You are designing an amusement park ride with cars that will spin in a circle around a center axis, and the cars are located at the vertices of a regular polygon. The sum of the measures of the angles' vertices is 6120°. If each car holds a maximum of four people, what is the maximum number of people who can be on the ride at one time?

The values that represent outputs of the function are given as follows:

8, 3, -5, -2 and 12.

The standard definition of a function is given as follows:

y = f(x).

In which:

Considering the table given in this problem, the input and output variables are given as follows:

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Answer:

-.15 km/ minute * 60 minutes

-9 km

Step-by-step explanation:

The rate is -.15 km per minute

We have 60 minutes

distance = rate  times time

change in elevation is the same as the distance change

change in elevation = -.15 km/ minute * 60

   change in elevation =-9 km

Answer:

(0.15 km/min) * (60 min)

Step-by-step explanation:

We see that the plane descends 0.15 kilometres every minute over the span of 60 minutes.

Use the distance-rate-time formula: d = rt, where d is the distance, r is the rate, and t is the time.

Here, our rate is r = 0.15 km/min and our time is t = 60 minutes. Then the total change in elevation is:

d = rt

d = 0.15 * 60 = 9 km

Note that we disregard the negative sign from -0.15 km/min because the question is asking for the change in elevation. Change is never a negative value.

Hence, the expression will be: 0.15 * 60, which simplifies to 9 km.

~ an aesthetics lover

The cost of each sandwich, given the number that was sold and the profit made was  $15.

Let S be the price of a sandwich and A be the price of a salad.

From the lunch sale, we know:

14 S + 14 A = $280

From the evening sale, we know:

42S + 154 A = $ 1400

Simplify the first equation by dividing through by 14:

S + A = $20

Solving this equation for S gives:

S = $20 - A

Substitute this equation into the second equation:

42 ( $20 - A ) + 154 A = $1400

$ 840 - 42 A + 154 A = $1400

112A = $560

A = $5

Substitute A = $5 into the first equation:

S + $5 = $20

S = $15

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A.  {(–1, 2), (0, 3), (1, 4), (2, 5)} → Non-linear function.

B. {(–3, 9), (–2, 4), (3, 9), (4, 16)} → Non-linear function.

C. y = –14x + 9 → Linear function

D.  y = x  → Linear function

A linear function has a straight line as its graph. A linear function has the form shown below.

a + bx = y = f (x).

A linear function consists of one independent variable and one dependent variable. The independent and dependent variables are x and y, respectively.

When the absolute value of the input value of the function is connected to more than 1 output value, then the function is linear else it is a non-linear function.

From the given choices;

A.  {(–1, 2), (0, 3), (1, 4), (2, 5)}

Here, the absolute value of 1 is connected to more than one point, so non-linear function.

B. {(–3, 9), (–2, 4), (3, 9), (4, 16)}

Here, the absolute value of 3 is connected to more than one point, so non-linear function.

C. y = –14x + 9 is equivalent to the slope-intercept form of linear function y = ax + b.

D.  y = x is a linear function.

Therefore, B and D are linear functions.

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Answer: The area is going to be 0.8

Step-by-step explanation:  The diameter is 1

You need the radius of the circle which is half the diameter. So the Radius(R) is 0.5.

After you find the radius of the circle to find the area of the circle you use the formula pie (R)^2. You are using 3.14

3.14(0.5)^2= 0.785

you then want to round your answer to the nearest tenth so the 8 turns the 7 into an 8.

So, the Area is 0.785 but after rounding it is 0.8.

Hope that helped :)

The 3 sets of data with the same median but different mean are given as follows:

The mean of a data-set is calculated as the sum of all values in the data-set divided by the number of values in the data-set.

The median of a data-set is the middle value of the data-set, the value which 50% of the data-set is less than and 50% of the data-set is more than.

Hence, for a data-set of five elements, which is an odd cardinality, the median is the third element of the ordered data-set.

Then the three data-sets can be constructed with five elements, in which the third element is the same but the sum of the five elements is different.

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Answer:

1.75 or 1 3/4 pieces each

Step-by-step explanation:

3 pieces per apple x 7 = 21

21/12 = 1.75

The solution is 1/4 + 1/3 = 7/12

The number of apples is shared among 12 people is given by the equation A = ( 1/4 ) + ( 1/3 ) = 7/12

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Let the number of apples be = 7 apples

Let the number of people be = 12 people

Now , let the number of apples each person gets be A = number of apples / number of people

Substituting the values in the equation , we get

Number of apples each person gets be A = 7/12

Now , the value 7/12 is represented as A = 1/12 + 6/12

And, cut 4 apples into thirds and cut 3 apples into fourths

Substituting the values in the equation , we get

A = ( 1/4 ) + ( 1/3 )   be equation (1)

On simplifying the equation , we get

A = ( 3 + 4 ) / ( 3 x 4 )

A = 7 / 12

Therefore , the value of A is 7/12

Hence , the number of apples shared is A = ( 1/4 ) + ( 1/3 )

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Answer:  36

Step-by-step explanation: If the coach wants to divide the team by the ratio of 1 to 3, then we will take 48 and divide by 4.

This leaves us with 12 x 4 = 48. Then we calculate 48 - 12 = 36

Now you have your 1 to 3 ratio with the teams being split into team 1 with 12 and team 2 with 36.

Answer:

-2

Step-by-step explanation:

Substituting the points (0,2) and (1,0) into the slope formula, \(m=\frac{2-0}{0-1}=-2\).

Answer:

2.44

Step-by-step explanation:

The maximum amount you can finance is $896.

We are given that;

The monthly gross income = $3,200

Now,

28% of your gross monthly income on your mortgage, including taxes and insurance

The percentage = 28%

3200* 28/100

=32*28

=896

Therefore, by percentage the answer will be $896.

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The probability that they both get a red apple is, 15/28

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

The probability of Ed's friend grabbing a red apple is,

= 6 red apples / (2 green apples + 6 red apples)

= 6/8

= 3/4.

Then, the probability of Ed grabbing a red apple from the remaining apples is,

= 5 red apples / (2 green apples + 5 red apples)

= 5/7.

So, the probability that both Ed and his friend get a red apple is,

= 3/4 x 5/7

= 15/28

Hence, the probability is 15/28

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Answer:

30 / 23

Step-by-step explanation:

to divide two fractions, multiply by the reciprocal.

The reciprocal of 1/5 is 5/1. We will rewrite the equation as:

\(\frac{6}{23}\) times \(\frac{5}{1}\)

6 x 5 = 30

23 x 1 = 23

the answer is 30 / 23

The Quotient is 30/23.

One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things.

Given:

6/23 divided by 1/5

As, division is not possible in fraction so we will perform the multiplication

= 6/23 ÷ 1/5

= 6/23 x 5

= 30/ 23

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Answer:

It is not a function.

Step-by-step explanation:

A relation can only be a function if every input (x-value) of the set of values of the relation, has exactly one output (y-value).

In the relation given, one input, -2, has two output related to it, 5 and 0. That's (-2, 5) and (-2, 0).

Therefore, the relation is not a function.

Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Answer:

pi/2 and 3pi/2

Step-by-step explanation:

on edge

The required solutions to sin(2x) = 2cos(x) are the following as :  \(\:x=\frac{\pi }{2}+2\pi n,\:x=\frac{3\pi }{2}+2\pi n\).

Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.

The equation of trigonometry functions is given in the question:

sin(2x) = 2cos(x)

We have to determine the solution to the given trigonometry equation

As per the question, we have

⇒ sin(2x) = 2cos(x)

Rewrite the above trigonometry equation,

⇒ sin(2x) - 2cos(x) = 0

⇒ 2sin(x)cos(x) - 2cos(x) = 0

Common factor out from the equation,

⇒ 2cos(x)[sin(x) - 1] = 0

Solving each part separately

2cos(x) = 0 and sin(x) - 1 = 0

cos(x) = 0 and sin(x) = 1

\(\:x=\frac{\pi }{2}+2\pi n, and \:x=\frac{3\pi }{2}+2\pi n\).

Thus, the required solutions to sin(2x) = 2cos(x) are the following:  \(\:x=\frac{\pi }{2}+2\pi n,\:x=\frac{3\pi }{2}+2\pi n\).

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This meta-cognitive analysis will help you improve your problem-solving skills and understanding of mathematics.

To approach solving a mathematical problem and understand the process, follow these steps:
1. Read and understand the problem: Carefully read the problem to grasp what it is asking for.

Identify the given information, unknowns, and any constraints.
2. Choose a strategy: Based on your understanding of the problem, select an appropriate method or technique to solve it.

This may include using formulas, equations, or visual representations like diagrams or graphs.
3. Apply the strategy: Implement the chosen method, being mindful of the given information and constraints.

Keep track of your steps and ensure you're following the rules of the chosen method.
4. Check your work: Once you've found a solution, double-check your calculations and review your steps to ensure accuracy.

If necessary, revise your approach and try again.
5. Reflect on the process: Consider the steps you took to solve the problem, and think about how the method used relates to the underlying mathematical concepts.

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Answer:

-7

Step-by-step explanation:

well, y-intercept is value of y when x = 0.

from the problem, we already have the answer, it is -7

but more detailed way is

m = -3

\( \frac{y - ( - 7)}{x - 0} = - 3 \\ y - ( - 7) = - 3x \\ y = - 3x - 7 \\ \)

y-intercept is value of y when x = 0

\(y = - 3(0) - 7 \\ y = - 7\)

a. 759

b. 8769

c. 96699

d. 36754209

The trick is looking at the first numbers for either possible answer. Pick the one that is the greatest going backward. If you're stuck with the same numbers as in d, just continue going back until you see something like the 7 being greater than the 5.

Answer:

Step-by-step explanation:

The solution of the quadratic equation (1/3)x² - (1/9)x - 2/9 = 0 are x = 1, - 2/3.

Any equation that can be written in the standard form where x stands for an unknown and a, b, and c are known quantities, with a 0, is said to be quadratic.

An assignment of values to the unknown variables that establish the equality in the equation is referred to as a solution.

Consider the expression,

(1/3)x² - (1/9)x - 2/9 = 0

Multiplying each side of the quadratic equation by 9,

9 × [ (1/3)x² - (1/9)x - 2/9 = 0 ]

3x² - x - 2 = 0

Using the quadratic formula,

\(x = \frac{-b \pm \sqrt{b^2-4ac} }{2a}\)

\(x = \frac{1 \pm \sqrt{1+24} }{6}\\ x = \frac{1 \pm \sqrt{25} }{6}\)

x = 1 and x = - 2/3

Hence, the solution of quadratic equation (1/3)x² - (1/9)x - 2/9 = 0 are x = 1, - 2/3.

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Answer:

326

Step-by-step explanation:

The value of the given expression is 326.

Given:

The given expression 2 hundreds + 12 tens + 6 ones.

To find:

The value of the given expression.

Explanation:

The numeric form of given expression is:

2 hundreds + 12 tens + 6 ones

2 hundreds + 12 tens + 6 ones

2 hundreds + 12 tens + 6 ones

Therefore, the value of the given expression is 326.

Answer:

19

Step-by-step explanation:

tan35=x/20

20tan35=x

x=14.0041507641942

x+5=19.0041507641942

The nearest foot is 19

Answer:

g(-5) = 8(-5) - 24 = -40 - 24 = -64

g(5) = 8(5) - 24 = 40 - 24 = 16

y = 8x - 24

8x = y + 24

x = (1/8)(y + 24) = (1/8)y + 3

g^-1(x) = (1/8)x + 3, -64 < x < 16

a) the Central Limit Theorem conditions are met. b) The 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views is approximately 0.7934 to 0.8466.

c) . A 90% confidence interval would be wider than the 95% interval

To verify the Central Limit Theorem (CLT) conditions, we need to check the following:

1. Random Sampling: The survey states that 800 adults were randomly selected, which satisfies this condition.

2. Independence: We assume that the responses of one adult do not influence the responses of others. This condition is met if the sample is collected using a proper random sampling method.

3. Sample Size: To apply the CLT, the sample size should be sufficiently large. While there is no exact threshold, a common rule of thumb is that the sample size should be at least 30. In this case, the sample size is 800, which is more than sufficient.

Therefore, the Central Limit Theorem conditions are met.

b. To find a 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views, we can use the formula for calculating a confidence interval for a proportion:

CI = p ± z * √(p(1-p)/n)

where:

- p is the sample proportion (82% or 0.82 in decimal form).

- z is the z-score corresponding to the desired confidence level. For a 95% confidence level, the z-score is approximately 1.96.

- n is the sample size (800).

Calculating the confidence interval:

CI = 0.82 ± 1.96 * √(0.82(1-0.82)/800)

CI = 0.82 ± 1.96 * √(0.82*0.18/800)

CI = 0.82 ± 1.96 * √(0.1476/800)

CI = 0.82 ± 1.96 * √0.0001845

CI ≈ 0.82 ± 1.96 * 0.01358

CI ≈ 0.82 ± 0.0266

The 95% confidence interval for the proportion of adults who believe in protecting the rights of those with unpopular views is approximately 0.7934 to 0.8466.

c. A 90% confidence interval would be wider than the 95% interval. The reason is that as we increase the confidence level, we need to account for a larger margin of error to be more certain about the interval capturing the true population proportion. As a result, the interval needs to be wider to provide a higher level of confidence.

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Problem 9

a = 500 = initial amount

b = 1+r/n = 1 + 0.034/52 = 1.000654 = approximate growth factor

The equation goes from \(y = a*b^x\) to \(y = 500*1.000654^x\) where x is the number of weeks and y is the account balance in dollars.

Plug in y = 700 and isolate x by using logarithms.

\(y = a*b^x\\\\y = 500*1.000654^x\\\\700 = 500*1.000654^x\\\\700/500 = 1.000654^x\\\\1.4 = 1.000654^x\\\\1.000654^x = 1.4\\\\\log(1.000654^x) = \log(1.4)\\\\x\log(1.000654) = \log(1.4)\\\\x = \log(1.4)/\log(1.000654)\\\\x = 514.652\\\\x = 515\\\\\)

It takes about 515 weeks for the account balance to reach $700

This is equivalent to roughly 515/52 = 9.904 years

===========================================================

Problem 10

The formula to calculate the monthly payment is not a simple exponential growth or decay function. I'm not sure how your teacher wanted you to answer this question. You'll have to get clarification on it.

If your teacher is asking something along the lines of "$240,000 is invested at a rate of 1.2% compounded bimonthly. How many years does it take to have the investment reach $300,000?" then you could follow these steps below.

a = 240,000 = initial amount

b = 1 + r/n = 1 + 0.012/24 = 1.0005 = growth factor

\(y = a*b^x\\\\y = 240000*1.0005^x\\\\300000 = 240000*1.0005^x\\\\240000*1.0005^x = 300000\\\\1.0005^x = 300000/240000\\\\\)

\(1.0005^x = 1.25\\\\\log(1.0005^x) = \log(1.25)\\\\x\log(1.0005) = \log(1.25)\\\\x = \log(1.25)/\log(1.0005)\\\\x = 446.3987\\\\x = 446\\\\\)

The x represents the number of bimonthly periods. There are 24 bimonthly periods in a year, which means it takes roughly 446/24 = 18.58 years for the starting balance of $240,000 to reach $300,000.

Keep in mind that the steps above are based on the assumption I made at the top of the problem. If that assumption is incorrect, then ignore the steps and answer entirely.

#9

\(\\ \rm\Rrightarrow P=P_o(1+r/n)^t\)

we need t

\(\\ \rm\Rrightarrow P=500(1+0.034/52)^t\)

\(\\ \rm\Rrightarrow 700=500(1+0.000654)^t\)

\(\\ \rm\Rrightarrow 700=500(1.000654)^t\)

\(\\ \rm\Rrightarrow \dfrac{7}{5}=(1.000654)^t\)

\(\\ \rm\Rrightarrow 1.4=1.000654^t\)

\(\\ \rm\Rrightarrow log1.4=log1.000654^t\)

\(\\ \rm\Rrightarrow log1.4=tlog1.000654\)

\(\\ \rm\Rrightarrow t=\dfrac{log1.4}{1.000654}\)

\(\\ \rm\Rrightarrow t\approx 514.6\approx 515weeks\)

#2

\(\\ \rm\Rrightarrow P=240000(1+0.012/25)^t\)

\(\\ \rm\Rrightarrow 300000=240000(1.0005)^t\)

\(\\ \rm\Rrightarrow \dfrac{5}{4}=(1.0005)^t\)

\(\\ \rm\Rrightarrow 1.25=(1.0005)^t\)

\(\\ \rm\Rrightarrow log1.25=log1.0005^t\)

\(\\ \rm\Rrightarrow log1.25=tlog1.0005\)

\(\\ \rm\Rrightarrow t=\dfrac{log1.25}{1.0005}\)

\(\\ \rm\Rrightarrow t=446.4\approx 446\)

Question is bit unclear to assume final units of time

The reminder of the equation using the long division method is 70X - 12.

long division method :

Four main steps to solving this problem:

\(x^2 - 3$\overline{)x^5 + 24x^3- 5x - 12}$( x^3 + 25x\\\\\)

           x₅ + 3 x³

          (-)    (-)                              

                 25x³ - 5x   -   12

                 25x³ - 75x

                 (-)      (+)                          

                            70x  - 12              

here

divisor - (x² - 3)

dividend - (x⁵ + 2x12x² - 5x - 12)

quotient - (x³ +25x)

the given question is incomplete the correct question is

Use long division to divide.

(x⁵ + 2x12x² - 5x - 12) / (x² - 3)

The reminder of the equation using the long division method is 70X - 12.

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Answer:

Step-by-step explanation:

Note: the question did not provide the quantity to work with, so we will assume some values, say quantity Q= 30

Generally, it is normal for the revenue to decrease when the price of a commodity increase, this is so that buyer will have to react to adjust to the change in price.

When price increase from $50 to $60, the total revenue will decrease

let say the quantity Q1=30 , and the new quantity after price increase is Q2=20

1. The revenue PxQ before price change will be

PxQ= P1xQ1=50*30

PxQ= $1500

1. The revenue PxQ after price change will be

PxQ=P2xQ2= 60*20

P2xQ2= $1200

This clearly shows that based on the assumed data, the total revenue will drop from1500 to 1200, a total of $300 in a decrease