You are driving (too fast) down a straight, country road. The posted limit is 40 miles per hour along this road. Two police officers are posted one mile apart along this road tracking vehicle speeds and are in contact with each other. At the first officer’s position, you drive by going 39 miles per hour. At the second officer’s position 63 seconds later, you drive by going 38 miles per hour. The second officer pulls you over and gives you a ticket. Were they justified in giving you a ticket, even though you were not caught speeding?

Hint: refer to the Mean Value Theorem to assist with your justification and reasoning.

Considering the discrete probability distribution, it is found that:

a) The mean is of: 6.3

b)

The mean of the distribution is given by the sum of each outcome multiplied by it's probability, hence it is obtained as follows:

E(X) = 0.1 x 2 + 0.3 x 5 + 0.4 x 7 + 0.2 x 9 = 6.3.

The variance of the distribution is given by the sum of the difference squared between each observation and the mean, multiplied by it's probability, hence it is obtained as follows:

Var(X) = 0.1 x (2 - 6.3)² + 0.3 x (5 - 6.3)² + 0.4 x (7 - 6.3)² + 0.2 x (9 - 6.3)² = 4.01.

The standard deviation is the square root of the variance of the distribution, hence it is obtained as follows:

S(X) = sqrt(4.01) = 2.

We have that:

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Markus' biweekly earnings (gross pay every two weeks) are $2,727.16.

The annual gross pay can be divided by 26 to get the biweekly earnings.

Another way to compute the biweekly earnings is by adding up the withholding taxes, deductions, and net earnings.

In practice, the net earnings are equal to the gross pay less withholding taxes and deductions.

Annual gross pay = $65,500

Payment period = biweekly (1st and 15th every month)

Social Security = $156.19

Medicare =            36.53

Federal tax  =     445.96

Total withholding = $636.68

Retirement = $45

Health Insurance = $200

Total deductions = $245

Net Earnings = $1,845.48

Biweekly ross pay (earnings) = $2,727.16 ($636.68 + $245 + $1,845.48)

Thus, Markus earns $2,727.16 every two weeks.

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Answer:

They spent a total of 1 and 1/2 hours swimming.

Step-by-step explanation:

It is because 1 1/4 plus 1 1/4 equals 1 2/4 which mean 2/4=1/2 so in total they spent 1 1/2 hours swimming

The amount in terms of the original amount is $1,404 and the year end amount is $6,604.

a. Original amount

Original amount = 5200 - (5200× .27)

Original amount = $5200 - $1,404

Original amount = $3,796

b. Year-end amount

Year-end amount  = 5200+  $3,796

Year-end amount =$8996

Therefore the original amount is $3,796 and the year end is $8996.

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The point Q'(x, y) = (- 1.5, - 1.5) is located in quadrant III and 3 units away from point Q(x, y) = (1.5, - 1.5).

In this question we find the location of an ordered pair on the coordinate plane and we are asked to find a possible solution that is in quadrant III and three units away from the original point.

A point (x, y) is in the quadrant III if x < 0 and y < 0 and we can determine a resulting point by using the following translation formula:

(x, y) → (x - 3, y)

If we know that (x, y) = (1.5, - 1.5), then the resulting point is:

Q'(x, y) = (1.5, - 1.5) + (- 3, 0)

Q'(x, y) = (- 1.5, - 1.5)

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A polynomial that satisfies given conditions is:

P(x) = x³ - x² + 81x - 81

In this question, we need to find a polynomial that satisfies given conditions.

We have been given that -9i is a root of polynomial.

This means, the conjugate of -9i that is, 9i must be a root of polynomial p.

From given information we can say that the zeros of polynomial p(x) must be (x - 1), (x + 9i), and (x - 9i)

So, we get a polynomial p(x) = 0

(x - 1)(x + 9i)(x - 9i) = 0

(x - 1)(x² - (9i)²) = 0

(x - 1)(x² - (-81)) = 0

(x - 1)(x² + 81) = 0

x³ - x² + 81x - 81 = 0

Therefore, a polynomial that satisfies given conditions is:

P(x) = x³ - x² + 81x - 81

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The expression we get from the given functions f and g defined for all real numbers x.

(f+g)(x)=4x+1

(f-g)(x)=2x+11

(f.g)(3)=-30

Given that,

All real numbers x are defined by the functions f and g.

f(x)=3x+6

g(x)=x-5

We have to find the expression

(f+g)(x), (f-g)(x) and (f.g)(3)

Take the functions,

f(x)=3x+6

g(x)=x-5

Now, First

(f+g)(x)

f(x)+g(x)           (Substitute in the place of f and g functions)

Which is

3x+6+x-5

4x+1

(f+g)(x)=4x+1

Now, second

(f-g)(x)

f(x)-g(x)

Which is

3x+6-(x-5)

3x+6-x+5

2x+11

(f-g)(x)=2x+11

Now, third

(f.g)(3)

f(3)×g(3)

Which is

(3(3)+6)×((3)-5)

(9+6)×(3-5)

15×-2

-30

(f.g)(3)=-30

Therefore, The expression we get from the given functions f and g defined for all real numbers x.

(f+g)(x)=4x+1

(f-g)(x)=2x+11

(f.g)(3)=-30

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Answer:

y=12

x=34

Step-by-step explanation:

x+y=46

3y-2=x

(3y-2)+y=46

4y-2=46

   +2.  +2

4y=48

/4.  /4

y=12

x+12=46

 -12.  -12

X=34

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The size sample that should be taken so that at 95% confidence the margin of error will be 2 months or less is:47.0596.

Using this formula to find the sample size

n = z² × σ² / e²

Where,
n = sample size =?

z = z-score = 1.96

σ = Standard deviation = 7 months

e = Margin of error = 2 months or less

Let plug in the formula

n = (1.96²× 7²) /2²

n = 3.8416 × 49 / 4

n =47.0596

Therefore the sample size is 47.0596.

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Answer: The size of the sugar order decreased by 40%.

Step-by-step explanation:

1,090 is 100%

654 is 60% of 1,090 (1,090 ÷ 0.6 = 654)

1,090 - 654 =  436, and 436 is 40% (0.4) of 1,090

1,090 (100%) - 436 (40%) = 654 (60%)

The percent of the decrease in the size of the sugar order is 40%.

Answer:

B

Step-by-step explanation:

OR means that they don't overlap and based on the answer you have in you know how to solve the innequality.

Making the subject as x, the expression is x = u/9

The given equation is

9x = u

It can be written as

u = 9x

We need to make x as the subject in the given expression

9x = u

u = 9x

here u is the subject

9x = u

x = u/9

Therefore, making the subject as x, the expression is x = u/9

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There will be 319 boards be required

and the total cost be $223,720.

Given, a classroom ceiling measures 6.8m by 4.7m. It is covered by boards measuring 1m by 1m.

Now, we have to find the number of boards needed altogether

So, the area of the ceiling is

Area = 6.8×4.7

Area = 319.6 m²

Now, the area of the board is

Area = 1 m²

So, 319 boards will be required to cover the ceiling.

Now, if one board costs $700 then,

the total cost be

= 700×319.6

= $223,720

Hence, There will be 319 boards be required

and the total cost be $223,720.

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Answer:

$1036.28

Step-by-step explanation:

Marking something up by 100% means doubling the price. Let's do this step first:

863.57 * 2 = 1727.14

Next, the discount is 40%

I would find this by taking the 10% value, multiplying that by 4 and subtracting that from our new value

10% = 172.714

40% = 690.856

Now our newest value:

1727.14 - 690.856

1036.284

Round to 2 decimal places (as is proper when dealing with cents):

1036.28

Thus, our newest (discounted) price is:

$1036.28

Answer: 5/8

Step-by-step explanation:

remove the +'s because -'s are more valued. -1/5 is 0.2 and because we're subtracting 1.45-0.2 its 1.25. -5/8 = 0.625 and if you subtract 1.25-0.625 its 0.625 so its just 5/8

[tex]\frac{5}{8} .[/tex]

[tex]1.45 + (-\frac{1}{5} )+ (-\frac{5}{8} )[/tex]

[tex]1.45 -\frac{1}{5} -\frac{5}{8}[/tex]

[tex]\frac{145}{100} -\frac{1}{5} -\frac{5}{8}[/tex]

[tex]\frac{145/5}{100/5} -\frac{1}{5} -\frac{5}{8}\\ \\\frac{29}{20} -\frac{1}{5} -\frac{5}{8}[/tex]

Note. You always need to multiply each fraction by the same number on both numerator and denominator.

[tex]\frac{29*2}{20*2} -\frac{1*8}{5*8} -\frac{5*5}{8*5}\\ \\\frac{58}{40} -\frac{8}{40} -\frac{25}{40}[/tex]

[tex]\frac{58-8-25}{40} \\ \\\frac{25}{40}[/tex]

[tex]\frac{25/5}{40/5}\\ \\\frac{5}{8}[/tex]

[tex]1.45 + (-\frac{1}{5} )+ (-\frac{5}{8} )= \frac{5}{8} .[/tex]

The probability that the tenth person randomly interviewed in that city is the fifth one to own a dog = 0.051

Given,

Consider the interview of a person is a trial.

Lets consider it success if a person  owns a dog and consequently , a person without a dog will be a failure.'

Let the random variable X represent the number of persons to be interviewed to get 5 dog owner: in other words, to get 5 successors.

Probability of a success in each trial is p = 0.3. Therefore probability of a failure in each trial is q = 1 - p = 0.7 .

Because trials are independent. X has a negative binomial distribution with parameters k = 5, p = 0.3

P(X =x ) = b(x: k, p) = [tex][(x-1)(k-1)] p^kq^r^-^k[/tex]

where, x = k , k + 1 , k + 2......(1)

Now, Lets find the probability that the tenth person randomly interviewed in that city is the fifth one to own a dog

Using equation (1), we get:

P(X = 10) = b(10: 5, 0.3)

                = [(10-1) (5 - 1)][tex](0.3)^5(0.7)^1^0^-^5[/tex]

               = [(9)(4)] [tex](0.3)^5(0.7)^1^0^-^5[/tex]

               = 0.05146

Hence, The probability that the tenth person randomly interviewed in that city is the fifth one to own a dog = 0.051

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The value of 12 - x can at most be 4 for the given inequality and it is true therefore, all itineraries are possible.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

Inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

Let's say the day spend in Benin, Ghana and Togo are B, G, and T respectively.

As per the given,

B + G + T = 30

Here, 2 ≤ B ≤ 12, G ≤ 13, and T ≤ 9.
(12 - B) + (13 - G) + (9 - T) = -30 + 12 + 13 + 9 = 4

Also, B ≥ 2 or B ≤ -2 ⇒ 12 - B ≤ 12 - 2 = 10

Hence "The value of 12 - x can at most be 4 for the given inequality and it is true therefore, all itineraries are possible".

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The cost of the tomatoes, in dollars per pound, using proportions, is of:

$0.86 per lb.

A proportion represents a fraction relative to a total amount, which is combined with the basic arithmetic operations, especially multiplication and division, to find the desired amounts in whichever context of a problem.

In this problem, the costs is obtained as follows:

Hence the cost in dollars per kg of the tomatoes is obtained as follows:

1.74 x 1.09 = $1.8966 per kg.

The relationship between kg and pounds is given as follows:

1 kg = 2.20 lb.

Hence the cost is written as follows:

$1.8966 per 2.20 lb.

The cost per pound of the tomatoes is of:

1.8966/2.20 = $0.86 per lb.

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Answer:

Slope is the same thing as gradient

The formula is

y2-y1/x2-x1

where y2 is =8

y1 is =5

x2 is=-7

x1 is =-4

when we substitute, your answers will be

= -1

Answer: 16

Step-by-step explanation:

To *increase* 24 in the ratio 2:3

To *increase* a quantity in given ratio consider new quantity and old quantity.

Formula: New quantity:old quantity=given ratio solution: let us take the new quantity as x, old quantity as 24(given) and given ratio=2:3(given)

-> x:24=2:3

-> x/24=2/3

-> Multiply with 24 on both sides to get x

-> 24*x/24=2/3*24

-> x=16

So, the *increase* of 24 in the ratio 2:3 is 16

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The coordinates of the image of the point (−9,−3) under the same translation will be (-7,-5).

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

It is given that the image of the point (-3, -6) under a translation is (-1, -8).

The coordinate by which the first given condition is translated as,

(-3, -6) - (x,y) =  (-1, -8)

(x,y) = (-3, -6) - (-1, -8)

(x,y) =(-3-(-1), -6-(-8)

(x,y) =(-3+1),(-6+8)

(x,y) =(-2,+2)

The coordinates of the image of the point (-9, -3) are under the same translation obtained as,

=(−9,−3)- (-2,+2)

=(-9-(-2) , (-3-(+2))

=(-9+2),(-3-2)

= -7,-5

Thus, the coordinates of the image of the point (−9,−3) under the same translation will be (-7,-5).

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9664.9 is the  Blanche's balance be from Account 2 over 5.5 years

percentage, a relative value indicating hundredth parts of any quantity.

Given,

Blanche has recently inherited $7900, which she wants to deposit into a savings account. She has determined that her two best bets are an account that compounds semi-annually at an annual rate of 3.7%

an account that compounds daily at an annual rate of 3.9% (Account 2).

We need to find how much Blanche's balance be from Account 2 over 5.5 years

A = p(1 + r/n)nt

A = 7900(1 + 0.037/2)²ˣ⁵⁵

A ≈7900(1 + 0.0185)^11

A ≈ 7900(1.0185)¹¹

A ≈ 7900(1.223)

A=9664.92

9664.9 is the  Blanche's balance be from Account 2 over 5.5 years

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[tex]p = \frac{kd^{2}}{u}[/tex] is an equation that expresses the relation.

Directly proportion means if variable x and y varies equally.

Increment of one variable result to another one.

The ratio of these variable remains same throughout.

Inversely proportion means if one variable increases the second one will decreases. It is opposite of directly proportion.

According to the question,

p varies directly. with the square of d and inversely with u

p ∝ d²

p ∝ 1/u

Combining both the equation,

p ∝ d²/u

Putting k as the constant

p = kd²/u is our required equation

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The best firm for the Appliance manufacturer for the repair work is Firm 2 .

In the question ,

it is given that ,

An appliance manufacturer wants to contract with a repair shop to handle authorized repairs in Indianapolis .

The acceptable range of the repair time is 50 minutes to 90 minutes.

the mean repair time for firm 1 = 74 minutes and standard deviation of 4 minutes .

the mean repair time for firm 2 = 72 minutes and standard deviation of 5.1 minutes .

the range is calculated using the formula

Range = Mean ± Standard Deviation

So , for firm 1 ,

the Range = 74 ± 4

= 74 [tex]+[/tex] 4       and      74 - 4

= 78     and   70

the range for firm 2 is

= 72 ± 5.1

= 72 [tex]+[/tex] 5.1      and      72 - 5.1

= 7.1        and       66.9  

The second company has a lower range and it should be preferred .

Therefore ,  The best firm for the Appliance manufacturer for the repair work is Firm 2 .

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Answer:

sada

Step-by-step explanation:

Please Add A Picture

Answer:

It is 120/529

Step-by-step explanation:

The steps are:
Step 1: When we divided, we change the dividing fraction into mutiplying fraction at the last fraction: 5/23 x 24/23
Step 2: We mutiply it on each row like 5 x 24 & 23 x 23
Step 3: When we finished with the answer, we put it like the order of the fraction: 120 & 529 so we get 120/529

Thats all the step by step explaination!


Please mark me brainliestttttttttttttttttttttttttttttttttttttttttttttttt !!!!!!!!!!!!!!!!!!!!!!!!11

Answer: 114

Step-by-step explanation:

firstly, convert meters to centimeters:

2.5m * 100cm in a meter = 250 cm

let the length of the first shelf equal x:

250 = x + (2x + 18) + (x - 12) + (x + 4)

combine like terms:

250 = 5x + ( 18 - 12 + 4) = 5x +10

subtract 10 from both sides:

240 = 5x, then solve for x

240/5 = x

x = 48 cm

the length of the second shelf was 2x + 18, so plug in 48 for x:

2(48) + 18 = 114

Answer:

114 [cm].

Step-by-step explanation:

1) if the length of the 1st shelf is 'x', then

2) the length of the 2d shelf is '2x+18', the 3d shelf is 'x-12' and the 4th shelf is 'x+4';

3) the sum of the all 4 shelves is 250 [cm], then it is possible to make up the equation:

x+(2x+18)+(x-12)+(x+4)=250;

4) the root of the equation above is x=48, then

5) the required length of the 2d shelf is 2*48+18=114 [cm].

1. The revised annual depreciation on December 31, 2022, is $3,650.

2. The journal entry to record depreciation on December 31, 2022 is as follows:

Debit Depreciation Expense $3,650

Credit Accumulated Depreciation $3,650

To record the depreciation expense for the year.

3. The balance in Accumulated Depreciation for Equipment on December 31, 2022, is $37,150.

Cost of equipment = $75,000

Purchase date = July 1, 2019

Estimated useful life = 5 years

Salvage value = $8,000

Depreciable amount = $67,000 ($75,000 - $8,000)

Annual depreciation expense = $13,400 ($67,000/5)

Accumulated Depreciation for two and half years to December 2021 = $33,500 ($13,400 x 2.5)

Book value after 2.5 years = $41,500 ($75,000 - $33,500)

New estimated useful life = 10 years

Revised salvage value = $5,000

Revised depreciable amount = $36,500 ($41,500 - $5,000)

Revised annual depreciation expense = $3,650 ($36,500/10)

Accumulated Depreciation on December 31, 2022 = $37,150 ($33,500 + $3,650)

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Answer:

[tex]-\frac{1}{2}(x-1)[/tex]

Step-by-step explanation:

The slope of the line is [tex]\frac{3-1}{1-5}=-\frac{1}{2}[/tex].

Using the point (1,3), the equation is [tex]y-3=\boxed{-\frac{1}{2}(x-1)}[/tex].