the time spent waiting in the line is approximately normally distributed. the mean waiting time is 5 minutes and the standard deviation of the waiting time is 2 minutes. find the probability that a person will wait for more than 9 minutes. round your answer to four decimal places.

In the given right triangle, using SOH CAH TOA, the value of x is 9

From the question, we are to determine the value of x in the given diagram.

The diagram, shows a right triangle with a hypotenuse of 18 and included angle of 30°. x is opposite side.

To determine the value of x, we will use SOH CAH TOA

Where

sin (angle) = Opposite / Hypotenuse

cos (angle) = Adjacent / Hypotenuse

tan (angle) = Opposite / Adjacent

Thus,

We can write that

sin (30°) = x / 18

1/2 = x / 18

Cross multiply

2 × x = 1 × 18

2x = 18

Divide both sides by 2

2x / 2 = 18 / 2

x = 9

Hence, the value of x is 9

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A sequence of transformations that would produce the same result include the following: C. a reflection over the x-axis and then a reflection over the y-axis.

In Mathematics and Geometry, a reflection over or across the x-axis is modeled by this transformation rule (x, y) → (x, -y).

By applying a reflection over the x-axis to the coordinate of the given triangle ABC, we have the following coordinates for A':

Coordinate A = (4, 3)   →  Coordinate A' = (4, -3)

By applying a reflection over the y-axis to the coordinate of the given triangle A'B'C', we have the following coordinates for A'':

Coordinate A' = (4, -3)   →  Coordinate A'' = (-(4), -3) = (-4, -3).

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Complete Question:

Triangle ABC is rotated 180º using the origin as the center of rotation.

Which sequence of transformations will produce the same result?

a translation up 4 and then a reflection over the y-axis

a translation up 4 and then a translation right 6

a reflection over the x-axis and then a reflection over the y-axis

a translation right 6 and then a reflection over the x-axis

Christopher's total bill including the 10% tip is $39.60.Christopher's meal at the cafe costs $36.00. To calculate the 10% tip, we need to find 10% of $36.00, which is $3.60.

To get the total bill including the tip, we need to add the cost of the meal and the tip together. So, $36.00 + $3.60 = $39.60. Therefore, Christopher's total bill including tip is $39.60. It's important to remember to always calculate the tip based on the cost of the meal before tax, and not to include the tax in the calculation.

Leaving a tip is a common practice in restaurants and cafes to show appreciation for good service, and it's typically between 15-20% of the cost of the meal. It's also important to consider the quality of service when deciding on how much to tip.

Christopher's total bill including the 10% tip is $39.60

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Answer: the last one

Step-by-step explanation:

factor the quadratic expression, the greatest common factor is 3, 3(4x^2-12x+9) is a perfect trinomial square. There is only one root 3/2 but it is a double

False. When performing regression analysis, different samples will not necessarily yield the same sample regression line.

This is because the sample regression line is based on the specific data points in the sample, and different samples may have different data points that can lead to different regression lines. However, if the samples are representative of the same population and the relationship between the variables is consistent, the regression lines may be similar. The term "content loaded" does not apply to this question.

False. When performing regression analysis, different samples will not all yield the same sample regression line. The regression line depends on the specific data points in the sample, so if you have different samples, it's likely that their regression lines will be different as well.

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Answer: y=108=108

Step-by-step explanation:

So first you will −21=−14y+6−21=−14+6 then you subtract 24 fom both sides

The areas of the sectors for arc lengths of 4, 5, 10, and l units are approximately 3.14, 3.93, 9.42, and 0.84l units², respectively.

To find the area of a sector of a circle, we need to use the formula:

Area of sector = (angle of sector/360) x πr²

where r is the radius of the circle.

For each given arc length, we need to find the angle of the sector first. The formula for finding the angle of a sector is:

angle of sector = (arc length / radius) x 180/π

Using this formula, we get:

For 4 units arc length:
angle of sector = (4/6) x 180/π ≈ 38.2 degrees
Area of sector = (38.2/360) x π x 6² ≈ 3.14 units²

For 5 units arc length:
angle of sector = (5/6) x 180/π ≈ 47.7 degrees
Area of sector = (47.7/360) x π x 6² ≈ 3.93 units²

For 10 units arc length:
angle of sector = (10/6) x 180/π ≈ 95.5 degrees
Area of sector = (95.5/360) x π x 6² ≈ 9.42 units²

For l units arc length:
angle of sector = (l/6) x 180/π ≈ (30l/π) degrees
Area of sector = [(30l/π)/360] x π x 6² ≈ 0.84l units²

So, the areas of the sectors for arc lengths of 4, 5, 10, and l units are approximately 3.14, 3.93, 9.42, and 0.84l units², respectively.
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Answer:

A: Chicken: 75 / Steak: 125 / Fish: 50

B: The wedding planner's claim is valid.

C: The wedding planner's claim is valid because if we follow the sample and use the ratio, the total amount of guests who might choose chicken and steak is about 200 people.

Apologies if this answer isn't thorough enough, I tried to do it as quickly as possible. Best of luck!

The probability of more than four successes. is 0.88618

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

n = 8 and p = 0.75

The individual probability is calculated as

P(x) = nCx * p^x * (1 - p)^(n - x)

For more than four successes, the values of x are

x = 5, 6, 7 and 8

So, we have

P(x > 4) = P(5) + P(6) + P(7) + P(8)

This gives

P(5) = 8C5 * 0.75^5 * 0.25^3

P(6) = 8C6 * 0.75^6 * 0.25^2

P(7) = 8C7 * 0.75^7 * 0.25^1

P(8) = 8C8 * 0.75^8 * 0.25^0

When evaluated, we have

P(x > 4) = 0.88618

Hence, the value is 0.88618

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The estimated spread in sample means or averages is d. the estimated standard error.

The estimated spread in sample means or averages is typically represented by the estimated standard error. The population standard deviation is a measure of the spread of values in the entire population, whereas the estimated standard error is a measure of the spread of values in a sample. The estimated standard error is calculated by dividing the sample standard deviation by the square root of the sample size, and it provides an estimate of the variability in sample means that is expected due to chance alone. Therefore, the correct answer to the question is d) the estimated standard error.

The estimated standard error is used to measure the variability of sample means or averages around the true population mean. It is calculated by dividing the sample standard deviation by the square root of the sample size. This value helps in understanding the precision of the sample mean as an estimate of the true population mean.

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The correct sample space for this random experiment is:
{BG, GB, BBG, BGB, GBB, GGB, GBG, GG} where B represents a boy and G represents a girl.

To find the correct sample space:

The first two outcomes, BG and GB, represent the couple having one boy and one girl in their first two children, respectively.

The next three outcomes, BBG, BGB, and GBB, represent the couple having two boys and a girl, a boy, a girl and a boy, and a girl and two boys, respectively, before having at least one boy and one girl.

The last three outcomes, GGB, GBG, and GG, represent the couple having two girls and a boy, a girl, a boy and two girls, and three girls, respectively, before having at least one boy and one girl

The sample space includes all possible combinations of children that the couple can have, including having only one boy or one girl, or having up to three children but stopping after they have one boy and one girl.

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The value of angle N is  10⁰.

The value of angle N is calculated by applying intersecting chord theorem as shown below;

This theory states that the tangent angle formed at the circumference is half of the arc angles formed by the intersecting chords.

If line NL is the diameter of the circle, then arc angle NL = 180⁰ (half of angle of a circle)

The value of arc LM is calculated as follows;

arc LM = 360 - ( 180 + 160)

arc LM = 20⁰

The value of angle N is calculated as follows;

∠N = ¹/₂ x 20⁰

∠N = 10⁰

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According to the scatter plot below, when x = 5, the value of y is 1.

We know that,

A scatter plot is a form of plot or mathematical diagram that displays values for two variables for a collection of data using Cartesian coordinates. One more variable can be presented if the points are programmed.

A scatter plot is a collection of dots drawn on two axes, horizontal and vertical. Scatter plots are useful in statistics because they illustrate the amount, if any, of correlation between the values of observed quantities or events (called variables).

With a particular confidence interval, a scatter plot might imply several types of relationships between variables.

Weight and height, for example, would be on the y-axis, whereas height would be on the x-axis. Positive (increasing), negative (falling), or null correlations exist (uncorrelated).

Here,

Based on the scatter plot below, when x=5 then value of y is 1.

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The statement "the margin of error of a confidence interval is the error from biased sampling methods" is false. The margin of error of a confidence interval is not the error from biased sampling methods.

The margin of error represents the range within which the true population parameter (such as the mean or proportion) is likely to be found with a certain level of confidence. It is not directly related to biased sampling methods, which refer to systematic errors in the sampling process that may lead to inaccurate or unrepresentative results.

The margin of error of a confidence interval is the measure of how much the sample statistic is likely to differ from the population parameter, given a certain level of confidence. It is affected by sample size, variability, and the chosen level of confidence, but not biased sampling methods.

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For a study that has one independent variable with three levels and 4000 participants per level, the recommended maximum number of analyses (comparisons or contrasts) to plan b. Two, because this is one less than the number of groups.

The recommended maximum number of analyses (comparisons or contrasts) to plan for a study that has one independent variable with three levels and 4000 participants per level is b. Two, because this is one less than the number of groups. Each level of the independent variable will need to be compared to the other two levels, resulting in two independent research questions. It is important to limit the number of analyses to avoid increasing the chance of making a Type I error.

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You need approximately 5 terms (starting from n=4) to achieve an error less than 0.001.  To determine the number of terms required to approximate the sum of the series with an error of less than 0.001.

We can use the alternating series error bound formula:

Error ≤ |Rn| ≤ an+1

Where Rn is the remainder or error in the nth partial sum, and an+1 is the absolute value of the (n+1)th term in the series.

In this case, the alternating series is:

∑
[infinity]
n=4
(−1)n+1
n4

To find the absolute value of the (n+1)th term, we can plug in n+1 for n:

|an+1| = |(−1)n+2/(n+1)4|

Since we want the error to be less than 0.001, we can set up the inequality:

|an+1| ≤ 0.001

Plugging in the formula for |an+1| and solving for n, we get:

|(−1)n+2/(n+1)4| ≤ 0.001

(n+1)4 ≥ 1000

Taking the fourth root of both sides, we get:

n+1 ≥ 5.623

n ≥ 4.623

Therefore, we need at least 5 terms to approximate the sum of the series with an error of less than 0.001.

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1. True or False? If Z is a random variable from a standard normal distribution and if P(Z

It seems like the question is incomplete. Please provide the complete question to get an accurate answer.

2. True or False? If z is a random variable with a standard normal distribution and if a is a positive number and if P(z > a) = 0.15, then P(-a < z < a) = 0.7?

Answer: True

Explanation: Since z follows a standard normal distribution, it is symmetric around the mean (which is 0). So, P(z > a) = P(z < -a) = 0.15. To find the probability between -a and a, we can use the property P(-a < z < a) = 1 - P(z > a) - P(z < -a) = 1 - 0.15 - 0.15 = 0.7.

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Your answer: B. The counselors form groups of 9 students based on the students' majors. Then, the counselors select all of the students in 6 randomly chosen groups.

Option A would best describe a cluster sample of students. The counselors are forming groups based on a common characteristic (number of classes taken) and then randomly select students from each group. This ensures that a variety of students are included in the sample and reduces the potential for bias.

Option B involves selecting all students in randomly chosen groups, which may not provide a representative sample of the entire student population.

Option C involves selecting students at regular intervals, which could result in a sample that is not random and may not accurately represent the entire student population.
Your answer: B. The counselors form groups of 9 students based on the students' majors. Then, the counselors select all of the students in 6 randomly chosen groups.

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The radius of the circle is 3 units and the center of the circle is (1, 0). Then the correct options are A, B, and E.

Given that:

Equation of circle, x² + y² - 2x - 8 = 0

Convert the equation into a standard form, then we have

x² + y² - 2x = 8

x² - 2x + 1 + y² = 9

(x - 1)² + y² = 3²

The radius of the circle is 3 units and the center of the circle is (1, 0). Then the correct options are A, B, and E.

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The complete question is given below.

Answer: The exponential function that models the population growth of the city over time is:

y = 350,000 * (1 + 0.044)^t

where t is the number of years since the start of the study, y is the city's population, and 0.044 is the annual growth rate expressed as a decimal.

The function is an example of exponential growth, where the population is increasing at a constant rate over time.

Step-by-step explanation:

The median of the set of numbers after arranging them in order from least to greatest {0.6, 0.9, 1.7, 1.1, 2.5, 0.6} is 1.

To find the median of a set of numbers, we need to first arrange them in order from least to greatest.

The set of numbers given is 0.6, 0.9, 1.1, 1.7, 2.5, and 0.6.

Arranging them in order, we get 0.6, 0.6, 0.9, 1.1, 1.7, 2.5.

Since there are six numbers in this set, the median is the middle number when they are arranged in order. In this case, the middle numbers are 0.9 and 1.1. To find the median, we take the average of these two numbers:

Median = (0.9 + 1.1)/2 = 1.

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Step-by-step explanation:

0.6,0.6,0.9,1.1,1.7,2.5

The median is 0.9+1.1 / 2

2 /2 = 1

the median of the distribution is 1

The producer surplus at the equilibrium point (1600, 80) is $64,000.

In order to calculate the producer surplus, we first need to find the equilibrium price and quantity, which you have already determined as (1600, 80). Now, let's find the supply function, S(x), and the price at which quantity supplied is zero.
You've provided the supply function as "p = S(x) 25 V", but it seems to have some typos. Assuming the correct supply function is p = 25x, let's proceed.
Set the supply function, p = 25x, equal to 0:
0 = 25x
x = 0
Now we have the points (0, 0) and (1600, 80) to calculate the producer surplus. Producer surplus is represented by the area of a triangle. The base of the triangle is the equilibrium quantity (1600), and the height is the equilibrium price (80).
Use the formula for the area of a triangle: Area = (1/2) * base * height
Producer Surplus = (1/2) * 1600 * 80
Producer Surplus = 0.5 * 128000
Producer Surplus = 64,000

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The value cosθ is 0.707.

The value angle z is -45⁰, and 45⁰.

The value of angle θ  is 45⁰ and 315⁰.

The value cosθ, and angle Z is calculated by applying trigonometry ratio as follows;

for question 6,

tan θ = opposite side/adjacent

tan θ = 5/5

tan θ = 1

θ = 45⁰ = z

cos θ = 0.707

for question 7;

tan z = opp/adjacent

tan z = -5/5

tan z = -1

z = arc tan (-1)

z = -45⁰ =

The value of θ is calculated as;

θ = 360 - 45

θ = 315

cos (315) = 0.707

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In summary, the inequality x ≤ 2 represents the problem "the price of a ball should not be more than $2" and means that the value of x (the price of the ball) must be less than or equal to 2.

An inequality is a mathematical expression that compares two values and indicates whether they are equal or not, or whether one is greater than or less than the other. In this case, we want to represent the problem "the price of a ball should not be more than $2" using an inequality.

Let x be the price of the ball. The expression "the price of a ball should not be more than $2" means that the price of the ball, represented by x, must be less than or equal to $2. We can write this inequality as:

x ≤ 2

The symbol "≤" means "less than or equal to," and it indicates that the value of x should be less than or equal to 2. For example, if the price of the ball is $1.50, then x is less than 2, and the inequality x ≤ 2 is true. However, if the price of the ball is $3, then x is greater than 2, and the inequality x ≤ 2 is false.

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A basis for the subspace is {1, [tex]x^2[/tex]}, and the dimension of the subspace is 2.

a. To find a basis for the subspace {a(1 + x) + b(x + x^2) : a, b ∈ R} of P2, we need to find a set of vectors that are linearly independent and span the subspace. We can rewrite the polynomials in the form a + bx + cx^2 and then look for a linearly independent set.

If we set a = 1 and b = 0, we get the polynomial 1 + x, which is in the subspace. If we set a = 0 and b = 1, we get the polynomial x + x^2, which is also in the subspace. These two polynomials are linearly independent since neither is a scalar multiple of the other.

Therefore, a basis for the subspace is {1 + x, x + x^2}, and the dimension of the subspace is 2.

b. To find a basis for the subspace {(a + b(x + x^2)) : a, b ∈ R} of P2, we again need to find a set of vectors that are linearly independent and span the subspace. We can rewrite the polynomials in the form a + bx + cx^2 and then look for a linearly independent set.

If we set b = 0, we get the polynomial a, which is in the subspace. If we set a = 0 and b = 1, we get the polynomial x + x^2, which is also in the subspace. These two polynomials are linearly independent since neither is a scalar multiple of the other.

Therefore, a basis for the subspace is {1, x + x^2}, and the dimension of the subspace is 2.

c. To find a basis for the subspace {p(x) : p(1) = 0}, we need to find a set of polynomials that satisfy the given condition and span the subspace.

A polynomial p(x) that satisfies p(1) = 0 must have a factor of (x - 1). Therefore, we can write any polynomial in the subspace as p(x) = (x - 1)q(x), where q(x) is a polynomial of degree 1 or 0.

If we set q(x) = 1, we get the polynomial x - 1, which is in the subspace. If we set q(x) = 0, we get the zero polynomial, which is also in the subspace. These two polynomials are linearly independent since neither is a scalar multiple of the other.

Therefore, a basis for the subspace is {x - 1}, and the dimension of the subspace is 1.

d. To find a basis for the subspace {p(x) : p(x) = p(-x)}, we need to find a set of polynomials that satisfy the given condition and span the subspace.

A polynomial p(x) that satisfies p(x) = p(-x) must be an even function. Therefore, we can write any polynomial in the subspace as p(x) = a + bx^2, where a and b are constants.

If we set a = 1 and b = 0, we get the polynomial 1, which is in the subspace. If we set a = 0 and b = 1, we get the polynomial x^2, which is also in the subspace. These two polynomials are linearly independent since neither is a scalar multiple of the other.

Therefore, a basis for the subspace is {1, x^2}, and the dimension of the subspace is 2.

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Answer:

15.75cm^2

Step-by-step explanation:

9 × 3.5 × 1/2 = 15.75cm^2

I hope the answer is correct

Answer:

AB=CD=10,AD=BC=29

Step-by-step explanation:

11111111111

Answer:

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

AD and AB are adjacent sides hence their sum is half the perimeter:

And we are given that AD is 9 more than twice AB:

Substitute this into first equation:

Find AD by substituting the value of AB:

So the side lengths are:

Answer:520? for the mean?neareast answer and 75 for the median

Step-by-step explanation:

The experimental probability it lands on yellow is 4/5

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

Number of times = 30

Results:  (R=7 Y=8 B=6 G=9)

The experimental probability it lands on yellow is

P(Yellow) = Y/Total

So, we have

P(Yellow) = 8/30

Simplify

P(Yellow) = 4/15

Hence, the probability is  4/15

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The area of the windshield swept by the wiper blade, found using the formula for finding the area of a sector of a circle is 1470·π cm²

A sector of a circle is a part of a circle surrounded by two radius and part of the circumference.

The length of the wiper = 60 cm

The length of swing arm from the pivot to the wiper-blade tip = 72 cm

The area the length of the swing arm to the wiper-blade tip sweeps can be obtained from the area of a sector of a circle as follows;

The area swept by the circle with a radius of 72 cm = (105/360) × π × 72² cm²

(105/360) × π × 72² cm² = 1512·π cm²

The area of the not swept by the wiper blade =  (105/360) × π × (72 - 60)² cm²

(105/360) × π × (72 - 60)² cm² = (105/360) × π × 12² cm² = 42·π cm²

The area swept by the wiper blade is therefore;

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