7) Solve 5x² + 7 = 3x over the set of complex numbers.

By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

WHat is Divisibility?

Divisibility is a mathematical property that describes whether one number can be divided evenly by another number without leaving a remainder. If a number is divisible by another number, it means that the division process results in a whole number without any remainder. For example, 15 is divisible by 3

To prove that 4 evenly divides 11n - 7n for any positive integer n, we can use mathematical induction.

Base Case:

When n = 1, 11n - 7n = 11(1) - 7(1) = 4, which is divisible by 4.

Inductive Step:

Assume that 4 evenly divides 11n - 7n for some positive integer k, i.e., 11k - 7k is divisible by 4.

We need to prove that 4 evenly divides 11(k+1) - 7(k+1), which is (11k + 11) - (7k + 7) = (11k - 7k) + (11 - 7) = 4k + 4.

Since 4 evenly divides 4k, and 4 evenly divides 4, it follows that 4 evenly divides 4k + 4.

By mathematical induction, we have proved that for any positive integer n, 4 evenly divides 11n - 7n.

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Answer:

x=60

Step-by-step explanation:

The sum of interior angles of a regular Pentagon is 540°

x+2x+2.5x+x+10+2x+20=540

8.5x=540-30

8.5x=510

x=510/8.5=60

Answer:

Step-by-step explanation:

Sum of interior angles of a regular polygon is:

Pentagon has 5 sides, so sum of angles is:

For the given pentagon we have sum of angle measures as below, and solving for x:

Answer:

-1 and -0.5

Step-by-step explanation:

Based on the given information, the regression that represents the estimated production function model for firm output in the industry is:

c. log(Q1) = 10.74 + 0.032 Li

The regression equation in option c represents a logarithmic relationship between the output (Q1) and the number of workers employed (Li). Taking the logarithm of the output variable allows for a more flexible functional form and captures potential diminishing returns to labor.

In the regression equation, the constant term (10.74) represents the intercept or the level of output when the number of workers is zero. The coefficient of 0.032 (0.032 Li) indicates the relationship between the logarithm of output and the number of workers employed.

Since the question states that employing another worker leads to a 32 percent increase in output, this aligns with the coefficient of 0.032 in the regression equation. It suggests that a 1 percent increase in the number of workers (Li) leads to a 0.032 percent increase in output, which is equivalent to a 32 percent increase.

Therefore, the regression equation in option c best represents the estimated production function model in this scenario.

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Answer:

-8

Step-by-step explanation:

midpoint = (W + X)/2

midpoint = [-11 + (-5)]/2

midpoint = -16/2

hence midpoint = -8

Answer:

the bus is cheaper by £12.4

Step-by-step explanation:

the total cost to travel by a bus is 3.50 * 4 = £14

the total cost to travel by a car is 3.60 +(1.90*12)

= £26.4

travelling by the bus is cheaper by (26.4 - 14) = £12.6

Step-by-step explanation:

a. To find dy/dx when y = 2xlog e (2x), we can use the chain rule. First, we rewrite the function as y = 2x(ln(2x) + 1) where ln is the natural logarithm. Then, we can take the derivative of y with respect to x:

dy/dx = 2(ln(2x) + 1) + 2x(1/2x) = 2ln(2x) + 2 + 2/x

b. To find f′(0) when f(x) = e^x^2/e^x+1, we can take the derivative of the function with respect to x:

f′(x) = (2xe^x^2(e^x+1) - e^x^2(e^x+1)) / (e^x+1)^2

Setting x = 0, we get:

f′(0) = 2e^0(e^0 + 1) - e^0(e^0 + 1) / (e^0 + 1)^2 = 1 / (e^0 + 1)^2 = 1 / 2^2 = 1/4

The answer is Trapezoid

What is a Trapezoid?

A trapezoid, also known as a trapezium, is a flat closed shape having 4 straight sides, with one pair of parallel sides. The parallel sides of a trapezium are known as the bases, and its non-parallel sides are called legs. A trapezium can also have parallel legs.

Given data ,

The trapezoid cannot be mapped onto itself

The isosceles trapezoid has no rotational symmetry. There is no way to rotate it such that it can be mapped onto itself.

Square , Regular Hexagon and Regular Pentagon all have rotational symmetry

Hence , Trapezoid cannot be mapped onto itself

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To shade the grid to show the percent of bikes that are mountain bikes, you would shade 75% of the grid (or three out of four squares).

To determine the total number of bikes in the school bike racks, given that 75% of them are mountain bikes and there are 15 mountain bikes, we can follow these steps:

1. Since 75% of the bikes are mountain bikes, we can write this as a fraction: 75/100.
2. We know that there are 15 mountain bikes, so we can set up a proportion:
(75/100) = (15/total bikes).
3. To solve for the total number of bikes, cross-multiply:
75 * (total bikes) = 100 * 15.
4. Simplify the equation:
75 * (total bikes) = 1500.
5. Divide by 75 on both sides:
total bikes = 1500/75.
6. Calculate the result:
total bikes = 20.

So, there are 20 bikes in the bike racks.

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Answer:

2(x+3)=2x+6

Step-by-step explanation:

Because You multiply 2*x and 2*3.

The X is a variable and it actually equals to 1. so it's basically 2*1

After you multiply 2*x and 2*3 you will get 2x+6

Answer:

C

Step-by-step explanation

the weather usually gets colder in the winter and people usually decorate for Christmas late fall and early winter.

therefore, if there is snow on the ground and Christmas lights on houses its most likely winter.

Complete question :

You take 325 milligram dosage of ibuprofen during the subsequent hour the amount of medication increases 29% each hour

a. Write an exponential growth model giving the amount y (in milligrams) of ibuprofen in your bloodstream t hours after the initial dose.

Answer:

y = 325(1 + 0.29)^t

Step-by-step explanation:

Using the exponential growth model:

y = a(1 + r)^t

Initial dosage, a = 325

Growth rate, r = 29% = 0.29

t = Time

Plugging the Given VALUEs:

y = 325(1 + 0.29)^t

y = amount of ibuprofen (in milligram) on blood stream after rime, t

Using monthly payment formula, the Smith Family's total monthly payment is approximately $2,360.99.

To calculate the total monthly payment for the Smith Family, we need to consider the mortgage payment, insurance, property tax, and HOA fees.

1. Mortgage Payment:

The loan amount is the house price minus the down payment:

$350,000 - $70,000 = $280,000.

To calculate the monthly mortgage payment, we need to determine the interest rate and loan term. Since you mentioned it's a 15-year loan, we'll assume an interest rate of 4% (which can vary depending on market conditions and the borrower's credit).

We can use a mortgage calculator formula to calculate the monthly payment:

M = P [i(1 + i)ⁿ] / [(1 + i)ⁿ⁻¹]

Where:

M = Monthly mortgage payment

P = Loan amount

i = Monthly interest rate

n = Number of months

The monthly interest rate is the annual interest rate divided by 12, and the loan term is 15 years, which is 180 months.

i = 4% / 12 = 0.00333 (monthly interest rate)

n = 180 (loan term in months)

Plugging in the values into the formula:

M = $280,000 [0.00333(1 + 0.00333)¹⁸⁰] / [(1 + 0.00333)¹⁸⁰⁻¹]

Using a calculator, the monthly mortgage payment comes out to be approximately $2,014.99.

2. Insurance:

The monthly insurance payment is given as $66.

3. Property Tax:

The monthly property tax payment is given as $230.

4. HOA Fees:

The HOA fees are stated as $600 per year. To convert this to a monthly payment, we divide by 12 (months in a year): $600 / 12 = $50 per month.

Now, let's add up all these expenses:

Mortgage payment: $2,014.99

Insurance: $66

Property tax: $230

HOA fees: $50

Total monthly payment = Mortgage payment + Insurance + Property tax + HOA fees

Total monthly payment = $2,014.99 + $66 + $230 + $50

Total monthly payment = $2,360.99

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The depth of water which is in the shape of a rectangular prism is \(16.75m\) when it is completely filled with water.

A solid (3-dimensional) object that has six faces that are rectangles.

It has the same cross-section along its length, which makes it a prism.

It is also a "block".

A rectangular prism is a three-dimensional shape that has six faces, where all faces (top, bottom, and side faces) of the prism are rectangles, so all pairs of opposite faces are congruent. Like all three-dimensional shapes, a rectangular prism also has volume and surface area. A rectangular prism is also known as a cuboid.

There are two types of rectangular prisms, which are classified depending on the shape of the faces or the angle that the faces make with the base.

In general, a rectangular prism without any specifications is a right rectangular prism.

Given:

A swimming pool is in the shape of a rectangular prism

The base of the pool has an area of 116 square feet

When the pool is completely filled it holds 1944 cubic feet of water

To find:

What is the depth of the water when the pool is completely full?

Solution:

To find out the depth of the water when it is completely filled with water we need to simply divide the total cubic feet of water when it is completely filled by the area of the rectangular prism which is as follows:

\(=1944/116\\=16.75 m\)

Hence the depth of water is \(16.75m\) when it is completely filled with water.

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Answer:

initial height = 0 feet

height after 2 seconds = 32 feet

takes 3 seconds until ball hits the ground

after 2.5 seconds the ball is at 20 feet

Step-by-step explanation:

According to recent data, women make up 34% and 26% of workers in science and technology (STEM) fields in Canada and the United States, respectively. The correct option is A. 34% and 26%.

According to recent data, women make up 34% and 26% of workers in science and technology (STEM) fields in Canada and the United States, respectively. This indicates that women are still underrepresented in STEM fields, despite the fact that there has been an effort to attract more women to STEM fields.

In both Canada and the United States, women have made significant progress in breaking down gender barriers in STEM fields. However, there is still work to be done to close the gender gap and increase representation of women in STEM fields.

Women's representation in STEM fields has increased in both Canada and the United States in recent years, but the percentage of women in STEM fields is still significantly lower than the percentage of men. More efforts are needed to close the gender gap in STEM fields and encourage more women to pursue STEM careers.

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We have the set of values: 98 87 86 100 79 92 88 95 89 86 96.

We have to calculate the IQR:

where Q3 is the third quartile and Q1 is the first quartile.

The first step is to sort the values in ascendent order:

Answer:

$336.44

Step-by-step explanation:

$402.44 - $66 = $336.44

Answer:

b

Step-by-step explanation:

B

The expected probability that the next flip is a head given the results of the previous 25 coin flips is 0.6 or 60%.

The expected probability of a head coming up next given the results of the 25 coin flips is 15/25 = 0.6.

This is due to the fact that 15 of the 25 flips were heads, so the probability of the next head is 15 out of the 25 total flips which is equal to 0.6 or 60%.

However, since the probability of heads (m) is unknown, the expected probability of a head coming up next is still unknown.

Therefore, the expected probability that the next flip is a head given the results of the previous 25 coin flips is 0.6 or 60%.

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By using normal distribution of probability, it is obtained that

Percentile rank of a turtle whose length is 21 inches is 22%

What is probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probality of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

Here, Normal Distribution of probability is used

Mean = 25.9 inches

Standard deviation = 6.3 inches

P(X \(\leq\) 21) = P(z \(\leq\) \(\frac{21 -25.9}{6.3}\))

               = P(z \(\leq\) -0.78)

               = 0.22

               = 22%

Percentile rank of a turtle whose length is 21 inches is 22%.

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The cooling process follows Newton's Law of Cooling, which may not hold true in all situations. External factors like cup material, insulation, and airflow can affect the cooling rate.

Based on the given information, when starting with 12 ounces of 180°F coffee in a cup, it takes 20 minutes for the coffee to cool down to a drinking temperature of 110°F in a room that is 70°F.

This scenario can be analyzed using Newton's Law of Cooling, which states that the rate of temperature change of an object is proportional to the difference between its current temperature and the surrounding temperature.

Let's denote the temperature of the coffee at time t as T(t) and the temperature of the room as T(room). According to Newton's Law of Cooling, we can express the rate of temperature change as:

(dT(t)/dt) = k(T(t) - T(room))

where k is a constant of proportionality.

In this case, we have the following conditions:

T(0) = 180°F (initial temperature of the coffee)

T(20) = 110°F (temperature of the coffee after 20 minutes)

T(room) = 70°F (temperature of the room)

Substituting these values into the equation, we can solve for the constant k. The resulting equation becomes:

(dT(t)/dt) = k(T(t) - 70)

Integrating both sides of the equation, we get:

∫ (1 / (T(t) - 70)) dT(t) = ∫ k dt

This integration can be solved to find the value of k.

Once we have the value of k, we can use it to determine the time it takes for the coffee to cool to a certain temperature, such as 110°F. By rearranging the equation and solving for t, we can find the desired time.

It's important to note that this analysis assumes that the cooling process follows Newton's Law of Cooling, which may not hold true in all situations. Additionally, external factors like cup material, insulation, and airflow can affect the cooling rate.

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Answer:

x = 53.6588°

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

Step-by-step explanation:

Step 1: Define

We are given a right triangle. We can use trig to find the missing angle.

Step 2: Identify Variables

POV from angle x

Angle = x

Adjacent = 16

Hypotenuse = 27

Step 3: Solve for x

Answer:

1171

Step-by-step explanation:

Answer:

y = -x +2

Step-by-step explanation:

Equation of a line in slope-intercept form :

   y = mx + b    where m = slope and 'b' is the y-axis intercept

y = -x-2    is in this form.....  slope m = -1      b = -2

   the parallel line will have the same slope = -1 and will look like

        y = -x + b

       to calculate the value of 'b' for this line, substitute in the point given:

             -2 = - (4) + b      shows b = 2

  so your line becomes   y = -x + 2

Answer:

  y =-x + 2

Step-by-step explanation:

    Parallel lines have same slope.

     y = -x - 2

Compare with the equation of the line in slope y-intercept form: y =mx + b

Slope = m = -1

So, equation of line: y = -x + b

Point(4 ,-2) is going through this line. so, substitute x = 4 & y = -2 in the above equation.

            -2 = -4 + b

          -2 + 4 = b

              \(\sf \boxed{b = 2}\)

Equation of the required line:

            \(\sf \boxed{\bf y = -x + 2}\)

The mathematical domain of the function is 0<or = 5<or = -0.3

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

the type of behavior that is appropriate for a given person, object, or institution; the reason why something exists; a role. any formal event or gathering that is public or social. a variable connected to or reliant upon another variable: A price depends on both supply and demand.

According to the above statements:-

The mathematical domain of the functions are:-

0<or = 5<or = -0.3

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Answer:

i think its the 3rd option

The amount Jack charges for mowing and raking leaves is $18 and $8 respectively.

Let

charge of mowing = x

charge of raking = y

4x + 10y = 152

6x + 8y = 172

Multiply (1) by 6 and (2) by 4

24x + 60y = 912

24x + 32y = 688

Subtract to eliminate x

60y - 32y = 912 - 688

28y = 224

divide both sides by 28

y = 224/28

y = 8

Substitute into (1)

4x + 10y = 152

4x + 10(8) = 152

4x + 80 = 152

4x = 152 - 80

4x = 72

divide both sides by 4

x = 72/4

x = 18

Therefore, $18 is charged for mowing and $8 is charged for raking.

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