Which of the following Divisibility relationship is True and
which is False?


a) 13|78


b) -6 | 24


c) 11 | -33


d) 23 | 96


e) 5 |126

Answer:

1.8%

Step-by-step explanation:

2.86-2.81 = .05 (find the difference between the two numbers)

2.81 / .05= .017 (divide the original number)

Multiply 100 to get a percentage

1.8% (rounding to the nearest tenth)

0.0455 quarters of paints is not enough to paint the wall. she needs 15 quarters.

She needs 15 quarters of paint  for one wall .

She has 2 1 / 4 gallons left over from painting the other walls and she also has another 5 quarts that her neighbour gave her.

Therefore,

4 quarts = 1 gallon

5 quarts = 5 / 4 gallons

Then,

total gallon = 9 / 4 + 5 / 4 = 14 / 4  = 7 / 2 gallons

Therefore,

1 gallons = 0.01301053418982 quarters

7 / 2 gallons = ?

cross multiply

number of quarters = 3.5 × 0.01301053418982

number of quarters = 0.0455 quarters

Therefore, 0.0455 quarters of paints is not enough to paint the wall. she needs 15 quarters.

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To construct a 3×3 matrix, not in echelon form, whose columns span ℝ³, we can choose three linearly independent vectors as the columns of the matrix.

To demonstrate that the constructed matrix has the desired property of spanning ℝ³, we can construct a specific example. Let's consider the matrix A:

A = [[1, 0, 0],

[0, 1, 0],

[0, 0, 1]]

In this case, A is a 3×3 matrix with three columns [1, 0, 0], [0, 1, 0], and [0, 0, 1]. Each column represents a standard basis vector in ℝ³.

To show that the columns of A span ℝ³, we need to demonstrate that any vector in ℝ³ can be expressed as a linear combination of the columns of A.

Let's consider an arbitrary vector x = [x₁, x₂, x₃]ᵀ in ℝ³. We can express x as a linear combination of the columns of A:

x = x₁[1, 0, 0] + x₂[0, 1, 0] + x₃[0, 0, 1]

Simplifying this expression, we get:

x = [x₁, x₂, x₃]ᵀ

Thus, we have shown that any vector x in ℝ³ can be expressed as a linear combination of the columns of the matrix A. Therefore, the columns of A span ℝ³.

Note: It is important to emphasize that there are many possible matrices that can be constructed to satisfy the given condition. The example provided here is just one of the many valid choices

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To determine the maximum number of 2/0 AWG THW aluminum compact conductors permitted in a 2½-inch PVC conduit, Schedule 80, we need to consult the applicable electrical code or standards.

The number of conductors allowed in a conduit is typically governed by factors such as fill capacity and heat dissipation.

The specific requirements may vary depending on the jurisdiction and the electrical code being followed. It is recommended to consult the local electrical code or a qualified electrician to ensure compliance with the regulations in your area.

They will be able to provide the precise guidelines and restrictions for conductor fill capacity based on the conduit size, type, and the specific application.

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Total distance of the triathlon race is 23.34 kilometers.

Reg enters a triathlon race. He swims 1.25 kilometers, bikes 20.5 kilometers, and runs 1.59 kilometers.

The total distance of the race is 23.34 kilometers.

Reg enters a triathlon race.

He swims 1.25 kilometers, bikes 20.5 kilometers, and runs 1.59 kilometers.

In order to calculate the total distance of the race, we need to find the sum of the distance Reg swam, biked and ran. Therefore, Total distance = Distance swam + Distance biked + Distance ranTotal distance = 1.25 + 20.5 + 1.59 km

Total distance = 23.34 km.

The summary of this problem is that the total distance of the triathlon race is 23.34 kilometers.

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Answer:3/4

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Since the figures are similar then the ratios of corresponding sides are equal, that is

\(\frac{AD}{WZ}\) = \(\frac{CD}{YZ}\) , substitute values

\(\frac{10}{46}\) = \(\frac{5}{YZ}\) ( cross- multiply )

10YZ = 230 ( divide both sides by 10 )

YZ = 23 → c

Answer:

11

Step-by-step explanation:

(2×3)^2 = 6^2 = 36

5^2 = 25

(2×3)^2 - 5^2 = 36 - 25 = 11

Answer:

11

Step-by-step explanation:

(2⋅3) ^2−5 ^2= (6+5)(6-5)=11*1= 11

Answer:x is 23

Step-by-step explanation:f(x) = x - 10

13 = x - 10

13 + 10 = x

23 = x

So x  is 23

Answer:

The value of x is 23

Step-by-step explanation:

Given:

\(f(x)=x-10\)

Find:

The value of x

Explanation:

\(f(x)=x-10\\f(x)=13\\\\13=x-10\\x=13+10\\x=23\)

Final Answer

Hence, the value of x is 23

The value of x for the intersecting chords is derived to be 1.9 and the segment FS is equal to 18

The property of intersecting chords states that in a circle, if two chords intersect, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

UF × FS = VF × FT

8(10x - 1) = 9 × 16

80x - 8 = 144

80x = 144 + 8 {collect like terms}

80x = 152

x = 152/80 {divide through by 80}

x = 1.9

FS = 10(1.9) - 1 = 18

Therefore, the value of x for the intersecting chords is derived to be 1.9 and the segment FS is equal to 18

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The center of the circle, and consequently the central point of the resort's swimming pool, is located at the intersection of the two legs of the right triangle, approximately 60 feet from one vertex and 120 feet from the other.

The upscale resort has ingeniously designed its circular swimming pool to encompass a central area containing a restaurant. This central area takes the form of a right triangle with legs measuring 60 feet and 120 feet, while the hypotenuse, the longest side of the triangle, spans approximately 103.92 feet. The vertices of the triangle neatly coincide with points on the circumference of the circular pool.

Due to the properties of a right triangle, the hypotenuse is also the diameter of the circle. This means that the circular pool is precisely constructed around the right triangle, with its center located at the midpoint of the hypotenuse.

To determine the exact coordinates of the center of the circle, we can consider the properties of right triangles. Since the legs of the right triangle are perpendicular to each other, the midpoint of the hypotenuse coincides with the point where the two legs intersect.

In this case, the center of the circle is the point of intersection between the 60-foot leg and the 120-foot leg of the right triangle.

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In physics, if quantity "s" represents a length and quantity "t" represents a time, then the quantities "v" and "a" can be defined as follows:

- Quantity "v" represents velocity, which is the rate of change of length with respect to time. It can be calculated by dividing the change in length (Δs) by the change in time (Δt): v = Δs/Δt. Velocity measures how fast an object's position changes over time.

- Quantity "a" represents acceleration, which is the rate of change of velocity with respect to time. It can be calculated by dividing the change in velocity (Δv) by the change in time (Δt): a = Δv/Δt. Acceleration measures how quickly an object's velocity changes over time.

In summary, velocity (v) is the rate of change of length with respect to time, while acceleration (a) is the rate of change of velocity with respect to time. These quantities are fundamental in describing the motion of objects and play a crucial role in physics and engineering.

Velocity (v) and acceleration (a) are important concepts in physics that describe the motion of objects. Velocity measures the rate at which an object's position changes over time, while acceleration measures the rate at which an object's velocity changes over time.

To understand these concepts better, let's delve deeper into the definitions of velocity and acceleration. Velocity is the ratio of the change in position (Δs) to the change in time (Δt): v = Δs/Δt. It tells us how far an object moves in a given amount of time. For example, if a car travels 100 meters in 10 seconds, its velocity would be 10 meters per second.

Acceleration, on the other hand, is the ratio of the change in velocity (Δv) to the change in time (Δt): a = Δv/Δt. It describes how quickly an object's velocity is changing. If a car accelerates from rest to a speed of 20 meters per second in 5 seconds, its acceleration would be 4 meters per second squared.

Both velocity and acceleration are vector quantities, meaning they have both magnitude and direction. The direction of velocity indicates the object's motion (e.g., forward or backward), while the direction of acceleration tells us whether the object is speeding up or slowing down.

These quantities are fundamental in analyzing the motion of objects in various fields such as physics, engineering, and sports. They help us understand how objects move, predict their future positions, and design systems to optimize performance. Whether it's the motion of a ball, a car, or a planet, velocity and acceleration provide essential insights into the behavior of physical systems.

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\(\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=4\pi \sqrt{3} \end{cases}\implies 4\pi \sqrt{3}=2\pi r\implies \cfrac{4\pi \sqrt{3}}{2\pi }=r\implies 2\sqrt{3}=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=2\sqrt{3} \end{cases}\implies A=\pi (2\sqrt{3})^2 \\\\\\ A=\pi ( ~~ 2^2\sqrt{3^2} ~~ )\implies A=\pi ( ~~ 2^2(3) ~~ )\implies A=\implies A=12\pi\)

Instantaneous voltage equation: v = X(1 - e^(-t/Y))
X = 11
Y = 1

a) Differentiate v with respect to t to give an equation for dv/dt:

Using the chain rule and the fact that the derivative of e^(ax) is a*e^(ax), we get:

dv/dt = X * (-1/Y) * e^(-t/Y) = -11/Y * e^(-t/Y)

Since Y = 1:

dv/dt = -11 * e^(-t)

b) Calculate the value of dv/dt at t = 2s and t = 4s:

For t = 2s:
dv/dt = -11 * e^(-2) ≈ -11 * 0.135 = -1.485

For t = 4s:
dv/dt = -11 * e^(-4) ≈ -11 * 0.018 = -0.198

c) Find the second derivative (d^2v/dt^2):

To find the second derivative, we differentiate dv/dt once more:

d^2v/dt^2 = d/dt(-11 * e^(-t)) = 11 * e^(-t)

In summary:

a) dv/dt = -11 * e^(-t)
b) At t = 2s, dv/dt ≈ -1.485; at t = 4s, dv/dt ≈ -0.198
c) d^2v/dt^2 = 11 * e^(-t)

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To form a triangle, the set of line segments must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, we need to check if the given line segments 8 cm, 4 cm, and 3 cm meet this requirement.

We can start by checking if the sum of the two smaller sides (3 cm and 4 cm) is greater than the largest side (8 cm). 3 cm + 4 cm = 7 cm, which is less than 8 cm. Therefore, these three line segments cannot form a triangle.

In general, for a set of line segments to form a triangle, the largest side must be smaller than the sum of the other two sides. In this case, the line segment of 8 cm is too long compared to the other two sides, which makes it impossible to form a triangle.

In conclusion, there are no line segments that meet the requirements to form a triangle with lengths of 8 cm, 4 cm, and 3 cm.

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The probability that fewer than 1690 blocks meet the specification in three or more of the six lots is  0.0000428%.

1. Let's calculate the probability of a single block meeting specification:

p(block meets spec) = 0.85

p(block doesn't meet spec) = 1 - 0.85

= 0.15

The number of blocks that meet the specification follows a binomial distribution with n = 2000 and p = 0.85.

Let X be the number of blocks that meet the specification.

Therefore, P(X < 1690) can be calculated using the binomial cumulative distribution function.Using a calculator or a software, we get:

P(X < 1690)

= 0.0006 (rounded to four decimal places)

Therefore, the probability that, in a given lot, fewer than 1690 blocks meet the specification is 0.0006 or 0.06%.

2. The number of blocks that meet the specification follows a binomial distribution with n = 2000 and p = 0.85.

We need to find the number of blocks k, such that

P(X < k) = 0.70

Using a calculator or a software, we get:

k = 1743

Therefore, the 70th percentile of the number of blocks that meet the specification is 1743.3.

The number of blocks that meet the specification in each lot follows a binomial distribution with n = 2000 and p = 0.85.

The probability that fewer than 1690 blocks meet the specification in a given lot is:

P(X < 1690) = 0.0006

From part 1, we know that the probability that fewer than 1690 blocks meet the specification in a given lot is 0.0006. Let Y be the number of lots with fewer than 1690 blocks meeting the specification.

Therefore, Y follows a binomial distribution with n = 6 and p = 0.0006.

We need to find P(Y ≥ 3).

Using a calculator or a software, we get:

\(P(Y ≥ 3) = 4.28 x 10^(-7)\) (rounded to nine decimal places)

Therefore, the probability that fewer than 1690 blocks meet the specification in three or more of the six lots is 4.28 x \(10^(-7)\) or 0.0000428%.

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Answer:

see explanation

Step-by-step explanation:

Given a quadratic in standard form , y = ax² + bx + c ( a ≠ 0 ), then

The x- coordinate of the vertex, which is also the equation of the axis of symmetry is

\(x_{vertex}\) = - \(\frac{b}{2a}\)

y = x² + 12x + 32 ← is in standard form

with a = 1, b = 12 , then

\(x_{vertex}\) = - \(\frac{12}{2}\) = - 6

Substitute x = - 6 into y for corresponding y- coordinate

y = (- 6)² + 12(- 6) + 32 = 36 - 72 + 32 = - 4

Thus

equation of axis of symmetry is x = - 6

vertex = (- 6, - 4 )

To find the y- intercept , let x = 0

y = 0² + 12(0) + 32 = 32 ← y- intercept

The axis of symmetry is x = -6, vertex is (-6,-4) and y-intercept is 32.

Important information:

Substitute \(x=0\) to find the y-intercept.

\(y=(0)^2+12(0)+32\)

\(y=32\)

The vertex form of a quadratic function is:

\(y=a(x-h)^2+k\)         ...(i)

Where a is constant, (h,k) is vertex and x=h is the axis of symmetry.

Adding and subtracting the square of half of coefficient of x, the given quadratic function can be written as:

\(y=x^2+12x+32+6^2-6^2\)

\(y=(x^2+12x+6^2)+32-36\)

\(y=(x+6)^2-4\)          ...(ii)

On comparing (i) and (ii), we get

\(a=1,h=-6,k=-4\)

Therefore, the axis of symmetry is x = -6, vertex is (-6,-4) and y-intercept is 32.

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The smallest non-infinite positive integer (whole number) this representation cannot represent is \(2^-^2^4\)

Each number is addressed as 1.fraction * 2^exponent.

The key here is to know there are limits for both exponent (8 bits) and a fraction (23 bits), however, these limits don't really coordinate.

For instance, we can make 2^24 with the 8 bits exponent, while we can't make 2^-24 with a fraction (since it just has 23 bits).

In this way, in the event that you need to make number 16777216 = 2^24, you just set the fraction to 0 and set the exponent to address 24.

In any case, on the off chance that you need to address 16777217 = 2^24 + 1, the solitary thing you can do is to add a little fraction so when it duplicates with 2^24 it produce 1, and that little fraction ought to be 2^-24, which shockingly can't be created by just 23 digits.

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Answer:

249.40 Option b

Step-by-step explanation:

When multiplying 21.5 x 11.60 you get $249.40

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Total surface area:

So

TSA

Answer:

-2

Step-by-step explanation:

(-1+-1)*(-1--1)

A negative plus a negative will stay negative.

2 negative signs will make a positive number. Example x-(-x)=0

A negative minus a positive will cancel out. For example -6-(-6)=0

Therefore, -1-(-1) will be 0

-2*0

-2

Answer:

-2

Step-by-step explanation:

To find the area of a triangle we use this equation:

\(\frac{1}{2} bh\\\)

b= base

h= height

So since we are given the information that the sides are 6 and the height is 5 we simply can plug the information right into the equation:

\(\frac{(6)(5)}{2}\)= 15

So the are is 15 inches sqaured, hope this helps :)

By solving a quadratic equation we can see that the width of the path measures 20 meters.

We know that the pool measures 18 meters by 20 meters, then the area of the pool alone is:

A = 18m*20m = 360 m^2

Now, if the path has a width x, then the rectangle that includes the path and the pool has dimensions:

(18m + 2x) and (20m + 2x)

And its area is given by:

(18m + 2x)*(20m + 2x)

And we know it is equal to 1520 m^2, then (i'm not writting the units in the computation):

(18 + 2x)*(20 + 2x) = 1520

360 + 4x^2 + 76x = 1520

Now we just need to solve that quadratic equation:

4x^2 + 76x - 1520 + 360 = 0

4x^2 + 76x - 1160 = 0

The solutions are:

x = (-76 ± √(76^2 - 4*4*(-1160))/(2*4)

x = (-76 ± 156)/4

We only care for the positive solution, which gives:

x = (-76 + 156)/4 = 20

We conclude that the width of the path measures 20 meters.

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Answer: Without replacing

Step-by-step explanation:

If you don't replace the first red marble, it decreases the number of red marbles in the mix, making the proportion of blue marbles relatively larger. For example, if there were 5 red and 5 blue marbles, there would be a 50% chance of drawing a blue marble. If the red drawn is not replaced, there is a 5/9 chance of drawing a blue marble, or a 55% chance of drawing one.

Answer:

(1, 4)

Step-by-step explanation:

a. The curvature at each point of a straight line is zero.

b. This means that dT/dθ is constant and has a magnitude of 1/r, since the length of the radius vector is always r. Therefore, we have:

K = |dT/ds| = |dT/dθ * 1/r| = 1/r,

as claimed.

Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends.

The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.

(a) Let's consider a straight line with equation y = mx + b, where m is the slope and b is the y-intercept.

The tangent vector of the line is given by T = (1, m), which has a constant magnitude of \(sqrt(1 + m^2).\)

The normal vector is N = (-m, 1), which also has a constant magnitude of sqrt(1 + m^2).

The curvature K is given by \(K = ||dT/ds|| / ||T||^2\), where s is the arc length.

Since the line is straight, the tangent vector is constant along the curve and \(dT/ds = 0. Therefore, K = 0 / ||T||^2 = 0.\)

Hence, the curvature at each point of a straight line is zero.

b. To show that the curvature at each point of a circle of radius r is K = 1/r, we can use the formula for curvature in terms of the radius of curvature:

K = 1/R,

where R is the radius of curvature. For a circle, the radius of curvature is equal to the radius of the circle itself, so we have:

K = 1/r.

This formula tells us that the curvature at each point of a circle is inversely proportional to the radius of the circle. In other words, as the radius of the circle gets smaller, the curvature gets larger, and vice versa.

To see why this formula is true, we can consider the definition of curvature as the rate at which the direction of a curve is changing as we move along it. For a circle, the direction of the curve is constantly changing as we move around it, but the amount of change is always the same. Specifically, the direction of the curve changes by an angle of 2π radians (i.e., a full circle) as we complete one full revolution around the circle. This means that the curvature of the circle is constant and equal to 1/r, where r is the radius of the circle.

To see why this is true, we can use the formula for the arc length of a circle:

s = rθ,

where s is the arc length, r is the radius of the circle, and θ is the angle subtended by the arc (in radians). For a full circle, θ = 2π, so we have:

s = 2πr.

Now, the curvature K can be defined as the rate at which the unit tangent vector T changes as we move along the curve:

K = |dT/ds|,

where |.| denotes the magnitude of a vector. For a circle, the unit tangent vector T is always perpendicular to the radius vector pointing to the center of the circle, so we can write:

dT/ds = dT/dθ * dθ/ds = dT/dθ * 1/r,

where we have used the chain rule and the fact that dθ/ds = 1/r (since s = rθ). Now, since the direction of the curve changes by an angle of 2π radians as we complete one full revolution around the circle, the unit tangent vector T returns to its initial direction after one full revolution. This means that dT/dθ is constant and has a magnitude of 1/r, since the length of the radius vector is always r. Therefore, we have:

K = |dT/ds| = |dT/dθ * 1/r| = 1/r,

as claimed.

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The value of a is \(1 +/- sqrt(16 - 16a).\)

Let’s begin by writing out the given equation: \(ax3 + x2 – 2x + 4a – 9\). We can rearrange this equation to make it easier to solve: (x+1)(ax2 -2a + 4). This indicates that (x+1) is a factor of the equation, and thus we can set the equation equal to 0. By doing so, we can solve for a.

We can now write this equation as 0 = ax2 -2a + 4. We can use the quadratic equation to solve for a. We first need to calculate the discriminant, which is equal to b2 - 4ac. In this case, b2 is (-2)2 = 4 and ac is a(4) = 4a. Thus, the discriminant is equal to 4 - 16a.

Next, we can solve for a using the quadratic equation. The equation is: \(a = [-b +/- sqrt(b2 - 4ac)]/2a\). In this case, \(a = [-(-2) +/- sqrt(4 - 16a)]/2\). By simplifying, we get \(a = [2 +/- sqrt(16 - 16a)]/2.\) This can be further simplified to a = 1 +/- sqrt(16 - 16a). Therefore, the value of a is∀⊅\(1 +/- sqrt(16 - 16a).\)

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Answer:

it would be d because 2 and 4 would only make sense to be 27° and 1 to be 153

Answer:

<1 = <3 = 153

<2 = <4 = 27

Step-by-step explanation:

Angle 1 and Angle 3 are equal since they are vertical angles

<1 = <3 = 153

<1 and <2 make a straight line so they add to 180

153 + <2 = 180

<2 = 180-153

<2 = 27

<2 and <4 are equal since they are vertical angles

<2 = <4 = 27

The number of teams she can make is 10.

Division is the process of putting a number into equal groups using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations. Other basic mathematical operations include addition, subtraction, multiplication.

The number of teams that can be made can be determined by dividing the total number of friends by the total number of players in each team. The whole number that is derived from the division process is the number of teams teams that can be made given the total number of friends and the number of people that have to be in each group.

Number of teams she can make = total number of friends / number of people in each group

31 / 3 = 10 remainder 1

So, only 10 teams can be made. one person would not be on any team.

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