You own a motel with 30 rooms and have a pricing structure that encourages rentals of rooms in groups. One room rents for $85.00, two for $83.00 each, and in general the group rate per room is found by taking $2 off the base of $85 for each extra room rented.

(c) Find a formula for a function R = R(n) that gives the total revenue from renting rooms to a convention host.
(d) Use functional notation to show the total revenue from renting a block of 9 rooms to a group. Calculate the value.

The number of 17 cars have clocks but no radios.

Subtraction is a mathematic operation. Which is used to remove terms or objects in the expression.

Given:

Out of 53 cars,41 had clocks,30 had radios and 6 had neither.

That means,

53-6 = 47 cars have either clocks or radios or both.

47 - 30 = 17 cars have no radio.

47 - 41 = 6 cars have no clocks.

Hence, 17 cars have clocks but no radios.

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Answer:

Improper, proper, proper, improper

Step-by-step explanation:

Step-by-step explanation:

To be a proper fraction the numerator (top number) must be less the the denominator (bottom number). Let’s start at the top.

27/27

This would be an improper fraction because the numerator is equal to the denominator, not less.

6/17

Because 6 is less then 17 this would make it a proper fraction

8/9

Same case as the last one, this is a proper fraction because the numerator is less then the denominator

21/5

21 is definitely more the 5 making this a improper fraction.

Hope this helped :)

There are 4 zeros in the graph and the multiplicity is 5.

The zeros of a function are defined as the values of the variable of the function such that the function equals 0. Graphically, the zeros of a function are the points on the x-axis where the graph cuts the x-axis. In other words, we can say that the zeros of a function are the x-intercepts of its graph. The number of zeros of a polynomial function is equal to the degree of the polynomial.

In the given graph,

There are 4 turning points in the graph.

The 4 zeros from the graph are

(-3, 0), (-2, 0), (1, 0) and (1.5, 0)

The graph touches the x-axis and bounces off of the axis, it is a zero with  multiplicity is 5.

Therefore, there are 4 zeros in the graph and the multiplicity is 5.

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The graph of the y+2x=6 is given in the attachment.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The standard equation of a line is expressed as y = mx + b, m is the slope

and b is the y-intercept.

Given the equation y = 2x - 2

If x = -2

y = 2(-2) - 2

y = -4-2

y = -6

If x  = 4

y = 2(4) - 2

y = 8-2

y = 6

The point (-2, -6) and (4, 6 )must be on the line graph.

Hence, the graph of the y+2x=6 is given in the attachment.

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Answer:I.65

Step-by-step explanation:

The publisher nedds to produce 2414 books and sell so that production cost will equal the money from sales.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

A small publishing company is planning to publish a new book.

The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing).

The one-time fixed costs will amount to $27,160.

The variable costs will be $8.75 per book.

The publisher will sell the finished product to bookstores at a price of $20.00 per book.

Let x be the number of books.

Cost = 8.75x + 27160

Revenue = 20x

Revenue = cost

20x = 8.75x + 27160

11.25x = 27160

x = 2414.2

x ≈ 2414 books.

Therefore, the required number of books are 2414 books.

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Answer:

-4

4

14

Step-by-step explanation:

A:

5 + (-3)(3) = 5 -9 = -4

B:

5+ (-3)(1/3) = 5 - 1 - 4

C:

5 + (-3)(-3) = 5 + 9 = 14

The animal listed in the table that weighs the most, eats the most,

and the animal that weighs the least, eats the least.

Molly's claim is correct.

The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

A table is given below:

Animals     Weight of the animals,   The weight of food packages

Cat                  6 Kg                                    300 grams.

Dog                 12 Kg                                  900 grams.

From the table:

The animal listed in the table that weighs the most, eats the most,

and the animal that weighs the least, eats the least.

Therefore, Molly's claim is correct.

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Answer:

150 in cubed

Step-by-step explanation:

A circle having radius 5 and centre at (0,0) has equation x² + y² = 25.

What is the equation of circle?

A circle is a closed curve that extends outward from a set point known as the centre, with each point on the curve being equally spaced from the centre. A circle with a (h, k) centre and a radius of r has the equation:

(x-h)² + (y-k)² = r²

Let (x,y) be any point on the circle.

Given that centre of the circle is origin (0,0).

Now, we know that the distance from any point on the circle to the centre is equal to the radius of the circle.

So, distance between point (x,y) and centre (0,0)  is equal to radius of the circle which is given 5 units.

Now, using the distance formula -

√[(x - 0)² + (y - 0)²] = 5

Squaring on both the sides of the equation -

(x - 0)² + (y - 0)² = 25

So, the equation of the circle with radius 5, centred at the origin is x² + y² = 25.

Therefore, the equation is x² + y² = 25.

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Answer: maybe look up the answer and ask ur teacher what to do

Step-by-step explanation:

Using the Chinese Remainder Theorem, the smallest positive integer solution is x1 = 62.

We can use the Chinese Remainder Theorem to find the smallest positive integer solution for this problem.

The Chinese Remainder Theorem states that if x ≡ a (mod m) and x ≡ b (mod n), then x is congruent to a unique value modulo mn. That is, there exists a unique solution x such that x is congruent to a modulo m and congruent to b modulo n, and the solution x is between 0 and mn - 1.

So, we want to find the smallest x such that:

x ≡ 6 (mod 8) and x ≡ 7 (mod 9)

We can start by finding a solution x1 such that x1 ≡ 6 (mod 8) and x1 ≡ 7 (mod 9). One such solution is:

x1 = 6 + 8k for some integer k

We can use the formula x1 = 6 + 8k to find a solution x1 that is also congruent to 7 (mod 9):

x1 = 6 + 8k = 7 + 9l (mod 9)

Expanding the right side of this equation, we get:

6 + 8k = 7 + 9l (mod 9)

6 - 7 = 9l - 8k (mod 9)

-1 = 9l - 8k (mod 9)

Since 9 and 8 are relatively prime, we can use the Extended Euclidean Algorithm to find integers r and s such that:

8r + 9s = gcd(8, 9) = 1

Using the Euclidean Algorithm, we can find r = -1 and s = 1. So,

-8 = 9(l - rk) (mod 9)

Since 9 is relatively prime to 8, l - rk is a multiple of 9. We can then rewrite the equation as:

-8 = 9j (mod 9)

Adding 9 to both sides of the equation, we get:

1 = 9j (mod 9)

So, j = 1.

Now, we have:

k = (1 - l) / r

Since r = -1, we can replace k with -l:

k = -l

So, we have:

x1 = 6 - 8l

And,

x1 = 7 + 9l (mod 9)

Combining these two equations, we get:

6 - 8l = 7 + 9l (mod 9)

Subtracting 9l from both sides, we get:

-2l = 13 (mod 9)

Dividing both sides by -2, we get:

l = -13 / -2 = 7 (mod 9)

So,

k = -l = -7 (mod 9)

And,

x1 = 6 - 8(-7) = 6 + 56 = 62 (mod 8)

So,

x1 = 62 (mod 8) and x1 = 7 (mod 9)

The smallest positive integer solution is x1 = 62

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Answer: The expected value for rolling a 1 or 6 is 50 points, and the expected value for rolling any other number is -5 points. The chance of rolling a 1 or 6 is 2/6, or 1/3. The chance of rolling any other number is 4/6, or 2/3. The expected value for rolling the die once is:

(1/3 * 50) + (2/3 * -5) = 16.67

So, if you rolled the die 100 times, you would expect to gain or lose:

100 * 16.67 = 1667 points

The answer is: a gain of about 1,667 points.

Step-by-step explanation:

Answer: The equation represents the value (in dollars) of a car t years after its purchase, so the purchase price of the car would have been the value of the car when t = 0. Plugging in t = 0 into the equation, we get:

V = 23900 * (0.91)^0

V = 23900

So the purchase price of the car was $23,900.

Regarding the rate of decrease in the value of the car, we can observe that the value decreases at a rate proportional to (0.91)^t, so the rate of decrease is proportional to 0.91.

Step-by-step explanation:

To find the derivative of a piecewise function, you need to take the derivative of each individual piece and then combine them into one piecewise function.

The derivative of each piece can be found using the usual rules of differentiation (such as the power rule, sum rule, product rule, etc.).

Once you have the derivatives of each piece, you can write the overall derivative as a piecewise function, where the expression for each piece is limited to a specific range of x-values. The limits of each piece are defined by the breakpoints in the original function.

For example, if the original function is given as:

f(x) = {x^2 for x < 0,

x for 0 <= x < 1,

2x for x >= 1}

Then the derivative of f(x) can be found as:

f'(x) = {2x for x < 0,

1 for 0 <= x < 1,

2 for x >= 1}

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Answer: 13

Step-by-step explanation: The two numbers are 967 and 445 making a=4 and b=9. We know a+b= 9+4 which is 13. For starters, you add the last digits of b67 and aa5 so 7+5=12 which is why the four digit number ends in two. When adding, the one from 12 would carry so the second to last digit on the four digit number would have to be 11. To get eleven you would add 7 and 4. The seven comes from the second digit in the b67 number including the one that came from 7+5=12. Now we know a=4. Knowing this now aa5= 445 and 1a12= 1412. We can now substract 445 from 1412 to get 967. b67= 967. To check 967+445=1412.  

Answer:

Answer is in attached photo.

Step-by-step explanation:

The solution is in the attached photo, do take note to solve this question, we can assign 2 variables to the 2 conditions stated in the question, and solve them simultaenously.

A. The thickness of the rectangular sheet of sugar paste is 1/5 cm.

B. The volume of the remaining pastry can be expressed as approximately 45.84 cm³.

The volume of a cuboid is equal to the product of the length, width, and height of a cuboid.

The volume of a cuboid is length × breadth× height

A) The volume of the cuboid pack of sugar paste is 5 cm x 8 cm x 9 cm = 360 cm³.

To find the thickness of the rolled-out rectangular sheet, we need to divide the volume of the pack by the area of the rectangular sheet:

thickness = volume/area

thickness = 360 cm³ / (30 cm x 60 cm)

thickness = 360 cm³ / 1800 cm²

thickness = 1/5 cm

So the thickness of the rectangular sheet of sugar paste is 1/5 cm.

B) The two circular pieces of pastry each have a diameter of 25 cm and thus a radius of 25/2 = 12.5 cm.

The volume of each circular piece of pastry can be calculated as:

V = π × (radius)² × thickness

V = π × (12.5 cm)² × 1/5 cm

V = π × 156.25 × 1/5 cm³

V = 50 × π cm³

Since Mary cuts out two circular pieces, the total volume of pastry that she removes is 2 x 50 x π cm³. The remaining volume of pastry is the original volume of the pack minus the volume of the two circular pieces:

Volume remaining = 360 cm³ - 2 × 50 × π cm³ = 45.84 cm³

The volume of the remaining pastry can be expressed as approximately 45.84 cm³.

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He should expected tomorrows's score to be about 75 points greater than today's score.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The input and output variables for this problem are given as follows:

The slope is given as follows:

m = 5.

Meaning that when the input increases by one, the output increases by 5, hence the expected score's increase with an increase in the input of 15 is given as follows:

15 x 5 = 75.

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The linear equation on the graph is:

y = x + 3

Here we have a linear equation.

Remember that the general one is y = a*x + b where b is the y-intercept, here we can see that the line intercepts the y-axis at y = 3

y = a*x + 3

And it passes through the point (-3, 0), replacing these values we get:

0 = a*-3 + 3

3a =  3

a = 3/3 = 1

The linear equation is:

y = x + 3

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Answer:

  3.75%

Step-by-step explanation:

You want to know the semiannual interest rate if the annual rate is 7.5%.

The rate of interest for a period is the annual rate divided by the number of periods in a year.

Interest compounded semiannually is compounded 2 times per year. The semiannual rate is ...

  7.5%/2 = 3.75% . . . . semiannual rate

Answer: 12 feet

Step-by-step explanation: If the length of the garden is 20 feet then that means 40 feet of fence was used to make both lengths of the garden. So we subtract 40 from 64 which leaves us with 24 feet and then we divide 24 by 2 to get 12 because there are 2 widths.

Hope this helps!

Using combinatorial reasoning, the expression of[tex](x y)5 is x^5y^5 + 5x^4y^6 + 10x^3y^7 + 10x^2y^8 + 5xy^9 + y^10[/tex]. Using the binomial theorem, it is[tex]1x^5 + 5x^4y + 10x^3y^2 + 10x^2y^3 + 5xy^4 + y^5[/tex].

a) Combinatorial reasoning involves breaking the expression down into different combinations of x and y, and then multiplying each combination. In this case, (x y)5 can be broken down into

[tex]x^5y^0 + x^4y^1 + x^3y^2 + x^2y^3 + x^1y^4 + x^0y^5[/tex],

and the coefficient of each term is the number of ways that combination can be derived from the expression. For example, there are 5 ways to arrange the combination [tex]x^4y^1[/tex], so its coefficient is 5. When the coefficients are multiplied with the combinations, they become

[tex]5x^4y^1 + 10x^3y^2 + 10x^2y^3 + 5xy^4 + y^5[/tex],

which is the expansion of (x y)5.

b) The binomial theorem states that for any expression of the form [tex](x + y)^n[/tex], the expansion can be found by multiplying the term[tex]x^n[/tex]with the coefficient of each term in Pascal’s triangle. For example, for[tex](x + y)^5[/tex], the coefficient of[tex]x^5[/tex] is 1, the coefficient of[tex]x^4y[/tex]is 5, the coefficient of[tex]x^3y^2[/tex]is 10, the coefficient of [tex]x^2y^3[/tex]is 10, the coefficient of[tex]x^1y^4 is 5[/tex], and the coefficient of[tex]y^5[/tex]is 1. Thus, the expansion of [tex](x + y)^5 is 1x^5 + 5x^4y + 10x^3y^2 + 10x^2y^3 + 5xy^4 + y^5.[/tex]

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Step-by-step explanation:

Median IJK = IM = PN + 2

Median PQR = PN

Therefore, IM = PN + 2

IM = PN + 2

PN = IM - 2

IM = (15 + 9 + PN)/2

PN = (15 + 9 + IM - 2)/2

15 + 9 + PN = 2IM

15 + 9 + IM - 2 = 2PN

25 + PN = 2IM

25 + IM - 2 = 2PN

PN = 2IM - 25

PN = 2PN - 25

3PN = 25

PN = 25/3

IM = PN + 2

IM = 25/3 + 2

IM = 29/3

Therefore, IM = 29/3 and PN = 25/3.

Answer:4/3

Step-by-step explanation: rise over run when finding slope, and the first point i can find (-3,-5) is 4 up and 3 right away from (0,-1)

Answer:

6

Step-by-step explanation:

The growth in balance from year 20 to year 25 is $274.57.

Answer:

-3550x - 12y + 20

Step-by-step explanation:

50x+ 20 - 60(1/5y+60x)

50x + 20 - 12y - 3600x

-3550x - 12y + 20

In normal scientific notation, round off each integer to three significant digits:

a. 4.227 x 10⁻²

b. 7.125 x 10⁶

c. 4.452 x 10⁻⁴

d. 2.300 x 10⁻⁴

e. 9.722 x 10⁵

f. 4.855 x 10³

Scientific notation is a method of expressing numbers that are either too large or too little to be represented in decimal form. In the United Kingdom, it is known as scientific form, standard index form, or standard form. Scientific notation is a method of writing extremely big or extremely tiny integers. When a number between 1 and 10 is multiplied by a power of 10, it is expressed in scientific notation.

Here,

a. 422.65 times 10⁻³ = 4.227 x 10⁻²

b. 71.246 times 10⁵ = 7.125 x 10⁶

c. 0.00044515 = 4.452 x 10⁻⁴

d. 22.9987 times 10⁻⁵ = 2.300 x 10⁻⁴

e. 9.7222 times 10⁵ = 9.722 x 10⁵

f. 0.0048545 times 10⁵ = 4.855 x 10³

The following numbers in standard scientific notation, rounding off each to three significant digits:

a. 4.227 x 10⁻²

b. 7.125 x 10⁶

c. 4.452 x 10⁻⁴

d. 2.300 x 10⁻⁴

e. 9.722 x 10⁵

f. 4.855 x 10³

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