You took a taxi to your house from the airport. The taxi company charges an initial fee of $5 and then $4 per mile. When the ride is over, you end up paying a total fare of $49. How many miles away is your house from the airport?

The distance between points (2, 3) and (-4, 5) is 6.3 units.

As we know according to the distance formula the distance between points (x₁, y₁) and (x₂, y₂) is given by,

[tex]d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]}[/tex]

Here we have been given points (2,3) and (-4,5)

Let us assume that  (x₁, y₁) = (2, 3)

and (x₂, y₂) = (-4, 5)

Let d represents the distance between points (2,3) and (−4,5)

Using above distance formula the distance d between given points would be,

[tex]\Rightarrow d = \sqrt{[(x_2 - x_1)^2 + (y_2 - y_1)^2]}\\\\\Rightarrow d = \sqrt{[(-4 - 2)^2 + (5 - 3)^2]}\\\\\Rightarrow d = \sqrt{[(-6)^2 + (2)^2]}\\\\\Rightarrow d = \sqrt{36+4}\\\\\Rightarrow d = \sqrt{40}\\\\\Rightarrow d = 6.3~units[/tex]

Therefore, the distance is 6.3 units.

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The complete question is:

What is the distance between points (2,3) and (−4,5)  ?

The multiplicative inverse of 'a' is indicated by a-1 or 1/a. In other words, the multiplicative inverse of a number is explained as 1 divided by the number.

The multiplication inverse of 3 is 1/3.

The multiplication inverse of 8 is. 1/8.

The multiplicative inverse is defined as the reciprocal of a given number. It is used to clarify mathematical expressions.

The word 'inverse' infers something opposite/contrary in effect, position, order, or direction. A number when multiplied by its multiplicative inverse results in 1.

The multiplicative inverse formula is called that the product of a number and its reciprocal is 1.

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The surface area of a cylinder is given by the formula 2πr (r + h) where r is the radius and h is the height.

Plugging in the given values, we get: 2π(6) (6 + 3) = 2π(6)(9) = 108π.

Rounded to the nearest thousandth, this is approximately 342.8.

The surface area of an object is the total area that the object's surface occupies. It is a measure of the total area of all the exposed surfaces of an object. It is typically measured in square units, such as square meters or square inches. The surface area of an object can be calculated using various formulas, depending on the shape of the object. For example, the surface area of a cube is the area of all six faces of the cube, while the surface area of a sphere is the area of the spherical surface. The surface area is an important property of an object in fields such as engineering, physics, chemistry, and architecture.

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The number of sets of one hot dog and one soda  he can buy is; 5 sets

We are given;

Cost of hotdog = $3

Cost of soda = $4

Total amount grant has = $38

Now, we are told that he wants to buy same set of hotdog as that of sodas. Thus, let the amount be x and we have the algebraic expression;

3x + 4x = 38

7x = 38

x = 38/7

x = 5³/₇

We will pick the whole number to get 5 sets

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Complete question is;

Grant is at a basket ball game and wants to buy as many $3 hotdog and $4 Sodas as he can. If grant has $38 and wants to buy as many sets of one hot dog and one soda as he can how can he buy?

The given equations 3x - y + 8 = 0 and 6x - ky = -16 represent coincident lines if the value of k is 2.

Given the pair of equations is

3x - y + 8 = 0

6x - ky = -16 describes coincident lines.

We have to calculate the value of k.

We know that,

For a pair of linear equations in two variables a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0,

If a₁/a₂ = b₁/b₂ = c₁/c₂, then the pair of linear equations is dependent and consistent.

We have, a₁ = 3, b₁ = -1, c₁ = 8

a₂ = +6, b₂ = -k, c₂ = +16

So, a₁/a₂ = 3/6 = 1/2

b₁/b₂ = -1/-k = 1/k

c₁/c₂ = 8/16 = 1/2

a₁/a₂ = b₁/b₂ = c₁/c₂ = 1/2

1/k = 1/2

k = 2

Therefore, the value of k is 2.

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The percentage of data within 2 standard deviations of the mean is given as follows:

100%.

Using a calculator, the measures for this problem are given as follows:

The bounds within two standard deviations of the mean are given as follows:

All the measures in this problem are within these bounds, hence the percentage is of 100%.

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Answer: x = 6 and y = -9

Step-by-step explanation:

Solve by reduction method

7x + 2y = 24

8x + 2y = 30

We will multiply the first equation by 8, and the second equation by -7, then both equations must be added.

8(7x + 2y = 24)

-7(8x + 2y = 30)

Add these equations to eliminate x

  2y = -18

Then we solve 2y = -18 for y. (We divide by 2)

      2y/2 = -18/2

      y = -9

We place the found value of y , in one of the original equations y in order to solve for x.

7x + 2y = 24

7x + 2(-9) = 24

7x - 18 = 24

We add 18 to both sides.

  7x - 18 + (18) = 24 + (18)

       7x = 42

We add 18 to both sides.

 7x/7 = 42/7

  x = 6

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We can use the proportion:

measurement in the drawing / scale = actual measurement

We know that the scale is 5 millimeters : 3 meters and the actual width of the parking lot is 42 meters. To find the width of the parking lot in the drawing, we can set up the proportion as:

width in drawing / 5 millimeters = 42 meters / 3 meters

To solve for the width in the drawing, we can cross-multiply and divide:

width in drawing = (42 meters * 5 millimeters) / 3 meters

Converting millimeters to meters:

width in drawing = (42 * 5 * 10^-3) / 3

width in drawing = (210 * 10^-3) / 3

width in drawing = 70 * 10^-3 meters = 0.07 meters

So the width of the parking lot in the drawing is 0.07 meters or 70 millimeters.

The value of y in the expression x + 7y = 18 when x = - 3 is 3.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

We know Substitution in mathematics is when we replace some specific numerical values with variables according to our wants or given in the problem.

Given, x = - 3 and x + 7y = 18.

Replacing x with - 3 in x + 7y = 18.

- 3 + 7y = 18.

7y = 18 + 3.

7y = 21.

y = 21/7.

y = 3

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the product of the given expressions will be x([tex]x^{5/12}[/tex])

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

[tex]x^{2/3}[/tex] * [tex]x^{3/4}[/tex]

= [tex]x^{2/3+3/4}[/tex]

=[tex]x^{17/12}[/tex]

=x([tex]x^{5/12}[/tex])

Hence the product of the given expressions will be x([tex]x^{5/12}[/tex])

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solved, 3x+2/x+7 = 3x²+21x+2/x+7

solution:

3x+2/x+7

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x times x+7/x+7

we get,

3x(x+7)/x+7 + 2/x+7

since 3x(x+7)/x+7 and 2/x+7  have the same denominator, add them by adding their numerators.

we get,

3x (x+7) +2/x+7

Do the multiplications in 3x(x+7)+2.

we get, 3x²+21x+2/x+7

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The point (7, 10.5) is on the graph of both equations and satisfies the system of equations.

To find the solution to a system of equations, we need to find the values of x and y that satisfy both equations simultaneously.

The system of equations is:

y = 2x - 3.5

x - 2y = -14

We can begin by solving one of the equations for one of the variables, for example, we can solve the first equation for y:

y = 2x - 3.5

Next, we can substitute this expression for y into the second equation:

x - 2(2x - 3.5) = -14

This gives us:

x - 4x + 7 = -14

-3x = -21

x=7

Now we can substitute this value of x back into the first equation to find the corresponding value of y:

y = 2(7) - 3.5

y = 10.5

So the solution to the system of equations is x = 7, y = 10.5.

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The subsequent three words in the list. 3 14, 32, 60, 98, ... is 276 . In this case, the order is 3, 14, 32, 60, 98, and 276.

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The next three terms in the sequence are 79, 90, and 101.

a) To find a formula for the sequence, we can use a difference table.

First, let's write out the first few terms of the sequence:

3, 14, 32, 60, 98, ...

Next, we'll create a difference table:

n | Term | Difference

1 | 3 |

2 | 14 | 11

3 | 32 | 18

4 | 60 | 28

5 | 98 | 38

We see that the difference is increasing by 10 each time, so our formula can be written as:

Term = 11n + 3

To check the formula, we can plug in a few values of n and see if it matches the terms in the sequence:

n = 1, Term = 11(1) + 3 = 14

n = 2, Term = 11(2) + 3 = 32

n = 3, Term = 11(3) + 3 = 60

The formula matches the terms in the sequence, so it is correct.

b) To find the next three terms in the sequence, we can use our formula:

n = 6, Term = 11(6) + 3 = 79

n = 7, Term = 11(7) + 3 = 90

n = 8, Term = 11(8) + 3 = 101

So the next three terms in the sequence are 79, 90, and 101.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{14x + 14x}\\\\\mathsf{= 14(\dfrac{1}{2}) + 14(\dfrac{1}{2})}\\\\\mathsf{= \dfrac{14}{1}\times \dfrac{1}{2} + \dfrac{14}{1} \times \dfrac{1}{2}}\\\\\mathsf{= \dfrac{14\times1}{1\times2} + \dfrac{14\times1}{1\times2}}\\\\\mathsf{= \dfrac{14}{2} + \dfrac{14}{2}}\\\\\mathsf{= 7 + 7}\\\\\mathsf{= 14}\\\\\\\huge\text{Therefore, your answer should be:}\\\huge\boxed{\mathsf{14}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

14x + 14x = 14

Step-by-step explanation:

Given expression,

→ 14x + 14x

Now we have to use,

→ x = 1/2

Let's simplify the expression,

→ 14x + 14x

→ 14(1/2) + 14(1/2)

→ (14/2) + (14/2)

→ 7 + 7

→ 14 => {final value}

Hence, required answer is 14.

For the value of k is equal to 6, the system of equations,

kx + 3y - (k – 3) = 0 and 12x + ky - k = 0 have infinitely many solutions

Here we have equations

kx + 3y - (k – 3) = 0

12x + ky - k = 0

For a system of 2 linear equations,

a₁x + a₂y + a₃ = 0

b₁x + b₂y + b₃ = 0

They will have infinitely many solutions if

a₁/b₁ = a₂/b₂ = a₃/b₃

here,

k = a₁,          3 = a₂          - (k – 3) = a₃

12 = b₁         k = b₂           - k = b₃

Hence

k/12 = 3/k = (3 - k)/(-k)

Taking up

3/k = (3 - k)/(-k)

we get

3 = k - 3

or, k = 6

hence for k = 6, the equations will have infinite solutions.

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Complete Question

What is the value of k such that the following pair of equations has infinitely many solutions?

kx + 3y - (k – 3) = 0

12x + ky - k = 0

The required number of actual meters represented by 18 centimeters on the blueprint is 3.6 meters.

The scale factor is defined as the ratio of the modified change in length to the original length.

Here,
A scale on a blueprint drawing of a house shows that 10 centimeters represent 2 meters.

Scale factor,
10 centimeter: 2 meters = 1 centimeters : 0.2 meters

So,
18 centimeters = 18 × 0.2 meters = 3.6 meters.

Thus, the required number of actual meters represented by 18 centimeters on the blueprint is 3.6 meters.

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Draw a circle over the number to begin plotting an inequality, such as x>9, on a number line (e.g., 9). If the sign also says equal to (or), then complete the circle.

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Answer:

= 7  7/8

Step-by-step explanation:

3 3/8 = 3 + 3/8 = 24/8 + 3/8 = (24+3)/8 = 27/8

2 1/3 = 2 + 1/3 = 6/3 + 1/3 = (6+1) / 3 = 7/3

Then:

3 3/8 x 2 1/3 = 27/8 x 7/3 = (27x7) / (8x3)

= 189 / 24 = 168/24 + 21/24 = 7 + 21/24

= 7 + 7/8

= 7 7/8

It will take 8 days for 50 children to catch the flu

The given equation states as follows:

P = 110/(1+7e⁻⁰²²ⁿ     (Where n stands for t)

P = 110/(1+7e⁻⁰²²ⁿ = 2.2

7.e⁻⁰²²ⁿ = 2.2 - 1

7.e⁻⁰²²ⁿ = 1.2/7

0.22n = In (12/7)

n= 8.02

Recall that n=t

Therefore t = .02

Therefore time = 8 days

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The type of the function y = -2x + 3 is a linear function.

Function in math is known as a rule that gives value of a dependent variable that corresponds to specified values of one or more independent variables.

Here we have given that the function y = -2x +3 and here we need to identify the type of the function.

As we all know that the type of function called linear function is defined as a function that has either one or two variables without exponents.

While we consider the definition we have identified that the given function is is the linear function because in the given function there is no exponents in it so it can fall under the category of the function called exponents.

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The formula for the sum rule is: P(A or B) = P(A) + P(B) - P(A and B)

The sum rule, also known as the addition rule of probability, states that the probability of any two events occurring together is the sum of the probability of each event occurring individually, minus the probability of them both occurring at the same time. The formula for the sum rule is:

P(A or B) = P(A) + P(B) - P(A and B)

where A and B are two events and P(A) and P(B) are the probabilities of each event occurring individually, and P(A and B) is the probability of both events occurring at the same time.

The sum rule is used when the two events are mutually exclusive, meaning that they cannot happen at the same time. In this case, P(A and B) = 0, so the formula becomes:

P(A or B) = P(A) + P(B)

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The probability that an individual got the flu given that they received the  vaccine is 0.739130435.

What is probability ?

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Bayes' theorem to solve for the probability that an individual got the flu given that they received the vaccine. Bayes' theorem states that:

P(A|B) = P(B|A) * P(A) / P(B)

where P(A|B) is the probability of event A given that event B has occurred, P(B|A) is the probability of event B given that event A has occurred, P(A) is the prior probability of event A, and P(B) is the prior probability of event B.

The probability of event B given that event A has occurred, P(B|A), can be calculated as the general chance of both events happening, which is .27278402.

So, using Bayes' theorem:

P(A|B) = P(B|A) * P(A) / P(B) = .27278402 * .33208489 / .06803995 = .739130435

Therefore, the probability that an individual got the flu given that they received the vaccine is 0.739130435.

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The probability that an individual got the flu is approximately 1.09.

Let's call the probability of receiving a placebo "P(placebo)" and the probability of not getting the flu "P(no flu)". Then, using the information given, we have:

P(placebo) = 0.33208489

P(no flu) = 0.93196005

P(placebo and no flu) = 0.27278402

To find the probability of getting the flu given that they received the vaccine (not a placebo), we can use the formula for conditional probability:

P(flu | vaccine) = P(flu and vaccine) / P(vaccine)

Since the individual either received a placebo or a vaccine (but not both), the probability of receiving a vaccine is given by:

P(vaccine) = 1 - P(placebo) = 1 - 0.33208489 = 0.66791511

The probability of getting the flu and receiving a vaccine is equal to the complement of the probability of getting the placebo and not getting the flu, which is:

P(flu and vaccine) = 1 - P(placebo and no flu) = 1 - 0.27278402 = 0.7272159

Finally, substituting these values into the formula for conditional probability, we get:

P(flu | vaccine) = P(flu and vaccine) / P(vaccine) = 0.7272159 / 0.66791511 = 1.09103623

So, the probability of getting the flu given that an individual received the vaccine is approximately 1.09.

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Answer:

Step-by-step explanation:

the answer to the first puzzle being choose will be 100 pieces is 8 out of 100

Based on the information provided, 95% of the number is equivalent to 342.

To find the 95% of the number, let's use the rule of three with the information provided to find the 100%.

Based on this, let's create a simple equation:

Therefore, 100% of this number is 360, now using this information, let's find the 95% of the same number.

You can double check this result using the 70% as follows

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Answer:

8

Step-by-step explanation:

[tex]x^2-2x \\x=4\\(4)^2-2(4)\\16-8\\8[/tex]

Answer:Kids grow at their own pace. Big, small, tall, short — there is a wide range of healthy shapes and sizes among children. Genetics, gender, nutrition, physical activity, health problems, environment, and hormones all play a role in a child's height and weight. And many of these things can vary widely from family to family.

Step-by-step explanation:

No, 0 is neither an infinite solution nor no solution.

The solution x = 0 implies that the value 0 satisfies the equation, so there is a solution. “No solution” implies that there is no value, not even 0, which would satisfy the given equation.

Let us take an example for a more reasonable interpretation,

An example is the equations

² + 1 = 0 and

− 3 = 2 − 3

Suppose that is real.

The first equation has no solution, while the second equation has a solution = 0.

Hence, 0 can be a solution to a system of equations.

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The total cost of the fence will be £841. The solution is obtained using the concept of perimeter of triangle.

What is perimeter of triangle?

Any two-dimensional figure's perimeter is determined by the space surrounding it. By summing the lengths of the sides, we can determine the perimeter of any closed shape.

We are given a right-angled triangle with one angle 59° and the adjacent side as 145 meters.

We know that tan θ = Opposite side/Adjacent side

⇒ tan 59° = Opposite side/145

⇒ 1.66 = Opposite side/145

⇒ 241 meters(approx) = Opposite side

Now, using pythagoras theorem,

⇒Hypotenuse^2 = Base^2 + Perpendicular^2

⇒Hypotenuse^2 = 241^2 + 145^2

⇒Hypotenuse^2 = 58,081 + 21,025

⇒Hypotenuse^2 = 79,106

⇒Hypotenuse = 281 meters(approx)

Perimeter of triangle = Sum of three sides

⇒ Perimeter = 145 + 241 + 281

⇒ Perimeter = 667 meters

The fence costs £ 1.26 per meter

Total cost of fence = 1.26 * 667 = £840.42 = £841

Hence, the total cost of the fence will be £841.

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