Find the 97th term of the arithmetic sequence 17, 26, 35, ...

The slope of the given lines are:

Graph 1 = 1/3

Graph 2 = -1/3

Graph 3 = 3

Graph 4 = -3

To find the slope (m) of a given line on a coordinate plane, choose any two points on the line, (x1, y1) and (x2, y2), then find the slope by plugging in the values of the coordinates into the formula below:

Slope of a line (m) = change in y / change in x = \(\frac{y_2 - y_1}{x_2 - x_1}\).

Find the slope of Graph 1:

Using two points on the line, (0, 0) and (3, 1):

Slope of graph 1 (m) = (1 - 0)/(3 - 0)

Slope of graph 1 (m) = 1/3

Find the slope of Graph 2:

Using two points on the line, (0, 0) and (-3, 1):

Slope of graph 2 (m) = (1 - 0)/(-3 - 0) = 1/-3

Slope of graph 2 (m) = -1/3

Find the slope of Graph 3:

Using two points on the line, (0, 0) and (1, 3):

Slope of graph 3 (m) = (3 - 0)/(1 - 0) = 3/1

Slope of graph 3 (m) = 3

Find the slope of Graph 4:

Using two points on the line, (0, 0) and (-1, 3):

Slope of graph 4 (m) = (3 - 0)/(-1 - 0) = 3/-1

Slope of graph 4 (m) = -3

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The total number of students who studied only two subjects is 13.

The given parameters:

The number of students who studied only two subjects can be determined by applying overlapping three sets formula as shown below;

\(Total = n(phy) + n(geo) + n(econ) + n(none)- n(double) - 2(all \ subjects)\\\\55 = 21 + 24 + 23 + 2x-n(double) - 2(x)\\\\55 = 68- n(double)\\\\n(double) = 68-55\\\\n(double) = 13\)

Thus, the total number of students who studied only two subjects is 13.

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Answer:

1

Step-by-step explanation:

(3x + 4)(px + q) = 12x^2 + ax - 20

3px^2 + 3qx + 4px + 4q = 12x^2 + ax - 20

3px^2 = 12x^2

p = 4

4q = -20

q = -5

px + q = 4x - 5

(3x + 4)(4x - 5) =

= 12x^2 - 15x + 16x - 20

= 12x^2 + x - 20

= 12x^2 + ax - 20

ax = x

a = 1

Answer:

l*b area of a square

Step-by-step explanation:

10*10

100f²

The general solution for the given differential equation is the sum of the complementary function and the particular solution:

\(y = y_h + y_p\\\\= C_1e^{6x} + C_2e^{-6x} + (-1/70)e^{3x} + (-1/70)e^{-3x}\)

where C₁ and C₂ are arbitrary constants determined by the initial or boundary conditions of the problem.

We are given the differential equation: d²y/dx - 36y = cosh(3x).

In this case, the homogeneous equation is d²y/dx - 36y = 0.

The characteristic equation associated with the homogeneous equation is obtained by replacing the derivatives with their corresponding algebraic expressions. In our case, we have r² - 36 = 0. Solving this quadratic equation, we find the roots to be r = ±6.

Since the roots are distinct and real, the general solution for the homogeneous equation is given by:

\(y_h = C_1e^{6x} + C_2e^{-6x}\)

where C₁ and C₂ are arbitrary constants determined by the initial or boundary conditions of the problem.

The term cosh(3x) can be written as a linear combination of exponential functions using the identities:

\(cosh(ax) = (e^{ax} + e^{-ax})/2, \\\\sinh(ax) = (e^{ax} - e^{-ax})/2.\)

Therefore, \(cosh(3x) = (e^{3x} + e^{-3x})/2.\)

Now, we assume the particular solution has the form:

\(y_p = A_1e^{3x} + A_2e^{-3x}\)

where A₁ and A₂ are undetermined coefficients.

Substituting these derivatives into the original differential equation, we get:

\((9A_1e^{3x} + 9A_2e^{-3x}) - 36(A_1e^{3x} + A_2e^{-3x}) = (e^{3x} + e^{-3x})/2.\)

To satisfy this equation, the coefficients of the exponential terms on both sides must be equal. Therefore, we have the following system of equations:

9A₁ - 36A₁ = 1/2,

9A₂ - 36A₂ = 1/2.

Solving these equations, we find A₁ = -1/70 and A₂ = -1/70.

Thus, the particular solution is:

\(y_p = (-1/70)e^{3x} + (-1/70)e^{-3x}\)

Finally, the general solution for the given differential equation is the sum of the complementary function and the particular solution:

\(y = y_h + y_p\\\\= C_1e^{6x} + C_2e^{-6x} + (-1/70)e^{3x} + (-1/70)e^{-3x}\)

where C₁ and C₂ are arbitrary constants determined by the initial or boundary conditions of the problem.

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Answer:

-2

Step-by-step explanation:

6x+3y=21

Bring the equation to y=mx+c form

3y=21-6x

y=-2x+7

When comparing, m=-2

Slope m=-2

Answer:

x = 11

Step-by-step explanation:

Step 1: Define consecutive integers

Int 1: x

Int 2: x + 2

Int 3: x + 4

Int 4: x + 6

Step 2: Set up equation

x + x + 2 + x + 4 + x + 6 = 56

Step 3: Solve for x

Step 4: Define integers

Int 1: 11

Int 2: 11 + 2 = 13

Int 3: 11 + 4 = 15

Int 4: 11 + 6 = 17

11, 13, 15, 17

Answer: List all of the solutions.

19

=

7

=

130

=

explanation:

The angle of rotation of a conic section is equal to -36 degrees.

Mathematically, the general form of the equation of a conic section is represented or modeled by this mathematical expression:

Ax² + Bxy + Cy² + Dx + Ey + F = 0

Where:

A, B, and C are not all equal to zero.

In Mathematics, the angle of rotation of a conic section can be calculated by using this formula:

Cot(2θ) = [A - C]/B

Where:

θ represents the angle of rotation of a conic section.

From the information provided, we have the following parameters:

3x² - 2√3xy + y² + 2x + 2√3 = 0

A = 3

B = -2√3

C = 1

Substituting the given parameters into the formula, we have;

Cot(2θ) = [3 - 1]/-2√3

Cot(2θ) = -2/2√3

Cot(2θ) =  -1/√3

1/tan(2θ) =  -1/√3

tan(2θ) = -√3

2θ = tan⁻¹(-√3)

2θ = -71.57

Angle of rotation, θ = -71.57/2

Angle of rotation, θ = -35.79 ≈ -36 degrees.

Note: A negative angle of rotation indicate a counterclockwise rotation.

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(a) The number of pathways in the plane from point (0, 0) to point (110, 111) when each step consists of walking one unit up or one unit to the right is known as the number of ways to go to a point in a grid using just right and up moves.

This is a classic combinatorial problem known as a binomial coefficient. The binomial coefficient C(110+111, 110) = C(221, 110) = 221!/(110!111!) is the number of ways to travel from (0, 0) to (110, 111).

(b) The number of paths from (0, 0) to (210, 111) where each step consists of walking one unit up or one unit to the right and the path must pass through (110, 111) is the product of two binomial coefficients.

First, as calculated in section 1, the number of pathways from (0, 0) to (110, 111) is C(110+111, 110) = C(221, 110). Second, there are C(210+211, 210) ways to get from (110, 111) to (210, 111). (210, 211). (421, 210). C(221, 110) * C is the total number of paths found by multiplying these two binomial coefficients (421, 210).

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Answer:

1 -1

2-4

3-9

4-16

5-25

6-36

7-49

8-64

9-81

10-100

11-121

12-144

Those are the first 12

Step-by-step explanation:

Answer:

Rectangle 1 ) 5.12E9m       Rectangle 2 ) 1.024E11m

Step-by-step explanation:

(3.2 x 10^5) x (1.6 x 10^4) = 5.12E9

(1.28 x 10^7) x (8 x 10^3) = 1.024E11

Answer:

5.12×10⁹ and 1.024×10¹¹

Step-by-step explanation:

area of rectangle 1 :

(3.2 × 10⁵)(1.6 × 10⁴) = (3.2×1.6)(10⁵×10⁴)

=5.12× (10^5+4)

=5.12×10⁹

area of rectangle 2 :

(1.28×10⁷)(8×10³) = (1.28×8)(10⁷×10³)

= 10.24×(10^7+3)

= 10.24×10¹⁰

=1.024×10¹¹

Answer:

f(3) = 512

Step-by-step explanation:

f(3) = 8^3

f(3) = 512

= 512

Therefore, the sign of m/n (-mn²) is positive.

To determine how successfully a program, practice, intervention, or initiative accomplishes its objectives, it might be evaluated. Evaluation is a systematic technique to accomplish this. Evaluations allow programs and efforts to learn what is effective and what needs to be improved.

Given that m is negative and n is positive, we can evaluate the expression:

m/n (-mn²)

= -(m² * n)

Since m is negative and n is positive, the product of m² and n will be negative. Then, multiplying it by -1 will give us a positive value.

Therefore, the sign of m/n (-mn²) is positive.

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Percentage of data within 2 population standard deviations of the mean is 68%.

To calculate the percentage of data within two population standard deviations of the mean, we need to first find the mean and standard deviation of the data set.

The mean can be found by summing all the values and dividing by the total number of values:

Mean = (20*2 + 22*8 + 28*9 + 34*13 + 38*16 + 39*11 + 41*7 + 48*0)/(2+8+9+13+16+11+7) = 32.68

To calculate standard deviation, we need to calculate the variance first. Variance is the average of the squared differences from the mean.

Variance = [(20-32.68)^2*2 + (22-32.68)^2*8 + (28-32.68)^2*9 + (34-32.68)^2*13 + (38-32.68)^2*16 + (39-32.68)^2*11 + (41-32.68)^2*7]/(2+8+9+13+16+11+7-1) = 139.98

Standard Deviation = sqrt(139.98) = 11.83

Now we can calculate the range within two population standard deviations of the mean. Two population standard deviations of the mean can be found by multiplying the standard deviation by 2.

Range = 2*11.83 = 23.66

The minimum value within two population standard deviations of the mean can be found by subtracting the range from the mean and the maximum value can be found by adding the range to the mean:

Minimum Value = 32.68 - 23.66 = 9.02 Maximum Value = 32.68 + 23.66 = 56.34

Now we can count the number of data points within this range, which are 45 out of 66 data points. To find the percentage, we divide 45 by 66 and multiply by 100:

Percentage of data within 2 population standard deviations of the mean = (45/66)*100 = 68% (rounded to the nearest percent).

Therefore, approximately 68% of the data falls within two population standard deviations of the mean.

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There are variations in the participation prices of boys and girls across unique sports, with boys having decreased representation in varsity soccer, better representation in freshman basketball, and identical illustration in varsity tennis compared to ladies.

Based on the given statements:

The percentage of boys who play varsity soccer is much less than the share of ladies who play varsity football.

The share of boys who play freshman basketball is extra than the share of girls who play freshman basketball.

The percentage of boys who play varsity tennis is the same as the variety of women who play varsity tennis.

We can finish subsequent:

Boys have a lower representation in varsity football as compared to ladies.

Boys have a higher representation in freshman basketball in comparison to ladies.

The percentage of boys playing varsity tennis is identical to the proportion of women playing varsity tennis.

These statements suggest differences in participation fees and proportions between boys and women in unique sports activities.

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The correct question is:

"The percentage of boys who play varsity soccer is ✔ less than the percentage of girls who play varsity soccer. the proportion of boys who play freshman b-ball is ✔ greater than the proportion of girls who play freshman b-ball. the percentage of boys who play varsity tennis is ✔ the same as the number of girls who play varsity tennis.

What can you conclude from the above statements?"

the answer is 15cm (pls mark brainlest)

Answer:

3:40

Step-by-step explanation:

We need both measurements in the same units.

1 m = 100 cm

2 m = 2 × 1 m = 2 × 100 cm = 200 cm

15 cm to 2 m = 15 cm to 200 m

Divide both numbers in the ratio by 5 cm.

15 cm to 200 cm = 3:40

The caramel topping demand curve will not change:

The cost of caramel topping is falling; there will be an increase in demand for caramel topping:

Butterscotch topping costs more money;

There will be less demand for caramel topping:

Ice cream now costs more money.

The quantity of caramel topping demanded would increase if the price of the topping dropped. Consequently, the demand curve for caramel topping would go lower.

Ice cream and caramel toppings are complementary products.

Products that are consumed together are said to be complementary.

The amount of ice cream demanded would drop if the price went up. There would be a drop in the number of caramel toppings needed as a result of the fall in demand.

a decline in the popularity of caramel toppings. With less demand, the demand curve for caramel toppings would move inward.

Butterscotch and caramel ice cream toppings serve as stand-ins.

Products that can be used in place of one another are known as substitute goods.

The quantity demanded for butterscotch topping would decline if the price of butterscotch topping rose, making it more expensive overall. Customers might switch to caramel topping. As a result, demand for caramel topping would rise and the demand curve would move outward.

Demand curve: what is it?

The demand curve is a graphical representation of how the cost of an item or service relates to how much is demanded over a given period of time.

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The least amount Rita has been charged in a month is her monthly fee is f.

Given that Rita pays a monthly fee of $f and pays an additional $p per minute of use. The least she has been charged in a month is $c. Let the total number of minutes Rita used in a month be m, then her monthly cost can be calculated as: $c = f + mp

To find the least amount Rita has been charged in a month, we need to minimize the value of c. This is achieved by minimizing the value of m, the total number of minutes Rita used in a month.

If Rita doesn't use her phone at all, the cost of the monthly fee, f, would be the least amount she has been charged in a month.

Hence,
\($c_{min} = f$$f = f + mp_{min} ⇒ mp_{min} = 0$\)

Therefore, f is the least amount Rita has been charged as monthly fee.

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Any value between 110 and 250 is within 2 standard deviations of the mean. In other words, any data point between 110 and 250 is considered within this range.

Within 2 standard deviations of the mean refers to the range that includes data points within two units of standard deviation from the mean. In this case, the mean is 180 and the standard deviation is 35.

To find the range within 2 standard deviations of the mean, we need to calculate the upper and lower bounds.

The upper bound can be found by adding 2 standard deviations (2 * 35 = 70) to the mean: 180 + 70 = 250.

The lower bound can be found by subtracting 2 standard deviations (2 * 35 = 70) from the mean: 180 - 70 = 110.

Therefore, any value between 110 and 250 is within 2 standard deviations of the mean. In other words, any data point between 110 and 250 is considered within this range.

It's important to note that this answer is specific to the given mean and standard deviation. If the mean and standard deviation were different, the range within 2 standard deviations would also be different.

Always calculate the upper and lower bounds based on the provided mean and standard deviation to determine the range within 2 standard deviations accurately.

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Answer:

140737488355328

Step-by-step explanation:

Formula

L_n = a*r^(n-1)

Givens

a = 2

4

Solution

L_24 = 2*4^(24 -1)

L_24 = 2 * 70368744177664

Note the only way I know that you can get this answer is to use the calculator that came with windows. I don't think even my programing language would get it.

L_24 = 140737488355328

Based on the given side lengths of 3cm, 7cm, and 7.4cm, the triangle is a(n) scalene triangle. In a scalene triangle, all sides have different lengths.

Triangles are described in terms of their sides and angles in geometry. A closed planar three-sided polygon shape with three sides and three angles is known as a triangle. The lengths of the sides of a scalene triangle vary. They are not equal, and the angles have three measurements. However, it still has a 180° angle sum, just like all triangles.

A scalene triangle is a triangle with three different side lengths and three different angle measurements. The total of all internal angles, however, is always equal to 180 degrees. As a result, it satisfies the triangle's condition of angle sum.

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Answer:

33

Step-by-step explanation:

Start by adding the 3 to the other side (2/3x=22)

Then, you divide 2/3 to cancel it out. To do that, multiply 22 by 3/2 which equals to 33.

Answer:

2/3x - 3 = 19

We first isolate the variable and solve for x, (we get rid of any constants first in the process)

2/3x - 3 = 19 the three is the constant so we get rid of it by adding three to both sides.

2/3x - 3 = 19

+3            +3

2/3x = 22

Now we divide by 2/3 on both sides

X = 33

\(\{2,3\}\) is a set containing two elements - numbers 2 and 3

\(\{\{2,3\}\}\) is a set containing one element - a set \(\{2,3\}\)

A negative net exposure position in foreign currency means that a Financial Institution will experience a loss if the foreign currency appreciates.

A net exposure position in foreign currency refers to the overall amount of foreign currency assets and liabilities held by a Financial Institution. When a Financial Institution has a negative net exposure position, it means that it owes more in foreign currency liabilities than it holds in foreign currency assets. In this case, if the foreign currency appreciates (increases in value relative to the domestic currency), the Financial Institution will need to pay more in domestic currency to fulfill its foreign currency obligations. Consequently, the Financial Institution will incur a loss.

On the other hand, a positive net exposure position (option D) implies that the Financial Institution will make a gain if the foreign currency depreciates (decreases in value relative to the domestic currency) because it will receive more domestic currency when converting its foreign currency assets.

Option A is incorrect because a negative net exposure position implies a loss, not a gain if the foreign currency appreciates. Option B is incorrect because not all of the statements are true. Option E is unrelated to the question and therefore not applicable.

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Answer:

20 people

Step-by-step explanation:

There hope you have a good day

The answers are :

a) The number of people travel more than 30 miles to work is 100 peoples.

b) The distance Sam travels is equal to 29 miles.

What is the histogram ?

A histogram is a visual way to display frequency of continuous data using bars.

It is given that a histogram shows the information about how people travel to work. The number of people travel to work is 550.

a)

We are aware that a histogram's bars correspond to the histogram's frequency. From , the histogram given , we can find out that the frequency density of those that are in this category is :

Frequency density = 5 + 5 + 5 + 5

or

Frequency density will be 20.

Here , in the given histogram , 1 unit on histogram represents 5 people. So , the actual frequency will be equal to :

Actual frequency = 20 × 5

or

Actual frequency = 100

The number of people travel more than 30 miles to work is 100 peoples.

b)

It is given that 205 of the 550 people travel further than Sam.

Frequency density will be :

= \(\frac{205}{550}\) × 110

= 41

The distance Sam travels is :

= 30 - [ \(\frac{1}{5}\) × ( 30 - 25 )]

= 30 - 1

= 29 miles

Therefore , the answers are :

a) The number of people travel more than 30 miles to work is 100 peoples.

b) The distance Sam travels is equal to 29 miles.

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Answer:

Range - a  is y<k

Range + a is y>k

Doman always all real numbers

Step-by-step explanation:

Answer:

domain- always all real numbers

and im not too certain about the last 2 but im pretty sure that

range-a is less than or equal to whereas range+a is more than or equal to.

I hope this helps! :)

Answer:  i got it

Step-by-step explanation:

i hope this helped