What are the 5 steps in dividing rational expressions?.

The total number of possible codes is 500.

According to the fundamental counting principle, if there are n ways to do one thing and m ways to do another, then there are n×m methods to accomplish both things.

Given that, the first digit of the four-digit code is 2 and the number is odd.

The first digit of the number is 2, therefore, there is only one possible number for the first digit.

Since the number is odd, the last digit of the number must be an odd number.

Therefore, there are 5 possible numbers, 1,3,5,7, and 9, for the last digit.

Now, for the second and the third digit there are 10 possible numbers, from 1 to 10.

Therefore, as per the principle of counting, the total number of possible codes is:

1 × 10 × 10 × 5

= 500

Hence, the total number of possible codes is 500.

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Answer:

87 degrees

Step-by-step explanation:

since 37 degrees + angle 1 equals to 124 degrees,  in order to found the measurement of angle 1 you just have to do  124 - 37 which is equal to 87 degrees, so 87 degrees is your answer.

Similar triangles may or may not be congruent.

The pair of triangles that can be proved by SAS is (a) the first pair

What is congruent triangles?

Congruence of triangles: 2 triangles are same to be congruent if all 3 corresponding sides square measure equal and every one the 3 corresponding angles square measure equal in measure.

Main body:

From the attached figures, we have the following observations

Figure 1

Two sides of both triangles are congruent

The angles between the sides are corresponding

The two congruent sides represent SS

The corresponding angles imply: SAS

This means that, the first pair of triangles are congruent by SAS postulate

Figure 2

Two angles of both triangles are congruent

The triangle share a common side

The two congruent angles represent AA

The common side imply: ASA

This means that, the second pair of triangles are congruent by ASA postulate

Figure 3 and 4

All sides of both triangles are congruent

This means that, the third and the fourth pairs of triangles are congruent by SSS postulate

Hence, the pair of triangles that can be proved by SAS is (a) the first pair

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The expressions are solved below :

sinu = -3/5 3π/2 < u < 2π is [ 4th quadrant ]

Now we know that

By using trigonometric identities,

When there are trigonometric functions present in an expression or equation, trigonometric Identities come in handy. Every value of a variable appearing on both sides of an equation is valid in terms of trigonometric identities. These trigonometric functions of one or more angles, such sine, cosine, and tangent, are involved in these geometric identities.

sin²u + cos²u = 1

cos²u= 1-sin²u

cos²u = 1 -(-3/5)²

cos²u= 1 - 9/25

cosu = +4/5

:. u is in 4th quadrant

Now

1.  sin2u = 2 sinu cosu

= 2 (-3/5)(4/5) = -24/25

2. cos2u = 2cos²u- 1

       = 2(4/5)²- 1

       = 7/25

3. tan2u = sin2u /cos2u

              = -24/7

The exact values of the sine, cosine, and tangent of the angle are found.

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Hooke's law is generalized in modern elasticity theory to say that the strain (deformation) of an elastic object or material is proportional to the stress...

When a spring is stretched 0.4 m beyond its natural length, it exerts a force of 150 N. How much effort is required to extend the spring's natural length by 0.9 m?

Hooke's law expresses the amount of force required to stretch a spring beyond its natural length (x=0).

Newtons Fs(x)=kx

Experiment is used to determine the value of the spring constant k. The query demonstrates an experimental stretching. A 150 N force extended the spring's natural length by 0.4 m.

Fs=150=k0.4k=1500.4 Nm Fs=150=k0.4k=1500.4 Nm

How much effort is required to extend the spring's natural length by 0.9 m?

Work is defined as force multiplied by distance. Hooke's Law, on the other hand, describes a variable force that depends on how much it is stretched, x. To solve this, an integral is required.

W=∫xf0Fs(x)dx

W=∫0.90kxdx=k2x2|0.90

W=1500.412x2|0.90

W=15008x2|0.90=15008(0.9)2

Answer

W equals 151.875 joules

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The three properties of a subspace must be demonstrated for the set of all vectors orthogonal to w, indicated as w?, in order to demonstrate that it is a subspace of Rn.

In mathematics, objects with both magnitude and direction are called vectors. The vector's size is determined by the magnitude. It is shown as a line with an arrow, where the length of the line indicates the vector's magnitude and the arrow points in the desired direction. In addition, it goes by the names Euclidean vector, Geometric vector, Spatial vector, or just "vector."

The term "orthogonal" in mathematics denotes a direction at a 90° angle. If two vectors are perpendicular to one another and the result of the dot product analysis is zero, then the vectors are said to be orthogonal.

a) Let u be any component of w and choose any z in w. Since z and w are orthogonal to one another, zu = 0. Now, let cz be the result of c and z for any scalar c. The equation (cz)u = c(zu) = c * 0 = 0 is known. As u was an arbitrary element of w, this demonstrates that cz is orthogonal to u and therefore cz is in w?

b) Let u be any component of w and consider z1 and z2 in w. Both z1u and z2u are known to be zero. Given that the first argument of the dot product is linear, we know that (z1 + z2)u = z1u + z2u = 0 + 0 = 0. As u was an arbitrary member of w, this demonstrates that z1 + z2 is orthogonal to u and that z1 + z2 is in w?

c) We have demonstrated that w? is closed under addition and scalar multiplication from a and b. We observe that the zero vector is obviously orthogonal to any vector in w and is thus in w? to demonstrate that it contains the zero vector. This demonstrates that w? is a subspace of Rn since it satisfies all three characteristics of a subspace.

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The work required to pump the oil over the top of the tank is 1.5080 × 10⁶

Given:

We start as we often do: we partition an interval into sub intervals. We orient our tank vertically since this makes intuitive sense with the base of the tank at  y=0 . Hence the top of the oil is at  y=10 , meaning we are interested in subdividing the  y -interval  [0,10]  into  n  sub intervals as

0 = y₁ < y₂ < ..... <yₙ₊₁ = 15

Consider the work  Wi  of pumping only the oil residing in the  ith  sub interval. The force required to move this oil is equal to its weight which we calculate as volume  ×  density. The volume of oil in this sub interval is  Vi=5²πΔyi ; its density is  48  lb/ft ₃ . Thus the required force is  4800πΔyi  lb.

We approximate the distance the force is applied by using any  y -value contained in the  ith  sub interval; for simplicity, we arbitrarily use  yi  for now (it will not matter later on). The oil will be pumped to a point 5 feet above the top of the tank, that is, to the height of  y=15  ft. Thus the distance the oil at height  yi  travels is  15−yi  ft.

In all, the approximate work  Wi  performed in moving the water in the  ith  sub interval to a point 5 feet above the tank is

Wi≈4800πΔyi(15−yi).

To approximate the total work performed in pumping out all the oil from the tank, we sum all the work  Wi  performed in pumping the oil from each of the  n  sub intervals of  [0,10] :

W≈∑i=1nWi=∑i=1n4800πΔyi(15−yi).

This is a Riemann sum. Taking the limit as the sub interval length goes to 0 gives

W=∫3006240π(35−y)dy

=6240π(35y−12y2)∣∣10 0

=  48000π ≈ 1.5080 × 10⁶

Hence we get the required work done.

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Your question is incomplete. Please find the missing content below.

a cylindrical tank 5 feet in diameter and 10 feet high is filled with oil whose density is 48 lbs/ft3 . how much work is required to pump the oil  up to a point 5 feet above the top of the tank.

The correct order from least to greatest for the values of r, s, and t is given by:

B. r, t, s.

The values are ordered considering the normal distribution, in which each z-score has an equivalent p-value, which gives the percentile of the score.

The values are given as follows:

The greater the percentile, the higher the measures, hence the measures are ordered from least to greatest as follows:

r, t and s.

Meaning that option B gives the correct option.

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The sequence 18 , 6 , -6 , -18 is Arithmetic sequence.

An arithmetic progression is a sequence where the differences between every two consecutive terms are the same.

In general an arithmetic sequence can be written like: {a, a+d, a+2d, a+3d, ... }.For the first term 'a' of an AP and common difference 'd'

Common difference of an AP: d = a₂ - a₁ = a₃ - a₂ = a₄ - a₃= ... = aₙ - aₙ₋₁

Given in the question,

The sequence 18 , 6 , -6 , -18

a₁ = 18 , a₂ = 6 , a₃ = -6 and a₄ = -18

Common difference : d =  a₂ - a₁

=> d = 6 - 18

=> -12

For a₃ - a₂

=> -6 - 6 = 12

Therefore , the common difference is same i.e. 12

Hence, the sequence is Arithmetic sequence

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In complex number a+ib a is real and ib is the imaginary part.

Complex numbers are the numbers that are communicated as a+ib where, a,b are genuine numbers and 'I' is a fanciful number called "particle". The worth of I = (√-1). For instance, 2+3i is a complicated number, where 2 is a genuine number (Re) and 3i is a imaginary number (Im).

We have, a + ib is a complex number in mathematics

where a is the real part and ib is the imaginary part of the complex number.

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Answer:  depth = 5 ft

width =  10 ft

length =  40 ft

Step-by-step explanation:

d =  depth

width = d + 5

length = d + 36

Volume = length x width x depth = 2000 cf

d(d+35)(d+5) = 2000

d([tex]d^{2}[/tex] + 40d + 175) = 2000

d^3 + 40d^2 + 175d = 2000

rewrite in standard cubic polynomial form : ax3 + bx2 + cx + d = 0

d^3 + 40(d^2) + 175d - 2000 = 0

Find the roots of the cubic polynomial:

factors of 2000 are 1, 5, 10 15, 20, etc.

Try the factor 5 first by plugging it in the equation:

5^3 + 40(5^2) + 175(5) - 2000 = 0  

Lucky break!  No need to find the other roots because they will be negative, and you can't have a negative value for a pool depth.

So, depth = 5 ft

width = 5 + 5 = 10 ft

length = 5 + 35 = 40 ft

An appropriate ending to the alternative hypothesis is less than 8 hours. The alternative hypothesis would be: The average amount of sleep students at their school get per night is less than 8 hours.

The alternative hypothesis is a statement used in statistical inference experiment which is contradictory to the null hypothesis and denoted by Ha or H1. In hypothesis testing, an alternative hypothesis is a statement that a researcher is testing.

The alternative hypothesis could take one of three forms, depending on the context of the test:

Which alternative hypothesis we use (< or > or ≠) is sometimes called the direction of the test. Which direction we choose depends on the context of the test.

In this case, it is suspected that students at the school are getting less than 8 hours of sleep on average, so that is the alternative hypothesis.

Ha: The average amount of sleep students at their school get per night is less than 8 hours.

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The cost per candle bought  by the Kayla is found as $2.

First off, Kayla purchases 5 candle holders despite the fact that 1 candle holder costs $3.50.

As a result of multiplying the cost with one candle holder with 5, which equals $3.50, we get $17.50.

After deducting 17.50 from 27.50,  10 is left.

Thus, if 5 candles cost $10.

Then, divide 10 by 5 = 2

Therefore, a candle was $2.

Thus, the cost per candle bought  by the Kayla is found as $2.

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the integral of the line, where c is the specified curve. The line integral is (x 9y) dx x2 dy, where C is the provided curve. The line segments from (0, 0) to (9, 1) and from (9, 1) to (10, 0), respectively, make up the integral c (x+2y)dx+x2dy, C. is 95/3

[tex]\int\limits^a_c {(x+9y,x^{2} )} \, dr_{2} = \int\limits^1_0{9+t+9-9t, (9+t )^2} .(1, -1)\, dt[/tex]

it is possible to parameterize the first line segment by

[tex]r_{1} (t) = (0,0)(1-t) + (9,1)t = (9t,t)[/tex] with 0 ≤ t ≤ 1 indicate this first section with [tex]C_{1}[/tex] then

[tex]\int\limits^a_c {(x}+9y,x^2 ) \, dr_{1} = \int\limits^1_0 {(9t+9t,81t^2) . (9,1)} \, dt\\ \\= \int\limits^1_0 {(162t + 81t^2) } \, dt\\\\= 108[/tex]

secondly the line segment [tex]C_{2}[/tex] can be characterised as

[tex]r_{2} (t) = (9,1)(1-t) + (10,0)t = (9+t,1-t)[/tex] again using interval  0 ≤ t ≤ 1  then

[tex]\int\limits^a_c {(x+9y,x^{2} )} \, dr_{2} = \int\limits^1_0{9+t+9-9t, (9+t )^2} .(1, -1)\, dt[/tex]

= -229/3

finally ,

= 108-229/3

= 95/3

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Step-by-step explanation:

The factors divisible by 3 are:

3,6,9,12,15,18,21,24,27,30,33,36,...

based on observations of his own children, jean piaget formed a theory about the cognitive development of all children. this is an example of inductive reasoning reasoning.

Inductive reasoning :

Inductive reasoning is a method of reasoning by proceeding from the specific to the general. Inductive reasoning or inductive logic is a type of reasoning in which a general conclusion is drawn from a set of specific observations.

It contrasts with deductive reasoning, which usually moves from general information to specific conclusions. Inductive reasoning is also known as inductive logic or bottom-up reasoning because it involves extending certain premises to broader generalizations.

Examples of Inductive Reasoning:

Here is the basic form of inductive reasoning, with premises and generalized conclusions based on concrete data:

1. All the swans I have seen are white. (Premise)

2. Therefore, all swans are white. (Conclusion)

In this example the conclusion is actually wrong

- There is also a black swan. This is the so-called "weak" argument. However, it is easy to strengthen the conclusion by increasing the likelihood.

1. All the swans I have seen are white. (Assumption)

2. Therefore, most swans are probably white. (Conclusion)

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Answer:

An equilateral triangle has all side lengths the same, and all angles are 60 degrees. Using this we can split the triangle along its altitude to get two right triangles with a hypotenuse of length 10 and a base of 1/2 of the original length, so 5. Now we can either use the Pythagorean theorem (a^2+b^2=c^2) or the fact that it is a 30 60 90 triangle (angles measure at 30 60 and 90 degrees) Pythagorean theorem is probably easier.

It stated that the squares of the two legs of a right triangle add to the square of the hypotenuse. So a(the altitude)^2+5(the base)^2=10(the hypotenuse)^2

A^2+5^2=10^2

A^2+25=100

A^2=75

A=sqrt(75)

A=5*sqrt(3)

Final answer:

The altitude of an equilateral triangle with side length 10 is 5sqrt(3), or about 8.66

Step-by-step explanation:

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In the equation y=kx  , y varies directly with x and k . The constant of variation, k, is 8 .

What is a constant?

A predetermined amount. In algebra, a constant is a number that stands alone or, occasionally, a letter like a, b, or c that denotes a fixed number. 5 and 9 are constants in the formula "x + 5 = 9," for instance.

Since the equation can be written in the form y=kx  , y varies directly with x and k . The constant of variation, k, is 8 .

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Answer:

There would be 12 buffalos and 4 ducks.

Step-by-step explanation:

Formula:  

Buffalos = 4 legs

Ducks = 2 legs

16 animals in total.

56 legs in total.

_________________

So, in order to find this answer, we need to multiply/divide (whichever way is easier for you) the buffalos as high as possible to 56, without actually getting to 56.

56 divided by 4 = 14.

Now, this is too close, so we need to go down 1 more than this because it has too many legs:

52 divided by 4 = 13.

(52 because 56 - 4 = 52).

Now, we have 13 buffalos with 4 more legs to choose from. Which does not work because ducks have 2 legs, which 13 + 2 = 15, which is not 16. Let's go down 4 more:

48 divided by 4 = 12

Now, we have 12 buffalos with 48 legs.

56 - 48 = 8. So, we need 8 more legs, in which we need to use ducks:

8 divided by 2 = 4 ducks

12 buffalos + 4 ducks = 16 animals!!!!

We did it!

There would be 12 buffalos and 4 ducks.

Check your answer:

12 x 4 = 48.

4 x 2 = 8

48 + 8 = 56.

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Answer:

x-9

Step-by-step explanation:

I didn't know if you wanted it graphed or simplified so I gave ya both, hope it helps!!!

Answer: x - 9

Step-by-step explanation:

= x + 3 - 12

= x + (3 - 12)

= x-9

Answer:

No, it is not possible to create a triangle with these measurements.

Step-by-step explanation:

It must follow these rules:

a + b > c

a + c > b

b + c > a

It cannot be equal to it.

When making a joint probability table, the type of probabilities is contained in the cells except those cells on the margin of the table joint probabilities, while those on the margins are marginal probabilities.

A joint probability refers to the probability that two independent events will both occur. two or more random variables. It is a statistical measure that calculates the probability of two events occurring together and at the same point in time i.e., joint probability is the probability of event Y occurring at the same time that event X occurs. A joint probability table represents a joint probability distribution for two or more random variables illustrating the relationship between variables (it uses variables or conditions instead of events). In the joint probability table, the type of probabilities that are contained in the cells are joint probabilities, while those on the margins are marginal probabilities (probabilities of values of the variables in the subset without reference to the values of the other variables.).

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If a team at a factory collected data on the number of nonconforming parts to construct an np-chart then the average fraction has been mentioned below.

The term "average" refers to the mean or centre tendency of a group of data. In other words, it serves as a gauge for the average or median value among a group of numbers. This may be computed by adding up all of the set's values and dividing the result by the total number of values. As an illustration, the average would be (1 + 2 + 3 + 4 + 5) / 5 = 3  if given numbers were 1, 2, 3, 4, and 5.

Average fraction may also be used to represent the expected value or usual outcome of a random variable. For example, if we flip a coin and assign a value of 1 to heads and a value of 0 to tails, the average of the potential outcomes.

How to solve?

= 0.2 and the standard deviation was s = 0.1.

Based on this information, the team can construct an np-chart to monitor the process and identify any potential issues.

The np-chart plots the number of nonconforming parts in each sample against the sample number.

The average fraction nonconforming (p) is indicated by a horizontal line on the chart, and any points that fall outside the upper and lower control limits, which are determined by the standard deviation (s), are considered to be out of control and require further investigation.

This allows the team to monitor the process and take corrective action if necessary to ensure that the number of nonconforming parts remains within acceptable limits.

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In both cases, i.e. Cari and Dana, Dana is correct because the triangle follows the  30-60-90 triangle rule.

What is the 30-60-90 Triangle?

The 30-60-90 triangle is referred to as a special right triangle because its angles have a particular ratio of 1:2:3. A right triangle in this context refers to any triangle with a 90° angle. A unique kind of right triangle called a 30-60-90 triangle always has angles that measure 30, 60, and 90 degrees.

Given, for Cari, the triangle has a length of 3, 3, and 9

And, for Dana, the triangle has a length of 2, 2[tex]\sqrt{3}[/tex], and 4

For a 30-60-90 triangle, sides are distributed in the form of x, x[tex]\sqrt{3}[/tex] , and 2x.

So, in Dana's case, triangle sides have sides in the form of x, x[tex]\sqrt{3}[/tex] , and 2x i.e. 2, 2[tex]\sqrt{3}[/tex], and 4 respectively.

Therefore, Dana is correct.

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The first is a polyhedron but the second one is not

What is polyhedron?

A polyhedron is a three-dimensional structure in geometry that has flat, polygonal faces, edges that are straight, and sharp vertices. A convex polyhedron is made up of finitely many points that are not all on the same plane and has a convex hull. Convex polyhedra include shapes like cubes and pyramids.

1. The solid is formed by polygonal faces, so it is a polyhedron. This solid has two congruent pentagonal bases, so it is a pentagonal prism.

Face: Each flat surface is called face.

Edges: The line segments where the faces intersect are called edges.

Vertex: The point where three or more edges intersect is called a vertex.

Bases: HIJKL, PQMNO

Faces: HIJKL, PQMNO

Edges: IJ , IN , IH , MH , JO , JK , ON, OP , MQ , QP , QL , LH , KL , KJ , KP

Vertices : H,I,J,K,L,M,N,O,P,Q

2. A solid called a polyhedron is composed of flat surfaces that enclose a single area of space. This object is not a polyhedron since its surfaces are curved. The presented figure is a solid with parallel bases that are congruently spaced apart and are joined by a curved surface. It is therefore a cylinder.

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Answer:

a/ 5

b/ 2

c/ 6

d/ 10

Step-by-step explanation:

For A you can see that 5 divided by 1 equal 5, and 10 divided by 2 = 5, so the scale factor is 5

for B you can see that 10 divided by 5 = 2, and 12 divided by 6 = 2, so the scale factor is 2.

there are 360 degrees of angle in a circle, when it reads 1/360th of the circumference is 0.58 cm, it is informing you that 1 degree equals 0.58 cm.

The question then becomes, how many 0.58 cm there are in 87 cm. This is a division problem, therefore 87 cm divided by 0.58 cm equals 150, which we would translate to 150 degrees.The ratio of the second one's arc to circumference will be the same as the ratio of its angle to the circle's total 360 degrees. This is equivalent to 334.6 cm / 504 cm = x / 360 in mathematics. The result of solving for x is 239 degrees.

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The continuity theorem, also known as the intermediate value theorem, asserts that if a function is continuous on a closed interval, then it takes on every value inside the interval between the function's minimum and maximum values.

a. Using the continuity theorem, we know that as n→∞, the distribution of Xn converges to a Poisson distribution if the probability mass function of Xn converges to the probability mass function of a Poisson distribution.

This is true because the probability mass function of Xn, which is bin(n, 1/n), converges to the probability mass function of a Poisson distribution as n→∞.

b. Similarly, using the continuity theorem, we know that as n→∞, the distribution of Yn converges to an exponential distribution if the probability mass function of Yn converges to the probability mass function of an exponential distribution.

This is true because the probability mass function of Yn, which is geometric with parameter p = a/n, converges to the probability mass function of an exponential distribution as n→∞.

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A) Probability = 0

B) Probability = 0.4059

C) Probability = 0.7647

D) Probability = 0.4118

A probability simple definition is what?

Probability is a metric used to express the possibility or chance that a particular event will occur. Probabilities can be expressed as fractions from 0 to 1, as well as percentages from 0% to 100%.

where a = 8 and b = 25 are the uniform distribution parameters.

A)

probability = P(X>25)= 1-P(X<25)= 1-(25-8)/(25-8)= 0.0000

B)

probability = P(X<14.9)= (14.9-8)/(25-8)=   0.4059

C)

probability = P(10<X<23)= (23-10)/(25-8)=   0.7647

D)

probability = P(18<X<27)= (25-18)/(25-8)=   0.4118

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You're answer would be 3.21.

↓ Rounding to a decimal...

[tex]3.2142857142857[/tex]

↓ Rounding to the nearest hundredth...

[tex]3.21[/tex]

Thus, your answer is 3.21.