the first several terms of a sequence {an} are: 14,−19,114,−119,124,.... assume that the pattern continues as indicated, find an explicit formula for an.

To study the effect of elevation above sea level on air temperature and air pressure while hiking from Heart Lake (elevation 2,179 feet) to the peak of Mt. Marcy (elevation 5,344 feet) in the Adirondack Mountains, the students should use the following instruments to collect their data:

1. Thermometer: A thermometer is an instrument used to measure air temperature. The students should take temperature readings at various elevations during their hike to determine the relationship between elevation and temperature.

2. Barometer: A barometer is an instrument used to measure air pressure. The students should take air pressure readings at various elevations during their hike to determine the relationship between elevation and air pressure.

By using these two instruments and comparing the data collected at different elevations, the students can study the effect of elevation on air temperature and air pressure.

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Answer: 182.9

Step-by-step explanation: if the next digit after the tenths place is 5 or higher, you round it up to the next number.

Answer: 10 in.

Step-by-step explanation:

1) Option II (1)

2) Option III (-5)

3) IV (None of these)

4) III (-4)

Answer:

1. The numerical coefficient of x^2y^2 is 1

2. -5

3. Monomial

4. -4(I know its x squared)

Step-by-step explanation:

1. We know if we multiply any number or variable with 1 it remains same.

here there is no number before (x^2)(y^2) so we assume it as 1.

Hence the answer is 1.

2. numerical coefficient is a constant multiplier of the variables in a term. In the term -5x2y, the numerical coefficient is -5. In the expression ax2 + bx + c, the numerical coefficient of the x2 term is "a" and the numerical coefficient of the x term is "b". "c" is properly referred to as the constant term.

3. in monomial there is only one term and pqr is only one term. binomial requires two terms like abc, pqr. and trinomial requires three terms like abc, pqr, mno.

4. -1^2 - 5 = -1 - 5 = -4 I know in rules of subtracting integer it equals to -4

To subtract integers, change the sign on the integer that is to be subtracted.

If both signs are positive, the answer will be positive.

If both signs are negative, the answer will be negative.

If the signs are different subtract the smaller absolute value from the larger absolute value.

Serena should focus on a certain amount and track her spending. Option B

From the information given, Serena wants to reduce debt and to do this she needs to pay attention on how she borrows and the possible way to pay her debts.

Some possible ways to reduce debts include;

Thus, Serena should focus on a certain amount and track her spending. Option B

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Step-by-step explanation:

Break it up into two trapezoids as shown

area = trap1 + trap2

      = 2 *   (7+3) / 2   + 3 *  ( 7 + 3) / 2 = 10 + 15 = 25 units^2

The vendor made a profit of ₹7 for 1 kg of goods.

To determine the profit made for 1 kg of goods, we need to calculate the difference between the selling price and the cost price per kg.

The vendor bought 10 kg of goods for ₹350, which means the cost price per kg is ₹350/10 = ₹35.

The selling price per kg is ₹42.

To calculate the profit, we subtract the cost price from the selling price:

Profit = Selling Price - Cost Price

= ₹42 - ₹35

= ₹7

Therefore, the vendor made a profit of ₹7 for 1 kg of goods.

It's important to note that profit is the positive difference between the selling price and the cost price, indicating the amount gained.

If the result had been negative, it would indicate a loss.

In this case, the vendor made a profit of ₹7 for every 1 kg of goods sold.

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Answer:

3. Given: R is the midpoint of both PT and QS and TSR. ∆ are right triangles. Prove: PQR. ∆. ~ TSR. ∆. 5. Given: AB = CB = 9 cm.

Step-by-step explanation:

Δ PQR ≅ Δ TSR  by AAS congruency rule.

Two triangles are said to be congruent if their corresponding sides and angles are congruent to each other.

The given information are QR = SR and ∠ QPR = ∠ STR

The proof is as follows :-

             Statement                                                      Reasons

               QR = RS                                                          Given

           ∠ QPR = ∠ STR                                                  Given

           ∠ PRQ = ∠ TRS                                   Vertically opposite angles

            Δ PQR ≅ Δ TSR                                      AAS congruency rule

AAS congruency rule :-

Two triangles are said to be congruent if two angles and the included side of one triangle are equal to two angles and the included side of another triangle.

Hence, the triangles are congruent by AAS congruency rule.

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Answer:

There are 68,640 different ways the runners can finish first, second, and third in the race.

Concept of Permutations

The number of different ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations.

Brief Overview

Since there are 42 runners competing for the top three positions, we have 42 choices for the first-place finisher. Once the first-place finisher is determined, there are 41 remaining runners to choose from for the second-place finisher. Similarly, once the first two positions are determined, there are 40 runners left to choose from for the third-place finisher.

Calculations

To calculate the total number of different ways, we multiply the number of choices for each position:

42 choices for the first-place finisher × 41 choices for the second-place finisher × 40 choices for the third-place finisher = 68,640 different ways.

Concluding Sentence

Therefore, there are 68,640 different ways the runners can finish first, second, and third in the race.

Answer:

the answer is b ok understand

Given:

Axis of symmetry of a parabola is \(x=4\).

A point on the parabola is (0,2).

To find:

The another point on the parabola.

Solution:

The point (0,2) lies on the parabola and the axis of symmetry of a parabola is \(x=4\).

It means, the another point on the parabola is the mirror image of (0,2) across the line \(x=4\) because the parabola is symmetric about the axis of symmetry.

If the point is reflected across the line \(x=4\), then

\((x,y)\to (-(x-4)+4,y)\)

\((x,y)\to (-x+4+4,y)\)

\((x,y)\to (-x+8,y)\)

Using this rule, we get

\((0,2)\to (-0+8,2)\)

\((0,2)\to (8,2)\)

Therefore, the other point on the parabola is (8,2).

The scatterplot with the least squares line provides insights into the relationship between average annual global surface temperature and the years from 2000 to 2015, allowing us to assess trends, strength of correlation, and make predictions within certain limitations.

The scatterplot represents the relationship between the average annual global surface temperature, in degrees Celsius, and the corresponding years from 2000 to 2015. The line drawn on the plot is the least squares line, which is the best fit line that minimizes the overall distance between the observed data points and the line.

The least squares line is determined using a statistical method called linear regression. It calculates the equation of a straight line that represents the trend in the data. This line serves as a mathematical model to estimate the average temperature based on the year.

By analyzing the scatterplot and the least squares line, we can make several observations. Firstly, we can see whether the temperature has been increasing, decreasing, or remaining relatively stable over the given years. If the slope of the line is positive, it indicates a positive correlation, implying that the temperature has been increasing. Conversely, a negative slope suggests a decreasing trend.

Additionally, we can evaluate the strength of the relationship between temperature and time by examining how closely the data points cluster around the line. If the points are closely grouped around the line, it suggests a strong correlation, indicating that the line is a good representation of the data. On the other hand, if the points are more scattered, the correlation may be weaker.

Furthermore, the line can be used to predict the average annual global surface temperature for future years beyond the data range of 2000 to 2015. However, it's important to note that such predictions should be made with caution and considering other factors that may affect global temperatures, such as climate change and natural variability.

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Question

The given scatterplot shows the average annual global surface temperature, in degrees celsius, for each year from 2000 to 2015. the line drawn is the least squares line for the data set.

Step-by-step explanation:

y = 50 - 7x

since each fish cost 7 this equation works no matter how many fish she buys.

Step-by-step explanation:

V=-2w+31 over 15

w=-15v+31 over 2

Answer:

In Equation 2 Make 3v the Subject Of The Formula.(3v= 3+4w)

Sub Equation 3 In equation 2(3+4w-4w=3)

4w-4w=3-3

w=0

For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}, the process is still "in order," while for the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}, the process might be "out of order."

To determine whether the process is still "in order" or "out of order," we can compare the current sample of output to the known mean and standard deviation of the process.

For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}:

Calculate the sample mean by summing up all the values in the sample and dividing by the number of values (n = 10):

Sample mean = (2.038 + 2.054 + 2.053 + 2.055 + 2.059 + 2.059 + 2.009 + 2.042 + 2.053 + 2.047) / 10 = 2.048.

Compare the sample mean to the known process mean (2.050):

The sample mean (2.048) is very close to the process mean (2.050), indicating that the process is still "in order."

Calculate the sample standard deviation using the formula:

Sample standard deviation = sqrt(sum((x - mean)^2) / (n - 1))

Using the formula with the sample values, we find the sample standard deviation to be approximately 0.019 liters.

Compare the sample standard deviation to the known process standard deviation (0.020):

The sample standard deviation (0.019) is very close to the process standard deviation (0.020), further supporting that the process is still "in order."

For the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}:

Calculate the sample mean:

Sample mean = (2.022 + 1.997 + 2.044 + 2.044 + 2.032 + 2.045 + 2.045 + 2.047 + 2.030 + 2.044) / 10 ≈ 2.034

Compare the sample mean to the process mean (2.050):

The sample mean (2.034) is noticeably different from the process mean (2.050), indicating that the process might be "out of order."

Calculate the sample standard deviation:

The sample standard deviation is approximately 0.019 liters.

Compare the sample standard deviation to the process standard deviation (0.020):

The sample standard deviation (0.019) is similar to the process standard deviation (0.020), suggesting that the process is still "in order" in terms of variation.

In summary, for the first sample, the process is still "in order" as both the sample mean and sample standard deviation are close to the known process values.

However, for the second sample, the difference in the sample mean suggests that the process might be "out of order," even though the sample standard deviation remains within an acceptable range.

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The slope of the line that divides the region bounded by the parabola \(y=5x-3x^2\)and the x-axis into two regions with equal area is 5.

To find the slope of the line that divides the region into two equal areas, we need to determine the point of intersection between the parabola and the x-axis. Since the line passes through the origin, its equation will be y = mx, where m represents the slope.

Setting the equation of the parabola equal to zero, we find the x-values where the parabola intersects the x-axis. By solving the equation\(5x - 3x^2 = 0\), we get x = 0 and x = 5/3.

To divide the region into two equal areas, the line must pass through the midpoint between these x-values, which is x = 5/6. Plugging this value into the equation of the line, we have y = (5/6)m.

Since the areas on both sides of the line need to be equal, we can set up an equation using definite integrals. By integrating the equation of the parabola from 0 to 5/6 and setting it equal to the integral of the line from 0 to 5/6, we can solve for m. After performing the integration, we find that m = 5.

Therefore, the slope of the line that divides the region into two equal areas is 5.

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Step-by-step explanation:

the slope-intercept form of a line (= linear function) is

y = ax + b

"a" is the slope of the line and represents the ratio "y coordinate change / x coordinate change" when going from one point to another on the line.

"b" is the y-intercept (the y value when x = 0; in other words, the y value where the line intercepts the y axis).

so, for the slope, let's compare 2 points. and let's pick just the first 2.

(1, 8) to (2, 11).

x changes by +1 (from 1 to 2).

y changes by +3 (from 8 to 11).

so, the slope is +3/+1 = 3/1 = 3

and our equation looks like

y = 3x + b

to get b, we use one point. I pick the first one for the smallest numbers :

8 = 3×1 + b = 3 + b

5 = b

the full line equation is therefore

y = 3x + 5

Answer:

0.25

Step-by-step explanation:

Answer:

The numbers are 36 and 68.

Step-by-step explanation:

Let the smaller number be x.

"The larger number is four less than two times the smaller

number."

The larger number is

2x - 4

The sum of the numbers is x + 2x - 4, or 3x - 4.

"The sum of the numbers is 104."

3x - 4 = 104

3x = 108

x = 36

The smaller number is 36.

The larger number is 2x - 4, or

2x - 4 = 2(36) - 4 = 72 - 4 = 68

The larger number is 68.

Answer: The numbers are 36 and 68.

Step-by-step explanation:

because when the exponent is an odd number a negative number stays negative

and when the exponent is an even number the sign changes and a negative number becomes positive

The length, b, of the longest side of the triangle is 13.17 cm

From the question, we are to determine the length, b, of the longest side of the triangle

From the given information,

Area of the triangle = 22.4 cm²

Then, we can write that

22.4 = 1/2 × a × 3.7 sin97

44.8 = a × 3.7 sin97

44.8 = a × 3.6724

a = 44.8/3.6724

a = 12.199

a = 12.2

Given that the sides of the triangle are a, b, and c,

Then,

From the law of cosines, we can write that

b² = c² + a² - 2ac cosB

b² = 3.7² + a² - 2×a×3.7 cos97°

b² = 3.7² + 12.2² - 2×12.2×3.7 cos97°

b² = 3.7² + 12.2² - 2×12.2×3.7 cos97°

b² = 173.53

b = √173.53

b = 13.17 cm

The length of b is 13.17 cm

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To find the elasticity of demand for the function D(p) = √(175-3p), you'll need to calculate the derivative of the function with respect to price (p) and then apply the elasticity formula.

First, find the derivative dD(p)/dp:
dD(p)/dp = (-3/2) * (175-3p)^(-1/2)

Next, use the elasticity formula:
Elasticity (E) = (p / D(p)) * (dD(p)/dp)

Plug in the values from the original demand function and its derivative:
E = (p / √(175-3p)) * ((-3/2) * (175-3p)^(-1/2))

This formula represents the elasticity of demand for the given function D(p). To find the elasticity at a specific price, simply replace "p" with the desired price value.

To find the elasticity of demand, we need to use the following formula: Elasticity = (% change in quantity demanded) / (% change in price)

To calculate this, we need to first find the derivative of the demand function:

d/dp √175-3p = -3/2(175-3p)^(-1/2)

Next, we can plug in the price value to get the quantity demanded at that price:

D(10) = √175-3(10) = √145

Then, we can use this information to calculate the percentage change in quantity demanded and price:
%ΔQ = (√175-3(15) - √175-3(10)) / √175-3(10) * 100% = -9.15%
%ΔP = (15-10) / 10 * 100% = 50%

Finally, we can plug these values into the elasticity formula:

Elasticity = (-9.15%) / (50%) = -0.183

Since the result is negative, we can conclude that the demand for this product is elastic, meaning that a small change in price will lead to a relatively large change in quantity demanded.

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According to the question the equation has been solved by using Pythagorean. The left-hand side of the identity simplifies to \(cos^2(x)\)

The Pythagorean Theorem can be used to find the correct angled triangle's missing length. The triangle contains three sides: the hypotenuse, this same opposite, which will always be the longest, and the adjacent side, which really doesn't touch the hypotenuse. The Pythagorean equation is: \(a^2+b^2=c^2.\)

We can start by using the reciprocal identity for cosecant:

\(cos(x) = 1/sin(x)\)

Then, we substitute this into the left-hand side of the identity:

\(sin(x)(csc(x) - sin(x)) = sin(x)(1/sin(x) - sin(x))\\= sin(x)/sin(x) - sin^2(x)\\= 1 - sin^2(x)\)

Using the Pythagorean identity for sine and cosine, we know that:

\(1 - sin^2(x) = cos^2(x)\)

Thus, the left-hand side of the identity simplifies to \(cos^2(x)\), which is equal to the right-hand side of the identity.

Therefore, the identity is verified.

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Answer:d

Step-by-step explanation:

The vertical asymptote of the given function is x = 2

An asymptote of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity.

Given function is  y = log(x-2)+10

The vertical asymptote for a function is a vertical line x=k and  where the function becomes unbounded.

The given function  x-2 =0

x =2

y = log (x-2) +10

put x=2, y = 10

Hence, the vertical asymptote is x =2

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The complete question is attached

The possible form of the point (6√3, - 6) in polar form are (r₁, θ₁) = (12, 11π / 6), (r₂, θ₂) = (12, - π / 6).

In this problem we find a point in rectangular form, that is, a point of the form (x, y). We are asked to find the polar form of the point, that is, a point described by the following expression:

(r, θ)

Where:

The magnitude is found by Pythagorean theorem:

r =√(x² + y²)

And the direction of the point is described by the following inverse trigonometric function:

θ = tan⁻¹ (y / x)

If we know that (x, y) = (6√3, - 6), then the point in polar form is:

r = √[(6√3)² + (- 6)²]

r = 12

θ = tan⁻¹ (- 6 / 6√3)

θ = tan⁻¹ (- √3 / 3)

θ = 11π / 6 rad / θ =  - π / 6 rad

There are two possible solutions: (r₁, θ₁) = (12, 11π / 6), (r₂, θ₂) = (12, - π / 6).

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Answer:

a point 12 comma 4 pi over 3 comma a point 12 comma negative 2 pi over 3 comma a point negative 12 comma negative pi over 3 comma a point negative 12 comma negative 5 pi over 3

Step-by-step explanation: option B

The correct order of the steps in the scientific method is: observation, hypothesis, experiment, result, and conclusion

The correct order of the steps in the scientific method is as follows:

e. Observation - Start by making observations or gathering information about a particular phenomenon or problem. This involves carefully observing and noting relevant details and patterns.

b. Hypothesis - Based on the observations, formulate a hypothesis, which is a proposed explanation or prediction that can be tested through experimentation.

c. Experiment - Design and conduct experiments or investigations to test the hypothesis. This step involves carefully controlling variables, collecting data, and performing measurements.

a. Result - Collect and analyze the data obtained from the experiments or investigations. This analysis helps determine if the results support or reject the hypothesis.

d. Conclusion - Draw a conclusion based on the analysis of the data. Evaluate whether the results support the hypothesis and discuss the implications and significance of the findings. The conclusion may also involve suggesting further research or revisions to the hypothesis.

The scientific method is a systematic approach used in scientific inquiry to investigate and understand the natural world. It allows researchers to gather evidence, test hypotheses, and draw reliable conclusions based on empirical data.

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The volume in cm 112098 cm³.

The volume of water in liters 112 liter.

The volume of a cylinder is equal to the product of the area of the circular base and the height of the cylinder.

Given: height= 28m= 2800cm, internal radius= 3.5 cm, external radius = 5 cm.

Volume of cylinder

= πr²h

= 3.14(5²-3.5²)2800

=3.14*12.75*2800

=112098 cm³

Volume of water in liter is 112.098 or 112 liter.

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Answer:

Equation: y-5=8(x+4)

Step-by-step explanation:

Point-slope form is y-y1=m(x-x1)

Since m=8, y1=5, and x1=-4, then we have y-5=8(x+4) as our final equation

Answer: