y = 4x – 18
y = -5x +9

Answer:

2 nonreal solutions

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 (a ≠ 0 )

then the nature of the roots are determined by the discriminant

b² - 4ac

• if b² - 4ac > 0 then 2 real and irrational solutions

• if b² - 4ac > 0 and a perfect square then 2 real and rational solutions

• if b² - 4ac = 0 then 2 real and equal solutions

• if b² - 4ac < 0 then no real solutions

5x² - 2x + 6 = 0 ← in standard form

with a = 5 , b = - 2 , c = 6

b² - 4ac

= (- 2)² - (4 × 5 × 6)

= 4 - 120

= - 116

since b² - 4ac < 0

then there are 2 nonreal solutions to the equation

The Fermi energy will be at the edge of the second band at zero temperature.

(a) Band structure is the diagrammatic representation of the dispersion of energies of the electronic states in the crystal as a function of the momentum, and their relative occupancies, under an applied electric field. It determines whether a solid is a metal, an insulator, or a semiconductor. For this reason, it is frequently used to examine the optical and electronic properties of a solid in condensed matter physics. The periodicity of the lattice is represented by the Brillouin zone. Using what we learned in class, sketch the band structure in the First Brillouin Zone (FBZ) for A1=10meV, A2=20meV, and A3=30meV, including at least the first three lowest bands, being sure to label the magnitude of the energy gaps as well as their positions in reciprocal space.

Below is the image of the first three energy bands in the FBZ for A1 = 10meV, A2=20meV, and A3=30meV.

(b) The location of the Fermi energy is determined by the electron concentration in the crystal. Fermi energy is the energy level at which the probability of occupying the state is one-half at 0 Kelvin.

Therefore, the Fermi energy is related to the valence and conduction band energies and the concentration of electrons. If the crystal has two electrons for each lattice site, the Fermi energy at zero temperature will be midway between the conduction and valence band edge. The Fermi energy level will be in the gap between the first and second bands, at the halfway point between the conduction band edge and the valence band edge. On the other hand, if the crystal has three electrons per lattice site, the Fermi energy will be at the edge of the second band at zero temperature.

(c) In a 1D crystal with a lattice spacing a=5 nm, U(x) is a periodic crystal potential that has the following form:

U(x)=A1sin(2πx/a)+A2sin(4πx/a)+A3sin(2πx/a)cos(2πx/a).

We are now told that A2 can be externally tuned. To create just one energy gap in the electronic band structure, A2 must be equal to zero. The energy gap would be centered at (π/a,0), where the band minimum for the second band is located.

If there are four electrons per lattice, the Fermi energy level will be in the second band, and the value of the Fermi energy level can be computed using the graph from part a.

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\(\begin{array}{ccll} miles&seconds\\ \cline{1-2} 2\times 10^{5} & 1\\ 9\times 10^{7}& x \end{array} \implies \cfrac{2\times 10^{5}}{9\times 10^{7}}~~=~~\cfrac{1}{x}\implies (2\times 10^{5})x=9\times 10^{7} \\\\\\ x=\cfrac{9\times 10^{7}}{2\times 10^{5}}\implies x=\cfrac{9}{2}\times\cfrac{ 10^{7}}{10^{5}}\implies x=4.5\times 10^{7-5}\implies x=4.5\times 10^{2}\)

Given:

The function is:

\(f(x)=10x^5+8x^4-15x^3+2x^2-2\)

To find:

All the possible rational zeros for the given function by using the Rational Zero Theorem.

Solution:

According to the rational root theorem, all the rational roots are of the form \(\dfrac{p}{q},q\neq 0\), where p is a factor of constant term and q is a factor of leading coefficient.

We have,

\(f(x)=10x^5+8x^4-15x^3+2x^2-2\)

Here,

Constant term = -2

Leading coefficient = 10

Factors of -2 are ±1, ±2.

Factors of 10 are ±1, ±2, ±5, ±10.

Using the rational root theorem, all the possible rational roots are:

\(x=\pm 1,\pm 2,\pm \dfrac{1}{2}, \pm \dfrac{1}{5},\pm \dfrac{2}{5},\pm \dfrac{1}{10}\).

Therefore, all the possible rational roots of the given function are \(\pm 1,\pm 2,\pm \dfrac{1}{2}, \pm \dfrac{1}{5},\pm \dfrac{2}{5},\pm \dfrac{1}{10}\).

Answer:hope these helps

Step-by-step explanation:

This result might not be particularly large or important because there might only be few differences between the research subjects.

Statistical significance is a measure of the probability that a result could have occurred by chance alone. In a study with a large sample size, even small differences between groups or conditions may be statistically significant.

In the case of a study with 5000 subjects, a statistically significant result at the 5% level would mean that there is less than a 5% chance that the result occurred by chance.

However, it's important to remember that statistical significance does not necessarily imply practical significance or importance.

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A binary tree is a structure in which each node is capable of having two successor nodes, called "left child" and "right child."

In a binary tree, each node can have at most two successor nodes, known as the left child and the right child. These successor nodes branch out from the parent node, forming two distinct paths or branches. The left child represents the left branch, and the right child represents the right branch. This hierarchical structure allows for efficient organization and traversal of data, as each node can connect to two other nodes, creating a branching pattern throughout the tree. The concept of left and right children enables various operations and algorithms to be performed on the binary tree, such as insertion, deletion, searching, and sorting.

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A function exists described as a relation between a set of inputs containing one output each. The value of h(g(3)) is 5.

A relationship between a group of inputs and one output is referred to as a function.

In plain English, a function is an association between inputs in which each input is connected to precisely one output.

A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Where, g(3) = 0

To get h, replace g(3) with 0 in the requested equation (0).

Since h(0) = 5 according to the question, your final response is 5.

Therefore, the value of h(g(3)) is 5.

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f(x) = ax + b, and it is the unique differentiable function with f'(x) = a for all x and f(0) = b. Proof: Suppose g(x) is another differentiable function with g'(x) = a for all x and g(0) = b. Then, g(x) = ax + b, and so f = g. so, the correct answer is A).

We have f'(x) = a for all x, so by the Fundamental Theorem of Calculus, we have

f(x) = ∫ f'(t) dt + C

= ∫ a dt + C

= at + C

where C is a constant of integration.

Since f(0) = b, we have

b = f(0) = a(0) + C

= C

Therefore, we have

f(x) = ax + b

Now, to prove that f is the unique differentiable function with f'(x) = a for all x and f(0) = b, suppose g(x) is another differentiable function with g'(x) = a for all x and g(0) = b.

Define h(x) = g(x) - f(x). Then we have

h'(x) = g'(x) - f'(x) = a - a = 0

for all x. Therefore, h(x) is a constant function. We have

h(0) = g(0) - f(0) = b - b = 0

Thus, h vanishes everywhere and so f = g. Therefore, f is the unique differentiable function with f'(x) = a for all x and f(0) = b. so, the correct answer is A).

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false :) thats ur answer

This is true because a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

The area under the probability distribution is a measure of the probability of all the possible outcomes. Since the sum of all the probabilities of all the possible outcomes must be 1, the total area under the probability distribution must also be 1. This is because the probability of an event happening is the area under the curve of the probability distribution at that event. Thus, the total area under the probability distribution must always equal 1.

This is true because a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

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Answer:

a) £105 300

b) £132 300

Step-by-step explanation:

a) 2700*39=105 300

b) 2700*49=132 300

Answer:

24 students

Step-by-step explanation:

2/5 = x/60 ----->   24/60 = x/60  --->   24/60 = 24/60

Answer:

Answer:

discovery of jupiter's mons which did not orbit earth

Step-by-step explanation:

Answer:

The answer will be B. V^6

The statement provides two quantities, A and B, expressed as ratios of positive integers c and d. The relationship between the quantities A and B cannot be determined from the information given.

The statement provides two quantities, A and B, expressed as ratios of positive integers c and d. However, no specific values or constraints are given for c and d. Without knowing the specific values or any relationship between c and d, it is impossible to determine the relationship between A and B.

The relative magnitudes of A and B will depend on the values of c and d. If the value of c is greater than d, then A would be greater than B. Conversely, if the value of d is greater than c, then B would be greater than A. However, without any information about the values of c and d or any relationship between them, we cannot determine the relationship between A and B.

Therefore, based on the given information, the relationship between quantities A and B cannot be determined.

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Answer:

18

Step-by-step explanation:

f(x)=2x and g(x)=x2+3, find (g ∘ f)(−3)

f(x)= 2(-3)= -6

g(x)= (-3)(2) +3= -6+3= -3

(g ∘ f) = -6 x -3= 18

Answer:

After one year, the enrollment will be 600 + 40 = 640. After two years, the enrollment will be 640 + 40 = 680. After three years, the enrollment will be 680 + 40 = 720. After four years, the enrollment will be 720 + 40 = 760. After five years, the enrollment will be 760 + 40 = 800.

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

(4-3) + (23) = 24

Answer:

He can buy 6 liters because £0.80 x 6 = £4.80. So he will have £5.00 - £4.80 = £0.20 left over. 20p.

Step-by-step explanation:

welcome

The two column proof to justify the complementary angles are;

Statement 1. ∠1 and ∠2 are complementary

∠2 and ∠3 are complementary

Reason 1: Given

Statement 2: m∠1 + m∠2 = 90°

Reason 2: Definition of Complementary Angles

Statement 3. m∠2 + m∠3 = 90°

Reason 3: Definition of Complementary Angles

Statement 4: m∠1 + m∠2 = m∠2 + m∠3

Reason 4: Transitive property of equality

Statement 5: m∠1 = m∠3

Reason 5: Substitution Property of Equality

Complementary angles are defined as angles that sum up to 90 degrees.

Now, from the question, we are given that;

∠1 and ∠2 are complementary, and ∠2 and ∠3 are complementary.

From the image attached, we can get a two column proof based on the given questions as;

Statement 1. ∠1 and ∠2 are complementary

∠2 and ∠3 are complementary

Reason 1: Given

Statement 2: m∠1 + m∠2 = 90°

Reason 2: Definition of Complementary Angles

Statement 3. m∠2 + m∠3 = 90°

Reason 3: Definition of Complementary Angles

Statement 4: m∠1 + m∠2 = m∠2 + m∠3

Reason 4: Transitive property of equality

Statement 5: m∠1 = m∠3

Reason 5: Substitution Property of Equality

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Complete Question is;

Identify the correct justification for each step, given that ∠1 and ∠2 are complementary, and ∠2 and ∠3 are complementary.

1. ∠1 and ∠2 are complementary

∠2 and ∠3 are complementary

2. m∠1 + m∠2 = 90°

3. m∠2 + m∠3 = 90°

4. m∠1 + m∠2 = m∠2 + m∠3

5. m∠1 = m∠3

Cⁿ₁ is always positive, then the second term has negative sign.

What does binomial expansion mean?

Theorem that states that any power of a binomial (a + b) can be expanded as a specific sum of products (aibj), such as (a + b)2 = a2 + 2ab + b2.

The i-th term of the binomial expansion \((x- y)^{n}\)

Ti = nCi - 1 . (x)ⁿ+¹⁺i  . (-y)i - 1

For any n, when i=2,

T₂ = nC₂₋₁  . xⁿ⁺¹⁻² . (-y)²⁻¹  = -Cⁿ₁ xⁿ⁻¹ . y

Given that is consistently positive, the second term has a negative sign.

Cn1 is consistently positive, and the second term is always negative.

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a. At values of x=1 and x =3 the local maximum and minimum values of g occur

b. The absolute maximum value of g(x) is approximately 0.76 and occurs at x = 4.

c. On the intervals [0, 1) and (3, 4] g concave downward

Since g(x) is defined as the definite integral of f(t) from 0 to x, we can use the First Fundamental Theorem of Calculus to find g'(x) in terms of f(x):

g'(x) = f(x)

Similarly, we can use the Second Fundamental Theorem of Calculus to find g''(x) in terms of f'(x):

g''(x) = f'(x)

(a) The local maximum and minimum values of g occur at critical points of g(x), which are values of x where g'(x) = f(x) = 0 or is undefined. From the graph of f(x), we see that f(x) = 0 at x = 1 and x = 3, so these are possible candidates for critical points of g(x). We also see that f(x) is undefined at x = 2, so this is another possible critical point. Evaluating g'(x) and g''(x) at each of these values, we have:

g'(1) = f(1) = 0, g''(1) = f'(1) < 0, so g(x) has a local maximum at x = 1.

g'(2) is undefined, so x = 2 is not a critical point of g(x).

g'(3) = f(3) = 0, g''(3) = f'(3) > 0, so g(x) has a local minimum at x = 3.

Therefore, the local maximum of g(x) occurs at x = 1, and the local minimum of g(x) occurs at x = 3.

(b) To find the absolute maximum value of g(x), we need to examine the values of g(x) at the endpoints of the interval [0, 4]. We have:

g(0) = 0

g(4) = R 4 0 f(t)dt = the area under the curve of f(x) from x=0 to x=4.

From the graph, we can see that the absolute maximum value of g(x) occurs when x is in the interval [1, 3], so we can evaluate g(x) at the critical points found in part (a) and the endpoints of the interval to find the absolute maximum value of g(x):

g(1) = R 1 0 f(t)dt ≈ 0.72

g(3) = R 3 0 f(t)dt ≈ 0.65

g(4) = R 4 0 f(t)dt ≈ 0.76

Therefore, the absolute maximum value of g(x) is approximately 0.76 and occurs at x = 4.

(c) The function g(x) is concave downward on an interval if its second derivative, g''(x), is negative on that interval. From part (a), we know that g''(x) = f'(x), so we need to find where f'(x) is negative. From the graph of f(x), we can see that f'(x) is negative on the intervals [0, 1) and (3, 4]. Therefore, g(x) is concave downward on the intervals [0, 1) and (3, 4].

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Answer:

378

Step-by-step explanation:

nth triangular number: n(n+1) / 2

27th triangular number: 27(27+1) / 2 = 27*28 / 2 = 378

Answer:

total=4.5+9=13.5

Step-by-step explanation:

0.5×3=1.5. 3×3=9

1.5×3=4.5 A=4.5. A=9. 4.5+9=13.5

The standard score for the distribution with mean at the height of 6 feet or 72 inches is 1.12.

The normal distribution of height of men is approximately normal with mean 69.2 inches and standard deviation of sigma=2.5 inches

According to the empirical rule of probability, about 95% observations falls within two standard deviation of mean.

Therefore,

Lower bound=μ + 2×σ

=69.2 + 2×2.5

=69.2 + 5.0

Lower bound = 74.2

Upper bound = μ - 2 × sigma

=69.2 - 5

Upper bound = 64.2

2. The distribution of the heights of young men is approximately normal with mean μ = 69.2 inches and standard deviation of σ = 2.5

The standard score of height of 72 inches is calculated by:

z = (72-69.2)/2.5

z = 2.8/2.5

z = 1.12

Therefore the standard score for the distribution with mean at the height of 6 feet or 72 inches is 1.12.

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Answer:

Possible

Step-by-step explanation:

This is done on any floor, the highest or the lowest. Simply drop the egg from one inch above your foot and it will not break. every answer above is wrong. The only way, having 2 eggs, is to starts from the 2º floor.

To find the speed at which the Salisbury family was driving, we can use the formula: Speed = Distance / Time. So, the Salisbury family was driving at a speed of 89 kilometers per hour.

The distance they traveled is the difference between their initial distance from home (750 km) and their distance from home after 4 hours (394 km):
Distance = 750 km - 394 km = 356 km
The time they took to cover this distance is 4 hours.

Now we can calculate the speed:
Speed = 356 km / 4 h = 89 km/h
Therefore, the Salisbury family was driving at a speed of 89 kilometers per hour.

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If Robert ate lunch at 11:am and he ate a snack 4and a half hours later, Robert ate his snack at 3:30 pm

To find out what time Robert ate his snack, we need to add 4 and a half hours to the time he ate lunch.

Since he ate lunch at 11:00 am, we can convert this time to 24-hour format by adding 12 hours to get 11:00 + 12:00 = 23:00.

Next, we add 4 and a half hours to 23:00 by converting the half hour to minutes and adding it to the minutes portion of the time:

23:00 + 4 hours + 30 minutes = 27:30

However, since there are only 24 hours in a day, we need to convert this time back to 12-hour format. To do this, we subtract 12 hours from 27:30 to get 15:30.

Therefore, Robert ate his snack at 3:30 pm (or 15:30 in 24-hour format).

In summary, we added 4 and a half hours to the time Robert ate lunch, converted the resulting time to 24-hour format, subtracted 12 hours to account for the excess of 24 hours, and then converted the time back to 12-hour format to obtain the time Robert ate his snack.

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