A cylinder has a base radius of 5 centimeters and a height of 17 centimeters. What is its volume in cubic centimeters, to the nearest tenths place?

a) The particle is moving to the right in the interval (0, 1/6) and (7/2, 5).

b) The particle is moving to the left in the interval (1/6, 7/2).

a) The particle is moving to the right when the velocity function is positive.

Let's find the velocity function v(t) by taking the derivative of the position function s(t):

v(t) = s'(t) = 12t^2 - 44t + 7

To determine the intervals where the particle is moving to the right, we need to find the values of t for which v(t) > 0.

Setting v(t) > 0:

\(12t^2 - 44t + 7 > 0\)

To solve this inequality, we can factor or use the quadratic formula:

The quadratic equation 12t^2 - 44t + 7 = 0 does not factor nicely, so let's use the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 12, b = -44, and c = 7. Substituting these values into the quadratic formula:

t = (-(-44) ± √((-44)^2 - 4(12)(7))) / (2(12))

t = (44 ± √(1936 - 336)) / 24

t = (44 ± √(1600)) / 24

t = (44 ± 40) / 24

Simplifying:

t = (44 + 40) / 24 = 84 / 24 = 7/2

t = (44 - 40) / 24 = 4 / 24 = 1/6

So the solutions to the quadratic equation are t = 7/2 and t = 1/6.

Now, we need to test the intervals:

For t < 1/6: Substitute a value less than 1/6 into the velocity function:

\(v(0) = 12(0)^2 - 44(0) + 7 = 7 > 0\)

For 1/6 < t < 7/2: Substitute a value between 1/6 and 7/2 into the velocity function:

\(v(1) = 12(1)^2 - 44(1) + 7 = -25 < 0\)

For t > 7/2: Substitute a value greater than 7/2 into the velocity function:

\(v(5) = 12(5)^2 - 44(5) + 7 = 43 > 0\)

Therefore, the particle is moving to the right in the interval (0, 1/6) and (7/2, 5).

b) The particle is moving to the left when the velocity function is negative.

To determine the intervals where the particle is moving to the left, we need to find the values of t for which v(t) < 0.

Setting v(t) < 0:

\(12t^2 - 44t + 7 < 0\)

We already found the solutions to the quadratic equation as t = 7/2 and t = 1/6. Now we need to test the intervals:

For 1/6 < t < 7/2: Substitute a value between 1/6 and 7/2 into the velocity function:

\(v(2) = 12(2)^2 - 44(2) + 7 = -13 < 0\)

Therefore, the particle is moving to the left in the interval (1/6, 7/2).

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The number of people are 72.

Highest Common Factor is the full name for HCF in mathematics.

According to the laws of mathematics, the highest positive integer that divides two or more positive integers without leaving a residual is known as the greatest common divisor, or gcd.

Least Common Multiple is the full name for LCM in mathematics.

LCM (a,b) in mathematics stands for the least common multiple, or LCM, of two numbers, such as a and b. The smallest or least positive integer that is divisible by both a and b is known as the LCM.

We need to know the size of the pieces in order to calculate how many people can be fed equal-sized pieces of cake from a 16 by 18-inch cake.

Assume that each piece is a square with sides measuring "x" in length. Each piece's area would be x², and the cake's overall area would be 16 x 18 inches, or 288 square inches.

We must divide the entire area of the cake by the area of each piece to determine the maximum number of pieces that can be cut from the cake:

288 / x² = (16*18) / x² = 288 / x²

Choosing a "x" value that evenly splits into 16 and 18 is necessary if we want every piece to be the exact same size. Since 2 is the greatest possible value, we can divide the cake into 8 rows of 9 squares, yielding a total of 72 pieces.

As a result, a cake measuring 16 inches by 18 inches can be divided into 72 equal-sized pieces, each measuring 2 inches by 2 inches.

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We can serve 18 people equal-sized pieces of cake from a cake that is 16 inches by 18 inches, assuming each piece is a square and we want the pieces to be exactly the same size.

A two-dimensional figure, form, or planar lamina's area is a measurement of how much space it takes up in the plane.

To find out how many people can be served equal-sized pieces of cake from a cake that is 16 inches by 18 inches, we need to first determine the size of each piece of cake.

The total area of the cake is:

16 inches x 18 inches = 288 square inches

To divide the cake into equal-sized pieces, we need to determine the size of each piece. Let's assume we want each piece to be a square. To find the size of each square, we need to find the square root of the total area of the cake:

√(288 square inches) ≈ 16.97 inches

Since we want the pieces to be exactly the same size, we'll round down to the nearest inch, which gives us:

Each piece of cake will be approximately 16 inches by 16 inches.

To find out how many people can be served equal-sized pieces of cake, we need to divide the total area of the cake by the area of each piece:

288 square inches ÷ (16 inches x 16 inches) = 18

Therefore, we can serve 18 people equal-sized pieces of cake from a cake that is 16 inches by 18 inches, assuming each piece is a square and we want the pieces to be exactly the same size.

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Answer:

52.15

Step-by-step explanation:

52.149

Since last digit is 9,

The tenth digit, which is 4 gets rounded to 5.

Therefore answer: 52.15

Answer: 52.15

Step-by-step explanation: you would round to .05 because the 9 is bigger than five. greater than five round up less than 4 keep the same :) hopes this helps

The decline in the number of farms means there is a reduction in the number of farms

The number of US farms after 5 years is 3584818

The equation that represents the number of farms is given as:

\(y=3962000e^{-0.02t\)

After 5 years, the value of t is 5.

So, we have:

\(y=3962000e^{-0.02*5\)

Evaluate the product

\(y=3962000e^{-0.1\)

Evaluate the exponent

\(y=3962000*0.9048\)

Evaluate the product

\(y=3584817.6\)

Approximate

\(y=3584818\)

Hence, the number of US farms after 5 years is 3584818

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Answer:

I believe it should come in the mail and online x

The probability that the height of a randomly chosen child is between 44.75 and 58.35 inches is approximately 0.8830.

To solve this problem, we need to find the area under the normal curve between the two given heights.

We can use the standard normal distribution by converting the given values into z-scores. The formula for calculating a z-score is

z = (x - μ) / σ

where x is the value we want to convert, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

For the lower bound of 44.75 inches

z1 = (44.75 - 53.3) / 4.3 = -1.98

For the upper bound of 58.35 inches

z2 = (58.35 - 53.3) / 4.3 = 1.17

Now, we need to find the area under the normal curve between these two z-scores. We can use a standard normal table or a calculator to find this probability.

Using a standard normal table, the probability of z being between -1.98 and 1.17 is approximately 0.8830.

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The solution to the equation |2 y-4|=12 and extraneous solution is y = 8 and y = -4 respectively.

Given equation is;

|2 y-4|=12

Now we have two cases;

Case 1: 2y - 4 = 12

Case 2: -(2y - 4) = 12  

Case 1: 2y - 4 = 12

Adding 4 to both sides

2y = 16

Dividing by 2 on both sides

y = 8

which satisfies the given equation |2 y-4|=12.

Hence, y = 8 is the solution.

Case 2: -(2y - 4) = 12

Multiplying negative sign throughout

2y - 4 = -12

Adding 4 to both sides

2y = -8

Dividing by 2 on both sides

y = -4

which does not satisfy the given equation |2 y-4|=12.

Hence, y = -4 is the extraneous solution.

Therefore, the solutions to the equation |2 y-4|=12 and check for extraneous solutions are y = 8 and y = -4 respectively.

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To estimate the mean BMI (m) in the population of American young women with a confidence interval of ±1 and 99% confidence, we can use the formula:

n = (Z * σ / E)^2

Where:

n = required sample size

Z = Z-value corresponding to the desired confidence level (99% confidence level corresponds to Z = 2.576)

σ = standard deviation of the population (given as 7.5)

E = margin of error (±1)

Plugging in the values, we have:

n = (2.576 * 7.5 / 1)^2

n = (19.314 / 1)^2

n = 372.36

Rounding up to the nearest whole number, we need a sample size of approximately 373 to estimate the mean BMI in the population with a 99% confidence level and a margin of error of ±1.

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Answer:

Solution,

Let,(x1,y1)=(-4,-3)

     (x2,y2)=(3,5)

Using distance formula,

AB=√(x2-x1)²+(y2-y1)²

    =√(3+4)²+(5+3)²

    =√49+64

    =√113 units.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relevant trig relations:

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

__

In this triangle this means ...

  sin(50°) = b/14   ⇒   b = 14·sin(50°) ≈ 10.7

  cos(50°) = a/14   ⇒   a = 14·cos(50°) ≈ 9.0

Of course, the other acute angle, A, is the complement of the given one:

  A = 90° -50° = 40°

So you have ...

Answer:In(e^3 x^4) simplifies to 3x^4.

Step-by-step explanation:

In(e^3 x^4) simplifies to just 3x^4, since the natural logarithm (ln or In) and exponential function (e^x) are inverse functions of each other.

To see why, recall that ln(e^y) = y for any real number y, and e^(ln x) = x for any positive real number x. Therefore:

ln(e^3 x^4) = 3x^4 ln(e)   (using the rule ln(xy) = ln(x) + ln(y) and ln(e) = 1)

= 3x^4 * 1   (since ln(e) = 1)

= 3x^4

Answer:

8n is the same as 8 times a number.

That means...

Continuation:

\(8 * n = 128\)

\(128 \div 8 = n\)

\(128 \div 8 = 16\)

Therefore, n is 16.

The t- test test's sizes for samples 1 and 2 are n1 and n2, respectively.

What can you infer from a sample t-test?

df for one sample t-test is n-1

where n is sample size

df for independent sample t-test is n1+n2-2

where n1 and n2 are respective sample sizes for sample 1 and sample 2 .

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To approximate the solution and maximize the given objective function we need to find the steepest ascent direction and iteratively update the values of x₁ and x₂ to approach the maximum value of z.

The method of steepest ascent involves finding the direction that leads to the maximum increase in the objective function and updating the values of the decision variables accordingly. In this case, we aim to maximize the objective function z = -(x₁ - 3)² - (x₂ - 2)².

To find the steepest ascent direction, we can take the gradient of the objective function with respect to x₁ and x₂. The gradient represents the direction of the steepest increase in the objective function. In this case, the gradient is given by (∂z/∂x₁, ∂z/∂x₂) = (-2(x₁ - 3), -2(x₂ - 2)).

Starting with initial values for x₁ and x₂, we can update their values iteratively by adding a fraction of the gradient to each variable. The fraction determines the step size or learning rate and should be chosen carefully to ensure convergence to the maximum value of z.

By repeatedly updating the values of x₁ and x₂ in the direction of steepest ascent, we can approach the solution that maximizes the objective function z. The process continues until convergence is achieved or a predefined stopping criterion is met.

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The middle 50% of the distribution for X, the bounds of which form the distance represented by the IQR, lies between the first and third quartiles of the data set.

Specifically, the first quartile (Q1) marks the 25th percentile of the data set, while the third quartile (Q3) marks the 75th percentile.

The difference between Q3 and Q1 is known as the interquartile range (IQR).The IQR is a helpful measure of spread in a data set since it excludes outliers from the calculation. Outliers are any data points that fall outside of 1.5 times the IQR above the third quartile or below the first quartile of the data set. Therefore, the middle 50% of the distribution for X lies between Q1 and Q3, with the IQR representing the range of values between these two quartiles.

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Answer:

SAS similarity theorem

Step-by-step explanation:

Both the triangles are similar by SAS similarity theorem.

1.1) The volume of the cube is 27 cubic centimeters. 1.2)the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) the mass of the water cube is 27 grams. 1.4) the weight of the water and the ice would be the same under the same conditions. 1.5)In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

1.1) The volume of the cube can be calculated using the equation: Volume = width x height x length. In this case, the cube measures 3 cm wide, 3 cm tall, and 3 cm long, so the volume is:

Volume = 3 cm x 3 cm x 3 cm = 27 cm³.

Therefore, the volume of the cube is 27 cubic centimeters.

1.2) Density is defined as mass divided by volume. The mass of the ice cube is given as 24.76 grams, and we already determined the volume to be 27 cm³. Therefore, the density of the ice cube is:

Density = Mass / Volume = 24.76 g / 27 cm³ ≈ 0.917 g/cm³.

Therefore, the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) The volume of the water cube is the same as the ice cube, which is 27 cm³. Given the density of liquid water as 1.00 g/cm³, we can calculate the mass of the water cube using the equation:

Mass = Density x Volume = 1.00 g/cm³ x 27 cm³ = 27 grams.

Therefore, the mass of the water cube is 27 grams.

1.4) The weight of an object depends on both its mass and the acceleration due to gravity. Since the volume of the water cube and the ice cube is the same (27 cm³), and the mass of the water cube (27 grams) is equal to the mass of the ice cube (24.76 grams), their weights would also be equal when measured in the same gravitational field.

Therefore, the weight of the water and the ice would be the same under the same conditions.

1.5) Ice floats on water because it is less dense than liquid water. The density of ice is lower than the density of water because the water molecules in the solid ice are arranged in a specific lattice structure with open spaces. This arrangement causes ice to have a lower density compared to liquid water, where the molecules are closer together.

When ice is placed in water, the denser water molecules exert an upward buoyant force on the less dense ice, causing it to float. The buoyant force is the result of the pressure difference between the top and bottom surfaces of the submerged object.

In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

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Answer:

Step-by-step explanation:

In a parallelogram,

 ⇒the angles adjacent to each other

    ⇒ are of the same measure

        ⇒so

             ∠A = ∠C

             ∠B = ∠D

Let's solve:

           \(7z +5 = 8z - 10\\5+10=8z-7z\\8z-7z=5+10\\z = 15\)

           \(5w-30=3w+10\\5w-3w=30+10\\2w = 40\\w=20\)

Let's check:

 ⇒ for all quadrilaterals like a parallelogram

    ⇒all the angle measures added up to 360, so:

     \((7z+5)+(8z-10)+(5w-30)+(3w+10)=360\\(7(15)+5)+(8(15)-10)+(5(20)-30)+(3(20)+10)=360\\(105+5)+(120-10)+(100-30)+(60+10)=360\\110+110+70+70=360\\220+140=360\\360=360\)

Thus:

  Answer: w = 20 and z = 15

Hope that helps!    

It should be noted that the opposite angles of a parallelogram are equivalent. Therefore, ∠A = ∠C and ∠B = ∠D.

Given:

Therefore, we obtain the following equations;

⇒ 7z + 5 = 8z - 10   and   5w - 30 = 3w + 10

Let us simplify each equation one by one.

Answer:

1

Step-by-step explanation:

Because, The mode is the value that appears most often in a set of data values. If X is a discrete random variable, the mode is the value x at which the probability mass function takes its maximum value. In other words, it is the value that is most likely to be sampled.

The expression 2^7 times 19 can be simplified by first evaluating the exponential term, 2^7, which is equal to 128. Therefore:2^7 times 19 = 128 * 19We can then evaluate the product of 128 and 19 using multiplication. When we do that, we get:2^7 times 19 = 2432Therefore, the choice that is equivalent to the expression 2^7 times 19 is 2432

Answer:

x=0

Step-by-step explanation:

Answer:

Any real number.

Step-by-step explanation:

3x + 15 = 2x + 10 + x + 5

First, add like terms.

3x + 15 = 3x + 15

Subtract 15 on both sides.

3x = 3x

Divide 3 on both sides.

x = x

Since x equals x, you can give any value (any real number) to x.

Since 3x = 3x, you can say x = 1, meaning 3 = 3.

Or, you can say x = 8. 3x = 3x will be 24 = 24.

x can be any number.

Answer:

Answer below

Step-by-step explanation:

The meaning of congruence in Maths is when two figures are similar to each other based on their shape and size.

Answer:exactly equal shape and size

Step-by-step explanation:

Answer:

Step-by-step explanation:

Height of model = 20 ft ⋅ (2 in)/(5 ft) = 8 in

Answer:

side length c = 8

side length d = 3

Step-by-step explanation:

The conversion factor is 2

That is because you take the bigger triangle and divide the side length with the smaller triangle

10/2 = 5

In order to find the side length C, take the length of the smaller triangle and multiply it by 2.

4 * 2 = 8

the length of the side length C is 8

Now, because it goes from the bigger triangle to the smaller triangle, do the opposite and divide 6/2, which equals 3.

The length of side length d is 3.

side length c = 8

side length d = 3

Answer:

10 ft.

Step-by-step explanation:

V = Bh where B = area of the base, which is a circle in your problem.

So, B = \(\pi r^{2}\)

225π = π\(r^{2}\)(9)

\(r^{2}\) = 25

r = 5 ft

diameter = 2r = 10 ft.

Answer: Rectangle, Rhombus, Square

Step-by-step explanation: