which is the best approximation of the volume of a cylinder with a radius of 10 mm, and a height of 5 mm? use 3.14 for pi.

The resulting three-dimensional figure has a base area of 50.27 square centimetres. Option (D) 314 sq. cm is the correct answer (rounded to the nearest whole number).

When a triangle is rotated 360 degrees around one of its sides, it forms a cone with a base equal to the rotated side's length and a height equal to the perpendicular distance from the cone's apex to the rotated side.

In this case, the rotated side is 8 cm long. The Pythagorean theorem can be used to calculate the perpendicular distance from the apex of the cone to the rotated side. Heron's formula can be used to calculate the triangle's height:

s =(6+8+10)/2 = 12

(s(s-6)(s-8)(s-10)) = (12(6)(4)(2)) = 243

The triangle's height is:

h = 2 * Area / 8 = 3√3

The radius of the cone's base is 8/2 = 4 cm. As a result, the volume of the cone is as follows:

V = (1/3) * π * r^2 * h = (1/3) * π * 4^2 * 3√3 ≈ 50.27 cm^3

The resulting three-dimensional figure has the same base area as a circle with a radius of 4 cm, which is:

A = π * r^2 = π * 4^2 ≈ 50.27 cm^2

As a result, the resulting three-dimensional figure has an approximate base area of 50.27 square centimetres. Option (D) 314 sq. cm is the correct answer (rounded to the nearest whole number).

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Answer: answer is d) 314 sq. cm

Step-by-step explanation: hope this helps!

Answer:

Step-by-step explanation:

Head: 220 times, tail 80 times. Find the probability of occurrence of each of events. 2.

The approximate circumference of Spaceship Earth is approximately 138.02 meters.

A circle's perimeter is known as its circumference. It is the circumference of the circle as a whole. A circle's circumference is calculated by multiplying its diameter by the constant. This measurement of a circle's diameter is necessary for someone crossing a circular park or for enclosing a circle. The units for the circumference, which is a linear variable, are the same as those for length.

The volume of the sphere is given as:

V = (4/3)πr³

Substituting the values:

[tex]r = (3(65,417)/4(3.14))^{(1/3)} = 21.96 meters[/tex]

The circumference of the circle is:

C = 2πr

Substituting the value of r:

C = 2(3.14)(21.96) = 138.02 meters

Hence, the approximate circumference of Spaceship Earth is approximately 138.02 meters.

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Therefore, it would take about 3322 years for the Gregorian and tropical years to be out of step by exactly one day.

Length is a physical quantity that describes how long or how far apart two points or objects are from each other in space. It is typically measured in units such as meters, feet, or inches, and is one of the basic dimensions used to describe the size and position of objects in the physical world.

given by the question.

The difference between the length of the Gregorian year and the tropical year is:

365.242500 - 365.242199 = 0.000301

This means that every year, the Gregorian calendar gains 0.000301 days on the tropical year. To be out of step by exactly one day, the Gregorian calendar needs to gain one full day on the tropical year, which would take:

1 / 0.000301 = 3322.26 years.

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Answer:

There are different ways to approach this problem, but one possible method is:

Define the event A as "the student owns a trampoline".

Find the probability of A: P(A) = 21/23, because 21 out of 23 students said they owned a trampoline.

Find the probability of the complement of A, which is "the student does not own a trampoline". We can denote this event as A', and it is equivalent to "the student is one of the 2 students who did not say they owned a trampoline". Therefore, P(A') = 2/23.

Check that P(A) + P(A') = 1, because the student either owns a trampoline or does not.

Answer the question: the probability that the student does not own a trampoline is P(A') = 2/23, or approximately 0.087 or 8.7% (rounded to one decimal place).

Therefore, the answer is: the probability that the student does not own a trampoline is 2/23, or approximately 0.087 or 8.7%.

The height of the house with an angel of elevation 25° from the line of sight of the observer is equal to 10 ft to the nearest foot.

The angle of elevation is the angle between the horizontal line and the line of sight which is above the horizontal line.

The height of the house is the sum of length from her eyes to the ground and the perpendicular length from her eyes to the top of the house.

we shall represent the perpendicular length from her eyes to the top of the house with x so that;

tan 25° = x/11 {opposite/adjacent}

x = 11 × tan 25°

x = 5.1294

height of the house = 5 ft + 5.1294 ft

height of the house = 10.1294 ft

Therefore, the height of the house with an angel of elevation 25° from the line of sight of the observer is equal to 10 ft to the nearest foot.

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Possible question:

Figure out the height of the house using these measurements. She's standing 11 feet from the house, her eyes are 5 feet from the ground, and the angle of elevation to the top of house is 25 degrees.

From the given graph, the points (1, 3) lies on dotted lines, thus they are not taken in the solution set for the inequality.

When expressions are compared using the operators "less than" (<), "less than or equal to" (<=), "greater than" (>), or "greater than or equal to" (>=), an inequality is created.

From the graph, the shaded region shows the solution for the inequality.

As we can see that the curve is drawn with the broken lines,the points lying on the curve will no be taken as in solution set of  inequality.

Thus,  the points (1, 3) lies on dotted lines, thus they are not taken in the solution set for the inequality.

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Complete question:

Which point is not included in the solution set for the inequality? (–2, 1) (1, 3) (4, 3) (5, -1)?

The graph for the question is attached.

If 30,15,90 and x are in proportion the value of x is 5.

The given terms 30, 15, 90 and x are in proportion, so they follow the proportion formula:

a : b = c : x.

We can use this to solve for the value of x.

First, let's set up the equation:

30 : 15 = 90 : x

To solve for x, we must multiply both sides of the equation by 15:

30 * 15 = 90 * x

Now we have:

450 = 90x

To solve for x, we need to divide both sides by 90:

450 / 90 = 90x / 90

Which simplifies to:

x = 5

Therefore, the value of x is 5.

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Answer: $35.05

Step-by-step explanation:

10% of 350.52 ≈ 35.05

Using arithmetic operation it is obtained that Austin should pour 11.74 more grams of salt to reach his desired amount of 50.94 grams.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

To determine how much more salt Austin should pour, we need to subtract the amount of salt he has poured from the total amount he wants to pour -

Use the arithmetic operation of subtraction.

Total amount of salt = 50.94 grams

Amount of salt poured so far = 39.2 grams

Therefore, the amount of salt that Austin still needs to pour is obtained by the expression -

50.94 grams - 39.2 grams = 11.74 grams

Therefore, Austin should pour 11.74 more grams of salt.

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The percentage of students who played video games in the survey is 52%.

To find this percentage, we first need to calculate the fraction of students who played video games. This can be done by dividing the number of students who played video games by the total number of students surveyed:

Fraction of students who played video games = 130/250

Simplifying this fraction by dividing both the numerator and denominator by 10, we get:

Fraction of students who played video games = 13/25

To convert this fraction to a percentage, we can multiply it by 100:

Percentage of students who played video games = (13/25) * 100

Simplifying this expression, we get:

Percentage of students who played video games = 52%

Therefore, 52% of the students in the survey played video games.

Hence, to find the percentage of students who played video games in a survey, we divide the number of students who played video games by the total number of students surveyed and then multiply the resulting fraction by 100 to get the percentage.

In this case, 130 out of 250 students played video games, so the percentage is 52%.

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Answer: The correct answer is "Fail to reject the null hypothesis. There is not enough evidence to oppose the company's claim."

Step-by-step explanation:

I took the test

It will be angle JZF.

Because if you add both of them, sum will be equal to 180°.

Answer:

The savings for the property investor would be $63,750 - $63,011.23 = $738.77, which is the answer to option B, $340,329.83.

Step-by-step explanation:

What is the interest?

Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.

To calculate the savings, we need to calculate the total amount of interest paid over the life of the loan for both options, and then subtract the smaller amount from the larger amount.

For the fixed-rate loan, the total amount of interest paid can be calculated by multiplying the interest rate by the loan amount and dividing it by the number of payments over the life of the loan:

$1,750,000 * 3% / (12 * 20) = $63,750

The total amount of interest paid over the life of the loan for the fixed-rate loan would be $63,750.

For the balloon mortgage, the total amount of interest paid can be calculated by subtracting the balloon payment from the loan amount and dividing it by the number of payments over the life of the loan:

($1,750,000 - $1,423,723) * 2.5% / (12 * 6) = $63,011.23

The total amount of interest paid over the life of the loan for the balloon mortgage would be $63,011.23.

Therefore, the savings for the property investor would be $63,750 - $63,011.23 = $738.77, which is the answer to option B, $340,329.83.

Answer:

the answe is B

Step-by-step explanation:

The savings for the property investor would be $63,750 - $63,011.23 = $738.77, which is the answer to option B, $340,329.83.

What is the interest?

Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.

To calculate the savings, we need to calculate the total amount of interest paid over the life of the loan for both options, and then subtract the smaller amount from the larger amount.

For the fixed-rate loan, the total amount of interest paid can be calculated by multiplying the interest rate by the loan amount and dividing it by the number of payments over the life of the loan:

$1,750,000 * 3% / (12 * 20) = $63,750

The total amount of interest paid over the life of the loan for the fixed-rate loan would be $63,750.

For the balloon mortgage, the total amount of interest paid can be calculated by subtracting the balloon payment from the loan amount and dividing it by the number of payments over the life of the loan:

($1,750,000 - $1,423,723) * 2.5% / (12 * 6) = $63,011.23

The total amount of interest paid over the life of the loan for the balloon mortgage would be $63,011.23.

Therefore, the savings for the property investor would be $63,750 - $63,011.23 = $738.77, which is the answer to option B, $340,329.83.

Answer:

a quarter of an hour, or 15 minutes is equal to 15 minutes × 60 = 90 seconds a quarter of an hour, or 15 minutes is equal to 15 minutes × 60 = 90 seconds

Answer:

90 seconds

Step-by-step explanation: We know that,

A quarter of an hour= 60×1/4 =15 mins

15 minutes is equal to 15 minutes × 60 = 90 seconds.

Jeriel would need to invest approximately $98,986.25 for the value of the account to reach $137,000 in 5 years, assuming continuous compounding.

The formula accrued amount compounded continuously is expressed as;

A = P × e^(rt)

Where A is accrued amount, P is principal, r is interest rate and t is time.

In this case, we are given that the final amount to be $137,000, the interest rate is 6.5% and the time is 5 years.

We want to solve for Principal P.

First, convert R as a percent to r as a decimal

r = R/100

r = 6.5/100

r = 0.065 per year

Plug these values into the above formula and solve for P.

A = P × e^(rt)

P = A / e^(rt)

P = 137,000.00 / e^(0.065 × 5)

p = $98,986.25

Therefore, the value of the principal P is $98,986.25.

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Total number of  cups of berries does the school cafeteria have is 600

Addition is a basic mathematical operation that involves combining two or more numbers or quantities to find a total or sum. In other words, it is the process of finding the total amount when two or more numbers are added together.

To find the total number of cups of berries in the school cafeteria, you can add the number of cups of strawberries and blackberries.

The school cafeteria has 150 cups of strawberries and 450 cups of blackberries, so

Total cups of berries = cups of strawberries + cups of blackberries

Total cups of berries = 150 + 450

Total cups of berries = 600

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The volume of the solid is 1.5 cubic units. From the solid in the first octant under the plane z = x + y, above the surface z = xy, and enclosed by the surfaces x = 0, y = 0, and x2 + y2 = 4

To find the volume of the solid by subtracting two volumes, we need to find the limits of integration for x, y, and z.

From the given information, we know that the solid is in the first octant and is enclosed by the surfaces x = 0, y = 0, and x2 + y2 = 4. Thus, the limits of integration for x and y are 0 to 2 since the radius of the circle x2 + y2 = 4 is 2.

Next, we need to find the limits of integration for z. To do this, we need to set the two given equations equal to each other:

xy = x + y

xy - x - y = 0

Using partial fraction decomposition:

xy - x - y = (x - 1)(y - 1) - 1

So, we have:

(x - 1)(y - 1) = z - 1

Thus, the limits of integration for z are 1 to 3.

Now, we can set up the integral to find the volume:

V = ∫∫∫ dV

V = ∫0^2 ∫0^(2 - x) ∫1^(x + y) dz dy dx

Evaluating this integral, we get the volume of the solid as 1.5 cubic units.

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We can deduce that X + 4 = 8 by looking at the top row & second column. The X value is therefore 4.

an arrangement of written or printed items on a page that are vertical. a vertical part of a printed page divided into two or more equal columns of numbers.

X + 4 corresponds to a value in the second column and top row.

The third row's value is equal to the first column's value plus two.

(Third row, second column) The value is 12 at the bottom right corner.

First row and the first column, top left, represents value as B.

It reads 8, first row, second column, in the upper right corner.

C is the value located on the bottom left (third row, first column).

We can deduce that X + 4 equals 8 from top row & second column. Hence, we can find X:

X plus 4 = 8

When we take 4 away from both sides, you get:

X = 4

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The households using television (HUT) figure is 75.06%.

The households using television (HUT) figure is a measure of the percentage of households that have turned on their televisions at a particular time. It is calculated by dividing the number of households watching TV by the total number of households and multiplying by 100%.

In this case, we are given that 90 million households in the US turned on their televisions at 8:00 p.m. on a Sunday night. The total number of US households is 119.9 million. Using this information, we can calculate the HUT figure as follows

Households using television (HUT) = (Number of households watching TV / Total number of households) x 100%

HUT = (90 million / 119.9 million) x 100%

HUT = 75.06%

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Photosynthesis is maximum in red light because chlorophyll, the primary pigment responsible for capturing light energy in plants, absorbs red light most efficiently.

What is red light in Photosynthesis?

Red light is a part of the electromagnetic spectrum with a longer wavelength and lower energy than blue and green light.

Red light is particularly effective for photosynthesis because it has a longer wavelength and lower energy, which allows chlorophyll to efficiently absorb it and use it for the photosynthetic process.

In photosynthesis, plants use light energy to synthesize glucose from carbon dioxide and water.

As a result, photosynthesis is maximum in red light because plants can absorb and utilize this light energy most efficiently for their growth and energy production.

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Answer:

The volume of a sphere is given by the formula:

V = (4/3)πr^3

where r is the radius of the sphere.

Since the diameter of Casper's balloon is 6 inches, the radius is 3 inches. Therefore, the volume of Casper's balloon is:

V1 = (4/3)π(3 inches)^3 = 113.1 cubic inches (approx.)

We know that Casper's balloon is seven times the volume of his brother's balloon. Let's call the volume of his brother's balloon V2. We can set up an equation:

V1 = 7V2

Substituting the value of V1, we get:

113.1 cubic inches = 7V2

Dividing both sides by 7, we get:

V2 = 16.2 cubic inches (approx.)

Therefore, the approximate volume of Casper's brother's balloon is 16.2 cubic inches.

The distance between points F and G is 12.806 units. The coordinates of F are (6,6) and the coordinates of G are (16,14).

Distance in a graph is a measure of the difference between two points. It is calculated as the shortest path between two points in a graph, usually measured in terms of the number of edges that must be traversed to get from one point to the other. Distance can also be measured in terms of the number of vertices that must be crossed to get from one point to the other.

The distance between two points F and G in the graph can be calculated using the distance formula.

The distance formula states that the distance between two points (x1, y1) and (x2, y2) =√ (x2-x1)² + (y2-y1)²

Therefore, to calculate the distance between points F and G, we will use the distance formula.

The coordinates of F are (6,6) and the coordinates of G are (16,14).

Substituting these values into the distance formula, we get the following:

Distance = √(16 - 6)² + (14 - 6)²

Distance = √100 + 64

Distance = √164

Distance = 12.806

The distance between points F and G is 12.806 units.

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As a question-answering bot, I cannot provide the solution of this question as it requires the use of MATLAB software which cannot be done in this platform. However, I can provide a general overview and steps that can be followed to solve the problem.  List all maximal orthogonal subsets of the above set. That is, group the vectors v, w, x, y, and z in as many ways as possible so that all the vectors in your group are orthogonal to each other and none of the vectors outside the group are orthogonal to all the vectors in the group. The maximal orthogonal subsets of the above set are: {v, y}, {w, x}, {z}b. Take the largest orthogonal subset and normalize all the vectors in that set as follows: >> V-v/norm(v) This code replaces v with itself divided by its size-so we get a vector pointing in the same direction but with length 1. The above code normalizes v, so you'll have to normalize the other vectors in your orthogonal subset as well, replacing v with the appropriate letter. Store the resulting vectors in MATLAB as columns of a matrix W. Enter them in alphabetical order from left to right.The largest orthogonal subset is {w, x}. The normalized vectors are w/norm(w) and x/norm(x). Store the resulting vectors in MATLAB as columns of a matrix W and enter them in alphabetical order from left to right. The resulting matrix would be: W = [1/√19 6/√19; 3/√19 1/√19; 0 -3/√19]Note: This solution is based on the assumption that the vectors are given in column form.

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Answer:

x = 80

y = 160

Step-by-step explanation:

The sum of all arc measures that make up a circle is 360°. Therefore:

[tex]\implies 200^{\circ} + y^{\circ} = 360^{\circ}[/tex]

[tex]\implies 200^{\circ} + y^{\circ} - 200^{\circ} = 360^{\circ} - 200^{\circ}[/tex]

[tex]\implies y^{\circ} = 160^{\circ}[/tex]

[tex]\implies y=160[/tex]

If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one-half the measure of its intercepted arc.

Therefore, according to the Tangent and Intersected Chord Theorem, the measure of angle x is equal to half of the measure of arc y:

[tex]\implies x^{\circ}=\dfrac{1}{2} y^{\circ}[/tex]

[tex]\implies x^{\circ}=\dfrac{1}{2} \cdot 160^{\circ}[/tex]

[tex]\implies x^{\circ}=80^{\circ}[/tex]

[tex]\implies x=80[/tex]

[tex]\hrulefill[/tex]

Answer: 5.7 inches

Step-by-step explanation:

To find the width of the home in the scale drawing, we can use algebra to solve for w.

First, we can simplify the equation w/0.6 = 9.5 by multiplying both sides by 0.6:

w/0.6 * 0.6 = 9.5 * 0.6

w = 5.7 inches

Therefore, the width of the home in the scale drawing is 5.7 inches.

Answer:

1 1/2 m

Step-by-step explanation:

A = LW

3 3/4 = L × 2 1/2

15/4 = 5L/2

L = 15/4 × 2/5

L = (3 × 5 × 2)/(2 × 2 × 5)

L = 3/2 = 1 1/2

Answer: 1 1/2 m

Answer:

$54.50

Step-by-step explanation:

$67.58 after 6% tax and 18% tip

Let x = pretax and pre-tip amount.

The amount of tax is 0.06x.

The amount of tip is 0.18x.

The total amount is x + 0.06x + 0.18x = 1.24x.

The amount after tax and tip is $67.58.

1.24x = 67.58

x = 67.58/1.24

x = 54.5

Answer: $54.50

The numerator of the fraction is 2.

The fraction can be written as 2/7, and since the numerator is nine less than the denominator, when the fraction reduces to (1/7) it means that the numerator must be 2.

To solve this problem, first determine what is given in the question: a fraction with a numerator that is nine less than the denominator, and that reduces to (1/7).

Using this information, the goal is to determine the numerator of the fraction.

To do this, simply subtract nine from the denominator and the result will be the numerator. In this case, the denominator is 7, so subtracting 9 from 7 gives us 2, which is the numerator of the fraction.

Therefore, the numerator of the fraction is 2.

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In this instance, the buoy forms the right corner of a triangle made up of the two ships and the buoy. To the closest tenth, the distance between the two ships is roughly  [tex]24.1[/tex] km.

To find the distance between the two ships, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the legs

(the sides that form the right angle) is equal to the square of the length of the hypotenuse (the side opposite the right angle).

In this case, the two ships and the buoy form a right triangle, with the buoy at the right angle.

Let d be the distance between the two ships, x be the distance of the northern ship to the buoy and y be the distance of the eastern ship to the buoy. Then we have:

[tex]d^2 = x^2 + y^2[/tex]

Substituting the given values, we get:

[tex]d^2 = (20 km)^2 + (13.5 km)^2[/tex]

[tex]d^2 = 400 km^2 + 182.25 km^2[/tex]

[tex]d^2 = 582.25 km^2[/tex]

[tex]d ≈ 24.1 km[/tex]

Therefore, the distance between the two ships is approximately 24.1 km, rounded to the nearest tenth.

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