g you saved on your new laptop because you bought it online. if this was a 5% savings from the original price, find the original cost of the laptop.

The given series converges, and the value of the integral is finite.

The Integral Test is a method used to determine the convergence or divergence of an infinite series by comparing it to the convergence or divergence of an improper integral. If the integral associated with the series is finite, then the series converges. If the integral is infinite or undefined, then the series diverges.

In this case, we have the series ∑(1+n)/(4n) from n = 1 to infinity. To apply the Integral Test, we consider the integral of the function 1+x/4x with respect to x from 1 to infinity.

Evaluating the integral ∫(1+x)/(4x) dx from 1 to infinity, we find that the integral is finite, indicating that the series converges.

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Answer:

2x+4

Step-by-step explanation:

Trust me

The cost of the truck with 3 passengers is A = $ 45

Given data ,

Let's denote the number of passengers as P and the weight of the truck in pounds as W.

For the base rate of $30 per vehicle, the equation can be written as:

Cost = $30

For additional passengers beyond the first two, the equation can be written as:

Cost += ($5) * (P - 2)

For excess weight over 4,000 pounds, the equation can be written as:

Cost += ($10) * (W - 4000) / 500

To find the cost of a truck that weighs 5,000 pounds with three passengers, we substitute the values into the equation:

Cost = $30 + ($5) * (3 - 2) + ($10) * (5000 - 4000) / 500

Simplifying the equation:

Cost = $30 + $5 + $10

Cost = $45

Hence , the cost of a truck that weighs 5,000 pounds with three passengers would be $45

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The volume of the pyramid sculpture with congruent bases and the same height is 106.4 cubic inches

If the prism can hold 319.2 cubic inches, and the pyramid sculpture has congruent bases and the same height, then the volume of the pyramid sculpture will be one-third (1/3) of the volume of the prism.

Let's denote the volume of the pyramid sculpture as V and the volume of the prism as P. We have the following relationship:

V = (1/3) × P

Substituting the given volume of the prism, we have:

V = (1/3) × 319.2

V = 106.4 cubic inches

Therefore, the volume of the pyramid sculpture with congruent bases and the same height is 106.4 cubic inches.

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The value of y in the right triangle is 9.3 units.

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, let's find the value of y in the right angle triangle.

Using trigonometric ratios,

sin 51 = opposite / hypotenuse

sin 51 = y / 12

cross multiply

12 sin 51  =y

y = 12 × 0.77714596145

y = 9.32575153748

y = 9.3 units

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Answer:

120$

Step-by-step explanation:

If researchers measure every member of a population, they have conducted a census. Correct option is C.

A census is a method of data collection that involves measuring or collecting information on every member of a population of interest.

Conducting a census can provide highly accurate and representative data for the entire population, as it eliminates the potential for sampling error or bias. This means that a census can greatly increase the external validity of a study, as the findings can be generalized to the entire population.

However, conducting a census can be time-consuming, resource-intensive, and impractical for certain populations or research questions. In some cases, a sample may be more feasible or appropriate for achieving the research objectives.

Therefore, while conducting a census can provide a high level of internal validity and eliminate potential sampling bias, it is not always the most practical or feasible method of data collection, and researchers must carefully consider the trade-offs between census and sampling methods depending on the specific research question and population of interest.

Therefore, correct option is C.

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To calculate the area of the rectangle, we multiply its length by its width. Given that the length is measured to be 6.4 ± 0.2 cm and the width is measured to be 8.3 ± 0.2 cm, we can calculate the area as follows:

Length = 6.4 cm ± 0.2 cm

Width = 8.3 cm ± 0.2 cm

The maximum possible length is 6.6 cm (6.4 cm + 0.2 cm), and the minimum possible length is 6.2 cm (6.4 cm - 0.2 cm).

Similarly, the maximum possible width is 8.5 cm (8.3 cm + 0.2 cm), and the minimum possible width is 8.1 cm (8.3 cm - 0.2 cm).

Now, we can calculate the area of the rectangle using the maximum and minimum values:

Maximum area = Maximum length × Maximum width = 6.6 cm × 8.5 cm = 56.1 cm²

Minimum area = Minimum length × Minimum width = 6.2 cm × 8.1 cm = 50.22 cm²

Therefore, the area of the rectangle is within the range of 50.22 cm² to 56.1 cm².

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Step-by-step explanation:

Solution :

Here ,

Let the radius of the base be r .

Here ,

Therefore ,

So , the radius of the base is 14 cm .

Answer:

(a^2+2)(a+2)

Step-by-step explanation:

Factor a^3+2a+2a^2+4.

Using Factoring by grouping

a^3+2a   +    2a^2+4

Factor out a from the first two terms and 2 from the last two terms.

a( a^2 +2) + 2 ( a^2+2)

Factoring out a^2+2.

(a^2+2)(a+2)

1. The probability that exactly 12 students drive to school is 0.169.

2.The probability that more than 15 students drive to school is 0.027.

3. The probability that no more than 10 students drive to school is 0.004.

4. The mean and standard deviation of the sample are 13.6 and 2.4, respectively.

5. The percentage falling within 1 standard deviation of the mean is approximately 68%, which satisfies the empirical rule for normal distributions.

This problem involves the binomial distribution, since each student either drives to school (success) or does not (failure), and the probability of success is given as 0.68 for each student.

(1) The probability that exactly 12 students drive to school is given by the binomial probability mass function:

P(X = 12) \(= (20 choose 12) * (0.68)^12 * (1 - 0.68)^(20 - 12) = 0.169\)

(2) The probability that more than 15 students drive to school is given by the complement of the probability that at most 15 students drive to school:

P(X > 15) = 1 - P(X <= 15) = 1 - sum[(20 choose i) * \((0.68)^i * (1 - 0.68)^{20 - i)}\) for i = 0 to 15.

This is approximately 0.027.

(3) The probability that no more than 10 students drive to school is given by the cumulative distribution function:

P(X <= 10) = sum[(20 choose i) * \((0.68)^i * (1 - 0.68)^{20 - i}\) for i = 0 to 10. This is approximately 0.004.

(4) The mean of the binomial distribution is given by the formula np, where n is the sample size and p is the probability of success.

Thus, the mean is 200.68 = 13.6.

The standard deviation of the binomial distribution is given by the formula sqrt(np(1-p)), which is approximately 2.4.

(5) The percentage falling within one standard deviation of the mean is approximately 68% by the empirical rule, which is the same as the percentage of students who drive to school in the university.

However, the empirical rule applies to normal distributions, and the binomial distribution is not exactly normal.

Nonetheless, for large sample sizes, the binomial distribution can be approximated by a normal distribution using the central limit theorem, which would make the empirical rule applicable.

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Answer:

There is answer for you sorry but this problem can not be put into standard form i tried but it didn't make any sense maybe you could rewrite the problem but that all i can do for you

Step-by-step explanation:

Step-by-step explanation:

angle 1 = 73°

angle 2 = 107°

angle 3 = 73°

angle 4 = 107°

angle 5 = 73°.

hope this helps you.

If you are solving for x, you can click on the pic, but if you are not, then this answer will be useless, hope it helps, you can always give me feedback!

Answer:

I would say company b

Step-by-step explanation:

Example: company a charges 250$ but you have 150 guest coming well 150 times 10 is 1500 plus 250 which would be 1750 versus company b charges 430 but you have 150 guest coming well 150 times 8 is 1400 plus 250 which is 1650 it’s 100 less

Answer:

The answer is 94.5

Step-by-step:

This is actually quite simple. Although, in order to do this you will need a calculator. First, you identify which trigonomic function you will use in order to find the value of x. for this problem you need to use the COS function. The equation for this is COS67= 67/x. Because you are trying to find x you would multiply each side by x. now the equation is xCOS67= 67. because you still can't find the value of x by doing this you will need to get x by itself. To get x by itself divide each side by COS67. the equation is now x= 94/ COS67. This is where the calculator comes in. On the calculator enter 94 divided by 67 then COS function. This gives you the measure of RS.

Answer:

yes

Step-by-step explanation:

they both equal 5x=1 where x = 1/5

Answer:

sure send it and I will do my best to help you..

that the demand for the product is said to be inelastic.

when the demand for a product is inelastic, it means that consumers are not very sensitive to changes in the price of the product. This could be because there are no close substitutes for the product, or because the product is a necessity that consumers cannot easily do without.

when market demand hardly changes with a small change in the price of a product, it indicates that the demand for the product is inelastic.


When the market demand for a product does not change significantly with a small change in the price, this indicates that the product's demand is inelastic. Inelastic demand means that the percentage change in quantity demanded is less than the percentage change in price. Consumers are less sensitive to price changes for inelastic goods, often because they are necessities or have few substitutes.

The demand for a product that hardly changes with small price fluctuations is best described as inelastic.

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The Fourier transform of the given function x(t) = 2e^(-6tu(3t - 6)) + 2rect(-2t) - Δ(4t) is 2/(jω + 6) + 2sinc(ω/2π)*e^(-jω0t) - e^(-jω0t).

To find the Fourier transform of the given function x(t) = 2e^(-6tu(3t - 6)) + 2rect(-2t) - Δ(4t), where t ∈ (-∞, +∞), we can break it down into three parts and apply the Fourier transform properties:

Fourier transform of 2e^(-6tu(3t - 6)):

The Fourier transform of e^(-at)u(t) is 1/(jω + a), so the Fourier transform of 2e^(-6tu(3t - 6)) can be calculated as 2/(jω + 6).

Fourier transform of 2rect(-2t):

The Fourier transform of rect(t) is sinc(ω/2π), so the Fourier transform of 2rect(-2t) can be calculated as 2sinc(ω/2π)e^(-jω0t), where ω0 = 2π2 = 4π.

Fourier transform of Δ(4t):

The Fourier transform of Δ(t - t0) is e^(-jωt0), so the Fourier transform of Δ(4t) can be calculated as e^(-jω0t), where ω0 = 2π*4 = 8π.

Putting all the parts together, the Fourier transform of the given function x(t) is:

2/(jω + 6) + 2sinc(ω/2π)*e^(-jω0t) - e^(-jω0t).

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Answer: In attached

Step-by-step explanation:

Use the given functions to set up and simplify

Attachment has your answer.

I’m not good at typing functions on this app so this image is all I could give.

Answer:

there you go..........

Answer:

(a) The three points P1(0,27), P2(1,29), and P3(2,31) lie on a straight line L because the slope between any two points is the same. The slope between P1 and P2 (m1) can be calculated as (29-27)/(1-0) = 2/1 = 2. Similarly, the slope between P2 and P3 (m2) is (31-29)/(2-1) = 2/1 = 2. Since the slopes are equal, the points lie on the same line.

(b) To predict the percentage of moviegoers who use social media to chat about movies in 2018, we can extend the trend line. We can assume that the trend continues with a constant slope of 2. Considering 2018 as t = 8 (since it is 8 years after 2010), we can calculate the y-value using the equation of the line.

L = mt + c

L = 28 + c (where c is the y-intercept)

To find the y-intercept (c), we can use any of the given points. Let's use P1(0,27):

27 = 2*0 + c

c = 27

Now, we can substitute the values back into the equation:

L = 2*t + 27

Therefore, the percentage of moviegoers who use social media to chat about movies in 2018 is L = 2*8 + 27 = 16 + 27 = 43%.

(c) The equation of the line L is L = 2*t + 27.

Answer:

The answer is A. f(1) = 5

Step-by-step explanation:

If f(x) is a function it can have only one value per x value, so f(1) = 1 cannot be true

Answer:The answer is B. f(2) = 1

Step-by-step explanation:

If f(x) is a function it can have only one value per x value, so f(1) = 1 cannot be true

The class width is 5 for the given frequency distribution.

What are class boundaries?

(a) Class width is the same for all the classes. It is the difference between the lower class limit of two consecutive classes

Therefore Lower limit of 50 - 54 = 50

Lower limit of 55 - 59 = 55

Class width = 55 - 50

Class width = 5

If calculated all have the same class width.

(b) Midpoint is the average of the sum of lower and upper-class limits of the class.

Temp  Freq Midpoint

50-54 1 52

55-59 3 57

60-64 5 62

65-69 11 67

70-74 7 72

75-79 7 77

80-84 1 82

(c) Class boundaries are to make the classes continuous mostly. We can find this by first calculating the difference between the upper-class limit and the lower-class limit of the next class and taking its average.

Add this average to the upper limit and subtract this average from the lower limit

Lower boundary for 50 - 54 = 50 - 0.5 = 49.5

Upper boundary for 50 - 54 = 54 + 0.5 = 54.5  

Temp  Freq Class Boundaries

50-54 1 49.5-54.5

55-59 3 54.5-59.5

60-64 5 59.5-64.5

65-69 11 64.5-69.5

70-74 7 69.5-74.5

75-79 7 74.5-79.5

80-84 1 79.5-84.5

The class width is 5 for the given frequency distribution.

Complete question: Use the given frequency distribution to find the

​(a) class width.

​(b) class midpoints.

​(c) class boundaries.

Temperature (°F) Frequency

32-36 1

37-41 3

42-46 5

47-51 11

52-56 7

57-61 7

62-66 1

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Answer:

-30% or 30% decrease

Step-by-step explanation:

What's percentage decrease?

How do we solve this problem?

Therefore, the answer is 30% decrease.

Answer:

-81

Step-by-step explanation:

-3 ^4

The negative is not included in the exponent

- (3)^4

- 3*3*3*3

-81