how do calculate probablility

a. The radius of the cylinder is 5.13 inches.

b. The radius will change in opposite to the height.

What is a cylinder?

One of the most fundamental curvilinear geometric shapes, the cylinder, has long been thought of as a three-dimensional solid. In basic geometry, it is regarded as a prism with a circle as its base.

a. We are given volume of cylinder as 894 cubic inches and the height is 10.8 inches.

So, we get

⇒ Volume = π\(r^{2}\)h

⇒ 894 = 3.14 * \(r^{2}\) * 10.8

⇒ 894 = 33.912 * \(r^{2}\)

⇒ \(r^{2}\)  = 26.36

⇒ r  = 5.13 inches

b. If the height of the cylinder is​ changed, but the volume stays the​ same, then the radius will change inversely. This means with increase in height, radius will decrease and vice versa.

Hence, the required solution have been obtained.

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The formula that relates the coefficient of self-induction l, the energy p stored in an electronic circuit, and the current i is given as: p = (1/2) * l * i^2



To find i, we can rearrange the formula as follows:

i = sqrt(2p/l)

Therefore, if we know the values of p and l, we can easily calculate the value of i using the above formula. It is important to note that the units of measurement for p, l, and i should be consistent in order for the formula to work correctly. For instance, if p is in joules and l is in henrys, then the resulting value of i will be in amps.

The energy (P) stored in an inductor with inductance (L) and current (I) is given by the formula:

P = 0.5 * L * I^2

To find the current (I) when you know the energy (P) and inductance (L), you can rearrange the formula as follows:

I = sqrt(2 * P / L)

This equation allows you to calculate the current in the electronic circuit given the energy stored in the inductor and the inductor's coefficient of self-induction.

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Statement (c) is correct for a simple graph. Every trail is a path, and every path is a trail.

In graph theory, a simple graph is an undirected graph with no loops or multiple edges between the same pair of vertices. A path in a graph is a sequence of vertices where each consecutive pair is connected by an edge. A trail in a graph is a path that allows for repeated vertices and edges.

Statement (a) is not correct because not every path is a trail. A path does not allow for repeated vertices or edges, whereas a trail does.

Statement (b) is not correct because not every trail is necessarily a path. A trail may contain repeated vertices or edges, but a path does not.

Statement (d) is not correct because paths and trails do have a relation. A trail is a more general concept that encompasses paths by allowing for repetition of vertices and edges.

Therefore, statement (c) is the correct statement. In a simple graph, every trail is a path, and every path is a trail.

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Answer:

missing side: 9x -3

Explanation:

length + width + height = perimeter

4x + 1 + 2x - 4 + height = 15x - 6

6x - 3 + height = 15x - 6

height  =  15x - 6 - 6x + 3

height = 9x -3

The order of steps for solving an equation are as follows;

In order to evaluate and solve any given equation or expression, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right.

Lastly, the mathematical operations of addition or subtraction would be performed from left to right with respect to any given equation or expression.

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Answer:

x = 11

z = 99

Step-by-step explanation:

        Vertically opposite angles are congruent.

      \(\boxed{\bf z = 99^\circ}\)

   99 + (10x - 29) = 180  {Linear pair}

    99 + 10x - 29 = 180

             10x + 70 = 180

Subtract 70 from both sides,

                      10x = 180 - 70

                     10x = 110

Divide both sides by 10

                          x = 110 ÷ 10

                          \(\sf \boxed{\bf x = 11^\circ}\)

The final cost of the item after a 35% discount and 9.8% sales tax is $53.54.

The given problem is related to percentage discounts and sales tax and can be solved using the following steps:

Step 1: Firstly, we need to determine the discount amount, which is 35% of the original price. Let's calculate it. Discount = 35% of the original price = 0.35 x $75 = $26.25

Step 2: Now, we will calculate the new price after the discount by subtracting the discount amount from the original price.New Price = Original Price - Discount AmountNew Price = $75 - $26.25 = $48.75

Step 3: Next, we need to calculate the amount of sales tax. Sales Tax = 9.8% of New Price Sales Tax = 0.098 x $48.75 = $4.79

Step 4: Finally, we will calculate the final cost of the item by adding the new price and the sales tax.

Final Cost = New Price + Sales Tax Final Cost = $48.75 + $4.79 = $53.54

Therefore, the final cost of the item after a 35% discount and 9.8% sales tax is $53.54.I hope this helps!

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The common difference is 4. To find it, you subtract the first two terms (5 and 9) to get 4. You can then use this answer to find the common difference in the sequence by subtracting each consecutive term. For example, 9-5=4, then 13-9=4, and so on.

The common difference is an important part of any arithmetic sequence. It is the number that is added to each term in the sequence to generate the next term. For example, the first two terms of the sequence are 5 and 9. The common difference of 4 is added to the first term (5) to get the second term (9). The common difference is then added to the second term (9) to get the third term (13), and so on. This is how the sequence is generated.  

The common difference is an important tool for analyzing the behavior of an arithmetic sequence. Knowing a common difference allows you to determine the nth term of the sequence, as well as the sum of the first n terms. It also helps you to identify patterns in the sequence and make predictions about future terms. Knowing a common difference is an essential part of analyzing arithmetic sequences.

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(a) -0.255 is the probability that a randomly selected credit card holder has a credit card balance less than $2500. (b) You randomly select 25 credit card holders. 0.0228 is the probability that their mean credit card balance is less than $2500.

Let us pull out the critical elements

Population: Normally distributed with mean of 2870

population standard deviation = 900 standard deviation of the sample mean (standard error) is 900 / √25. or 180

As population sigma is known, we do not have apply any corrections

P(xbar < $2500) = ?    

Since μ and σ are known (population mean and standard deviation) we can use a simple Z test.

Ztest = (2500-2870 )/ 180  or -370/180 = -2.055

As this is very close to -2 one can use the rule of thumb for probability within ± 2 sigma  being 95.44% to get a close estimate.   If the area between -2 and 2 sigma = .9544 then the area outside = .0456.  Half of this (the amount under the curve LESS THAN -2) would be .0228

Using a calculator or computer for an exact answer we find (using a TI-83/86):

nmcdf(-9E6,2500,2870,180) = .0199

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Option D is correct. (187.09, 350.64) is the answer.

Given that CSC9 = -8.1

To solve the equation for 0 ≤ q < 360, we will use the following formula:

CSC9 = 1/SIN9

⇒ 1/SIN(90°-q)

⇒ SIN(90°-q)

⇒ -1/8.1

Now, SIN(90°-q) is negative, it means the angle 90°-q is in the second or third quadrant.

We will use a calculator to find the values of q.

We get:

90°-q = SIN⁻¹(-1/8.1)

90°-q = -7.4767...

q = 90° + 7.4767...

q = 97.4767... °

90°-q = SIN⁻¹(-1/8.1)

90°-q = 7.4767...

q = 90° - 7.4767...

q = 82.5233... °

So, we get two values of q: 97.48° and 82.52°

Now, 0 ≤ q < 360, it means that we have to add or subtract 360° from these values.

We get the following values:

q₁ = 97.48°

q₂ = 97.48° - 360° = -262.52°

q₃ = 82.52°

q₄ = 82.52° + 360° = 442.52°

We will round these answers to the nearest hundredth.

We get: CSC9 = -8.1 has the following solutions:

q₁ = 97.48°

q₃ = 82.52°

The rounded answers are

q₁ = 97.48° ≈ 97.48

q₃ = 82.52° ≈ 82.52

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Answer:

yes it is true

Step-by-step explanation:

write the first five elements then write their cubes then write the cubes in the same form

for eg:

4³=16= 3×5+1= 3n+1

7³=49=3×16 +1= 3n + 1

and so on till the fifth element...

The addition of the new girl who can jump 19 feet will affect the statistics of the long jump distances for the girls on the varsity team as follows:

Mean: The mean distance jumped will increase. To see why, consider that the mean is calculated by adding up all the distances and dividing by the number of girls. Since the new girl can jump 19 feet, her distance is much greater than the other distances, and this will pull the mean up. Therefore, the mean will increase.

Median: The median distance jumped cannot be determined with the information given. To see why, note that the median is the middle value when the distances are arranged in order. Since we are not given the exact number of girls on the team or the order of their distances, we cannot determine whether the addition of the new girl will change the median distance jumped or not.

Standard deviation: The standard deviation of the distances jumped cannot be determined with the information given. To see why, note that the standard deviation is a measure of how spread out the distances are from the mean.

Adding a new girl who can jump 19 feet may or may not affect the spread of the distances, depending on the number of girls on the team and the variability of their distances. Therefore, we cannot determine whether the standard deviation will increase, decrease, or stay the same.

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Answer:

A) x = 3 or -1

B) x = -7

C)x = -7

Step-by-step explanation:

A) x² + 2x + 1 = 2x² - 2

Rearranging, we have;

2x² - x² - 2x - 2 - 1 = 0

x² - 2x - 3 = 0

Using quadratic formula, we have;

x = [-(-2) ± √((-2)² - 4(1 × -3))]/(2 × 1)

x = (2 ± √16)/2

x = (2 + 4)/2 or (2 - 4)/2

x = 6/2 or -2/2

x = 3 or -1

B) ((x + 2)/3) - 2/15 = (x - 2)/5

Multiply through by 15 to get;

5(x + 2) - 2 = 3(x - 2)

5x + 10 - 2 = 3x - 6

5x - 3x = -6 - 10 + 2

2x = -14

x = -14/2

x = -7

C) log(2x + 3) = 2log x

From log derivations, 2 log x is same as log x²

Thus;

log(2x + 3) = logx²

Log will cancel out to give;

2x + 3 = x²

x² - 2x - 3 = 0

Using quadratic formula, we have;

x = [-(-2) ± √((-2)² - 4(1 × -3))]/(2 × 1)

x = (2 ± √16)/2

x = (2 + 4)/2 or (2 - 4)/2

x = 6/2 or -2/2

x = 3 or -1

Farm Joe used \(7\frac{6}{15}\) kg of soil in this month.

The total weight of soil that Farm Joe ordered was:

3 bags x 4 2/5 kg/bag = 12 6/15 kg = 12 2/5 kg

The weight of the first bag used was 4 2/5 kg.

The weight of the second bag remaining is 2 3/4 kg.

The weight of the third bag remaining is 7/8 kg.

The total weight of soil used in this month can be found by subtracting the weight of the second and third bags remaining from the total weight of soil ordered:

12 2/5 kg - 2 3/4 kg - 7/8 kg

Converting all fractions to fifteenths:

12 8/15 kg - 5 1/15 kg - 1/15 kg = 7 6/15 kg

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The solution to the systems of equations graphically is (2, 4)

From the question, we have the following parameters that can be used in our computation:

y = 2x

y = -x + 6

Next, we plot the graph of the system of the equations

See attachment for the graph

From the graph, we have solution to the system to be the point of intersection of the lines

This points are located at (2, 4)

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1) The equation of line is; y = (1/3)x + 1

2) The x - intercept is -3 and the y-intercept is 2

3) Area of CAT is; 6 sq.units

4) Perimeter is; 14.325 units

1) The coordinates of the line AC on the graph are;

A(-3, 0) and C(3, 2)

Thus, equation of line is gotten from the formula;

(y₂ - y₁)/(x₂ - x₁) = (y - y₁)/(x - x₁)

(2 - 0)/(3 + 3) = (y - 0)/(x + 3)

2/6 = y/(x + 3)

3y = x + 3

y = (1/3)x + 1

2) The x - intercept is -3 and the y-intercept is 2

3) Area of CAT is;

Area = 1/2 * base * height

Area = 1/2 * 6 * 2

Area = 6 sq.units

4) Perimeter of ACT is gotten by;

AT + CT + AC

AC = √((2 - 0)² + (3 + 3)²)

AC = √40

Thus;

Perimeter = 2 + 6 + √40

Perimeter = 14.325

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Answer:

4/3

Step-by-step explanation:

gradient=

\( \frac{change \: in \: y}{change \: in \: x?} \)

7--5=12

16-7=9

12÷9=4/3

the gradient is the same as slope

thus the answer is 4/3

The following table shows how the relation is a function when t is the independent variable and not a function when t is the dependent variable:

t   0   1   2   3   4   5

v   0   1   2   3   4   5

A vertical line drawn from the independent variable axis (x-axis) meets the function graph only once because a function is a relationship between an input and an output in which each input has just one output.

The independent variable is the input, while the dependent variable is the output.

Filling out the table in such a way that when t is the independent variable, the relationship is a function, and when t is the dependent variable, the relation is not a function, results in the following table:

t   0   1   2   3   4   5

v   0   1   2   3   4   5

Given that each value of the independent variable t has a corresponding value of the velocity v, the aforementioned is a function.

However, when t is the dependent variable, the independent variable value of 1 produces two outputs of 1 and 5, which results in the following table:

t   0   1   2   3   4   5

v   0   1   2   3   4   5

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The integral ∫(1/(4+t²)) dt with the substitution t = 2 tan θ is: (1/4)θ + C.the integral ∫(1/√(9-4z²)) dz with the substitution z = sin θ becomes: -8/5 ∫(1/√(1+u²)) du.

(a) To find the integral ∫(1/√(9-4z²)) dz using the substitution z = sin θ, we need to substitute z = sin θ and dz = cos θ dθ into the integral.

When z = sin θ, the equation 9 - 4z² becomes 9 - 4(sin θ)² = 9 - 4sin²θ = 9 - 4(1 - cos²θ) = 5 + 4cos²θ.

Now, let's substitute z = sin θ and dz = cos θ dθ into the integral:

∫(1/√(9-4z²)) dz = ∫(1/√(5+4cos²θ)) cos θ dθ.

We can simplify the integral further by factoring out a 2 from the denominator:

∫(1/√(5+4cos²θ)) cos θ dθ = 2∫(1/√(5(1+4/5cos²θ))) cos θ dθ.

Next, we can pull out the constant factor of 2:

2∫(1/√(5(1+4/5cos²θ))) cos θ dθ = 2/√5 ∫(1/√(1+4/5cos²θ)) cos θ dθ.

Now, let's simplify the integrand:

2/√5 ∫(1/√(1+4/5cos²θ)) cos θ dθ = 2/√5 ∫(1/√(5/4+cos²θ)) cos θ dθ.

Notice that 5/4 can be factored out from under the square root:

2/√5 ∫(1/√(5/4(1+(4/5cos²θ)))) cos θ dθ = 2/√5 ∫(1/√(5/4(1+(2/√5cosθ)²))) cos θ dθ.

Now, let u = 2/√5 cos θ, du = -2/√5 sin θ dθ:

2/√5 ∫(1/√(5/4(1+(2/√5cosθ)²))) cos θ dθ = 2/√5 ∫(1/√(5/4(1+u²))) (-du).

The integral becomes:

-2/√5 ∫(1/√(5/4(1+u²))) du.

Simplifying the expression under the square root:

-2/√5 ∫(1/√((5+5u²)/4)) du = -2/√5 ∫(1/√(5(1+u²)/4)) du.

We can factor out the constant factor of 1/√5:

-2/√5 ∫(1/√(5(1+u²)/4)) du = -2/√5 ∫(1/√(5/4(1+u²))) du.

Now, let's pull out the constant factor of 1/√(5/4):

-2/√5 ∫(1/√(5/4(1+u²))) du = -8/5 ∫(1/√(1+u²)) du.

Finally, the integral ∫(1

/√(9-4z²)) dz with the substitution z = sin θ becomes:

-8/5 ∫(1/√(1+u²)) du.

(b) To find the integral ∫(1/(4+t²)) dt using the substitution t = 2 tan θ, we need to substitute t = 2 tan θ and dt = 2 sec²θ dθ into the integral.

When t = 2 tan θ, the equation 4 + t² becomes 4 + (2 tan θ)² = 4 + 4 tan²θ = 4(1 + tan²θ) = 4 sec²θ.

Now, let's substitute t = 2 tan θ and dt = 2 sec²θ dθ into the integral:

∫(1/(4+t²)) dt = ∫(1/(4+4tan²θ)) (2 sec²θ) dθ.

We can simplify the integral further:

∫(1/(4+4tan²θ)) (2 sec²θ) dθ = ∫(1/(4sec²θ)) (2 sec²θ) dθ.

Notice that sec²θ cancels out in the integrand:

∫(1/(4sec²θ)) (2 sec²θ) dθ = ∫(1/4) dθ.

The integral becomes:

∫(1/4) dθ = (1/4)θ + C,

where C is the constant of integration.

Therefore, the integral ∫(1/(4+t²)) dt with the substitution t = 2 tan θ is:

(1/4)θ + C.

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The new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees are approximately (4.993, 2.048).

To find the new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees, we can use the rotation formula:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

Where (x, y) are the original coordinates, (x', y') are the new coordinates after rotation, and theta is the angle of rotation in radians.

Converting the angle of rotation from degrees to radians:

theta = 5 degrees * (pi/180) ≈ 0.08727 radians

Plugging in the values into the rotation formula:

x' = 5 * cos(0.08727) - 2 * sin(0.08727)

y' = 5 * sin(0.08727) + 2 * cos(0.08727)

Evaluating the trigonometric functions and simplifying:

x' ≈ 4.993

y' ≈ 2.048

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The exact value of sin(cos^-1(2/5)) is √21 / 5.

We know that cos(cos^-1(x)) = x for all x in [-1, 1]. Hence,

cos(cos^-1(2/5)) = 2/5

Now we need to find sin(cos^-1(2/5)).

We can use the identity sin^2(x) + cos^2(x) = 1 and substitute cos(x) = 2/5 to get:

sin^2(cos^-1(2/5)) + cos^2(cos^-1(2/5)) = 1

sin^2(cos^-1(2/5)) + (2/5)^2 = 1

sin^2(cos^-1(2/5)) = 21/25

Taking the positive square root (since sine is positive in the first and second quadrants), we get:

sin(cos^-1(2/5)) = √(21/25)

= √21 / 5

Therefore, the exact value of sin(cos^-1(2/5)) is √21 / 5.

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Answer:

The answer is A actually. D is wrong

Step-by-step explanation:

Answer: its A got it right

Step-by-step explanation:

Answer:

Sally is currently 4 years old.

Step-by-step explanation:

Kaden is 18 years older than Sally now. In 5 years, Kaden will be 3 times as old as Sally. How old is Sally now?

Let Kaden's current age be \(k\) and Sally's current age be \(s\). We can write the following algebraic equation using the fact that Kaden is currently 18 years older than Sally:

\(k=s+18\)

Next, we will use the fact that in 5 years, Kaden will be 3 times as old as Sally. If Kaden and Sally's current ages are \(k\) and \(s\) respectively, then their ages in 5 years will be \(k+5\) and \(s+5\) respectively. Therefore, we have:

\(k+5=3(s+5)\)

We have two equations with two variables. To solve for either variable, we need to create an equation with only one variable. Therefore, let's substitute the first equation into the second:

\((s+18)+5=3(s+5)\)

Distribute and combine like terms:

\(s+18+5=3s+15,\\s+23=3s+15\)

Subtract \(s\) from both sides, then subtract 15 from both sides:

\(8=2s\)

Divide both sides by 2:

\(s=\frac{8}{2}=\boxed{4}\)

Therefore, Sally is currently 4 years old.

Answer:

Sally is 4 years old now.

Step-by-step explanation:

Let Sally's age = x

Kaden's age = x + 18

In 5 years, they are both 5 years older than now.

Sally will be x + 5

Kaden will be x + 18 + 5 = x + 23

"In 5 years, Kaden will be 3 times as old as Sally."

x + 23 = 3(x + 5)

x + 23 = 3x + 15

-2x = -8

x = 4

Answer: Sally is 4 years old now.

Central tendency, is the term that relates to the way data tend to cluster around some middle or central value.

Measures of central tendency are summary statistics that represent the center point or typical value of a dataset. Examples of these measures include the mean, median, and mode. These statistics indicate where most values in a distribution. Mode in statistics is the number of times a number is repeated. The number which is repeated maximum times in a series of data is known as the modular number. The mode is used to compare data that has extreme figures. Central tendency simply means most scores in a normally distributed set of data tend to cluster near the center of a distribution.

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The answer to following questions are as follows:-A)experiment

B)meaning “statistically non significant” C)explained below

A wave is a dynamic disturbance that propagates over one or more quantities in the domains of physics, mathematics, and allied sciences. When waves are periodic, those parameters repeatedly oscillate around an equilibrium value at a certain frequency.

The answers are: a) It is an experiment since some claims are not supported by evidence.

b) When the analysis reveals that there are substantial variations between the observed, "not statistically significant" refers to "statistically non significant." And we are unable to analyse any of the statistics' results.

c) The fact that Motorola, a cell phone company, funded this research reveals to us that this claim is untrue because Motorola conducts this research to boost their sales.

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Answer:

so that means 10 parents went and 3 children went

Step-by-step explanation: first you count by 10,s to get to 100 like this 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 and then 10 parents went and then you would count by 6 to get to 18 like this 6, 12, 18.

The first 3 terms of the sequence are 21, 24 and 29

From the question, we have the following parameters that can be used in our computation:

n² + 20

This means that

f(n) = n² + 20

The first 3 terms of the sequence is when n = 1, 2 and 3

So, we have

f(1) = 1² + 20 = 21

f(2) = 2² + 20 = 24

f(3) = 3² + 20 = 29

Hence, the first 3 terms of the sequence are 21, 24 and 29

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The ability to order items in a sequence, such as longest to shortest, is known as Seriation.

Seriation is a cognitive skill that involves arranging objects, events, or ideas in a particular order or sequence. It is a crucial aspect of cognitive development and is typically acquired during early childhood. Seriation is the ability to mentally order objects along a quantitative dimension, such as size, weight, or length.

Seriation involves comparing and ordering items based on specific criteria. For example, if given a group of objects of different lengths, a child who has developed seriation skills will be able to arrange the objects in order from shortest to longest. Similarly, if given a group of numbers, a child who has developed seriation skills will be able to arrange them in order from smallest to largest.

Seriation is an important cognitive skill that is used in various areas of life, including academic, professional, and personal domains. It allows individuals to organize information and ideas in a logical and meaningful way, which can facilitate more efficient processing and understanding of complex concepts.

Overall, seriation is a fundamental cognitive skill that plays a crucial role in various aspects of life, including problem-solving, decision-making, and organization. It is an essential skill that supports the development of higher-order thinking skills, such as analysis, evaluation, and synthesis.

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