For a school fundraiser, Percy bought a big box of rubber ducks and wrote prize amounts, in dollars, on the bottom of each rubber duck. The prize amounts were $5, $10, $20, $50, and $100. The number of ducks with each prize amount varied so that the total value for all the ducks with each prize amount was always $500.Percy then put all the rubber ducks in his school’s swimming pool. At the fundraiser, participants used a long net to catch a duck from the pool. They won the amount written on the bottom of the rubber duck, and then they threw the duck back into the pool before the next person’s turn. Since the ducks were returned to the pool after they were caught, the chances of winning any particular amount remained the same. Amir paid $15 to play the game once. If we assume he randomly selected a duck, what is the probability that Amir won more money than he paid to play the game?

Step-by-step explanation:

First find how many plants Samantha can plant in half an hour. To figure that out do 12 divided by 3 because in 1.5 hours she can plant 12 plants.

12÷3=4

Samantha can plant 4 plants in half an hour. Since 2.5 hours in 1 more hour than 1.5 hours multiply 4 by 2 to get the total amount she can plant in one hour.

4 x 2 = 8

Samantha can plant 8 plants in an hour. Now add 8 to 12 because 12 plants is 1.5 hours and 8 plants is 1 hour and 1.5 + 1 = 2.5 hours.

8 + 12 = 20.

Samantha can plant 20 plants in 2.5 hours.

Answer:

x=60

Step-by-step explanation:

1/5x=12

this is the equation your question isn't quite clear so I'm not sure if you want the equation or the evaluated problem.

(5/1) 1/5x=12 (5)

x=60

I hope this helps :)

Answer:

Therefore, 2 + 2 with a square root of 9 is equal to 8.

Step-by-step explanation:

We can simplify the expression "square root of 9" to just 3. Then, we have:

2 + 2(3) = 2 + 6 = 8

Therefore, 2 + 2 with a square root of 9 is equal to 8.

Tnx   :)  :)  ;)

Answer:

\(\textsf{C.} \quad C = \$10 + \$5h\)

Step-by-step explanation:

Given information:

Given variables:

The Park admission fee of $10 is independent of the fee charged per hour per sport.  Therefore, it is represented by a constant in the equation.

The fee per hour of sledding is dependent on the number of hours spent.  Therefore, it is represented by the cost of the specific sport multiplied by the given variable for time (h).

Therefore the equation that represents the cost of sledding per hour is:

C = $10 + $5h

\(\huge \boxed{\sf C}\)

Each hour costs 5 dollars for sledding and an extra fee of 10 dollars.

\(\sf C = 5h + 10\)

An equation contains variables and integers.

C and h are variables which means the value changes.

5 and 10 are integers.

Step-by-step explanation:

Break it up into two trapezoids as shown

area = trap1 + trap2

      = 2 *   (7+3) / 2   + 3 *  ( 7 + 3) / 2 = 10 + 15 = 25 units^2

The probability of getting a score of 80% or higher on a 5-question true/false quiz when guessing (with a 50-50 chance of being correct) on every question is 1/16, while the probability of getting a score of 80% or higher on a 20-question true/false quiz is 1/1048576.

        What is the probability of getting a score of 80% or higher on a 5-question true/false quiz when guessing (with a 50-50 chance of being correct) on every question

                  A quiz consists of 5 questions. A student guesses each of the questions. The probability of guessing a question correctly is 0.5.

        Therefore, the Probability of getting a score of 80% or higher is = Probability of getting 4 or 5 questions right. To get 4 out of 5, we have to consider all possibilities of choosing 4 out of 5 questions correctly. A number of ways of choosing 4 out of 5 questions correctly is 5.

       A number of ways of guessing the 5 questions is 2^5.

       Therefore, the probability of getting 4 out of 5 correct is 5/32. To get 5 out of 5, we have to consider only one possibility.

       A number of ways of guessing 5 questions is 2^5.

       Therefore, the probability of getting 5 out of 5 correct is 1/32.

        So, the probability of getting a score of 80% or higher = Probability of getting 4 or 5

questions right = 5/32 + 1/32 = 6/32 = 3/16.

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What if instead, the quiz has 20 questions,

           If the quiz has 20 questions, the probability of getting a score of 80% or higher is 1/2^20 = 1/1048576.

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The value of the diameter of the cone part of the funnel to the nearest tenth is,

⇒ d = 7.2 cm

We have to given that;

A funnel can hold 159π cm³ of fluid.

And, Its height (without the stem) is 12 cm.

Now, We know that;

Volume of cone = πr²h/3

Where, r is radius of cone.

Hence we get;

⇒ 159 = 3.14 × r² × 12 / 3

⇒ 159 = 12.56 r²

⇒ r² = 12.65

⇒ r = √12.65

⇒ r = 3.556

⇒ r = 3.6 cm

Thus, The value of the diameter of the cone part of the funnel to the nearest tenth is,

⇒ d = 2r

⇒ d = 2 x 3.6

⇒ d = 7.2 cm

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Answer:The distance cover by Noah in 1 hour to cover distance is 6.5 miles

Step-by-step explanation:

To determine the maximum number of 2/0 AWG THW aluminum compact conductors permitted in a 2½-inch PVC conduit, Schedule 80, we need to consult the applicable electrical code or standards.

The number of conductors allowed in a conduit is typically governed by factors such as fill capacity and heat dissipation.

The specific requirements may vary depending on the jurisdiction and the electrical code being followed. It is recommended to consult the local electrical code or a qualified electrician to ensure compliance with the regulations in your area.

They will be able to provide the precise guidelines and restrictions for conductor fill capacity based on the conduit size, type, and the specific application.

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Answer:

7 or 8

Step-by-step explanation:

The molar solubility of scandium fluoride can be calculated using the solubility product constant (Ksp) and stoichiometry. The molar solubility is approximately 7.61 × 10^(-9) mol/L.

The solubility product constant (Ksp) is an equilibrium constant that represents the equilibrium between a solid compound and its dissociated ions in a saturated solution.

For scandium fluoride (ScF3), the equilibrium can be represented as follows:

ScF3 (s) ⇌ Sc³⁺ (aq) + 3F⁻ (aq)

The solubility product expression for this equilibrium is:

Ksp = [Sc³⁺][F⁻]³

Given that the Ksp value for scandium fluoride is 5.8 × 10^(-24), we can use this information to calculate the molar solubility.

Step 1: Assign variables to the molar solubility.

Let x represent the molar solubility of ScF3 in mol/L.

Step 2: Write the equilibrium expression.

Since the stoichiometry of the reaction is 1:3, the equilibrium expression becomes:

Ksp = (x)(3x)³ = 27x⁴

Step 3: Substitute the Ksp value and solve for x.

Plugging in the Ksp value of 5.8 × 10^(-24), we have:

5.8 × 10^(-24) = 27x⁴

Step 4: Solve for x.

Taking the fourth root of both sides, we get:

x⁴ = (5.8 × 10^(-24))/27

x⁴ ≈ 7.61 × 10^(-26)

Taking the square root of both sides, we find:

x ≈ 7.61 × 10^(-9) mol/L

Therefore, the molar solubility of scandium fluoride is approximately 7.61 × 10^(-9) mol/L.

In summary, by using the solubility product constant (Ksp) and stoichiometry, we can calculate the molar solubility of scandium fluoride. In this case, the molar solubility is approximately 7.61 × 10^(-9) mol/L, indicating that scandium fluoride has a very low solubility in water.

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Answer:

17

Step-by-step explanation:

Answer:

Part 1:

4. The slope is -4.

5. The slope is 17/4.

6. The slope is -2/3.

Part 2:

4. y = -4x - 11

y-intercept is (-11/4, 0)

5. y = 17/4x - 12

6. y = -2/3x + 4/3

Step-by-step explanation:

To draw the digital circuit corresponding to the expression x(yz' + z), we can break it down into logical operations.

The given expression involves the logical operations of NOT, AND, and OR. In the circuit diagram, we would have three inputs: x, y, and z. Firstly, we need to calculate the complement of z (represented as z') using a NOT gate. The output of the NOT gate would then be connected to one input of the AND gate. The other input of the AND gate would be connected directly to the input y.

The output of the AND gate would be connected to one input of the OR gate. Finally, the input x would be directly connected to the other input of the OR gate. The output of the OR gate would be the result of the expression x(yz' + z).

The circuit would consist of an input x connected directly to an OR gate, while an input y would be connected to one input of an AND gate along with the complement of input z (z') obtained through a NOT gate. The output of the AND gate would be connected to the other input of the OR gate, and the output of the OR gate would represent the result of the given expression x(yz' + z).

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A. The relationship between ∠7 and ∠8 is that they are vertically opposites angles and they are equal.

B. Since 5y-29 and 3y+19 are vertically opposites angles, we can say equate the two angles (i.e. 5y-29 = 3y+19) and then solve for y.

C. y = 24, ∠7 =  89° and ∠8 = 89°

Angle geometry deals with the study of angles, their measurement, and their properties. An angle is formed when two lines or line segments intersect each other at a point.

A. The relationship between ∠7 and ∠8 is that they are vertically opposites angles. Since vertically opposites angles are equal, we can say  ∠7 = ∠8.

B. Since 5y-29 and 3y+19 are vertically opposites angles, we can say equate the two angles (i.e. 5y-29 = 3y+19) and then solve for y

C. 5y-29 = 3y+19

5y-3y= 19 + 29

2y = 48

y = 48/2

y = 24

Let's find either the value of  5y-29 or 3y+19:

Put y = 24 in 5y-29

5y-29 = 5(24) - 29 = 91°

∠7 + (5y-29) = 180°  (sum of angles on a straight line is 180°)

∠7 +  91° = 180°

∠7 = 180 - 91 = 89°

Since  ∠7 = ∠8

∠8 = 89°

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Answer:

0

Step-by-step explanation:

It is a horizontal line.

Answer:

undefined

Step-by-step explanation:

The slope of a line is found by

m = (y2-y1)/(x2-x1)

   = (-9 -10)/(-9 - -9)

   = -19/ (-9+9)

   = -19/0

We cannot divide by zero so the slope is undefined

Answer:

MOTHematics (i dont know if I'm right ;w; )

Answer:

Step-by-step explanation:

Circumference = pi * d

1/12 = 30/360 = You need to find 30 degrees

Known:

D = 36

1/12 = percentage

Unknown:

Answer = ?

1/12 * pi * d

= 1/12 * pi * 36

= 1/12 * 36 * pi

= 3 pi

The answer is 3 pi.

Hope this helped,

Kavitha

Answer:

AC = 3 π

Step-by-step explanation:

given dia of a circle = 36 cm

radius r = 36 / 2 = 18

angle Ф = 30°

req'd:  Arc length of a circle AC.

                       Ф

arc length = -----------  x  2 π r

                      360

         30°

AC = --------- x 2 π (18)

         360

AC = 3 π

Answer:

they get  a 7/24th piece of cake.

Step-by-step explanation:

if we divide 3 1/2 by 12 we get 7/24

we use the 3 1/2 because that is how many cakes there are.
we use 12 because there are 12 boys that want to split the cake equally.

Answer:

15 girls

Step-by-step explanation:

Well, the ratio of 2/3, boys to girls. So, you would then try to find an (almost) common denominator, so 2/3 is equivalent to 10/15. In this case, there would be 15 girls

Lol hope this helps

a) The probability is 0.254%. b) The probability is 21.053%. c) The probability is 9.561%. d) The probability is  30.166%.

a) To find the probability that a chip is defective, we calculate the weighted average of the defective rates based on the supply percentages of each supplier:

(0.5 * 0.002) + (0.3 * 0.003) + (0.2 * 0.004) = 0.00254, or approximately 0.254%.

b) To calculate the probability that a defective chip was supplied by S3, we use Bayes' theorem:

P(S3|Defective) = (P(Defective|S3) * P(S3)) / P(Defective)

P(Defective|S3) = 0.004 (probability of defective chip given it is from S3)

P(S3) = 0.2 (percentage of supply from S3)

P(Defective) = weighted average of defective rates = 0.00254 (from part a)

P(S3|Defective) = (0.004 * 0.2) / 0.00254 ≈ 0.21053, or approximately 21.053%.

c) To find the probability that at least one chip out of 10 supplied by S1 is defective, we use the complement rule:

P(at least one defective) = 1 - P(no defective)

P(no defective) = (1 - 0.002)^(10) ≈ 0.90439

P(at least one defective) = 1 - 0.90439 ≈ 0.09561, or approximately 9.561%.

d) The number of system failures in a car in the first year follows a Poisson distribution with a rate of 1.2. The probability of having no system failures in one car is given by:

P(X = 0) = e^(-1.2) * (1.2^0) / 0! = e^(-1.2) ≈ 0.30166, or approximately 30.166%.

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Answer:

x=80* y=20* and X=100*

Step-by-step explanation:

If we assume PQ || OR then by alternate interior angles x is equal to 80 degrees and y is equal to 20 degrees.

We know that a triangle adds up to 180 degrees.

Angle ROX and XRO add up to 100 degrees. Leaving RXO equal to 80 degrees. (180-100=80).

By opposite angles, QXP is equal to 80 degrees also.

Then we are left with solving for X.

Supplementary angles add up to 180 degrees.

Subtract angle OXR from 180 and we are left with angle OXP = X = 100 degrees.

The graph of 7f(x) is the same as that of f(x) but vertically stretched by a factor of 7.

Given below are the effects on the graph of f(x) if it is changed to f(x) + 7, f(x + 7), or 7f(x):Effect of f(x) + 7:The effect of adding 7 to the function f(x) is known as vertical translation. Adding a constant amount to the function shifts it upwards or downwards depending on whether the constant added is positive or negative, respectively.

The vertical shift does not affect the horizontal component of the function. Hence, the new function f(x) + 7 will have the same graph as f(x) but shifted 7 units upward.Effect of f(x + 7):The effect of adding 7 to x in the function f(x) is called horizontal translation.

The function f(x) shifts to the left if we substitute x + 7 for x in the function f(x). Similarly, if we replace x with x - 7 in f(x), the function moves to the right. Thus, the graph of f(x + 7) is the same as that of f(x) but shifted 7 units to the left.Effect of 7f(x):The effect of multiplying f(x) by a constant k is called vertical scaling. If the scaling factor k is greater than 1, the function is stretched vertically; if k is less than 1 but greater than 0, it is compressed vertically. If k is negative, the function is flipped vertically about the x-axis. Multiplying f(x) by 7 causes the y-coordinate of each point on the graph to be multiplied by 7, resulting in a vertical scaling.

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Answer: The answer would be x = 19/3, 5/3

Step-by-step explanation:

Since we are finding the x intercepts, we must set the equation to equate 0. So:

0 = 3 |x-4| - 7

Then, we want to simplify the right side so it is just the absolute value, so lets start by adding 7 to both sides.

0 = 3 |x-4| - 7

+7              +7

7= 3 |x-4|

Now we divide both sides by 3.

7= 3 |x-4|

3        3

7/3 = |x-4|

Now, due to the properties of absolute value, we must solve this twice, since absolute value always leads to a positive value, we want to set up one equation where 7/3 is positive and one where it is negative.

7/3 = x-4        -7/3 = x-4

add 4 to both sides

7/3 = x-4        -7/3 = x-4

+4      +4          +4     +4

Then, you get your two x values

x= 6.333... or 19/3 AND x = 1.66666 or 5/3

Answer:

The sum of the exterior angles of a decagon is 360°

The sum of the exterior angles in an any polygon = 360°

Alternate method:

Each exterior angle in a polygon : 360 ÷ number of sides

Here, decagon has 10 sides.

Then, each exterior angle: 360 ÷ 10 = 36°

Then all 10 sides together has : 36° x 10 = 360°

Step-by-step explanation:

Answer:

\(N = \{1,2,3,4,5,6,.....\}\)

Step-by-step explanation:

Required

Determine the sets of natural number

Represent this set with letter N

From definition of natural numbers, they are integer numbers starting from 1;

In other words: 1,2,3,4,5, and so on.

To represent this as a set of N, we have

\(N = \{1,2,3,4,5,6,.....\}\)

The ..... means that the counting still continues

Answer: b. 1923

Step-by-step explanation:

The solution to the value of x is 5 < x < 15

A triangle is a shape that has 3 sides and angles. According the triangle rule, the sum of any two sides of a triangle is equal to the third.

From the given triangle shown;

15+x > 20 + 15 > 20 + x

Simplify

15+x > 20

x > 20 - 15

x > 5

Also;

20+15 > 20 + x

35 > 20 + x

35 - 20 >x

x < 15

Hence the solution to the value of x is 5 < x < 15

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