A furniture maker cut a wooden log shaped like a cylinder and sanded the entire surface of it. The log had a radius of 2 in. and a volume of 96π in.^3 How many square inches of the log did the furniture maker sand in terms of π? PLEASE THANKUUUSM

Enter the correct answer in the box in terms of π.
____________ in^2

 (√7)^3  is equal to 7^(3/2)

The Power of a Power Property

The Power of a Power Property states that when you have a base raised to an exponent, and that base is also raised to an exponent, you can simplify the expression by multiplying the exponents.

For example, (a^x)^y = a^(xy)

In the case of square root of 7^3, the expression (√7)^3 can be written in the form of base and exponent, where the base is √7 and the exponent is 3.

Now, we can use the Power of a Power Property to simplify the expression, by multiplying the exponents.

So, (√7)^3 = (7^(1/2))^3 = 7^(1/2 * 3) = 7^(3/2)

This means that the square root of 7^3 is equal to 7^(3/2) because the Power of a Power Property allows us to simplify the expression by multiplying the exponents.

It's worth noting that the square root of 7^3 is the same as taking the cube root of 7^3, which is 7^(3/3) = 7^1 = 7.

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The series for this problem is absolutely convergent, as the limit assumes a value lower than 1.

The infinite series for this problem is defined as follows:

[tex]\sum_{i = 1}^{\infty} \frac{1}{n!}[/tex]

Hence the general term is given as follows:

[tex]a_n = \frac{1}{n!}[/tex]

The limit is given as follows:

[tex]L = \lim_{n \rightarrow \infty} \left|\frac{a_{n + 1}}{a_n}\right|[/tex]

The (n + 1)th term is given as follows:

[tex]a_{n + 1} = \frac{1}{(n + 1)!}[/tex]

The factorial can be simplified as follows:

(n + 1)! = (n + 1) x n!.

Hence the limit will be calculated of:

1/[(n + 1) x n!] x n! = 1/(n + 1).

The result of the limit is given as follows:

[tex]L = \lim_{n \rightarrow \infty} \frac{1}{n + 1} = 0[/tex]

As the limit assumes a value of zero, the series is absolutely convergent.

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Answer:

Step-by-step explanation:

ans = x^2 - 3x + 5

Answer:

In a right triangle, the angle opposite the hypotenuse (side c) is always 90 degrees, so we can use the trigonometric function sine to find the length of side c.

sin(A) = opposite / hypotenuse

sin(50) = b / c

so c = b / sin(50)

c = 13 m / sin(50)

c ≈ 22.361 m

So the length of side c is approximately 22.361 meters

Answer:

e

Step-by-step explanation:

e

The answer for lateral surface area of the Triangular prism is 180 cm²

Any solid object's lateral area can be calculated using the lateral area formula. Any figure's lateral area only includes the non-base faces. Calculating the lateral surface area of various forms, such as the cuboid, cube, cylinder, cone, and sphere, is made easier using lateral area formulas.

The lateral area for a triangular prism

A triangular prism's lateral area is equal to the sum of its side faces' areas (which are 3 rectangles). Specifically, it is the total surface area less the surface areas of the two bases. Additionally called the lateral surface area (LSA). Due to the two dimensions involved in its calculation, we measure it in square units.

The total of the three regions is the triangular prism's lateral area. Consequently, the triangular prism's lateral area formula is

Triangular prism lateral surface area (LSA) = ah + bh + ch (or) (a + b + c) h.

We are aware that the perimeter of the base is (a + b + c) (triangle). Hence,

Triangular prism's lateral surface area (LSA) is equal to the product of the base's perimeter and the prism's height.

base perimeter × height

Explanation

The Given Image of the solid is Matching to a prism.so we are calculating the lateral surface area of the prism

The dimensions of each base are:

a = 5cm

b = 4 cm

c = 3 cm

The height of the triangular prism = 15cm.

Thus, the lateral area of triangular prism = (a + b + c ) h

= (5 + 4 + 3) 15

= (12) 15

= 180 cm²

Answer: The lateral area of the given triangular prism = 180 cm²

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There are 30 boys and 20 girls in the classroom.

Let the variable p represent the number of people. Next, we would translate the given word problem into an algebraic equation by using a ratio as follows;

Number of girls + Number of boys = Total number of people

2p + 3p = 50

5p = 50

Dividing both sides of the equation by 5, we have the following:

p = 50/5

p = 10 people.

For the number of girls, we have:

2g = 2(10)

2g = 20 girls.

For the number of boys, we have:

3g = 3(10)

3g = 30 boys.

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Answer:a

Step-by-step explanation:

According to the figure the two triangles congruency state cannot be determined

Triangles are considered congruent when their sides and angles match those specified by the triangle congruency rules.

The triangle congruency rules.

Side - Side - Side = SSS.

Angle - Side - Side = SAS

Side - Angle - Angle = ASA

Angle, Angle, and Side = AAS

Hypotenuse plus one leg = HL

To demonstrate that the triangles are congruent, the is need for three parameters to be known except for right triangle

In the problem, only two parameters can be deduced the side and the angle equal by vertical angle theorem

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The result of the calculation is 680.

The number 3.115 has four significant figures, the number 0.2281 has four significant figures, the number 712.5 has three significant figures and the number 45 has two significant figures. This means that when performing calculations with these numbers, the answer must be rounded to the least number of significant figures, which is two.

The calculation is 3.115 + 0.2281 + 712.5 - 45. Using the rules of significant figures, we can calculate this as 3.1 + 0.2 + 713 - 45.

The result of the calculation is 675.3 and this must be rounded to the least number of significant figures, which is two. Therefore, the result of the calculation is 680.

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Answer: 12/4

Step-by-step explanation: 12/4 = 3/1 = 3

The number of dimes more than nickels in the jar is 17.

The first step is to determine the total number of coins in the jar.

Total number of coins in the jar = (sum of ratios x number of quarters) / ratio that represents the number of quarters

Sum of ratios = 2 + 3 + 5 = 10

Total number of coins in the jar = (10 x 85) / 5 = 170

Number of dimes in excess of nickels = [(ratio representing dimes - ratio representing quarters) / sum of ratios) x total number coins

[(3 - 2) / 10] x 170

(1/10) x 170 = 17

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Step-by-step explanation:

2/2

23/23

749876/749876

...

you did not show us any fractions to select.

a fraction is always 1, when the value on the top is the same value as on the bottom.

Answer:

5.35%

Step-by-step explanation:

3 month 5.25%

So 4 times a year

(1+5.25%/4)^4 = 1.0535

So effective rate is 5.35%

The number of tens that he regrouped as ones is equal to 2 tens.

The number of books that are on each shelf is equal to 66 books.

In Mathematics, a quotient simply refers to a mathematical expression that is typically used for the representation of the division of a number by another number.

Based on the information provided above, the number of books on each shelf is given by this quotient:

Quotient = 264/4

Quotient = 66

For the number of tens that Mr. Kent regrouped as ones on the shelf, we have the following:

26/4 = 24/4 + 2 = 2 tens.

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Answer:

c < 10 = The bag contains fewer than 10 carrots.

c > 10 = Catherine biked farther than 10 miles.

c < 20 = The chair is shorter than 20 inches

c > 20 = Carlos scored over 20 points

The reason studying the rainfall on the first day of September, October, and  November is not a random sample is: These are three consecutive months.

Random sample can be defined as the type of  sample in which some number of people  or group of people are choose from a large population when conducting a test.

The reason why studying the rainfall on the first day of September, October, and  November is not a random sample was because the September, October and November are  three consecutive months.

Based on this the sample should be spread out  to the entire year and should include more than three months.

Therefore these are three consecutive months.

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The value of x is -20 and can be calculated using basic proportionality theorem.

The Basic Proportionality Theorem, often known as the Thales Theorem, was developed by the well-known Greek mathematician Thales.

Basic Proportionality Theorem asserted that the ratio of any two related sides is always the same for any two equiangular triangles.

Thales provided the basic proportionality theorem based on this idea (BPT). Similar triangles have introduced this idea before. If two triangles resemble one another, then

The corresponding angles of both triangles are equal.

The corresponding sides of both triangles are proportional to one another.

Since the ratio of other side pair is 1:1, similarly 4x+20 = 3x

20 = 3x-4x

20 = -x

x = -20

Therefore, the value of x is -20

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The translation of point A to point B is done by translation vector (- 3, - 6).

In this problem we find the a point that is part of a rectangle and that must be translated by means of a rigid transformation formula, that is, a translation formula that does not alter the features of the rectangle. We need to determine the translation vector by means of the following formula:

T(x, y) = B(x, y)  - A(x, y)

Where:

If we know that A(x, y) = (6, 9) and B(x, y) = (3, 3), then the translation vector is:

T(x, y) = (3, 3) - (6, 9)

T(x, y) = (- 3, - 6)

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The correct solution to the system of equation is (-2, -3)

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

6g-3h=-3

7=h-5g

Divide through 6g-3h=-3  by 3

so, we have

2g-h=-1

Make h the subject

h = 2g + 1

So, we have

7 = 2g + 1 - 5g

Evaluate the equation

-3g = 6

So, we have

g = -2

This becomes

h = 2 * -2 + 1

Evaluate

h = -3

Hence, the solution is (-2, -3)

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Answer:

2) Acute triangle, isosceles

3) Both are 65 degrees

4) (diagram)

5) a) both 25 degrees

b) midpoint

Step-by-step explanation:

2) If you're struggling search up "draw a triangle" and you'll find a website that will draw it for you. It will help you get an idea of it looks like and its nature.

3) We know that sides AB and AC are 5cm. So this triangle is an isosceles which makes the 2 remaining angles equal (if you draw a diagram it will be clear)

So:

180-50/2 = 65

ABC and ACB = 65 degrees each

4) Construct the line AH down the middle like in the diagram I drew.

5) a) Since AH is a straight line, we know that the angle AHB will be 90 degrees. After question 3 we also know that angle ABH is 65 degrees.

BAH = 180-90-65

BAH = 25 degrees

CAH = 50 - 25

CAH = 25 degrees

b) AH is the midpoint for BAC because the 2 segments formed are both 25 degrees.

Answer: Fall Out Boy's service is cheaper than Five Seconds of Summer's service.

Step-by-step explanation: The cost of Five Seconds of Summer's tutoring service can be represented by the equation:

C = 5 + 5h

where C is the total cost and h is the number of hours.

The cost of Fall Out Boy's tutoring service can be represented by the equation:

C = 9 + 3h

To compare the cost of the two services, we can use the substitution method. We can set the number of hours (h) equal to a variable and substitute that variable into the equation for both services.

For example, if we set h = 4 (4 hours of tutoring), we get:

C(Five Seconds of Summer) = 5 + 5(4) = 25

C(Fall Out Boy) = 9 + 3(4) = 21

The cost of Fall Out Boy's service is $21 and the cost of Five Seconds of Summer's service is $25. Therefore, Fall Out Boy's service is cheaper for 4 hours of tutoring.

We can also graph the cost of the two services on a coordinate plane. The x-axis represents the number of hours and the y-axis represents the cost. The equation for Five Seconds of Summer's service would be y = 5 + 5x and the equation for Fall Out Boy's service would be y = 9 + 3x

Service | Equation

Five Seconds of Summer y = 5 + 5x

Fall Out Boy |                        y = 9 + 3x

Answer:

A school year is 36 weeks long, so 3/4 of the school year is 36 * (3/4) = 27 weeks.

If Sunny works at the library for three weeks longer than three over four of the school year, he works for 27 + 3 = 30 weeks.

So, Sunny works at the library for 30 weeks in the school year.

The number of weeks in the school year that Sonny worked at the library is; 30 weeks

We are told that Sunny works at the library for three weeks longer than three over four of the school year a school year is 36 weeks long.

Now, since he works three weeks longer than three over four of the school year, then the expression is;

³/₄(36) + 3

= 27 + 3

= 30 weeks

That figure represents the number of weeks in the school year that Sonny worked at the library.

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18) The expression with greater value are a and b. = 256  (19) the density of the object is X⁶ (20) The mass of the object is Y¹⁴  (21) The simplified expression is (3x)²  (22) Tobe uses the multiplication law for the exponent

The given parameters are

18) (a)   2³ · 2⁵ Using the multiplication law of indices, the two numbers are in the same base therefore add their powers

This implies 2³⁺⁵ = 2⁸ = 256

(b) (4)⁷/(4)³

Using the multiplication law of indices, the two numbers are in the same base therefore add their powers

4⁷⁻³ = 4⁴ = 256

(19)  Mass = X¹⁵ grams

Volume = X³ cm₁

Density = Mass/Volume

= X¹⁵/X³³

X¹⁵⁻³ = X⁶

Density = X⁶

(20) Density = Y¹⁰ grams/cm³

Volume = Y⁴ cm³

Mass = Density*volume

Mass = Y¹⁰ · Y⁴

= Using the multiplication law of indices, the two numbers are in the same base therefore add their powers

Y¹⁰⁺⁴

= Y¹⁴

(21) [ (3x)¹/³ · (3x)²/³)] / (3x)²/³

Using both multiplication and division laws of indices

(3x)²⁻¹

This is equal to  (3x)¹

(22) 8⁷· 8³ · 8²

Using the multiplication law of indices, the two numbers are in the same base therefore add their powers

8⁷⁺³⁺² = 8¹²

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HE hundred digit less than the tens digit ,the tens digit is has to 9 .This is because of 9is the only positive integer less than 10 and only it also greater than 8 in one digit numbers. result when 8 is subtracted from it.

When you have an optimistic outlook on life, you have optimism and confidence and focus more on the positives than the negatives.

Be optimistic about the future and carry on with your normal life.

A positive person chooses to focus on the positive aspects of their life, finds delight in the little things, and adopts the mindset that while there are many things outside of their direct control, they can select what they choose to give their attention to.

According to one idea, having a positive outlook makes it easier for you to handle stressful situations, which lessens the negative consequences of stress on your body's health.

we already know that ones digit is 5 less than the tens digit, so it is 9-5=4,and the hundreds digital has to be 1, so the answer is 194.

so, let we can solve it as by the problem,

by the problem

units will be considered as a x

ok

x greater than or equal 9

tens digit digit is more than 5 units

we know that,

so, tens digit value is 9

hundreds digit value is 1

let we find ones digit value x+5<=9

x<=4

hundreds digit is less than

x+5

x+5-8>=0

x-3>=0

x>=3

>3=4

thus the x is 4

then the number is 194

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The absolute value of the given expression is 8.

Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

Given that an expression |10| - |‐5| + |‐3| we need to find its absolute value,

|10| - |‐5| + |‐3|

= 10 - 5 + 3

= 5 + 3

= 8

Hence, the absolute value of the given expression is 8.

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This means x = 5a pairs up with y = 0.

=========================================================

Explanation:

The two lines have the same x-intercept, which means they cross the x axis at the same location. This is the solution to the system since this point is on both lines simultaneously.

To find the x-intercept, plug in y = 0 and solve for x.

(1/5)x+4y = a

(1/5)x+4*0 = a

(1/5)x = a

x = 5a

We don't know the value of 'a', so we cannot determine the numeric value of x.

The x-intercept is located at (x,y) = (5a,0) and this is the solution to the system.

The solutions for the inequality "y is greater than one fifth times x plus 3" lies in both quadrant I and quadrant II.

In Mathematics, a quadrant can be defined as the area that is occupied by the values on the x-coordinate and y-coordinate of a cartesian coordinate.

Generally speaking, there are four (4) major quadrants in any graph and these include the following:

y is greater than one fifth times x plus 3 ⇒ y > x/5 + 3.

Next, we would use an online graphing calculator to plot the given inequality. Therefore, the required solution is the shaded area above the dash line as shown in the graph attached below.

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The triangles are congruent by ASA theorem.

Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal. In other words, congruent triangles are triangles that have the same size and shape.

Therefore, If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent by ASA(angle side angle).

Therefore, the triangle are congruent by ASA(angle side angle)

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In the triangle, we will use the Law of Cosines to find the value of angle q. angle q in the triangle is approximately 61.2° (rounded to one decimal place).

The Law of Cosines is a mathematical formula used in trigonometry to find the length of a side or an angle in a triangle.

The formula can be used to find the length of a side or an angle in a triangle, given the length of the other sides and angles.

The Law of Cosines is particularly useful when only two sides and the angle between them are known, or when only two angles and the side between them are known.

To use the Law of Cosines, you need to identify the sides and angles that you know and plug them into the formula. Then, you can use algebra to solve for the unknown side or angle.

The Law of Cosines is related to the Pythagorean Theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side.

The Law of Cosines can also be used in three-dimensional geometry to find the distance between two points in space.

The Law of Cosines is a useful tool in many fields, including engineering, physics, and computer graphics, and is widely used in solving geometric problems.

In this triangle, we have x = 66.1 cm, y = 22.8 cm, and angle f = 23.3º. We want to find angle q, which is opposite side x.

We can use the Law of Cosines to find the value of cos(q), and then use the inverse cosine function to find the value of q in degrees.

cos(q) = (x² + y² - x²)/(2xy)

cos(q) = (66.1² + 22.8² - 22.8²)/(2 * 66.1 * 22.8)

cos(q) = 67.8664/150.6448

cos(q) = 0.449

q = cos⁻¹(0.449)

q = 61.2°

Therefore, angle q in the triangle is approximately 61.2° (rounded to one decimal place).

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