In the equation y = 2x + 3 , what is the output if the input is 6?

The amount of taxes collected is proportional to the population, so if the population increased by 3 million - 2 million = 1 million, the amount of taxes collected should increase by the same factor.

So, in 2017, 4 billion * (3 million / 2 million) = 6 billion dollars in taxes were collected.

Answer:

Since the amount of taxes collected is proportional to the population of the city, we can write the relationship between the amount of taxes and the population as:

T = kP

where T is the amount of taxes, P is the population, and k is the constant of proportionality.

From the information given, we can find the value of k:

4 billion = k * 2 million

k = 4 billion / 2 million = 2

So, for the population of 3 million in 2017, the amount of taxes collected would be:

T = k * P = 2 * 3 million = 6 billion

So, in 2017 the city collected 6 billion dollars in taxes.

The value of expression y ' (-1) is, 24.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ y = (4x² - 5)³

Now, We can differentiate with respect t x as;

⇒ y (x) = (4x² - 5)³

⇒ y' (x) = 3(4x² - 5)² × (4×2x - 0)

⇒ y' (x) = 3 (4x² - 5)² × 8x

⇒ y' (x) = 24x (4x² - 5)²

Substitute x = 1, we get;

⇒ y ' (1) = 24 × 1 (4 × 1² - 5)²

⇒ y' (1) = 24 (- 1)²

⇒ y' (1) = 24

Thus, The value of expression y ' (-1) = 24

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Answer:

below

Step-by-step explanation:

20750 is to 172.2 as   x is to 103.9

20750 /172.2 = x / 103.9

x = $ 12519.89

The height of the tower is 600 feet

What is angle of elevation and the angle of depression?

Angle of elevation: The angle of elevation is the angle produced by the line of sight with the horizontal when the item is above the horizontal level.

Angle of depression: The angle of depression is the angle produced by the line of sight with the horizontal when the item is below the horizontal level.

Let's call the height of the tower "h".

Using trigonometry, we can set up equations based on the angles of elevation and depression:

tan 38° = h / 300

tan 29° = (h - 300) / 300

Solving for h,

h = 300 * tan 38°

h = 300 * 0.8192

h = 245.76

Now,

300 * tan 29° = (h - 300) / 300

300 * 0.5672 = (h - 300) / 300

h - 300 = 300 * 0.5672 / 0.5672

h - 300 = 300

h = 600

So, The height of the tower is 600 feet, rounded to 2 decimal places.

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Answer:

44/87

Step-by-step explanation:

There are 87 fair managers.  44 of them have a college degree.  Being that he is a fair manager, the chance of him having a college degree is 44 out of 87, otherwise written as 44/87.

Answer:

118°

Step-by-step explanation:

$2.4 is the discount used to purchase a pair of sunglasses

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

Given that Alexandra bought a pair of sunglasses online for $24.

She used a coupon code to get a 20% discount.

The website also applied a 10% processing fee to the price after the discount.

20%-10%=10%

Now 10% of price is 24

10/100×24=x

2.4=x

24+2.4=26.4 is the actual price.

Hence, $2.4 is the discount used to purchase a pair of sunglasses

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Answer:

The width of the rectangle is 9

Step-by-step explanation:

l + l + w + w = perimeter

(x - 8) + (x - 8) + (x) + (x) = 52  

We don't know the length so put it as a variable

x + x + x + x - 8 - 8 = 52         Group together like-terms.

4x - 16 = 52                            Combine like-terms                  

4x = 68                                  Add 16 to both sides

x  =   17                                Divide both sides by 4

We now have the value for the length (x = 17) however we need the value for the width. Just subtract 17 - 8 since the width is 8 in. less than its length.

17 + 17 + 9 + 9 = 52

Answer:

YXZ=AXZ

because if you see the letters they form triangle

The measure of the central angle associated to the circular arc is equal to 4 / 3 rad.

Herein we find the information of the radius of a circle and the length of its circular arc, whose relationship is shown by the following formula:

s = θ · r

Where:

If we know that r = 6 yd and s = 8 yd, then the measure of the central angle is:

θ = s / r

θ = (8 yd) / (6 yd)

θ = 4 / 3 rad

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The mean and standard deviation of the sampling distribution of the sample mean (average) of the SAT math scores are:

(b) Mean = 515, SD = 114/√100

The mean of the sampling distribution of the sample mean is equal to the population mean (515), because the expected value of the sample mean is equal to the population mean. The standard deviation of the sampling distribution of the sample mean is called the standard error, and it is equal to the population standard deviation divided by the square root of the sample size (114/√100).

The result (b) is determined based on the central limit theorem, which states that as the sample size increases, the distribution of the sample mean approaches a normal distribution with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size.

In this case, the population mean is 515 and the population standard deviation is 114, so the standard deviation of the sampling distribution of the sample mean is equal to 114/√100. This result can be mathematically proven using the formula for the standard deviation of the sample mean:

SD of sample mean = σ/√n, where σ is the population standard deviation and n is the sample size.

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Answer:

0.6

Step-by-step explanation:

96/160 = 0.6

Just divide.

The decimal is 0.60, which is 60% of 1.

Answer:

96 of 160 is 60%

102.4 of 160 is 64%

120 of 160 is 75%

128 of 160 is 80%

Hope this helped!

Step-by-step explanation:

The solution of the initial value problem xy' + y = 8e is equal to

log (x ) =  - log ( 8e - y ) .

Solution of the initial value problem is:

xy' + y = 8e

⇒ x (dy /dx ) + y = 8e

⇒ x (dy/dx ) = 8e -y

⇒  dx / x  = ( 1 / (8e -y ) ) dy

Integrate both the sides we get,

⇒ log (x ) =  - log ( 8e - y ) + c  ____(1)

Now , we have y ( 1 ) = -1 + 8e

Substitute the value  y ( 1 ) = -1 + 8e in (1) we get,

⇒ log ( 1 ) = - log ( 8e - ( -1 + 8e )) + c               ( value of log (1) = 0 )

⇒ 0 = - log ( 8e + 1 - 8e ) + c

⇒ 0 = log ( 1 ) + c

⇒ c = 0

Now substitute c =0 in (1) we get,

log (x ) =  - log ( 8e - y )

Therefore, the explicit solution of the initial value problem is equal to

log (x ) =  - log ( 8e - y ) .

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Answer:

a) The equation to solve this problem would be:

10 + 3.75h = 41.88

b) To solve for h, we first need to subtract 10 from both sides:

3.75h = 31.88

Then, divide both sides by 3.75:

h = 8.50 (rounded to the nearest tenth)

So Amanda rented the bike for 8.5 hours.

Step-by-step explanation:

Answer:  a) To solve the problem, we can use the equation:

Cost = 10 + 3.75h

Where h is the number of hours Amanda rented the bike.

b) We know that the cost is about $41.88, so we can plug that in for the cost and solve for h:

41.88 = 10 + 3.75h

31.88 = 3.75h

h = 31.88/3.75

h = 8.5 hours

So Amanda rented the bike for 8.5 hours. (rounding to the nearest tenth)

Step-by-step explanation:

Answer:

Brandi needs to receive a score of 46 on the final to have an average score of 80.

Step-by-step explanation:

First, let's understand what is being told to us. We are being asked to find the score Brandi needs on the final, or x. Since the final is worth 2 tests, the final is equal to twice the score she receives, or 2x. Next, we need the average of all the tests, including the final, to be equal to 80. It's important to also note that we will be taking the average of 6 scores. Now, let's use all of our information to write an equation to solve:

( 79 + 80 + 74 + 63 + 92 + 2x ) / 6 = 80.   [Combine like terms]

( 388 + 2x ) / 6 = 80   [Multiply by 6]

388 + 2x = 480   [Subtract 388 from both sides]

2x = 92   [Divide both sides by 2]

x = 46

So, Brandi needs to receive a score of 46 on the final to have an average score of 80.

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With the help of given pie chart, He is Under for some categories and over for other categories.

What is a pie chart?

The “pie chart” is also known as a “circle chart”, dividing the circular statistical graphic into sectors or sections to illustrate the numerical problems. Each sector denotes a proportionate part of the whole. A pie chart requires a list of categorical variables and numerical variables. To find out the composition of something, Pie-chart works the best at that time. In most cases, pie charts replace other graphs like the bar graph, line plots, histograms, etc.

The total value of the pie is always 100%.

Now,

Categories   Spend value    Spending guidelines    Over/Under(O/U)

Rent              $2200               $1830                            O-$370

Student

Loan             $350                $305                              O-$45

Food             $750                $1220                            U-$470

Car payment $150       Together in transportation

and Car            +

insurance      $75                 $671                               U-$446                                            

Savings         $50                 $610                               U-$560

I would suggest Jonathan to save more and spend less on rent and more on food for better health.

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The length of the statue on the drawing is 6.33 inches.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

1 inch = 3 feet

The length of the statue = 19 feet

Now,

3 feet = 1 inch

Multiply 19/3 on both sides.

19 feet = 6.33 inch

Thus,

The statue on the drawing is 6.33 inches.

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The function representing number of fish each 't' year

n ( t ) = (600t + 500) / ( 0.5t + 1) best defines option A. The number of fish get larger every year , but does not exceed the number 1200.

Let 'n' represents the number of fish.

't' represents the year.

The function representing the number of fish in 't' years is :

n ( t ) = (600t + 500) / ( 0.5t + 1)

Number of cans poured in the lake by farmer is equal to 5

Number of fish in each can = 100

Let t = 1

n(1) = 600(1) + 500 / 1.5

     = 733.33

t= 2

n(2) =  600(2) + 500 / 2

       =850

n(3) = 600(3) + 500 / 2.5

      = 920

Therefore, the function n ( t ) = (600t + 500) / ( 0.5t + 1) best describes the option A. The number of fish get larger every year , but the number does not exceed  1200.

The above question is incomplete, the complete question is:

The wildlife game commission poured 5 cans of fish (each can contained approximately 100 fish) into a farmer's lake. the function n defined by

n ( t ) = (600t + 500) / ( 0.5t + 1) represents the approximate number of fish in the lake as a function of time (in years).Which one of the following best describes how the number of fish in the lake changes over time?

A. The number of fish gets larger each year, but does not exceed 1200.

B. The number of fish gets smaller every year but does not get smaller then 1200.

C. The number of fish gets larger each year, but does not exceed 600.

D. The number of fish gets larger each year, but does not exceed 500.

E. The number of fish gets smaller every year, but does not get smaller than 500.

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Out of the following statements A)It will be called every time the event listener is triggered, C. It must be passed to the event listener as the second argument and   D.It can be either an anonymous or a named function that is true of the event listener's callback function.

An event listener's callback function is a function that is triggered when an event is fired and the callback function is responsible for handling the event. A callback function must be passed to the event listener as the second argument, and it can be either an anonymous or a named function.

The callback function will be called every time the event listener is triggered, and it must always define a parameter for the event object. This allows the callback function to access the event object's properties and methods to handle the event accordingly. The event object contains information about the event, such as the type of event, the target element, and more. By accessing this information, the callback function can determine how to handle the event.

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if Monique wanted to run 7/8 mile and she went to the school track which was one quarter of a mile long. The number of lap Monique will complete is

One complete lap around a track or across a pool, from one end to the other: The track has 400 meters or approximately 25 mile per lap.

A lap is end to end of a track and in the problem a lap is 1/4 mile and Monique wants to complete 7/8 miles'. the comparison is as follows

assuming the number of laps is L

1 lap = 1/4 mile

L laps = 7/8 miles

cross multiplying

1 * 7/8 = L * 1/4

multiplying by 4 for each side

1 * 7/8 * 4 = L * 1/4 * 4

1 * 7/8 * 4 = L * 1

7/8 * 4 = L

hence option C is correct

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The answers are k = 12√2 and [tex]\theta=\frac{\pi }{2}+2\pi n[/tex]

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Given are questions related to trigonometric functions:

a) k cos² (π/6) - k sin² (π/6) = 6√2

Finding k,

k cos² (π/6) - k sin² (π/6) = 6√2

Taking k common,

k [cos² (π/6) - sin² (π/6)] = 6√2

Since, cos²x-sin²x = cos2x

Therefore,

k[cos2(π/6)] = 6√2

k[cos(π/3)] = 6√2

Since, cos(π/3) = cos 60° = 1/2

Therefore,

k[1/2] = 6√2

k = 6√2 × 2

k = 12√2

b) sinx / cscx+cotx

[tex]\frac{sinx}{cscx+cotx}= \frac{sinx}{\frac{1}{sinx}+\frac{cosx}{sinx}}= \frac{sinx}{\frac{1+cosx}{sinx}}= \frac{sin^2x}{1+cosx}= \frac{1-cos^2x}{1+cosx}= \frac{(1+cosx)(1-cosx)}{1+cosx}\\\\= 1-cosx[/tex]

Hence, proved.

c) sinθ = 2cos²θ + 1

Solving for θ

[tex]\sin \left(\theta\right)-2\cos ^2\left(\theta\right)-1=0[/tex]

[tex]-3+\sin \left(\theta\right)+2\sin ^2\left(\theta\right)=0[/tex]

[tex]\sin \left(\theta\right)=1,\:\sin \left(\theta\right)=-\frac{3}{2}[/tex]

[tex]\sin \left(\theta\right)=1 : \theta=\frac{\pi }{2}+2\pi n\\\sin \left(\theta\right) = -\frac{3}{2} : no solution\\\theta=\frac{\pi }{2}+2\pi n[/tex]

Where n is any integer,

Hence, the answers are k = 12√2 and [tex]\theta=\frac{\pi }{2}+2\pi n[/tex]

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Answer: false

Step-by-step explanation: 1st we collect the Like Terms which would make the new equation 3y + 8 = 3y + 5 then we can cancel the 3y's bc they're equal and leaves us with 8 = 5 which we could see is false, so this equation is false

To calculate the total cost of the fence, we need to know the length of the fence.

In a right-angled triangle, the length of the fence can be calculated using the Pythagorean theorem, which states that the length of the hypotenuse (the fence) is equal to the square root of the sum of the squares of the other two sides (the base and the height of the triangle).

So, the length of the fence (C) = square root of (A^2 + B^2), where A is the base and B is the height of the triangle.

If the base of the triangle is x and the height of the triangle is y, then the cost of the fence can be calculated using the formula:

Cost = (length of fence) x (cost per meter)

Cost = (square root of (x^2 + y^2)) x 1.26

In order to calculate the cost, the farmer needs to know the values of x and y.

The total cost of the triangular shaped fence is A = £ 530

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be represented as ΔABC

Now , the measure of side AB = 145 m

Now , the measure of ∠BAC = 59°

From the trigonometric relations

tan θ = opposite / adjacent

tan 59° = BC / 145

Multiply by BC on both sides , we get

BC = 241.320524941 m

Now , the hypotenuse of the triangle is

H = √ ( 145 )² + ( 241.320524941 )²

H = √ ( 21,025 + 58,235.595757

H = √79,260.595757

H = 281.53258 m

Now , the total perimeter of triangle is P = 281.53258 + 241.320524941 + 145

P = 667.85310877 m

Now , fence costs £1.26 per meter

A = 667.85310877 m / £1.26

So , the total cost is A = £ 530

Hence , the total cost is A = £ 530

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Answer:

11.390625 in^3

Step-by-step explanation:

2.25^3 = 11.390625 in^3

The amount of rainfall in Nashville than in Miami would be 0.67.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the rainfall in Albany is 0.33. The amount of rainfall in Miami is calculated as:-

Rainfall = 1 - 0.33

Rainfall = 0.67

Hence, the amount of rainfall in Nashville than in Miami would be 0.67.

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For Given Fraction 5/3, The total number of votes is 7648.

What is a fraction?

In Maths, a fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator. The numerator defines the number of equal parts taken, whereas the denominator defines the total number of equal parts in a whole.

For example, 5/10 is a fraction.

Here, 5 is a numerator and 10 is a denominator.

There are four different types of fractions. They are:

Unit Fraction – In a fraction, the numerator with 1 is called a unit fraction. For example, ½, ¼

Proper Fraction – If a numerator value is less than the denominator value, it is called a proper fraction. Example: 7/9, 8/10

Improper Fraction – If a numerator value is greater than the denominator value, then it is called an improper fraction. Example: 6/5, 11/10

Mixed Fraction – If a fraction consists of a whole number with a proper fraction, it is called a mixed fraction. Example 5 ¾, 10 ½

Now,

As given ratio is 5/3 for Yes votes to no votes

so total votes is 5x+38x

and also given that no votes i.e. 3x=2868

so, x=956

Hence,

            Total votes=8*956=7648

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The value of h can be any value other than 2.

The augmented matrix of a consistent linear system must have a unique solution, which means the determinant of the coefficient matrix must be non-zero.

       [1 h

        3 6]

The determinant of this matrix is (1 * 6) - (3 * h) = 6 - 3h.

For the determinant to be non-zero and the system to be consistent, 6 - 3h must not be equal to zero, so h cannot be equal to 2.

Therefore, the value of h can be any value other than 2.

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Answer:

Step-by-step explanation:

4x+3x=6+2

7x/7=8/7

=1.143

Answer: X=22

According to equation given :-

4x-2=3x+6 ----------------------(1)

4x - 2 +3x+6=180 -------------(2)

hence put equation (1) in (2) which that

4x - 2 +4x-2=180

2* ( 4x-2 ) = 180

4x-2 =90

4x = 88

x= 22 (answer)

Three different formulas or rules for the terms of a sequence {an} if the first three terms of this sequence are 1,2,4 are as follows:

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