Please help me answer this question in khan academy

f(x) is a linear function that increases with x. represents the number of free nights earned as a function of x, the number of nights that you stay.

We know that f(x) represents the number of free nights earned as a function of x, the number of nights that you stay.

Such that:

f(x) = x/10.

Notice that, if x = 10, then:

[tex]f(10) = 10/10 = 1[/tex]

This means that if you stay for 10 nights, then you get a free night.

If you stay for 20 nights, then you win two free nights, and so on.

f(x) is a linear function that increases with x.

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Answer:

Step-by-step explanation:

The true statement is (A) A customer earns 1 free night per 10 nights stayed.

The function is given as:

From the above function, we can see that the number of nights (x) is divided by 10.

This means that, for every 10 nights stayed, the visitor gets one free night.

Hence, the true statement is (A) A customer earns 1 free night per 10 nights stayed.

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An equation of the circle that will pass through the four (4) vertices of the square is (x + 2)² + y² = 2².

Mathematically, the general form of the equation of a circle is given by;

(x - h)² + (y - k)² = r²

Where:

Note: The center of a circle lies on the midpoint of the diagonal of a square, which is formed by joining its endpoints (opposite).

Midpoint on x-coordinate is given by:

Midpoint = (-2 - 2)/2

Midpoint = -4/2 = -2.

Midpoint on y-coordinate is given by:

Midpoint = (-2 + 2)/2

Midpoint = 0/2 = 0.

Thus, the center (h, k) = (-2, 0).

For the radius, we have:

r = √(-2)² + 0²

r = √4 = 2.

Substituting the parameters into the general equation, we have;

(x - (-2))² + (y - 0)² = 2²

(x + 2)² + y² = 2²

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Answer:

look below

Step-by-step explanation:

first way ,10 x 22 = 220

second way , 20 x 11 = 220

There are many ways other than this but I cant tell all of them.  for example, the person can just give Rs. 1000 to the shopkeeper and receive a change of Rs. 780

There are 12 ways he can pay this amount using the notes he has the answer is 12.

A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.

Let x be the number of Rs10 notes and y be the Rs20 note

10x + 20y = 220

The whole number of x and y which satisfy the above equation:

x = 0, y =11

x = 2, y =10

x = 4, y =9

x = 6, y =8

x = 8, y =7

x = 10, y =6

x = 12, y =5

x = 14, y =4

x = 16, y =3

x = 18, y =2

x = 20, y =1

x = 22, y =0

Total number of ways = 12

Thus, there are 12 ways he can pay this amount using the notes he has the answer is 12.

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Answer:

Shown in the attachment.

Step-by-step explanation:

Shown in the attachment.

Answer:

$4020.52

Step-by-step explanation:

The future value is the principal multiplied by the amount $1.00 is worth in the future.

$4,000 × 1.00513 = $4020.52

Answer:  9 eggs were left.

Step-by-step explanation:

A dozen eggs usually mean there are 12 eggs. We have two ways to solve the problems.

First way:

The egg used to make breakfast: 12 x 25% = 12 x 0.25 = 3

The eggs were left: 12 - 3 = 9

Second way:

12 x (1 - 0.25)

= 12 x 0.75

= 9

a. The department that accounts for approximately one-fifth of the annual budget, based on the pie chart, is the Research Department.

b. The percentage of the annual budget used by the Marketing and Sales departments combined is 30%.

c. If 18% of the annual budget is used for Research, approximately the percentage used for Marketing is 9%.

A pie chart is a graphical representation of data in a circle.  In this pie chart, the area or percentage of the whole circle is 100%

Thus, we can obtain the values of the different groups represented in the pie chart by systematically dividing the circle accordingly.

The rule to follow is that vertical angles are always congruent (equal) as they have two lines that intersect to form opposite angles.

Research, Sales, and Marketing = 50% of the budget (half of the pie chart)

Research = 18%

Sales and Marketing = 32% (50% - 18%)

Research equals Media and Support and Media and Support are equal.

Therefore, Media is 9% (18%/2) and Support is also 9%.

Since opposite angles are always equal, Engineering (opposite to Sales and Marketing combined) is 32%.

This results in a total of 100% (18% + 32% + 9% + 9% +32%)

The pie chart attached shows how the annual budget for Equipment Producers Incorporated is divided by department. Use this chart to answer the questions below.

c) If 18% of the annual budget is used for Research, approximately what percentage is used for Marketing?

Thus, the department that accounts for approximately one-fifth of the annual budget, based on the pie chart, is the Research Department.

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Answer:

D. c/6 - x

Step-by-step explanation:

Rearranging with subject '6y':

6y = c - 6x

Dividing the above equation by 6 to get subject 'y':

y = c/6 - x

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Extract the common factor 6.

[tex]\bf{6(x+y)=c }[/tex]

Divide both sides by 6.

[tex]\bf{x+y=\dfrac{c}{6} }[/tex]

Subtract x from both sides.

[tex]\bf{y=\dfrac{c}{6}-x \ \ \to \ \ \ Answer }[/tex]

Therefore, the correct option is "D".

If they worked for k hours, the amount of work done would be [tex]\mathbf{ \dfrac{k(x+y)}{xy}}[/tex]hours.

Algebraic expression involves the use of variables and their arithmetic operations.

Given that:

If we have a function denoted by k (hours) indicating the work they both can do together. Then we can conclude that they can both work for:

[tex]\mathbf{=\dfrac{k}{x}+\dfrac{k}{y}}[/tex]

[tex]\mathbf{ \dfrac{k(x+y)}{xy}}[/tex]

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Answer:

81m + 27t

Step-by-step explanation:

Using distributive property, this expression can be solved.

So 9(9m + 3t) has operations in it.

9 would be multiplied by whatever is in the parenthesis followed by the variable.

So 9 * 9 = 81.

9 * 3 = 27.

So putting it together with the variables.

It would be:

⇒ 81m + 27t  

3x² + 6x - 24

Simplify 3.

3(x² + 6x - 8)

Think of x² +2x−8. Factor the expression by grouping. First, we need to rewrite the expression as x² + ax + bx - 8. To find a and b, set up a system to be solved.

Since ab is negative, a and b have opposite signs. Since a+b is positive, the positive number has a greater absolute value than the negative. Show all pairs of integers whose product is −8.

Calculate the sum of each pair.

The solution is the pair that gives sum 2

Rewrite x² + 2x − 8 as (x² − 2x ) + (4x − 8).

Simplify x in the first group and 4 in the second.

Simplify the common term x−2 with the distributive property.

The entire factored expression is rewritten.

3 ( x − 2 )( x + 4 ) ===> Answer

We conclude that the correct option is "B".

When x = 64 and y = 3, we will have:

z = 3,313.21

First, we know that z varies directly with x and inversely with y², then we can write:

z = k*x/y^2

Where k is a constant.

We know that z = 182 when x = 25 and y = 8, replacing that we can find the value of k.

182 = k*25/(8²)

k = 182*8²/25 = 465.92

Now, we just need to evaluate the function in x = 64 and y = 3.

z = (465.92)*64/3² = 3,313.21

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Using proportions, it is found that the meaning of 1 + x is the percent of original price being paid.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, the total cost of the toy is given by:

15.85(1 + x).

In which x is the sales tax.

We have that:

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Answer:

y = 3x - 13

Step-by-step explanation:

We are given the points (7,8) and (3,-4)

We want to write an equation of the line that passes through those 2 points.

There are 3 ways to write the equation of the line:

Although while any one of these options work, the most common way is to use slope-intercept form, so let's do it that way.

First, we need to find the slope of the line.

The slope (m) can be found using this formula: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] are points.

Even though we already have 2 points, let's label their values to avoid any confusion.

[tex]x_1=7\\y_1=8\\x_2=3\\y_2=-4[/tex]

Now substitute these values into the formula.

m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m=[tex]\frac{-4-8}{3-7}[/tex]

Subtract.

m=[tex]\frac{-12}{-4}[/tex]

Divide.

m = 3

The slope of the line is 3.

Here is the equation of the line so far:

y = 3x + b

We now need to find b.

As the equation passes through  (7,8) and (3,-4), we can use either one of the points to help us solve for b.

Taking (7,8) for instance:

Substitute 7 as x and 8 as y in the equation.

8 = 3(7) + b

Multiply

8 = 21 + b

Subtract 21 from both sides

-13 = b

Substitute -13 as b in the equation.

y = 3x - 13

Topic: finding the equation of the line

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A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of the line that passes through the points (7,8) and (3,-4) is y=3x-13.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is the y-intercept.

The slope of the equation will be,

Slope, m = (-4-8)/(3-7) = -12/-4 = 3

Substitute one of the points in the equation of the line,

-4 = 3(3) + C

C = -13

Hence, the equation of the line that passes through the points (7,8) and (3,-4) is y=3x-13.

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Applying partial fractions, the system of equations that can be used to find the values of A and B is given as follows:

The partial fraction is given as follows:

[tex]\frac{-15x + 10}{(5x - 2)^2} = \frac{A}{5x - 2} + \frac{B}{(5x - 2)^2}[/tex]

Applying the least common multiple at the right side, we have that:

[tex]\frac{-15x + 10}{(5x - 2)^2} = \frac{A(5x - 2) + B}{(5x - 2)^2}[/tex]

[tex]\frac{-15x + 10}{(5x - 2)^2} = \frac{5Ax - 2A + B}{(5x - 2)^2}[/tex]

Hence, comparing both sides of the equality:

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Answer:

The answer is Be

Step-by-step explanation:

5A=-15

-2A+B=10

The  last day for taking the cash discount is May 5  and discount is taken is: $12,398.6.

Since the invoice was dated April 12, the last day for taking the cash discount is May 5.

Cash discount

Using this formula

Amount paid =Invoice amount × (1-rate)

Let plug in the formula

Amount paid=$13,190 ×(1-6%)

Amount paid=$13,190×0.94

Amount paid=$12,398.6

Therefore the  last day for taking the cash discount is May 5 and the amount to be paid is: $12,398.6.

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Answer:

1.33 repeating

Step-by-step explanation:

you just do 4 divided by 3.

Please mark as brianliest if i got it right

The value of the quotient is  [tex]\frac{45\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})} = 45(\cos(\frac{\pi}{6}) + i\sin(\frac{\pi}{6}))[/tex]

The expression is given as:

[tex]\frac{90\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{2\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})}[/tex]

Divide 90 by 2

[tex]\frac{45\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})}[/tex]

As a general rule, we have:

[tex]\frac{\cos(\frac{\pi}{A}) i\sin(\frac{\pi}{A})}{\cos(\frac{\pi}{B}) i\sin(\frac{\pi}{B})} = \cos(\frac{\pi}{2B/A}) + i\sin(\frac{\pi}{2B/A})[/tex]

The above means that:

A = 4 and B = 12

So, we have:

2B/A = 2 * 12/4

Evaluate

2B/A = 6

So, the equation becomes

[tex]\frac{\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})} = \cos(\frac{\pi}{6}) + i\sin(\frac{\pi}{6})[/tex]

Substitute [tex]\frac{\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})} = \cos(\frac{\pi}{6}) + i\sin(\frac{\pi}{6})[/tex] in [tex]\frac{45\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})}[/tex]

[tex]\frac{45\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})} = 45(\cos(\frac{\pi}{6}) + i\sin(\frac{\pi}{6}))[/tex]

Hence, the value of the quotient is  [tex]\frac{45\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})} = 45(\cos(\frac{\pi}{6}) + i\sin(\frac{\pi}{6}))[/tex]

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Complete question

What is the quotient of [tex]\frac{90\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{2\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})}[/tex]

The required value of mean and variance is 203 and 3942 respectively.
Hence option B is correct.

The sample includes the following claims: 192, 113, 200, 287, and 225.

The statistic is the study of mathematics which deal with relations between comprehensive data.

Mean(x) = 192+113+200+287+225/5
x = 203

variance =[tex]\frac{\sum(x-x_i)^2}{n^2-1}[/tex]

=summation of squared value/n^2−1

=15769/25−1

=15769/24

=3942

Thus, the required value of mean and variance is 203 and 3942 respectively.

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Answer:

a. f(0) = -6

b. f(2) =10

c. f(-4) = 32

d. f(b) = 3b^2+2b-6

e. f(4a) = 48a^2+8a-6

The function values for the function f(x) = 3x² + 2x - 6, for the values are:

a. f(0) = -6

b. f(2) = 10

c. f(-4) = 34

d. f(b) = 3b² + 2b - 6

e. f(4a) = 48a² + 8a - 6

To calculate function value f(k) for a function f(x), we substitute variable x = k, in the function f(x).

In the question, we are asked to find the function value for the function f(x) = 3x² + 2x - 6 for:

a. f(0)

b. f(2)

c. f(-4)

d. f(b)

e. f(4a).

We calculate these in the following ways:-

a. f(0):

We substitute the value of x = 0 in the function f(x).

Therefore f(0) = 3(0)² + 2(0) - 6,

or, f(0) = 0 + 0 - 6 = -6.

Therefore, the function value f(0) for the function f(x) = 3x² + 2x - 6 is -6.

b. f(2):

We substitute the value of x = 2 in the function f(x).

Therefore f(2) = 3(2)² + 2(2) - 6,

or, f(2) = 12 + 4 - 6 = 10.

Therefore, the function value f(2) for the function f(x) = 3x² + 2x - 6 is 10.

c. f(-4):

We substitute the value of x = -4 in the function f(x).

Therefore f(-4) = 3(-4)² + 2(-4) - 6,

or, f(-4) = 48 - 8 - 6 = 34.

Therefore, the function value f(-4) for the function f(x) = 3x² + 2x - 6 is 34.

d. f(b):

We substitute the value of x = b in the function f(x).

Therefore f(b) = 3(b)² + 2(b) - 6,

or, f(b) = 3b² + 2b - 6.

Therefore, the function value f(b) for the function f(x) = 3x² + 2x - 6 is 3b² + 2b - 6.

e. f(4a):

We substitute the value of x = 4a in the function f(x).

Therefore f(4a) = 3(4a)² + 2(4a) - 6,

or, f(0) = 48a² + 8a - 6.

Therefore, the function value f(0) for the function f(x) = 3x² + 2x - 6 is 48a² + 8a - 6.

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The percentage of the original sample that is left after 115 days is; 23.4733%

Formula for radioactive decay is;

A = A₀ * (1/2)^(t/t_¹/₂)

where;

A = quantity of the substance remaining

A₀ = initial quantity of the substance

t = time elapsed

t_¹/₂ = half life of the substance

Thus;

A/A₀ =  (1/2)^(115/55)

A/A₀ =  0.234733 or 23.4733%

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Answer:

0.98 miles

Step-by-step explanation:

Answer:

1/25

Step-by-step explanation:

The bag has:

The probability of picking a yellow marble is 2/10=1/5.

So, the answer is (1/5)² = 1/25

Answer:

[tex]\frac{1}{6}[/tex]

Step-by-step explanation:

Given

ab = [tex]\frac{1}{4}[/tex]

bc = [tex]\frac{1}{3}[/tex]

ac = [tex]\frac{1}{3}[/tex]

We will use the first equation to find b in terms of a.

b = [tex]\frac{1}{4a}[/tex]

Now we will substitute b into 2nd equation to find c in terms of a.

[tex](\frac{1}{4a} )(c)=\frac{1}{3} \\\frac{c}{4a} =\frac{1}{3} \\3c = 4a\\c = \frac{4a}{3}[/tex]

Now we will substitute c into 3rd equation to find value a.

[tex]a(\frac{4a}{3} )=\frac{1}{3} \\\frac{4a^{2} }{3} =\frac{1}{3} \\4a^{2} =1\\a^{2} =\frac{1}{4} \\a=\sqrt{\frac{1}{4} } \\=\frac{1}{2}[/tex]

Now we will substitute a into first equation to find b.

b = [tex]\frac{1}{4(\frac{1}{2}) } \\=\frac{1}{2}[/tex]

Next we will substitute a into the 3rd equation to find c.

c = [tex]\frac{4(\frac{1}{2}) }{3} \\=\frac{2}{3}[/tex]

Now we got all 3 values, when we multiply them together,

a x b x c = [tex]\frac{1}{2} *\frac{1}{2} *\frac{2}{3} \\=\frac{2}{12} \\=\frac{1}{6}[/tex]

Answer:

  7z^2/y -8z^4y -(9/2)z^2y^4

Step-by-step explanation:

The quotient of division of a polynomial by a monomial is the sum of quotients of each of the terms divided by the monomial. "Simplify" in this context generally means that no common factors remain factored out.

The rules of exponents apply:

  (a^b)/(a^c) = a^(b-c)

  a^-b = 1/a^b

The problem is effectively three (3) division/simplification problems.

  [tex]\dfrac{-14z^4y^2+16z^6y^4+9z^4y^7}{-2z^2y^3}=\dfrac{-14z^4y^2}{-2z^2y^3}+\dfrac{16z^6y^4}{-2z^2y^3}+\dfrac{9z^4y^7}{-2z^2y^3}\\\\=7z^{4-2}y^{2-3}-8z^{6-2}y^{4-3}-\dfrac{9}{2}z^{4-2}y^{7-3}=\boxed{\dfrac{7z^2}{y}-8z^4y-\dfrac{9}{2}z^2y^4}[/tex]

__

Additional comment

We have elected to retain the original order of variables (z then y) and the original order of terms. Ordinarily, standard form would have the variables in alphabetical order (y then z) and the terms in order by decreasing degree. This order of terms also makes the leading coefficient positive. (The minus sign for a negative leading coefficient sometimes gets lost.)

The solution of the given inequality is:

x ≤ 15.24

We know that the maximum that she can spend on gasoline is the 12% of $400.

That is:

(12%/100%)*$400 = 0.12*$400 = $48

Now, we know that each gallon of gas costs $3.15, then if x is the number of gallons of gas that she buys, we have the inequality:

x*$3.15 ≤ $48

To solve the inequality, we need to divide both sides by $3.15

x ≤ $48/$3.15

x ≤ 15.24

So the maximum number of gallons of gasoline that she can buy is 15 gallons (actually a little more).

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Answer:

$12.03

Step-by-step explanation:

I = prt

I = (875)(0.055)(3/12)

I = 12.03

Answer: $12.03

The events are not mutually exclusive.

Two events that cannot occur at the same time are called Mutually exclusive event.

It is given that

A sample of 75 books is selected from a library.

Event A:  At least 10 of the authors are female

Event B : At least 10 of the books are fiction.

Both can happen simultaneously

Therefore the events are not mutually exclusive.

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The function will go somewhere between x = 4 and x = 5

The function is given as:

y = 2^x

The question implies that:

If the maximum y value on a graph is x = 20; What is the maximum x value on the graph of y = 2^x

To do this, we start by setting y to 20.

So, we have:

2^x = 20

Take the logarithm of both sides

x log(2) = log(20)

Divide by log(2)

x = 4.32

4.32 is between 4 and 5

Hence, the function will go somewhere between x = 4 and x = 5

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