Forty volunteer drivers are separated into two groups of 20 drivers each at random. The first group is asked to pay particular attention to braking smoothly when approaching a red light or stop sign. The second group is given no special instructions. All drivers report, at the end of a month, the gallons of gasoline used. The mean for the first group is 43.16 gallons of gas. The mean for the second group is 54.63 gallons of gas. The difference in means for the two groups is -11.47 gallons of gas. The data for both groups are combined and redistributed at random into two groups of 20. The means for each redistributed group are calculated, and the difference in means is recorded. The differences are represented in the histogram.
Which of these conclusions and justifications is the most reasonable?

The probability that the sample contains exactly two defective parts from a production process with a 6% defect rate is 0.0299. Option B is answer

To find the probability, we can use the binomial probability formula. The formula is P(X=k) = (n C k) * (p^k) * ((1-p)^(n-k)), where n is the sample size, k is the number of successes (defective parts), p is the probability of success (defect rate), and (n C k) represents the combination formula.

In this case, n = 5 (sample size), k = 2 (number of defective parts), and p = 0.06 (probability of a part being defective). Plugging these values into the formula, we get P(X=2) = (5 C 2) * (0.06^2) * ((1-0.06)^(5-2)) = 10 * 0.0036 * 0.8464 = 0.0299.

Therefore, the probability that the sample contains exactly two defective parts is 0.0299 (Option B).

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Answer:

-------------------------

Simplify the expression.

First distribute, then collect like terms:

The answer is that there are 32 ways to place two indistinguishable kings on an empty chess board so that they do not attack each other.

To answer this question, we need to understand the basic rules of chess. A king can move one square in any direction, including diagonally. So, to ensure that two kings are not attacking each other, we need to place them on two squares that are not adjacent to each other, and not on the same diagonal line.
There are 64 squares on a chess board, and the first king can be placed on any of those squares. The second king, however, has fewer options because it cannot be placed on the same row, column or diagonal as the first king.
The number of ways to place the second king will depend on where the first king was placed. For example, if the first king was placed in one of the corners, then the second king will have only two possible squares to be placed in. On the other hand, if the first king was placed in the center of the board, then the second king will have fewer options.
Overall, there are 32 possible squares for the second king to be placed in, which means that there are 32 possible ways to place two indistinguishable kings on an empty chess board so that they do not attack each other.
In summary, the answer is that there are 32 ways to place two indistinguishable kings on an empty chess board so that they do not attack each other.

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Answer:

Jack would have to buy 18 gum balls to be certain he gets 6 gum balls that are the same color.

Answer:

It's 16

Step-by-step explanation:

Imagine taking out 5 reds, after that 5 green ones and then 5 yellow gum balls. So the 16th must be number 6 of any color.

The circumference of the given circle is 14π mm.

We have,

The circumference of a circle with radius r is given by the formula:

C = 2πr

In this case,

The radius of the circle is given as 7 mm.

Substituting the value of r in the above formula.

C = 2π(7) mm

Simplifying this expression, we get:

C = 14π mm

Therefore,

The circumference of the given circle is 14π mm.

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a.

i. The initial value (IV) is 37.

ii. The percent increase or decrease is 4%.

b.

i. The initial value (IV) of the function is -0.7.

ii. The percent decrease is 40%.

a.

i. The initial value (IV) of the function is 37.

ii. The percent increase or decrease is 4%, because the base of the exponential function is 1.04, which is 1 plus 4% (0.04).

b.

i. The initial value (IV) of the function is -0.7.

ii. The percent decrease is 40%, because the base of the exponential function is 0.6, which is 60% (0.6) of the initial value (-0.7).

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The complete question:

1. For each equation, find the initial value and the percent increase or decrease.

a. f(x) = 37(1.04)ˣ

i. IV:__

ii. % Inc/Dec:_

b. f(x) = (-0.7) (0.6)ˣ

i. IV:

ii. % Inc/Dec:___

Step-by-step explanation:

1:3    means you need to find 1 /(1+3) = 1/4 th of the way to 5,8 from -2,0

x:   from -2 to +5 is 7 units     1/4th * 7 = 7 /4   added to -2

              is  - 1/4

y: from 0 to 8    is 8 units   1/4 th * 8  = 2 added to 0   is   2

(-1/4 , 2)

the maximum value of the function is y = -1 + 6cos(2π/7(26.75-5)) = 5.

The function y = -1 + 6cos(2π/7(x-5)) is a periodic function with a period of 7. The maximum value of the function occurs when the cosine function reaches its maximum value of 1.

So, we need to find the value of x that makes the argument of the cosine function equal to an odd multiple of π/2, which is when the cosine function is equal to 1.

2π/7(x-5) = (2n + 1)π/2, where n is an integer

Simplifying this equation, we get:

x - 5 = (7/4)(2n + 1)

x = 5 + (7/4)(2n + 1)

Since the function has a period of 7, we can restrict our attention to the interval [5, 12].

For n = 0, we get x = 5 + 7/4 = 23/4

For n = 1, we get x = 5 + (7/4)(3) = 26.75

For n = 2, we get x = 5 + (7/4)(5) = 33.25

For n = -1, we get x = 5 + (7/4)(-1) = 1.75

For n = -2, we get x = 5 + (7/4)(-3) = -4.75

Out of these values of x, the only one that lies in the interval [5, 12] is x = 26.75.

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The proportion of male babies less than two months old in the United States that weigh more than 10.1 pounds is 0.7554 or approximately 75.54%.

We are given the following information:

Mean = 11.9 pounds

Standard deviation = 2.6 pounds

To find the proportion of babies that weigh more than 10.1 pounds, we need to find the z-score and then find the corresponding area under the standard normal distribution curve.

1: Calculate the z-scoreWe can calculate the z-score using the formula:

z = (x - μ) / σ

where x is the weight of the baby in pounds, μ is the mean weight of male babies less than two months old in the United States, and σ is the standard deviation of the weights of male babies less than two months old in the United States.

Let's plug in the given values:x = 10.1 pounds

μ = 11.9 pounds

σ = 2.6 pounds

z = (10.1 - 11.9) / 2.6z = -0.6923 (rounded to four decimal places)

2: Find the area under the standard normal distribution curve

We can use a standard normal distribution table or a calculator to find the area under the curve for a z-score of -0.6923. Using a calculator, we get:

P(z > -0.6923) = 0.7554 (rounded to four decimal places)

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Rounding to the nearest whole number, we would expect to wait between 39 and 53 minutes about 29 times out of 29 visits using standard deviation.

We can use the normal distribution to find the probability of waiting between 39 and 53 minutes for each visit, and then multiply that probability by the number of visits to get the expected number of times waiting in that range.

First, we need to standardize the range of waiting times using the formula:

z = (x - mu) / sigma

where x is the waiting time, mu is the mean waiting time, sigma is the standard deviation, and z is the corresponding z-score.

For the lower limit of 39 minutes:

z1 = (39 - 46) / 3 = -2.33

For the upper limit of 53 minutes:

z2 = (53 - 46) / 3 = 2.33

Next, we can use a standard normal distribution table or calculator to find the probability of waiting between -2.33 and 2.33, which is approximately 0.9902.

Therefore, the expected number of times waiting between 39 and 53 minutes out of 29 visits is:

Expected number = 0.9902 * 29 = 28.68

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First, we need to find the number of students who bring lunch:

1/3 x 36 = 12 students bring lunch.

Next, we need to find the number of students who order lunch:

1/2 x 12 = 6 students order lunch.

So, the total number of students who eat lunch each day is:

12 (who bring lunch) + 6 (who order lunch) = 18 students.

Answer:

150 square inches

Step-by-step explanation:

The formula is A=2(wl+hl+hw)

Plug in the values.

2(9+33+33)

Evaluate.

=150

(Assuming both the length and width is 3)

Answer:

$21.78

Step-by-step explanation:

2.79 X 5 = 13.95

13.95 + 7.83 = 21.78

Answer:

Step-by-step explanation:

To show that points C(-4, 3), A(6, 1), and T(2, -3) form a right-angled triangle, we can calculate the slopes of the lines connecting these points.

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:

slope = (y2 - y1) / (x2 - x1)

Let's calculate the slopes of the lines formed by the points:

Slope of line CA:

m_CA = (1 - 3) / (6 - (-4))

= (-2) / 10

= -1/5

Slope of line CT:

m_CT = (-3 - 3) / (2 - (-4))

= (-6) / 6

= -1

Slope of line AT:

m_AT = (-3 - 1) / (2 - 6)

= (-4) / (-4)

= 1

Since two lines are perpendicular if and only if the product of their slopes is -1, we can check if the product of the slopes of CA and AT is -1. If it is, then the triangle formed by the points C, A, and T is a right-angled triangle.

Product of slopes m_CA and m_AT:

(-1/5) * (1) = -1/5

The product of the slopes is -1/5, which is not equal to -1. Therefore, the points C(-4, 3), A(6, 1), and T(2, -3) do not form a right-angled triangle.

Hence, we can conclude that the points C, A, and T do not form a right-angled triangle based on the slopes of the lines connecting them.

The test statistic if the sample proportion is 20/50 and the hypothesized proportion was 0.5 is:  -1.414.

Using z-test formula to determine the test statistic

z = (p - P) / [tex]\sqrt[/tex]((P(1-P))/n)

Where:

p = sample proportion = 20/50 = 0.4

P = hypothesized proportion = 0.5

n= sample size = 50

Let plug in the formula

Test statistic  = (0.4 - 0.5) / [tex]\sqrt[/tex]((0.5(1-0.5))/50)

Test statistic = (-0.1) / [tex]\sqrt[/tex]((0.25)/50)

Test statistic = (-0.1) / [tex]\sqrt[/tex](0.005)

Test statistic = (-0.1) / 0.0707

Test statistic = -1.414

Therefore the test statistic  is -1.414.

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Answer:

50.85% increase

Step-by-step explanation:

The formula for % change is (new-old)/old.

So (89-59)/59 = 30/59 = 0.5084745763 = 50.85% increase

After rewriting the final answer will be 1.

Given,

|z−6|−|z−5| , if z<5

Now,

|z-6| will be less than 0 since z is less than 5  and |z-5| will be less than 0 since z is less than 5.

So we can rewrite it as  6-z  and 5-z by removing the absolute value signs and converting them in positive .

(6-z) - (5-z)

Further,

6-z-5+z

= 1

Hence Rewriting can be done without absolute values.

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Answer:

The area is 12.57, rounded to the nearest then is 13.

Step-by-step explanation:

A=πr2=π·22≈12.56637

Answer:

Yes

Step-by-step explanation:

If you look at the graph of y = 16x^4 - 81, you see that it intersects the x-axis at two distinct places so there are two real solutions.  Whenever a polynomial function intersects the x-axis, there are at least one or more real roots.

I attached a picture of the graph using Desmos, where you'll see that there are two real roots.

Answer:

180 cm³

Step-by-step explanation:

split the side (the side facing us) into three rectangles. one rectangle immediately beneath top step, next under middles step and so on.

area under top step = (2 + 2 + 2) X 3 = 18.

area under middle step = (2 + 2) X 3 = 12

area under bottom step = 2 X 3 = 6

total area of this side (cross-section) = 18 + 12 + 6 = 36.

volume = 36 X length

=  36 X 5

= 180 cm³

The answers are explained below.

Given are the questions to be solved with the help of proportionality,

Let the unknown values be x,

a) 32 / x = 8 / 6

x = 24

Hence the height of the tree is 24 ft.

b) 3.5 / 5 = x / 3

x = 2.1

Hence the cups of flour needed is 2.1 cups.

c) 2 / 90 = 5 / x

x = 225

Hence 5 cubic ft sand will weigh 225 lbs.

d) 18.50 / 35 = 12.50 / x

x = 23

Hence $12.5 will costs for 23.

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Two regular pentagons and a regular decagon, all with the same side length, can completely surround a point. A square, a regular pentagon, and a regular $n$-gon, all with the same side length, also completely surround a point. n is 20.

A polygon having 5 sides or 5 angles is called a pentagon. The terms "pentagon" and "gonia," which both denote five angles, are the components of the word "pentagon." End to end, the four sides of a hexagon come together to create a shape. The geometric form known as a pentagon has five sides or five angles. In this case, "Penta" stands for five, and "gon" for an angle. One of the several kinds of polygons is the pentagon.

A point has an angle sum of 360 degrees.

The square's internal angles are all 90 degrees.

The regular pentagon has 108 degree internal angles.

Our unidentified polygon's interior angle is 360 - 108 - 90, or 162 degrees.

We can quickly calculate that this polygon's outer angle is 18 degrees.

Any regular polygon's outward angles add up to 360 degrees.

You get 20 times when you divide 360 by 18.

So, the polygon we don't know has 20 sides.

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The expected gain or loss from playing the game 15 times is -$75.00, indicating an expected loss of $75.00.

To determine the expected gain or loss from playing the game 15 times, we need to calculate the expected value.

The probability of getting three tails (winning) in a single coin toss is (1/2) * (1/2) * (1/2) = 1/8, since each coin toss is independent and has a 1/2 probability of landing tails.

The probability of losing in a single coin toss is 1 - 1/8 = 7/8.

If we play the game 15 times, the expected number of wins is (1/8) * 15 = 15/8, and the expected number of losses is (7/8) * 15 = 105/8.

The amount gained from winning is $10, and the amount lost from losing is $2.

Therefore, the expected gain or loss can be calculated as follows:

Expected gain or loss = (Expected number of wins * Amount gained) - (Expected number of losses * Amount lost)

= (15/8 * $10) - (105/8 * $2)

Simplifying this expression, we find:

Expected gain or loss = $187.50 - $262.50

= -$75.00

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The sample space has 13 outcomes.

We have to given that;

A player randomly selects a marble from a bag.

And, In the bag which has 5 blue marbles, 6 red, 1 orange, and 1 yellow.

Since, The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Now, We can formulate;

Total number of marbles = 5 + 6 + 1 + 1

Total number of marbles = 13

Hence, there are 13 possible outcomes for the player's selection.

Therefore, We get;

The sample space has 13 outcomes.

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Answer:Yes, because ∛84 = ∛(2 × 2 × 3 × 7) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 84 is an irrational number.

Step-by-step explanation:

Answer: i think so

Step-by-step explanation:

(a) The people that did not own a car are 13

(b) The sentence to describe the problem is "13 of every 20 people do not own a car"

Given that

Number of friends = 20

Percentage that do not own a car = 65%

Using the above as a guide, we have the following:

People = 65% * 20

Evaluate

People = 13

Writing a sentence to describe the problem, we have:

The statement is given as

65% of people do not own a car".

This can be rewritten as

"13 of every 20 people do not own a car"

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The rectangular equation that represents the polar equation r = (cot²θ)(csc θ) is y³ = x², which is an option (d).

The polar equation r = (cot²θ)(csc θ) can be written in rectangular form using the relationships x = r cos θ and y = r sin θ.

Substituting these expressions into the polar equation, we get:

r = (cot²θ)(csc θ)

r = (cos θ/sin θ)²(1/sin θ)

r = cos² θ/sin³ θ

x = r cos θ = cos³ θ/sin³ θ

y = r sin θ = cos² θ/sin² θ

As per the variable of x and y,

y³ = x².

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Answer:

Yes because if you were to continue enlarging the shape it would continue to follow the path/line of 10,1

Step-by-step explanation:

If A and B are mutually exclusive events, P(A ∩ B) = 0, and the general addition law can be simplified to the sum of the individual probabilities for A and B

Given data ,

If events A and B are mutually exclusive, it means that they cannot occur simultaneously. In this case, the intersection of events A and B, denoted as A ∩ B, would indeed have a probability of 0

And , P(A ∪ B) = P(A) + P(B)

Therefore , if A and B are mutually exclusive, the probability of either event A or event B occurring is equal to the sum of their individual probabilities.

Hence , the probability is solved

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