Sarah has a coupon for an oil change with synthetic oil for $49.95. She can buy 5 quarts of synthetic oil, which is what her car needs, for $37.54 and an oil filter for $9.47. How much can she save by doing the oil change herself?

Answer:

12 minutes

Step-by-step explanation:

11/x = 55/60

11 x 5 = 55

60/5=12

12.01 minutes

time = distance / speed

where distance is the distance traveled, speed is the average speed of the travel, and time is the time taken to cover the distance.

We are given that the distance traveled is 11 miles and the average speed is 55 miles per hour. To convert the speed to miles per minute, we can divide it by 60 since 1 hour is equal to 60 minutes:

55 miles per hour = 55/60 miles per minute

= 0.9167 miles per minute (rounded to four decimal places)

Now we can substitute the values into the formula:

time = distance / speed

= 11 miles / 0.9167 miles per minute

≈ 12.01 minutes (rounded to two decimal places)

Therefore, it would take approximately 12.01 minutes to travel 11 miles at an average speed of 55 miles per hour.

*IG:whis.sama_ent

The probability, expressed as a percent rounded to the nearest tenth, that the sample mean will be within $1 of the population mean is 91.5%.

To find the probability that a random sample of size two will have a sample mean within $1 of the population mean, we need to first calculate the population mean and standard deviation.

The population mean is the average of the given values:

(2 + 4 + 4 + 5 + 5 + 7) / 6 = 4.5

The population standard deviation can be calculated using the formula:

σ = [tex]\sqrt{S(x-u)^{2}/N }[/tex]

where S represents the sum of, x is each value, u is the population mean, and N is the population size.

Using this formula, we get:

σ = [tex]\sqrt{(2-4.5)^{2}+ (4-4.5)^{2}+(4-4.5) +(5-4.5)^{2} +(5-4.5)^{2}+ (7-4.5)^{2} /6}[/tex] = 1.5

Now we can find the probability of getting a sample mean within $1 of the population mean using the t-distribution since the population standard deviation is unknown and the sample size is less than 30. Since we are looking for the probability of the sample mean being within $1 of the population mean, we need to find the probability of getting a sample mean between 3.5 and 5.5 dollars.

We can use a t-distribution table or a calculator to find the probability. For a sample size of 2, the degrees of freedom is 1, and using a t-distribution table with a significance level of 0.05, we get a t-value of 12.71.

Therefore, the probability of getting a sample mean between 3.5 and 5.5 dollars is approximately 91.5% (calculated using a t-distribution calculator or the t-distribution table), rounded to the nearest tenth.

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Area of a circle is given by

[tex]\text{A} = \pi \times r^2[/tex]

We need to know the radius

[tex]\text{r} = \dfrac{\text{d}}{2}[/tex]

[tex]\text{r} = \dfrac{\text{74}}{2}[/tex]

[tex]\text{r} = 37 \ \text{mm}[/tex]

The radius is 37 mm and pi = 3.14

[tex]\text{A} = 3.14 \times (37)^2[/tex]

[tex]\text{A} = \boxed{\bold{4298.66 \ \bold{mm}^2}}[/tex]

This requires the circle theorem and the angle at the center postulate.

It simply states that the angle subtended by an arc at the centre is twice the angle subtended at the circumference.

Thus

8) m∡CA = 72 x 2 = 144°

9) m∡AD = 144/2 = 72°  - Angle Bisected by radius.

10) m∠C = ∠∡CA/2 = 72/2 = 36°

11) where the angles in the polygon are given as:

4y + 14)°
105°

7y+1)°
7x +1)°


Then, x and y are given as follows.

Note that 105° and (7y+1)° are opposite angles in a polygon = 180°
Also

(4y + 14)° + (4y + 14)° = 180

Thus

105° + (7y+1)° = 180 ......1

(7x +1)° + (4y + 14)° = 180 .....2



Simplifying the first equation:

105° + (7y+1)° = 180

7y + 106 = 180

7y = 74

y =  10.57


(7x +1)° + (4y + 14)°  = 180

(7x + 1)° + (4  (10.57) +  14)° = 180

(7x + 1)° + 54.28° = 180

7x + 55.28   = 180

7x =  124.72

x = 17.82

So we can conclude that , x is approximately 17.82 and y is approximately 10.57.

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Sasha will deposit $450 at 6% simple interest. The formula for calculating the balance of an account with simple interest is given by A = P(1 + rt), where A is the final amount, P is the initial principal balance, r is the annual interest rate (expressed as a decimal), and t is the time in years.

In this case, the initial principal balance P is $450, the annual interest rate r is 6% or 0.06 as a decimal, and the time t is 2 years. Plugging these values into the formula gives us:

A = 450(1 + 0.06 * 2)

Evaluating this expression gives us a final amount of approximately $477 in the account after two years.

Sasha will deposit the rest of her money ($850 - $450 = $400) at 2% compounded annually. The formula for calculating the balance of an account with annual compounding is given by A = P(1 + r/n)^(nt), where A is the final amount, P is the initial principal balance, r is the annual interest rate (expressed as a decimal), n is the number of times the interest is compounded per unit time (per year in this case), and t is the time in years.

In this case, the initial principal balance P is $400, the annual interest rate r is 2% or 0.02 as a decimal, n is 1 since it’s compounded annually, and the time t is 2 years. Plugging these values into the formula gives us:

A = 400(1 + 0.02/1)^(1 * 2)

Evaluating this expression gives us a final amount of approximately $416.16 in the account after two years.

Therefore, there will be approximately $60.84 more money in Sasha’s account at 6% simple interest than at 2% compounded annually after two years.

Answer:

The prime factorization of 75 is:

75 = 3 * 5^2

The greatest common factor (GCF) of the number 75 is 1, since 1 is the highest factor that can be shared by all the prime factors of 75.

Therefore, the factored form of 75 using the GCF is:

75 = 1 * 3 * 5^2

PLEASE MARK BRAILYEST! :D

The proposition can be proven by showing that the left and right cosets of H in G form a partition of G.

As H is a G subgroup, it comprises the identity element e within G. For any g element in G, the left coset gH comprises ge = g and the right coset Hg contains eg = g. Thus, there are non-empty left as well as right cosets.

G's each element belongs to both the left and the right cosets of H. Hence, all left (or right) cosets' union in G covers every G element. The left and right cosets of H in G build non-empty subsets that do not intersect with one another. Their union equals G; thus, they certainly construct a partition for G.

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Answer:

To prove that there exist infinitely many integers n such that n^2 + 1 is squarefree, we can use a proof by contradiction.

Assume the contrary, that there are only finitely many integers n such that n^2 + 1 is squarefree. Let's denote these integers as n_1, n_2, ..., n_k, where k is a finite positive integer.

Consider the number N = (n_1^2 + 1) * (n_2^2 + 1) * ... * (n_k^2 + 1) + 1.

Note that N is an integer and is greater than each of the numbers n_i^2 + 1 for i = 1 to k. Since n_i^2 + 1 is squarefree for each i, N is also squarefree, as it is not divisible by any square number other than 1.

However, N cannot be equal to any of the n_i^2 + 1, as N is strictly greater than each of them. This contradicts our assumption that n_1, n_2, ..., n_k are all the integers such that n^2 + 1 is squarefree.

Therefore, our assumption must be false, and there exist infinitely many integers n such that n^2 + 1 is squarefree. This completes the proof by contradiction.

Step-by-step explanation:

[tex]PEk = 2^{(k-1)} / (2^{(N-k+1)} - 1)[/tex] which is the desired equation.

An equation is a mathematical statement that shows that two expressions are equal. It typically contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

Let P(ej) denote the probability of outcome ej for j=1,2,...,N. Then we know that:

P(ej+1) = 2P(ej) for j=1,2,...,N-1

Also, we know that the sum of probabilities of all outcomes is 1:

P(e1) + P(e2) + ... + P(eN) = 1

We can use the geometric sequence formula to find P(ek) in terms of P(e1) as follows:

[tex]P(ek) = P(e1) * (2^{(k-1)})[/tex]

Substituting for P(ej+1) in terms of P(ej) gives:

[tex]P(ej+1) = 2P(ej) = 2^1 * P(ej)[/tex]

[tex]P(ej+2) = 2P(ej+1) = 2^2 * P(ej)[/tex]

...

[tex]P(ek) = 2^{(k-1)} * P(e1)[/tex]

We can sum the probabilities of all outcomes to get:

[tex]1 = P(e1) + 2P(e1) + 2^2 P(e1) + ... + 2^{(N-1)}P(e1)[/tex]

Using the formula for the sum of a geometric series, we get:

[tex]1 = P(e1) * [(2^N - 1)/(2 - 1)][/tex]

Simplifying, we get:

[tex]P(e1) = 1/(2^N - 1)[/tex]

Substituting this value for P(e1) in the expression for P(ek) gives:

[tex]P(ek) = (1/(2^N - 1)) * (2^{(k-1)})[/tex]

Simplifying, we get:

[tex]P(ek) = 2^{(k-N)} / (2 - 1/2^{(N-k+1)})[/tex]

Multiplying by 2/2, we get:

[tex]P(ek) = 2^{(k-1)} / (2^{(N-k+1)} - 1)[/tex]

Substituting k=N, we get:

P(Ek) = 1/2

Substituting k=1, we get:

[tex]P(E1) = 2^{(N-1)} / (2^N - 1)[/tex]

Therefore, we have shown that:

[tex]P(Ek) = 2^{(k-1)} / (2^{(N-k+1)} - 1)[/tex]

for k=1,2,...,N.

To show that PEk=2k-1/2N-1, we can substitute k=N-j+1 for j=1,2,...,N:

[tex]PEk = P(EN-j+1) = 2^{(N-j)} / (2^j - 1)[/tex]

Letting t = j-1, we can rewrite this as:

[tex]PEk = 2^{(N-t-1)} / (2^{(t+1)} - 1[/tex]

Multiplying the numerator and denominator by 2, we get:

[tex]PEk = 2^{(N-t)} / (2^{(t+2)} - 2)[/tex]

Substituting t = N-k, we get:

[tex]PEk = 2^{(k-1)} / (2^{(N-k+1)} - 1)[/tex]

which is the desired result.

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Part a: translation: (x,y) ---> (x + 1, y - 8); D'(3, -1), E'(8, -2),  F'(4, -8), G'(-1, -7).

Part b: reflection : in the x axis :D'(2,-7), E'(7,-6), F'(3,0) and G'(-2,-1).

In geometry, a translation is a transfer that occurs either laterally to the left or right as well as vertically up or down.

It may also consist of a mix of the two. Instead, you should evaluate the coordinates of the important locations in the first and second figures if you need must describe a translation. The number of units that have been moved horizontally, vertically, and in which directions are noted verbally.

Given that:

Part a: translation: (x,y) ---> (x + 1, y - 8)

D(2,7) -> D'(2 + 1, 7 - 8) = D'(3, -1)

E(7,6) -> E'(7+ 1,6- 8) = E'(8, -2)

F(3,0) -> F'(3+ 1,0- 8)  = F'(4, -8)

G(-2,1) -> G'(-2+ 1,1- 8) = G'(-1, -7)

Thus, the coordinates of D'E'F'G' -  D'(3, -1), E'(8, -2),  F'(4, -8), G'(-1, -7).

Part b: reflection : in the x axis

vertices D(2,7), E(7,6), F(3,0) and G(-2,1).

value of x will remain same, but y get negative.

(x,y) -- (x, -y)

D'(2,-7), E'(7,-6), F'(3,0) and G'(-2,-1).

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Correct question:

Parallelogram DEFG with vertices D(2,7), E(7,6), F(3,0) and G(-2,1):

a: translation: (x,y) ---> (x + 1, y - 8)

b: reflection : in the x axis

The value of tan (2∅) in the right triangle is  - 960 / 644.

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

Therefore, the triangle is a right angle triangle because it follows the Pythagoras's principle as follows:

c² = a² + b²

where

Therefore,

15² + 8² = 17²

Let's find ∅ using trigonometric ratios,

tan ∅ = opposite / adjacent

tan ∅ = 15 / 8

Therefore,

tan 2∅ = 2 tan ∅ / 1 - tan² ∅

tan 2∅ = 30 / 8 ÷ 1 - (15 / 8)²

tan 2∅ = 30 / 8 ÷ 1 - 225 / 64

tan 2∅ = 15 / 4 ÷  64 - 225/ 64

tan 2∅ = 15 / 4 ÷ -161 / 64

tan 2∅ = 15 / 4 × 64 / -161

tan 2∅ =  - 960 / 644

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The value of tan (2∅) in the right triangle is  - 960 / 644.

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

Therefore, the triangle is a right angle triangle because it follows the Pythagoras's principle as follows:

c² = a² + b²

where

Therefore,

15² + 8² = 17²

Let's find ∅ using trigonometric ratios,

tan ∅ = opposite / adjacent

tan ∅ = 15 / 8

Therefore,

tan 2∅ = 2 tan ∅ / 1 - tan² ∅

tan 2∅ = 30 / 8 ÷ 1 - (15 / 8)²

tan 2∅ = 30 / 8 ÷ 1 - 225 / 64

tan 2∅ = 15 / 4 ÷  64 - 225/ 64

tan 2∅ = 15 / 4 ÷ -161 / 64

tan 2∅ = 15 / 4 × 64 / -161

tan 2∅ =  - 960 / 644

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The geometric sequence in the list of options is A. 3, 12, 48, . . .

A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed number.

A. 3, 12, 48, . . . is a geometric sequence because each term is obtained by multiplying the previous term by 4.

B. 3, 1, . . . is not a geometric sequence because there is no fixed ratio between terms.

C. 0, 1, 3, 9, . . . is not a geometric sequence because the ratio between terms is not constant.

D. 3, 6, 12, 21, . . . is not a geometric sequence because the ratio between terms is not constant.

Therefore, the only geometric sequence is A. 3, 12, 48, . . .

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Answer:

3, 12, 48, . . .

Step-by-step explanation:

got it right

The quantity of Willow's books that are mysteries would be = 125 books.

To calculate the quantity of books that are mysteries the following is carried out.

The total number of books that willow has = 225 books

The total number of books that are mysteries = 5/9 of 225

That is ;

= 5/9 × 225/1

= 1125/9

= 125 books.

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Option B is the correct answer: chocolate-peanut butter cups and chocolate-caramel bites.

Xzavier should choose the two candies with the highest price per pound to maximize his spending.

The prices per pound are as follows:

$13.88 for chocolate-covered cashews

$11.46 for chocolate-covered peanut butter cups

$9.62 for Chocolate-Caramel Bites

$8.24 for Gourmet Gummy Bears

Chocolate-covered Cashews and Chocolate-Peanut Butter Cups are the two chocolates with the highest per-pound pricing.

As a result, Xzavier purchased a half-pound of Chocolate-covered Cashews and a half-pound of Chocolate-Peanut Butter Cups.

Option B is the correct answer: chocolate-peanut butter cups and chocolate-caramel bites.

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Step-by-step explanation:

The narrowest definition of the number -2 is that it is an integer that is less than zero and has an absolute value of 2. In other words, it is the additive inverse of the number 2, and can be written as "-2 = -1 * 2".

(i)  distributed in [tex]4 \times 3 = 12[/tex] different ways. (ii)statistical distribution of the balls is done in one of three ways. [tex](1 + 2 = 3)[/tex]  . (iii) there are 6 ways to divide the balls. [tex](4 + 2 \times 1).[/tex]  (iv)  to distribute the balls   [tex](1+2+1)[/tex].

(i) Both balls and boxes are labeled:

Since one box already contains a ball, there are four options for where to place the first ball, and only three options remain for the second ball. The two balls can be distributed in  [tex]4 \times 3 = 12[/tex] different ways.

(ii) Balls are labeled, but boxes are unlabeled:

There is just one method to arrange the balls if there is only one ball in each box. There are two ways to determine which box receives both balls if only one box possesses them. The statistical distribution of the balls is done in one of three ways.

(1 + 2 = 3).

(iii) Balls are unlabeled, but boxes are labeled:

There are four alternatives available to the box if they are both in the same box. If they are in different boxes, the first ball's box has two options, leaving the second ball with just one. Accordingly, there are 6 ways to divide the balls.

(4 + 2 * 1).

(iv) Both balls and boxes are unlabeled:

There is only one method to arrange the balls if there is one ball in each box. There are two methods to decide which box gets both balls if only one box has both balls.

There is just one method to arrange the balls if neither box incorporates a ball. There are therefore a total of 4 options to distribute the balls (1+2+1).

Therefore,(i)  distributed in [tex]4 \times 3 = 12[/tex] different ways. (ii)statistical distribution of the balls is done in one of three ways. [tex](1 + 2 = 3)[/tex]  . (iii) there are 6 ways to divide the balls. [tex](4 + 2 \times 1).[/tex]  (iv)  to distribute the balls   [tex](1+2+1)[/tex].

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Answer:

Pretty sure it’s A, D, A

Step-by-step explanation:

Answer:

-1.5

Step-by-step explanation:

Remember that the slope is the rise over the run, or: Slope = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].

[tex]\frac{6 - -3}{-1 - 5} = \frac{9}{-6} = -1.5[/tex]

So, your slope is -1.5.

27 can be written as a product of 3 and 9, where 9 is a perfect square.

In mathematics, a perfect square is an integer that is equal to the square of another integer. In other words, a perfect square is a non-negative integer that can be expressed as the product of an integer with itself.

To write 27 as a product of two integers such that one of the factors is a perfect square, we need to find a perfect square that divides 27.

The perfect square that divides 27 is 9, which is equal to [tex]3^2[/tex].

So, we can express 27 as the product of two factors, 3 and 9. One of the factors, 9, is a perfect square because it is equal to [tex]3^2[/tex]. Therefore, we have written 27 as a product of two integers where one of the factors is a perfect square.

We can also express 27 as 1 x 27 or 27 x 1, but neither of these representations includes a perfect square as a factor.

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The correct answer is d. observations, which is only the pretest summary.

A pretest summary is a summary of the data collected during a preliminary test or trial run.

The correct answer is d. observations.

The pretest summary is a summary of the data collected during a preliminary test or trial run, and it typically includes summary statistics such as the mean, variance, and degrees of freedom (df). However, the number of observations or sample size is typically not included in the pretest summary, as it is generally assumed to be the same as the number of observations in the full dataset. The number of observations is usually included in the full dataset summary, along with other descriptive statistics.

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Answer:

A. $1,166.40

Step-by-step explanation:

Since they have to travel a round trip, the total distance traveled will be 2*1,701 = 3,402 miles.

The total amount of gasoline needed can be found by dividing the total distance by the average gas mileage of the RV:

Gasoline needed = 3,402 miles ÷ 10.5 miles/gallon = 324.57 gallons

The total cost of gasoline can be found by multiplying the gasoline needed by the cost per gallon:

Total cost = 324.57 gallons × $3.60/gallon = $1,169.25

Therefore, Clinton and Stacy will spend approximately $1,169.25 on gasoline for the round trip to Yellowstone National Park and back home.

The closest option to this answer is A. $1,166.40.

Hope this helps!

The probability of the event is 4/13 when the odds in favor of the event are 4 to 9.

When the odds in favor of an event are given as a ratio of "a to b", the probability of the event can be calculated as:

Probability of the event = a / (a + b)

In this case, the odds in favor of the event are 4 to 9.

Therefore, we have:

a = 4 (the number of favorable outcomes)

b = 9 (the number of unfavorable outcomes)

Substituting these values into the formula, we get:

Probability of the event = 4 / (4 + 9)

Probability of the event = 4 / 13

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Answer:

yes she is correct

Step-by-step explanation:

Answer:

1984

________________________________________________________

Given:

To find the inverse of f(x), we first switch x and y and then solve for y. So, x = y-3/y+4, which we can rewrite as x(y+4) = y-3. Simplifying, we get xy + 4x = y-3, and then we can isolate y on one side: y-xy = 4x-3. Factoring out y on the left side, we get y(1-x) = 4x-3, and then we can divide both sides by (1-x) to get y = (4x-3)/(1-x). This is our inverse function.

Find:

To find the inverse of g(x), we follow the same process of switching x and y and solving for y. So, x = 4y+3/1-y, which we can rewrite as x(1-y) = 4y+3. Simplifying, we get -xy + y = 4x+3, and then we can isolate y on one side: y(-x+1) = 4x+3. Dividing both sides by (-x+1), we get y = (4x+3)/(-x+1). This is our inverse function.

Solve:

As for the given set of values, we have 187, 191, 202, 209, 218, and 1984. The outlier is obviously 1984, and its presence will not affect the range because the range is simply the difference between the largest and smallest values, which will be the same regardless of the presence of an outlier. However, the outlier will greatly affect the interquartile range, which is the difference between the upper and lower quartiles. This is because the upper and lower quartiles are the median of the upper half and lower half of the data, respectively, and including an outlier in one of these halves can greatly skew the median and thus the interquartile range.

The area of the shaded region on the actual triangle is: 2/16 = 1/8 inches²

So the answer is (B) 1/8 inches².

The size of a two-dimensional surface or region, such as a floor's surface, a painting's face, or the contours of a piece of land, is measured in terms of area.

It represents the amount of space that is enclosed or occupied by the surface or region under consideration and is typically measured in square units, such as square metres or square feet.

The area of the shaded region on the actual triangle is related to the area of the shaded region on the map by the square of the scale factor. In this case, the scale factor is 1 inch = 1/4 square inches, so the square of the scale factor is:

(1/4)² = 1/16

This means that the area of the shaded region on the actual triangle is 1/16th the area of the shaded region on the map.

The area of the shaded area on the map is 2 inches², matching the area of the triangle on the map, which is 2 inches²

Therefore, the shaded area on the actual triangle has the following area:

2/16 = 1/8 inches².

Therefore, the response is (B) 1/8 inches².

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a) The vector parametric equation for the helical path is r(t) = <28cos(12πt), 28sin(12πt), 5t*12>, where t is the parameter and 0 ≤ t ≤ 1.

b) You walked a total distance of 840π feet.

a) To find the vector parametric equation for the helical path, we first note that the spiral staircase makes 6 complete revolutions as we climb from the bottom to the top. This means that as we climb 60 feet, we will make 6 full revolutions around the z-axis. Since the radius of the spiral is 28 feet, we can use the equation for a helix to describe our path.

r(t) = <28cos(θ), 28sin(θ), ht>

where θ is the angle of rotation around the z-axis and h is the height we have climbed. We know that we make 6 full revolutions, or 12π radians, as we climb from the bottom to the top, so we can substitute θ = 12πt. We also know that we climb 60 feet in one hour, so our height function is h(t) = 5t*12.

Thus, our vector parametric equation for the helical path is r(t) = <28cos(12πt), 28sin(12πt), 5t*12>, where t is the parameter and 0 ≤ t ≤ 1.

b) To find the distance we walked, we need to integrate the magnitude of the velocity vector over the interval [0,1].

The velocity vector is the derivative of the position vector:

v(t) = < -336πsin(12πt), 336πcos(12πt), 60>

The magnitude of the velocity vector is:

|v(t)| = sqrt((-336πsin(12πt))^2 + (336πcos(12πt))^2 + 60^2) = 336π

Thus, the distance we walked is:

distance = ∫|v(t)|dt from 0 to 1 = ∫336π dt from 0 to 1 = 336π(1-0) = 336π

Therefore, we walked a total distance of 840π feet.

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Answer:

[tex]\frac{15}{(x-7)*(x+3)} = \frac{3/2}{x-7} + \frac{-3/2}{x+3}[/tex]

Step-by-step explanation:

Set up the partial fraction decomp:

[tex]\frac{15}{(x-7)*(x+3)} = \frac{A}{x-7} + \frac{B}{x+3}\\[/tex]

Multiply across:

[tex]15 = (\frac{A}{x-7} + \frac{B}{x+3})*(x+3)*(x-7)\\15 = A(x+3) + B(x-7)\\[/tex]

You can do this two ways from this point, you can plug in values for x to solve for A and B individually or set up a system of equations to find A and B

[tex]15 = Ax + 3A + Bx -7B\\Ax + Bx = 0\\3A - 7B = 15\\[/tex]

From the first equation we can see that A = -B, plugging into the second equation we get that

-10B = 15, so therefore B = -3/2 and because of the first equation A = 3/2 giving us our answer