There are 10 brown, 10 black, 10 green, and 10 gold marbles in bag. A student pulled a marble, recorded the color, and placed the marble back in the bag. The table below lists the frequency of each color pulled during the experiment after 40 trials.


Outcome Frequency
Brown 13
Black 9
Green 7
Gold 11


Compare the theoretical probability and experimental probability of pulling a gold marble from the bag.
The theoretical probability, P(gold), is 25%, and the experimental probability is 27.5%.
The theoretical probability, P(gold), is 50%, and the experimental probability is 11.5%.
The theoretical probability, P(gold), is 25%, and the experimental probability is 25%.
The theoretical probability, P(gold), is 50%, and the experimental probability is 13.0%.

Answer:

8

Step-by-step explanation:

640/80=8

8*80=640

Answer:

The answer is 8.

Step-by-step explanation:

80x=640

80x /80 = 640 /80

x=8

Answer:

A= 18

Step-by-step explanation:

To find the height, find the blocks inside the shape that is completely attached (they have to be in a straight vertical line).  In this case, you can see that three vertical blocks in the middle of the shape is completely attached.  That means your height is 3.

To find the width, look at the how many horizontal boxes make up the top.  6 block inside the shape corispond with 6 blocks on top of the shape, so the width is six.

Multiply 6 by 3 to get 18.

The required manager has 12 fifty-dollar bills as of the given condition.

Let's denote the number of twenty-dollar bills as "x" and the number of fifty-dollar bills as "y".

We know that the convention manager has a total of 48 bills, so:
x + y = 48

We also know that the total amount of money she has is $1320, which can be expressed as:
20x + 50y = 1320

To solve for "y", we can rearrange the first equation to get:
y = 48 - x

Then substitute this expression for "y" in the second equation:

20x + 50(48 - x) = 1320

Expanding the expression and simplifying:
20x + 2400 - 50x = 1320
-30x = -1080
x = 36

So the manager has 36 twenty-dollar bills. To find the number of fifty-dollar bills, we can use the first equation:

x + y = 48

36 + y = 48

y = 12

Therefore, the manager has 12 fifty-dollar bills.

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Answer:

N+1

Step-by-step explanation:

It begins with = 2

then n+1=3

then n+2=4 and so on it is n+1

During the winter season, a family sets up a hot chocolate stand near a local ice skating rink. They sell cups of hot chocolate for $1.50 each and typically sell 50 cups per day.

However, due to changes in weather conditions and customer preferences, the family decides to conduct a market experiment by varying the price of hot chocolate to assess the impact on sales volume. The experiment involves increasing the price to $2.00 per cup and monitoring the resulting sales.

By increasing the price of hot chocolate from $1.50 to $2.00 per cup, the family aims to observe how the change in price affects the demand for their product. The experiment helps them understand the price elasticity of demand, which measures the responsiveness of quantity demanded to changes in price. If the increase in price leads to a significant decrease in sales volume, it suggests that the demand for hot chocolate is elastic, meaning consumers are sensitive to price changes. Conversely, if sales remain relatively stable despite the price increase, it indicates that the demand is inelastic, indicating that consumers are less sensitive to price changes. The family can analyze the results of this experiment to make informed pricing decisions and optimize their profitability during the winter season.

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A graph that is commonly used to compare the relationship between a categorical and a quantitative variable is a box plot, also known as a box-and-whisker plot.

A type of graph is particularly useful for visually displaying the distribution, central tendency, and variability of the quantitative variable across different categories.
In a box plot, the categorical variable is represented along the x-axis, while the quantitative variable is represented on the y-axis. For each category, a box is drawn to show the interquartile range (IQR), which contains the middle 50% of the data. The line inside the box represents the median, a measure of central tendency. Whiskers extending from the box show the range of the data, excluding possible outliers.
This graphical representation allows for easy comparison between categories, making it an effective tool for analyzing the relationship between a categorical and a quantitative variable.

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The Sno-Cone has two identifiable 3D figures, which are cone and hemisphere. Our key point here is to solve the volume of the cone and the hemisphere then add their volumes to solve for the total volume of the Sno-Cone.

The volume of the cone can be solved using the equation

The radius of the sno-cone and its height are provided in the problem. Just substitute it on the equation above and compute, we get

The next thing to solve is the volume of the hemisphere. The volume of the hemisphere is half of the volume of a sphere, which is represented in the equation as

The radius of the cone is the same as the radius of the hemisphere. Substitute it on the equation above and compute, we get

The overall volume of the sno-cone is the sum of the volume of the hemisphere and cone computed above.

There

Answer: D) 0.392

Step-by-step explanation:

0.300

0.090

0.002

__________

0.392

Answer:

cylinder <3

Step-by-step explanation:

Answer:

a cylinder

Explanation:

The polar coordinates for (-73√2, 72) are approximately (103.077, 6.017).

A. To convert the Cartesian coordinates (-72, 73√2) to polar coordinates (r, θ), we can use the following formulas:

r = √(x^2 + y^2)

θ = arctan(y/x)

Substituting the values, we have:

r = √((-72)^2 + (73√2)^2) ≈ 103.077

θ = arctan((73√2)/(-72))

Since the angle θ can be in the range 0 < θ ≤ 2π, we need to adjust the angle based on the quadrant of the Cartesian coordinates. In this case, the point lies in the third quadrant, so we add π to the angle obtained from the arctan function.

θ ≈ arctan((73√2)/(-72)) + π ≈ 3.267 + 3.141 ≈ 6.408

Therefore, the polar coordinates for (-72, 73√2) are approximately (103.077, 6.408).

B. To convert the Cartesian coordinates (-73√2, 72) to polar coordinates (r, θ), we can use the same formulas as before:

r = √(x^2 + y^2)

θ = arctan(y/x)

Substituting the values, we have:

r = √((-73√2)^2 + 72^2) ≈ 103.077

θ = arctan(72/(-73√2))

Similarly, since the point lies in the second quadrant, we add π to the angle obtained from the arctan function.

θ ≈ arctan(72/(-73√2)) + π ≈ 2.876 + 3.141 ≈ 6.017

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Answer:

61,000

Step-by-step explanation:

Move it 4 places to the right.

Answer:

\(a_{n}\) = 103 - 3n

Step-by-step explanation:

there is a common difference between consecutive terms , that is

97 - 100 = 94 - 97 = 91 - 94 = - 3

This indicates the sequence is arithmetic with explicit equation

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 100 and d = - 3 , then

\(a_{n}\) = 100 - 3(n - 1) = 100 - 3n + 3 = 103 - 3n

The purpose of this test is to evaluate the effects of rotational acceleration on the semicircular ducts and dynamic equilibrium. This test is called Rotational Acceleration Test.

The purpose of the rotational acceleration test is to assess how the semicircular ducts and the body's dynamic equilibrium respond to rotational movements. The semicircular ducts are part of the vestibular system, which is responsible for detecting changes in head position and rotational movements.

During the test, the individual is subjected to controlled rotational acceleration, usually in a specially designed chair or device. The rotational acceleration induces a sense of spinning or movement, stimulating the semicircular ducts.

By observing the individual's responses, such as eye movements or changes in body posture, healthcare professionals can gather information about the functioning of the vestibular system and the body's ability to maintain balance.

This test is particularly useful in diagnosing disorders of the vestibular system, such as vestibular dysfunction, vertigo, or balance disorders. It helps healthcare providers determine the extent of the impairment and develop appropriate treatment plans or interventions to improve balance and reduce symptoms.

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Steps to calculate the area are shown below and the figure is attached below.

The steps of calculating the area of the given figure are,

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Because some of the athletes participated in more than one event.

Answer:

1162.5 words

Step-by-step explanation:

6m = 155 words

45m = \(\frac{45}{6}\) × 155 words

        = 1162.5 words

Answer:

Step-by-step explanation:

If:

155 words =  6 minutes :

Then:

1  minute  = 155/6  = 25.8   words

45 minutes is:

45 × 25.8 = 1,162.5

Two rays with a common endpoint form an angle. An angle is defined as a geometric figure formed by two rays that share a common endpoint. In other words, an angle is formed when two rays emanating from a common point, and this common point is known as the vertex.

The rays are the sides of the angle, and the angle is measured in degrees. Angles have different measures, ranging from 0 degrees to 360 degrees. The two rays that make up an angle are also called the sides or arms of the angle. The angle is measured in degrees, and the size of the angle depends on the distance between the two sides of the angle that meet at the vertex.

In geometry, an angle can be named in different ways, depending on the context in which it is being used. Angles are essential in mathematics, physics, and other scientific fields, where they are used to measure the rotation of an object, determine the direction of an object, and in other applications involving rays and lines. Two rays with a common endpoint form an angle.

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Answer:

\(5x = - 1 - 1 = 5x \div 5 = - 2 \div 5 = 2 \div 5\)

a) The relationship between b and c is that c cannot be zero.

b) b can be any nonzero constant and c is equal to 2.5 in this case.

In two dimensions, the compatibility equations for strain are,0

∂εx/∂y + ∂γxy/∂x = 0

∂εy/∂x + ∂γxy/∂y = 0

where εx and εy are the normal strains in the x and y directions, respectively, and γxy is the shear strain.

Using the given strain field, we can calculate the strains,

εx = -4.5cx² + 10.5cy

εy = 1.5cx² - 7.5cy²

γxy = 1.5bxy

Taking partial derivatives and plugging them into the compatibility equations, we get,

⇒ -9cx + 0 = 0

⇒ 0 + (-15cy) = 0

These equations must be satisfied for the strain field to be compatible. From the first equation,

We get cx = 0, which means c cannot be zero.

From the second equation, we get cy = 0,

Which means b can be any nonzero constant.

For part b:

We are asked to find the displacements u and v corresponding to the given strain field at points (3, 7), assuming they are zero at point (0, 0) and using c = 2.5.

To find the displacement components,

We need to integrate the strains with respect to x and y. We get,

u = ∫∫εx dx dy = ∫(10.5cy) dy = 5.25cy²

v = ∫∫εy dx dy = ∫(1.5cx² ) dx - ∫(7.5cy²) dy = 0.5cx³ - 2.5cy³

Plugging in the values of c and b, we get,

u = 5.25(2.5)(7)²  = 767.62

v = 0.5(2.5)(3)³ - 2.5(7)³ = -8583.75

Therefore,

The displacements at points (3, 7) are u = 767.62 and v = -8583.75.

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Answer: 4 19/36 inches

Step-by-step explanation:
To add the two measurements together, you need to find a common denominator. In this instance, it will be 36.

2 * 4 = 8, 9 * 4 = 36, which means our first measurement turns into 10 8/36

1 * 9 = 9, 4 * 9 = 36, which means our second measurement turns into 5 9/36

Adding these together we get 15 17/36.

Subtract this from 20.

The amount of string that is left is 4 19/36 inches.

Hope this helped!

An equation of a direct proportion is y=−2x, y=4x

What is direct proportion?

By definition, an equation of direct proportion has the following form: y=k x

Where k is the constant of proportionality.

The equation of the line y=m x+b, where m is the slope and \($\mathrm{b}$\) the \($\mathrm{y}$\) intercept.

When b=0, means that the line passes through the origin. Therefore, it would be:

y=m x

(which is similar to y=k x )

Then, the slope of the line would be the constant of proportionality.

By definition, the slope can be positive or negative.

Keeping on mind the information above, you can see that the equation that have that form are:

y=-2 x

y=4 x

Complete question: Which is an equation of a direct proportion? y=−2x y=12x−2 y=−2x+3 y=4x

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Answer:

32

Step-by-step explanation:

Let x be "A number."  

" . . . first subtracting 22 . . ." suggests the first thing that should be done:

       x-22

" increased by 60%" means increse the number from above (x-22) by a factor of (1 + 0.60).  This takes the number (x-22) and adds 60% (0.60) to it.

     (x-22)*(1.6) = (1.6x - 35.2)

" . . . making it half the original size."  half the original size is:

        (1/2)x

      Now put the two expressions together:

      (1.6x - 35.2) = (1/2)x

       1.6x - 35.2 = 0.5x

       1.1x  = 35.2

         x   =  32

      "A number" is 32.  

Check the answer:

1) Subtract 22:  32-22 = 10

2) Increase by 60%:  16

Is 16 half the original number of 32?  YES

The solution to the system of equations is x = 3 and y = -8.  the two expressions for y and solve for x.

To solve the system of equations using the equal values method, we'll equate the two expressions for y and solve for x.

Given the equations:

y = 5x - 23   ...(Equation 1)

y = 2 1/2 - 3 1/2x   ...(Equation 2)

First, let's simplify Equation 2 by converting the mixed fractions into improper fractions:

y = 2 + 1/2 - 3 - 1/2x

y = 5/2 - 7/2x

Now, we'll equate the two expressions for y:

5x - 23 = 5/2 - 7/2x

To solve for x, we'll eliminate the fractions by multiplying the entire equation by 2:

2(5x - 23) = 2(5/2 - 7/2x)

10x - 46 = 5 - 7x

Next, we'll simplify the equation by combining like terms:

10x + 7x = 5 + 46

17x = 51

To isolate x, we'll divide both sides of the equation by 17:

x = 51/17

x = 3

Now that we have the value of x, we can substitute it back into either Equation 1 or Equation 2 to find the corresponding value of y. Let's use Equation 1:

y = 5(3) - 23

y = 15 - 23

y = -8

Therefore, the solution to the system of equations is x = 3 and y = -8.

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Answer:

difference in volume = 26.96h cm³

Step-by-step explanation:

The volume of a prism is the product of the base area and the height. A trapezoid prism has a trapezium as the base shape. Therefore,

volume of a trapezoid prism = area of a trapezium × height

area of the base(trapezoid) = 140 cm²

Volume = 140h

Volume of a cylinder = πr²h

where

r = radius

h = height

volume = πr²h

volume = π × 6² × h

volume = 3.14 × 36 × h

volume = 113.04h

To know how much larger the volume of the prism is than the volume of the cylinder we have to take the difference of the volume.

Recall the height are the same

difference in volume = 140h - 113.04h

difference in volume = 26.96h cm³

Answer:

1/2

Step-by-step explanation:

The numerator in 8/15 has to be closer to 0 to be closer to 0.

The numerator in 8/15 has to be closer to 15 to be closer to 1.

Ther numerator in 8/15 has to be closer to the middle, which it is, to be closer to 1/2.

If the total charge on 8 particles is -56 units and all the particles have the same charge, then the charge on each particle is equal to -7 units.

The charge on each particle can be determined by division.

Division is a part of the basic operations of arithmetic which are four in number, the rest being addition, subtraction, and multiplication. It can be considered the opposite of multiplication and involves separating into equal parts or groups.

The change on each particle can be calculated by dividing the total charge units by the total number of particles. Hence,

charge on each particle = total charge units ÷ total number of particles

charge on each particle = -56 / 8

charge on each particle = -7

Therefore, the charge on each particle is equal to -7 units if all the particles have the same charge.

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Step-by-step explanation:

X = 3

-14x=-42

-3/5 + x=12/5

X-5=-2

X/4=6/8

X= -3

-6+x=-9

X/3=9

Answer:

The answer is (3,2) or x=3 and y=2

Step-by-step explanation:

Answer: It is (3,2)

Step by step explanation