suppose the exchange rate of Euros to US dollars is $0.89 Euros to $1. How many euros can an individual exchange for $60?
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Answer:

Step-by-step explanation:

y = 5x + 1

Table for input-output values is,

x        0         1           2           3

y        1          6          11          16          

Now we can plot these points to get the graph.

y = x + 2

Table for the Input-output values,

x       0         1           2          3

y       2         3          4          5

We can get the graph as attached.

Answer:

x = -4

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

x /2 −12=−14

1 /2 x+−12=−14

1/ 2 x−12=−14

Step 2: Add 12 to both sides.

1 /2 x−12+12=−14+12

1 /2 x=−2

Step 3: Multiply both sides by 2.

2*( 1 2 x)=(2)*(−2)

x = −4

Answer:

-1

Step-by-step explanation:

step 1: X/2-12=-14

step2 : X/2=-14+12

step3 : X/2=-2

step4 : X=-2/2

step5 : X=-1

Answer:

Cost = $51.96

Step-by-step explanation:

The radius of a regular hexagonal window, r = 2 feet

The area of a hexagonal shaped figure is given by :

\(A=\dfrac{3\sqrt3}{2}r^2\)

Put r = 2 feet in above formula

\(A=\dfrac{3\sqrt3}{2}\times (2)^2\\\\A=10.392\ \text{unit}^2\)

Replacement glass for energy-efficient windows costs $5.00 per square foot. It means, the total cost will be :

\(A=10.392\times 5\\\\A=\$51.96\)

So, the required cost will be $51.96. Hence, the correct option is (d).

The formula for finding the volume a hemisphere is given by

Given the diameter of 26inches, the radius would be

Substituting for r in the volume of a hemisphere will give

Hence, the volume of the hemisphere is 1464pi cubic inches

if the square has the same perimeter as the rectangle then the value of y is 92.

The perimeter of a square is equal to the sum of all four sides, so a square with a side of 7 cm has a perimeter of 4 * 7 cm = 28 cm.

The perimeter of the rectangle is equal to twice the sum of the length and width. So for a rectangle of length y/8-3cm and width 4cm, the perimeter is 2 * (y/8-3+4) cm = (y/4-3+8) cm = y/4 . +5 cm.

Since squares and rectangles have the same perimeter, the two perimeter formulas can be equal.

28cm = y/4+5cm

You can solve for y by isolating it on one side of the equation.

years/4+5 = 28

y/4 = 23

y=92

So the value of y is 92.

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Answer:

15

Step-by-step explanation:

180-15

Hello!

the sum of the angles in the triangle = 180°

so the 3rd angle = 180° - 165° = 15°

Answer:

(-2, 3)

Step-by-step explanation:

4x + 5y = 7

3x - 2y = -12

Let's solve this by elimination. We want to eliminate one variable at a time. This means we need to multiply the equations to create a common multiple to cancel out a variable.

Let's work with y.

5y and -2y: For these values to cancel out, we need to multiply each term to create a common multiple.

2(4x + 5y = 7)

5(3x - 2y = -12)

Multiply.

8x + 10y = 14

15x - 10y = -60

Eliminate.

23x = -46

Divide both sides by 23.

x = -2

Now that we know x, let's plug it back into one of equations to find y.

4x + 5y = 7

4(-2) + 5y = 7

Multiply.

-8 + 5y = 7

Add.

5y = 15

Divide.

y = 3

Now we know x and y; let's plug both back into the equation we have not checked yet.

3x - 2y = -12

3(-2) - 2(3) = -12

Multiply.

-6 - 6 = -12

Subtract.

-12 = -12

Your solution is correct.

(-2, 3)

Hope this helps!

The minimum dimensions of the rectangular box is 90mm by 90mm by 36mm when converted to millimeter

There are three dimensions of a rectangular box which are the length, width, and height . The three measurements are multiplied together using Length × Width × Height in the same units.

The radius of the circular mat = 4.5cm and 45{converted to millimeter}

the total length of the mat = 2 × 45mm {2radius = diameter}

the total length of the mat = 90mm

Since the length of the circular mat is the same around the mat, hence the rectangular box has two dimensions of length of 90mm and width of 90mm

The total thickness of the 12 mats will determine the height of the rectangular box so;

the thickness of a mat is given as 3mm

total thickness of 12 mats = 3mm × 12

total thickness of 12 mats = 36mm

Therefore, the rectangular box will have a minimum dimension of length 90mm by width 90mm by height 36mm

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Answer:

D. 20 inches

Step-by-step explanation:

Area = length * width

20 * 20 = 400 square inches

20 inches

Answer:

addition property of equality

Step-by-step explanation:

you are adding 1 to the other side!

Answer:  $4,000

Step-by-step explanation:

If the total earnings were $40,000 and the base pay was $10,000, then the commission earned would be $40,000 - $10,000 = $30,000.

Since the commission rate is 40%, we can set up the equation:

40% x Total Sales = Commission Earned

We know that the commission earned is $30,000, and we also know that 15 cars were sold. Therefore, we can solve for the average price of each car:

40% x Total Sales = Commission Earned

40% x (15 x Price per Car) = $30,000

6 x Price per Car = $30,000

Price per Car = $5,000

However, this is just the average price per car. Since the commission is based on the total sales, we need to calculate the actual commission earned on each car:

Commission per Car = 40% x Price per Car

Commission per Car = 40% x $5,000

Commission per Car = $2,000

Therefore, the total earnings of $40,000 divided by the number of cars sold (15) gives the amount earned per car:

Amount earned per Car = Total Earnings / Number of Cars Sold

Amount earned per Car = $40,000 / 15

Amount earned per Car = $4,000

An open circle at 5 and a bold line starting at 5 and pointing to the right (>) is the correct representations of the inequality

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g 5 < 6, x ≥ 2, etc.

Given: the inequality –3(2x – 5) < 5(2 – x)

First, we have to solve for x in the inequality

–3(2x – 5) < 5(2 – x)

Clear the parenthesis:

-6x + 15 < 10 - 5x

Collect like terms:

-6x + 5x < 10 - 15

-x < -5

Divide both sides by -1:

x > 5              ( Note:  Dividing both sides by -1 will change the < to > )

This is what will determine our answer

Since our answer is x > 5.  An open circle will be at 5 and a bold line starts at 5 and is pointing to the right (>)

Therefore,  the correct representations of the inequality is  an open circle is at 5 and a bold line starts at 5 and is pointing to the right

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This represents the distance that Mr. Stein drove, given that Mr. Smith drove x miles. The value of x must be between 0 and 140, since Mr. Smith cannot drive more than 140 miles and less than 0 miles.

An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It can be simplified, evaluated, or manipulated using algebraic rules and properties.

Let x be the number of miles Mr. Smith drove. Then, the number of miles Mr. Stein drove is \(140 - x\)  , since they drove a total of 140 miles and Mr. Smith already drove x miles.

the algebraic expression for how many miles Mr. Stein drove is:

\(140 - x\)

Therefore, This represents the distance that Mr. Stein drove, given that Mr. Smith drove x miles. The value of x must be between 0 and 140, since Mr. Smith cannot drive more than 140 miles and less than 0 miles.

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The corresponding element in the range of the function F when 7 is in the domain is 4.6.

The expression for the given function F following as:

F(x) = 6(x) - 19 / 5

The corresponding element in the range of the function F is the output of the function when 7 is input into the function.

To find this output, we can substitute 7 for X in the expression for the function F:

F(7) = 6(7) - 19 / 5

F(7) = 42 - 19 / 5

F(7) = 23 / 5

F(7) = 4.6

Thus, when 7 is in the domain, the equivalent element in the range of the function F is 4.6.

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ANSWER:

2034.72 cubic units

STEP-BY-STEP EXPLANATION:

The volume of the cylinder is given by the following equation;

The radius is equal to 6 and the height is equal to 18, let's substitute them and calculate the volume of the shown cylinder, like this:

The volume of cylinder is equal to 2034.72 cubic units

Answer:

some ppl got summer school

Step-by-step explanation:

Answer:

3*(5 + q) = 15 + 3*q

Step-by-step explanation:

The distributive property is:

A*(B + C) = A*B + A*C

We know that you buy 5 small pots and q packages of seeds for $3 each.

And we know that the equation that models the cost is:

3*(5 + q)

Now we can simply apply the distributive property to rewrite this expression as:

3*(5 + q) = 3*5 + 3*q = 15 + 3*q

So the equivalent expression is: 15 + 3*q

The extremas of the function f(x) = x³ - 7x² + 10x are given as follows:

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The number of students who participated in the survey, based on the histogram showing the number of hours students watch television on the weekend, is 125.

A histogram is a pictorial or graphical representation of categorical data, proportional to the frequency of a variable and whose width is equal to the class interval.

The number of students who watched between 0 - 4 hours = 20

The number of students who watched between 5 - 9 hours = 40

The number of students who watched between 10 - 14 hours = 30

The number of students who watched between 15 - 19 hours = 20

The number of students who watched between 20 - 24 hours = 15

The total number of students who participated = 125

Thus, using the histogram, the total number of students who participated in the survey was 125.

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Step 1: Y= 27 - 4x

To find X - intercept / zero, substitute Y = 0

0 = 27 - 4x

Step 2: 0 = 27 - 4x

Move variable to the left-hand side and change it's sign.

4x = 27

Step 3: 4x = 27

divide both sides of the equation by 4

X = 27/4

solution: X = 27/4

Alternate form: X = 6 3/4, X = 6.75

Answer:

1/36

Step-by-step explanation:

There is a 1/6 probability the first die will be a 6

There is a 1/6 probability the second die will be a 6

There is a (1/6 * 1/6) = 1/36 probability that both will be a 6

Answer:

(a) \(y'= 2cos(2x - \pi)\)

(b) \(y=2x - \pi + 1\)

(c) \(y=-\frac{x}{2} +\frac{\pi + 4}{4}\)

Step-by-step explanation:

\(y=sin(2x-\pi)+1\)

Find the derivative of this function by using the chain rule and the power rule.

We know that the derivative of sinx = cosx. Find the derivative of this entire function first, \(sin(2x-\pi)+1\), then multiply this by the derivative of the inside function, \(2x-\pi\).

Use the chain rule to find the derivative of sin(2x - π) + 1, which is cos(2x - π), then multiply this by the derivative of (2x - π). The derivative of π is 0, because it is a constant. The derivative of 2x is 2 based on the Power Rule.

Simplify this expression.

This is the derivative of \(y=sin(2x-\pi)+1\); therefore, we can write:

In order to find the equation of the tangent line at \(x=\frac{\pi}{2}\), we will need to find the slope of the tangent line and the x- and y- coordinates (we already know the x- cord).

The steps to finding the equation of the tangent line at a certain are:

We know that y' = 2cos(2x - π). Let's plug x = π/2 into this equation for x to find the slope of the tangent line.

Simplify inside the parentheses.

Now we know that the slope of the tangent line is 2.

Let's plug x = π/2 into the original function, y.

Simplify inside the parentheses.

This tells us that the y-value, when x = π/2, equals 1. Our coordinates that we can use are (π/2, 1).

Now we can use point-slope form to write an equation for the tangent line to y at x = π/2.

Point-slope equation:

We have \((x_1, \ y_1)\), which are the x- and y- coordinates, and \(m\), which is the slope of the tangent line.

Substitute these values into the equation:

Distribute 2 inside the parentheses.

Add 1 to both sides of the equation.

This is the equation of the tangent line of \(y=sin(2x-\pi)+1\) at \(x=\frac{\pi}{2}\).

In order to find the equation of the normal line at x = π/2, we can use the information that the tangent line is perpendicular to the normal line.

This information is helpful because this means that their slopes are opposite reciprocals.

Let's use the point-slope equation again, but instead of m = 2, m will be the opposite reciprocal of 2 ⇒ -1/2. We will still use the same coordinate points.

Distribute -1/2 inside the parentheses.

Add 1 to both sides of the equation.

You can leave it written as this, or write it as:

This is the equation of the normal line of \(y=sin(2x-\pi)+1\) at \(x=\frac{\pi}{2}\).

Answer:

339.12 in³

Step-by-step explanation:

volume of cone: v = Bh/3 = πr²h/3

v = (3.14 * (12/2)² * 9 )/ 3 = 339.12

The average baggage-related revenue per passenger is $16.30 per passenger.

Expected value formula: x×p(x)

First step

No passenger=0×.54

No passenger=0

Second step

One checked luggage for first bag=.30×$25

One  checked luggage for first bag=$7.50

Third step

Two piece  for the first and second bag=.16×($25+$30)

Two piece  for the first and second bag=.16×$55

Two piece  for the first and second bag=$8.80

Last step

Expected value=$7.50+$8.80

Expected value=$16.30

Therefore the average baggage-related revenue per passenger is $16.30 per passenger.

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Answer:   He must sell 7 cabinets.

Step-by-step explanation:

So it gives us the equations y= 400x + 1400  and the equations  y=600x and to find the break even point we need to set the two equations equal each other to solve for x.

400x + 1400 = 600x

-400x               -400x

1400 = 200x

 x = 7    

I don't completely know but if every nine years the 2,000 doubles then in 54 years it would have doubled six times so it would look something like this

2,000^6 so I hope that helps at all

Answer:

The slope of the tangent line to the curve at the given point is -11/7.

Step-by-step explanation:

Differentiation is an algebraic process that finds the gradient (slope) of a curve.  At a point, the gradient of a curve is the same as the gradient of the tangent line to the curve at that point.

Given function:

\(4x^2+5xy+y^4=370\)

To differentiate an equation that contains a mixture of x and y terms, use implicit differentiation.

Begin by placing d/dx in front of each term of the equation:

\(\dfrac{\text{d}}{\text{d}x}4x^2+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=\dfrac{\text{d}}{\text{d}x}370\)

Differentiate the terms in x only (and constant terms):

\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=0\)

Use the chain rule to differentiate terms in y only. In practice, this means differentiate with respect to y, and place dy/dx at the end:

\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

Use the product rule to differentiate terms in both x and y.

\(\boxed{\dfrac{\text{d}}{\text{d}x}u(x)v(y)=u(x)\dfrac{\text{d}}{\text{d}x}v(y)+v(y)\dfrac{\text{d}}{\text{d}x}u(x)}\)

\(\implies 8x+\left(5x\dfrac{\text{d}}{\text{d}x}y+y\dfrac{\text{d}}{\text{d}x}5x\right)+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

\(\implies 8x+5x\dfrac{\text{d}y}{\text{d}x}+5y+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

Rearrange the resulting equation in x, y and dy/dx to make dy/dx the subject:

\(\implies 5x\dfrac{\text{d}y}{\text{d}x}+4y^3\dfrac{\text{d}y}{\text{d}x}=-8x-5y\)

\(\implies \dfrac{\text{d}y}{\text{d}x}(5x+4y^3)=-8x-5y\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8x-5y}{5x+4y^3}\)

To find the slope of the tangent line at the point (-9, -1), substitute x = -9 and y = -1 into the differentiated equation:

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8(-9)-5(-1)}{5(-9)+4(-1)^3}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{72+5}{-45-4}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{77}{49}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{11}{7}\)

Therefore, slope of the tangent line to the curve at the given point is -11/7.

Answer:

 11.6 (6 is repeating)

Step-by-step explanation:

1.75 divided by 15% of 75