Find the volume of this cylinder if r = 3 and h = 10.
(V = лr²h)

Answer:

[tex]\textsf{B)} \quad \dfrac{x^2+3x-4}{2x-1}[/tex]

Step-by-step explanation:

Given rational expression:

[tex]\dfrac{\dfrac{x^2+2x-3}{x-4}}{\dfrac{2x^2+5x-3}{x^2-16}}[/tex]

[tex]\textsf{Factor}\;\;x^2+2x-3:[/tex]

[tex]\implies x^2+3x-x-3[/tex]

[tex]\implies x(x+3)-1(x+3)[/tex]

[tex]\implies (x-1)(x+3)[/tex]

[tex]\textsf{Factor}\;\;2x^2+5x-3:[/tex]

[tex]\implies 2x^2+6x-x-3[/tex]

[tex]\implies 2x(x+3)-1(x+3)[/tex]

[tex]\implies (2x-1)(x+3)[/tex]

[tex]\textsf{Factor}\;\;x^2-16:[/tex]

[tex]\implies x^2-4x+4x-16[/tex]

[tex]\implies x(x-4)+4(x-4)[/tex]

[tex]\implies (x+4)(x-4)[/tex]

Therefore:

[tex]\implies \dfrac{\dfrac{x^2+2x-3}{x-4}}{\dfrac{2x^2+5x-3}{x^2-16}}=\dfrac{\dfrac{(x-1)(x+3)}{x-4}}{\dfrac{(2x-1)(x+3)}{(x+4)(x-4)}}[/tex]

[tex]\textsf{Apply\:the\:fraction\:rule}:\quad \dfrac{\dfrac{a}{b}}{\dfrac{c}{d}}=\dfrac{a\cdot \:d}{b\cdot \:c}[/tex]

[tex]\implies \dfrac{ (x-1)(x+3)(x+4)(x-4)}{(x-4)(2x-1)(x+3)}[/tex]

Cancel the common factors:

[tex]\implies \dfrac{ (x-1)(x+4)}{(2x-1)}[/tex]

Expand the numerator:

[tex]\implies \dfrac{x^2+3x-4}{2x-1}[/tex]

The length of this hammer is going to be 38cm

Length has the dimension of distance in the International System of Quantities. The majority of measuring systems choose a base unit for length from which all other units are derived.

The formula that we would use to get the length is

r₁ + r₂ = L

Where r₁  is the lenght 9 cm from the head

29 cm is the length from the bottom

When we add these two, we would have the length of the hammer

29 + 9 = 38cm'

Hence the length of the hammer is 38 cm

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The equation for a horizontal line that passes through the points (a, b) is y = b, where b is constant because b is the y-intercept in the equation y = mx + b.

As a result of the fact that in the equation y = mx + b, where 'b' is the y-intercept, there is no change in the value of y on the horizontal line and the slope is zero, the equation of a horizontal line is y = b, where 'b' is constant.A horizontal line's points all share the same y-coordinate.

When two points share the same y-coordinate, b, the line's equation is y=b. The coordinates (0,b) are known as the y-intercept of a horizontal line y=b. Horizontal lines are consistently perpendicular to the x-axis. The formula for the lines is always y = a y= a y= a, where a stands for a real number.

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Answer:

Step-by-step explanation:

It's gonna be true in just trust me when i say that im that guy

Answer:

true

Step-by-step explanation:

The minors of the 2 x 3 matrix are -3, -2, -1, 9, -2, -3, 6, and 5. The cofactors are -18, 16, 5, -3, -18, 18, 3, -12, and -5.

Minor of 2: -3

Cofactor of 2: -18

Minor of -8: -2

Cofactor of -8: 16

Minor of 5: -1

Cofactor of 5: 5

Minor of 3: 9

Cofactor of 3: -3

Minor of 9: -2

Cofactor of 9: -18

Minor of 6: -3

Cofactor of 6: 18

Minor of -1: -3

Cofactor of -1: 3

Minor of -2: 6

Cofactor of -2: -12

Minor of -3: 5

Cofactor of -3: -5

The minors of the 2 x 3 matrix are -3, -2, -1, 9, -2, -3, 6, and 5. The cofactors are -18, 16, 5, -3, -18, 18, 3, -12, and -5.

The given 2 x 3 matrix is composed of the values 2, -8, 5, 3, 9, 6, -1, -2, and -3. The minors of the matrix can be found by using the Laplace expansion formula and removing the row and column of the element in question. This yields the minors -3, -2, -1, 9, -2, -3, 6, and 5. The cofactors of the matrix can be calculated by taking the determinant of the minor and multiplying it by the sign of the element in question. This results in the cofactors -18, 16, 5, -3, -18, 18, 3, -12, and -5.

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The number of bags of oranges did Shannon use on Tuesday will be 3 bags.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Shannon operates an orange juice stand. On Monday she used 1 1/2 bags of oranges. On Tuesday she used 2 times as many oranges as on Monday.

The number of oranges will be calculated as,

⇒  2 × (1 ¹/₂)

⇒  2 × (1 + ¹/₂)

⇒  2 + 2 × ¹/₂

⇒  2 + 1

⇒  3 bags

The number of bags of oranges did Shannon use on Tuesday will be 3 bags.

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A triangle that has sides with lengths of 3cm, 6cm and 9cm is not a right-angled triangle.

In Mathematics, the Triangle Inequality Theorem is represented by this mathematical expression:

b - c < a < b + c

Where:

a, b, and c represent the side lengths of this triangle.

By applying the Triangle Inequality Theorem to the side lengths of this triangle, the right-angled triangle that can be formed would be determined as follows:

6 + 3 > 9

9 > 9 (False and not a right-angled triangle).

In conclusion, we can logically deduce that the two (2) short side lengths does not exceed the long side lengths and as such it is not a right-angled triangle.

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The confidence interval is given as : 2.379 < u < 3.221

How to solve for the confidence interval

we have the following details to solve the problem with

n = 9 residents

mean = x = 2.8

s = 0.68

significance level ∝ = 1 - c

= 1 - 0.9

= 0.1

the confidence interval is given as:

C.I = x ± t ∝/2 , n - 1 * s/√n

t ∝/2 , n - 1 is the critical value. This is = 1.859

C.I = 2.8 ± 1.859 * 0.68 / √9

C.I = 2.8 ± 0.421

C.I = 2.8 - 0.421,  2.8 + 0.421

C.I = 2.379 < u < 3.221

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A ratio or value that may be stated as a fraction of 100 is called a percentage.

A percentage is a figure or ratio that can be stated as a fraction of 100 in mathematics. If we need to determine a percentage of a number, multiply it by 100 and divide it by the total. So, a part per hundred is what the percentage refers to. Percent signifies for every 100. The sign "%" is used to denote it.

The value must be divided by the entire value, and the resulting number must then be multiplied by 100 to get the percentage.

The simplest way to use percentages is to compare two numbers, with the second number being rebased to 100.

Therefore, the answer is 25%.

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The image of the point (2, 3) in the line y=−x is (-3, -2).

Let there be a point P(2, 3) on the cartesian plane. The image of this point in the line y=−x will lie on a line that is perpendicular to this line and the distance of this point from y=−x will be equal to the distance of the image from this line.

Let Q be the image of p and let the co-ordinate of Q be (h, k)

The slope of line y=−x is −1

Line joining P, Q will be perpendicular to y=−x so, its slope =1.

Let the equation of the line be y=x+c since this passes through points (2,3)

3=2+c⇒c=1

and the equation y=x+1

The point of intersection R lies in the middle of P & Q. Point of the intersection of lines y=−x and y=x+1 is

2y =1 , y= [tex]\frac{1}{2}[/tex] and x = [tex]-\frac{1}{2}[/tex]

Hence, [tex]\frac{h+2}{2} = -\frac{1}{2}[/tex] and [tex]\frac{k+3}{2} = \frac{1}{2}[/tex]

⇒ h=−3 and k =−2

So, the image of the point (2, 3) in the line y=−x is (-3, -2).

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The correct question is:

What is the image of the point (2,3) in the line y= -x?

In the given word problem the Gunnar's car can travel 399.17 miles travel using 17.82 gallon of gas.

A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world." In order for kids to understand the word problem, they must be familiar with the terminology that goes along with the mathematical symbols that they are used to.

Gunnar's car travel using per gallon of gas = 22.4 miles.

According to the given question,

Gunnar's car can hold 17.82 gallons of gas. Then number of miles does Gunnar's car can travel is ,

=> 22.4 × Car's total tank has hold

=> 22.4 × 17.82

=> 399.17 miles

Hence the Gunnar's car can travel 399.17 miles travel using 17.82 gallon of gas.

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Answer: It assigns a unique output to each input.

This statement is true of all functions, including the function f(x) = 3x - 12.

A function assigns a unique output to each input, meaning that for each value of x that is input into the function, there is a corresponding and unique value of y that is output. This is also called the vertical line test, if for any vertical line cuts the graph of a function at most one time, it is a function.

It does not matter whether it is linear or nonlinear or whether the correlation is positive or negative, the statement that It assigns a unique output to each input is true for all functions.

Step-by-step explanation:

If H is the circumcenter of triangle EFG , EH = 5.06 , and LH = 2.74 then FL is calculated to be 4.25

Applying Pythagoras theorem, △EFG

Information given from the question is interpreted as

LH = opposite

FL = adjacent

FH = EH = hypotenuse

Using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required distance

5.06² = 2.74² + x²

x² = 25.6036 - 7.5076

x² =  18.096

x = √18.096

x = 4.2539

x = 4.25 (to the nearest hundredth)

hence x = FL = 4.25

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(a) They are no longer independent because they are related and will more than likely have related blood types. (b) A probability area model will give an accurate theoretical probability is they must be independent.

Genetic information is transmitted from parent to kid through inheritance. Members of the same family typically share traits in common because of this. The process of fertilizations occurs during sexual reproduction when the sperm and egg cells join forces to create the first cell of the new organism.

Genetic material from the two parents is present in each of the newborn's cells. If you look at the shared traits of family members, such as average height, nose and ear shape, eye and hair color, and hair and eye color, you can see how genetic material is passed down.

Blood type is affected by genetic inheritance. if they were brothers or father and son then they are no longer independent because they are related and will more than likely have related blood types.

true in order to assume a probability area model will give an accurate theoretical probability is they must be independent.

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In Q1, The equation k = y² + a is correct,

To make y the subject of the formula, √k = y + a is incorrect, it should be √k = y + √a

√k - √a = y

In Q2, t = v/4 + 1 is correct

t - 1 + v/4 is incorrect, it should be t - 1 = v/4

t - 1/4 = v

so the correct answer is t-1/4=v

Both the triangles are not similar.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

Two triangles are comparable if they have two pairs of sides that are in the same ratio and if the included angles are likewise equal.

The square of any ratio between any two matching sides of two comparable triangles is equal to the ratio of their areas. As an illustration, Area of ABC/Area of DEF equals (AB)2/(DE)2 = (BC)2/(EF)2 = (AC)2(DF)2 for any two comparable triangles ABC and DEF.

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A reference point used to appropriately scale the dilation of a figure.

A dilation’s center is a fixed point in the plane around which all points expand or shrink. Under a dilation (k 1), the sole invariant (not changing) point is the center, which might be within, outside, or on a figure. Scale Factor: In a dilatation, the scale factor is the amount by which the figure is stretched or shrunk. Dilation Center: The center of dilation is a reference point used to scale the dilation of a figure suitably.

Dilation of the pupil allows more light into the eye, much as opening a door allows light into a dark room. Dilation allows your eye doctor to examine for a variety of common eye issues, including diabetic retinopathy.

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2 fingers dilation is normally 2 cm in measurement.

Dilation is the process of increasing an object's size without altering its form. Depending on the scale factor, the object's size may rise or shrink. A square of side 5 units can be widened to a square of side 15 units using dilation math, but the square's form doesn't change.

A dilation is a function f from a metric space M into itself that, for any locations x, y in M, fulfills the identity d=rd, where d is the distance between x and y and r is a positive real integer. Such a dilatation is a resemblance of the space in Euclidean space.

Meaning of Dilation in Math. Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size.

Normally 1 finger dilation represents 1 cm so by unitary methord 2finger dilation is 2 cm

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The extension of two fingers is usually 2 cm.

Dilation is the process of enlarging an object without changing its shape. Depending on the magnification, the size of the object will increase or decrease. A 5 unit square can be expanded to a 1l5 unit square using dilation math, but the shape of the square remains the same. A dilation is a function f from the metric space M to itself, satisfying the identity d=rd for any position x,y in M. where d is the distance between x and y and r is a positive real number. Such an extension resembles the space of Euclidean space.

Stretching Used in Mathematics To change the size of an element, we use a transition called Stretch. Grow is used to enlarge or shrink an object. The result of this transformation is an image with the same shape as the original image. However, there is variation in the size of the shape.

Normally, one finger will stretch 1 cm, so in the unified method, two fingers will stretch 2 cm.

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Rachel's personal loan of $4,500 with a 12% annual interest rate for 36 months will have a finance charge of $6,230.16, meaning that she will need to pay a total of $10,730.16 to pay off the loan amount.

The finance charge on Rachel's loan can be calculated by multiplying the loan amount by the interest rate and then multiplying by the loan term (in months).

Finance Charge = (Loan Amount x Interest Rate x Loan Term)

Finance Charge = ($4,500 x 0.12 x 36 months)

Finance Charge = $6,230.16

The finance charge on Rachel's loan can be calculated by multiplying the loan amount by the interest rate and then multiplying by the loan term (in months). In this case, Rachel took out a $4,500 loan with a 12% annual interest rate for 36 months. The total finance charge for this loan can be calculated as follows: Finance Charge = ($4,500 x 0.12 x 36 months) = $6,230.16. This means Rachel will need to pay a total of $10,730.16 to pay off the loan, including the finance charge. This also means that Rachel's monthly payments of $173.06 will go towards the principle balance of the loan and the interest accrued during each month.

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The statement that is true on the ice cream shops selling sundaes is C: the two shops never charge the same price for sundaes with the same number of scoops

Larry's Ice Cream Shop has scoops modeled by the model 1.2x + 1 while  Ice Cream World's price is modeled by 0.4 ( 0.3x + 1 ).

They will therefore have the same price at :

1.2x + 1  = 0.4 ( 0.3x + 1 )

1. 2 x + 1 = 0. 12 x + 0.4

1. 2 x - 0. 12 x = 0. 4 - 1

1. 08 x = - 0. 6

x = - 0. 6 / 1. 08

x = - 0. 5556

This means that the two shops never charge the same price.

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The segment joining the midpoints of two sides of a triangle is parallel to and half the length of the third side.

The midpoint theorem states that the line segment drawn from the midpoint of any two sides of the triangle is parallel to the third side and is half of the length of the third side of the triangle.

A line segment that connects two midpoints of the sides of a triangle is called a midpoint segment.

There are two important properties of the midsegments Theorem:

The Midsegment Theorem states that the midsegment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle, and the length of this midsegment is half the length of the third side

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Answer:

4.97% is your answer

Step-by-step explanation:

The inequality to represent the number of matinee tickets, x, and evening tickets, y, Aiden can buy is,

⇒ 5x + 10y ≤ 50

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

Aidan is going to buy movie tickets for his friends. matinee tickets are $5 each and evening tickets are $10 each. Aidan can spend at most $50 dollars.

Now, Let the number of matinee tickets Aiden can buy = x

And, The number of evening tickets Aiden can buy = y

So, We can formulate;

The correct inequality is,

⇒ 5x + 10y ≤ 50

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Danielle earned a total of $1,058.25 last week.

A commission is a percentage of total sales as determined by the rate of commission. A commission is a profit paid due to making a sale.

commission=rate of commission⋅total sales.

To find the commission on a sale, multiply the rate of commission by the total sales.

commission = rate of commission⋅total sales.

commission = 7.75% x $4,300

commission = 0.0775 x $4,300

commission = $333.25

Danielle's earnings will be the addition of both her commission and base salary

Total = commission + base salary

Total = $333.25 + $725

Total = $1,058.25

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Statement A is correct. The ratio of the number of gallons of red paint to the number of gallons of blue paint in shade B is 2:1.

What is the ratio?

Equivalent ratios are those that are the same when compared. Two or more ratios can be compared to determine whether or not they are equal. For example, the ratios 1:2 and 2:4 are equivalent.

Given that,

Shade A                                                                            Total

Number of Gallons of Blue Paint: 8   12  16   24             60

Number of Gallons of Red Paint   12  18  24   36            90

Shade B      

Number of Gallons of Blue Paint:  5     7   9   12             33

Number of Gallons of Red Paint   10    14  18   24          66

The ratio of the number of gallons of red paint to the number of gallons of blue paint in shade B is 66: 33 = 2:1.

It means for every 2 gallons of red paint for every 1 gallon of blue paint.

The ratio of the number of gallons of red paint to the number of gallons of blue paint in shade A is 90:60 = 3:2.

It means for every 3 gallons of red paint for every 2 gallons of blue paint.

The total gallon in shade A is (60 + 90) = 150.

If she adds 1 gallon of blue paint to 20 gallons of shade A.

Then she creates 150/20 = 7.5 gallons of blue paint in shade B.

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To have your result appear in a certain table cell, click there. Click Formula under Table Tools on the Layout tab.

A sequence is a group of numbers (sometimes known as "terms"), for instance, 2, 5, 8. Some sequences have a particular pattern that can be used to extend them indefinitely. Use the example of 2,5,8 and continue the series by adding 3. There are formulas that outline the locations of words inside a sequence. Informally, a sequence is a group of objects that are arranged in some way in mathematics (or events). It is made up of parts, much like a set (also called elements or terms). The entire, potentially infinite number of arranged objects is referred to as the length of the sequence. putting two or more things in a logical order. Chronological.

given

To have your result appear in a certain table cell, click there. Click Formula under Table Tools on the Layout tab.

Once you have confirmed that Word has included the cells you wish to sum in the Formula box's text within the parentheses, click OK.

The equation =SUM(ABOVE) sums the figures in the column above the one you are in.

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The substitution principle in math we substitute the value of one variable with another one and solve the equation.

By changing the value of another variable in an equation, the variable can be eliminated using this method. Thus, the elimination by substitution method is the name given to this technique.

As we are aware, the substitution approach entails solving the equation to determine the value of the variable, which is then substituted in the other equation. The elimination approach, in contrast, involves removing variables from the equation such that the equation's system can be reduced to being the function of a single variable.

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The sum of the additive inverse of 29 and 61 is equal to -90.

The sum of the additive inverse of two numbers is equal to zero. The additive inverse of a number is the (opposite) number which when added to the original number yields zero. The formula for calculating the additive inverse of a number is additive inverse (x) = - x. The additive inverse of 29 and 61 can be calculated using the formula, additive inverse (29) = -29 and additive inverse (61) = -61.

Therefore, the sum of the additive inverse of 29 and 61 will be -29 + -61 = -90. This can be confirmed by adding 29 and 61 which will yield 90 and then subtracting 90 from zero to yield -90. In other words, the sum of the additive inverse of 29 and 61 is equal to -90.

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