A mechanic buys 2 barrels of oil. If there are 63 gallons in every barrel and approximately 3.785 liters for every gallon, approximately how many liters of oil did the mechanic buy?

Let's call the first number in the series "x", and the last number in the series "y".

We know that the series is a consecutive series of odd numbers, and we also know that y is 6 less than the last number in the series.

Since the series is a consecutive series of odd numbers, we can say that the difference between any two consecutive numbers in the series is 2.

So, we can write an equation to represent this information:

y = x + (n-1) * 2

where n is the number of numbers in the series.

We also know that y is 6 less than the last number in the series, so we can add this information to our equation:

y = x + (n-1) * 2 - 6

To solve for n, we can rearrange the equation:

n = (y - x + 6) / 2 + 1

Now, if we know the value of x and y we can substitute them in the equation and find the number of terms in the series.

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The population of Americans over age 100 was changing at a rate of 0.0378 million people/decade at the beginning of 2000.

To find how fast the population of Americans over age 100 was changing at the beginning of 2000, we need to take the derivative of the function P(t) with respect to t. The derivative of P(t) with respect to t is given by:

P'(t) = 0.54*0.07e0.54t

At the beginning of 2000, t = 0. So, we need to plug in t = 0 into the derivative to find how fast the population was changing at that time:

P'(0) = 0.54*0.07e0.54*0 = 0.0378

Therefore, the answer will be 0.0378.

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a. The median number of calls = 55

b. The first and third quartiles, Q1 = 48 and Q3 = 66

c. The first decile and the ninth decile, D1 = 45 and D9 = 71.

d. The 33rd percentile = 52.5

To answer the questions, let's first organize the data in ascending order:

38 40 41 45 48 48 50 50 51 51 52 52 53 54 55 55 55 56 56 57 59 59 59 62 62 62 63 64 65 66 66 67 67 69 69 71 77 78 79 79

(a) The median is the middle value of a dataset when arranged in ascending order.

Since we have 40 observations, the median is the value at the 20th position.

In this case, the median is the 55th visit.

(b) The quartiles divide the data into four equal parts.

To find the first quartile (Q1), we need to locate the position of the 25th percentile, which is 40 * (25/100) = 10.

The first quartile is the value at the 10th position, which is 48.

To find the third quartile (Q3), we need to locate the position of the 75th percentile, which is 40 * (75/100) = 30.

The third quartile is the value at the 30th position, which is 66.

Therefore, Q1 = 48 and Q3 = 66.

(c) The deciles divide the data into ten equal parts.

To find the first decile (D1), we need to locate the position of the 10th percentile, which is 40 * (10/100) = 4.

The first decile is the value at the 4th position, which is 45.

To find the ninth decile (D9), we need to locate the position of the 90th percentile, which is 40 * (90/100) = 36.

The ninth decile is the value at the 36th position, which is 71.

Therefore, D1 = 45 and D9 = 71.

(d) To find the 33rd percentile, we need to locate the position of the 33rd percentile, which is 40 * (33/100) = 13.2 (rounded to 13). The 33rd percentile is the value at the 13th position.

Since the value at the 13th position is between 52 and 53, we can calculate the percentile using interpolation:

Lower value: 52

Upper value: 53

Position: 13

Percentage: (13 - 12) / (13 - 12 + 1) = 1 / 2 = 0.5

33rd percentile = Lower value + (Percentage * (Upper value - Lower value))

                = 52 + (0.5 * (53 - 52))

                = 52.5

Therefore, the 33rd percentile is 52.5.

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Answer:

The customary method of finding the inverse is some variant of the method I'm going to use below. Whatever method you use, make sure you do the exact same steps in the exact same order every time, so you remember those steps when you get to the test.

Find the inverse of y = 3x – 2.

Here's how the process works:

Here's my original function:  

y = 3x - 2

Now I'll try to solve for "x =":  

y + 2 = 3x

(y + 2)/3 = x

Once I have " x =", I'll switch x and y; the "y =" is the inverse.  

y = (x + 2)/3

Then the inverse is y = (x + 2) / 3

If you need to find the domain and range, look at the original function and its graph. The domain of the original function is the set of all allowable x-values; in this case, the function was a simple polynomial, so the domain was "all real numbers". The range of the original function is all the y-values you'll pass on the graph; in this case, the straight line goes on for ever in either direction, so the range is also "all real numbers". To find the domain and range of the inverse, just swap the domain and range from the original function.

Step-by-step explanation:

The expression which describes the total number of candies distributed to the students is given by xy.

The total amount of candy that each student received from Ms. Russell would be given as the product of the candies that each student received with the total number of students who were present in the class. Hence, the multiplication method can help in the determination of the total number of candies easily.

Total number of students in the class of Ms. Russell = x students

x = 7 students

Number of candies that each student received = y candies

y = 23 candies

Total number of candies distributed to all the students = xy

Therefore, the Total number of candies distributed to all the students = 23×7 = 161 candies

Thus, all the students together received 161 candies from their teacher.

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Answer:

$89.7

Step-by-step explanation:

First, find the 40% of 149.5, which is 59.8. Then, subtract the percentage (59.8) from 149.5 which equals 89.7.

So it is $89.7 dollars when it is 40% off.

HOPE THIS HELPS!!!!

BEST OF LUCK!!!

Answer:

Slope of green line:

\(m = \frac{ - 3 - 3}{4 - ( - 4))} = - \frac{6}{8} = - \frac{3}{4} \)

Slope of red line:

\(m = \frac{3 - ( - 5)}{3 - ( - 3)} = \frac{8}{6} = \frac{4}{3} \)

The slopes of these two lines are negative reciprocals of each other.

Therefore, the correct answer is True (A).

Answer:

30+75x

Step-by-step explanation:

To find the consumer's and producer's surplus, we need more information about the demand and supply functions or the market equilibrium.

You provided the demand function D(x) = 25, but we require additional details to proceed with the calculations. The consumer's surplus is the difference between the maximum price consumers are willing to pay and the price they actually pay. It represents the benefit or surplus gained by consumers in a market transaction.

The producer's surplus is the difference between the minimum price producers are willing to accept and the price they actually receive. It represents the benefit or surplus gained by producers in a market transaction.

To calculate these surpluses, we typically need information about the supply function, equilibrium price, and equilibrium quantity. These values help determine the areas of the consumer's and producer's surpluses on the supply-demand graph.

Please provide the necessary information about the supply function, equilibrium price, or any other relevant details so that I can assist you in calculating the consumer's and producer's surplus accurately.

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Answer: 120

Step-by-step explanation:

The factorial function multiplies all numbers below that number going to 1. For example,

   2! = 2 * 1 = 2

   3! = 3 * 2 * 1 = 6
   4! = 4 * 3 * 2 * 1 = 24

Thus, 5! would be 5 * 4 * 3 * 2 * 1 = 120.

Answer:

it B

Step-by-step explanation:

just took the test.

shsnwnzjdbsbxfn

Answer:     g(x) =2^x -1  

Step-by-step explanation:   I took the test

When the second derivative of a function equals zero, it indicates a possible point of inflection or a critical point where the concavity of the function changes. It is a significant point in the analysis of the function's behavior.

The second derivative of a function measures the rate at which the slope of the function is changing. When the second derivative equals zero at a particular point, it suggests that the function's curvature may change at that point. This means that the function may transition from being concave upward to concave downward, or vice versa.

Mathematically, if the second derivative is zero at a specific point, it is an indication that the function has a possible point of inflection or a critical point. At this point, the function may exhibit a change in concavity or the slope of the tangent line.

Studying the second derivative helps in understanding the overall shape and behavior of a function. It provides insights into the concavity, inflection points, and critical points, which are crucial in calculus and optimization problems.

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When the second derivative of a function equals zero, it indicates a critical point in the function, which can be a maximum, minimum, or an inflection point.

The second derivative of a function measures the rate at which the slope of the function is changing. When the second derivative equals zero, it indicates a critical point in the function. A critical point is a point where the function may have a maximum, minimum, or an inflection point.

To determine the nature of the critical point, further analysis is required. One method is to use the first derivative test. The first derivative test involves examining the sign of the first derivative on either side of the critical point. If the first derivative changes from positive to negative, the critical point is a local maximum. If the first derivative changes from negative to positive, the critical point is a local minimum.

Another method is to use the second derivative test. The second derivative test involves evaluating the sign of the second derivative at the critical point. If the second derivative is positive, the critical point is a local minimum. If the second derivative is negative, the critical point is a local maximum. If the second derivative is zero or undefined, the test is inconclusive.

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The probability of return was the least for the Dining hall method and greatest for the Class delivery method. Therefore, E is the correct answer here.

There cannot be a positive or negative association between a categorical and a numerical variable. here the delivery method is a categorical variable.

We cannot determine what the total number for any of the delivery methods was as we are only given the conditional probability of whether they were returned or not.

We can clearly see that the probability of return was the least for the Dining hall method and greatest for the Class delivery method. Therefore, E is the correct answer here.

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\(12>-2(y-4)\\\\\implies -\dfrac{12}2 <y-4~~~;[\text{Dividing by a negative number, so reverse the inequality.}]\\\\\implies -6<y-4\\\\\implies -6+4<y\\\\\implies -2<y\\\\\implies y>-2\\\\\text{Interval,}~ (-2,\infty)\)

There is a 0.5477 probability that a randomly selected customer will arrive less than 5 minutes after the previous customer during the 3 pm to 5 pm time period. (option a)

Given that the arrival rate of cars at the bank's drive-through window during the 3 pm to 5 pm time period is 15 customers per hour, we can calculate the average time between arrivals as follows:

Average time between arrivals = 1 / arrival rate

= 1 / 15

= 0.0667 hours (since there are 60 minutes in an hour, this is equivalent to 4 minutes)

Now, we need to find the probability of a customer arriving less than 5 minutes after the previous customer. Since the time between arrivals follows the exponential distribution, we can use the cumulative distribution function (CDF) of the exponential distribution to calculate this probability. The CDF gives us the probability of an event occurring within a certain time frame.

To find the probability of a customer arriving less than 5 minutes after the previous customer, we need to calculate the probability of an arrival occurring within a 5-minute time frame, which is equivalent to 0.0833 hours. So, we can substitute λ = 15 and x = 0.0833 in the formula for the CDF and get:

F(0.0833) = 1 - e¹⁵ˣ⁽⁻⁰°⁰⁸³³⁾

= 0.5477 (rounded to four decimal places)

Therefore, the answer is option (a) 0.5477.

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Answer:

$55*($7s)

Step-by-step explanation:

So there is a one time fee for the bus. Its $55. You only pay for it once. However each student has to pay $7 to get on the bus. So 7 times how ever many students there are plus 55 dollars for the bus rent fee.

Answer:

If you can only pick one option I'd choose D.)

Step-by-step explanation:

Option D is only two numbers away from 456,700

The second closest number would be option B.)

Answer:

\(D) . \: 456,698 = 456,700 \: to \: the \: hundreds \: place.\)

For accounting purposes, depreciation is an allocation of a cost of an asset.

Both depreciation and amortization are techniques for spreading out an asset's cost throughout its useful life, although they are employed for various asset categories. Whereas amortisation is used for intangible assets like patents, copyrights, and trademarks, depreciation is utilised for tangible assets like buildings, machinery, and equipment. Depreciation is a method used to account for an asset's decline in value as a result of damage or obsolescence. During the course of the asset's useful life, the asset's cost is distributed to match the income it produces.

Depreciation is an accounting technique used to distribute a tangible asset's cost over the course of its useful life.

Hence, for accounting purposes, depreciation is an allocation of a cost of an asset.

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The Ray EB bisects ∠AEC. Since ray EB divides ∠AEC into two congruent angles, it is the angle bisector.

The student question is to prove that ray EB bisects ∠AEC given that m∠AEB = 45° and ∠AEC is a right angle.

Step 1: Identify the given information. We know that m∠AEB = 45° and ∠AEC is a right angle.

Step 2: Determine the measure of ∠AEC. Since ∠AEC is a right angle, its measure is 90° by the definition of a right angle.

Step 3: Apply the Angle Addition Postulate. This postulate states that the sum of the measures of two adjacent angles

is equal to the measure of the angle formed by their non-common sides. In this case, m∠AEB + m∠BEC = m∠AEC.

Step 4: Substitute the given values into the equation. We know that m∠AEB = 45° and m∠AEC = 90°. So, 45° + m∠BEC = 90°.

Step 5: Use the subtraction property to find the measure of ∠BEC. Subtract 45° from both sides of the equation:

m∠BEC = 45°.

Step 6: Compare the measures of ∠AEB and ∠BEC. Since m∠AEB = 45° and m∠BEC = 45°, ∠AEB is congruent to ∠BEC.

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Answer:

4.718592

Step-by-step explanation:

To get to -14.4 from 18 you multiply 18 x 0.8

Repeat that until you get to the 7th term

18 (1st)

18 x 0.8 = -14.4 (2nd)

-14.4 x 0.8 = 11.52 (3rd)

11.52 x 0.8 = 9.216 (4th)

9.216 x 0.8 = 7.3728 (5th)

7.3728 x 0.8 = 5.89824 (6th)

5.89824 x 0.8 = 4.718592 (7th)

Answer:

f(n + 1) = n + 17

Step-by-step explanation:

substitute x = n + 1 into f(x) , that is

f(x) = 2x - x + 16 = x + 16 , then

f(n + 1) = n + 1 + 16 = n + 17

Answer:

f(n)= n+17

Step-by-step explanation:

Expected completion time of the path other than the critical path is 18.16 weeks.

a) The expected times and variances for each of the activities are as follows:

Activity 1:

Expected Time = 9.83 weeks

Variance = 0.69 weeks

Activity 2:

Expected Time = 10.33 weeks

Variance = 2.78 weeks

Activity 3:

Expected Time = 9.83 weeks

Variance = 0.69 weeks

Activity 4:

Expected Time = 7.83 weeks

Variance = 1.36 weeks

b) The expected completion time of the critical path is 19.66 weeks.

The expected completion time of the path other than the critical path is 18.16 weeks.

c) The variance of the critical path is 1.38 weeks.

The variance of the path other than the critical path is 4.14 weeks.

d) If the time to complete the activities on the critical path is normally distributed, the probability that the critical path will be finished in 22 weeks or less is -98.

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Answer:

X would be 63.9

Hope it helps

Step-by-step explanation:

The value of the variable 'x' using the cosine formula will be 63.9 units.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The value of 'x' is given by the cosine of the angle ∠QSR. And the cosine of an angle is the ratio of the base and hypotenuse of the right-angle triangle. Then we have

cos 35° = x / 78

x = 63.9

The value of the variable 'x' using the cosine formula will be 63.9 units.

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Check below, please.

1) Let's fill in our Possibility Tree Diagram considering that the text tells us that each day you flip a coin. Since there are two possibilities either W or T we can start out this way:

2) Day 1 Day 2

So our tree is already filled let's now enlist all the possible outcomes

3)

Each letter for one day.

4) Now let's check what is the probability of playing Water tag on both days:

Thus this is the answer.

Answer:

4 would be it, but not negative 4 because then you get -8

Step-by-step explanation:

Answer:

0 ≤ t ≤ 18

Step-by-step explanation:

The cost of renting the boat without any discount is $8 per hour. However, Leila has a discount coupon for $3 off, so the effective cost per hour would be $8 - $3 = $5.

Let's assume Leila rents the boat for t hours. The total cost of renting the boat for t hours would be $5 multiplied by t, which is 5t.

According to the problem, Leila wants to spend at most $93. Therefore, we can set up the following inequality:

5t ≤ 93

This inequality represents the condition that the total cost of renting the boat (5t) should be less than or equal to $93.

Simplifying the inequality:

5t ≤ 93

Dividing both sides by 5 (since the coefficient of t is 5):

t ≤ 93/5

t ≤ 18.6

Since we cannot rent the boat for a fraction of an hour, we can round down the decimal value to the nearest whole number:

t ≤ 18

0 ≤ t ≤ 18

Answer: 0≤t≤12

Step-by-step explanation:

(I’m not sure if it’s 5 dollars off per hour, or total, but here’s what I did!)

If Leila has a $3 coupon, than she can spend +$3 because when you get a coupon, you can spend more, so 93+3 is equal to 96, now we just divide by 8 (because a boat costs $8 per hour) and we get 96/8=12.

Then, in inequality form it’s t≤12, because she can rent the boat for at most 12 hours, you could also do 0≤t≤12, because you can’t rent it for a negative amount of time, but either works.

Answer:

The value of x = 13cm and y = 12cm.

Step-by-step explanation:

P is the exterior point to the circle with centre O

Radius = 5cm

Length of the tangent = 12 cm

Distance between the point and centre of the circle = x cm

We know that

The angle between the radius of the circle and the tangent at the point of contact is 90°

By Pythagoras Theorem

Hypotenuse² = Side²+Side²

⇛x² = 12²+5²

⇛x² = 144+25

⇛x² = 169

⇛x² = 13²

We know that

The lengths of tangents drawn from the exterior point to the circle are equal.

Answer: The value of x=13cm and y = 12cm.

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Answer:

9cm

Step-by-step explanation:

If the triangles are similar then their lengths are in a ratio to each other, Ex: PR is 3 times LN, 2*3 = 6cm

This gives us a ratio of 1:3

PQ = LM*3 = 3cm*3 = 9cm