The co-interior angle of 105 degree is ​

The statement is proven true by induction: for any positive integer n, the sum of (2i - 1)³ from i = 1 to n is equal to n²(2n² - 1).

To prove the statement using mathematical induction, we need to establish two conditions: the base case and the inductive step.

Base Case:

Let's start with the base case, where n = 1.

When n = 1, we have p₁ ∑ (2i - 1)³ = 1³ = 1.

On the right-hand side, we have 1 * (2 * 1² - 1) = 1.

Since the statement holds true for n = 1, the base case is satisfied.

Inductive Step:

Next, we assume that the statement holds true for some positive integer k, i.e., pₖ ∑ (2i - 1)³ = k²(2k² - 1).

Now, we need to prove that the statement also holds for n = k + 1, i.e., pₖ₊₁ ∑ (2i - 1)³ = (k + 1)²(2(k + 1)² - 1).

Starting with the left-hand side:

pₖ₊₁ ∑ (2i - 1)³ = (pₖ ∑ (2i - 1)³) + (2(k + 1) - 1)³

                 = k²(2k² - 1) + (2k + 1)³ (using the inductive hypothesis)

                 = 2k⁴ - k² + 8k³ + 12k² + 6k + 1

Simplifying the right-hand side:

(k + 1)²(2(k + 1)² - 1) = (k² + 2k + 1)(2k² + 4k + 2 - 1)

                         = 2k⁴ + 4k³ + 2k² + 4k³ + 8k² + 4k + 2k² + 4k + 2 - k² - 2k - 1

                         = 2k⁴ + 8k³ + 12k² + 6k + 1

Comparing the left-hand side and right-hand side, we can see that they are equal.

Therefore, by the principle of mathematical induction, the statement is proven true for all positive integers n.

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The equation expressing y as a function of t is y(t) = A * sin(B(t - C)) + D, where A is the amplitude, B is the frequency, C is the phase shift, and D is the vertical shift.

To express y as a function of t, we can use a sinusoidal function due to the given information that y varies sinusoidally with time. The general form of a sinusoidal function is y(t) = A * sin(B(t - C)) + D, where A represents the amplitude, B represents the frequency, C represents the phase shift, and D represents the vertical shift.

In this scenario, we are provided with the deepest point at t = 4 min, where y = -1000 m, and the shallowest point at t = 9 min, where y = -200 m. These points allow us to determine the amplitude and vertical shift of the sinusoidal function. The amplitude is the absolute value of half the difference between the deepest and shallowest points, which in this case is |(-1000 - (-200))/2| = 400 m. The vertical shift is the average of the deepest and shallowest points, which is (-1000 + (-200))/2 = -600 m.

The frequency and phase shift are not explicitly given in the problem statement. Without this information, it is not possible to determine the specific values of B and C. Therefore, the equation expressing y as a function of t becomes y(t) = A * sin(B(t - C)) + D, where A = 400 and D = -600. The variables B and C would depend on the specific characteristics of the porpoising motion, which are not provided in the problem.

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Answer:

x = 5.8 ( rounded to nearest tenth)

Answer:

5.8 foot

Step-by-step explanation:

With reference angle 71

perpendicular (p)= x

base(b) = 2

Now

tan 71 = p/b

2.9 = x / 2

x = 5.8 foot

Using the same guideline, for a four-credit class, you would ideally spend:

4 credits * 2-3 hours/credit = 8-12 hours per week.

it is suggested that students allocate around 2-3 hours of study time per credit hour per week for a college-level course. However, the actual study time required may vary based on individual learning styles, prior knowledge, and the specific requirements set by professors or institutions.

Let's apply this general guideline to your scenario:

One three-credit class that is less demanding:

Assuming 2-3 hours of study per credit hour, for a three-credit class, you would ideally spend:

3 credits * 2-3 hours/credit = 6-9 hours per week.

Two three-credit classes that are typically demanding:

Similarly, for each of the two three-credit classes, you would spend:

3 credits * 2-3 hours/credit = 6-9 hours per week.

Since you have two such classes, the total time would be:

2 * (6-9) hours = 12-18 hours per week.

One four-credit class that is very challenging:

Using the same guideline, for a four-credit class, you would ideally spend:

4 credits * 2-3 hours/credit = 8-12 hours per week.

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Answer: To find an equivalent system of equations, we can use algebraic operations to manipulate the original equations while preserving the solutions.

One way to eliminate one of the variables is to multiply one of the equations by a constant that will make the coefficients of one of the variables in the two equations opposite in sign. Here, we can multiply the first equation by -5 and the second equation by 2 to eliminate the x variable:

-10x - 20y = -20

10x - 10y = 10

Adding these two equations, we get:

-30y = -10

Dividing both sides by -30, we get:

y = 1/3

Substituting this value of y into one of the original equations, we can solve for x:

2x + 4(1/3) = 4

2x + 4/3 = 4

2x = 8/3

x = 4/3

Therefore, an equivalent system of equations is:

x = 4/3

y = 1/3

These two equations have the same solution as the original system.

Step-by-step explanation:

The slope of this line is m = 1.

An equation of this line is y = x.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following data points on the line:

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (1 - 0)/(1 - 0)

Slope (m) = 1/1

Slope (m) = 1

At data point (1, 1), an equation of this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

Where:

y - 1 = 1(x - 1)

y = x - 1 + 1

y = x

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Answer:

Equilateral triangle

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer I believe is $5.44

P(male | republican) is a conditional probability.

A conditional probability is a type of probability that measures the likelihood of an event occurring given that another event has already occurred.

The given information is :

Gender  Republican   Total

Male          0.35           0.70

Female      0.25           0.50

Total           0.60          1.20

To calculate P(male | republican), we can use the formula for conditional probability:

P(male | republican) = P(male and republican) / P(republican)

we have P(republican) = 0.60 (the proportion of people who are Republican) and

P(male and republican) = 0.35 (the proportion of people who are both male and Republican).

Plugging these values into the formula, we get:

P(male | republican) = 0.35 / 0.60

= 0.5833

Hence, P(male | republican) is a conditional probability.

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Answer:

Step-by-step explanation:

3x - 7x -21 < -13

-4x < -13 + 21

-4x < 8

x > -2

\(3x - 7(x + 3) < -13 \\3x - 7x - 21 < -13 \\3x - 7x < -13 + 21 \\-4x < 8 \\x > -2\)

Answer:

400 = (x - 10)²

x² -20x -300 = 0

x = 30 and x = -10

Length side of the garden = 20 feet

Step-by-step explanation:

Given:

Area of square garden = 400 square feet

Length side of the garden = (x - 10) feet

Find:

Length side of the garden

Computation:

Area of square = side²

Area of square garden = Length side of the garden²

400 = (x - 10)²

400 = x² -20x + 100

x² -20x -300 = 0

x² -30x  + 10x -300 = 0

x(x - 30) + 10(x - 30) = 0

(x - 30)(x + 10) = 0

So,

x = 30 and x = -10

Use x = 30 positive number

Length side of the garden = (x - 10) feet

Length side of the garden = (30 - 10) feet

Length side of the garden = 20 feet

Answer:

a1 = 2

Step-by-step explanation:

what does a1 mean?

35, 32 29, 26, 23, 20 , 17, 14, 11, 8, 5, (2)

Answer:

7 seconds

Step-by-step explanation:

You would get 49 from doing -784 divided by -16 then you do the square root of 49 which is 7

ANSWER= 7 seconds

The time taken by the pebble to hit the ground will be = 7 seconds

Expression we get when operations such as addition , subtraction , multiplication , division , are operated upon on variable and constants.

Equation of height as a function of time = h(t) = - 16 (t^2)

cliff is at a height of = 784 feet

comparing both the above equation , we get

-16 (t^2) = 784

t^2 = 49

t = 7 seconds

The time taken by the pebble to hit the ground will be = 7 seconds

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Answer:

Step-by-step explanation:

An x- intercept would be -6 and a y-intercept would be -6 also.

Answer:

Step-by-step explanation

Left at 6:15 am

How many hours until 2:15pm? 8 hours

How many minutes from 2:15 until 2:30? 15

So it took 8 hours and 15 minutes

Step-by-step explanation:

...

...

...............

.......

.

.

....

.

.

Answer:

So we rearrange the equation to R=I/PT

Then we substitute: R= 90/300(2)

Calculating the answer should be about 0.15

or I =15%

Step-by-step explanation:

The following are the measures of angles and sides using the sine and cosine rules:

1). QR = 15, m∠P = 52°, m∠Q = 43°

2). BC = 21, DC = 10.4, m∠C = 22°

3). VX = 10.7, WX = 10.2, m∠V = 39°

4). HF = 18.4, m∠H = 28.7, m∠F = 15.3

The sine rule is a relationship between the size of an angle in a triangle and the opposing side. While the cosine rule relates the lengths of the sides of a triangle to the cosine of one of its angles.

1). Using the sine rule:

19/sin85 = 13/sunQ

Q = sin⁻¹[(13 × sin85)/19] {cross multiplication}

Q = 43

m∠P = 180° - (85 + 43) = 52°

QR = sin⁻¹[(19 × sin52)/sin85]

QR = 15.

2). m∠C = 180 + (19 + 139) = 22°

Using the sine rule:

BC = (12 × sin139)/sin22

BC = 21.

DC = (12 × sin19)/sin22

DC = 10.4

3). m∠V = 180 - (41 + 100) = 39°

Using the sine rule:

VX = (16 × sin41)/sin100

VX = 10.7

WX = (16 × sin39)/sin100

WX = 10.2

4). Using the cosine rule:

HF² = 7² + 13² - 2(7)(13)cos136°

HF = √338.8491

HF = 18.4

applying sine rule;

F = sin⁻¹[(7 × sin136)/18.4]

F = 15.3

m∠H = 180 - (15.3 + 136) = 28.7

Therefore, the measures of angles and sides using the sine and cosine rules are:

1). QR = 15, m∠P = 52°, m∠Q = 43°

2). BC = 21, DC = 10.4, m∠C = 22°

3). VX = 10.7, WX = 10.2, m∠V = 39°

4). HF = 18.4, m∠H = 28.7, m∠F = 15.3

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Answer:

y = -5/6x -1

Step-by-step explanation:

The three components needed to create the equation of a line are: the x and y coordinates, the slope, and the y intercept.

Both the x and y coordinates and the slope is given. To find the y intercept, we will create an equation following the template of point-slope form.

y = slope * x + y int.

4 = -5/6 * -6/ + y int.

4 = 5 + y int.

y int. = -1

We will reinstate this into our equation, and this will be our answer!

y = -5/6x -1

This is the equation!

The range of rounds down nearest integer function is {-2,1,5} while domain is {-2.3,√2,4.6}.

A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.

Given the rounds down nearest integer function INT(x)

x = -2.3,√2,4.6

Since the domain is the set of all x's values thus  {-2.3,√2,4.6} will be the domain.

For x = -2.3 ⇒ INT(-2.3) = -2

For x = √2 = 1.414 ⇒ INT(√2) = 1

For x = 4.6 ⇒ INT(4.6) = 5

So range  {-2,1,5}

Hence "The range of rounds down nearest integer function is {-2,1,5} while domain is {-2.3,√2,4.6}".

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Complete Question :

Isaac surveyed the employees at a law firm. Each employee was asked to record their highest level of education completed. The

results are shown in the table below.

Highest Level of Education Completed

Education Level

Percentage

High School

5%

Community College

10%

Four-Year College

60%

Graduate School

25%

Two-hundred sixty people completed the survey. How many of those people completed graduate school?

Answer:

65 people

Step-by-step explanation:

Given the following :

Number of survey participants = 260

Percentage that completed graduate school = 25%

Number of participants who completed graduate school ;

Total Number of participants × percentage that completed graduate school

260 participants × 25%

260 × 0.25

= 65

Answer:

65 people

Step-by-step explanation:

I took the test and that was the correct answer

Mike's claim that (5,28.6) is a point on the exponential function g(x) is incorrect

The points are given as:

(3,6.5) and (4,17.55)

Calculate the rate of change using:

r = y4/y3

This means that:

r = 17.55/6.5

r = 2.7

So, the next point on the graph is:

Next point = 2.7 * y4

Substitute 17.55 for y4

Next point = 2.7 * 17.55

Evaluate

Next point = 47.39

This means that the next point on the graph is (5,47.99)

Hence, Mike's claim that (5,28.6) is a point on the exponential function g(x) is incorrect

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The respective names of the point of concurrency is:

1. Circumcenter

2. Incenter.

3. Centroid

4. Orthocenter

Point of concurrency:

The point of concurrency is a point where three or more lines or rays intersect with each other.

Circumcenter:

The circumcenter is the point of concurrency of the perpendicular bisectors of all the sides of a triangle.

Incenter:

The incenter is the point of concurrency of the angle bisectors of all the interior angles of the triangle.

Centroid:

The point where three medians of the triangle meet is known as the centroid.

Orthocenter:

The point where three altitudes of the triangle meet is known as the orthocenter.

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In the following question, among the various parts to solve- a) the probability that the individual waits more than 7 minutes is 0.3. b)the probability that the individual waits between 2 and 7 minutes is 0.5.

a) The probability that an individual will wait more than 7 minutes can be found as follows:

Given that the waiting time of an individual is a continuous uniform distribution and that a bus arrives at the bus stop every 10 minutes.Since the waiting time is a continuous uniform distribution, the probability density function (PDF) can be given as:fX(x) = 1/(b-a)where a = 0 and b = 10.

Hence the PDF of the waiting time can be given as:fX(x) = 1/10The probability that an individual waits more than 7 minutes can be obtained using the complementary probability. This is given by:P(X > 7) = 1 - P(X ≤ 7)The probability that X ≤ 7 can be obtained using the cumulative distribution function (CDF), which is given as:FX(x) = P(X ≤ x) = ∫fX(t) dtwhere x ∈ [a,b].In this case, the CDF of the waiting time is given as:FX(x) = ∫0x fX(t) dt= ∫07 1/10 dt + ∫710 1/10 dt= [t/10]7 + [t/10]10= 7/10Using this, the probability that an individual waits more than 7 minutes is:P(X > 7) = 1 - P(X ≤ 7)= 1 - 7/10= 3/10= 0.3So, the probability that the individual waits more than 7 minutes is 0.3.

b) The probability that the individual waits between 2 and 7 minutes can be calculated as follows:P(2 < X < 7) = P(X < 7) - P(X < 2)Since the waiting time is a continuous uniform distribution, the PDF can be given as:fX(x) = 1/10Using the CDF of X, we can obtain:P(X < 7) = FX(7) = (7 - 0)/10 = 0.7P(X < 2) = FX(2) = (2 - 0)/10 = 0.2Therefore, P(2 < X < 7) = 0.7 - 0.2 = 0.5So, the probability that the individual waits between 2 and 7 minutes is 0.5.

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The constant of proportionality in the expression \(\frac{y}{x}xy\) is \(xy\).

The given expression \(\frac{y}{x}xy\) can be simplified as \(\frac{y}{x} \cdot xy\).

To find the constant of proportionality, we look at the coefficient that multiplies both \(x\) and \(y\), which in this case is \(xy\). This means that for every \(x\) unit increase, there will be a \(y\) unit increase, and the ratio between \(y\) and \(x\) is constant and equal to \(xy\).

Therefore, the constant of proportionality in the expression \(\frac{y}{x}xy\) is \(xy\), which represents the relationship between \(y\) and \(x\) in the given expression.

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Answer:

I wish you and your family a very happy makar Sankranti ! May you are filled with extreme joy and happiness start a new year with great enthusiasm and positivity. ♥️

Answer:

see below

Step-by-step explanation:

ED = 2 units

DF = 7 units

EF^2 = 2^2 + 7^2

EF^2 = 4 + 49

EF^2 = 53

EF = 7.28

Given the equations:

3y - 6x = 24..............................1

8 + 2x = y..................................2

Substitute (8 + 2x) for y in equation 1.

3(8 + 2x) - 6x = 24

24 + 6x - 6x = 24

24 = 24

Since, we have 24 = 24, we can say the system of equations have infinite solutions.

ANSWER:

A. infinite solutions