thus, the blue marble is predicted to be picked 120 times, in the experiment of picking a marble from a bag containing 3 red and 2 blue marbles and performing this experiment 300 times, using the theoretical probability.

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Answer:

Right option is B.

Step-by-step explanation:

[tex] \sf \longrightarrow \frac{ \sec x \sin( - x) + \tan( - x) }{1 + \sec( - x) } \\ \\ \sf \longrightarrow \frac{ \sec x( - \sin x) - \tan x}{1 + \sec x} \\ \\ \sf \longrightarrow \frac{ - \frac{1}{ \cos x } \times \sin x - \tan x }{1 + \sec x} \\ \\ \sf \longrightarrow \frac{ - \tan x - \tan x}{1 + \sec x} \\ \\ \sf \longrightarrow \frac{ - 2 \tan x}{1 + \sec x} \\ \\ \sf \longrightarrow \frac{ \frac{ - 2 \sin x}{ \cos x} }{1 + \frac{1}{ \cos x} } \\ \\ \sf \longrightarrow \frac{ \frac{ - 2 \sin x}{ \cos x} }{ \frac{ \cos x + 1}{ \cos x} } \\ \\ \boxed{ \sf{\longrightarrow \frac{ - 2 \sin x}{ \cos x + 1} }}[/tex]

Answer:

Step-by-step expl

2.73 A,16.3 V

As x increases, y value decreases.

The rate of change for y as a function of x is decreasing, therefore the function is a decreasing function.

For all values of x, the function value y, decreases to 0.

The y intercept of the graph is the function value y=8

When x=1, the function value y=5.

From the given graph, it is clear that the curve is decreasing for all values of x. Hence, the rate of change of the give curve is decreasing.

Therefore, the giving function is called as decreasing function.

Since, the function is decreasing for all values of x, the value of y decreases to 0.

Form the graph, it is clear that the y-intercepts is at y=8.

Also, the value of y at x=1 is 5 from the graph.

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Answer:

104.607kph

Step-by-step explanation:

Conversion from mph to kph = 1.609mph

Answer:

31

Step by step:

You need to do it in reverse:

Devidng Becomes multiplying so its 3.8x10=38

Then same for this + = - do its 38-7=31

So answer is 31

From the list of options, the set that is equal to the set  {1, 2, 3, ...} is {x | x N, x ≥ 1}

The set is given as:

{1, 2, 3, ...}

The three dots (...) after 3 implies that the elements of the set include other values such as 4, 5, 6 and so on

Using the above scenario, we can see that the set  {1, 2, 3, ...} contains only positive integers.

All positive integers are natural numbers and they are denoted by N

From the list of options, we have:

{x | x R, x ≥ 1}

This represents the set of all real numbers greater than or equal to 1.

Note that this set includes decimal numbers i.e. 1, 1.5, 1.89 and so on

This does not represent the set  {1, 2, 3, ...}

{x | x R, x > 1}

This represents the set of all real numbers greater than 1.

Note that this set includes decimal numbers i.e. 1.5, 1.89 and so on

This does not represent the set  {1, 2, 3, ...}

{x | x N, x ≥ 1}

This represents the set of all natural numbers greater than or equal to 1.

Note that this set does not include decimal numbers i.e. 1, 2, 3, 4 and so on

This does represent the set  {1, 2, 3, ...}

Hence, the set that is equal to the set  {1, 2, 3, ...} is {x | x N, x ≥ 1}

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Based on the transformed function of y = sin(x) and the given parameters, the value that is closest to the amplitude of the transformed function is 54

The amplitude of the function is calculated

Amplitude = Highest  - Lowest

From the graph, we have the following points

Highest = 84

Lowest = 30

Substitute the known values in the above equation

Amplitude = 84 - 30

Evaluate the difference

Amplitude = 54

Based on the transformed function of y = sin(x) and the given parameters, the value that is closest to the amplitude of the transformed function is 54

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Rearranging the equation so q is the independent variable is; q = -1.6r

We are given the expression;

-7q + 12r = 3q - 4r

Since we want to make q the subject, let us rearrange the equation with variables having q on the left and others on the right side to get;

-7q - 3q = -4r - 12r

-10q = -16r

q = 16r/10

q = -1.6r

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The option B is a correct option which is y = 26x and y = -0.030(x-500)2 15,900 represent the quadratic and linear function.

According to the statement

we have given that Vertex

(h,k) = (500, 15900)

And One of the points on the graph

(x,y) = (0,8400)

FIRST PART: we have to find the quadratic function

We can find the quadratic function by parabola's equation formula

y = a (x - h)² + k  -(1)

Input the numbers to the formula, to find the value of a

y = a (x - h)² + k

8400 = a(0 - 500)² + 15900

8400 = a (500)² + 15900

8400 = 250000a + 15900

-250000a = 15900 - 8400

-250000a = 7500

a = 7500/-250000

a = 0.03

Now,

Submit a to the formula (1)

y = a (x - h)² + k

y = 0.03 (x - 500)² + 15900

this is the quadratic equation.

SECOND PART: Find the linear function

the total cost = cost each helmet × the number of helmet

y = 26x

So,

The option B is a correct option which is y = 26x and y = -0.030(x-500)2 15,900 represent the quadratic and linear function.

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Disclaimer: This question was incomplete. Please find the full content below.

Question: A company plans to sell bicycle helmets for $26 each. The company's business manager estimates that the cost, y, of making x helmets is a quadratic function with a y-intercept of 8,400 and a vertex of (500, 15900)

x= number of helmets

y = amount in dollars

Which system models this situation?

a) y = 26x and y = 8,400(x-500)2+15,900

b) y = 26x and y = -0.030(x-500)2+15,900

c) y = x/26 and y = -0.030(x-500)2+15,900

d) y = x/26 and y =8,400(x-500)2+15,900

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Answer:

B. y = 26x and y = -0.030(x-500)2+15,900

Step-by-step explanation:

At the DVD rental store, Jamie found 6 DVDs that she wanted, but can only rent 4. Jamie can make 15 possible choices, as per combinations of DVDs.

Number of Possible Combinations:

Given Information is as follows,

Total number of DVDs that Jamie wanted, n = 6

Number of DVDs Jamie can rent at a  time, x =4

The Combinations formula is given as,

ⁿCₓ = n! / (n-x)! x!

Here, n = 6 and x = 4

Substituting these values of n and x in the Combinations formula, we get,

⁶C₄ = 6! / (6-4)! 4!

⁶C₄ = 6! / 2! 4!

⁶C₄ = 6×5×4! / 2! 4!

⁶C₄ = 6×5 / 2

⁶C₄ = 3×5

⁶C₄ = 15

Thus, Jamie can make 15 possible combinations of DVDs.

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Answer:

x=m/9

Steps:

m=9x

m/9=x

x=m/9

Answer:

see explanation

Step-by-step explanation:

to find the intersection equate g(x) and h(x) , that is

(x + 7)(x - 5) = x - 5 ← expand left side using FOIL

x² + 2x - 35 = x - 5 ( subtract x - 5 from both sides )

x² + x - 30 = 0 ← in standard quadratic form

(x + 6)(x - 5) = 0 ← in factored form

equate each factor to zero and solve for x

x + 6 = 0 ⇒ x = - 6

x - 5 = 0 ⇒ x = 5

substitute these values into either g(x) or h(x) for corresponding values of y

substituting into h(x)

h(- 6) = - 6 - 5 = - 11 ⇒ (- 6, - 11 )

h(5) = 5 - 5 = 0 ⇒ (5, 0 )

Based on the given parameters, the 15 ft rope will reach the swimmer

From the question, we have the following equation:

sin 55 = 10/x

Multiply both sides of the equation by x

x * sin 55 = 10/x * x

Evaluate the product

x * sin 55 = 10

Divide both sides by sin 55

x = 10/sin 55

Evaluate sin 55

x = 10/0.8192

Evaluate the quotient

x = 12.21

From the question, the lifeguard tosses a ring in a 15ft rope to the swimmer

15 is greater than 12.21

This means that the 15 ft rope will reach the swimmer

Hence, the 15 ft rope will reach the swimmer

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Answer:

x = 20

Step-by-step explanation:

x°

2x°

(x + 10)°

little box on the bottom left means this is a right angle which is 90°

add up all the angles and make it equal to 90°

( x° + 2x° + (x + 10)° ) = 90°

4x + 10 = 90

4x = 80

x = 20

Since we can see the "square" at the bottom left corner of the angle, the square indicates that the angle is a right angle (which measures 90°).

We can also see three smaller angles forming the right angle. Therefore, the sum of the measure of the smaller angles = 90°.

According to the diagram, the measures of the smaller angles are x°, 2x°, and (x + 10)° respectively. Then we get the following equation:

[tex]\implies x + 2x + (x + 10) = 90\°[/tex]

Here, we had the equation: [tex]\underline{x + 2x + (x + 10) = 90\°}[/tex]

[tex]\implies x + 2x + x + 10 = 90\°[/tex]              [tex]\text{(Ope} \text{ning the parentheses)}[/tex]

[tex]\implies 4x + 10 = 90\°[/tex]                             [tex]\text{(Combining like terms)}[/tex]

[tex]\implies 4x + 10 - 10 = 90 - 10[/tex]          [tex]\text{(Subtracting 10 on both sides)}[/tex]

[tex]\implies 4x = 80[/tex]                                    [tex]\text{(Simplifying both sides)}[/tex]

[tex]\implies \dfrac{4x}{4} = \dfrac{80}{4} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{(Dividing 4 on both sides)}[/tex]                            

[tex]\implies \boxed{x = 20}[/tex]                                      [tex]\text{(Simplifying both sides)}[/tex]

Therefore, the value of x, in the diagram provided, is 20.

ANSWER:

Quadrant ll

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