Prove that an odd integer n > 1 is prime if and only if it is
not expressible as a sum of three or more consecutive positive
integers.

The reaction of the graduate student on inflation is that a cost-of-living increase to her stipend.      

Inflation is the pace of expansion in costs over a given time-frame. Inflation is regularly a wide measure, like the general expansion in costs or the expansion in the typical cost for many everyday items in a country.

Inflation is term which states there is an expansion in the cost level for any labor and products.

In the unique situation, a set of experiences graduate living in the US got a payment of 18,000 dollar. However, there is a critical expansion that US economy endures. In this way the expense of products and the administrations accessible to individuals increments quickly. Individuals presently need to spend more on everything. Accordingly the alumni understudy requirements to request the typical cost for most everyday items to be remembered for the payment as need might arise to spend more on living.

Thus, graduate student argue on the a cost-of-living increase to her stipend.      

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Answer:

y=2x+16

Step-by-step explanation:

finally got it lol

Therefore, the interest on the notes would be:(a) $70 (b) $45 (c) $92 (d) $70.

To determine the interest on the given notes, we can use the simple interest formula:

Interest = Principal * Rate * Time

(a) For $5,600 at 5% for 90 days:

Principal = $5,600, Rate = 5% (or 0.05), Time = 90 days/360 (converted to years)

Interest = $5,600 * 0.05 * (90/360) = $70

(b) For $1,280 at 9% for 5 months:

Principal = $1,280, Rate = 9% (or 0.09), Time = 5 months/12 (converted to years)

Interest = $1,280 * 0.09 * (5/12) = $45

(c) For $6,900 at 8% for 60 days:

Principal = $6,900, Rate = 8% (or 0.08), Time = 60 days/360 (converted to years)

Interest = $6,900 * 0.08 * (60/360) = $92

(d) For $2,000 at 7% for 6 months:

Principal = $2,000, Rate = 7% (or 0.07), Time = 6 months/12 (converted to years)

Interest = $2,000 * 0.07 * (6/12) = $70

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To solve this problem, we can use the formula for finding the nth term of an arithmetic sequence.

a_n = a_1 + (n-1)d
where a_n is the nth term, a_1 is the first term, and d is the common difference between consecutive terms.
We know that the third term is 5, so we can plug in n = 3 and a_3 = 5:
5 = a_1 + 2d
We also know that the eleventh term is 18, so we can plug in n = 11 and a_11 = 18:
18 = a_1 + 10d
Now we have two equations with two variables (a_1 and d) that we can solve simultaneously.
First, we can solve for a_1 in terms of d from the first equation:
a_1 = 5 - 2d
Then we can substitute this expression for a_1 into the second equation:
18 = (5 - 2d) + 10d
Simplifying:
18 = 5 + 8d
13 = 8d
d = 13/8
Now we can use either equation to solve for a_1:
a_1 = 5 - 2d = 5 - 2(13/8) = -1/4
Finally, we can use the formula to find the seventh term, plugging in n = 7, a_1 = -1/4, and d = 13/8:
a_7 = (-1/4) + 6(13/8) = 39/8
So the answer is (d) 14.

To find the 7th term of an arithmetic sequence where the third term is 5 and the eleventh term is 18, follow these steps:
1. Determine the common difference (d) between terms. Since there are 8 terms between the 3rd and 11th term (11-3 = 8), we can calculate the common difference as follows:
  d = (18 - 5) / 8 = 13 / 8
2. Find the first term (a) of the sequence. We know that the third term is 5, so we can use the formula for the nth term of an arithmetic sequence:
  an = a + (n - 1)d
  5 = a + (3 - 1)(13 / 8)
  5 = a + (2)(13 / 8)
  5 = a + 13 / 4
  a = 5 - 13 / 4 = 7 / 4
3. Calculate the 7th term (a7) using the formula:
  a7 = a + (7 - 1)d
  a7 = (7 / 4) + (6)(13 / 8)
  a7 = (7 / 4) + (39 / 4)
  a7 = 46 / 4 = 23 / 2 = 11.5
So, the 7th term of the arithmetic sequence is 11.5. However, this is not among the given options. There might be a mistake in the question or the options provided.

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The interval of completion times containing the middle 95% of test-takers is approximately [40, 74].

We are given the mean μ = 57 and the standard deviation σ = 8 of the length of time needed to complete a certain test, which is normally distributed.A) We need to find the percent of people that take between 49 and 65 minutes to complete the exam.To find this, we can use the z-score formula as follows;z = (x - μ) / σ, where x = completion time= 49 minutesz1 = (49 - 57) / 8= -1z2 = (65 - 57) / 8= 1

Now, we need to find the area under the normal curve between these z-scores as shown in the figure below;z1 = -1, z2 = 1We can see that the area under the normal curve between -1 and 1 is approximately 0.6826. Therefore, the percent of people that take between 49 and 65 minutes to complete the exam is 68.26%.B) We need to find the interval of completion times containing the middle 95% of test-takers.To find this, we need to find the z-scores corresponding to the middle 95% of test-takers from the normal distribution table or calculator.

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Answer:

3

Step-by-step explanation:

she put 4 stickers on each car

Answer:

C

Step-by-step explanation:

since after you simplify c u end up with 2:6

Choice C

16:48

divide by 2

8:24

divide by 2

4:12

divide by 2

2:6

choice A

6:2

divide by 2

3:1

Choice B

27:9

divide by three

9:3

divide by three

3:1

If a finite group G has exactly one subgroup of a given order, then that subgroup is a normal subgroup of G

To show that if a finite group G has exactly one subgroup of a given order, then that subgroup is a normal subgroup of G, follow these steps:

1. Let H be the unique subgroup of G with a given order, say n.

2. Take any element g in G and consider the set gHg⁻¹, which is the conjugate of H by g. Here, g⁻¹ denotes the inverse of g.

3. We want to show that gHg⁻¹ is also a subgroup of G with the same order as H.

4. Notice that |gHg⁻¹| = |H|, since the mapping from H to gHg⁻¹ given by h ↦ ghg⁻¹ is a bijection.

5. Since there is only one subgroup of G with order n, we must have gHg⁻¹ = H.

6. As this holds for any element g in G, it means that H is a normal subgroup of G, by the definition of a normal subgroup.

So, if a finite group G has exactly one subgroup of a given order, then that subgroup is a normal subgroup of G.

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Answer:

625 students

Step-by-step explanation:

The expression is equivalent to "\(z^4 * (z + 6)^2 + (z + 6)\)".

To clarify, I understand the expression as: "z * (z + 6) * z * (z + 6) * z + (z + 6)". Let's break down the expression and simplify it step by step:

Distribute the multiplication:

z * (z + 6) * z * (z + 6) * z + (z + 6)

becomes

z * z * z * (z + 6) * (z + 6) * z + (z + 6)

Combine like terms:

z * z * z simplifies to \(z^3\)

(z + 6) * (z + 6) simplifies to (z + 6)^2

The expression now becomes:

\(z^3 * (z + 6)^2 * z + (z + 6)\)

Multiply \(z^3\) and z:

 \(z^3 * z\) simplifies to \(z^4\)

The expression becomes:

  \(z^4 * (z + 6)^2 + (z + 6)\)

So, an equivalent expression to "z (z + 6)z (z + 6)z + (z + 6)" is "\(z^4 * (z + 6)^2 + (z + 6)\)".

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The length of the missing side SB using concept of similar triangles is; SB = 9

Similar triangles are defined as triangles that have the same shape, but their sizes may vary. Thus, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

Now, using the concept of similar triangles on the given triangles, we have;

CU/UT = BU/SU

Plugging in the relevant values;

6/(18 + 6) = BU/12

BU = (12 * 6)/24

BU = 3

Thus;

SB = 12 - 3

SB = 9

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Step-by-step explanation:

what we see on the left side is that both terms contain (y + 6).

so, the left side is actually

(y + 6) × (x - 5)

therefore,

(x - 5)

is the missing factor on the right side.

After the reflection over the line x = 0, the coordinates will be:

J' = (2, 1)

K' = (0, 4) = K

For any point (x, y), if we apply a reflection across the line x = 0, the image after the reflection will be (-x, y).

So it only changes the sign of the x-component.

In the graph, we can see that J = (-2, 1). So after the reflection, we will have:

J' = (2, 1).

And we also can see that K = (0, 4), then after the reflection, we have:

K' = (-0, 4) = (0, 4) = K

So point K does not change under that reflection.

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Answer:

h(x)

h(x)

f(x) g(x) h(x)

Step-by-step explanation:

Edge 2020

~theLocoCoco

h(x) , h(x) , and f(x) g(x) h(x)

Explanation

using speed and distance relationship

Rate = distance / time

rafael runs 6 miles in 59 minutes

distance = 6 miles

time = 59 minutes

Rate = 6 / 59

Rate = 0.102 miles / minutes

to calculate how many miles he ran in minutes at the same rate

rate = 0.102 miles / minutes

Rate = distance / time

distance = rate x time

distance = 0.102 x 35

distance = 3.55 miles

approximately = 4 miles

Rafael ran 3.55 miles in 35 minutes

The answer is 3.55 miles

Answer:

The correct answer is option B (20 years)

Answer: The Answer Is 20 Years and for second question 1,750

Step-by-step explanation: So, for an amortized expense the first-year payment will subtracted from the $5,000 patent. This will continue until the payment of the patent is run out. so, we can do 5000/250 (250 accounting for each year) to get 20. so, in 20 years the patent will run out.

This will help for the second question you had as well being "What will the accumulated amortization of Mila and Dante’s $5,000 patent be after seven years, given a $250 amortized expense each year?" Just to simplify it multiply 250*7 to get 1,750. This will be the amortized expense in 7 years.

Hope this helped!

z_1 and z_2 are complex number;

i) z₁z₂ = 8(cos(7π/12) + isin(7π/12))

ii) z₁/z₂ = 2(cos(π/12) + isin(π/12))

To calculate z₁z₂ and z₁/z₂, we need to perform the complex number operations on z₁ and z₂. Let's break down the calculations step by step:

i) To find z₁z₂, we multiply the magnitudes and add the angles:

z₁z₂ = 4cos(cos(π/4) + isin(π/4)) * 2cos(2π/3) + isin(2π/3))

= 8cos((cos(π/4) + 2π/3) + isin((π/4) + 2π/3))

= 8cos(7π/12) + isin(7π/12)

ii) To find z₁/z₂, we divide the magnitudes and subtract the angles:

z₁/z₂ = (4cos(cos(π/4) + isin(π/4))) / (2cos(2π/3) + isin(2π/3))

= (4cos((cos(π/4) - 2π/3) + isin((π/4) - 2π/3))) / 2

= 2cos(π/12) + isin(π/12)

i) z₁z₂ = 8(cos(7π/12) + isin(7π/12))

ii) z₁/z₂ = 2(cos(π/12) + isin(π/12))

Please note that the given calculations are based on the provided complex numbers and their angles.

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Using linear functions, the cost will be the same, of $70, when there are 5 students.

A linear function is modeled by:

y = mx + b

In which:

In this problem, the functions are:

The costs are the same when:

45 + 5x = 35 + 7x

2x = 10

x = 5.

The cost is:

y = 45 + 5 x 5 = $70.

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Answer:

Meena has twelve (12) ₹20 notes and thirty six (36) ₹10 notes

Step-by-step explanation:

The amount Meena has as notes in ₹10 and ₹20 denominations = ₹600

The number of ₹10 notes = 3 × The number of ₹20 notes

Let 'x' represent the number of ₹20 notes Meena has, we get;

The number of ₹10 notes = 3 × x

The total number of notes = x × 20 + 3·x × 10 = 50·x = ₹600

∴ 600/50 = 12

The number of the ₹20 notes, x = 12

The number of the ₹10 = 3 × x

∴ The number of the ₹10 = 3 × 12 = 36

Given that:

The expressions are \(3z−2, 2x^3+x-12, 9b, 9x-2\).

Solution:

Monomial : It contains single terms.

Binomial : It contains two terms.

Trinomial :  It contains three terms.

Polynomial : It contains atleast one algebraic term.

Degree of polynomial : It is highest power of the variable.

\(3z-2\) ,  here z is the variable. So, it is a polynomial with degree 1 and it is a binomial.

\(2x^3+x-12\) ,  here x is the variable with highest power 3. So, it is a polynomial with degree 3 and it is a trinomial.

\(9b\) ,  here b is a constant. So, it is not a polynomial and it is a monomial.

\(9x-2\) ,   here x is the variable. So, it is a polynomial with degree 1 and it is a binomial.

The point of diminishing returns is (20.98, 21247.3).

The point of diminishing returns occurs when the marginal cost of producing an extra unit of output exceeds the marginal revenue generated from selling that unit. Mathematically, it is the point at which the derivative of the production function equals zero and the second derivative is negative.

Given the polynomial function N(x) of degree 3, we can find the point of diminishing returns by finding the critical points where the first derivative equals zero and evaluating the second derivative at those points.

The derivative of N(x) is N'(x) = -18x² + 360x + 2250. To find the critical points, we set N'(x) = 0:

0 = -18x² + 360x + 2250

Dividing by -18 simplifies the equation:

0 = x² - 20x - 125

Using the quadratic formula, we find the solutions to the equation:

x₁,₂ = (20 ± √(20² - 4(1)(-125))) / 2(1)

x₁,₂ = 10 ± 5√5

Thus, the two critical points of N(x) are at x = 10 - 5√5 and x = 10 + 5√5.

To determine the point of diminishing returns, we evaluate the second derivative N''(x) = -36x + 360 at these critical points:

N''(10 - 5√5) = -36(10 - 5√5) + 360 ≈ -264.8

N''(10 + 5√5) = -36(10 + 5√5) + 360 ≈ 144.8

From the evaluations, we find that N''(10 + 5√5) is negative while N''(10 - 5√5) is positive. Therefore, the point of diminishing returns corresponds to x = 10 + 5√5.

To find the corresponding y-coordinate (N(10 + 5√5)), we can substitute the value of x into the original function N(x).

Hence, the point of diminishing returns is approximately (20.98, 21247.3).

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Answer:

76124

Step-by-step explanation:

CORRECT 100%

Answer:

it looks like a cube to me lol

Yes, the point (-5,3)  satisfy the inequality 3x+2y<12.

What is inequality?

In Algebra, inequality is a Mathematical statement that shows the relation between two expressions using the inequality symbol.

The expressions on both sides of an inequality sign aren't equal. It means that the expression on the left- hand side should be lesser than or lower than the expression on the right- hand side or viceversa.

However, also it's called non fictional inequalities, If the relationship between two algebraic expressions is defined using the inequality symbols.

Still, “< ”, “ ≥ ”, “ If two real figures or the algebraic expressions are related by the symbols “> ”. ”

We have an expression;

3x + 2y < 12

We have point (-5, 3);

So, for checking the statisfaction of inequality we have to put the point in the expression;

Here, x = -5 and y = 3

so, 3(-5) + 2(3) < 12

     -15 + 6 < 12

      -9 < 12

Which is true.

Hence, we see the clearly that it the points (-5,3) satisfies the given expression 3x + 2y < 12.

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110.25 kW. The minimum power rating of the motor can be calculated using the formula for power, P = Fv, where P is the power, F is the force, and v is the velocity.

First, we need to convert the mass from tons to kilograms:
1.5 ton = 1.5 x 1000 kg = 1500 kg
Next, we need to calculate the force required to lift the mass at a constant speed. Since the elevator is moving at a constant speed, the force required is equal to the weight of the mass:
F = mg
F = (1500 kg)(9.8 m/s^2)
F = 14700 N

Now, we can plug in the values for force and velocity into the formula for power:
P = Fv
P = (14700 N)(7.5 m/s)
P = 110250 W
Finally, we need to convert the power from watts to kilowatts:
P = 110250 W / 1000
P = 110.25 kW
Therefore, the minimum power rating of the motor should be 110.25 kW.

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Answer:

Step-by-step explanation:

As we use prime factorization for 200, we get 2 × 2 × 2 × 5 × 5 = 200. So, the only prime factors of 200 are 2 and 5.

Answer:

5*5*2*2*2

Step-by-step explanation:

200 divided by 2 is 100. 100 divided by 2 is 50. 50 divided by 2 is 25. 25 divided by 5 is 5

Answer: \(\frac{1}{27}\)

Step-by-step explanation:

Anything to the third power means it is multiplied by itself 3 times.

   --> \((\frac{1}{3})^{3} =(\frac{1}{3})(\frac{1}{3})(\frac{1}{3})=\frac{1}{27}\)

Answer:

(-5)^3 = -125

Step-by-step explanation:

(-5)^3

= (-5) × (-5) × (-5) = -125

= (-5)^3 = -125

(-5) to the power of 3 is just (-5) multiplied by itself 3 times so (-5) to the power of 3 is (-5)^3 which is -125

Step-by-step explanation:

it's quite easy to go around this problem.

first you gotta consider the negative (-) sign..

you know when a negative sign multiplies another negative sign you'll get a positive sign.

example

-5*-5= ?

since you know the negative sign would turn to a positive sign when they multiply each other.

and be mindful of problems with different signs like

−6×9, you'll definitely get a negative answer

Now to your question.

(−5)^3, if you're struggling with composite expression,all you need is to break it down to simplified form

since it's -5 raised to the power of 3

you can as well write it as -5*-5*-5 (pay attention to the negative sign). then go through with your calculations

if you do it correctly, you'll arrive at the answer

-125