A pharmaceutical company produces caffeine pills that are each supposed to contain 200mg of caffeine. A plant that produces thousands of these pills per batch took an SRS of 15 pills from their latest batch to see if they contained the proper amount of caffeine. The sample data had a mean of 200.4mg of caffeine per pill with a standard deviation of 0.8mg. The amounts were roughly symmetric with no outliers. Based on this sample, which of the following is a 95% confidence interval for the mean amount of caffeine (in mg) per pill in this batch?
options
200.4±1.96(0.8)
200±1.96(0.8/sqrt(15))
200.4±1.96(0.8/sqrt(15))
200.4±2.145(0.8/sqrt(15))
200±2.145(0.8/sqrt(15))

Answer:

The box plot shows information

about the heights, in cm, of a Yr 10

group of Year 10 students.

Yr 7

130

a) The table shows information about

the heights, in cm, of a group

of Year 7 students.

Complete the boxplot for Year 7.

b) The heights distributions of Year 10

and Year 7 are compared.

140

height

(cm)

150

160

Height (cm)

median

170

least

upper

lower

quartile quartile

height

145 158 154 166

range

25

A- The median height is higher for Yr 7 than for Yr 10

Select the statements that apply. B-The interquartile range is higher for Yr 7 than for Yr 10

C - The data range is wider for Yr 7 than for Yr 10

D- The median height is lower for Yr 7 than for Yr 10

180

(3)

(2)

Total marks: 5

Step-by-step explanation:

A - The median height is higher for Yr 7 than for Yr 10. (Incorrect)

B - The interquartile range is higher for Yr 7 than for Yr 10. (Correct)

C - The data range is wider for Yr 7 than for Yr 10. (Correct)

D - The median height is lower for Yr 7 than for Yr 10. (Incorrect)

Therefore, the correct statements are B and C.

Answer: 1 hour and 20 minutes

Step-by-step explanation:

We can use the formula:

time = distance / speed

Let's call the distance of the journey "d".

When the train is travelling at 40 km/h, it takes 3 hours to complete the journey. So we have:

3 = d / 40

Solving for "d", we get:

d = 3 x 40 = 120 km

Now we want to know how long it will take for the train to complete the same journey at 90 km/h. We can use the formula again:

time = distance / speed

Plugging in the values we know:

time = 120 / 90

Simplifying, we get:

time = 4/3 hours or 1 hour and 20 minutes

Therefore, the train will take 1 hour and 20 minutes to complete the journey at 90 km/h.

Required answer :-

Step-by-step explanation:

A train travelling at 40km/h takes 3 hours for a journey. So, Speed will be 40 km/hr

Time will be 3 hours.

Speed = Distance/time

Distance = Speed × time

Distance = 40 × 3

Distance = 120 km.

Now, we have to find that how long will it take the train to complete the same journey, travelling at 90km/h.

Now, Speed will be 90 km/hr

Distance = Speed × time

Time = Distance/speed

Time = 120/90

Time = 4/3 hours

1 hour = 60 minutes

4/3 × 60

4 × 20

80 minutes

1 hour 20 minutes.

Therefore, The train will take 1 hour 20 minutes to complete the journey, travelling at 90km/h.

The standard form of a conic section represented by r = 6/(cos x + 3sin x) is  r^2 = 6(x + 3y) and the represented equation is a line.

The equation r = 6/(cos x + 3sin x) is in polar form, where r represents the distance from the origin to a point (x, y) in the plane, and x is the angle that the line connecting the origin to (x, y) makes with the positive x-axis. To determine the standard form of the conic represented by this equation, we need to convert it to Cartesian coordinates.

Using the trigonometric identity cos x = x/r and sin x = y/r, we can rewrite the equation as:

r = 6/(x/r + 3y/r)

Multiplying both sides by r, we get:

r^2 = 6(x + 3y)

This is the standard form of a conic section in Cartesian coordinates, namely an equation of a line. Therefore, the conic represented by the equation r = 6/(cos x + 3sin x) is a line in the Cartesian coordinate system.

In summary, to determine the standard form of a conic represented by an equation given in polar form, we can use trigonometric identities to rewrite it in Cartesian coordinates.

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Answer:

P= 40 ft

Step-by-step explanation:

Perimeter is the sum of all the lengths

So,

Perimeter= 6+4+15+10ft

= 35ft

Nearest ten can be 40ft or 30ft

If you succeed In understanding then kindly mark my answer the brainliest. Thank you :)

The solution for X is 5. An equation is a mathematical statement that shows the equality of two expressions.

It typically consists of variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division.

To solve for X, we first need to distribute the 5 to the expression in parentheses:

30 = 5X + 25

Then, we can isolate the variable term by subtracting 25 from both sides:

5 = 5X

Finally, we can solve for X by dividing both sides by 5:

X = 5

Therefore, the solution for X is 5.

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Answer:

Step-by-step explanation:

We know that a triangle angles total equals 180 so we could use the numbers and the equation, add it up and then find the value of x

(7x + 3) + 85 + 50 = 180

7x + 138 = 180

7x = 180-138

7x = 42

x = 6

Now that we found the value of x we can know substitute the value into the equation to find the value of the angle.

7x+3

42+3

45

After selling x pints of Boldly Buttered Popcorn icecream and y pints of Lovely Lavender Lemon on the charged of $10 for each, his profit equation is written as P = 6x + 6y = 6( x + y).

We have, Mr. McCoy's new ice cream shop. He sold two flavors of icecream. He sold his Boldly Buttered Popcorn ice cream and his Lovely Lavender Lemon ice cream. The quantity of sold Boldly Buttered Popcorn ice cream = x pints

The quantity of sold Lavender Lemon ice cream = y pints

Cost of each pint of ice cream = $4

Selling price of each pint of ice cream

= $10

First, total pints of icecream he sold

= pints of Boldly Buttered Popcorn ice cream+ pints of Lavender Lemon ice cream = ( x + y) pints

Now, Cost of (x + y) pints of ice cream

= $4 ( x + y)

Similarly, selling price of ( x + y ) pints of icecream = $ 10 ( x + y)

As we know, when selling price is greater than cost price then profit will occur. Equation for profit P = selling price - cost price = $ 10 ( x + y) - $4 ( x + y)

= 10 x + 10y - 4x - 4y

P = 6(x + y)

Hence, required equation is 6x + 6y.

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Complete question:

Mr. McCoy's new ice cream shop is doing great! Last month, he sold out of his Boldly Buttered Popcorn ice cream and his Lovely Lavender Lemon ice cream. He sold x pints of Boldly Buttered Popcorn and y pints of Lovely Lavender Lemon. Each pint cost him $4 to make, and he charged $10 for each. Write an equation for his profit or loss on ice cream selling.

The probability of getting 2 socks of the same color given by the following solution is 65/132.

Beginning with the first sock, we have three options: blue, white, or grey. If we wanted to know the likelihood of drawing only one blue sock, we might divide the number of blue socks in the drawer by the total number of socks (2 / 12).

We have three options for the second sock: blue, white, or grey. Keep in mind that we are drawing without replacement, so there is now one fewer sock in the drawer. Thus, with three alternatives for the first sock and three options for the second sock, the total number of combinations is three times three, or nine. The following are all of the potential combinations: (blue, blue), (blue, white), (blue, grey), (white, blue), (white, white), (white, grey), (white, blue), (white, white), (white, grey), (grey, blue), (grey, white) (gray, gray).

So the probability of 2 socks of the same color is, in equation form:

P(2 socks of same color) = P(blue sock first) * P(blue sock second) + P(white sock first) * P(white sock second) + P(gray sock first) * P(gray sock second).

= 2/12*1/11 + 4/12*3/11 + 6/12*5/11

= 65/132

Therefore, the probability of getting 2 socks of the same color 65/132.

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Complete question:

Mixed in a drawer are 2 blue​ socks, 4 white​ socks, and 6 gray socks. You pull out two​ socks, one at a​ time, without looking. Find the probability of getting 2 socks of the same color.

Answer:

The volume of the aquarium can be found by multiplying its length, width, and height:

Volume = length x width x height

Volume = 19 in x 15 in x 12 in

Volume = 3,420 cubic inches

Therefore, when the aquarium is full, it can hold 3,420 cubic inches of water.

Step-by-step explanation:

Answer:

Let's start by defining our variables:

Now, let's write the system of inequalities to represent the constraints:

The company has 260 boards of mahogany, so x ≤ 260.

The company has 320 boards of black walnut, so y ≤ 320.

The company expects to sell at most 380 boards, so x + y ≤ 380.

We cannot sell a negative number of boards, so x ≥ 0 and y ≥ 0.

Graphically, these constraints represent a feasible region in the first quadrant of the xy-plane bounded by the lines x = 260, y = 320, and x + y = 380, as well as the x and y axes.

To maximize profit, we need to write a function that represents the objective. The profit for selling one board of mahogany is $20, and the profit for selling one board of black walnut is $6. Therefore, the total profit P can be calculated as:

To maximize P, we need to find the values of x and y that satisfy the constraints and make P as large as possible. This is an optimization problem that can be solved using linear programming techniques.

The solution to this problem can be found by graphing the feasible region and identifying the corner point that maximizes the objective function P. However, since we cannot draw a graph here, we will use a table of values to find the maximum profit.

Let's consider the corner points of the feasible region:

Corner point (0, 0):

P = 20(0) + 6(0) = 0

Corner point (260, 0):

P = 20(260) + 6(0) = 5200

Corner point (0, 320):

P = 20(0) + 6(320) = 1920

Corner point (100, 280):

P = 20(100) + 6(280) = 3160

Corner point (200, 180):

P = 20(200) + 6(180) = 5520

Corner point (380, 0):

P = 20(380) + 6(0) = 7600

The maximum profit is $7600, which occurs when the company sells 380 boards of wood, all of which are mahogany.

The cost of petrol for the trip to UWC is R1.2384.

In general, cost refers to the amount of resources (usually money) that must be expended to produce or acquire something. It can be thought of as the value of the resources that are given up in order to obtain something else.

To calculate the cost of petrol for the trip to UWC, we need to know the distance traveled and the amount of fuel consumed.

Let's assume that the distance from Andrew's home to UWC is 20 kilometers (km). Then, the amount of fuel consumed for the trip is:

[tex]Fuel consumed = (0.0052 k/100 km) * 20 km = 0.00104 k[/tex]

where k stands for liters of petrol.

To convert the amount of fuel consumed to liters, we need to multiply by 100, since the fuel consumption rate is given in liters per 100 km:

[tex]Fuel consumed = 0.00104 k * 100 = 0.104 liters\\Fuel consumed = 0.00104 k * 100 = 0.104 liters[/tex]

Now we can calculate the cost of petrol for the trip:

[tex]Cost of petrol = (0.104 liters) * (R11.90/liter) = R1.2384[/tex]

Therefore, the cost of petrol for the trip to UWC is R1.2384.

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The algebraic expression "two-ninths of h" can be written as (2/9)h, where h is the variable being multiplied by the fraction 2/9.

"Two-ninths of h" is an algebraic expression that represents a quantity that is equal to two-ninths of the value of h. It can be written as 2h/9 or (2/9)h. In this expression, h represents an unknown value or variable, and 2/9 is a constant that specifies the fraction of h that is being considered. This expression can be used in mathematical equations to represent a specific portion or amount of h, depending on the context of the problem.

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Part A: The group of points labeled N is called a scatter plot. The point labeled M is an outlier.

Part B: The association between students' test scores and the number of hours they study is that as the number of hours students study increases, their test scores tend to increase as well.

A scatter plot is a type of graph that displays the relationship between two variables. It is often used to show how one variable is affected by another.

Part A: The presence of point M could be due to an error in recording data, or it could be due to an unusual event or circumstance that is not representative of the population.

Part B: This suggests that the more time students put into studying, the better their test scores will be. However, it is important to note that the graph does not necessarily imply that studying for more hours will necessarily lead to higher test scores, as the scatter plot also shows that there are other factors that could affect test scores.

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Part A: The group of points labeled N is called a scatter plot.

The point labeled M is called an outlier.

The presence of point M is likely due to the fact that the student studied for only one hour, yet achieved a perfect score

Part B: The association between students' test scores and the number of hours they study is that as the number of hours students study increases, their test scores tend to increase as well.

A scatter plot displays the relationship between two variables. It is often used to show how one variable is affected by another.

Part A: The group of points labeled N is called a scatter plot.

The point labeled M is called an outlier.

The presence of point M is likely due to the fact that the student studied for only one hour, yet achieved a perfect score.

Part B: The scatterplot shows a weak positive association between students' test scores and the number of hours they study.

As the number of hours studying increases, the test scores tend to increase, although there is considerable variability in this relationship. The outlier at 1, 100 indicates that there may be other factors other than study time that influence test scores.

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7/6 is wider  George Washington's mouth than his eye.

"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."

We always count the unit or amount value first and then calculate the more or less amount value. For this reason, this procedure is called a unified procedure.

Many set values ​​are found by multiplying the set value by the number of sets.

A set value is obtained by dividing many set values ​​by the number of sets.

According to our question-

eye length = 11/6

difference= 3 - 11/6

7/6

Hence, 7/6 is wider  George Washington's mouth than his eye.

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We have that, using Euclid's algorithm, we find the inverse of 200 modules 1001 is -5 (or 1001+5).

To find the inverse of a module m using Euclid's algorithm, the steps are as follows:

1. Calculate the greatest common divisor (GCD) of a and m using the Euclidean algorithm.

2. Let a = GCD * s + m*t, where s is the inverse of a module m.

3. The GCD in terms of a and my is written as 1 = m-s*a.

4. Find s = -a, so the inverse of a module m is -a (or m+s).

For example, a = 2, m=17, so GCD = 1 = 17-8*2 and the inverse of 2 modulo 17 is -8 (or 17+8). Similarly, for a = 34, m= 89, the GCD = 1 = 89-34*2 and the inverse of 34 modulo 89 is -34 (or 89+34). Finally, for a = 200, m= 1001, the GCD = 1 = 1001-5*200 and the inverse of 200 modulo 1001 is -5 (or 1001+5).

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Answer:

36

Step-by-step explanation:

9x-31+7x-2+4x+33=360

x=18

7(18)-2

124

180-124=36

Assume that the first box has 4 red balls and 3 blue balls and the second box has 5 red balls and 4 blue balls. the probability that this ball is from the second box is 12/55.

Given that we need to choose one of the two boxes at random and select one of the balls in this box at random.

Let us assume that the first box has 4 red balls and 3 blue balls and the second box has 5 red balls and 4 blue balls.

Let the probability of selecting a blue ball from the first box be P(A) = (3/7)

Let the probability of selecting a blue ball from the second box be P(B) = (4/9)

So, the probability of selecting a blue ball is:

P(A) + P(B) = (3/7) + (4/9)= (27+28)/63= 55/63

If we have chosen a blue ball, then the probability that it is from the second box will be:

P(B|A) = P(B∩A) / P(A)P(B∩A) = P(A) × P(B|A) = (3/7) × (4/9) = 12/63

So, the probability that the blue ball is from the second box is:

P(B|A) = P(B∩A) / P(A)= (12/63) / (55/63)= 12/55

Therefore, the probability that this ball is from the second box is 12/55.

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The solution to the equation 3/4x - 5 = x, is equals to -20.00 (correct to 2 decimal places).

To solve the equation 3/4x - 5 = x for x, we can start by isolating the variable term on one side of the equation and the constant term on the other side. We can do this by adding 5 to both sides of the equation:

3/4x - 5 + 5 = x + 5

3/4x = x + 5

Next, we can isolate x on one side of the equation by subtracting x from both sides:

3/4x - x = x + 5 - x

-1/4x = 5

Finally, we can solve for x by dividing both sides of the equation by -1/4:

x = -20

Therefore, by using isolating the variable term and solving for x. we find the solution of 3/4x - 5 = x, correct to 2 decimal places, is x = -20.00.

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Solution is y(t) = ((c1e2t − c2e2t) (1 0) + (c1e8t + c2e8t) (0 1))

The differential equations of the given system are: y1′=5y1+3y2y2′=3y1+5y2 The solutions to these equations are:y1(t)=c1e2t+c2e8t y2(t)=−c1e2t+c2e8tNow,

let's rewrite the solution in the vector form y(t) = c1y1 vector(t) + c2y2 vector(t).The vector form of y1(t) and y2(t) is as follows: y1 vector(t) = (1 0) (c1e2t) + (0 1) (c2e8t)y2 vector(t) = (-1 0) (c1e2t) + (0 1) (c2e8t)

Therefore, the solution in the vector form y(t) = c1y1 vector(t) + c2y2 vector(t) is as follows: y(t) = c1((1 0) (c1e2t) + (0 1) (c2e8t)) + c2((-1 0) (c1e2t) + (0 1) (c2e8t))y(t) = (c1e2t − c2e2t) (1 0) + (c1e8t + c2e8t) (0 1)y(t) = ((c1e2t − c2e2t) (1 0) + (c1e8t + c2e8t) (0 1))

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Answer:

-4 >= x or x <= -4

Step-by-step explanation:

19 <= 7 - 3x

12 <= -3x

divide by negative flip the sign

-4 >=

Answer:

x ≤ -4

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The inequation is,

→ 19 ≤ 7 - 3x

Then the value of x will be,

→ 19 ≤ 7 - 3x

→ 7 - 3x ≥ 19

→ -3x ≥ 19 - 7

→ -3x ≥ 12

→ x ≤ 12/(-3)

→ x ≤ -12/3

→ [ x ≤ -4 ]

Hence, the answer is x ≤ -4.

Answer:

<D = 130°

Step-by-step explanation:

Supplementary = 180°

<C = 50°

<D = ?

<C + <D = 180°

180° - 50° = 130°

<D = 130°

Answer: 41666666669 / 50000000003

Step-by-step explanation:

The correct answer is number line A. Number Line A shows that Rose has $25 remaining to spend on decorations. The number line shows that she has already spent $5, as indicated by the arrow pointing from 0 to 5.

Number line is the  visual representation of numbers on a straight line. These are often used to represent linear equations, as well as to learn basic mathematical concepts such as addition, subtraction, multiplication, and division.

The number line shows that she has a total of $30 available for decorations, as indicated by the arrow pointing from 0 to 30. Between the two arrows, it is clear that Rose has $25 remaining to spend on decorations.

Number Line B does not accurately represent Rose’s situation because the arrow pointing from 0 to 20 does not indicate that Rose has already spent $5. Number Line C does not accurately represent Rose’s situation because the arrow pointing from 0 to 25 does not indicate that Rose has a total of $30 available to spend.

To solve this problem, Rose needs to identify the total amount of money she has available to spend on decorations and the amount of money she has already spent. Once she has identified these two values, she can use a number line to represent her situation.

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The conclusion (a) is correct i.e., There is sufficient evidence to support the claim that more than 50% of adults are opposed to federal tax dollars being used for foreign aid.

In USA, an obligation to pay a tax to the federal government rather than a state government

Sample Size (n) = 882

Number of Success ( X) = 415

The Hypothesis is given by :

[tex]H_{0}[/tex] : p = 0.50

H₁ : p > 0.50

The point estimate of the proportion is calculated by :

p^ = X/n

= 415/882

= 0.47

Therefore, a point estimate is 0.47 .

The test statics is calculated by :

[tex]Z = \frac{\vec{}p - p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]

= [tex]\frac{0.47 - 0.50 }{\sqrt{\frac{0.50(1-0.50)}{882} } }[/tex]

= - 1.781.

Therefore, the test statistics is -1.781.

The p-value is obtained from normal distribution at test statistic (-1.781).

The p-value is 0.037.

Since the p-value is less than level of significance (0.01) which means we reject the null hypothesis.

Therefore, The conclusion (a) is correct i.e., There is sufficient evidence to support the claim that more than 50% of adults are opposed to federal tax dollars being used for foreign aid.

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Answer:

  x = y = z = (√6)/3 cm ≈ 0.8165 cm

Step-by-step explanation:

You want the dimensions of the cuboid with the largest volume and a total surface area of 4 cm².

For a fixed surface area, the figure with the largest volume is a regular figure. In this case, it is a regular cuboid, or cube.

The total surface area of a cube with edge length s is ...

  A = 6s²

Then the edge length of the desired cube is found from ...

  4 = 6s²

  s² = 2/3 = 6/9 . . . . . . divide by 6; write with square denominator

  s = √(6/9) = (√6)/3

The dimensions of the box are ...

  x = y = z = (√6)/3 cm ≈ 0.8165 cm

ANSWER

Jules paid $0.70 for one pencil

STEPS

Cost of One Pencil.

Let's assume the cost of one notebook be x and one pencil be y.

According to the given information,

Shanika bought 1 notebook and 5 pencils at a cost of $10.00. Therefore,

1x + 5y = 10 --- equation 1

Jules paid $14.90 for 1 Notebook and 12 pencils. Therefore,

1x + 12y = 14.9 --- equation 2

We need to find the cost of one pencil, i.e., y.

We can solve the above equations simultaneously to find the value of y.

Multiplying equation 1 by 12 and equation 2 by 5, we get:

12x + 60y = 120 --- equation 3

5x + 60y = 74.5 --- equation 4

Subtracting equation 4 from equation 3, we get:

7x = 45.5

x = 6.5

Substituting the value of x in equation 1, we get:

1(6.5) + 5y = 10

5y = 3.5

y = 0.7

Therefore, Jules paid $0.70 for one pencil.

ChatGPT

Answer:

Jules pay:

$0.7

Step-by-step explanation:

1n + 5p = 10                  Eq. 1

1n + 12p = 14.9              Eq. 2

n = cost of one notebook

p = cost of one pencil

From Eq. 1

n = 10 - 5p               Eq. 3

From Eq. 2

n = 14.9 - 12p            Eq. 4

Equalizing Eq. 3 and Eq. 4:

10 - 5p = 14.9 - 12p

12p - 5p = 14.9 - 10

7p = 4.9

p = 4.9 / 7

p = 0.7

From Eq. 3:

n = 10 - 5p

n = 10 - 5*0.7

n = 10 - 3.5

n = 6.5

Check:

From Eq. 2:

n + 12p = 14.9

6.5 + 12*0.7 = 14.9

6.5 + 8.4 = 14.9

Then:

1 pencil = $0.7

Answer: 72°

Step-by-step explanation:

To find the interior angle of this shape, use the formula 180(n-2)/n, where n is the amount of sides. Plugging 5 in for the interior angle of a pentagon, you get 180(3)/5, or 108°.

Using the statement that PR intersects QS, we can see that triangle QOR is isosceles (to get this, look at triangle PQR, and note that because it has 2 equal side lengths, and its last length is not equivalent to the other 2 sides, it is isosceles). Solving for angle PRQ, we know one angle is 108°, and the other two are equal. The total angle in a triangle is 180°, so (180°-108°)/2 = 36° (angles QPR and PRQ).

Since the angle of R = 108°, we can find angle PRS as 108° - 36°, or 72°. Since triangles PQR and QRS are similar (share the same angles and side lengths), we can see that angle RQS and RSQ are both 36°.

Since ORS is a triangle, its angle total is 180°. Since we know the angles ORS and OSR (respectively) already as 72° and 36°, we can subtract these angles to find angle ROS. 180°-72°-36° = 72°

The time difference of 15 minutes, or 25 percent (15 divided by 60 times 100), is called the time saved.

An experiment is a controlled study in which a scientist manipulates a variable in order to determine its effects. An experiment must have a testable hypothesis, be replicable, and produce empirical evidence.

Discussing the time difference in an experiment. In an experiment, it takes one hour to memorize all of the words on a list, and two years later, they are relearned in 45 minutes.

The time difference of 15 minutes, or 25 percent (15 divided by 60 times 100), is referred to as the time saved.

Time saved is the difference between the total time it takes to finish a process with a particular method and the total time it would take to complete the same process without that method.

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