a jar contains 2 red marbles numbered 1 to 2 and 8 blue marbles numbered 1 to 8. a marble is drawn at random from the jar. find the probability of the given event. enter your answers as either decimals or fractions, not as percents.(a) the marble is redyour answer is :

The density and uncertainty in the density of the sphere is (1828.28 ± 0.0984)  kg/m³

The radius of a sphere is (6.20 ± 0.30)  cm

Mass of the sphere is (1.81 ± 0.09)  kg

We know that the formula for the density,

Density = mass/volume

d = m/V

As we know tha volume of the sphere is, [tex]V=\frac{4}{3} \pi r^3[/tex]

[tex]V=\frac{4}{3} \pi r^3\\\\V=\frac{4}{3} \pi (6.2\times 10^{-2})^3\\\\V=0.00099~m^3[/tex]

So, the density would be,

d = (1.81) / (0.00099)

d = 1828.28 kg/m³

We can find the uncertainty in volume as follows :

[tex]\frac{\delta V}{V}=3\frac{\delta r}{r}\\\\\frac{\delta V}{V}=3\times \frac{0.003}{0.0620} \\\\\frac{\delta V}{V}=0.0484[/tex]

and the uncertainty in the mass would be,

[tex]\frac{\delta m}{m}=\frac{0.09}{1.81} \\\\\frac{\delta m}{m}=0.05[/tex]

The uncertainty in the density of the sphere would be,

[tex]\frac{\delta d}{d}=\frac{\delta V}{V}+\frac{\delta m}{m}\\\\\frac{\delta d}{d}=0.0484+0.05\\\\\frac{\delta d}{d}=0.0984[/tex]

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The average acceleration over the given time interval is option C -10 m/s²

By dividing the change in velocity by the change in time, the average acceleration will be determined. Therefore, let's first determine the velocity function:

x = 4t² - 3t³

v = dx / dt

v = d( 4t² - 3t³) / dt

v = 8t - 9t²

Then,

at t = 0 sec , v = 0 m/s.

at t = 2 sec , v = 8(2) - 9(2²) = 16 - 36 = -20 m/s.

Average acceleration;

The rate of change in velocity is referred to as the average acceleration. To calculate the average acceleration of anything, we divide the change in velocity by the time since the initial measurement. A crazy ball's average acceleration, for instance, would be 20 cm/s/s if its velocity rose from 0 to 60 cm/s in 3 seconds.

avg.acc = (- 20 - 0) / (2 - 0) = -20 / 2 = -10 m/s²

That is,

-10 m/s² (option c) will be the average acceleration over the given interval.

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The given question is incomplete. Completed question is here;

The coordinates of an object is given as a function of time by x=4t^2-3t^3,where x is in meter and t is in second .what is its average acceleration over the time interval from 0 to 2 seconds

Answer:

x = 9

Step-by-step explanation:

(8x+16) + (9x+11) = 180

17x + 27 = 180

180 - 27 = 153

17x = 153

153/17 = 9

x = 9

Answer:

To solve the equation 8x+16+9x+11=180, add 8x and 9x to both sides to get 17x+27=180. Subtract 27 from both sides to get 17x=153. Divide both sides by 17 to get x=9.

On solving the provided question, we can say that so the equation formed is  1540-6x = 236 +6 x and in 108  2/3 minutes the tanks become equal with 888 gallons each

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

when does tank 1 = tank 2  when there is 6 gpm

tank 1 = 1540

tank2 = 236

so the equation formed is

1540-6x = 236 +6 x

1304 = 12x

108 * 2/3  = x

6*108*2/3  = 652 gallons

236+652=888

1504-652=888

in 108  2/3 minutes the tanks become equal with 888 gallons each

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The rule for the transformation above include the following: B. (x' , y') = (x - 6 , -y + 1).

In Geometry, a reflection over the x-axis is given by this transformation rule (x, y) → (x, -y). This ultimately implies that, a reflection over the x-axis would maintain the same x-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive:

(x, y)                               →              (x, -y)

This ultimately implies that, the parallelogram was reflected over the x-axis and then translated by 6 units to the left, and followed by a vertical translation downward by 1 unit.

(x' , y') = (x - 6 , -y + 1)

(x' , y') = (1 - 6 , -2 + 1)

(x' , y') = (-5, -1)

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The total price is 40.8, which can be represented by the coordinates (15, 40.8).

The equation y = 2.72x can be used to calculate the price of gasoline in terms of the number of gallons purchased.

The equation y = 2.72x can be used to calculate the total price of any number of gallons of gasoline. In this equation, y represents the total price and x represents the number of gallons of gasoline. In this equation, y represents the total price and x represents the number of gallons. If we input 15 gallons into the equation, we can calculate the total price of gasoline. To do this, we must substitute 15 for x in the equation, giving us y = 2.72(15). We can then calculate the total price by multiplying 2.72 and 15, which yields 40.8. Thus, for 15 gallons of gasoline, the total price is 40.8, which can be represented by the coordinates (15, 40.8).

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The perimeter of the larger figure is: 20 units.

Similar figures have perimeters and side lengths that are related in such a way that, the ratio of their perimeters is equal to the ratio of their corresponding side lengths.

Therefore, if x represents the perimeter of the larger figure, then:

x/15 = 4/3

Cross multiply to find x:

3x = 60

x = 60/3

x = 20

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The directed graph of a relation r on a finite set a be used to R not equal to ∅ and it is reflexive, symmetric, transitive, anti symmetric, then the R is equivalence relation and an order relation.

Let the relation R R R be asymmetric. A loop in the directed graph corresponds to an ordered pair of the form ( a , a ) (a , a) (a , a). By the definition of asymmetric, the relation R R R cannot contains any ordered pairs of the form ( a , a ) (a , a) (a , a) and thus the directed graph cannot contain any loops.

They are typically represented by labeled points or small circles. We connect vertex a to vertex b with an arrow, called an edge, going from vertex a to vertex b if and only if arb. This type of graph of a relation r is called a directed graph or digraph .

It is a set where either there are many components or only the beginning or ending are provided. By n(A), we refer to the total number of components, and if n(A) is a characteristic number, then the set is constrained.

Let A be finite non-empty set.

Then the exist relation R on A which is both equivalence and order relation.

Suppose A = {[tex]a_{1} , a_{2} , a_{3} , ...... a_{n} ,[/tex]}

And, R = { [tex](a_{1} ,a_{1}) , (a_{2} ,a_{2} ) ,(a_{3} ,a_{3} )........(a_{n} ,a_{n} )[/tex] }    

R not equal to ∅ and it is reflexive, symmetric, transitive, anti symmetric.

Then R is equivalence relation and an order relation.

Therefore,

The directed graph of a relation r on a finite set a be used to R not equal to ∅ and it is reflexive, symmetric, transitive, anti symmetric, then the R is equivalence relation and an order relation.

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The percentage of actual yield to theoretical yield of SO3 + H2O → H2SO4

is B. 86.9%

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, For the reaction represented by the equation SO3 + H2O → H2SO4, calculate the percentage yield if 500g but the theoretical yield is 575g.

Therefore, The percentage of actual yield to theoretical yield is,

= (500/575)×100%.

= 0.8695×100%.

= 86.95%.

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The true statement is Option B, The midpoint Riemann sum approximation overestimates the definite integral.

Given data,

In this case, since the function f changes from increasing to decreasing and the graph of f changes from concave up to concave down, we can infer that the function has a local maximum point within the interval [1, 3].

The midpoint Riemann sum approximation for the definite integral breaks the interval [1, 3] into four subintervals of equal width, and it uses the midpoint of each subinterval to approximate the value of the function within that subinterval.

Now, when the function is increasing, the midpoint Riemann sum approximation will tend to underestimate the value of the definite integral since it approximates the function using values that are smaller than the actual function values.

However, when the function changes from increasing to decreasing, the midpoint Riemann sum approximation will tend to overestimate the value of the definite integral since it approximates the function using values that are larger than the actual function values.

Hence , the midpoint Riemann sum approximation overestimates the definite integral.

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Answer:

[tex]\boxed{\sin D = 0.39 }[/tex]

Step-by-step explanation:

DEF is a right triangle with hypotenuse = 18 and one leg = 7

The law of sines states that the ratios of the sides of a triangle to the sine of the angle opposite that side must be the same for all sides

[tex]\dfrac{18}{\sin 90} = \dfrac{7}{sin D}[/tex]

sin(90) is 1

So the above equation becomes

[tex]18 = \dfrac{7}{\sin D}[/tex]

Cross multiplying we get
[tex]\sin D = \dfrac{7}{18}\\\\\sin D = 0.3889\\[/tex]

Rounded to the nearest hundredth ( i.e. 2 decimal places):

[tex]\sin D = 0.39 \quad \quad \textrm{ANSWER}\\\\[/tex]

The solution to the inequality in question is less than or equal to 4300 pounds and 2.6875 cubic yards of sand can be hauled in the truck to still classify as a passenger vehicle.

From the question itself, we can deduce that the inequality is -

Let us assume that the amount of stuff carried by the vehicle is = x

So, the inequality becomes -

= 4200 + x ≤ 8500 pounds

So, if we solve this we will find that the weight of stuff to be carried is going to be -

= x ≤ 8500 - 4200

= x ≤  4300

It should be no more than 4300 pounds.

We can still classify it as a passenger vehicle by carrying only 1.4655 pounds of sand because -

= 2.6875 *1600 = 4300 pounds

This means that by carrying 2.6875 pounds we maintain the rules to remain a passenger vehicle.

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The value of s on the right triangle is s = 4.

Here we can assume that the two triangles are similar triangles, then, the measures of the hypotenuses of the right triangles must be the same one.

Remember that the hypotenuse is the side that is opposite to the 90° angle, then we can write the equation:

s + 43 = 47

s = 47 - 43 = 4

That is the value of s.

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The value of

x₁/x₂ = y₁/y₂ = c₁/c₂

the given lies are parallel to each other having no solution .

A finite collection of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.

Simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are no solutions when the lines are parallel, and there are a finite number of solutions when the two equations graph as the same line.

The equation are

x + y = 25

2x + 2y = 50

The value of

x₁/x₂ = y₁/y₂ = c₁/c₂

So the given lies are parallel to each other having no solution .

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Answer: y=2x+3

Step-by-step explanation:

2x−y=−3

Step 1:

Add -2x to both sides.

2x−y+−2x=−3+−2x−y=−2x−3

Step 2: Divide both sides by -1.−y−1=−2x−3−1y=2x+3

The normal distribution chart below for the weights of the factory are 9.02, 9.07, 9.12, 9.17, 9.22 from left to right.

The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability. When data points are closely spaced from the mean, there is a small variation, and when they are far spaced from the mean, there is a large variation. The standard deviation determines how much the values deviate from the mean. The most popular way to assess dispersion is standard deviation, which is based on all values.

From the given samples of 9oz of chips we have the following values:

Mean = 9.12 ounces

SD = 0.05 ounces

The normal distribution of the chart below will have the following values:

The mean or the center value of the graph with the highest peak is:

Mean = 9.12

The value to the right of the mean value will be:

Mean + SD = 9.12 + 0.05 = 9.17

Mean + 2(SD) = 9.12 + 2(0.05) = 9.22

Similarly, the value to the left of the mean value will be:

Mean - SD = 9.12 - 0.05 = 9.07

Mean - 2(SD) = 9.12 - 2(SD) = 9.02

Hence, the normal distribution chart below for the weights of the factory are 9.02, 9.07, 9.12, 9.17, 9.22 from left to right.

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Assuming that the rates are constant, we can see that Tom can paint the fence in 7.5 hours.

Here we will use equations of the form:

(rate at which person x paints)*(time) = 1 fence painted.

We know that Chuck can paint a fence in 5 hours, then if C is the rate (assuming this is constant), we can write:

C*5 hours = 1 fence

C = (1/5) fences per hour.

And let's say that Tom's rate is T.

When they work together, the rate is:

(C + T)

And they can paint the fence in 3 hours, then:

(C + T)*3 hours = 1 fence

Replacing the value of T we will get:

( 1/5 fences per hour + T)*3 hours = 1 fence

1/5 fences per hour + T = 1/3 fences per hour.

T = (1/3 - 1/5) fences per hour

T = (5/15 - 3/15) fences per hour

T = 2/15 fences per hour.

Then Tom paints the fence in:

(15/2) hours = 7.5 hours.

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Functions that take a positive integer n as input and return a real number are F(n) = 100n log n and g(n) = n (log n)2. A different algorithm's time complexity is represented by g(n), whereas another algorithm's time complexity is represented by F(n).

As n approaches infinity, F(n) and g(n) both expand as O(n log n), which indicates that the growth rate of the two functions is proportional to n log n as n gets very big. However, because the coefficient 100 in F(n) is smaller than the coefficient 1 in g, it develops more slowly than g(n) (n).

Hence, functions that take a positive integer n as input and return a real number are F(n) = 100n log n and g(n) = n (log n)2.

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Rule: Y is equal to the square root of X.

Equation: Y = √X

What is algebraic expression?

An algebraic expression is when we use b and words in solving a particular mathematical question.

In this table, the relationship between the values of X and Y appears to be Y = √X.

This can be expressed as a mathematical rule and equation as follows:

Rule: Y is equal to the square root of X.

Equation: Y = √X

We can use this rule to complete the table as following figure.

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The solution to the inequality 5/w > 4/45, using interval notation, is given as follows:

(-∞, 56.25).

The inequality for this problem is defined as follows:

5/w > 4/45.

Applying cross multiplication, we have that the solution can be obtained as follows:

4w < 45 x 5

w < 45 x 5/4

w < 56.25.

The solution is found similarly to an equality, isolating the desired variable, and finding the desired range of values.

The solution w < 56.25 is composed by values to the left of x = 56.25 on the number line, that is, values between negative infinity and 56.25, hence the interval is given as follows:

(-∞, 56.25).

The problem is incomplete, hence it was adapted to show the solution to an inequality, and then written in interval notation.

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Answer:

The volume of each cylinder is given by the formula: V = πr^2h, where r is the base radius and h is the height of the cylinder.

When 25 cylinders are put into the half-filled container, the water level rises to the top of the container, which means that the total volume of the 25 cylinders is equal to the volume of the container. Let's assume the volume of the container is V_container.

So, 25 * πr^2 * h = V_container

Dividing both sides by 25πh gives: r^2 = V_container / (25πh)

Taking the square root of both sides gives: r = √(V_container / (25πh))

Since h = 10 cm, we can substitute this value in the formula above: r = √(V_container / (25π * 10))

Since r is the base radius of the cylinder, it must be positive. So, the final equation becomes:

r = √(V_container / (25π * 10)) cm = 5√(5/π) cm. shown

By using 3.14 for the value of π, we can calculate the value of r:

r = 5√(5/π) = 5√(5/3.14) = 5 * √(5/3.14)

= 5 * √(1.5873) = 5 * 1.259 = 6.295 cm (rounded to the first decimal place)

So, the base radius of the cylinder is approximately 6.3 cm.

Answer:

x = 7/2

y = 0

Step-by-step explanation:

–6x + y = –21

2x − 13y = 7

Times the second equation by 3

-6x + y = -21

6x - 39y = 21

-38y = 0

y = 0
Now put -0 back for y and solve for x

-6x = -21

x = 7/2

Answer:

I think it would be infinitely many solutions

Step-by-step explanation:

The solutions of the system tend towards zero, as the exponential term dominates the other terms.

The general solution of the given system of equations can be expressed as:

x(t) = c1e^(-t) + c2te^(-t)

y(t) = c3e^(-t) + c4te^(-t)

where c1, c2, c3 and c4 are constants of integration.

The direction field of the system can be drawn by plotting the slopes of the two equations at each point. The trajectories of the solutions can be sketched by plotting the solutions of the system at different points in time. As t approaches infinity, the solutions of the system tend towards zero, as the exponential term dominates the other terms.

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Step-by-step explanation:

the triangle GAS is congruent with the triangle IOL (I know, it is tempting to say OIL, but it is important to show the sequence of the corresponding corners, so G corresponds to I, A to O and S to L) by AAS (angle-angle-side) : 2 angles and a not included but corresponding side are equal between the 2 triangles.

The ith observation in the data set is represented by the number xi. The sample's average value is. V stands for variation. All of the values in a data set are added up to form x.

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The perimeter of Rebekah's new mural is 9 meters.

The whole distance that a rectangle's borders, or its sides, cover is known as its perimeter. Given that a rectangle has four sides, the perimeter of the rectangle will be equal to the total of its four sides.

Given:

A rectangular mural measures 1 meter by 3 meters.

Rebekah creates a new mural that is 0.5 meters longer.

The perimeter of Rebekah's new mural,

= 2 (1.5 + 3)

= 9 meters.

Therefore, the perimeter is 9 meters.

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Answer:

9

Step-by-step explanation:

4^4 and 678^678  are the only two interesting numbers that divide 2023^2023.

To find all interesting numbers that divide 2023^2023, we need to find all positive integers n such that n^n divides 2023^2023.

Since 2023^2023 = 2023 * 2023 * ... * 2023 (2023 times), we can see that the factors of 2023^2023 are simply the powers of 2023.

So, a number n^n divides 2023^2023 if and only if 2023^(n-1) divides 2023^2023. This means that n-1 must be a factor of 2023.

The factors of 2023 are 3 and 677. Therefore, the values of n that satisfy the condition are 4 (3+1) and 678 (677+1), which correspond to the interesting numbers 4^4 and 678^678. These are the only two interesting numbers that divide 2023^2023.

Therefore, 4^4 and 678^678  are the only two interesting numbers that divide 2023^2023.

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The expressions for the real part, imaginary part, and magnitude of the complex function f(x) = 1/(1-ix) are: Re[f(x)] = Re[1/(1-ix)] = Re[1] / Re[1-ix] = 1 / (1 - x^2), Im[f(x)] = Im[1/(1-ix)] = Im[1] / Re[1-ix] = -x / (1 - x^2) and |f(x)| = √(Re[f(x)]^2 + Im[f(x)]^2) = √(1 / (1 - x^2)^2 + (-x / (1 - x^2))^2) = 1 / |1 - ix|

Given the complex function f(x) = 1/(1-ix), where I = √-1, we can find the real part, imaginary part, and magnitude as follows:

Real part: The real part of a complex number is equal to the real part of the numerator divided by the real part of the denominator. Here, the numerator is 1, so the real part of the numerator is 1. The denominator is 1-ix, so the real part of the denominator is 1, and the imaginary part of the denominator is -x. The real part of the complex function is then given by:

Re[f(x)] = Re[1/(1-ix)] = Re[1] / Re[1-ix] = 1 / (1 - x^2)

Imaginary part: The imaginary part of a complex number is equal to the imaginary part of the numerator divided by the real part of the denominator. Here, the numerator is 1, so the imaginary part of the numerator is 0. The denominator is 1-ix, so the real part of the denominator is 1, and the imaginary part of the denominator is -x. The imaginary part of the complex function is then given by:

Im[f(x)] = Im[1/(1-ix)] = Im[1] / Re[1-ix] = -x / (1 - x^2)

Magnitude: The magnitude of a complex number is equal to the square root of the sum of the squares of the real and imaginary parts. The magnitude of the complex function is then given by:

|f(x)| = √(Re[f(x)]^2 + Im[f(x)]^2) = √(1 / (1 - x^2)^2 + (-x / (1 - x^2))^2) = 1 / |1 - ix|

Therefore, the expressions for the real part, imaginary part, and magnitude of the complex function f(x) = 1/(1-ix) are: Re[f(x)] = Re[1/(1-ix)] = Re[1] / Re[1-ix] = 1 / (1 - x^2), Im[f(x)] = Im[1/(1-ix)] = Im[1] / Re[1-ix] = -x / (1 - x^2)

and |f(x)| = √(Re[f(x)]^2 + Im[f(x)]^2) = √(1 / (1 - x^2)^2 + (-x / (1 - x^2))^2) = 1 / |1 - ix|.

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Surface area of the cylinder would be 231.1 sq ft.

How do you find a surface area of a cylinder?

A cylinder's volume is π r² h, and its surface area is 2π r h + 2π r².

The surface area of a cylinder with height h and radius r can be found using the formula:

2πr^2 + 2πrh

Given a cylinder with height 6 ft and radius 7 ft, the surface area is:

2π * 7^2 + 2π * 7 * 6 = 147.1 + 84 = 231.1 sq ft (rounded to the nearest tenth).

Therefore, Surface area of the cylinder would be 231.1 sq ft.

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If the area of the triangle is 50m² the length of it's other two sides is 10m each and hypotenuse is 14.1m

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.

A right angled triangle is a triangle with 90°. Since of one of the angle is 45° , this means that the triangle is isosceles and the other two sides will be equal. This means a= b

Area of triangle = 1/2absinC

50 = 1/2 b²sin90

50× 2 = b²× 1

b² = 100

b = √ 100

b =10m

b = 10m

a= 10m

using Pythagoras theorem

c² = 10²+10²

c² =100+100

c²= 200

c =√200

c = 14.1m

therefore the measure of the other two sides is 10m each and the hypotenuse is 14.1m

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