The volume of prism R is 40 m³. Prism R and prism S have the same height. The area of the base of prism S is half the area of the base of prism R. What is the volume of prism S? 1) 10 m³ 2) 20 m³ 3) 40 m³ 4) 80 m³​

The length of the rope in this scenario is 33.912 meters based on given diameter.

To find the length of the rope wound around the cylindrical pipe, we need to take the circumference of the pipe and the number of times the rope is wound around it.

The diameter of the pipe is given as 600 mm, which means the radius is half of that, or 300 mm. To find the circumference, we use the formula C = 2πr, where π is pi (approximately 3.14) and r is the radius. Therefore, the circumference of the pipe is 2 x 3.14 x 300 = 1884 mm.

The rope is wound around the pipe 18 times, so the total length of the rope is 18 times the circumference of the pipe, which is 18 x 1884 = 33,912 mm or 33.912 meters.

To calculate or find the length of the rope wound around the cylindrical pipe, we multiply the circumference of the pipe by the number of times the rope is wound around it. Therefore, the length of the rope in this scenario is 33.912 meters.

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The transformation T: R^3 → R^2 defined by T(x1, x2, x3) = (|x1|, 0) is not linear transformation as it violates the additivity and homogeneity properties of linearity.

To show that the transformation T: R^3 → R^2 defined by T(x1, x2, x3) = (|x1|, 0) is not linear, we need to demonstrate that it violates at least one of the two properties of linearity, namely, additivity and homogeneity.

Additivity: T(u + v) = T(u) + T(v) for all vectors u and v in R^3.

Let u = (1, 2, 3) and v = (4, 5, 6) be two vectors in R^3. Then,

T(u) = T(1, 2, 3) = (|1|, 0) = (1, 0)

T(v) = T(4, 5, 6) = (|4|, 0) = (4, 0)

T(u + v) = T(1+4, 2+5, 3+6) = T(5, 7, 9) = (|5|, 0) = (5, 0)

However,

T(u) + T(v) = (1, 0) + (4, 0) = (5, 0)

Since T(u + v) ≠ T(u) + T(v), the transformation T is not additive and hence not linear transformation.

Homogeneity: T(cu) = cT(u) for all vectors u in R^3 and all scalars c.

Let u = (1, 2, 3) be a vector in R^3, and let c = 2 be a scalar. Then,

T(u) = T(1, 2, 3) = (|1|, 0) = (1, 0)

T(cu) = T(2, 4, 6) = (|2|, 0) = (2, 0)

However,

cT(u) = 2(1, 0) = (2, 0)

Since T(cu) ≠ cT(u), the transformation T is not homogeneous and hence not linear.

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Based on the two-way table, it appears that there is an association between grade level and preference for school color.

As the grade level increases, there is a trend towards a greater preference for blue. Among sixth graders, there were 17 students who preferred blue and 39 who preferred green. Among seventh graders, 27 preferred blue and 27 preferred green. Finally, among eighth graders, 41 preferred blue and 14 preferred green. It is important to note, however, that this trend may not necessarily imply causation. There could be other factors at play that are contributing to this association, such as the age of the students or the characteristics of the school environment. Additionally, the sample size in each grade level is relatively small, which could lead to some variability in the results.

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This is the slope-intercept form of the equation of the line. To convert it to the standard form, we need to rearrange it so that the x and y terms are on the same side of the equation:= (13/4)x + y = -7

How to find standard form?

To find the standard form of the line that passes through the given points (-4, 6) and (0, -7), we need to first find the slope of the line using the slope formula:

slope = (y₂ - y₁) / (x₂- x₁)

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Using the given points, we get:

slope = (-7 - 6) / (0 - (-4))

slope = -13/4

Now that we have the slope of the line, we can use the point-slope form of the equation of a line:

y - y₁= m(x - x₁)

where m is the slope and (x1, y1) is one of the points on the line. Using the point (-4, 6), we get:

y - 6 = (-13/4)(x - (-4))

y - 6 = (-13/4)x - 13

y = (-13/4)x - 7

This is the slope-intercept form of the equation of the line. To convert it to the standard form, we need to rearrange it so that the x and y terms are on the same side of the equation:

(13/4)x + y = -7

This is the standard form of the equation of the line that passes through the given points.

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The weight of the liquid can be calculated as follows:

Weight = Volume x Density

The volume is given as 182.8 milliliters.

The density is given as 0.135 grams over milliliter.

Weight = 182.8 x 0.135 = 24.67 grams

Therefore, the weight of the liquid that exactly fills a 182.8 milliliter container if the density of the liquid is 0.135 grams over milliliter is 24.67 grams.

Probably this

Answer: {x|4<x<10}

Step-by-step explanation:

Answer:

x > 3/2

Step-by-step explanation:

2x -3 > 0

2x > 3

x > 3/2

Answer:

To solve the inequality 2x-3>0, we can use algebraic manipulation to isolate x on one side of the inequality.

First, we can add 3 to both sides of the inequality:

2x - 3 + 3 > 0 + 3

Simplifying the left side and the right side, we get:

2x > 3

Next, we can divide both sides of the inequality by 2:

2x/2 > 3/2

Simplifying the left side and the right side, we get:

x > 3/2

Therefore, the solution to the inequality 2x-3>0 is x > 3/2.

The nth term from the quadratic sequence  "2, 8, 18, 32, 50,..." Would be 2n², where n reffers to the position of number.

By observation and by trial and error.

The first term, n = 1    = 2*1*1 = 2

Second term, n =2,     = 2*2*2 = 8

Third term , n =3,                = 2*3*3 = 18

Third term, n = 4,       = 2*4*4 = 32

Fourth term, n =5,     2 * 5* 5 = 50

For nth term,        2 *n *n = 2n²

Therefore the nth term of quadratic sequence would be 2n².

Sequences with a term are referred to as quadratic sequences. The fact that the first differences between terms are not equal but the second differences between terms are can be used to identify them.

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The surface area of the triangular prism as per the area formula is as follows:

1104m².

The space that any composite shape occupies is referred to as the area of composite shapes. In order to create the desired shape, a few polygons are connected to create a composite shape. These figures or forms can be constructed using a variety of geometrical elements, including triangles, squares, quadrilaterals, and others.

To determine the area of a composite object, divide it into simple shapes like a square, triangle, rectangle, or hexagon. In essence, a composite shape is a combination of fundamental shapes. It goes by the name's "composite" or "complex" shapes.

In the triangular prism given,

We have 2 triangles and 3 rectangles.

So, to find the surface area of the prism we need to find the area of the individual shapes and add them up.

Length of 1st rectangle = 20m and breadth = 19m.

Area = l × b

= 20 × 19

= 380m².

Length of 2nd rectangle = 19m and breadth = 16m.

Area = l × b

= 19 × 16

= 304m².

Length of the 3rd rectangle = 19m and breadth = 12m.

Area = l × b

= 19 × 12

= 228m².

Now coming to the triangles,

Both the triangles are equal with base = 16m and height = 12m.

Area = 1/2 × b × h

= 1/2 × 16 × 12

= 96m².

We have two triangles so, area of 2 triangles = 2 × 96 = 192m².

Therefore, total area = 380 + 304 + 228 + 192

= 1104m².

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Answer:

(a-b)/(b-a)

Step-by-step explanation:

The gradient = difference of y values / difference of corresponding x value

=  (a-b)/(b-a)

The equation d=65t models the distance, d, that Malcolm's family travels after t hours. Malcolm's family travels 65 miles per hour faster than Theo's family.

The equation d=65t models the distance, d, that Malcolm's family travels after t hours. To calculate how much faster Malcolm's family travels than Theo's family, we must first know the speed of Theo's family. Let's say Theo's family travels at 25 miles per hour. To calculate the difference in speed between the two families, we must subtract 25 mph from 65 mph. The difference is then 40 mph, meaning Malcolm's family travels 40 mph faster than Theo's family.

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The coordinates of the vertices of the translated shape are (-4, 7), (-1, 7), (-4, 5), and (1, 5).

Transforming an object from one place to another without altering its size or shape is known as translation. Contrarily, the term "transformation" refers to a wider range of procedures that can alter the size, shape, or orientation of an item. Rotation, reflection, and scaling are some more forms of transformation in addition to translation.

The given vector is (-5, 3).

To translate the graph add the vector to the coordinates as follows:

(1, 4) + (-5, 3) = (-4, 7)

(4, 4) + (-5, 3) = (-1, 7)

(1, 2) + (-5, 3) = (-4, 5)

(6, 2) + (-5, 3) = (1, 5)

Hence, the coordinates of the vertices of the translated shape are (-4, 7), (-1, 7), (-4, 5), and (1, 5).

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To draw a Venn diagram of two sets in class 7, draw two overlapping circles inside a rectangle representing the universal set, label each circle with the name of its corresponding set, and identify the elements that belong to each set and the overlapping region.

Steps to draw venn diagram :

These are the steps to draw a Venn diagram for two sets, follow these steps.

1. Draw two overlapping circles, one for each set. Label them A and B.

2. Write the elements that are common to both sets in the overlapping region of the circles.

3. Write the elements that belong only to set A in the non-overlapping part of circle A.

4. Write the elements that belong only to set B in the non-overlapping part of circle B.

For example, let's say we have two sets:

A = {1, 2, 3, 4, 5}

B = {3, 4, 5, 6, 7}

To draw a Venn diagram for these sets, we would follow these steps:

1. Draw two overlapping circles, one for A and one for B.

2. Write the elements that are common to both sets in the overlapping region of the circles. In this case, the common elements are 3, 4, and 5.

3. Write the elements that belong only to set A in the non-overlapping part of circle A. In this case, the elements that belong only to set A are 1 and 2.

4. Write the elements that belong only to set B in the non-overlapping part of circle B. In this case, the elements that belong only to set B are 6 and 7.

5. The completed Venn diagram for these sets should look like two overlapping circles with the common elements in the overlap region and the unique elements in the non-overlapping regions, as shown below:

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Answer:

Ali will cover 1,080m altogether.

Step-by-step explanation

If the field is 80m by 100m and there are 2 sides of each of those measurements to make a whole round around the field, then one round would be (80m x 2) + (100m x 2) = 360. Since Ali wants to do three laps around the field, then you multiply 360 x 3 to get 1080m total.

The predicted number of wins for a team that allowed 80 runs is 72.

What is equation?

An equation is a formula that uses the equals sign to connect two expressions to show that they are equal.

To find the predicted number of wins for a team that allowed 80 runs, we need to substitute x = 80 into the given equation:

y = 80.98 - 0.108x

y = 80.98 - 0.108(80)

y = 80.98 - 8.64

y ≈ 72.34

Rounding this to the nearest integer, we get:

y = 72

Therefore, the predicted number of wins for a team that allowed 80 runs is 72.

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The answer is option C, 8√2.

The length of the diagonal side of the square is 8 fr. Hence the gardener wants to divide a square piece of lawn in half diagonally, which means to find the length of a diagonal bisector of a square. Let's solve the problem: Length of the diagonal side of the square = 8 fr.

Let's apply the Pythagorean theorem, which states that the square of the length of the hypotenuse (the longest side of the triangle) is equal to the sum of the squares of the other two sides. Therefore, the formula to find the length of the diagonal (d) of the square with side a is given by d = a√2.

Now we can find the length of the diagonal of the square using the formula given above: d = a√2d = 8√2Thus, the length of the diagonal side of the square is 8 fr. Hence the length of the diagonal of the square is 8√2 fr. Therefore, the answer is option C, 8√2.

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Step-by-step explanation:

[tex] \sqrt{x} = {x}^{ \frac{1}{2} } [/tex]

Its like because when you try to cut down it would be

[tex] {}^{2} \sqrt{ {x}^{1} } [/tex]

So to simplify things down it would be

[tex] \sqrt{x} [/tex]

For each cup of sugar, we need 5/3 cups of milk.

A fraction is used to express a portion of a whole or a ratio of two values. It is represented by a numerator and a denominator separated by a horizontal line, with the numerator above and the denominator below.

To find : how much milk is needed for each cup of sugar

we need to use the given ratio of sugar to milk and invert it:

1/5 cup of sugar per 1/3 cup of milk

To find how much milk is needed for each cup of sugar, we need to divide the amount of milk by the amount of sugar:

(1/3 cup of milk) ÷ (1/5 cup of sugar) = (1/3) × (5/1) = 5/3 cup of milk per cup of sugar

Therefore, for each cup of sugar, we need 5/3 cups of milk.

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The perimeter of the baby quilt is approximately 48.66 feet.

A quilt that is 3 feet long cannot have a surface area of 64 square feet, hence it appears that the information provided is incorrect. When calculating the area of a quilt, the length and breadth are multiplied. If the quilt is just 3 feet long, for example, the width would need to be 64/3 = 21.3 feet, which is not a practical size for a baby quilt.

Let's assume the information provided is false and try to determine the perimeter of a baby quilt whose surface area is 64 square feet.

To do this, we must first determine the quilt's proportions. Given that a rectangle's area is determined by multiplying its length by its width, we may determine the width by dividing the area by the length.

width = area / length, or 64 / 3 = 21.33 feet (rounded to two decimal places)

The baby quilt is 3 feet by 21.33 feet.

We add the lengths of the four sides to find the perimeter.

The perimeter is equal to 2 (length + width)/2 (3 + 21.33) = 48.66 ft (rounded to two decimal places)

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To complete the table of equivalent ratios of lengths to widths, we need to find the missing values that make the ratios in each row equal to each other. One way to do this is to use cross-multiplication.

First, we can compare the first and second rows to find the value that makes them equivalent:

x/18 = 8/y

Multiplying both sides by 18y, we get:

xy = 144

So the missing value in the first row is 144/18 = 8, and the missing value in the second row is 144/8 = 18.

Next, we can compare the third and fourth rows:

10/30 = 12/z

Multiplying both sides by 30z, we get:

10z = 360

Dividing both sides by 10, we get:

z = 36

So the missing value in the third row is 36, and the missing value in the fourth row is 12/10 * 36 = 43.2.

Therefore, the completed table is:

8 18

8 144/10 = 14.4

10 30

12 36

a)The probability that at least 10 of the 15 randomly chosen individuals have no citations is 0.6723.  b) the probability that fewer than half of the 15 randomly chosen individuals have at least one citation is 0.3826. c) the probability that the number of individuals among 15 who have at least one citation is between 5 and 10, inclusive, is 0.7278.

Recall that in Exercise 30 (Section 3.3) the pmf of Y, the number of traffic citations for a randomly selected individual insured by a particular company, was given as follows:

Y=y 0 1 2 3 4 5

P(Y=y) 0.52 0.29 0.10 0.05 0.03 0.01

a. We can use the binomial distribution to model the number of individuals among 15 who have no citations, with the probability of success being P(Y=0)=0.52. Then, the probability of at least 10 individuals having no citations is:

P(X >= 10) = 1 - P(X < 10) = 1 - P(X <= 9)

Using a binomial table or calculator, we find that:

P(X <= 9) = 0.3277

Therefore,

P(X >= 10) = 1 - P(X <= 9) = 1 - 0.3277 = 0.6723

b. We can use the binomial distribution again to model the number of individuals among 15 who have at least one citation, with the probability of success being P(Y>0)=1-P(Y=0)=1-0.52=0.48. Then, the probability of fewer than half (less than 7) individuals having at least one citation is:

P(X < 7) = Σ P(X = k), where k = 0,1,...,6

Using a binomial table or calculator, we find that:

P(X < 7) = 0.6174

Therefore,

P(X >= 7) = 1 - P(X < 7) = 1 - 0.6174 = 0.3826

c. We need to find the probability that the number of individuals among 15 who have at least one citation is between 5 and 10, inclusive. We can use the binomial distribution with the probability of success being P(Y>0)=0.48. Then, the probability is:

P(5 <= X <= 10) = Σ P(X = k), where k = 5,6,...,10

Using a binomial table or calculator, we find that:

P(5 <= X <= 10) = 0.7278

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Your question is incomplete, but probably the complete question is :

Exercise 30 (Section 3.3) gave the pmf of Y, the number of traffic citations for a randomly selected individual insured by a particular company. What is the probability that among 15 randomly chosen such individuals

a. At least 10 have no citations?

b. Fewer than half have at least one citation?

c. The number that have at least one citation is between 5 and 10, inclusive?*

Answer:

35g^2+38g+8

Step-by-step explanation:

35g^2+38g+8

From the calculations, we can see that each of the external angles of the polygon would have a measure of  60 degrees.

The external angles of a polygon are the angles formed by extending one side of the polygon and forming a new angle with the adjacent side. To find the external angle of a polygon, you can use the following formula:

External angle = 360° / number of sides

In this case we have been told that what we have is a hexagon thus;

4xternal angle is; 360/6

= 60 degrees

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Check the picture below.

The given expression is [tex](f+g)(x)[/tex]  so the value of this expression is [tex]= x^3 + 1/2 x^2 + 3/4 x - 5[/tex]

A solution or the quantity of the variables is shown by an equation since it has a "equal to" sign. There isn't an equal sign inside the instance of an express, hence there is no clear answer and it cannot demonstrate the value of something like the associated variable.

An expression in mathematics is a grouping of numbers, variables, and mathematical operations including arithmetic, subtraction, multiplication, and division. You may compare expressions to sentences in your mind. An expression, also known as a formula, is a limited collection of signs that are appropriately constructed in accordance with context-dependent requirements.

[tex](f+g)(x) = f(x) + g(x)[/tex]

[tex]= (x^3 - 1/2 x^2 + x) + (x^2 - 1/4 x - 5)[/tex]

[tex]= x^3 - 1/2 x^2 + x + x^2 - 1/4 x - 5[/tex]

[tex]= x^3 + 1/2 x^2 + 3/4 x - 5[/tex]

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Answer:

A is definitely correct and possibly C as well

Step-by-step explanation:

Wyatt is correct so it’s not B or D and E doesn’t make sense.

The measure of arc BC is 264°

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.

Since the triangle is isosceles, this means that angle B = angle C

therefore angle A = 180- ( 24+24)

= 180- 48

= 132°

From the theorem that says that the angle at the circumference is twice the angle at the centre.

therefore arc BC = 2 × 132

arc BC = 264°

therefore the measure of arc BC is 264°

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Answer: y=6x-4

Step-by-step explanation:

Answer:

9374

Step-by-step explanation:

First add Saturday and Sunday totals (9681+8905)=18586

then subtract Friday's total from this number (18586-9212)=9374