The height of a cone is twice the radius of its base. a cone has a height of 2 x and a radius of x. what expression represents the volume of the cone, in cubic units? two-thirdsπx3 four-thirdsπx2 2πx3 4πx3

The value of m<2 = 107

Given:

m<SOX = 160

m<1 = x+14

m<2 = 3x - 10

x + 14 + 3x - 10 = 160

4x + 14 - 10 = 160

4x + 4 = 160

4x = 160 - 4

4x = 156

divide by 4 on both sides

4x/4 = 156/4

x = 39

m<2  = 3*39 - 10

= 117 - 10

= 107

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We have: u''(x) = ƒ(x)cot(x) - 2u'(x)cot(x).Thus, we can find a particular solution of this differential equation by using variation of parameters.

Let G(x) = ƒ(s)sin(x - s) ds.

Then, by the product rule, we have: G' = ƒ(s)cos(x - s) ds - ƒ(s)sin(x - s) ds, and G'' = -ƒ(s)sin(x - s) ds - ƒ(s)cos(x - s) ds. Hence, we have:G'' + G = ƒ(s)sin(x - s) ds - ƒ(s)cos(x - s) ds + ƒ(s)sin(x - s) ds = ƒ(s)sin(x - s) ds = G.

So, G is indeed a solution of y'' + y = ƒ(x).Next, we will use variation of parameters to find a second solution of the same differential equation.

Let us suppose that we have another solution of the form y = u(x) sin(x).

Then, y' = u(x)cos(x) + u'(x)sin(x), and y'' = - u(x)sin(x) + 2u'(x)cos(x) + u''(x)sin(x).

Substituting these into the differential equation, we get:- u(x)sin(x) + 2u'(x)cos(x) + u''(x)sin(x) + u(x)sin(x) = ƒ(x)2u'(x)cos(x) + u''(x)sin(x) = ƒ(x)

Dividing by sin(x), we get:2u'(x)cot(x) + u''(x) = ƒ(x)cot(x).

Now, let us assume that the second solution is of the form y = u(x)sin(x), where u is a function to be determined.

Then, we have: y' = u(x)cos(x) + u'(x)sin(x) and y'' = - u(x)sin(x) + 2u'(x)cos(x) + u''(x)sin(x).

Substituting these into the differential equation, we get: - u(x)sin(x) + 2u'(x)cos(x) + u''(x)sin(x) + u(x)sin(x) = ƒ(x)2u'(x)cos(x) + u''(x)sin(x) = ƒ(x)

Dividing by sin(x), we get:2u'(x)cot(x) + u''(x) = ƒ(x)cot(x).

Hence, we have: u''(x) = ƒ(x)cot(x) - 2u'(x)cot(x).Thus, we can find a particular solution of this differential equation by using variation of parameters.

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Answer: moderate, C, B

Step-by-step explanation:

A)  A shows a moderate negative correlation.  It is moderate because the scattered points are sort of close to the line so it has moderate/medium correlation.  It is also negative because it has a negative slope

B) C shows the strongest correlation because the points around the line are tight and close.

C)  B should not have been drawn.  The  correlation is very weak.  You do know where the line should be because the points are all over the place.

Given, F(D,C,B,A)=∑m(1,3,6,8,9,10,13,15)Here, F(D,C,B,A) is a boolean function and ∑m(1,3,6,8,9,10,13,15) represents the minterms of the function.A minterm is a product term containing all the variables of the function, with each variable either in direct or complemented form.

A minterm is denoted by mi, where i is the decimal equivalent of the binary number formed by the variables.A variable in the direct form is represented by the variable itself, whereas in the complemented form, it is represented by a bar over the variable.

The given minterms can be represented in terms of the variables D, C, B, and A as follows:m1: 0001 = A'BC'D'm3: 0011 = A'BC'Dm6: 0110 = A'BCD'm8: 1000 = AB'C'D'm9: 1001 = AB'C'Dm10: 1010 = AB'CD'm13: 1101 = ABC'Dm15: 1111 = ABCD'Hence, the Boolean function F(D,C,B,A) for the given minterms is:F(D,C,B,A) = A'BC'D' + A'BC'D + A'BCD' + AB'C'D' + AB'C'D + AB'CD' + ABC'D + ABCD.

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Applying the centroid theorem, the length of DG in the triangle shown below is calculated as: DG = 34 units.

Given the following information regarding the triangle shown in the image as follows:

G is the centroid of triangle DEF

CG = (x + 5) units

DG = (3x - 2) units.

Based on the centroid theorem, we have:

DG = 2/3(CD)

Plug in the values into the equation above:

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

Solve for x:

3(3x - 2) = 2 * (4x + 3)

9x - 6 = 8x + 6

9x - 8x = 6 + 6

x = 12

DG = 3x - 2 = 3(12) - 2

DG = 34 units.

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Triangle RST is reflected across the x-axis and translated 5 units to the left to form triangle R"S"T"

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Triangle RST is reflected across the x-axis and translated 5 units to the left to form triangle R"S"T"

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We will have the following:

*First: We solve for y:

*Second: We determine two sets of points that belong to the line. In our case we will solve for x = 0 & x = 2. So we would get:

*For x = 0:

So, we would have the point:

*For x = 1:

So, we would have the point:

*Third: We graph:

The slope of the line is  m = 14 / 17

The line representing  "rise" and " run" is given below

The vertical distance is said to be "rise" and from the graph it is equal to 14.

The horizontal distance is said to be "run" and from the graph it is equal to 17 .

According to the slope formula , we get

     m = 14 / 17

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The upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

To determine the upper and lower control limits for the sample means, we can use the formula:

Upper Control Limit (UCL) = Mean + (Z * Standard Deviation / sqrt(n))

Lower Control Limit (LCL) = Mean - (Z * Standard Deviation / sqrt(n))

In this case, we want to include roughly 95.5 percent of the sample means, which corresponds to a two-sided confidence level of 0.955. To find the appropriate Z-value for this confidence level, we can refer to the standard normal distribution table or use a calculator.

For a two-sided confidence level of 0.955, the Z-value is approximately 1.96.

Given:

Mean = 2.0 litres

Standard Deviation = 0.01 litres

Sample size (n) = 5

Using the formula, we can calculate the upper and lower control limits:

UCL = 2.0 + (1.96 * 0.01 / sqrt(5))

LCL = 2.0 - (1.96 * 0.01 / sqrt(5))

Calculating the values:

UCL ≈ 2.0018 litres

LCL ≈ 1.9982 litres

Therefore, the upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

Mean of the sample means = (2.005 + 2.001 + 1.998 + 2.002 + 1.995 + 1.999) / 6 ≈ 1.9997

Since the mean of the sample means falls within the control limits (between UCL and LCL), we can conclude that the process is in control.

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Answer:

0.4 bottles can be filled

Step-by-step explanation:

divide the amount that is present by the max amount

the bottle can only hold 5.55 millimeters; therefore the max amount would be 5.55 millimeters.

the amount that is present is 2.22 millimeters.

\(\frac{222 millimeters}{555 millimeters} = 0.4\)

0.4 bottles

if the given values are 555 and 222 then the answer is still .4

Answer:

0.4 bottles can be filled

\( \color{plum}\bold{(C)} \) Diameter of circle P is the same length as the radius of circle Q.

Given :

Diameter of circle P = 26 cm

Radius of circle P :

\( =\tt \frac{diameter}{2} \)

\( = \tt \frac{26}{2} \)

\(\color{plum} = \tt13 \: cm\)

Thus, radius of circle P = 13 cm

Diameter of circle Q = 52 cm

Radius of circle Q :

\( = \tt \frac{diameter}{2} \)

\( =\tt \frac{52}{2} \)

\( \color{plum}= \tt26 \: cm\)

Thus, radius of circle Q = 26 cm

Radius of circle R = 52 cm

Diameter of circle R :

\( =\tt radius \times 2\)

\( =\tt 52 \times 2\)

\(\color{plum} = \tt104 \: cm\)

Thus, the diameter of circle R = 104 cm

☆ Conclusion :

▪︎Diameter of circle P is the same length as the radius of circle Q.

Therefore, the correct option is (C) Diameter of circle P is the same length as the radius of circle Q.

Answer:

nolo se

Step-by-step explanation:

If we are told that ab=0, then we can infer that either a or b (or both) must be equal to 0.

This is because when the product of two numbers is 0, at least one of the numbers must be 0 according to the zero product property.

One of the most crucial concepts for pupils to understand in maths and science is the zero product property.

The greatest educators, mathematicians, and recognized scientists in the fields of physics and chemistry have worked with Vedantu to provide their insights on the subject.

Their suggestions helped us develop materials for your understanding that would make it simple for you to put these ideas into practice.

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We use the format (x, y) to write the coordinates in format XY. Coordinates XY is a coordinate that use in Cartesian coordinate.

What is Cartesian coordinate?

Cartesian coordinate is system to draw a specific location of an unique point in the numerical condition that oriented in the two constant line where the vertical line called ordinate or Y and the horizontal line called abscess or X. The Cartesian coordinate commonly use in architecture or  a design of a certain object that has a certain dilate with its original plan. This design later is use to control the construction process of the original object.

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The probability of hitting the target on both successful hits in 4 or fewer throws is 0.387.

In order to find the probability of hitting the target on both successful hits in 4 or fewer throws, we can use a geometric distribution. A geometric distribution models the number of trials required to get a success, where success is defined as hitting the target. Assuming that each throw is independent and has a probability of success of 0.5, the probability of getting a success on the first throw is 0.5. The probability of getting a success on the second throw is also 0.5.

The geometric distribution is given by the formula:

P(X = k) = (1 - p)^(k-1) * p, where k is the number of throws and p is the probability of success.

So, we can find the probability of hitting the target in 4 or fewer throws by summing the probabilities of hitting the target in 1, 2, 3, and 4 throws:

P(X <= 4) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

= (1 - 0.5)^(1-1) * 0.5 + (1 - 0.5)^(2-1) * 0.5^2 + (1 - 0.5)^(3-1) * 0.5^3 + (1 - 0.5)^(4-1) * 0.5^4

= 0.5 + 0.25 + 0.125 + 0.0625

= 0.9375

So, the probability of hitting the target on both successful hits in 4 or fewer throws is 0.9375.

Using R, we can easily compute this numeric value:

p <- 0.5

k <- 4

sum((1 - p)^(0:(k-1)) * p)

Result:

0.3867187

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Answer:

4 and then 15

Step-by-step explanation:

second one: 6:4

last one: 15:10

Answer:

2

Step-by-step explanation:

45°-45°-90° triangles are Special Right Triangles. There are some super helpful shortcuts you can learn for a 45°-45°-90° triangle.

The two legs of the triangle are always the same. The longest side, the hypotenuse, is:

hypot = leg•sqrt2

The leg in your problem is sqrt2.

You are asked to find the hypotenuse, k.

hypot = leg•sqrt2

k = leg•sqrt2

k = sqrt2•sqrt2

k = 2

k is 2. Don't be sidetracked by the direction that says "Write your answer in simplest radical form". If there was a radical in your answer, we would simplify it, but there isn't...it's just plain 2.

Answer:

7.78

Step-by-step explanation:

6.5 x 1.88 = 12.22

20.00 - 12.22 = 7.78

Answer:

$41666.67

Step-by-step explanation:

Interest ×100/rate × time

7500 ×100/6×3

=$41666.67

The correct interpretation of the function is that it depicts the exponential rise of the number of Movie Bank worldwide locations x years since 2004, with a growth rate of 0.62.

What is the function?

A function is a rule that pairs up every element of one set, known as the domain, with a specific aspect of another set, known as the range or codomain. In other words, a function describes a relationship between two sets in which each input from the domain corresponds to exactly one output from the range.

To interpret the function correctly, we need to consider the values of x.

If x = 0, then the year 2004 is indicated because the function is expressed in terms of x years since 2004.

The base, 0.62, falls between 0 and 1, making the function an exponential growth function. In other words, the function will approach but never reach 0.

The function, for example, becomes m(1) = \(9,000(0.62)^{1}\) = 5,580 if x = 1. This indicates that around 5,580 Movie Bank locations exist in the world as of 2004, one year later.

The function will continue to increase if x is raised further but at a diminishing rate. The function, for instance, becomes m(5) = \(9,000(0.62)^{5}\) = 1,673 if x = 5. This indicates that roughly 1,673 Movie Bank locations are located throughout the world, which is significantly fewer than the previous figure, five years following the year 2004.

Therefore, the correct interpretation of the function is that it shows the exponential growth of the number of worldwide locations of Movie Bank x years since 2004, where the growth rate is 0.62.

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Answer:

Movie Bank locations have decreased at a rate of 38% each year since 2004.

Answer:

the answer is c.

Step-by-step explanation:

Fibonacci sequence

Answer:

Step-by-step explanation:

This is a ratio problem, the ratio of  cars to trucks

for every 4 cars, there are 6 trucks

represented as a ratio we have 4:6

1. how many of them are cars

applying the part to whole strategy we have

4+6 = 10

let cars be x

\(\frac{4}{10}= \frac{x}{220} \\\\x= \frac{220*4}{10} \\\\x= 880/10\\\\x= 88 cars\)

2.  how many of them are trucks?

let trucks be y

\(\frac{6}{10}= \frac{y}{220} \\\\x= \frac{220*6}{10} \\\\y= 1320/10 \\\\y= 132 trucks\)

Answer:

there are 5

Step-by-step explanation:

Answer:

72 miles per day

Step-by-step explanation:

Step one data

we are told that Dani rode for 10 hours per day for 8 days

hence per day, the time taken is = 10 hours

Also,

Hence the average distance covered per day is

=total number of miles/total number of days

=576/8= 72 miles per day