The total number of burgers sold from a restaurant from Monday to Sunday can be modeled by the function f(d)=200d^3 + 542d^2 + 179d + 1605 and the number of visitors to the restaurant from Monday to Sunday can be modeled by g(d)= 100d + 321, where d is the number of days since Monday. What is the average number of burgers per person?

15° and 165°

Step-by-step explanation:

Step 1 :

Let x and y denote the angles with x as the smaller angle and y as the larger angle

When 2 angles are supplementary, the sum of both the angles is 180 degrees.

Hence x + y = 180

Step 2:

Given that the larger angle is 15 more than 10 times the smaller angle

Hence y = 15 + 10 x

Step 3 :

Solving for the 2 equations we have

11x = 165 => x = 15

=> y = 180-15 = 165

Hence the 2 angles are 15 and 165 degrees.

Answer:

22.7

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

hello :

the nth term is : Bn= B1×R^n-1

calculate B3  (when n=3)    R= -1/3   B1 = 54

B3 =54×(-1/3)^(3-1)

B3 =54×(1/9)=6

Knowing about geometric sequences we have that its third term will be given by 6

Geometric Progression (PG) is a numerical continuity in which the division of a term with its previous one, except the first, will result in a single value, the so-called ratio (q), that is: PG: (a1, a2, a3, a4, ..., an), where q = (a2/a1 = a3/a2 = a4/a3,.

Given that:

The formula of the term will be:

[tex]Bn= B1*R^n-1[/tex]

Calculated the B3 we have:

[tex]B3 =54*(-1/3)^{(3-1)}\\B3 =54*(1/9)=6[/tex]

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Answer:

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] (3n + 7)

Step-by-step explanation:

We require to find the first term a₁ and the common difference d

The n th term is given by 3n + 2, thus

a₁ = 3(1) + 2 = 3 + 2 = 5

a₂ = 3(2) + 2 = 6 + 2 = 8

d = 8 - 5 = 3

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ], substitute values

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ (2 × 5) + 3(n - 1) ] = [tex]\frac{n}{2}[/tex] (10 + 3n - 3) = [tex]\frac{n}{2}[/tex] (3n + 7)

Answer:

Sn = (3/2)n² + (7/2)n

Step-by-step explanation:

Sn = (n/2)[2a + (n-1)d]

a = 3(1)+2 = 5

d = second term - 5 = 3(2)+2 - 5 = 3

Sn = (n/2)[2(5) + (n-1)(3)]

= (n/2)[10 + 3n - 3]

= (n/2)(7 + 3n)

Sn = (3/2)n² + (7/2)n

Answer:

<ABC = 98.

Step-by-step explanation:

We know that the triangle is lying on a flat line, which is 180 degrees. We know that angle ABC and angle CBD are supplementary as they both use line ABD as their transversal.

Set up the equation (3 + 5x) + 82 = 180.

Solve for x, and you get 19.

Plug it back in to (3 + 5x), we get <ABC = 98.

The midpoint of AB is point G

The complete question has been attached below. As you can see, we have a line segment which is defined as a part of a line that is bounded by two different points that are at the end of the segment. So here we know that:

Therefore, the midpoint can be calculated as:

[tex]M:midpoint \\ \\ \\ M=\frac{A+B}{2} \\ \\ M=\frac{-6+8}{2} \\ \\ M=1[/tex]

So the midpoint is [tex]M=1[/tex] that matches point G. Finally:

Conclusion: The midpoint of AB is point G

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Answer:y=-24

Step-by-step explanation:

Move all terms not containing

y

to the right side of the equation.

Answer:

-7/4

Step-by-step explanation:

Did you mean -7?

The final price of a $1049 television on a 12% sale, with a 4.5% sales tax, is $964.66.

The final price on a $1049 television that is on sale for 12% off can be found by deducting the discount from the original price, and then adding the sales tax on the discounted price.

First, let's find the discount: 12% of $1049 is (12/100)*1049 = $125.88. So, the price after discount would be 1049 - 125.88 = $923.12.

Next, we need to add the 4.5% sales tax. Sales tax is calculated on the discounted price, so 4.5% of $923.12 is (4.5/100)*923.12 = $41.54.

Finally, we add the tax to the discounted price to get the final price: $923.12 + $41.54 = $964.66. So, the final price of the television is $964.66.

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Answer:

The number of square tiles required to cover the bathroom floor is approximately 31.

Step-by-step explanation:

The dimensions of the rectangular floor of the bathroom are:

Length = 10.5 ft.

Breadth = 6.5 ft.

The dimensions of the square tiles are:

Side = 1.5 ft.

The area of the rectangular floor of the bathroom is:

[tex]Area\ of Bathroom\ floor=Length\times Breadth\\=10.5\times6.5\\=68.25[/tex]

The area of 1 square tile:

[tex]Area\ of\ 1\ square\ tile=(SIde)^{2}\\=(1.5)^{2}\\=2.25[/tex]

The number of tiles required to cover the bathroom floor is:

[tex]Number\ of\ tiles=\frac{Area\ of\ bathroom\ floor}{Area\ of\ 1\ square\ tile} \\=\frac{68.25}{2.25}\\ =30.3333\\\approx31[/tex]

Thus, the number of square tiles required to cover the bathroom floor is approximately 31.

Answer:

Step-by-step explanation:

If QPS is a right angle we know a right angle equals 90 degrees. so you can find your answer by doing 90-35.

Therefore getting 56.

Hope this helps :)

Answer:

The answer is 24

Step-by-step explanation:

If each person eats 1/3 of the pizza then that means it takes 3 people to eat a whole pizza so you multiply three times 8 and you get twenty four.

Answer:

yes

Step-by-step explanation:

when addi g the ones place it would result in 14 so u would need to regroup the 1 into the tens place

The dimensions of the rectangle shown on the coordinate plane is The base is 9 units and the height is 4 units.

Option: B.

Step-by-step explanation:

We are given with the coordinate points of a rectangle.

The points are  (1, -1), (10, -1), (10, -5), (1, -5).

From the given graph, the bigger side is the base and the height is the smaller side.

The points  (1, -1), (10, -1) and (1, -5), (10, -5) can be used to find the base of the rectangle.

The points (10, -1), (10, -5) and  (1, -1), (1, -5) can be used to find the height of the rectangle.

Let us find the base using coordinate point (1, -5), (10, -5) .

Since the base runs horizontally on the x-axis, we have to find the run.

run = [tex]x_2-x_1[/tex].

run = 10-1.

run (base)= 9 units.

Let us find the base using coordinate point (10, -1), (10, -5) .

Since the height runs vertically on the y-axis, we have to find the rise.

rise = [tex]y_2-y_1[/tex].

rise = -5-(-1).

rise=-5+1.

rise (height)= 4 units.      ( Units are always measured in positive.)

∴ The base is 9 units and the height is 4 units.

Answer:

- 3

Step-by-step explanation:

hello:

-2-17+12-(-4)=(-2-17)+(12+4)= -19+16= -3

Answer:

-3

Step-by-step explanation:

-2-17+12-(-4)

From BODMAS, we begin witht the bracket

=-2-17+12+4

= -2-17+16

= -19+16

= -3

Answer:

y=-1/3x-8

Step-by-step explanation:

y-y1=m(x-x1)

y-(-9)=-1/3(x-3)

y+9=-1/3x+3/3

y+9=-1/3x+1

y=-1/3x+1-9

y=-1/3x-8

Answer:

the answer is to 72 divided by 1/3 is 216

The result of the division 72 divide by 1/3 is : 216.

Here, we have,

given that,

What is 72 divide by 1/3

we know that,

72 divide by 1/3 is the same thing as 72 times 3/1.

i.e. 72 ÷ 1/3

=> 72 × 3/1

now, we know that,

So 72 x 3 = 216

=> 216/1

And 216 divided by 1 is 216.

so, we get,

Hence, The result of the division 72 divide by 1/3 is : 216.

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Answer:

x = 4.5.

Step-by-step explanation:

5(2x + 1) = 50

10x + 5 = 50

10x = 50 -  5

10x = 45

x = 4.5.

Answer:

There will be 6 necklaces

Step-by-step explanation:

102/17 is 6

Answer:Juanita can make 6 bracelets.

Step-by-step explanation:

Divide 102 and 17 then you should get 6.

D. (-2,-1)

Hope it helps you.

Answer:

D

Step-by-step explanation:

Given the 2 equations

y = 2x + 3 → (1)

y = - [tex]\frac{1}{2}[/tex] x - 2 → (2)

Since both equations express y in terms of x, equate the right sides

2x + 3 = - [tex]\frac{1}{2}[/tex] x- 2

Multiply through by 2 to clear the fraction

4x + 6 = - x - 4 ( add x to both sides )

5x + 6 = - 4 ( subtract 6 from both sides )

5x = - 10 ( divide both sides by 5 )

x = - 2

Substitute x = - 2 into (1) for corresponding value of y

y = 2(- 2) + 3 = - 4 + 3 = - 1

Solution is (- 2, - 1 ) → D

Answer:

1.Distribute values

(3x+12)-(2x+8)

2.Add common terms

x+4

Answer:

country a = 19,812 cars

country b = 6,604 cars

Step-by-step explanation:

a = country a

b = country b

the 2 eqations are:

a + b = 26,416

a = 3b

now substitute 3b for a in the first equation:

3b + b = 26,416

add the variables:

4b = 26,416

now divide 26,416 by 4 (26,416/4)

b = 6,604

so country b has 6,604 cars

to find country b, substitute the number of cars in country b (which is 6,604) in the second equation:

a = 3b

a = 3 × 6,604

a = 19,812

so country a has 19,812 cars

Answer:

$366.66

Step-by-step explanation:

You start with a credit card balance of $1950. If you reduce this balance by 13% each month for 12 months, using the formula for geometric series (a(r^n)), your final balance at the end of 12 months will be approximately $452.98.

The student's question is asking about reducing a credit card debt balance by a fixed percent each month. In this case, the student is reducing their debt by 13% every month for 12 months. To get a clear picture, let's go through this step by step.

Initially, the credit card balance is $1950. In the first month, the student reduces the debt by 13% which is $253.5. So, the remaining balance at the end of first month would be $1950 - $253.5 = $1696.5

This process is repeated each month. For example, in the second month, the student reduces the new amount of $1696.5 by 13%. The debt will continue to decrease in this manner each month.

To calculate the balance at the end of 12 months, we would use the formula for geometric series: a(r^n), where 'a' is the initial amount of debt($1950), 'r' is the percentage (1 - 13% or 0.87) and 'n' is the number of months (12).

Your final balance at the end of 12 months would be $1950*(0.87^12) which approximately equals $452.98. Hence, by reducing your debt by 13% each month for 12 months, your balance will be approximately $452.98. But remember, maintaining steady payments and not adding to the balance by new purchases is also important in managing credit card debt.

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First write 18% as a decimal by moving the decimal point two places to the left to get .18.

The word "of" means multiply, so we have (.18)(75) which is 13.5.

Answer:

13.5

Step-by-step explanation:

18% of 75

18% /100% x 75

0.18 x 75

13.5

Answer:

32 cups of water is needed to fill a 2 gallon water tank.

Step-by-step explanation:

Here, the amount of water to be filled in the fish tank = 2 gallons

The utensil to measure water   =  a measuring cup

Now, as we know:

1 quart  = 0.25 gallons

⇒ 4 pints =  1  gallons

⇒ 8 pints =  2 gallons

Also, 1 pint  = 0.5 quart

⇒ 2 pints =  1 quarts

⇒ 8 pints =  4 quarts

⇒ 16 pints =  8 quarts

Again,  1 cup = 0.5 pint

⇒ 2 cup  = 1  pint

⇒ 32 cup  = 16  pints

Hence, 32 cups of water is needed to fill a 2 gallon water tank.

The height of the redwood tree can be determined through trigonometry, using the tangent of the angles given and the distances provided. The height of the tree from point B is found to be 1.8 feet, and the total height of the tree from point A is found to be approximately 30.9 feet.

In this question, we can use trigonometry to solve the problem. From point B, we see two angles. The smaller angle, 85.8°, is the angle from the line extending to the tree and line AB, and the greater angle is 90°. Therefore, the angle between the line extending to the top of the tree and line AB is (90-85.8)= 4.2°.

Using the tangent function, which is the ratio of the opposite side to the adjacent side in a right triangle, we can solve for h. Tan 4.2° = h/24.8 feet. Solving for h gives us h = 24.8 feet * tan 4.2°. Using a calculator, we find that h is approximately 1.8 feet.

Similarly, let's calculate the height from point A. From point A, the angle of elevation to the top of the tree is 10.4°. The distance from the tree to point A is the sum of the length of AB (24.8 feet) and the length from B to the tree (h/tan 85.8°). So, the total height of the tree is h (from point B) + distance from A to the tree * tan 10.4°. This calculation gives us h = 1.8 feet + (24.8 feet + 1.8 feet/tan 85.8°)*tan 10.4°. After doing the calculations, we find that the height of the tree is approximately 30.9 feet when rounded to one decimal place.

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Answer:

domain={0,3}

range={1,9}

Step-by-step explanation: