Canada and the European Union require that cars be equipped with "daytime running lights," headlights that automatically come on at a low level when the car is started. Many manufacturers are now equipping cars sold in the United States with running lights. Will running lights reduce accidents by making cars more visible? An experiment conducted in a driving simulator suggests that the answer may be "Yes." What concerns would you have about generalizing the results of such an experiment?

To simplify [tex]\frac{2-i}{5+i} = \frac{9}{26} -\frac{7}{26} i[/tex] , multiply the numerator and denominator by the conjugate of the denominator.

A complex number's conjugate A+bi equals a-bi. A real number is the result of a complex number and its conjugate. That fact will be used here.

[tex]\frac{2-i}{5+i} =\frac{2-i}{5+i} . \frac{5-i}{5-i}[/tex]

[tex]= \frac{(2-i)(5-i)}{(5+i)(5-i)}[/tex]

[tex]=\frac{10-2i-5i-1}{25-5i+5i+1}[/tex]

[tex]=\frac{9-7i}{26}[/tex]

[tex]=\frac{9}{26}-\frac{7}{26}i[/tex]

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Step-by-step explanation:

a probability is always the ratio

desired cases / totally possible cases

in our case the desired cases are all students with financial aid : 6101

and the totally possible cases are 10730.

so, the probability to pick a student at random, who receives financial aid is

6101 / 10730 = 0.568592731... = 56.8592731...% ≈

≈ 57%

At x = 0 and x = 2, the curve defined by y² = x³ - 3x² has a horizontal tangent.

We have,

First, let's find the derivative of y with respect to x.

We can rewrite the equation as:

y² = x³ - 3x²

y = (x³ - 3x²)^(1/2)

Now, differentiating y with respect to x using the chain rule:

dy/dx = (1/2) * (x³ - 3x²)^(-1/2) * (3x² - 6x)

Next, we set the derivative equal to 0 to find the values of x where the curve has a horizontal tangent:

(1/2) * (x³ - 3x²)^(-1/2) * (3x² - 6x) = 0

We can disregard the constant factor of (1/2) since it doesn't affect the solution.

Thus, we have:

(x³ - 3x²)^(-1/2) * (3x² - 6x) = 0

To have a horizontal tangent, the slope of the curve should be 0, which means the derivative is equal to 0.

Now, we have two factors to consider:

(x³ - 3x²)^(-1/2) = 0, which means the expression inside the parentheses is equal to 0. However, this does not yield a real solution.

(3x² - 6x) = 0, which means the quadratic term equals 0.

Solving this quadratic equation:

3x² - 6x = 0

3x(x - 2) = 0

This equation has two solutions: x = 0 and x = 2.

Therefore,

At x = 0 and x = 2, the curve defined by y² = x³ - 3x² has a horizontal tangent.

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Answer:

2 grams per millimeter

Step-by-step explanation:

the point (2,1) shows us this.

(1) The measure of the angle CFD = 48°.

(2) The measure of the angle AFE = 48°.

(3) Pair of supplementary angles: Angle BFC and angle CFD.

(4) Pair of adjacent angles: Angle AFB and angle BFD.

What are the properties of angles?

The angle properties of lines are:

Vertically opposite angles are equal, for example, a = d, b = c.

Adjacent angles add to 180, for example, a + b = 180, a + c = 180. Corresponding angles are equal, for example, a = e, b = f, c = g, d= h.

(2) In the given figure, m∠BFC = 42°

By using the property of linear pair, we can write

       ∠BFC + ∠CFD = 180

         42 + ∠CFD = 180

        ∠CFD = 58.

(2) Angle CFD and angle AFE are opposite angles and opposite angles are same in measurement so we can write

             m∠AFE = 58°.

(3) Pair of supplementary angles: Angle BFC and angle CFD.

(4) Pair of adjacent angles: Angle AFB and angle BFD.

Hence,

(1) The measure of the angle CFD = 48°.

(2) The measure of the angle AFE = 48°.

(3) Pair of supplementary angles: Angle BFC and angle CFD.

(4) Pair of adjacent angles: Angle AFB and angle BFD.

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The monthly cost for 66 minutes of calls will be $15.84.

Monthly cost is the payment or the bill amount that needs to be paid at the end of the month.

The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes)

The monthly cost for 45 minutes of calls = $14.40

The monthly cost for 102 minutes = $19.53

The above values can be paired in groups so as to satisfies the coordinates of a linear function

(45,14.40)  and (102,19.53)

Finding the slope of the graph using these points

slope, m=Δy/Δx

m=Δy=19.53 - 14.40 = 5.13

Δx=102 - 45 = 57

m = 5.13/57 =0.09

Finding the equation of the linear function using m = 0.09, and point (45,14.40)

m=Δy/Δx

0.09=y-14.40/x-45

0.09(x-45)=y-14.40

0.09x-4.05=y-14.40

0.09x-4.5+14.40=y

y=0.09x + 9.9

So for 66 minutes, the cost will be;

x = 66, y = ?

y=0.09*66 + 9.9

y=5.94+9.9 = $15.84

The monthly cost for 66 minutes of calls is $15.84.

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The graph of Stewart's assignment added as an attachment

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

Number of assignments = 36

Rate of assignment per day = 4

This means that the equation of the scenario is

Number of assignments remaining = Initial number of assignments - Rate of assignment per day * Number of days

Represent the number of assignments remaining with y and the number of days with x

So, we have the following representation

y = Initial number of assignments - Rate of assignment per day * x

Substitute the known values in the above equation, so, we have the following representation

y = 36 - 4 * x

Evaluate the products

y = 36 - 4x

So, the equation is y = 36 - 4x and the graph is added as an attachment

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The number of ounces of water that would be wasted in one day is 12.173 ounces.

An equation in which two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls) 40% are girls, and 14% are boys. The ratio formula is written as a: b a/b for any two numbers. Contrarily, the percentage formula is written as a:b::c:da:b::c:da:b=cd.

Given,

The faucet drips per every minute.

1 min -------1/4 ml

for 60 min -----?

x=(1/4)×60

x=15 ml

For one day,

15 ml×24 hours=360 ml

Therefore, 360 ml=12.173 ounces.

Hence, the number of ounces of water that would be wasted in one day is 12.173 ounces.

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Answer:

θ = 56°

Step-by-step explanation:

As OA and OB are both radii, triangle AOB is an isosceles triangle:

⇒ m∠ABO = m∠OAB = 48°

Interior angles of a triangle sum to 180°:

⇒ m∠ABO + m∠OAB + m∠AOB = 180°

⇒ 48° + 48° + m∠AOB = 180°

⇒ m∠AOB = 180° - 48° - 48°

⇒ m∠AOB = 84°

Angles on a straight line sum to 180°:

⇒ m∠AOB + m∠DOB = 180°

⇒ 84° + m∠DOB = 180°

⇒ m∠DOB = 180° - 84°

⇒ m∠DOB = 96°

The tangent of a circle is always perpendicular to the radius.

Therefore, tangent BC is perpendicular to radius OB, and tangent DE is perpendicular to radius OD, so:

OBCD is a quadrilateral.

The interior angles of a quadrilateral sum to 360°:

⇒ m∠OBC + m∠BCD + m∠CDO + m∠DOB = 360°

⇒ 90° + θ + 28° + 90° + 96° = 360°

⇒ θ + 304° = 360°

⇒ θ = 360° - 304°

⇒ θ = 56°

Answer: 2

Step-by-step explanation:

The transition to -24 degrees will take three hours .The balance between energy coming into and going out of the planet's system determines its temperature.

Explanation:

-8% / -24 = 3.

The transition to -24 degrees will take three hours.

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Answer:

9/20 or 0.45

Step-by-step explanation:

The least common multiple of 12, 20 and 6 is 60. Reducing the fractions to the denominator 60 we have:

[tex] \bold{ \dfrac{7}{12} + \dfrac{4}{20} - \dfrac{2}{6} = \dfrac{35}{60} + \dfrac{12}{60} - \dfrac{20}{60} } \\ \\ \bold{= \frac{35 + 12 - 20}{60} = \frac{27}{60} = \frac{9}{20} }[/tex]

If any addend is an integer, an I is placed as denominator and the same operation is done.

Answer:

No

Step-by-step explanation:

To prove 2 triangles an congruent we need three pieces of information

SSS or SAS or ASA or RHS

S - Side

A - Angle

R - Right angle

H - Hypotenuse

We have an angle side and another side

So these two triangles can be proved congruent by SAS

Hope this helped and have a good day

Answer:

20.8

Step-by-step explanation:

y = x^2

Given the value of y = 432, the equation would be:

432 = x^2

x is found by finding the square root of 432

sqrt 432 = sqrt (x^2)

x = 20.8

Check:

20.8^2 = 432.64

Your final answer would be 20.8.

The [tex]n^{th[/tex] term of an exponentially increasing sequence can be found using the formula:

[tex]a_n = a_1[/tex] × [tex]r^(^n^-^1^)[/tex]

To find the [tex]n^{th[/tex] term of a sequence, you can use a formula that defines the relationship between the terms of the sequence. In this particular sequence, the terms seem to be increasing exponentially, with each term being the square of the previous term.

The [tex]n^{th[/tex] term of an exponentially increasing sequence can be found using the formula:

[tex]a_n = a_1[/tex] × [tex]r^(^n^-^1^)[/tex]

where [tex]a_n[/tex] is the nth term of the sequence, [tex]a_1[/tex] is the first term of the sequence, and r is the common ratio.

In this case, the first term is 2, and the common ratio is the previous term divided by the term before it. In this sequence, the common ratio is [tex]\frac{4}2=2[/tex]

Therefore, the [tex]n^{th}[/tex] term of the sequence can be found using the following formula:

[tex]a_n = 2[/tex] × [tex]2^{(n-1)[/tex]

So to find the [tex]n^{th[/tex] term, you would plug in the value of n into the formula. For example, to find the fifth term of the sequence, you would plug in 5 for n:

[tex]a_5 = 2[/tex] × [tex]2^{(5-1)[/tex]

= 2 × [tex]2^4[/tex]

= 2 × 16 = 32

So the fifth term of the sequence is 32

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.13 can be expressed in the form of percentage as 13%.

In order to convert numbers in decimal into percentage we only need to multiply the given number with 100 and after multiplying the number with hundred it can be written in percentage form. Like in the question given number is 0.13 and we need to express this in form of percentage. So in order to express this number in percentage we just multiply it with 100 which will be equal to 13% i.e

0.13 x 100 = 13%

By multiplying a decimal value by 100 and adding the percentage (%) sign, you can turn a decimal value into a percentage. A decimal multiplied moves the decimal point two places to the right.

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Answer:

The two equations that can be used are 7.50a + 4.50s = 3150, and

 a + s = 500.

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

a + s = 3,150  NO

7.5a + 4.5s = 3,150 YES

a + s = 500    YES

7.5s + 4.5a = 500  NO

Step-by-step explanation:

We know that a + s = 500.

Total sales would be the product of the number of adult and student tickets times their repsective prices:

Total Sales ($) = $7.50a + $4.50s = $3150

Leaving off the units for the next steps, we have two equations and we can rearrange one of them to substitute into the other.  

1)   Rearrange the first equation to isolate a:  a = 500-s

Now use this definition of a in the second equation:

7.50a + 4.50s = 3150

7.50(500-s) + 4.50s = 3150

3750 - 7.5s + 4.50s = 3150

 -3s = -600

    s = 200  student tickets were sold

Use a+s=500 to find a:  

a+200 = 500

     a=300   300 adult tickets were sold.

================

The two equations we used to find this answer were:

7.50a + 4.50s = 3150, and

 a + s = 500

Answer:

-3

Step-by-step explanation:

5 + ( -8 )

-8 - 5 = -3

so final answer: -3 because ( - 8 ) so the ( - ) would go on the answer

Answer: -3

Step-by-step explanation: It would be -3 because since we are adding a negative it would go toward the negative side. Also, it can be modeled as:

5 - 8

This would still = -3.

The Central Limit Theorem establishes that the sampling distribution of the sample means of size n can be approximated to a normal distribution with mean and standard deviation s = /n for a normally distributed random variable X, with mean and standard deviation.

The Central Limit Theorem can also be used with skewed variables if n is at least 30.

The sampling distribution of the sample percentage for a proportion p in a sample of size n will be about normal, with mean and standard deviation s = p(1-p)/n.

The mean is the difference between the means when two normal variables are subtracted, and the standard deviation is the square root of the sum of the variances.

Average gas mileage (A): Mean 36, SD 6, sample size 50:

So, μA = 36, sA = 6/√50 = 0.8485

Gas mileage B: Mean 42, SD 8, and sample size of 50:

So, μB = 42, sB = 8/√50 = 1.1314

Arrangement of the difference:

Mean: 36 - 42 = -6 where A - B

Standard deviation: 1.4142

Locate the point estimate.

This is the mean difference, which is -6 mpg.

To determine our level, we must deduct 1 from the confidence interval and divide the result by two. So: 1 - 0.95/2 = 0.025

Now that z has a pvalue of, we must locate it in the Ztable.

Z = 1.96 since it has a pvalue of.

Identify the margin of error M as follows.

M = zs = 1.96 * 1.4142 = 2.77

2.77 mpg is the error margin.

The sample mean plus M determines the interval's upper end. Therefore, it is -6 + 2.77 = -3.23 mpg.

The difference between the population mean gas mileage for engines A and B and how to interpret the data, in mpg, have a 95% confidence interval of (-8.77, -3.23) means, whereas the standard deviation is the sum of the variances' square roots.

Average gas mileage (A): Mean 36, SD 6, sample size 50:

So, μA = 36, sA = 6/√50 = 0.8485

Gas mileage B: Mean 42, SD 8, and sample size of 50:

So, μB = 42, sB = 8/√50 = 1.1314

Arrangement of the difference:

Mean: 36 - 42 = -6 where A - B

Standard deviation: 1.4142

Locate the point estimate.

This is the mean difference, which is -6 mpg.

B. Determine the error margin.

By subtracting 1 from the confidence interval and dividing the result by 2, we can determine our level. So: 1 - 0.95/2 = 0.025

We must now locate z in the Ztable because it has a pvalue of

Z = 1.96 since that has a p value of.

Find the margin of error now. such that M

M = zs = 1.96 * 1.4142 = 2.77

The error margin is 2.77 mpg.

C. Build the 95% confidence interval for the difference between the population-mean fuel economy for engines A and B, then analyze the findings (5 pts)

The sample mean multiplied by M determines the interval's upper end. Consequently, it is -6 + 2.77 = -3.23 mpg.

The 95% confidence interval for the difference between population mean gas mileage for engines A and B and how to interpret the data, in mpg, is (-8.77, -3.23).

You should calculate the population standard deviation when the dataset you’re working with represents an entire population, i.e. every value that you’re interested in. The formula to calculate a population standard deviation, denoted as σ.

A % confidence interval (CI) for the population mean is given by Example 6.2 A meat inspector has randomly measured 30 packs of acclaimed 95% lean beef. The sample resulted in the mean 96.2% with the sample standard deviation of 0.8%.

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1/8 of a number is 56. The number is equal to 448.

let the number=x

1/8 of a number means we have to multiply 1/8 with x.

1/8 of a number =1/8x

now according to the condition, 1/8 of a number is 56 which means that we have 1/8x equal to 56.

1/8x=56

which gives us a simple algebraic equation in a single variable x. we can solve it accordingly .i,e multiplied 8 on both sides of the equation gives

x=56*8

x=448.

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For queuing system B, the average time in queue ids going to change significantly as a result of increased utilization.

This is because queuing system B is initially heavily loaded and has less capacity to handle more requests. As a result, an increase in utilization can cause a significant increase in average queue latency on system B compared to system A.

Average Queue Time is a measure of the time a customer or request spends being processed by a server. It is affected by several factors such as server load, customer or request arrival rate, and server service rate. As the load on the queuing system increases, it means that the server is being used more frequently and is no longer available to process incoming requests. This will increase the average time in the queue as more requests accumulate and have to wait to be processed. The greater the increase in occupancy, the greater the impact on average latency.

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When collecting quantitative data you can use a statistical formula to give you a rough estimate of the sample size you will need. When collecting qualitative data, however, the rule of thumb is to have as representative of a sample as possible that will allow you to exhaust the knowledge you could learn from the population.

Macroinvertebrate sampling provides a relatively easy way to assess the water quality of a stream. The types and numbers of macroinvertebrates (mostly insect larvae/nymphs) that form the biological community at a particular stream location are shaped by both the nature of the stream and the quality of water that drains into the stream.

6x³ -4x² +4 is the additive inverse of polynomial -6x³ +4x² -4

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

The given polynomial is  -6x³ +4x² -4

Polynomial is minus six x cube plus four x square minus four.

Additive inverse simply means changing the sign of the number and adding it to the original number to get an answer equal to 0.

6x³ -4x² +4 is the additive inverse of -6x³ +4x² -4

because -6x³ +4x² -4+6x³ -4x² +4=0

Hence, 6x³ -4x² +4 is the additive inverse of polynomial -6x³ +4x² -4

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The probability that they all are women is 0.0333 and that two of them are men is 0.50

There are 6 men and 4 women in your committee, that gives you a total of 10 people to choose from.

Without restrictions, there's a total of 10C3 ways to choose a subcommittee of 3 people.

a) A subcomitte of 3 people consisting of all women can be chosen in 6C0*4C3 ways.

So, the probability for the first problem is 6C0*4C3/10C3 = 0.0333

b) A subcommittee consisting of 2 men and 1 woman can be chosen in 6C2*4C1 ways.

So, the probability for this problem is 6C2*4C1/10C3 = 0.50.

Therefore, the probability that they all are women is 0.0333 and that two of them are men is 0.50.

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Disclaimer

the question given by you is incomplete, the answer is solved as per a similar question and the question is

A committee consist of six men and four women. A subcommittee is made by randomly choosing three of the committee members. What is the probability that: a. they are all women b. two of them are men?

Answer: 11.5 maybe ? {sorry if its wrong]

Step-by-step explanation:

3, possibilities are there for the digit that was written.

Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.

Create a square on paper by using a pencil. Tw dimensions make it up. A shape's area on paper is the space it takes up.

Imagine that your square is made up of smaller unit squares.

The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.

To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.

According to our question-

Not a multiple of 3, 7+5+7+0=19

Not a multiple of 3, 7+5+7+1=20

Multiple of three: 7+5+7+7+2=21

Not a multiple of 3, 7+5+7+3=22

Not a multiple of 3, 7+5+7+4=23

Multiple of three: 7+5+7+7+5=24

Not a multiple of 3, 7+5+7+6=25

Not a multiple of 3, 7+5+7+7=26

7+5+7+8=27 multiple of 3

Not a multiple of 3, 7+5+7+9=28

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Answer: [tex]x\leq -1[/tex]

Step-by-step explanation: The closed point indicates that it can be equal to that number. The arrow is going back on the number line, meaning it is going to be less. Thus, it is less than or equal to -1.

The area of the ring between these two circles if the radius of the larger and the smaller circle is 10 and 6 is 200.96.

Given:

two circles have the same center $c.$

the larger circle has radius $10$

and the smaller circle has radius $6.$

we are asked to determine the  the area of the ring between these two circles.

⇒ Area of the ring =  Area of larger circle - area of smaller circle

⇒ Area of circle = πr²

⇒ Area of larger circle  = π(10)²

= 100π

⇒ Area of small circle = π(6)²

= 36π

Area of the ring =  Area of larger circle - area of smaller circle

Area of the ring = 100π - 36π

= 64π

= 200.96

Hence the area of the ring is 200.96

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