find the radius and height of the right-circular cylinder of largest volume that can be inscribed in a right circular cone with radius 6 inches and height 10 inches. answer accurate to 3 decimal place. (volume of a cylinder

Answer:

x is approximately 3.449.

Step-by-step explanation:

We are given the following proportion: 21/24 = 7/8 = 49/x

To find x, we can cross-multiply and simplify:

21/24 = 7/8 = 49/x

247= 218 = 49*x

168 = 168 = 49x

x = 168/49 = 3.44948979591836734693877551020408

x = 3.449489795918367

So, x is approximately 3.449.

The total length needed in inches for the 12 strips of metal is 370¹/₂ inches.

The total length for the 12 strips of metal is determined using a combination of the mathematical operation of multiplication and unit conversion.

The 2 feet are converted to 24 inches (2 x 12) using unit conversion and multiplication.

The total length is determined by multiplication, involving the multiplicand and the multiplier, which results in a product called the result.

The number of strips of metal = 12

The length of each strip = 2 ft and 6⁷/₈ inches = 30⁷/₈ inches

1 foot = 12 inches

The total length = 370¹/₂ inches (30⁷/₈ inches x 12)

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Answer: 137000 cm³

Step-by-step explanation:

formula to find the volume of a hemisphere= [tex]\frac{2}{3}[/tex] x πr³

formula to find the volume of a cylinder= πr²×h

both the shapes will have the same radius therefore to get the radius you should divide the diameter by two *you probably already know abt it*

so 46/2= 23 (the radius of both the shapes)

In order to get the height of the cylinder you should subtract the radius of the hemisphere from the total height given as the radius is the same all around the hemisphere **but remember not to mistake the diameter as the radius when subtracting a hemisphere's height from a total height**

height of the cylinder= 90cm- 23cm= 67

Therefore now substitute the values into the formulas and find the volumes of the two shapes separately...

volume of a hemisphere= [tex]\frac{2}{3}[/tex] x πr³

                                         = [tex]\frac{2}{3}[/tex]× π × 23³

                                         = 25482.5 cm³

volume of a cylinder= πr²×h

                                  = π × 23² × 67 (including the height calculated above)

                                 = 111347.5 cm³

Now add the volumes you found which will give you the volume of water that the tank holds when it if full.

volume of a cylinder + volume of a Hemisphere

111347.5 + 25482.5

136830

137000 cm³ (make sure to estimate the final answer to 3s.f or else you'll                     lose your accuracy mark)

The triangle AGHI can be labeled by using the given information.

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Answer: -12k-21

Step-by-step explanation:

you must distribute the -3

Option D shows the correctly represents the solution to the given inequality: | x | ≤ 7

A number is a solution to that of an inequality in x if it can be used to replace x with a statement that is true.

The inequality = x ≤ 7.

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The surface area of the cylinder is 125.66

The surface area of a cylinder is the area occupied by its surface in a three-dimensional space. A cylinder is a three-dimensional structure having circular bases which are parallel to each other. It does not have any vertices. Generally, the area of the three-dimensional shapes refers to the surface area.

The surface area of a cylinder is calculated with the formula:

= 2π × r × h + 2πr2= 2πr (h + r) Square units

A=2πrh+2πr2

With the following parameters from the question:

r = 2

h = 8

Substituting the parameters into the formula

A = 2πrh+2πr2=

A = 2·π·2·8+2·π·22

A = 125.66371

Hence, the surface area of the cylinder is  125.66371

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Answer:

81

Step-by-step explanation:

When the value of p is - 1, then p- 1 ≤ 0.5 is the required inequality.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

We have the inequalities;

(A). p- 1 ≤ 0.5

When p = -1,

-2  ≤ 0.5.

(B). -p - 1 ≤ -0.5

When p = -1,

0  ≤ -0.5.

This is contradiction.

(C).  p - 1 ≥ 0.5

When p = -1,

-2  ≥ 0.5.

This is contradiction.

(D). -p -1 ≥ 0.5

When p = -1,

0  ≥ 0.5.

This is contradiction.

Therefore, p- 1 ≤ 0.5 is the required inequality.

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The complete question:

Which inequality is true when the value of p is -1?

(A). p- 1 ≤ 0.5

(B). -p - 1 ≤ -0.5

(C).  p - 1 ≥ 0.5

(D). -p -1 ≥ 0.5

Answer:

A) y = 3/2 x - 1

Step-by-step explanation:

y + 4 = 3/2 (x + 2)  This is the point slope form of a line.

y + 4 = 3/2 x + 3    Subtract 4 from both sides

y = 3/2 x -1

Answer:[tex]\frac{89}{9}[/tex] or [tex]9 \frac{8}{9}[/tex] or 9.8

Put a line above the 8 after the decimal point signaling that it will always be 8 after the decimal point.

Step-by-step explanation:

6*3+1=19

9*8+2=74

1*2+1=3

[tex]\frac{19}{6} + \frac{74}{9} - \frac{3}{2} = \frac{89}{9}[/tex]

If the order of the choices is relevant ,72 times can this be done.

Suppose we want to choose 6 colors, without replacement , from 8 distinct colors. If the order of the choices is relevant

The permutation of arranging 'r' things from a collection of 'n' objects into an order or sequence is known as nPr in mathematics. Permutation is calculated using the formula nPr = (n!) / (n-r)! N permutations = nPr = n!/ (n-r)! Combination, nCr, is the selection of r items from a collection of n objects such that the order of the objects does not matter.

N permutations are as follows: 9P6 = 8!/(8-6)! = 8*7*6*5*4 = 6,720.

N combinations = nCr = n!/((n-r)!r!) is the response to b.

N combinations = = 8C6 = = 8!/((8-6)!6!) = (8*7*6)/(2*1) = 72

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Answer:

19

Step-by-step explanation:

First we need to add all these numbers together

20+25+7+27+18+17=114

Next, we have to divide all these numbers by the number of values there are.

If we count, there are 6 values that we added together.

After that, we divide 114 by 6 to get the answer

114/6=19.

Step-by-step explanation:

this is a college question ???

and you don't know how to do this ?

remember middle school and high school ? besides math classes themselves, did you never track your class scores and such ?

the average or mean value is always the sum of all data points divided by the number of data points.

here we have 6 data points.

the average is

(20+25+7+27+18+17)/6 = 114/6 = 19

Let w be the width of the rectangle. Then, the length is w + 4. The perimeter is 2(w + 4) + 2w = 56, so 2w + 8 = 56, and w = 24. The length is 28.

The given information is that the length of the rectangle is 4 inches longer than its width, and the perimeter of the rectangle is 56 inches. To find the length and width of the rectangle, we need to solve a system of equations. First, let w be the width of the rectangle, so that the length of the rectangle is w + 4. To find the perimeter of the rectangle, we can use the formula 2(w + 4) + 2w = 56. Substituting in w for the width, we get 2w + 8 = 56. Solving this equation for w, we get w = 24. The length of the rectangle is w + 4, so the length is 28. Therefore, the width of the rectangle is 24 inches and the length is 28 inches.

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We cannot the time period of 25 min using two ropes that when lit burn in one hour. Hence, option C is the correct answer.

This problem is an example of a mathematical puzzle. In order to measure a time period of 30 min, all we need to do is burn one rope from both ends. Since it takes 60 minutes for the rope to burn when lit from one end, it will take half that time i.e., 30 min to burn when lit from both ends.

We can also measure a time period of 35 min if we burn one rope from both ends and the other a bit differently. If we burn a rope from both ends, it will take 30 mins. As for the extra 5 mins, we can take the other rope and first burn it from both ends and then burn it from the middle again. That makes 2 separate ropes and thus the burning time is 15 min. We can then again burn one of these from the middle and wait until one of them completely burns out. This will give us a time period of 35 minutes.

As for 50 minutes, we can use the same method as above for burning one rope completely from both ends and the other from the ends and the middle. We can't really burn the ropes in a way that will give us the time period of 25 min so option C is the correct answer.

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Theresa bought 5 bath towels and 2 hand towels for a total amount of $62.25.

Theresa buys 5 bath towels and 2 hand towels.

Bath towels: $13.25 x 5 = $66.25

Hand towels: $4.50 x 2 = $9.00

Total: $66.25 + $9.00 = $75.25

Since Theresa spent a total of $62.25, she saved $13.25. The difference between the amount she spent on bath towels and the amount she spent on hand towels should be equal to the amount she saved.

Bath towels: $66.25 - $17.25 = $49.00

Hand towels: $9.00 + $17.25 = $26.25

Total: $49.00 + $26.25 = $75.25

Therefore, Theresa bought 5 bath towels ($66.25) and 2 hand towels ($9.00).

Theresa bought 5 bath towels and 2 hand towels for a total of $62.25.

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Answer:

Largest angle=136

middle angle=34

smallest angle=10

Step-by-step explanation:

largest angle= A, 4B

middle angle= B

smallest angle= C, B-24

A+B+C=180

4B+B+B-24=180

5B+B=204

6B=204

B=34

A=4(34), 136

B=34

C=34-24, 10

The result is between 1 and 9, which is assigned to the variable dice.

To generate a random number between 1 and 9, inclusive, we can use the formula: (Math.random() * (9 - 1 + 1)) + 1. This formula randomly generates a number between 0 and 1, and then multiplies it by the range (9 - 1 + 1) to give us a result between 0 and 8. We then add 1 to this result to ensure that the final number is between 1 and 9.

To assign this number to the variable dice, we can use the following statement:

var dice = Math.floor((Math.random() * (9 - 1 + 1)) + 1);

Math.random() generates a random number between 0 and 1, which is then multiplied by the range (9 - 1 + 1) to give us a result between 0 and 8. Math.floor rounds this number down to the nearest whole number. We then add 1 to ensure that the result is between 1 and 9, which is assigned to the variable dice.

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The triple point of a substance, Tₜ, is the temperature and pressure at which the three phases of the substance, solid, liquid, and gas, can coexist in thermodynamic equilibrium.

The triple point can be calculated using the Clausius-Clapeyron equation, which states that the pressure and temperature of the triple point are related by the equation:

ln(Pₜ/P₀) = (ΔHₜ / R) (1/Tₜ - 1/T₀)

where Pₜ and Tₜ are the pressure and temperature of the triple point, P₀ and T₀ are the pressure and temperature of an arbitrary reference point, ΔHₜ is the enthalpy of vaporization, and R is the universal gas constant.

To calculate the triple point, values for P₀ and T₀ are selected and the enthalpy of vaporization is determined from tabulated data. Then, the equation is rearranged to solve for Tₜ, and the pressure and temperature of the triple point can be found.

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The value of x that makes the given pair of ratios equivalent is: A. 32.

In Mathematics, a ratio simply refers to a mathematical expression that is typically used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

In Mathematics, a proportion can be defined as an equation which is typically used to represent the equality of two (2) ratios.

This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities as follows;

x/16 = 50/25

Cross-multiplying, we have the following:

25x = 16 × 50

25x = 800

x = 800/25

x = 32.

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According to the report, 80% of those who purchased new cars received loans, compared to 60% of those who purchased older cars.

The population size estimate is calculated by dividing the total number of people getting a service or the total number of unique items delivered (M) by the percentage of people reporting receiving the service or item in a representative survey (P).

Given a car dealership wants to conduct a survey of 100 people who bought ​a new or used car at the dealership in the last three months. ​

number of people          new car       old car     received Loan       No loan

   2,000                             yes                No           1600                    400

      500                            No                  Yes           300                    200

Percentages of people who received Loans bought new cars:

Percentage = 2000-400 / 2000

Percentage = 1600/2000

Percentage = 80%

Percentages of people who received Loans bought used cars:

Percentage = 300 * 100 / 500

Percentage = 3/5 * 100

Percentage = 60%

Therefore, According to the survey, 60% of the people Who bought used cars got loans while 80% of people who bought new cars gets loan.

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Answer: To find the inverse of a function, we first need to make sure that the function is one-to-one, meaning that no two different input values map to the same output value.

If the function B is one-to-one, we can find the inverse by switching the x and y values, and then solving for y.

y = B^-1(x)

We can then use algebraic manipulation to solve for y.

For example, if B(x) = 2x + 1, we can find the inverse by switching x and y:

x = 2y + 1

Solving for y:

y = (x - 1)/2

So the inverse function of B(x) = 2x + 1 is B^-1(x) = (x - 1)/2

Please note that if the function B is not one-to-one, it will not have an inverse.

Step-by-step explanation:

Therefore, as a result, the answer to the given triangle issue is

ΔA"B"C "≅ ΔABC  is congruent.

A triangle qualifies as a polygon because it has sides or vertices. It is a basic geometric form. Triangle ABC refers to a triangle well with sides A, B, and C. Whenever the edges are not collinear, a single plane and triangle are produced in Euclidean geometry. Any triangle with three sides & three corners is referred to as a polygon.

Here,

Triangle ABC is reflected across the y-axis to form triangle A'B'C.

After that, triangle A was created by dilation by a factor of 3 "B"C".

Again for triangles ABC and A"B"C, determine the correct response."

So,

We are conscious that reflection goes through a thorough alteration,

thus the original object's size and shape remain unchanged.

After consideration, figures always correspond to their pictures.

A'B'C, ABC, etc (i)

Dilation is a flexible technique. The shape remains the same even though the size has changed.

As a result, figures after dilation invariably resemble their photos.

ΔA'B'C' ≅ ΔA "B"C" ... (ii)

I and (ii) together give us

ΔA"B"C "≅ ΔABC

ABC and ABC are triangles that are similar.

Therefore, option A is the best decision.

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The value of dc/dt when dp/dt = 41 and c = 15 is -41/75.

At any given time, the rate of change of the variables p and c with respect to time is denoted by dp/dt and dc/dt, respectively. The equation given to us is p^2 = (20-c)^3. We are given the values of dp/dt = 41 and c = 15. Thus, we are required to calculate the value of dc/dt.

To solve for dc/dt, we differentiate both sides of the equation with respect to time. On the left side, we get 2p*dp/dt, and on the right side, we get -3(20-c)^2*dc/dt. Equating both sides and solving for dc/dt, we get dc/dt = -41/(3(20-15)^2) = -41/75.

Hence, the value of dc/dt when dp/dt = 41 and c = 15 is -41/75.

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Due tο the 90 degree angle created by the axes at the origin and the measurements at point p, the system is knοwn as being rectangular.

What is Cartesian coordinate system?

A Cartesian coordinate system in a plane is a system of cοordinates that uniquely identifies each pοint by a pair of numerical coordinates. The coordinates (Xp, Yp) shοw where point p is in relation to the origin. Because the angle created by the axes at the οrigin and the angle created by the measurements at point p are bοth 90 degrees, the system is referred tο as rectangular. Thus, the measurement has sides of Xp and Yp, fοrming a rectangle.

These numerical coοrdinates are the signed distances from two fixed perpendicular οriented lines to the point, measured in the same unit of length.

In any case, for any convex polygon (including rectangle) the test is very simple: check each edge of the polygοn, assuming each edge is oriented in cοunterclockwise direction, and test whether the point lies tο the left of the edge (in the left-hand half-plane). If all edges pass the test - the pοint is inside. If at least οne fails - the point is outside.

In order to test whether the point (xp, yp) lies οn the left-hand side οf the edge (x1, y1) - (x2, y2), you just need tο calculate

D = (x2 - x1) * (yp - y1) - (xp - x1) * (y2 - y1)

If D > ∅, the pοint is on the left-hand side. If D < ∅, the point is on the right-hand side. If D = ∅, the pοint is on the line.

The previous versiοn of this answer described a seemingly different version οf left-hand side test . But it can be easily shοwn that it calculates the same value.

In order to test whether the point (xp, yp) liesοn the left-hand side of the edge (x1, y1) - (x2, y2), yοu need to build the line equation for the line containing the edge. The equatiοn is as follows

A × x + B × y + C = ∅

where

A = -(y2 - y1)

B = x2 - x1

C = -(A * x1 + B * y1)

Now all you need to dο is to calculate

D = A * xp + B * yp + C

If D > ∅, the pοint is on the left-hand side. If D < ∅, the point is on the right-hand side. If D = ∅, the point is on the line.

However, this test, again, wοrks for any convex polygon, meaning that it might be too generic fοr a rectangle. A rectangle might allow a simpler test... For example, in a rectangle (οr in any other parallelogram) the values of A and B have the same magnitude but different signs for opposing (i.e. parallel) edges, which can be explοited to simplify the test.

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Yes, the conditions to calculate a confidence interval for a proportion are satisfied.

n = 738

p = 170/738 = 0.2297

np ≥ 10 and n(1-p) ≥ 10

np = 0.2297*738 = 169.686 ≥ 10

n(1-p) = 738(1-0.2297) = 568.314 ≥ 10

Therefore, the conditions for calculating a confidence interval for a proportion are satisfied.

Yes, the conditions for calculating a confidence interval for a proportion are satisfied. The sample size of the poll was 738 randomly selected customers of a major U.S. cell-phone carrier. Out of these 738 customers, 170 had walked into something or someone while talking on a cell phone. This gives us a population proportion of 170/738 or 0.2297. We need to ensure that np ≥ 10 and n(1-p) ≥ 10. Calculating these values, np = 0.2297*738 = 169.686 which is greater than 10 and n(1-p) = 738(1-0.2297) = 568.314 which is also greater than 10. Therefore, the conditions for calculating a confidence interval for a proportion are satisfied.

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The graph of a system of two equations is a pair of lines in the plane for the two variables (x and y).

Simple sets of two or more linear equations make up a system of linear equations. A system of two equations has a graph that is a pair of lines in the plane for two variables (x and y).

Equations with the same variables are grouped together as systems of equations. The only difference is that you're using inequalities as opposed to equations when working with a system of inequalities. To resolve such a system, you must identify the values of the variables that will cause each inequality to be true simultaneously.

The first equation:

[tex]$y=\frac{1}{2} x+3$$[/tex]

[tex]$5 \stackrel{?}{=} \frac{1}{2}(4)+3 \quad$[/tex]

Plug in x = 4 and y = 5

5 = 5

The second equation:

y = x + 1

[tex]$5 \stackrel{?}{=} 4+1 \quad$[/tex] Plug in x = 4 and y = 5

5 = 5

(4,5) is indeed a solution.

Therefore, the correct answer is option b) (- 2.75, 0) and (2.75, 0).

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Answer: 156, 56, 336

Answer:

85,510 and 185.

Step-by-step explanation:

let the first number be "a"

let the second number be "b"

let the third number be "c"

we know that

b=6a

c=100+a and

a+b+c=780

If we substitute the first 2 equations on the third one we get:

a+6a+100+a=780

8a+100=780

8a=780-100

8a=680

8 8

a=85

b=6a

b=6×85

b=510

c=100+a

c=100+85

c=185

Answer:42.5

Step-by-step explanation:

A linear equation can be used to model this situation, where the volume of water in the tank (V) is equal to the initial volume plus the rate of flow multiplied by the number of minutes (t).

V = 55 + 8t

This equation can be used to find the volume of the water in the tank at a specific time. To find the volume of the water in the tank 25 minutes after Baxter begins filling it, we can substitute 25 for t in the equation:

V = 55 + 8(25) = 55 + 200 = 255 gallons

To find how many minutes it will take for Baxter to fill the tank if the maximum volume of water is 395 gallons, we can use the equation to solve for t.

395 = 55 + 8t

Subtract 55 from both sides:

340 = 8t

Divide both sides by 8:

t = 42.5

So, it will take 42.5 minutes for Baxter to fill the tank with a maximum volume of 395 gallons.

A linear equation can be used to model a situation where a quantity is changing at a constant rate.

Let V be the volume of water in the tank at time t in minutes.

The rate of change of the volume of water is 8 gallons per minute, so we can write the equation as:

V = 55 + 8t

This equation tells us that the volume of water in the tank is 55 gallons when t = 0 (at the start of filling the tank) and it increases by 8 gallons for every minute after that.

To find the volume of water in the tank 25 minutes after Baxter starts filling it, we can plug in t = 25 into the equation:

V = 55 + 8(25)

V = 55 + 200

V = 255 gallons

To find how many minutes it will take to fill the tank to the maximum volume of 395 gallons, we can use the equation and solve for t:

V = 55 + 8t

395 = 55 + 8t

340 = 8t

t = 340/8

t = 42.5 minutes

So it will take 42.5 minutes to fill the tank to the maximum volume of 395 gallons.