Mai-Lin measures her heart rate whenever she exercises and tries to make sure that she is staying in her target heart rate zone. The American Heart Association suggests a target heart rate of T=0.75(220-a), where T is a person's target heart rate and a is his or her age.
a. Prove that given a person's target heart rate, you can calculate his or her age using the formula a=220- T/0.75.

We are given the series in the following form, ∑ (-1)^n/2n 1 Since the given series is a convergent alternating series, we can evaluate the sum using an integration trick.

We can do so by associating the given series with an equivalent power series of x in the form, ∑ (-1)^n/2n xn We know that the power series of a geometric series is given by the formula,∑ ar^n We use this formula and substitute -x for r. Therefore, the equivalent power series for the given series is,\(∑ (-1)^n/2n (-x)^n\) We know that the geometric series can be integrated term by term. Therefore, we can integrate both sides of the power series. Let S be the sum of the given series, S =\(∑ (-1)^n/2n 1S = ∑ (-1)^n/2n\) x when -1 < x ≤ 1 Since the power series converges uniformly, we can integrate both sides to obtain,\(∫S dx = ∑ (-1)^n/2n ∫ xn dx\)  where the limits of integration are from 0 to x.Now, let us evaluate the integral, \(∫ xn dx∫ xn dx= x^(n+1)/(n+1)\) Thus, we obtain, \(S = ∑ (-1)^n/2n ∫ xn dxS = ∫ [(-x)^0/2.0 + (-x)^1/2.1 + (-x)^2/2.2 + ...] dxS = ∫ [1 - x^2/2 + x^4/2.2 - x^6/2.4 + ...] dx\)Integrating the series term by term, we obtain,\(S = x - x^3/2.3 + x^5/2.5 - x^7/2.7 + ...\)Thus, S = tan^-1 x, for -1 < x ≤ 1

Therefore, the given series can be evaluated by identifying it as the value of an integral of a geometric series.

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The required sum of the measures of angles D and F is 260 degrees.

Let's represent the measures of angles D, E, and F as D, E, and F, respectively.

From the given information, we have the following equations:

D + E = 110 (The sum of the measures of angles D and E is 110)

E + F = 150 (The sum of the measures of angles E and F is 150)

Now, we want to find the sum of the measures of angles D and F, which is D + F.

To find D + F, we need to eliminate E from the equations. We can do this by adding equations (1) and (2):

(D + E) + (E + F) = 110 + 150

Now, the E terms cancel out:

D + F = 260

So, the sum of the measures of angles D and F is 260 degrees.

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Answer:

A: Line graph

Step-by-step explanation:

A pie chart is just percentages, so that wouldn't work. A box and whisker plot is for a number line, so that wouldn't work. A stem and leaf plot is for representing quantitative data in a graphical format, so that wouldn't work. The only logical choice is a line graph, since y could be the cost, and x could be the speed.

answer is 40

Step-by-step explanation:

Answer:

The ratio between Roberto and David is 3:11

Step-by-step explanation:

If Roberto were to have 18 cards when we start, then David would have 24. Roberto has 3/4 the amount that David has. Then Roberto gives half of his cards (9) to David. Roberto now has 9 cards and David has 33.

The ratio of Roberto's cards to David's cards will be 3:11.

Algebra is the study of graphic formulas, while logic is the interpretation among those signs.

The number of Roberto's baseball cards is 3/4 the number of David's cards. If Roberto gives 1/2 of his cards to David.

If Roberto were to have 18 cards when we start, then David would have 24.

Roberto has 3/4 the amount that David has. Then Roberto gives half of his cards (9) to David. Roberto now has 9 cards and David has 33.

The ratio between Roberto and David is 3:11

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Answer:

Step-by-step explanation: Hello! My name is Madison and I will being helping you how to go about doing these problems! First things first.

1) 50,000 divided by 12 would be 4166.6 repeating.

2)

The company may need to reconsider its decision to charge extra for the sports channel or come up with better marketing strategies to promote it.

Based on the given information, we can use statistical inference to determine whether the marketing director's claim is true or not. The sample size of 405 is sufficiently large enough for us to use the normal distribution to calculate the confidence interval. Firstly, we need to calculate the sample proportion of viewers who are willing to pay for the sports channel, which is given as 27/405 = 0.0667 (rounded to 4 decimal places). We can then calculate the standard error of the proportion using the formula SE = sqrt[p(1-p)/n], where p is the sample proportion and n is the sample size. Substituting the values, we get SE = sqrt[(0.0667 x 0.9333)/405] = 0.0161 (rounded to 4 decimal places). Next, we can calculate the 95% confidence interval using the formula CI = p ± Z*SE, where Z is the Z-score corresponding to the desired confidence level. For a 95% confidence level, Z = 1.96. Substituting the values, we get CI = 0.0667 ± 1.96 x 0.0161, which gives us a confidence interval of (0.0357, 0.0977) (rounded to 4 decimal places). Since the confidence interval does not include the marketing director's claim of more than 6%, we can conclude that there is not enough evidence to support the director's claim. In fact, the lower bound of the confidence interval suggests that only 3.57% of subscribers may be willing to pay for the channel, which is significantly lower than the claim. Therefore, the company may need to reconsider its decision to charge extra for the sports channel or come up with better marketing strategies to promote it.

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The equation y = 3/4x describes the relationship

From the question, we have the following parameters that can be used in our computation:

The graph

The graph is a linear graph, and we have the following points on the graph

(x, y) = (0, 0) and (4, 3)

Because the line passes through the origin i.e. (0, 0), the equation that describes the relationship is then represented as

y = Y/X * x

Where

(X, Y) = (4, 3)

So, we have

y = 3/4x

Hence, the equation is y = 3/4x

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Answer:

9

Step-by-step explanation:

put in order least to greatest

-9 -9 -7 -6 -5 -4 -3  0

9-0=9

range cannot be negative because it is the space between numbers and distance cannot be negative

Answer: The range is 9.

The circumference of a circle can be obtained using the formulae

If the radius of the circle is given:

If the diameter of the circle is given:

From the first circle given

The radius (r) is given to be = 11.5m

Hence, the circumference of the circle is

Hence, c = 72 meters

For the second circle

We were given the diameter of the circle = 12m

Hence, the circumference of the circle is

Hence, c = 38 meters

For the third circle

The radius of the circle = 24m

Hence, the circumference of the circle is

Hence, c = 151 meters

The limit does not exist.

In order for such a limit to occur, the fraction \(\frac{x^{2} }{x^{2} +y^{2} }\) must be comparable to the same value \(L\), regardless of the way we take to get there \((0,0)\).

Try approaching \((0,0)\) along the x-axis.

This means setting \(y=0\) and finding the limit \(lim_{x-0} \frac{x^{2} }{x^{2} +y^{2} }\).

We obtain:

\(lim_{x-0,y=0}\frac{x^{2} }{x^{2} +y^{2} } =lim_{y=0}}\frac{x^{2} }{x^{2} +0 }\\=lim_{x-0}} \frac{x^{2} }{x^{2} } \\\\=lim_{x-0}}1\\=1\)

Now evaluate approaching \((0,0)\) along the y-axis.

This means setting \(x=0\) and finding the limit \(lim_{y-0} \frac{x^{2} }{x^{2} +y^{2} }\).

\(lim_{y-0,x-0} \frac{x^{2} }{x^{2} +y^{2} } =lim_{y-0} \frac{0}{0+y^{2} } \\=lim_{y-0} \frac{0}{y^{2} } \\=lim_{y-0} 0\\=0\)

Approaching the origin via these two methods results in distinct limits.

\(lim_{x-0,y-0} \frac{x^{2} }{x^{2} +y^{2} }\) ≠ \(lim_{y-0,x-0}\frac{x^{2} }{x^{2} +y^{2} }\)

Therefore the limit does not exist.

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The correct question is given below:

Find the limit, if it exists, or show that the limit does not exist.

\(lim_{(x,y) -(0,0)} \frac{x^{2} }{x^{2} +y^{2} }\)

Answer:

–21.8 – 18.3

Step-by-step explanation:

because you keep change flip

Answer:

-21.8 - 18.3 ;)

6.56 × 1.2= 7.872 = 7.9 [ to 2 significant figures]

Significant figure

Significant figures are the number of digits in value, often measurement, that contribute to the degree of accuracy of the value. We start counting significant figures at the first non-zero digit. Calculate the number of significant figures for an assortment of numbers.

fewest; the same significant figures with; measured numbers

Without mincing words let us dive straight into the solution to the above question. In order to be able to use the significant figures properly one must know the rules attached to it uses. This is so, because they contributes to the precision of measurements.

When performing multiplication or division calculation, the number of significant figures in the answer[result] will be determined by the one with the smallest number of significant figure in the problem.

Therefore, if we have 6.56 which is three[3] significant figures and 1.2 which is two[2] significant figures, then the number of significant figures will be two[2].

6.56 × 1.2= 7.872 = 7.9[ to 2 significant figures].

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The error for the 3rd week, using SES forecast with α=0.3, is -0.1.

To calculate the error for the 3rd week using SES (Simple Exponential Smoothing) forecast, we first need to calculate the forecasted value for the 3rd week. The forecasted value is calculated using the formula:

\(F_t = α * A_{t-1 }+ (1 - α) * F_{t-1}\)

Where:

\(F_t\) is the forecasted value for week t

\(A_{t-1}\) is the actual value for the previous week (week t-1)

\(F_{t-1}\) is the forecasted value for the previous week (week t-1)

α is the smoothing factor

Given the time series values for weeks 1, 2, 3, and 4 as 22.00, 7.00, 10.00, and 13.00 respectively, and α=0.3, we can calculate the forecasted value for the 3rd week as follows:

F₃ = 0.3 * 7.00 + (1 - 0.3) * 10.00

= 2.1 + 7

= 9.1

The error for the 3rd week is then calculated as the difference between the actual value and the forecasted value:

Error₃ = Actual Value₃ - Forecasted Value₃

= 10.00 - 9.10

= -0.1

Therefore, the error for the 3rd week, using SES forecast with α=0.3, is -0.1.

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Using the segment addition postulate, we have that:

5. The graph is given at the end of the answer.

6. The value of x is of x = 9.

7. The length is of PQ = 46.

8. The length is of QR = 46

9. The length is of PR = 92.

The segment addition postulate is a geometry axiom that states that a line segment, divided into a number of smaller segments, has the length given by the sum of the lengths of the segments.

For item 5, the diagram is given at the end of the answer.

For item 6, due to the congruence, Q is the midpoint, that is:

PQ = QR.

Hence:

6x - 8 = 10x - 44

4x = 36

x = 9

For the remaining items, the lengths are given as follows:

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Answer:

135

Step-by-step explanation:

(12-2) is in parentheses, so it should be solved first to get 10. 3^3 is 27. 27*10 = 270; 270/2 is 135.

Answer:

135

Step-by-step explanation:

You are gonna use PEMDAS to solve (),Exponents,Multiply,Divide,Add,Subtract

Answer:

jasen is 16

micheal is 9

Step-by-step explanation:

x+y=25

x-y=7

Answer:

£336 more

Step-by-step explanation:

2100/5 = 420 One fifth of the total lottery.

Colin has four shares so 4X420 = 1680

He then splits it into 10 (2+3+5) parts. 1680/10=168

Wife: 168X5=840

Son: 168X3=504

Wife-Son 840-504=336

Answer:

336£

Step-by-step explanation:

To get the amount of money colin gets

(2100*4)/5=1680

Lets do a table:

2. 5. 3. Sum:10

(2*1680)/10. (5*1680)/10. (3*1680)/10

=336. =840. =504

#1

Take any two points

Slope

#2

Slope:-

Difference

Answer:

Part a you find the rate of change by finding the slope of the line the value is 8 it is (y2-y1)/(x2-x1) 48-24/6-3=24/3=8

Part b current year is 8 dollars a bushel and previous year is 7 dollars

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Given

V = πr²h

Isolate h by dividing both sides by πr²

\(\frac{V}{\pi r^2}\) = h → C

The statements that are TRUE regarding the box plots are:

A, D, and E.

The box plots are given in the image attached below.

The values displayed by a box plot for a given data are:

Interquartile range = Third Quartile - First Quartile.

Thus, shelter's A median is 21, shelter B's 18.

Interquartile range for shelter A = 28 - 8 = 20

Interquartile range for shelter B = 28 - 10 = 18

Therefore, the statements that are TRUE regarding the box plots are:

A, D, and E.

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In a process with rework, we find the bottleneck as the resource with the highest implied utilization.

The above statement is True.

Bottleneck:

A bottleneck is a process in a process chain where the performance of the entire chain is degraded due to limited capacity. Bottlenecks lead to downtime, excess inventory, customer pressure and low employee morale.

Another example is a surface mount board assembly line with multiple pieces of equipment lined up. A common-sense strategy in general is to set and move the bottleneck until the end of the process, leading the better and faster machines to keep the printed circuit board (PCB) powered at all times, and preventing the slower machines from coming to a complete halt. Strategies that can lead to detrimental (or destructive) significant overall process drawbacks.

The product with the highest usage (again, the resource with the lowest capacity is not always the case) is the bottleneck. Defines the bottleneck as the resource with the highest specified usage in a process that involves rework. Better predictions can be identified by simply averaging the prediction errors. In the manufacturing process, each flow unit must have the same output. The recycling process requires only one turnaround time.

Rework also has a processing time different from that of a typical flow unit.

Complete Question:

In a process with rework, we find the bottleneck as the resource with the highest implied utilization. T/F?

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Answer:

Step-by-step explanation: 2.35%+95%

Answer is 97.35%

Answer:

the answer is -2.1

Step-by-step explanation:

you get this by putting that -4 where the x is and solving so it would look something like this

1.7x+4.7    for x= -4

1.7(-4) + 4.7

-6.8 + 4.7

-2.1

The probability of winning at least one award is 1 - 0.2373 = 0.7627 or 76.27%.

If the probability of winning an MTV music award after being nominated is 25%, the probability of not winning is 75%. Thus, the probability of not winning any of the five awards is (0.75)^5 = 0.2373.

As for how many awards Ariana Grande should expect to win, we can use the expected value formula: E(x) = n * p, where n is the number of trials (in this case, 5) and p is the probability of success (0.25). Therefore, E(x) = 5 * 0.25 = 1.25. So, Ariana Grande can expect to win about 1 award.

Finally, to calculate the standard deviation associated with this probability, we can use the formula: σ = sqrt(n * p * (1-p)). Plugging in the values, we get σ = sqrt(5 * 0.25 * 0.75) = 0.866. Therefore, the standard deviation associated with this probability is approximately 0.866.

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Answer: x = 0.75

Step-by-step explanation:

3x+x - 3 =0

4x - 3=0

4x = 3

x = 0.75

Polynomials are divided using synthetic division by the simplified form of long division.

Polynomials are divided using a technique called synthetic division, which uses a condensed version of long division. The procedures listed below can be used to divide a polynomial P(x) by a binomial of the form x - c (where c is a constant):

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Answer:

The size of the figure which remains the same

Step-by-step explanation:

if the size of the figure, shape etc remains the same then there can not be a translation as nothing has moved making this a non-description of translation

\(f(x) = (2/3)(x - 6)/(x + 3)\)

The domain of the function is given as follows:

x > 0.

The function in this problem is defined for values of x to the right of x = 0, hence the domain is given as follows:

x > 0.

The graph is given by the image presented at the end of the answer.

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