The cost of a plane ticket varies directly as the number of miles in the trip. A 3000 mile trip costs $400. What is the cost of a 450 mile trip

Answer:

y=7*3^x

Step-by-step explanation:

y=ab^x

(0,7) ⇒ 7=ab^0 ⇒ 7=a

(5, 1701) ⇒ 1701= 7b^5 ⇒ b^5=243 ⇒ b^5= 3^5 ⇒ b=3

y=7*3^x

the equation of the horizontal line passing through (-3, 4) is y = 4.

The equation of a horizontal line is of the form y = c, where c represents the y-coordinate of any point on the line. In this case, we are given that the line passes through the point (-3, 4). Since the line is horizontal, the y-coordinate remains constant for all points on the line.

Therefore, the equation of the horizontal line passing through (-3, 4) is y = 4. This means that no matter what x-value we choose, the y-value will always be 4.

In other words, all the points on this line will have a y-coordinate of 4.

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Complete question is below

Write the equation of the horizontal line that passes through (-3, 4).

The equation for the horizontal line that passes through a given point is y = b.

A horizontal line is a straight line that is parallel to the x-axis. The equation of a horizontal line is of the form y = c, where c is a constant. Since the line is horizontal, the value of y remains constant for all values of x. Therefore, the equation of a horizontal line passing through a given point (a, b) is y = b.

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Answer:

The one you have selected is correct.

Step-by-step explanation:

Answer:

its b

Step-by-step explanation:

its b

The function y = tan(-3θ) has a period of π/3 and two asymptotes: a vertical asymptote and a horizontal asymptote. The vertical asymptote occurs when -3θ is an odd multiple of π/2, and the horizontal asymptote is the x-axis.

The period of the function y = tan(-3θ) can be determined by considering the period of the tangent function, which is π. In this case, the negative sign and coefficient of 3 in front of θ compress the graph horizontally by a factor of 3. Therefore, the period of the function is π/3.

The vertical asymptotes occur when the tangent function approaches infinity or negative infinity. In the given function, this occurs when -3θ is an odd multiple of π/2. The vertical asymptotes are located at θ = -π/6, θ = -π/2, θ = -5π/6, etc.

The horizontal asymptote for the function y = tan(-3θ) is the x-axis (y = 0). As θ approaches positive or negative infinity, the tangent function oscillates between positive and negative infinity but does not approach a specific value. Thus, the x-axis serves as the horizontal asymptote for the function.

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Answer:

C

Step-by-step explanation:

A) 12+5 not greater than 23, so this is wrong

B) 12+15 not greater than 29, so this is wrong

C) 30-16 is greater than 12 this is correct

a) The average rate of change over the interval [−2,2] is 4.

b) The instantaneous rates of change at the endpoints of the interval are the same (12), but they are not equal to the average rate of change over the interval (4).

A) To find the average rate of change of g(x) over the interval [-2,2], we need to calculate the slope of the line passing through the points (-2,g(-2)) and (2,g(2)).

g(-2) = (-2)³ - 6 = -8 - 6 = -14

g(2) = (2)³ - 6 = 8 - 6 = 2

Therefore, the slope of the line passing through these two points is:

(g(2) - g(-2))/(2 - (-2)) = (2 - (-14))/(2 - (-2)) = 16/4 = 4

B) To compare this rate with the instantaneous rates of change at the endpoints of the interval, we need to find the derivative of g(x):

g'(x) = 3x²

At x=-2, the instantaneous rate of change of g(x) is:

g'(-2) = 3(-2)² = 12

At x=2, the instantaneous rate of change of g(x) is:

g'(2) = 3(2)² = 12

We can see that the instantaneous rates of change at the endpoints of the interval are the same (12), but they are not equal to the average rate of change over the interval (4). This is because the function g(x) is not a straight line and its rate of change varies across the interval.

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205 lbs is approximately equal to 92.9864 kg  ( rounded to four decimal places )

The conversion factor to convert lbs to kilogram is 0.453592

1 lbs = 0.453592 kg

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

The mass in kg = The mass in lbs × conversion factor

Substitute the values in the equation

1 lbs = 0.453592 kg

205 lbs =  0.453592 × 205

Multiply the numbers

= 92.9864 kg ( rounded to four decimal places )

Therefore, 205 lbs is 92.9864 kg

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Answer:

c/sin(60°) = 14/sin(25°)

c = 14sin(60°)/sin(25°) = 28.7

Answer:

Yes he did. The error is that you are supposed to add 2x to 3x to get 5x. So 5x = 10, x = 2

Step-by-step explanation:

When Sam cashes out the account, it will be worth $1,060.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. To calculate the amount of money Sam will have in his savings account after 3 years, you can use the formula for simple interest:

I = P * r * t where: I = interest, P = principal (initial amount deposited) = $1,000, r = annual interest rate = 2%, t = time in years = 3

So the interest earned after 3 years is:

I = $1,000 * 2% * 3

I = $60

The total amount of money in the account after 3 years will be:

P + I = $1,000 + $60

P + I = $1,060

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The quadratic example is ax² + b x + c = 0 where x stands for an unknown value and where a, b, and c stand for known numbers is known as a quadratic equation in algebra.

Quadratic equations are second-degree polynomial equations with at least one squared term. It is also referred to as quadratic equations.

The numerical coefficients a, b, and c are known, while the unknown variable x is. For example , x2 + 2x + 1. It also goes by the name quadratic equation as in: b x +c=0    

The terms a, b, and c are also referred to as quadratic coefficients.    

'Examples of Quadratics

x² –x – 9 = 0

5x² – 2x – 6 = 0
3x² + 4x + 8 = 0

-x² +6x + 12 = 0  (an example of non-quadratic equation is x³ − x² − 5 = 0)

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Answer:

D. 1/7

Step-by-step explanation:

There are seven cans of paint and only one of them are white, so there's a 1/7 of a chance she'll paint her bedroom white.

Answer:

Step-by-step explanation:

Finding probability is easy, we just add up all the options and then find out how many of them are white and write that as a fraction.

Since there are 7 options and one is white, the probability is:

Answer:

not a function

Step-by-step explanation:

{(7,4),(5, -1),(3,-8),(1,-5),(3,6)}

This is not a function

The input of x=3 goes to two different outputs y=-8 and y=6

Answer: B.

Step-by-step explanation:

By substituting the given values into the function and simplifying, we obtained the simplified expression (7h) / [2(-2+h)].

To simplify the given difference quotient, let's start by evaluating g(-3+h) and g(-3).

Given: g(x) = 7/(x+1)

Evaluating g(-3+h):

Replace x with (-3+h) in the function g(x):

g(-3+h) = 7/((-3+h)+1)

= 7/(-2+h)

Evaluating g(-3):

Replace x with -3 in the function g(x):

g(-3) = 7/(-3+1)

= 7/(-2)

= -7/2

Now, substitute these values into the difference quotient and simplify:

[g(-3+h) - g(-3)] / h

= [7/(-2+h) - (-7/2)] / h

= [7/(-2+h) + 7/2] / h

To simplify the expression further, we can find a common denominator for the two fractions in the numerator:

= [7(2) + 7(-2+h)] / [2(-2+h)]

= [14 - 14 + 7h] / [2(-2+h)]

= (7h) / [2(-2+h)]

Therefore, the simplified difference quotient is (7h) / [2(-2+h)].

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The option that describes the best decision for Larry is Larry buys the second lawn mower because he thinks the extra $5 are worth not having to do the assembly.

The cost of the first lawnmower after the discount is:

= 275 x (1 - 20%)

= 275 x 0.80

= $220

The cost of the second lawnmower is:

= 299 x 0.75

= $224.25

The difference between the lawnmowers is around $5. This $5 is the cost of the assembly on the second lawnmower and Larry might decide that this cost is worth it.

Options for this question include:

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= 70% of the flowers are carnations

Probability tells you which outcome is more likely to occur in any given event. You could determine the probability of the particular outcome by dividing the number of times that the outcome has occurred by the total no of events.

we are given that,

6/10 = 3/5 of the flowers are pink, do

we know .2/5 of the flowers are red .

Since 1/3 of the pink flowers are roses, 2/3 of

the pink flowers are on Carnations .

we are given that 2/4 of the red

flowers are carnations .

The number carnations are

\(\frac{3}{5} * \frac{2}{3} + \frac{2}{5} * \frac{3}{4}\)

\(=\frac{2}{5} +\frac{3}{10}\)

\(= \frac{4 + 3}{10}\)

\(=\frac{7}{10}\)

covert into percent

\(=\frac{7}{10} 100\)

= 70%

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Answer:

yes 1/6 is a rational number.

Answer:

181,050 pieces of paper.

Step-by-step explanation:

If she needs 3,550 copies of a 51 page document, you can easily solve this problem by multiplying the amount of copies needed by pages per copy. 3,550 x 51 is 181,050.

The expression [(8y - 4x)^2] can be simplified by expanding the square and combining like terms. The final simplified expression will be in terms of y^2, x^2, and xy.

To simplify the expression [(8y - 4x)^2], we need to expand the square using the formula (a - b)^2 = a^2 - 2ab + b^2.

Applying the formula, we have:

[(8y - 4x)^2] = (8y)^2 - 2(8y)(4x) + (4x)^2

             = 64y^2 - 64xy + 16x^2

The final simplified expression is 64y^2 - 64xy + 16x^2, which is in terms of y^2, x^2, and xy. This means that the original expression [(8y - 4x)^2] has been simplified to the form that combines like terms and eliminates any unnecessary parentheses.

It's important to note that the expression can be further simplified if there are any specific values or relationships between the variables y and x. However, without additional information, the expression 64y^2 - 64xy + 16x^2 is the simplified form based on the given expression.

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Answer:

Yes Lana will reach her goal she'll have 10,414.58 by the end of the 6 years,

Step-by-step explanation:

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

Explanation:

Let's name the friends A, B, C

If person A is first, then B or C could be second and third.

So we have ABC or ACB as two possible outcomes.

If B is first, then either A is second or C is second. Meaning we have BAC or BCA.

If C is first, then we have CAB or CBA

Overall here are the 6 different ways to have the runners finish

Note how for the first slot we have 3 ways to pick the winner. Then after that selection is made, we have 2 choices left, then 1 choice for third place. Therefore, 3*2*1 = 6 different outcomes are possible.

We can use the factorial operation on the calculator to do this with one button press, so we'd say 3! = 6. The exclamation mark means "multiply from 3 down to 1, counting down the whole time".

Another example of a factorial is:

5! = 5*4*3*2*1 = 120

The values of x in f(x) = 3|x - 2| + 6 when f(x) = 18 are 6 and -2

The function is given as:

f(x) = 3|x - 2| + 6

The value of f(x) is

f(x) = 18

So, we have:

3|x - 2| + 6 = 18

Subtract 6 from both sides

3|x - 2| = 12

Divide both sides by 3

|x - 2| = 4

Remove the absolute bracket

x - 2 = 4 or x - 2 = -4

Add 2 to both sides

x = 6 or x = -2

Hence, the values of x are 6 and -2

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Answer:

Probability ≈ 0.0714

Step-by-step explanation:

Consider permutation and combination;

\(Total Combinations - 8C4,\\8C4 = 8! / 4! * ( 8 - 4 )!,\\8 * 7 * 6 * 5 / 4!,\\\\Total Combinations = 70,\\\\Combinations of Dance Classes - 5C4,\\5C4 = 5! / 4! * ( 5 - 4 )!,\\5 * 4 * 3 * 2 * 1 / 4 * 3 * 2 * 1,\\\\Dance Classes = 5,\\\\Probability - 5 / 70 = 0.0714,\\Conclusion; Probability = ( About ) 0.0714\)

In case of a 2.5% increase in your pay which is now $25,000, your new salary will be $25,625.

First, you need to determine the percent increase i.e.2.5% of 25,000 (old salary),

            2.5%      x     25,000     =     ?

           2.5/100   x    25,000     =  625

So, the $625 would be the increased amount in your salary which is equal to 2.5% of your old salary (i.e. 25,000).

In order to find out the amount of your new salary that you will be receiving, you have to add the increased amount to the amount of your old salary, as follows:

amount of the new salary =  amount of the old salary + percent increase

                                       =     $25,000 +   $625

                                       =       $ 25,625

When an increase of 2.5% is made in your salary which is now $25,000, then your new salary becomes $25,625.

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Answer:

19

Step-by-step explanation:

Since these two are vertical angles, their measure must be equal. Therefore:

\(3x-3=6(x-10) \\\\3x-3=6x-60 \\\\3x+57=6x \\\\3x=57 \\\\x=19^{\circ}\)

Hope this helps!

Answer:

19

Step-by-step explanation:

The two angles are vertically opposite angles, so they are equal.

3x - 3 = 6 (x - 10)

3x - 3 = 6x - 60

3x - 6x = - 60 + 3

-3x = -57

x = -57/-3

x = 19

Answer:

It is the distribution of the statistic if we were to draw all possible samples of a given size from the population and calculate the statistic for each sample.

Step-by-step explanation:

The sampling distribution of a statistic refers to the range of all possible sample values of the statistic that could be drawn from the parent population under the specified sampling plan.

In other words, it is the distribution of the statistic if we were to draw all possible samples of a given size from the population and calculate the statistic for each sample.

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The amount of sandwiches purchased in total is 27.

The term "system of equations" or "equation system" in mathematics refers to a finite set of equations for which common solutions are sought. A set of simultaneous equations is sometimes known as a system of equations or an equation system.

Let the sandwiches be represented as x.

Let the fries be represented as y and drinks be represented as z.

The total cost is given as $100, that is:

x + y + z = 100 (equation 1)

Drinks and fries' cost $73.27, this can be written as:

y + z = 73.27 (equation 2)

Substitute the value of y + z = 73.27 in equation 1:

x + 73.27 = 100

x = 100 - 73.27

x = 26.73

The total amount spent on sandwiches is $26.73.

One sandwich cost $0.99.

The number of sandwiches purchased in $26.73 is:

n = 26.73/ 0.99

n = 27

Hence, the total number of sandwiches purchased is 27.

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Answer: 1.8 L/h

Step-by-step explanation:

To convert the rate of water dripping from a tap from millilitres per second (ml/sec) to litres per hour (L/h), we need to use conversion factors.

Step 1:

First, let's convert the rate from millilitres per second to litres per second.

There are 1000 millilitres in a litre, so we can divide the rate in millilitres per second by 1000 to get the rate in litres per second:

\(\LARGE \boxed{\textsf{0.5 ml/sec $\div$ 1000 = 0.0005 L/sec}}\)

Step 2:

We can convert the rate from litres per second to litres per hour. There are 3600 seconds in an hour, so we can multiply the rate in litres per second by 3600 to get the rate in litres per hour:

\(\LARGE \boxed{\textsf{0.0005 L/sec $\times$ 3600 = 1.8 L/h}}\)

Therefore, the rate of water dripping from the tap is 1.8 L/h.

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Answer:

10q^2+3q

Step-by-step explanation:

All you have to do is combine like terms I think

(I haven't done this stuff in ages so I'm most likely wrong)

Answer:

10q^2+3q

Step-by-step explanation:

2q^2 +3q +8q^2

Combine like terms

10q^2+3q