# 25-29) A cast iron cylinder serves as a counterbalance that is used in a window
manufacturer's double-hung window design. The cylinder has a height of 7.45 in and a
diameter of 2.7in. The weight density of cast iron is 0.259 lbs/in³.
What is the volume of the cylinder?
Volume = 42.63374
What is the surface area of the cylinder?
Surface area =
What is the weight of the cylinder?
Weight =
V=7₂².h
3.14 (1.352). 7.45
= 42.63374
2.7÷2=1.35
3.14(
W=dw.v
W=

Answer:

8b + 4 = 6

Step-by-step explanation:

8b + 4 = 6

It didn't say you have to solve for b, but just in case...

8b = 6 - 4 = 2

b = 2/8 = 1/4

The property which is demonstrated by this expression 6 + 7 = 7 + 6 include the following: C. commutative property.

In Mathematics, the Commutative Property of Addition states that when two (2) or three (3) numerical values (numbers) are added together, the output (end result) would always remain the same, irrespective of the way in which the numerical values are arranged.

Generally speaking, the Commutative Property of Addition allows the addends to be re-ordered without causing a change in the result, output, or outcome.

By applying the Commutative Property of Addition, we have the following;

6 + 7 = 7 + 6

13 = 13

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Complete Question:

Which property is demonstrated below?

6 + 7 = 7 + 6.

A. associative property

B. distributive property

C. commutative property

D. identity property

The length of MN is roughly 13.89 units.

The polygonal shape of a triangle has three sides and three corners. It is one of the fundamental geometric shapes. Triangle ABC is a symbol for a triangle with vertices A, B, and C. When three points are not collinear, unique triangles and planes are found using Euclidean geometry.

Triangle JKL and triangle MNO are comparable, thus we can use the aspect ratio to determine the appropriate side lengths.

MN is 'x' in length. Then, it appears as follows:

JK/MN = 26/x, and KL/NO = 19/x

We can use their ratio to get x because we are aware of the lengths of JK and KL. We obtain: using the first ratio.

26/x = 58/26

x=26*26/58

x = 26^2/58

x = 13.89 (rounded to nearest integer)

Therefore, MN is approximately 13.89 units long. 

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Answer:

[tex]t=14.7[/tex]

Step-by-step explanation:

In the equation: [tex]t-9.25=5.45[/tex] we need to get [tex]t[/tex] by itself. To do that, we need to add [tex]9.25[/tex] from one side to the other. We do this because on the side where [tex]t[/tex] is, [tex]9.25[/tex] is being subtracted and we have to do the opposite of that. So:

[tex]t-9.25=5.45[/tex]

  [tex]+9.25[/tex]     [tex]+9.25[/tex]

In this case, we got [tex]t[/tex] by itself. The new equation is:

[tex]t=14.7[/tex]

"Every linear transformation is a matrix transformation." This is false. Not all linear transformations are matrix transformations, even if all matrix transformations are linear transformations.

A point, line, or geometric object can be changed in four different ways that are all referred to as transformations. The Pre-Image refers to the object's initial shape, and the Image, after transformation, refers to the object's ultimate shape and location.

Bring out the pattern blocks, tangrams, and geoboards for another low-prep, high-engagement method of teaching geometric transformations. Students can produce an original design and then hand it off to a partner so that they can add a reflection, rotation, or translation to it.

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Answer:

3 loaves? 2 rye flour

7 loaves? 4⅔ rye flour

10 loaves? 6⅔ rye flour

Step-by-step explanation:

To get how many cups of rye flour the baker will use, for example: to get how many cups of rye flour the baker will use in 3 loaves? we multiply the number of cups the baker uses to make one loaf of bread

[tex]3 \: loaves \: = \frac{2}{3} \times 3[/tex]

[tex] \frac{2}{3} \times 3 = 2[/tex]

Now let's work out the others using the same method shown above

[tex] \frac{2}{3} \times 7 = 4 \frac{2}{3} [/tex]

[tex] \frac{2}{3} \times 10 = 6 \frac{2}{3} [/tex]

Answer:

2 cups = 3 loaves, 4 2/3 (4.66666667 in decimal form) cups of rye in 7 loaves, and 6 2/3 (6.66666666667 in decimal form) cups of rye in 10 loaves.

Step-by-step explanation:

What do we know?  We know that 2/3 cups of rye is equal to one loaf of bread.  We need to figure out how many cups of rye are in three loaves, seven loaves, and ten loaves.  To do this, we will first figure out how many cups of rye are in three loaves.  Since we know that 2/3 cups of rye is in 1 loaf, we take 2/3 cups and multiply it by three over one, or, three, for the three loaves.  That comes out to 6/3.  Now, we simplify.  Three goes into six, evenly, twice with no remainder.  So, 2 cups of rye goes into 3 loaves.  The decimal for this would be 2.0.

Applying the same method, 2/3 cups times 7.  We get 14/3.  Three goes into fourteen 4 times with a remainder of 2.  So, the answer would be 4 2/3 cups of rye in 7 loaves.  To get the decimal version, divide 14 into 3.

2/3 times 10 equals 20/3.  3 goes into twenty six times with a remainder of two.  So, 6 2/3 cups of rye in 10 loaves.  To get the decimal version, simply divide 20 into 3.

On solving the provided question, we can say that the new equation of the line is = (y +6) = 1/2(x-3) => x - 2y = 9

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

coordinates are (3, -6)

the perpendicular equation is y = -2x

so, m. the slope = 1/2

the new equation of the line is = (y +6) = 1/2(x-3)

2y + 12 = x = 3

x - 2y = 9

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The solution for this equation system is x= 29, y=53, (29, 53).

[tex](1)y=3x-34\\ \\(2)y=2x-5[/tex]

[tex](2x-5)=3x-34\\\\2x-5=3x-34[/tex]

[tex]2x-5+5=3x-34+5\\ \\2x=3x-29[/tex]

[tex]2x-3x=3x-29-3x\\ \\-1x=-29\\ \\-x=-29[/tex]

[tex]-x(-1)=-29(-1)\\ \\x=29[/tex]

To find a value of "y", use the calculated value of "x" (29), and substitute in any of the two equations to find the value of "y". For this solution, we're going to use equation 2.

[tex]y=2(29)-5\\ \\y=58-5\\ \\y=53[/tex]

On step 6 we proved that the value of "x=29" returns a value of "53" when evaluating with equation 2. Now, if equation 1 returns the same "y" value when evaluating "x=29", then the calculated values of both "x" and "y" are correct. Let's verify!

[tex]y=3(29)-34\\ \\y=87-34\\ \\y=53[/tex]

Both of the equations return the same value of "y" (53) when evaluated with "x=29". Therefore, the solution for this equation system is x= 29, y=53, (29, 53).

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Answer: 174 miles

Step-by-step explanation: 14.5 (14 1/2) times 12 is 174

The simplified expression is equal to 2/3.

        2m⁰ * n⁶ / (3n⁵)

       2 * n⁶ / (3n⁵)

        2 * n / (3n) = 2/3

So the simplified expression is equal to 2/3.

The rules of arithmetic and exponentiation that I used to simplify the expression are general mathematical principles that are applicable to many mathematical problems. However, the specific techniques for simplifying an expression will depend on the particular expression and the context in which it is being used.

For example, there might be additional rules or simplification techniques that are specific to a particular field of mathematics, such as algebra, calculus, or geometry. In these cases, it's important to understand the specific rules and techniques that apply to the problem at hand in order to simplify an expression effectively.

In general, the goal of simplifying an expression is to make it easier to understand and manipulate mathematically, either for further calculations or for understanding the relationships between the variables involved.

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The distance around the track along its outer edge is  238 + 100 x π metres and the area of the track is  1250 x π  + 2380 square metres.

The racetrack is divided by two parallel sections and two semi-circular endpoints. The two parallel segments are 119 metres long, and the track is 10 metres wide. The inner length of the two parallel sections is 70 metres.

To calculate the distance around the track's outer edge, multiply the lengths of the two parallel segments by the diameter of the two semi-circular ends. C = 2 x π x r, where r is the radius of the semi-circle, may be used to compute the circumference of each semi-circular end.

The radius of each semi-circle is calculated by subtracting the track width (10 metres) from half the inner distance between the two parallel sections (70 metres / 2 = 35 metres). So, the radius of each semi-circle is 35 metres - 10 metres = 25 metres.

As a result, the circumference of each semi-circle is 2 x π x 25 = 50 x π  metres. As a result, the circumference of the track along its outside border is 119 metres + 119 metres + 50 x π  metres + 50 x π  metres = 238 + 100 x π metres.

To calculate the area of the track, first calculate the areas of the two semi-circular ends and the two parallel segments, then add them. A = π[tex]r^{2}[/tex], where r is the radius of the semi-circle, may be used to compute the area of each semi-circular end.

Each semi-circle has an area of π x [tex]25^2[/tex] = 625 x π  square metres. The size of the two parallel lengths is 1190 square metres (119 metres x 10 metres). The track's total area(A) = 625 x π  + 625 x π  + 1190 + 1190

A= 1250 x π  + 2380 square metres.

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Answer:

12000

Step-by-step explanation:

4500:12=470

425:125=100

1000×12=12000

The deceptive amount claim is b). P (A n B) = P (A) + P (B) -P ( A U B). This assertion is false since it omits the point where A and B intersect, which is P. (A n B).

The deceptive claim is b). P (A n B) = P (A) + P (B) -P ( A U B). This claim is false because it disregards the fact that P is where A and B overlap (A n B). The stated statement does not take into consideration the intersection of two events, which is the likelihood that both occurrences will occur.

One must factor in the likelihood that the two occurrences will intersect when calculating the likelihood that two events will occur simultaneously. The given statement deducts the probability of the union of two occurrences from the sum of the probabilities of the two separate events because the probability of the union of two events is the chance that at least one of the events occurs. As it ignores the intersection, this method is inaccurate for estimating the likelihood of both occurrences occurring simultaneously. The probability of the intersection must be considered in order to calculate the likelihood of two occurrences occurring simultaneously.

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The length and the width are 21cm and 16cm respectively.

The formula for calculating the perimeter of a rectangle is expressed as;

P = 2(l +w)

Given that;

But we have that;

Length = 5 + w

Substitute the value

74 = 2(5 + w + w)

collect like terms

74=2 (5 + 2w)

expand the bracket

64 = 4w

Make 'w' the subject of formula

w = 16cm

Then, length = 5 + 16 = 21cm

Hence, the values are 16cm and 21cm

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The rate of exponential decay is 0.19.

f(x) = 202.5x is the equivalent function.

The correct option is A.

An exponential function's curve is created by a pattern of data called exponential decay, which exhibits higher decreases over time.

The exponential decay function:

Aₙ = A₀(1-r)ˣ, where y = Final amount, A₀ = Initial amount, r = Rate of decay in decimal form, x = Time.

Given:

The function f(x) = 500(1 − 0.19 )ˣ/2,

models the price of a share of stock over time.

Compared to the definition,

we get,

The rate of exponential decay is 0.19.

When x = 0,

Then f(x) = 202.5x

Therefore, f(x) = 202.5x is the equivalent function.

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The probability of randomly selecting a girl from Ms. Garcia's class is 5/9.

Which means that for every 5 students in the class, 4 of them are boys and 5 of them are girls.

To calculate the probability of selecting a girl from the class, we need to divide the number of girls by the total number of students:

Number of girls: 5 students

Total number of students: 4 students + 5 students = 9 students

Probability of selecting a girl: 5 students / 9 students = 5/9

So the probability of randomly selecting a girl from Ms. Garcia's class is 5/9.

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Answer:

Let's first convert 1/6 mile into minutes by multiplying the distance by the number of minutes per mile:

1/6 mile * (1 minute/1/6 mile) = 6 minutes/mile

Next, let's convert the 7/9 minutes into miles:

7/9 minutes * (1/6 mile/minute) = 7/9 * 1/6 mile = 7/54 miles

Now that we have the distance and time in the same units, we can calculate Ed's speed as:

Speed = Distance / Time = 7/54 miles / 7/9 minutes = 7/54 miles / (7/9 * 1 minute) = 7/54 miles / (7/9) minutes = 7/54 miles / (7/9) = 54/7 miles/minute

So, Ed's speed is 54/7 miles per minute.

Step-by-step explanation:

The length of the side x is 60.

Pythagorean Theorem is a mathematical statement that states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. It can be written as c^2 = a^2 + b^2

Let the unknown side in the first triangle be a

We know that;

a^2 = 55^2 - 25^2

a= 49

Then again;

x^2 = 35^2 + 49^2

x = 60

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The length of the arc is 42.98 inches, so the correct option is A.

For an arc defined by an angle θ on a circle of radius r the length of the arc is given by:

L = (θ/360°)*2*pi*r

Where pi = 3.1416

Here we know that:

r = 10.26 inches

θ = 240°

Then we can replace that in the formula above, we will get:

L = (240°/360°)*2*3.1416*10.26 in

L = 42.98 inches

The correct option is A.

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The quantity of has he had left in his car after taking both friends home would be = 4.76gallons

The total amount of gas in gallons in his car = 6 gallons

The amount of gas he used to take one of his friends home = 1.04 gallons.

The second friend he used a total of = 1/5 = 0.2 gallons.

The total amount of gas he uses = 1.04+0.2 = 1.24 gallons.

Then the amount of gas remaining = 6 - 1.24 = 4.76gallons.

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Answer: For every one who is annoyed with the dude aboves answer the correct answer is: D 4.56

Step-by-step explanation:

The sample mean is significantly different from the population mean. The confidence level used was 95%.

To build a confidence interval to decide whether this example mean is fundamentally not the same as the populace mean, there are a few stages that should be taken.

To begin with, work out the standard error of the mean (SEM) for the example, which is the standard deviation separated by the square base of the example size (SEM = σ/√n). For this situation, the SEM is 3/5 = 0.6 mcg/dL.

Then, compute the critical value for the confidence interval picked by increasing the SEM by the t-esteem from the t-dissemination for the given confidence interval. For instance, in the event that a 95% confidence interval is picked, the t-esteem is 1.96. This provides us with a basic worth of 0.6 x 1.96 = 1.176 mcg/dL.

At last, build the certainty span utilizing the example mean and the basic worth. The certainty span is (15 - 1.176, 15 + 1.176), or (13.824, 16.176). This implies that we are 95% sure that the genuine populace mean exists in this reach.

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In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Multiplication is often referred to as repeated addition because what the multiplication problem is telling you is that you have a certain number of groups of something, all containing a specific number. Confused yet? Here's an example.

You have 3 bags of candy, and each bag contains 5 pieces of candy. How many pieces of candy do you have?

There are two ways to solve this problem. The first is by adding up the pieces of candy:

5 + 5 + 5 = 15

The other way to solve this problem is to use multiplication, because you have 3 groups of candy with 5 pieces of candy in each bag.

3 * 5 = 15

The answer to this multiplication problem is the product, which in this case is 15.

Here's another example. The classroom has 8 rows of chairs and each row has 7 chairs in it. How many chairs are there?

Again, you could add:

7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 = 56

Or, you can find the product by multiplying:

7 * 8 = 56

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CORRECT QUESTION FORMAT IS GIVEN BELOW -----

Q. What is the Product in Math?

The median weight of the players on the football team is approximately 160 lbs.

The box plot provides a visual summary of the data which shows the distribution of the weights of the players on the football team. The box plot consists of a box and two "whiskers" which represent the upper and lower quartiles of the data. The box is bounded by the upper quartile and lower quartile and the two whiskers represent the highest and lowest values in the data set, excluding any outliers. The median weight of the players is represented by the line in the middle of the box, which is approximately 160 lbs. The box plot is a useful tool for summarizing the data and provides a quick and easy way to visualize the distribution of the players' weights. The median weight of 160 lbs gives us an idea of the average weight of the players, which can be used to determine the overall strength of the team.

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The complete question is

a high school has 40 players on the football team. the summary of the players' weights is given in the box plot. what is the median weight of the players and find lbs.

Answer:

-1, 7

Step-by-step explanation:

Based on the graph (it's a little blurry!) it looks like f(x) = 0 when x = -1 and x = 7.  The question is asking, for what values of x is y=0?  Answer is x = -1, 7

Answer:A

Step-by-step explanation:

The number 7 will be placed in the middle circle.

To place the numbers 2, 6, 7, 8, and 9 in the circles so that the sums across and down are equal, you can use the following method:

1. Place the median number (7) in the middle circle.

2. Place the two smallest numbers (2 and 6) on either side of the median number.

3. Place the two largest numbers (8 and 9) in the top and bottom circles.

Here is a list of them. Each group of three numbers makes up a side of the triangle. Of course, within a side you can replace round numbers that are not on a corner, but that does not really give any new solutions.

So, the final arrangement would be:

6 2 7

9 8 7

6 2 7

Therefore, the number 7 will be placed in the middle circle.

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Answer:

3.1.1) There are four terms in this expression.

3.1.2) The coefficient of x^3 is 0.5.

3.1.3) The constant term is 8.

3.1.4) The degree of the expression is 5.