A carnival game allows a group of players to each draw and keep a marble from a bag. The bag contains 5 gold marbles, 25 silver marbles, and 70 red marbles.

A player wins a large prize for drawing a gold marble and a small prize for drawing a silver marble. There is no prize for drawing a red marble.

At the start of the game, the probability of winning a large prize is 0.05 and the probability of winning a small prize is 0.25.

1. Suppose that the first player draws a silver marble and wins a small prize. What is the probability that the second player will also win a small prize?

2. If a group of four plays the game one at a time and everyone wins a small prize, which player had the greatest probability of winning a large prize?

3. How could the game be made fair for each player? That is, how could you change the game so that each player has an equal chance of winning a prize?

The given function is a quadratic equation, not a linear one, and so it would be represented by a parabolic curve on a graph, not a straight line.

The function you're asking about, f(x) = 9x² - 36/3x + 6, is a quadratic equation. Quadratic equations are represented by parabolas on the graph not a straight line. Parabolas usually have a shape like a U (or an upside down U, depending on the equation).

The equation you've given should result in a parabolic graph. The straight line equations and graphs you’re referring to, like y = 9+3x, would not represent your function. The line graph with a y-intercept of 9 and a slope of 3 is not a representation of your function.

Also, it's important to note that the equation you provided, f(x) = 9x² - 36/3x + 6, can be simplified to f(x) = 9x² - 12x + 6.

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The amount after 15 years is approximately $26,971.67.

To calculate the amount after 15 years, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where:

In this case, P = $10,000, r = 0.0625 (6.25% as a decimal), n = 12 (monthly compounding), and t = 15. Substituting these values into the formula:

A = $10,000(1 + 0.0625/12)^(12*15) = $26,971.67 (approximately).

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Answer:

The system of equations has no solution

Step-by-step explanation:

We have to find the number of solutions of system of equations shown in the graph.

Since, the number of solutions of system of equations is that point of thew graph on which the graph of two equations meet.

Since, we can see from the graph the two lines are parallel

Hence, they can never meet.

Hence, the system of equations has no solution.

Hence, first option is correct.

volume for cylinder = pi x r^2 x h

 radius = half the diameter = 8/2 =4

height = 3 times the radius = 3*4 =12

using 3.14 for pi

volume = 3.14 x 4^2 x 12 = 602.88 cubic inches

To solve this problem, we would be needing the actual height or size of the book which is not given in the problem. However for the sake of calculation let us assume that the average height of a book is 8.5 inches.

Then the next step we have to do is to convert the height of the first grader from units of meter to units of inches. We know that:

1 meter = 39.37 inches

Therefore the height of the first grader is 39.37 inches.

Taking the ratio with the bigger number in the numerator (height of the 1st grader / height of the book):

ratio = 39.37 inches / 8.5 inches

ratio = 4.63

Therefore this means that the first grader is about 4.63 times taller than the book.

5 nickels , 2 quarters, and 1 pennies = 8 coins.

 he received 2 quarters

Answer:

Sample Response:  Shifts in supply and demand occur when the amount of goods available increases or decreases, or when the demand for a particular good increases or decreases. Shifts in supply can happen when consumers change their spending habits, when competitors produce similar goods, or when the availability of labor or resources changes. Shifts in demand occur when the price changes or when the number of people trying to buy the good changes. It can also happen when people's tastes change.

The new picture will have a length of 4.5 inches and a width of 3 inches.

There is asking about the size of a scaled-down photo in comparison to the original photo that has a length of 6 inches and a width of 4 inches. Given the ratio of the new picture to the size of the first picture is 1.5 to 2, we need to calculate the new dimensions.

The scale factor from the original to the new photo is 1.5 / 2, which simplifies to 0.75. Thus, we multiply the original dimensions by 0.75 to find the dimensions of the new picture:

Length of new picture = 6 inches * 0.75 = 4.5 inches

Width of new picture = 4 inches * 0.75 = 3 inches

Graph of the line [tex]y = \frac{2}{3} x+490[/tex] is drawn with slope [tex]m = \frac{2}{3}[/tex] and y-intercept 490 and x-intercept = -735.

"Slope of the line is defined as the ratio of difference in the increment in y coordinates to the difference in increment in x-coordinates."

Formula used

standard equation of line

y = mx + c

m = slope of the line

c = y- intercept

According to the question,

Given equation of line,

[tex]y = \frac{2}{3} x+490[/tex]

Compare it with standard equation of line y = mx + c we get,

Slope [tex]m = \frac{2}{3}[/tex]

y-intercept = 490

Calculate x-intercept by putting y=0

x-intercept = -735

Now plot it on the graph as shown and join the points with slope [tex]m = \frac{2}{3}[/tex]

Hence, graph of the line [tex]y = \frac{2}{3} x+490[/tex] is drawn with slope [tex]m = \frac{2}{3}[/tex] and y-intercept 490 and x-intercept = -735.

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The person under is wrong but there chart is right. 100%-15%=85%

85%=.85

F(x)= 40(.85)^x

Write that in desmos graphing and you will get the chart.

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Answer:

y= -5

Step-by-step explanation:

rewrite as standard form    [tex]4.2(y-(3-))=(x-2)^{2}[/tex]

(h.k) = (2, -3), P=2

y= -3 -P

y= -3 -2

y= -5

The equation of circle will be;

⇒ x² + y² = 25

What is Circle?

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The circle is shown in figure.

Centre of circle = (0, 0)

Radius of circle = 5

Now,

We know that;

The standard form of circle with radius 'r' and center (h, k) is,

⇒ (x - h)² + (y - k)² = r²

Hence, The equation of circle with radius '5' and center (0, 0) is,

⇒ (x - 0)² + (y - 0)² = 5²

⇒ x² + y² = 25

Thus, The equation of circle will be;

⇒ x² + y² = 25

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Answer:

Area of the circle will be  (4.20 [tex]\pi[/tex])

Step-by-step explanation:

We have to find the area of the circle with diameter given is 4.10 m.

Since radius of a circle is represented by [tex](\frac{diameter}{2})[/tex]

Therefore, radius of the circle = [tex](\frac{4.1}{2})[/tex] = 2.05 m

Formula of the area of a circle is A  = [tex]\pi r^{2}[/tex]

So area of the circle with radius 2.05 m will be

A = [tex]\pi (2.5)^{2}[/tex]

  = 4.20 [tex]\pi[/tex]

Area of the circle will be  (4.20 [tex]\pi[/tex])

The length of the longest part is 15 units.

The length of the longest part in a segment divided into parts in the ratio of 5:3 with a difference of 6 units is 15 units.

The length of the longest part is 15 units.

Final answer:

To determine the lengths of the legs of a right triangle with a hypotenuse of 7 inches and an acute angle of 50°, we use the trigonometric functions cosine and sine. The adjacent leg (A) is approximately 4.5 inches and the opposite leg (B) is approximately 5.4 inches, both to the nearest tenth.

Explanation:

The student asked: "What are the lengths of the legs of a right triangle if one of the acute angles is 50° and the hypotenuse is 7 inches?"

To find the lengths of the legs of a right triangle, we can use trigonometry. The cosine of an angle in a right triangle is equal to the adjacent leg divided by the hypotenuse, and the sine of an angle is equal the opposite leg divided by the hypotenuse.

Since we know the hypotenuse (7 inches) and one acute angle (50°), we can find:

the length of the opposite leg (leg B) using sine (sin(50°) = leg B / 7 inches).

By solving these equations:

leg A = cos(50°) × 7 inches

leg B = sin(50°) × 7 inches

After calculating, we find:

leg A ≈ 4.5 inches (to the nearest tenth)

leg B ≈ 5.4 inches (to the nearest tenth)

To find the largest positive integer $n$ such that $rac{(n + 1)^2}{n + 23}$ is an integer, we need to find the largest perfect square that is less than or equal to $n + 23$. The largest such $n$ is $41$.

To find the largest positive integer $n$ such that $rac{(n + 1)^2}{n + 23}$ is an integer, we can start by considering the numerator. The expression $(n + 1)^2$ is a perfect square, so it will always be divisible by $n + 23$ if $n + 23$ is also a perfect square. Therefore, we need to find the largest perfect square that is less than or equal to $n + 23$.

Let's consider some examples. If $n + 23 = 25$, then $n = 2$. If $n + 23 = 36$, then $n = 13$. If $n + 23 = 49$, then $n = 26$. If $n + 23 = 64$, then $n = 41$. Therefore, the largest value of $n$ such that $rac{(n + 1)^2}{n + 23}$ is an integer is $41$.

There are no positive integers $n$ that satisfy the given condition, and we cannot compute the largest such $n$.

To find the largest positive integer $n$ such that $\frac{(n + 1)^2}{n + 23}$ is an integer, we need to consider the factors of the numerator and denominator.

Let's expand the numerator, $(n + 1)^2$, using the binomial expansion formula:

$(n + 1)^2 = n^2 + 2n + 1$

Now, we divide this expression by $n + 23$ and express the result as an integer:

$\frac{n^2 + 2n + 1}{n + 23}$

We can use polynomial long division to divide $n^2 + 2n + 1$ by $n + 23$:

- (n - 21)
__________
n + 23 | n^2 + 2n + 1
- (n^2 + 23n)
_____________
-21n + 1
- (-21n - 483)
_____________
484

We obtain a remainder of 484. In order for the fraction to be an integer, the remainder must be 0. However, in this case, the remainder is not 0, which means that $\frac{(n + 1)^2}{n + 23}$ is not an integer for any positive integer $n$.

Therefore, there are no positive integers $n$ that satisfy the given condition, and we cannot compute the largest such $n$.

Complete question :-

There are exactly four positive integers $n$ such that \[\frac{(n + 1)^2}{n + 23}\] is an integer. Compute the largest such $n$.

Answer:

[tex]1[/tex] units.

Step-by-step explanation:

Here body weight is 14 pounds =[tex]\frac{14}{2.205}[/tex] kg =[tex]6.35[/tex] kg (∵ 1 kg ≈ 2.205 ponds ).

Normally, 75 ml of blood needs, if the body weight is 1 kg. Therefore total amount of blood for the body weight 14 pounds [tex](6.35 kg) = 6.35*75 ml=476.25 ml[/tex] [tex]=.47625 l[/tex]  and we know that 1 litter of blood =2.11338 point of blood.

Hence total amount of blood = [tex]0.47625*2.11338[/tex] points =[tex]1.006497[/tex] units≈ [tex]1[/tex] units.

AC = sqrt(56^2 + 33^2) = 65cm

EC = sqrt(65^2 - 16^2) = 63 cm

to find AD 33-25 = 8

8^2 + 56^2 = AD^2

64 + 3136=3200^2

square root (3200) = 56.5685 round off to 56.6cm