In the game of roulette, a player can place a $6 bet on the number 10 and have a 1/38 probability of winning. If the metal ball lands on 10, the player gets to keep the $6 paid to play the game and the player is awarded an additional $210. Otherwise, the player is awarded nothing and the casino takes the player's $6.


(a) What is the expected value of the game to the player? (Round to the nearest cent as needed.)


(b) If you played the game 1000 times, how much would you expect to lose?


Note that the expected value is the amount, on average, one would expect to gain or lose each game. (Round to the nearest cent as needed.)

(3x+5)-(\(x^{2} - 3\))=9

\(x^{2}\)-3x-8=-9

\(x^{2}\)-3x=-1

\(x^{2}\)-3x+1=0

The simplified form of the expression 4x(x + 1) − (3x − 8)(x + 4) is -3x^2 - 4x - 32.

To simplify the expression 4x(x + 1) − (3x − 8)(x + 4), we can expand the parentheses and combine like terms.

Expanding the first term, we get 4x^2 + 4x.

Expanding the second term, we have -(3x)(x) - (3x)(4) - (-8)(x) - (-8)(4), which simplifies to -3x^2 - 12x - (-8x) - (-32), further simplifying to -3x^2 - 12x + 8x - 32.

Combining like terms, we obtain -3x^2 - 4x - 32.

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Answer:

1/6 because 3 is one of the sides of the 6

The odds against rolling a 3 are 5:1 and the probability of rolling a 3 is 1/6

It is a branch of mathematics that deals with the occurrence of a random event.

There are five numbers (1, 2, 4, 5, 6) that are not 3, so the number of ways to roll a number that is not 3 is 5.

The total number of possible outcomes is 6, since there are six sides on the die.

Therefore, the odds against rolling a 3 are:

5:1

This can also be expressed as a probability by dividing the number of unfavorable outcomes by the total number of outcomes:

P(not rolling a 3) = 5/6

Alternatively, the probability of rolling a 3 is 1/6, so we can also say:

P(rolling a 3) = 1/6

And the probability of not rolling a 3 is:

P(not rolling a 3) = 1 - P(rolling a 3)

= 1 - 1/6

= 5/6

Hence, the odds against rolling a 3 are 5:1 and the probability of rolling a 3 is 1/6

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Answer:

24

Step-by-step explanation:

You just do 6 / 1/4 = 24

"How many sticks of gum can you eat at one time?" is the finest and most right response. Then the correct option is A.

A statistical question is one that may be addressed by gathering data from several sources.

A statistical question is one that may be addressed by gathering data and in which the data is likely to vary. This is not the same as a question with a predetermined response.

The first choice or letter A, "How many sticks of gum can you eat at one time?" is the finest and most right response among the options supplied by your query.

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Given:

Right triangle A: Base = 2 inches and Height = 7 inches.

Right triangle B: Base = 10 inches and Height = 35 inches.

To find:

The scale factor applied to Right triangle A to produce Right triangle B.​

Solution:

We have,

Base of right triangle A = 2 inches

Base of right triangle B = 10 inches

Now,

\(\text{Scale factor}=\dfrac{\text{Side of right triangle B}}{\text{Corresponding side of right triangle A }}\)

\(Scale\text{Scale factor}=\dfrac{\text{Base of right triangle B}}{\text{Base of right triangle A }}\)

\(\text{Scale factor}=\dfrac{10}{2}\)

\(\text{Scale factor}=5\)

Therefore, the scale factor of 5 applied to Right triangle A to produce Right triangle B.​

Answer:hi

Step-by-step explanation:

Answer:

9.75

Step-by-step explanation:

-25 = -4p + 19

-25 - 19 = -4p

-39 ÷ -4 = p

9.75 = p

Answer:

42

Step-by-step explanation:

A. inequality that compares the temperatures of the two cities is: -2 > -6. B. inequality means city R, represented by -2 on the number line greater than the temperature of city S, represented by -6 on the number line. C.  city R is warmer than city S.

In mathematics, an inequality is a statement that compares two values or expressions and indicates that one is greater than, less than, or equal to the other. Inequalities are used to describe relationships between values that are not necessarily equal, and they are written using special symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

For example, the inequality 3x + 2 < 10 means that the expression 3x + 2 is less than 10. This inequality can be solved for x by subtracting 2 from both sides and then dividing by 3, yielding x < 2. This means that any value of x that is less than 2 will satisfy the inequality.

The inequality that compares the temperatures of the two cities is: -2 > -6

This inequality means that the temperature of city R, represented by -2 on the number line, is greater than the temperature of city S, represented by -6 on the number line. In other words, city R is warmer than city S.

On the number line, the further to the right a number is, the greater it is. Since -2 is to the right of -6, this indicates that -2 is greater than -6, which represents the fact that city R is warmer than city S.

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Answer:

the total is $153.9

Step-by-step explanation:

The total for the adults is $19.9

The children $27

Popcorn $224

$9.95×2=$19.9

$6.75×4=$27

$28×6=$168

Answer:

Let M be the minimum monthly payment and A be the additional monthly payment of $30. Let B be the balance on the store credit card.

From the problem, we have:B = M * 58 (if only minimum payments are made)

B = (M + A) * 24 (if an additional $30 is paid each month)

Simplifying these equations, we get:M = B / 58

M + A = B / 24

Substituting the first equation into the second equation, we get: B / 58 + A = B / 24

Solving for A, we get:A = B / 24 - B / 58

A = B * (58/24 - 1/58)

Simplifying, we get:A = B * 0.08275862

To find the percent of time that Haddad will save by paying the extra $30 per month, we need to find the difference in time between the two scenarios and divide by the longer time (58 months).

The time it takes to pay off the balance with only the minimum payments is 58 months, while the time it takes to pay off the balance with the additional $30 each month is 24 months.

The difference in time is:58 - 24 = 34

So Haddad will save 34 / 58 = 0.5862, or 58.62% of the time by paying the extra $30 per month.

The interest Raymond will pay this month is $54.98

What does APR mean?

APR means annual percentage rate, which means that since we are computing monthly interest, the annual rate which is the whole 12 months needs to be divided by 12 to ascertain the equivalent monthly interest rate

monthly interest=21.99%/12

What is the monthly interest amount in dollars?

The monthly interest amount in dollars is determined as the monthly interest rate multiplied by the credit card balance at the end of the month

monthly interest=$3,000*21.99%/12

monthly interest=$54.98

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Answer:

4,5,6

Step-by-step explanation:

A midsegment connects two midpoints, and this triangle would be made up of all midsegments.  If we know that midsegments are half of the side length, then we can get our answer.

The required value of y for the given segment AB is given as y = 16, -8.

A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.

here,
A(0, 4), B(5, y), and AB = 13.

Applying the distance formula,
D = √[[x₂ - x₁]² + [y₂- y₁]²]

Substitue the value in the above expression,
13 = √[[5 - 0]² + [y - 4]²]
169 = 25 + [y - 4]²
[y - 4]² = 144
y - 4 = ± 12

y = 16, -8

Thus, the required value of y for the given segment AB is given as y = 16, -8.

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The width of the deck given that the entire deck needs 40 feet to trim is 8 feet

Let's assume the width of the rectangular deck is "w".

The perimeter of the deck can be calculated by using the formula: P = 2(l + w), where P is the perimeter, l is the length, and w is the width.

Here, the length of the deck is given as 12 feet.

So, P = 2(12 + w)

We also know that the total trim required is 40 feet.

So, P = 40 feet

Equating both the expressions for P, we get:

2(12 + w) = 40

Simplifying the equation, we get:

24 + 2w = 40

2w = 16

w = 8

Therefore, the width of the deck is 8 feet.

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Answer:

-x+6≤5

-x≤5-6

-x≤-1

x≤1

Answer: 55+ (8* M)

Step-by-step explanation: I think that's the answer

The vertex of point A' in the dilated triangle A'B'C' is (6, 4.5).

1. Start by calculating the distance between the vertices of the original triangle ABC:

  - Distance between A(4, 3) and B(3, -2):

    Δx = 3 - 4 = -1

    Δy = -2 - 3 = -5

    Distance = √((-\(1)^2\) + (-\(5)^2\)) = √26

  - Distance between B(3, -2) and C(-3, 1):

    Δx = -3 - 3 = -6

    Δy = 1 - (-2) = 3

    Distance = √((-6)² + 3²) = √45 = 3√5

  - Distance between C(-3, 1) and A(4, 3):

    Δx = 4 - (-3) = 7

    Δy = 3 - 1 = 2

    Distance = √(7² + 2²) = √53

2. Apply the scale factor of 1.5 to the distances calculated above:

  - Distance between A' and B' = 1.5 * √26

  - Distance between B' and C' = 1.5 * 3√5

  - Distance between C' and A' = 1.5 * √53

3. Determine the coordinates of A' by using the distance formula and the given coordinates of A(4, 3):

  - A' is located Δx units horizontally and Δy units vertically from A.

  - Δx = 1.5 * (-1) = -1.5

  - Δy = 1.5 * (-5) = -7.5

  - Coordinates of A':

    x-coordinate: 4 + (-1.5) = 2.5

    y-coordinate: 3 + (-7.5) = -4.5

4. Thus, the vertex of point A' in the dilated triangle A'B'C' is (2.5, -4.5).

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Answer:

Step-by-step explanation:

60 minutes per hour
2.82gal *60mins = 169.2gal per hour.
303 gallons / 169.2 gph = about 1.7907 hours

Answer:

r= 10.745

Step-by-step explanation:

Answer:

x=5 and y=2

Step-by-step explanation:

I hope this helps

Answer:

A)  (-7, 6)

Step-by-step explanation:

The graph of the inverse function is a reflection in the line y = x.

The mapping rule for a reflection in the line y = x is:

Therefore, if point (6, -7) is on the graph of the function f(x), the point that is on the graph of the inverse function f⁻¹(x) is:

since the 2 ines of the parallelogram represent the diagonals

the diagonals of a parallelogram will always bisect each other

thismeans the point formed in the middle will always be the midpoint of each diagonal.

then

and

then

x=4

y=8

Using the weighted mean, it is found that Trent can earn scores of at least 62 on the final exam to pass the course if he needs a "C" or better.

The complete problem is given as follows:

"Trent earns scores of 62, 86, and 80 on three chapter tests for a certain class.

His homework grade is 68 and his grade for a class project is 64.

The overall average for the course is computed as follows: the average of the three chapter tests makes up 50% of the course grade; homework accounts for 10% of the course grade; the project accounts for 20% of the course grade and the final exam accounts for 20% of the course grade.

What range of scores can Trent earn on the final exam to pass the course if he needs a "C" or better?

A "C" or better requires an overall course score of 70 or better, and 100 is the highest score that can be earned on the final exam."

The weighted mean is given by the sum of all elements in a data-set multiplied by it's weight, divided by the sum of the weights.

For this problem, we have that:

Hence his weighted mean is given by:

76 x 0.5 + 68 x 0.1 + 64 x 0.2 + 0.2x = 57.6 + 0.2x.

For a grade C, he needs a score of at least 70, hence:

57.6 + 0.2x ≥ 70.

0.2x ≥ 12.4

x ≥ 12.4/0.2

x ≥ 62.

Hence Trent can earn scores of at least 62 on the final exam to pass the course if he needs a "C" or better.

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Answer:

8,957,172 people

Explanation:

Population = 1,218 people per square mile

Land area of New Jersey = 7,354 square miles

Total population:

people living in per square mile × total land area

1,218 × 7,354

8,957,172

The percent cost of 1 kg rice is less than the cost of 1 kg sugar by 11 1/9%.

We first calculate the difference between the original value and the new value when comparing a rise in a quantity over time. The relative increase in comparison to the initial value is then determined using this difference, and it is expressed as a percentage.

Let the cost price of rice is R and cost price of sugar is S.

Case 1 :  total cost of 5 kg rice and 6 kg sugar is Rs. 940.

5R + 6S = 940 ...(1)

Case 2 : rate of rice increased by 20% and the rate of sugar decreased by 10%.

The new cost price of rice = R + 20% of R = 1.2R

The new cost price of sugar = S - 10% of S = 0.9S

So, the total cost of 4 kg rice and 3 kg sugar will be Rs. 627.

Thus,

4 × 1.2R + 3 × 0.9S = 4.8R + 2.7S = 627 ..(2)

From equations (1) and (2) we have,

(5R + 6S)/(4.8R + 2.7R) = 940/627

R/S = 8/9

Hence, if the price of rice is 8 then the price of sugar is 9.

It is clear that the price of sugar is more than that of rice.

The percent cost by which cost of rice is less than sugar is:

(9 - 8)/ 9 (100) = 11 1/9%.

Hence, the cost of 1 kg rice is less than the cost of 1 kg sugar by 11 1/9%.

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The triangle ∠ADC is a central angle, m∠ADC is 60 degrees, and m∠ABC is 30°.

The central angle is the angle that a circle's arc occupies in its centre. The arms of the central angle are formed by the radius vectors. In other terms, it is an angle whose vertex is the centre of a circle, with the two radii lines acting as its arms and intersecting the circle at two distinct places. These two points make an arc when they are coupled together. The angle that this arc at the circle's centre subtends is called the central angle.

Half of the central angle is the circumferential angle.

∠ABC is equal to 1/2 of ∠ABC.

∠ABC = \(\frac{1}{2}*60\)

∠ABC = 30°

Option b. 30° is the right response, so.

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