One option in a roulette game is to bet $15 on red. (There are 18 red compartments, 18 black compartments, and two compartments that are neither red nor black.) If the ball lands on red, you get to keep the $15 you paid to play the game and you are awarded $15. If the ball lands elsewhere, you are awarded nothing and the $15 that you bet is collected. What is the expected value for playing roulette if you bet $15 on red?​

The average rate of change of the population per year is -5666.66

From the question, we have the following parameters that can be used in our computation:

Year  Population

1972  1,090,000

1982  1,060,000

1992  940,000

2002 860,000

2012 800,000

2022 770,000

Given that the year is from 1972, we have

year 20 = 1992  940,000

year 50 = 2022 770,000

So, we have

Average rate = Difference in values/Difference in years

This gives

Average rate = (770,000 - 940,000)/30

Evaluate

Average rate = -5666.66

Hence, the rate is -5666.66

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Given the ratio of Year 7 pupils to Year 8 pupils as 9:5 and the ratio of Year 8 pupils to Year 9 pupils as 1:11, the ratio of Year 7, Year 8, and Year 9 pupils together is 9:5:55.

The ratio refers to the relative size of values.

Ratios are fractional values, depicted as fractions, decimals, or percentages.  Ratios can also be denoted in ratio form (:).

Ratios are computed as the comparative values that each quantity has in relation to other quantities or values.

The ratio of Year 7 pupils to Year 8 pupils = 9:5

The ratio of Year 8 pupils to Year 9 pupils = 1: 11

The ratio of Year 7, Year 8, and Year 9 = 9:5:55 (11 x 5)

The sum of ratios = 69 (9 + 5 + 55)

Thus, the ratio of Year 7, Year 8, and Year 9 is 9:5:55.

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There are only Year 7 pupils, Year 8 pup,ils, and Year 9 pupils in a group The ratio of Year 7 to Year 8 is 9:5. The ratio of Year 8 to Year 9 is 1: 11.

Find the ratio Year 7: Year 8: Year 9. Give your ratio in its simplest form with integer parts.

The quadratic equation with integer coefficients that has the given solution set {-10, 9} is x² + x - 90 = 0.

Polynomial is an equation written with terms of the form kx^n.

where k and n are positive integers.

There are quadratic polynomials and cubic polynomials.

Example:

2x³ + 4x² + 4x + 9 is a cubic polynomial.

4x² + 7x + 8 is a quadratic polynomial.

We have,

If the given solution set is {-10, 9}.

Then the quadratic equation can be written in factored form as:

(x + 10) (x - 9) = 0

Expanding the product,

x² + x - 90 = 0

Therefore,

The quadratic equation with integer coefficients that has the given solution set {-10, 9} is x² + x - 90 = 0.

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The exact value of the expression tan(0/2) for the given value of 0 is 0.

In mathematics, it is important to understand how to simplify expressions and solve for their exact values. One such expression is tan(0/2), where 0 is a given value. In this explanation, we will break down the steps to simplify this expression and find its exact value without using a calculator.

The expression we are given is tan(0/2), which can be simplified using the formula for the tangent of half an angle. This formula states that tan(x/2) = sin(x) / (1 + cos(x)).

In our given expression, we have x = 0, so we can substitute it into the formula and get:

tan(0/2) = sin(0) / (1 + cos(0))

Now, we know that sin(0) = 0 and cos(0) = 1, so we can simplify further:

tan(0/2) = 0 / (1 + 1) = 0/2 = 0

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Therefore, (18²)⁻³ can be written as 18² - 10^⁻³ using positive exponents only.

An equation is a mathematical statement that shows that two expressions are equal. Equations can be used to represent relationships between variables, or to solve problems. Equations use mathematical symbols, such as the equal sign (=), to show the equality between the two expressions. For example, the equation 2x + 3 = 7 represents the relationship between the variable x and the constants 2 and 3. The equation can be solved for x to find its value. In this case, solving for x would give us x = 2.

Using positive exponents only, we can write (182)⁻³ as follows:

(182) can be written as 10²

-3 can be written as 10⁰/ 10³

So, (18²)⁻³ can be written as:

18² - 10⁰ / 10³= 18² - 10⁻³

Therefore, (18²)⁻³ can be written as 18² - 10^⁻³ using positive exponents only.

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The area of a 40° sector of this circle is 4m², the correct option is D.

Suppose the circle has radius of 'r' units, then, its area is given as:

[tex]A = \pi \times r^2[/tex]

sq. units

Since radius of a circle is half of its diameter, so if diameter is of 'd' length, then r= d/2, thus, area can be rewritten as:

[tex]A = \pi \times r^2[/tex]

sq. units

Given;

A circle has an area of 36 m².

Now,

40° of circle= 360/40=9

Area of circel;

=36/9

=4

Therefore, the area of 40° of circle will be 4m^2

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The interquartile range is 16.00

To construct a box and whisker plot in Excel using the Quartile.INC function for the given data, follow these steps:

1) Enter the data into a column in Excel.

2) Select the data column and click on the "Insert" tab in the top menu.

3) Click on "Insert Statistic Chart" and select "Box and Whisker" from the dropdown menu.

4) In the "Chart Elements" menu on the right, click on the arrow next to "Axis Titles" and select "Primary Vertical Axis Title" to add a title for the y-axis.

5) Label the y-axis "Number of Rooms Sold".

6) Right-click on the y-axis and select "Format Axis" from the dropdown menu.

7) In the "Number" menu, select "Number" as the category and set the number of decimal places to 0.

8) In the "Chart Elements" menu, click on the arrow next to "Chart Title" and select "None" to remove the chart title.

9) The resulting box and whisker plot should show the quartiles, the median, and any outliers.

To find the interquartile range, subtract the first quartile (Q1) from the third quartile (Q3). The Quartile.INC function in Excel returns the exclusive quartiles (i.e., does not include the median in either quartile), so the interquartile range is calculated as:

IQR = Q3 - Q1

Using the Quartile.INC function with the given data, we get:

Q1 = 78.5

Q3 = 94.5

Therefore, the interquartile range is

IQR = Q3 - Q1 = 94.5 - 78.5 = 16

Rounding to two decimal places, the interquartile range is 16.00.

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Answer:

the correct responses are:

The graph will have a vertical asymptote at x = π/2.

The graph will have a vertical asymptote at x = 3π/2.

The graph will have a vertical asymptote at x = 2π.

The graph will not go through the point (π/4, 1).

Step-by-step explanation:

The statements that are true about the graph of f(x) = cot(x) are:

The graph will have a vertical asymptote at x = π/2.

The graph will have a vertical asymptote at x = 3π/2.

The graph will have a vertical asymptote at x = 2π.

These are true because the cotangent function has vertical asymptotes at every odd multiple of π/2, which includes π/2, 3π/2, and 5π/2, and so on.

The statement that the graph will go through the point (π/4, 1) is false. The cotangent function does not pass through this point, although it does have a vertical asymptote at x = π/4.

Therefore, the correct responses are:

The graph will have a vertical asymptote at x = π/2.

The graph will have a vertical asymptote at x = 3π/2.

The graph will have a vertical asymptote at x = 2π.

The graph will not go through the point (π/4, 1).

Answer:

Step-by-step explanation:

The given statement indicates that (a) Your average pay is $40 (b) The standard deviation is 45.12 (c) If you retain both positions, your anticipated income is $400.

Because it aids in comprehending observations when the data is dispersed, standard deviation is significant. The standard error of the data will be higher the more evenly spread the data is.

a) On average, you make $220 - $180 = $40 more from Job A.

b) The standard deviation of the difference in the amount you make from Job A and Job B is given by:

σ(A - B) = √[σ(A)² + σ(B)²]

= √[(30)² + (35)²]

≈ 45.12

c) To determine whether to take the deal, we need to compare the expected earnings from the two scenarios. If you quit Job B and accept your mom's offer, your total earnings would be:

Earnings = (1/2) × $220 + $100 = $210

On the other hand, if you keep both jobs, your expected earnings would be:

Earnings = $220 + $180 = $400

Since $400 is greater than $210, you would not take the deal if making the most money is the most important thing to you.

It is important to remember that this choice may also be influenced by aspects like the amount of time and effort needed for each work, the chance for professional advancement, job security, and other non-financial considerations.

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The value of JL is 21

A line segment is defined as the part of a straight line that is bounded by two distinct end points.

It is known to contain all the points on the line that is between its endpoints.

From the information given, we have that the point K is found between J and L and the line segment, JL

Then, we have;

JK + KL = JL

substitute the values, we have;

x + 8 + 10 = 7x

collect the like terms

x - 7x = -10 - 8

subtract the like terms

-6x = -18

x = 3

So. JL = 7(3) = 21

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Answer:

$66,600

Step-by-step explanation:

First you add everything up.

50,000 + 1,400 = 51,400

51,400 + 2,500 = 53,900

53,900 + 1,600 = 55,500

Now you need to get 20% of 55,500

20% of 55,500 is 11,100

Now you add them

55,500 + 11,100 = 66,600

The percent tip Ruby left was 27%.

What is percent?

A percentage is a quantity or ratio that is stated as a fraction of one hundred. The percent sign, "%," is frequently used to represent it.

Calculate the tip amount:

The total cost of the meal including the tip is $34.29, and the cost of the meal before the tip is $27. Therefore, the tip amount is:

Tip = Total cost - Cost of meal

Tip = $34.29 - $27

Tip = $7.29

Calculate the percent tip:

The percent tip is the tip amount divided by the cost of the meal, multiplied by 100 to express the result as a percentage:

Percent tip = (Tip / Cost of meal) x 100%

Percent tip = ($7.29 / $27) x 100%

Percent tip = 27%

Therefore, the percent tip Ruby left was 27%.

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Answer:

Step-by-step explanation:

Percentage of girls = 35%

Percentage of boys = 100 - 35 = 65%

There are 910 boys:

65% = 910

Find the number of students in the school:

1% = 910 ÷ 65 = 14

100% = 14 x 100 = 1400

Answer: There are 1400 students in the school

Answer:

C

Step-by-step explanation:

180-2x-2=180*7/9

x=19

The inequality in standard form that represents the restaurant owner's

desired revenue is x² + 2x - 80 ≤ -65.

Inequalities are defined as the expressions consisting of both variables and constants connected by inequality signs like ≠, >, <, ≤ and ≥.

Part A :

Cost : 10 + x

Customers : 16 - 2x

Part B :

Given that,

Hourly revenue = Price paid by each customer × average number of customers per hour.

Price paid by each customer = 10 + x

Average customers per hour = 16 - 2x

Given that the restaurant owner wants a minimum revenue of $130 per hour.

(10 + x) (16 - 2x) ≥ 130

(10 × 16) + (16x) - (10 × 2x) - 2x² ≥ 130

160 + 16x - 20x - 2x² ≥ 130

-2x² - 4x + 160 ≥ 130

Dividing the equation throughout by -2,

x² + 2x - 80 ≤ -65

The inequality sign changes as we multiply or divide with a negative number.

Hence the required inequality is x² + 2x - 80 ≤ -65.

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The complete question is given below.

Noah manages a buffet at a local restaurant. He charges $10 for the buffet. On average, 16 customers choose buffet as their meal every hour. After surveying several customers, Noah has determined that for every $1 increase in the cost of the buffet, the average number of customers who select the buffet will decrease by 2 per hour. The restaurant owner wants the buffet to maintain a minimum revenue of $130 per hour.

Part A

Write two expressions for this situation, one representing the cost per customer and the other representing the average number of customers. Assume that the x represents the number of $1 increases in the cost of buffet.

Part B

To calculate the hourly revenue from the buffet after x $1 increases, multiply the price paid by each customer and the average number of customers per hour. Create inequality in standard form that represents the restaurant owner's desired revenue.

The answer is C) 6 units of consumption goods.

What is Cost of producing?

The overall cost incurred by a business to manufacture a product or provide services is referred to as the cost of production. Supplies and raw materials consumed during production, as well as labor costs, are often included in production costs.

The opportunity cost of producing 3 units of capital is 6 units of consumption goods, as we can see from the data in the production possibilities curve.

Moving from producing 4 units of capital to producing 3 units of capital involves giving up 3 units of consumption goods (from 7 to 4), and moving from producing 3 units of capital to producing 2 units of capital involves giving up another 3 units of consumption goods (from 4 to 1).

Therefore, the opportunity cost of producing 3 units of capital is 6 units of consumption goods.

So, the answer is C) 6 units of consumption goods.

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The rate of the current is 5/11 of the speed of the barge in still water.

Let's call the speed of the barge in still water "s" (in miles per hour) and the speed of the current "c" (also in miles per hour).

When the barge travels upstream (against the current), its effective speed is reduced by the speed of the current, so the speed of the barge relative to the riverbank is (s - c). On the return trip, the current is going in the same direction as the barge, so the effective speed of the barge relative to the riverbank is (s + c).

distance upstream = (s - c) x 8 miles

distance downstream = (s + c) x 3 miles

(s - c) x 8 = (s + c) x 3

8s - 8c = 3s + 3c

5s = 11c

c = 5s/11

Therefore, the rate of the current is 5/11 of the speed of the barge in still water.

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The correct symbol forms are:

a)  x ≥ 7 is equivalent to  p v q

b) 11 > x > 7 is equivalent to p ∧ r

c)  11 > x ≥ 7 is equivalent to  ( p v q) ∧ r

We have the following definitions:

p = "x > 7"

q = "x = 7"

r = "11 > x"

a) The statement "x ≥ 7" is true if x is greater than 7 or if x is equal to 7. In other words, "x > 7 or x = 7" must be true. Using the given definitions, we can see that this is equivalent to p v q.

b) 11 > x > 7.  The statement "7 < x < 11" means that x is greater than 7 and less than 11. In other words, both "x > 7" and "x < 11" must be true. hence, it can be expressed as the conjunction of "x > 7" and "x < 11," which is equivalent to p ∧ r.

c) 11 > x ≥ 7. Combining answer from part a and b, this is equivalent to:

  ( p v q) ∧ r

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The domain of the function g(x) = √x - 4 as an inequality is x ≥ 0.

The domain of a function is simply the set of all possible inputs for the function.

Given the function in the question;

g(x) = √x - 4

Domain: ?

To determine the domain of the function, set the radicand in √x to greater than or equal to 0 and find where the expression is defined,

x ≥ 0

Hence, the domain is all values of x that makes the expression defined.

Interval notation: [0,∞)

Set-Builder notation or inequality : { x|x ≥ 0 }.

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Answer:

83 There is an elixir

total quantity of elixir = 500 mL

quantity of elixir use in one dose = 6 mL

number of dose in 500 mL = 500/6

83.333

a) (i) Average velocity = -96.8 ft/s

   (ii) Average velocity = -95.2 ft/s

   (iii) Average velocity = -92.8 ft/s

b) The instantaneous velocity of the pebble after 3 seconds is approximately -96 ft/s.

What is average velocity?

The change in position or displacement (x) divided by the time intervals (t) in which the displacement happens yields the average velocity. Depending on the sign of the displacement, the average velocity can be positive or negative.

(a)

(i) The time period from t = 3 to t = 3.1 is 0.1 seconds. The average velocity of the pebble during this time period can be found by taking the difference in position (y) divided by the difference in time (t).

Average velocity = (y(3.1) - y(3)) / (3.1 - 3)

Substituting [tex]y = 225 - 16t^2[/tex], we get:

[tex]Average\ velocity = [(225 - 16(3.1)^2) - (225 - 16(3)^2)] / (0.1)[/tex]

Average velocity = -96.8 ft/s (rounded to one decimal place)

(ii) The time period from t = 3 to t = 3.05 is 0.05 seconds. The average velocity of the pebble during this time period can be found using the same formula as above:

[tex]Average\ velocity = (y(3.05) - y(3)) / (3.05 - 3)[/tex]

Substituting [tex]y = 225 - 16t^2[/tex], we get:

[tex]Average\ velocity = [(225 - 16(3.05)^2) - (225 - 16(3)^2)] / (0.05)[/tex]

Average velocity = -95.2 ft/s (rounded to one decimal place)

(iii) The time period from t = 3 to t = 3.01 is 0.01 seconds. The average velocity of the pebble during this time period can be found using the same formula as above:

Average velocity = (y(3.01) - y(3)) / (3.01 - 3)

Substituting [tex]y = 225 - 16t^2[/tex], we get:

[tex]Average \ velocity = [(225 - 16(3.01)^2) - (225 - 16(3)^2)] / (0.01)[/tex]

Average velocity = -92.8 ft/s (rounded to one decimal place)

(b)

The instantaneous velocity of the pebble at any given time t can be found by taking the derivative of the position function y(t) with respect to time:

[tex]\frac{dy}{dt} =-32t\\[/tex]

Substituting t = 3, we get:

[tex]\frac{dy}{dt} =-96ft/s\\[/tex]

Therefore, the instantaneous velocity of the pebble after 3 seconds is approximately -96 ft/s.

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Answer:#

Step-by-step explanation:

In the congruent triangles; ΔABC and ΔBDE, ∠ABC  = ∠DBE by CPCT that is Corresponding parts of Congruent Triangle.

So,

ΔABC and ΔBDE, are congruent  triangles

Thus,

∠ABC  = ∠DBE (Corresponding parts of Congruent Triangle) CPCT.

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Answer:

x= 7 ;

y+x=18

y=18-x

y=18-7

y=11

Answer:

= 34

Step-by-step explanation:

(32)-5+7

32 - 5 + 7

= 32 + 2

= 34.

The most likely to watch TV for 4 hours is distribution B. Therefore, option B is the correct answer.

In statistics, a simple random sample is a subset of individuals chosen from a larger set in which a subset of individuals are chosen randomly, all with the same probability. It is a process of selecting a sample in a random way.

Given that, average number of hours American adults watch TV is 4 hours.

In distribution A, B, C and D, the most likely to watch TV for 4 hours is distribution B and less likely to watch TV for 4 hours is distribution A.

Therefore, option B is the correct answer.

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Given the planes [tex]4x-5y+z=4[/tex] and [tex]5x-4y+3z=-2[/tex], find the angle between them.

Using the formula,

[tex]\theta=cos^{-1} (\frac{A_{x}B_{x}+A_{y}B_{y}+A_{z}B_{z} }{\sqrt{A^2_{x}+A^2_{y}+A^2_{z}}\sqrt{B^2_{x}+B^2_{y}+B^2_{z}} } )[/tex]

Where vector, [tex]A= < 4,-5,1 >[/tex] and vector [tex]B= < 5,-4,3 >[/tex].

Plug these values into the formula above...

[tex]\Longrightarrow \theta=cos^{-1} (\frac{A_{x}B_{x}+A_{y}B_{y}+A_{z}B_{z} }{\sqrt{A^2_{x}+A^2_{y}+A^2_{z}}\sqrt{B^2_{x}+B^2_{y}+B^2_{z}} } )[/tex]

[tex]\Longrightarrow \theta=cos^{-1} (\frac{(4)(5)+(-5)(-4)+(1)(3) }{\sqrt{(4)^2+(-5)^2+(1)^2}\sqrt{(5)^2+(-4)^2+(3)^2} } )[/tex]

[tex]\Longrightarrow \theta=cos^{-1} (\frac{43 }{\sqrt{42}\sqrt{50} } )[/tex]

[tex]\Longrightarrow \theta=cos^{-1} (\frac{43 }{10\sqrt{21} } )[/tex]

[tex]\Longrightarrow \theta \approx 20.2\textdegree[/tex]

Answer:

Step-by-step explanation:

Expanding (x + y)^2, we get:

(x + y)^2 = x^2 + 2xy + y^2

We are given that xy/2 = 7, so 2xy = 14. We are also given that x^2 + y^2 = 28. Substituting these values, we get:

(x + y)^2 = x^2 + 2xy + y^2 = x^2 + y^2 + 2xy = 28 + 14 = 42

Therefore, (x + y)^2 = 42.