Use the general slicing method to find the volume of the following solid. The solid with a semicircular base of radius 11 whose cross sections perpendicular to the base and parallel to the diameter are squares

The required number word that is one more than fourteen is "fifteen."

A number system is described as a technique of composing to represent digits. It is the mathematical inscription for describing the numbers of a given set by using numbers or other characters in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.

Here,
In the number system when we add 1 to the number 14, what we get is 15 in words it is fifteen
So,
one + fourteen = fifteen

Thus, the required number word that is one more than fourteen is "fifteen."

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Answer:

4.2 yrs hope this helped. :)

Step-by-step explanation:

MTH1W is a grade 9 mathematics course that covers key mathematical concepts and problem-solving skills. Topics covered include algebraic expressions and equations, graphs of linear relationships, solving systems of linear equations, quadratic relationships, trigonometry, similar triangles and circles, Pythagorean theorem, distance formula, area and volume of geometric shapes, and statistics and probability. This course helps students build a strong foundation in algebra and geometry, and develop important problem-solving skills for future math courses. The sections on algebraic expressions, linear and quadratic relationships, and trigonometry provide students with the skills to manipulate mathematical expressions and solve real-world problems. The sections on geometry and statistics cover key concepts in these areas, providing students with a well-rounded understanding of mathematics.

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1.1. Given any negative real number s, the cube root of s is negative.

1.2. For any real number s, if s is negative, then the cube root of s is negative.

1.3. If a real number s is negative, then the cube root of s is negative.

The cube root of a real number can be either positive or negative, depending upon the sign of the original number. If the original number is positive, then the cube root can be either positive or negative.

If the original number is negative, then the cube root must and should be negative. This is because multiplying any negative number by itself three times will result in a negative number.

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The factor of [tex]6x^{2}y+8-30y-40[/tex] is 2 ( [tex]3x^{2}y-15y-20[/tex] ).

The factor is a number or quantity by which a given number, quantity, or expression is multiplied to produce another number, quantity, or expression. Factors are usually whole numbers, but they can also be expressions or fractions. Factors are used to simplify or solve equations and expressions. Factors can also be used to determine the greatest common factor (GCF) of two or more numbers or expressions.

The first step is to factor out the greatest common factor (GCF), which in this case is 2. The GCF of [tex]6x^{2}y+8-30y-40[/tex] is 2. Once the GCF is factored out, the expression can be written as 2([tex]3x^{2}y-15y-20[/tex]). Finally, the remaining factors can be combined to get the final factor of 2([tex]3x^{2}y-15y-20[/tex]).

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Answer:

30.39 and 10.26 pounds.

Step-by-step explanation:

Step 1 of 2: if the variables x (for 41% alloy) and y (for 54% alloy), then

Step 1 of 2: it is possible to make up the system of two equations:

[tex]\left \{ {{x+y=0.45*40} \atop {0.41x+0.54y=0.45(x+y)}} \right. < = > \ \left \{ {{y=\frac{72}{13} } \atop {x=\frac{162}{13}}} \right.[/tex]

then the mass of the alloy containing 41% of coper is 162/13:0.41≈30.39

the mass of the alloy containing 54% of copper is 72/13:0.54=10.26.

The probability that a defective component will be detected only by the first inspector is 0.19

The probability that a defective component will be detected by exactly one of the two inspectors is 0.38

The probability that all three defective components in a batch escape detection by both inspectors is 0.

It is given that The first inspector detects 81% of all defectives that are present, and the second inspector does likewise.

Therefore P(A)=P(B)=81%=0.81

At least one inspector does not detect a defect on 38% of all defective components.

Therefore, bar P(A∩B)=0.38

As we know:

bar P(A∩B)=1-P(A∩B)=0.38

P(A∩B)=1-0.38=0.62

A defective component will be detected only by the first inspector.

P(A∩barB)=P(A)-P(A∩B)

=0.81-0.62

P(A∩barB)=0.19

The probability that a defective component will be detected only by the first inspector is 0.19

Part (B) A defective component will be detected by exactly one of the two inspectors.

This can be written as: P(A∩barB)+P(barA∩B)

As we know:

P(barA∩B)=P(B)-P(A∩B) and P(A∩bar B)=P(A)-P(A∩B)

Substitute the respective values we get:

P(A∩ barB)+P(bar A∩B)=P(A)+P(B)-2P(A∩B)

=0.81+0.81-2(0.62)

=1.62-1.24

P(A∩ barB)+P(bar A∩B)=0.38

The probability that a defective component will be detected by exactly one of the two inspectors is 0.38

Part (C) All three defective components in a batch escape detection by both inspectors

This can be written as: P(bar A∪ bar B)-P(bar A∩B)-P(A∩ barB)

As we know bar P(A∩B)=P(bar A∪ bar B)=0.38

From part (B): P(bar A∩B)+P(A∩bar B)=0.38

This can be written as:

P(bar A∪ bar B)-P(bar A∩B)-P(A∩bar B)=0.38-0.38=0

The probability that all three defective components in a batch escape detection by both inspectors is 0

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The impulse on an object is equal to the change in momentum of the object. In this case, the ball's initial momentum is 10 kg * 15 m/s = 150 kg m/s. After the collision, the ball's final momentum is -10 kg * 23 m/s = -230 kg m/s.

The change in momentum of the ball is: -230 kg m/s - 150 kg m/s = -80 kg m/s.

So, the impulse on the ball is -80 kg m/s.

Why the length of the third (3) side of a triangle cannot be less than the total of any two (2) of its sides is shown in the diagram: B. by demonstrating that two sides with lengths of 4 and 3 cannot ever come together to form a vertex.

The definition of a triangle is a two-dimensional geometric figure with exactly three (3) sides, three (3) vertices, and three (3) angles. According to the length of their sides, triangles fall into one of the following three (3) categories:

By applying the Triangle Inequality Theorem to this diagram (see attachment), we have:

4 + 12 > 3 (True).

3 + 12 > 4 (True).

4 + 3 > 12 (False).

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The incorrect statement is that You can solve for the unknown side in any triangle, if you know the lengths of the other two sides, by using the Pythagorean theorem.

Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude.

Pythagoras theorem is only applied for right angled triangles.

There is hypotenuse which is the longest side for only right angled triangles. So we cannot find the length of the third side of any triangle using the Pythagorean theorem.

Hence the statement that you can solve for any triangle's unknown side using the Pythagorean theorem is incorrect.

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Answer:

below

Step-by-step explanation:

1 is FIRST degree

degree of 2 would be a second degree

Maximum value: 9, located at point (-3, 9).

Minimum value: -5/3, located at point (1, -5/3).

[tex]y=\frac{1}{3}x^{3} +x^{2} -3x[/tex]

Check attached images 1 and 2.

[tex]\frac{d}{dx} =y'\\ \\y'=(3*\frac{1}{3})x^{3-1} +2*x^{2-1} -(1*3)x^{1-1} \\ \\y'=x^{2} +2x-3[/tex]

Use the quadratic formula.

Check attached image 3.

a = 1

b = 2

c = -3

[tex]x_{1} =\frac{-(2)+\sqrt{(2)^{2}-4(1)(-3) } }{2(1)} =1\\ \\x_{2} =\frac{-(2)-\sqrt{(2)^{2}-4(1)(-3) } }{2(1)} =-3[/tex]

Quick analysis. This results tell us that the minimun and maximum points different that infinity of the original function ([tex]y=\frac{1}{3}x^{3} +x^{2} -3x[/tex]) are located in points x = 1 and x = -3. Now, we need to discover who's the maximum point and who's the minimum. For this, evaluate both point in the original function.

[tex]y=\frac{1}{3}x^{3} +x^{2} -3x\\ \\f(x)=\frac{1}{3}x^{3} +x^{2} -3x\\ \\f(1)=\frac{1}{3}(1)^{3} +(1)^{2} -3(1)\\\\ =\frac{1}{3}+1-3 \\\\ =\frac{1}{3} +\frac{3}{3}-\frac{9}{3} \\ \\=\frac{1+3-9}{3} \\ \\=-\frac{5}{3}[/tex]

[tex]f(-3)=\frac{1}{3}(-3)^{3} +(-3)^{2} -3(-3)\\ \\=\frac{1}{3}(-27) +(9)-(-9)\\ \\=\frac{-27}{3} +9+9\\ \\=-9+9+9\\ \\=9[/tex]

Maximum value: 9, located at point (-3, 9).

Minimum value: -5/3, located at point (1, -5/3).

Check out the graph (attached image 4) to better understand the method used for this solution.

Note. See that the "x" coordinates where the function has maximum and minimum points are the exact same "x" coordinates where the derivative touches the "y" axis, that's why we calculated the roots of the derivative and then evaluated in the original function.

Answer:

A train traveling at a constant speed of 105 miles per hour covers a distance of 315 miles in 3 hours. To find the distance in feet, we need to convert miles to feet:

315 miles * 5,280 feet/mile = 1,654,400 feet

So, in 3 seconds, the train travels approximately:

1,654,400 feet / (60 seconds/minute * 60 minutes/hour) = 9,072 feet

Therefore, in 3 seconds, the train traveling at a constant speed of 105 miles per hour travels approximately 9,072 feet.

Answer:

To convert miles per hour to feet per second, multiply the speed in mph by 5280/3600 = 1.46667.

105 mph * 1.46667 ft/s = 153.333 ft/s

To find the distance travelled in 3 seconds, multiply the speed by time:

153.333 ft/s * 3 s = 315 ft

As per the standard deviation, the probability of 8≤ X < 11 is 0.1429.

A random variable X is a mathematical representation of the possible values that a random process or experiment can take on. X has a normal distribution, meaning that its distribution follows a bell-shaped curve.

The standard deviation measures how spread out the values of X are around the mean.

If X has a mean of μ and a standard deviation of 2, then 68% of the values of X will fall within one standard deviation of the mean.

This means that about 68% of the values of X will fall between μ-2 and μ+2.

To find the probability that X falls between 8 and 11, we need to use the cumulative distribution function (CDF).  

Using the standard normal distribution table, we find that P(X < 8) = 0.8413 and P(X < 11) = 0.9842.

Thus, the probability that 8≤ X < 11 is

=> 0.9842 - 0.8413 = 0.1429,

which rounded off to the 4th decimal place is 0.1429.

Complete Question:

Random variable X has a normal distribution with mean μ and standard deviation 2. The pdf f(x) of X satisfies the following conditions: (A) f(6) > f(16), (B) f(1) < f(17). When u is an integer, what is P(8≤ X < 11) (round off to the 4th decimal place)?

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Answer:

2.02

Step-by-step explanation:

2% annual rate

compound monthly so every month you get 2%/12 =0.167%

effectively in a year = 12 months you'll get

(1+0.167%)^12 =  2.02%

input 2.02

Answer:

The demand curve is shown below, with the equation P = 50 - 1Qp. The supply curve is shown below, with the equation P = 40 + 1Qs. The point at the market equilibrium is shown with an asterisk, where the two curves intersect.

Demand Curve: 60- 50- * 40- 30- 20- 10- Price 0 2.5 5 10 7.5 Quantity 12.5 15 Q ON

Supply Curve: 60- 50- 40- * 30- 20- 10- Price 0 2.5 5 10 7.5 Quantity 12.5 15 Q ON

Answer:

this is a true statement

Step-by-step explanation:

Given the L-shaped line

where p 1 = ( 0, 2, 2 )

L → Р = Ро + tυwhere p = ( x, y, z ) and p 0 = ( 1, 1, 0 ) and v = ( 1, 2, 2 )

The components p 1 and L constitute a plane with the normal vector n given by

→ \sn \s= \sλ \s1 \s( \sp \s0 \s− \sp \s1 \s)

when R = 1

L 1 is the desired line and is orthogonal to L, so

L 1 p = p 1 + t 1 v 1 = p 1 + t 1 v 1 where

2 v n with 2 R v 1 = 2 v n with 2 R

It is more advantageous to parameterize relations or implicit equations since they become explicit functions once parameterized.

A circle, for example, may be defined as x 2 + y 2 = r 2. When a relation passes the vertical line test, you know it is a function; a circle does not.

When you try to define the circle directly, you get: y = r 2 x 2. Again, this is not a function; it is the combination of two functions.

When we parameterize a circle, we get: x = r cos t

y \s= \sr \ssin \st

t \s∈ \sR

Both x and y are explicit functions that may be plotted, integrated, or differentiated as needed.

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The parametric equation of the plane is x = 11/6 t, y = -5/2t, z = 1 1/2 t.

(x, y, z) = (0, 2, 2) + t(i - j +2 k)

A plane that is parallel to this line will have the general equation:

x - y + 2z = c

We make it contain the point by substituting in the point and solving for c:

0 + 2 +2(2) = 4

c = 4

The plane x - y + 2z = 4 contains the point (0, 1, 2) and is perpendicular to the line.

To find the point where the line intersects the plane, substitute the parametric equations of the line into the equation of the plane:

x - y + 2z = 4

(1 + t) − (2 − t) + 2(2t) = 4

1+t-2+t+ 4t = 4

6t = 5

t = 5/6

x = 11/6, y = 7/6, z=5/3

The line intersects the plane at the point (11/6, 7/6, 5/3)

The vector, v, from the given point to the intersection point

v = (11/6 - 0)i + (7/6 - 2)j + (5/3 - 2)k

v = 11/6 i -5/2 j - 1/2 k

The vector equation of the line is:

(x, y, z) = (0, 2, 2) + t (11/6 i -5/2 j - 1/2 k)

The parametric equations are:

x = 11/6 t,

y = -5/2t,

z = 1 1/2 t

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The hypotenuse of a right triangle with side lengths 4cm and 5cm is √41 cm.

Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

hypotenuse = √( a² + b² )

Given that;

Plug in the given values and solve for hypotenuse.

hypotenuse = √( a² + b² )

hypotenuse = √( 4² + 5² )

hypotenuse = √( 16 + 25 )

hypotenuse = √41

Therefore, the hypotenuse is √41.

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The point slope form of the equation is y-5=4(x-3).

What is point slope form of the equation?

The slope of a straight line and a point on the line are both components of the point-slope form. The equations of infinite lines with a specified slope can be written, however when we specify that the line passes through a certain point, we obtain a singular straight line. In order to calculate the equation of a straight line in the point-slope form, only the line's slope and a point on it are needed.

Here the given point [tex](x_1,y_1)=(3,5)[/tex] and slope m=4 then using equation of line formula,

=> [tex]y-y_1=m(x-x_1)[/tex]

=> y-5 =4(x-3)

Hence the point slope form of the equation is y-5=4(x-3).

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The relationship of proportion is shown below.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal.

According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Correlation is the term used to describe the relationship between two variables. The degree of link or correlation between two variables is known as proportionality or variation.

It comes in two types: direct variation or percentage, which indicates a positive correlation between the two variables. It occurs when the two variables change simultaneously.

In contrast, a negative relationship or correlation is shown by an indirect variation or proportion. Specifically, the reverse of what occurs with direct variation.

One rises while the other variables, you guessed it, fall. Because you can establish and identify how two variables connect to one another, correlations are crucial to take into account.

Note that y=1/x (indirect) and x = y (direct).

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The triangle that is produced is a right-angled triangle, as can be seen in the diagram. ∴ Area of a right-angled triangle [tex]=\frac{1}{2} \times$ base $\times[/tex]height

The triangle that is produced is a right-angled triangle, as can be seen in the diagram.

∴ Area of a right-angled triangle [tex]=\frac{1}{2} \times$ base $\times[/tex]height

Additionally, the right-angled triangle's area ($) (0,0),

[tex](\mathrm{x}, 0),(0, \mathrm{y})=$ $\frac{1}{2}|x y|$ sq.units[/tex]

⇒ Area of the right-angled triangle formed by the points

(0,0),(4,0),(0,3) =  [tex]$\frac{1}{2}|4 \times 3|$[/tex]  sq.units

[tex]$=\frac{1}{2} \times(12)[/tex]

= 6 sq.units

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The equation of line that is tangent to the function f is y = 8x - 6 and

y = 8x + 10.

Let's start with the generic equation of a line:

y = ax + b

This line must be parallel to the line 8x - y + 5 = 0, and it must have the same slope.

The slope of the line 8x - y + 5 = 0 is 8, so our line has a = 8 :

y = 8x + b

Now we must determine the b values that make this line tangent to the function f(x) = 2x².

First, compute the derivative of f(x) in relation to x:

4x = df(x) / dx

For any value of x, this derivative is the slope of the tangent line to the function. We require a slope of 8, so:

4x = 8

x = 8/4

x = ±2

To calculate the y-values, we have:

f(1) = 2 x 1² = 2

f(-1) = 2 x (-1)² = 2

Using the points (1,2) and (-1,2) from our parallel line, we get:

2 = 8 x 1 + b is the first line using (1,2).

b = -6

(-1,2) is used in the second line: 2 = 8 x -1 + b

b = 10

The value of b represents the line's y-intercept, so the line with a smaller y-intercept is y = 8x -6, and the line with a larger y-intercept is y = 8x + 10.

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Answer:

x = 15

Step-by-step explanation:

30 + 4x = 90   These angles are complementary which means that they add to 90.  Subtract 30 from both sides

30 - 30 + 4x = 90 - 30

4x = 60   Divide both sides by 4

x = 15

The smallest possible value of k is 0.

Let's call a_n = n + k.

We see that this sequence satisfies both conditions (1) and (2).

For condition (1),

Since a_n = n + k, the sequence is non-decreasing as long as [tex]$k \ge 0$[/tex].

For condition (2),

Since a_n = n + k,

We have [tex]$n(n + 1)/2 \ge a_n = n + k$[/tex], which rearranges to [tex]$k \ge -n$[/tex].

To make sure that k is an integer,

we take the ceiling of -n, i.e., [tex]k \ge \lceil -n \rceil[/tex]

Therefore, the smallest such k is [tex]\max{0, \lceil -n \rceil} = \lceil -n \rceil[/tex]

Since we want to find the smallest k for any given n,

we need to find the smallest n such that [-n] is positive,

Since k must be positive.

The smallest positive n is n = 1, and [-1]=0,

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Step-by-step explanation:

A whole can be divided into many parts and the number of parts will depend on the unit of measurement we use to divide it.

A whole can be divided into fifty equal parts, each of which is called a "fiftieth." So, one whole would be equal to 50 fiftieths.

1 whole = 50 fiftieths

Alternatively, we can say that one fiftieth is equal to 1/50th of a whole. This can be represented as a decimal or a fraction.

1 fiftieth = 1/50th of a whole = 0.02 (decimal)

Answer:

A

Step-by-step explanation:

the sum of the arcs in a circle = 360°

here the major arc = 260° , then

the minor arc = 360° - 260° = 100°

the measure of the tangent- tangent angle x is half the difference of the measures of the intercepted arcs, that is

x = [tex]\frac{1}{2}[/tex] (260 - 100) = [tex]\frac{1}{2}[/tex] × 160 = 80

Answer:

Inverse

Step-by-step explanation: