A steel rod of mass 25kg is melted down to create ball bearings of radius 4mm. One kilogram of this steel has a volume of 150[tex]cm^3[/tex]. How many ball bearings could be made from this steel rod?

Answer:

To factor completely using the GCMF (Greatest Common Monomial Factor), we first need to identify the common monomial factor of all three terms. In this case, the common monomial factor is 2x²:

10x^5 + 8x^4 - 4x² = 2x²(5x^3 + 4x^2 - 2)

Now, we can see that the expression can be factored further, but it cannot be factored using the GCMF. However, we can use other factoring techniques, such as grouping or factoring by grouping, to factor the remaining expression:

2x²(5x^3 + 4x^2 - 2) = 2x²(5x^3 + 10x^2 - 6x^2 - 2)

= 2x²(5x^2(x + 2) - 2(x + 2))

= 2x²(5x^2 - 2)(x + 2)

Therefore, the expression 10x^5 + 8x^4 - 4x² can be factored completely as 2x²(5x^2 - 2)(x + 2).

Step-by-step explanation:

Answer:

Let's denote the length, width, and

height of the cuboid as "l", "w", and

"h, respectively. Then, we have:

lw= 24 (Area of one face)

Ih 32 (Area of another face)

wh 48 (Area of the third face)

To solve for the dimensions of the

cuboid, we can use a system of

equations. We can start by solving

for one of the variables in terms of

the other two. For example, from the

first equation, we have:

W 24/

Substituting this into the second

equation, we get:

Ih 32

I(24/)h = 32

24h 32

h 32/24

h 4/3

Next, we can substitute the values of

h and w into the third equation to

solve for:

wh = 48

I(24/)(4/3) = 48

I2 72

= sqrt(72)

I= 6sqrt(2)

Finally, we can use the values of I

and w to solve for the remaining

dimension:

lw 24

(6sqrt(2))(24/(6sqrt(2))) = 24

W = 4sqrt(2)

Therefore, the lengths of the sides of

the cuboid are:

Length () = 6v2 cm

Width (w) = 4/2 cm

Height (h) = 4/3 cm

The image was created by translating 5 units down, 5 units up, 1 unit down, and 1 unit up. ABCD and A'B'C'D' are two polygons on the graph.

The first polygon, ABCD, has vertices at (4,4), (12,4), (8,4), and (1,1),). (3,1). The vertices of the second polygon, A'B'C'D', are located at (1,1), (3,1), (3,2), and (1,2). (0.5,.25).

We can establish the translation that was applied to produce the image by comparing the coordinates of the two polygons. The two polygons' initial coordinate is (1,-1) and their second coordinate is (1,-1). (1,-6). The translation is 5 units lower because of the 5-unit difference in the y-coordinate. The second coordinate for the two polygons is (3,-5) and (3,-10). The translation is 5 units lower because of the 5-unit difference in the y-coordinate.

The third coordinate of the second polygon is (7,-5) and (7,-10). The translation is 5 units lower because of the 5-unit difference in the y-coordinate. The fourth coordinate of both polygons is (5,-1). (5,-6). The translation is 5 units lower because of the 5-unit difference in the y-coordinate.

The translation of the image was five units down, five units up, one unit down, and one unit up.

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Answer: C = 1/4

Step-by-step explanation: I got it right on my test

Hope this helps :)

Answer:

To write Z in Euler form, we first need to find its magnitude and argument.

The magnitude of Z is given by:

|Z| = √(Re(Z)^2 + Im(Z)^2)

where Re(Z) is the real part of Z, and Im(Z) is the imaginary part of Z.

In this case:

Re(Z) = √3

Im(Z) = √3 i

So:

|Z| = √(√3^2 + (√3)^2) = √(3 + 3) = √6

The argument of Z is given by:

arg(Z) = tan^(-1)(Im(Z) / Re(Z))

In this case:

arg(Z) = tan^(-1)((√3) / √3) = tan^(-1)(1) = π/4

Therefore, Z in Euler form is:

Z = |Z| e^(i arg(Z)) = √6 e^(i π/To write Z in Euler form, we first need to find its magnitude and argument.

The magnitude of Z is given by:

|Z| = √(Re(Z)^2 + Im(Z)^2)

where Re(Z) is the real part of Z, and Im(Z) is the imaginary part of Z.

In this case:

Re(Z) = √3

Im(Z) = √3 i

So:

|Z| = √(√3^2 + (√3)^2) = √(3 + 3) = √6

The argument of Z is given by:

arg(Z) = tan^(-1)(Im(Z) / Re(Z))

In this case:

arg(Z) = tan^(-1)((√3) / √3) = tan^(-1)(1) = π/4

Therefore, Z in Euler form is:

Z = |Z| e^(i arg(Z)) = √6 e^(i π/4)

Answer:

(2, -2)

Step-by-step explanation:

To rotate a point in a coordinate plane 90 degrees clockwise, we need to switch the x and y coordinates and negate the new x coordinate.

So let's apply this formula to the point (-2, -2):

- The new x-coordinate will be the original y-coordinate: -2

- The new y-coordinate will be the negation of the original x-coordinate: -(-2) = 2

Therefore, after rotating (-2, -2) 90 degrees clockwise, we get the point (2, -2).

We can visualize this by plotting both points on a coordinate plane and drawing a line of reflection that represents the rotation:

```

Before rotation:

|

|

|

-------+-------

|

(-2,-2)

After rotation:

|

|

(2,-2)|

-------+-------

|

```

As shown in the diagram above, after rotating (-2,-2) 90 degrees clockwise, it lands at (2,-2).

The transformation that it could have been is either a rotation or a reflection, over one of the vertices of the figure.

The possible transformations on a figure are listed as follows:

Either a reflection or a rotation can happen over one of the vertices of the graph, which will keep it's coordinates constant, and thus the transformation in the context of this problem is either one of these two.

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The fraction that represents the addition model of part A is 5/10, and for part B is 3/100.

Parts of a whole are defined as fractions. The top and bottom numbers of a fraction are explained in the fundamentals of fractions. The number at the top represents the number of selected pieces of a whole, while the number at the bottom reflects the entire number of components.

According to the given information:

Based on the information provided, a grid A with 10 equal columns is depicted, with 5 shaded in. This will be expressed as a score of 5/10.

A second grid B, same in size, with 100 squares shaded in is also presented. This will be expressed as 3/100.

In this situation, Emma's response is erroneous because he added 5 to 3 and received an 8/100.

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Answer:

40 units

Step-by-step explanation:

12+12+8+8=40 units

According the question 89+82  expressiοn is the same as 8(9+2).

An expressiοn in math is a sentence with a minimum οf twο numbers οr variables and at least οne math οperatiοn. This math οperatiοn can be additiοn, subtractiοn, multiplicatiοn, οr divisiοn.

Algebraic expressiοns are classified οn the basis οf the number οf terms in the expressiοn. The variοus types οf algebraic expressiοns are:

The difference between expressiοns and equatiοns is that an expressiοn signifies a cοmbinatiοn οf numbers, variables, and οperatiοn symbοls whereas an equatiοn will always use an equal (=) οperatοr between twο math expressiοns.

The expressiοn 8(9+2) can be simplified using the distributive prοperty οf multiplicatiοn οver additiοn:

8(9+2) = 89 + 82

Therefοre, the answer is: 89+82

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The value of the numer is negative seven ( -7 ).

Given the statement in the question; the quotient of a number and negative eight is seven-eighths.

Let's translate the given statement into an algebraic equation to solve for the unknown number.

"The quotient of a number and negative eight" means that we are dividing the number by -8.

We can represent this using the division symbol " / ":

Let the number be represented by x.

x / (-8)

"Is" means "equals" " = "

"Seven-eighths" can be written as a fraction:

7/8

Nowm putting it all together, we get:

x / (-8) = 7/8

To solve for x, we can multiply both sides by -8:

x = (-8) × (7/8)

Simplifying the right side, we get:

x  = -7

Therefore, the value of x is -7.

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Step-by-step explanation:

Think we can get a better picture, maybe more light? I wouldn't mind helping if you can

The correct option is C. Point B as only the line BC touching the circle at point B is tangent to the circle.

The tangent to a circle theorem states that a line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency

We can observe that the line BC touches the circle at point B and the radius of the circle will be perpendicular to the line BC

Therefore, since the radius of the circle is perpendicular to the line BC at point B, then it is tangent to the circle

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The answer of the given question based on finding the values of a and b are 12 and 9, respectively.

A triangle is  geometric shape that consists of the three straight sides and three angles. Triangles are one of  basic shapes in geometry and often used in the various mathematical applications.

Since  triangles are similar, their corresponding sides are in the proportion. That is:

AB/DE = BC/EF = AC/DF

We can use this proportion to find the values of a and b.

From the diagram, we can see that:

AB = 12 + a

BC = 9 + b

AC = 15

DE = 8

EF = 6

Using the proportion, we get:

AB/DE = BC/EF

(12 + a)/8 = (9 + b)/6

Cross-multiplying, we get:

6(12 + a) = 8(9 + b)

72 + 6a = 72 + 8b

6a = 8b

a/b = 4/3

Similarly, using the other part of the proportion, we get:

AC/DF = 15/DF = (AB + BC)/(DE + EF) = (12 + a + 9 + b)/(8 + 6)

15DF = 21 + a + b

Substituting the value of a/b = 4/3, we get:

15DF = 21 + (4/3)b + b

15DF = 21 + (7/3)b

45DF = 63 + 7b

45DF = 7(b + 9)

Dividing both sides by 7, we get:

DF = (b + 9)

Substituting this value in the previous equation, we get:

45(b + 9) = 63 + 7b

45b + 405 = 63 + 7b

38b = 342

b = 9

Substituting the value of b in the equation a/b = 4/3, we get:

a/9 = 4/3

a = 12

Therefore, the values of a and b are 12 and 9, respectively.

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Answer:

a= positive

b= When the graph goes up it means it has a positive trend.

c= the direction does not make sense because the measurements for the x and y coordinate do not correlate with each other.

Step-by-step explanation:

Answer:

Their average velocity during their trip was 59.19 miles per hour.

Step-by-step explanation:

To calculate the average velocity of the family's trip, we divide the total distance traveled by the time it took to travel that distance:

Average velocity = total distance ÷ time

In this case, the total distance traveled is 509 miles and the time it took to travel that distance is 8.6 hours. So, we can plug these values into the formula:

Average velocity = 509 miles ÷ 8.6 hours

Simplifying this equation, we get:

Average velocity = 59.19 miles per hour (rounded to two decimal places)

Therefore, the family's average velocity during their trip was 59.19 miles per hour.

The cοst οf οne adult ticket is $12 and the cοst οf οne child ticket is $5.

A system οf linear equatiοns can be sοlved graphically, by substitutiοn, by eliminatiοn, and by the use οf matrices.

The cοrrect system οf equatiοns tο sοlve fοr a and c is:

12a + 5c = 169 (equatiοn 1)

22a + 10c = 314 (equatiοn 2)

These equatiοns represent the tοtal ticket sales and revenue οn twο different days.

Tο sοlve this system, we can use the methοd οf eliminatiοn.

-24a - 10c = -338

22a + 10c = 314

-2a = -24

Dividing bοth sides by -2:

a = 12

Nοw we can substitute a = 12 intο equatiοn 1 tο sοlve fοr c:

12(12) + 5c = 169

144 + 5c = 169

5c = 25

c = 5

Therefοre, the cοst οf οne adult ticket is $12 and the cοst οf οne child ticket is $5.

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The statement that best assesses the linearity of the relationship between age and vertical jump, given that the scatterplot appears to be approximately linear, is:

Although it is given that the scatterplot is reasonably linear, because the residual plot has no obvious pattern, it is appropriate to use the line of best fit to predict vertical jump based on age.

The second option is correct.

What is a  residual plot ?

A  residual plot is described as a graphical technique that attempts to show the relationship between a given independent variable and the response variable given that other independent variables are also in the model.

If the residual plot has no obvious pattern, it suggests that the relationship between the variables is linear and that the line of best fit is appropriate for predicting the vertical jump based on age.

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Answer:

thx to the comments

Step-by-step explanation:

The expressiοn that tells the weight οf the flοur left in the bag is 2 - 0.25

A finite cοmbinatiοn οf symbοls that are well-fοrmed in accοrdance with cοntext-dependent principles is referred tο as an expression or mathematical expression. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression.

Here, we have

Given: From a 2-pound bag of flour, Marcella took 1/4 pound to bake bread.

We have to find the expression that tells the weight of the flour left in the bag.

Marcella took 1/4 pound to bake bread = 0.25

If Marcella took 0.25 pounds from a 2-pound flour bag then she left with 1.75 pounds.

Hence,  the expression that tells the weight of the flour left in the bag is 2 - 0.25

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The answer of the given question based on the inequality is option B) all real numbers.

A real numbers are  set of numbers that include all rational and irrational numbers, which can be expressed as decimal expansions that go on forever without repeating. The set of real numbers is denoted by symbol ℝ and includes numbers such as 1, 2, 3, -4, -5/6, π, √2, and e.

B.) all real numbers

A statement "0 is greater than or equal to 0" is always true, regardless of  value of  variable or any other conditions. This is because any number is always equal to the itself, and 0 is no exception. Therefore, solution to this inequality is all the real numbers.

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The data is skewed to the lower values because many patients only call the doctor once or twice a year when they are sick.

Spread and distribution of data are statistical concepts that describe how a set of data is spread out or distributed.

Distribution refers to how the data is distributed or arranged. It is typically described in terms of its shape, center, and spread. Common types of distributions include normal distribution, skewed distribution, and uniform distribution. The distribution can be visualized using various graphs such as histograms, box plots, and scatter plots.

Based on the histogram description, the best answer is:

The data is skewed to the lower values because many patients only call the doctor once or twice a year when they are sick.

The histogram shows that the frequency of calls is highest for the 1 to 25 interval, with decreasing frequency for each subsequent interval. The fact that the shaded bars stop at relatively low frequencies for each interval suggests that there are very few patients who call the doctor frequently, skewing the data towards the lower values. The histogram also shows a wide range of values, or spread, with the highest interval going up to 100, but the low frequencies in each interval suggest that the data is not normally distributed.

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Answer:its b

Step-by-step explanation:

Using Cauchy-Euler equation, the solution of the second-order homogeneous differential equation  is y2(x) = c3 * x^(1/3) + c4 * x^(4/3) - (1/2) * c4 * x

The given LODE is a second-order homogeneous differential equation with constant coefficients. The characteristic equation is given by:

9r^2 - 6r + 2 = 0

Using the quadratic formula, we find the roots to be:

r = (1/3) ± i/sqrt(3)

Thus, the general solution to the differential equation is:

y(x) = c1 * x^(1/3) * cos((1/3)*arccos(sqrt(3)*r)) + c2 * x^(1/3) * sin((1/3)*arccos(sqrt(3)*r))

To find the first solution, we can choose either the cosine or sine term. Let's choose the cosine term for simplicity:

y1(x) = x^(1/3) * cos((1/3)*arccos(sqrt(3)*r))

To find the second solution, we can use the method of reduction of order. Assume that the second solution has the form:

y2(x) = v(x) * y1(x)

Substituting this into the differential equation, we obtain:

9x^2(v''(x)*y1(x) + 2v'(x)*y1'(x) + v(x)*y1''(x)) - 6x(v'(x)*y1(x) + v(x)*y1'(x)) + 2v(x)*y1(x) = 0

Simplifying this equation by dividing by x^2*y1(x), we get:

9v''(x) + (18/r)x*v'(x) + ((2/r^2) - 1)v(x) = 0

where r = sqrt(3)

This is a Cauchy-Euler equation, which can be solved by assuming a solution of the form:

v(x) = x^m

Substituting this into the equation, we obtain:

9m(m-1) + (18/r)m + ((2/r^2) - 1) = 0

Simplifying this equation, we get:

9m^2 + 6m + 1 = 0

Using the quadratic formula, we find the roots to be:

m = (-1/3) or (-1/3)

Thus, the second solution is given by:

y2(x) = c3 * x^(1/3) + c4 * x^(1/3) * ln(x)

To determine the first four leading terms in the second solution, we can use the Taylor series expansion of the natural logarithm:

ln(x) = (x-1) - (1/2)(x-1)^2 + (1/3)(x-1)^3 - ...

Substituting this into the second solution, we obtain:

y2(x) = c3 * x^(1/3) + c4 * x^(1/3) * [(x-1) - (1/2)(x-1)^2 + (1/3)(x-1)^3 - ...]

Simplifying this expression, we get:

y2(x) = c3 * x^(1/3) + c4 * x^(1/3) * (x-1) - c4 * x^(1/6) * (1/2)(x-1)^2 + c4 * x^(1/3) * (1/3)(x-1)^3 - ...

Thus, the first four leading terms in the second solution are:

y2(x) = c3 * x^(1/3) + c4 * x^(4/3) - (1/2) * c4 * x

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The magnitude of CD is 5 miles and its direction is approximately 53.13°.

option D.

To find the magnitude and direction of CD, we first need to calculate the distance between points C and D, which will give us the magnitude of the vector CD.

The distance formula between two points (x1, y1) and (x2, y2) is:

d = √((x2 - x1)² + (y2 - y1)²)

Plugging in the values for points C and D, we get:

d = √((0 - (-4))² + (1 - 4)²)

= √(16 + 9)

= √(25)

= 5 miles

To find the direction of CD, we can use the arctan function to find the angle that CD makes with the x-axis.

tan(θ) = (y2 - y1) / (x2 - x1)

Plugging in the values for points C and D, we get:

tan(θ) = (1 - 4) / (0 - (-4))

= -3/4

Taking the arctan of both sides, we get:

θ = arctan(-3/4)

≈ -36.87°

However, since CD points in the negative x-direction, we need to add 90 degrees to get the correct direction.

θ = arctan(-3/4) + 90°

≈ 53.13°

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Step-by-step explanation:

The formula to calculate the circumference of a circle is:

Circumference = 2πr

where "r" is the radius of the circle and "π" is the mathematical constant pi, approximately equal to 3.14159.

Given that the circumference of the circle is 20 ft, we can plug in the values into the formula and solve for "r":

20 = 2πr

Divide both sides of the equation by 2π:

r = 20 / (2π)

Simplify the expression by using the approximation of π as 3.14159:

r = 20 / (2 x 3.14159)

r = 3.1831 ft (rounded to four decimal places)

Therefore, the radius of the circle is approximately 3.1831 feet.

Answer:

Length of Bridge A = 4821

Length of Bridge B = 4635

Step-by-step explanation:

Let's call the length of Bridge A "x" which is measured in feet. According to the problem, the length of Bridge B is "186 feet shorter than Bridge A." This can be written as the following:

Length of Bridge B = x - 186

The problem also tells us that the "combined length of the two bridges is 9456 feet," which we can write as:

Length of Bridge A + Length of Bridge B = 9456

Now we can substitute the expression we found for the length of Bridge B into this equation. This can be shown as the following:

x + (x - 186) = 9456

Simplifying this equation, we can combine the two x terms and get the following:

2x - 186 = 9456

Now, we can solve for x

2x - 186 + 186 = 9456 + 186

2x = 9642

x = 4821

So the length of Bridge A is 4821 feet. To find the length of Bridge B, we can use the expression we found earlier:

Length of Bridge B = x - 186 = 4821 - 186 = 4635

Therefore, the length of Bridge A is 4821 feet, and the length of Bridge B is 4635 feet.

Mark has 23 marbles and Don has 48 marbles.

What is equation?

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equals sign (=). The expressions on both sides of the equation can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

Mark and Don, are selling their marbles at a garage sale. Don has more marbles than Mark and his number of marbles is equal to "2 more than 2 times the number of marbles Mark has."

Let x be the number of marbles that Mark has. Then, we can represent the number of marbles that Don has as 2x + 2.

Since the total number of marbles is 71, we can set up the equation:

x + (2x + 2) = 71

Simplifying the left side of the equation, we get:

3x + 2 = 71

Subtracting 2 from both sides, we get:

3x = 69

Dividing both sides by 3, we get:

x = 23

So Mark has 23 marbles. To find out how many marbles Don has, we can substitute x = 23 into the expression we derived earlier:

2x + 2 = 2(23) + 2 = 48

Therefore, Don has 48 marbles.

In total, they have 23 + 48 = 71 marbles, as given in the problem statement.

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Answer:

C) 25

Step-by-step explanation:

A square has all four sides equal.

5x = 10x - 25

-5x = -25

x = 5

Now put 5 in for x, and you get the answer is 25

Answer:

x = 8

Step-by-step explanation:

Let x be the number of blue seats in each section.

Then the total number of seats in each section is:

14 + x

Since there are 4 identical sections, the total number of seats in the theater is:

4(14 + x) = 56 + 4x

We know that the theater has 88 seats, so:

56 + 4x = 88

Simplifying the equation:

4x = 32

x = 8

Therefore, each section has 14 red seats and 8 blue seats.

The expression for the number of blue seats in each section is x = 8.

Answer:

---------------------------------

Let b be the number of blue seats.

There are 4 sections, each has 14 red and b blue seats, with the total number of seats being 88.

The equation to reflect this would be:

Its solution would be:

The solution to  4^x = 5^x +^2 is

x = -2log 5/( log 5 - log 4)

Option C is correct.

We will rewrite the equation as:

4^x = 5^x * 5^2

applying  the logarithm function to both sides of the equation.

log(4^x) = log(5^x * 5^2)

simplifying the right side of the equation, using the properties of logarithms,

log(4^x) = log(5^x) + log(5^2)

log(4^x) = xlog(4) = x2log(2)

log(5^x) + log(5^2) = xlog(5) + log(25)

Substituting these results back into the original equation, we have:

x2log(2) = x*log(5) + log(25)

x*(2*log(2) - log(5)) = log(25)

Divide  both sides by (2*log(2) - log(5)), we get:

x = x = -2log 5/( log 5 - log 4)

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The answer of the given question based on the  number best describes a typical rating in the contest the answer is 7.9.

The median is  measure of central tendency in statistics that represents  middle value of  dataset. It is  value that separates  highest 50% of  values from the lowest 50%.

To find  median of a dataset, you first need to sort  data in ascending or descending order.

The median rating is 7.9, which means that half of the contestants scored above 7.9 and half scored below. This suggests that 7.9 is a representative value of the ratings overall.

Additionally, the interquartile range (IQR) is a measure of the spread of the middle 50% of the ratings, and it is given as 0.8. This means that the ratings between the 25th and 75th percentile fall within a range of 0.8, which suggests that the ratings are fairly tightly clustered around the median of 7.9.

Therefore, the number that best describes a typical rating in the contest is 7.9.

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