Rose and Angel are caterers. Both Rose and Angel charge a flat fee plus a fee per guest. Rose charges a flat fee of $50 plus $12 per guest. The table shows how much Angel charges for different numbers of guests. Angel's Catering Charges Number of Guests Charge ($) 10 $180 15 $255 25 $405 30 $480 Part A Who charges the greater flat fee? O A. Rapse O B. Angel Part B Vhat is the difference in total charges between Angel and Rose for a party that includes 50 guests? Enter the answer in the box. Autohide sh Growth: Math 6+ GA 2015 Question ITU Shelf nositi​

Answers

Answer 1

Answer:

a. Angel has a greater flat fee

b. Difference = $130

Step-by-step explanation:

Given

Rose:

[tex]Flat\ Fee = \$50[/tex]

[tex]Rate = \$12[/tex]

Angel

Guests --- Charges

10 -------- $180

15 -------- $255

25 -------- $405

30 -------- $480

Solving (a): Who charges the greater flat fee?

We have that the flat fee of Rose is:

[tex]Flat\ Fee = \$50[/tex]

For Angel, we need to determine the equation of the given table

Start by calculating the slope (m) of the table

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

Where x and y represent any two corresponding values of the guests and the charges.

[tex](x_1,y_1) = (10, 180)[/tex]

[tex](x_2,y_2) = (30, 480)[/tex]

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

[tex]m = \frac{480 - 180}{30 - 10}[/tex]

[tex]m = \frac{300}{20}[/tex]

[tex]m = 15[/tex]

Next, we calculate the equation using:

[tex]y - y_1 = m(x - x_1)[/tex]

Where

[tex]m = 15[/tex]

[tex](x_1,y_1) = (10, 180)[/tex]

[tex]y - 180 = 15(x - 10)[/tex]

[tex]y - 180 = 15x - 150[/tex]

Add 180 to both sides

[tex]y - 180 + 180 = 15x - 150 + 180[/tex]

[tex]y= 15x + 30[/tex]

From the equation above:

The slope = 15 --- This represents the hourly rate

and

y intercept = 30 --- This represents the flat fee

This is better represented as:

Angel

[tex]Flat\ Fee = \$30[/tex]

[tex]Rate = \$15[/tex]

and

Rose:

[tex]Flat\ Fee = \$50[/tex]

[tex]Rate = \$12[/tex]

By comparison, Angel has a greater flat fee

Solving (b): Difference between total charges of 50 guests for both caterers.

For angel, the equation is:

[tex]y= 15x + 30[/tex]

and x = 50.

So:

[tex]y = 15 * 50 + 30[/tex]

[tex]y = 750 + 30[/tex]

[tex]y = 780[/tex]

For Rose,

First, we need to determine the equation.

[tex]Flat\ Fee = \$50[/tex]

[tex]Rate = \$12[/tex]

The equation is:

[tex]y = Flat\ Fee + Rate * x[/tex]

[tex]y = 50 + 12 * x[/tex]

So, the total charges for 50 guests is:

[tex]y = 50 + 12 * 50[/tex]

[tex]y = 50 + 600[/tex]

[tex]y = 650[/tex]

The difference is then calculates as:

[tex]Difference = 780 - 650[/tex]

[tex]Difference = \$130[/tex]


Related Questions

Help me out real fast pleaseeeeeeee

Answers

Answer:

25/6 = 4 1/6

Step-by-step explanation:

what you do is 5/6 times 5 i am pretty sure this is right

Answer:

B. 4 1/6

Step-by-step explanation:

1. Identify your key factors:

Terrance: 5

Brother: 5/6

2. Let's make them both fractions:

T: 30/6  B: 5/6

3. Now subtract the difference:

30/6-5/6

25/6

4. Simplify:

4 1/6

ASAP ASAP 30 POINTS

A ratio table shows ratios that are....

A)equivalent
B)subtracted
C)unequal

Answers

Answer:

A ) equivalent

Step-by-step explanation:

<333 .! :)

Answer:

I agree with the answer equivalent because I am also doing the assignment

Have a great day!

PLEASE HURRY) The graph indicates the running route for Tobias

Which best describes his run

A. From time 0 to 6, he went fast and then slowed down.
B. From time 6 to 10, he was at his slowest.
C. From time 12 to 14, he went very slow.
D. From time 14 to 18, he went toward the starting point.

Answers

Answer: B. From time 6 to 10, he was at his slowest.

Step-by-step explanation: I just took the same quiz so HURRY!!!

Answer:

b

Step-by-step explanation:

what 1+1







duwjus



w7wjqiw​

Answers

Answer:

hmm.......i think it's 11

it might be 2

no 11

ehh maybe 11

oh my god

so uhmmmmmm

it's either 11

or it's 2

im having a mental crisis

PLZ HELP FAST

Enter an equation in standard form to model the linear situation.

A pool that is being drained contained 19,000 gallons of water. After 2 hours, 14,500 gallons of water remain.​

Answers

The answer would be 4,500 gallons left.

The model y=1.8x−76.9 represents the relationship between the temperature (°F) and the number of ice cream cones sold. Using the model, approximate the temperature when there are 95 ice cream cones sold. Round your answer to the nearest tenth.

Answers

Answer: 75.1

Step-by-step explanation:

Answer:

86.0*

Step-by-step explanation:

i am not 100% sure

is Water is stored in response to changing demand a cause or effect

Answers

the answer is effect

Answer:

this a effect you can change the change the water

Convert 5700 milligrams into pounds. Round your answer to the nearest hundredth.

Answers

The value of the 5,700 milligrams in pounds is approximately 0.01 lb

What is a unit of measurement?

A unit of measurement is a specified magnitude of a quantity that is accepted and adopted by convention or backed by law, and used as a measurement standard.

In other to successfully convert a quantity in one unit to another unit, both units (initial and destination unit) should refer to the same characteristics of the object being measured.

Once both units are confirmed to refer to the same quantity, conversion factors are used to multiply the quantity in the first unit in order to express it in the other unit.

The given parameters are;

The quantity to be converted to pounds = 5,700 milligrams

The factor of conversion is 1,000 mg ≈ [tex]2.205 \times 10^{-6}[/tex] lb

Therefore;

[tex]5,700\: mg = 5,700 \times 2.205 \times 10^(-3) ≈ 0.0126[/tex]

Therefore, to the nearest hundredth, we have;

5,700 mg ≈ 0.01 lb

Learn more about unit conversion in mathematics here:

https://brainly.com/question/141163

#SPJ1

I really need help with -8 - 4(5m + 9)

Answers

Answer:the answer to this will be 14m

The life span of a domestic cat is normally distributed with a mean of 15.7 years and a standard deviation of 1.6 years. a. Find the probability that a cat will live to be older than 14 years. b. Find the probability that a cat will live between 14 and 18 years. c. If a cat lives to be over 18 years, would that be unusual? Why or why not? d. How old would a cat have to be to be older than 90% of other cats?

Answers

Answer

a. 0.856

b. 0.78071

c. It is not unusual

d. 13.65 years old

Step-by-step explanation:

The life span of a domestic cat is normally distributed with a mean of 15.7 years and a standard deviation of 1.6 years.

We solve this question using z score formula:

z = (x-μ)/σ, where

x is the raw score

μ is the population mean

σ is the population standard deviation.

a. Find the probability that a cat will live to be older than 14 years.

For x > 14 years

z = 14 - 15.7/1.6

z = -1.0625

Probability value from Z-Table:

P(x<14) = 0.144

P(x>14) = 1 - P(x<14) = 0.856

b. Find the probability that a cat will live between 14 and 18 years.

For x = 14 years

z = 14 - 15.7/1.6

z = -1.0625

Probability value from Z-Table:

P(x = 14) = 0.144

For x = 18 years

z = 18 - 15.7/1.6

z= 1.4375

Probability value from Z-Table:

P(x = 18) = 0.92471

The probability that a cat will live between 14 and 18 years is calculated as:

P(x = 18) - P(x = 14)

0.92471 - 0.144

= 0.78071

c. If a cat lives to be over 18 years, would that be unusual? Why or why not?

For x > 18 years

z = 18 - 15.7/1.6

z= 1.4375

Probability value from Z-Table:

P(x<18) = 0.92471

P(x>18) = 1 - P(x<18) = 0.075288

Converting this to percentage:

0.075288 × 100 = 7.5288%

Hence, 7.5288% of the cats live to be over 18 years. Hence, it is not unusual.

d. How old would a cat have to be to be older than 90% of other cats?

From the question above, 10% of the cats would be older than 90% of other cats.

Hence, we find the z score of the 10th percentile

= -1.282

Hence,

-1.282 = x - 15.7/1.6

Cross Multiply

-1.282 × 1.6 = x - 15.7

- 2.0512 = x - 15.7

x = 15.7 -2.0512

x = 13.6488 years old

Approximately = 13.65 years old

Solve the following system of equations using the elimination method. 8x – 5y = 5 –8x – 6y = 6
A)

(2,–3)

B)

(0,1)

C)

(–2,3)

D)

(0,–1)

Answers

Answer:

x = 0, y = -1

Step-by-step explanation:

Evaluate 32 divided by 1.6
show work long division

Answers

Answer:

[tex]20[/tex]

Step-by-step explanation:

[tex]-----------------------------------[/tex]

[tex]\frac{32}{1.6}[/tex] = [tex]\frac{16}{0.8}[/tex] = [tex]\frac{8}{0.4}[/tex] = [tex]\frac{4}{0.2}[/tex] = [tex]\frac{2}{0.1}[/tex]

[tex]-----------------------------------[/tex]

[tex]Since[/tex] [tex]you[/tex] [tex]could[/tex] [tex]divide[/tex] [tex]it[/tex] [tex]to[/tex] [tex]0.1[/tex], [tex]just[/tex] [tex]switch[/tex] [tex]the[/tex] [tex]decimal[/tex] [tex]with[/tex] [tex]the[/tex] [tex]0[/tex] [tex]and[/tex] [tex]take[/tex] [tex]away[/tex] [tex]the[/tex] [tex]decimal[/tex] [tex]point.[/tex] [tex]You[/tex] [tex]will[/tex] [tex]get[/tex] [tex]10[/tex]. [tex]Lastly[/tex], [tex]change[/tex] [tex]the[/tex] [tex]division[/tex] [tex]to[/tex] [tex]multiplication.[/tex]

( Remember that this does not apply to all equations. )

[tex]-----------------------------------[/tex]

[tex]When[/tex] [tex]you[/tex] [tex]multiply[/tex] [tex]10\cdot2[/tex], [tex]you[/tex] [tex]get[/tex] [tex]20.[/tex] [tex]Which[/tex] [tex]is[/tex] [tex]the[/tex] [tex]answer.[/tex]

[tex]-----------------------------------[/tex]

Hope this helps! <3

[tex]-----------------------------------[/tex]

35h+25=45h what does h equal

Answers

Answer:

h= 2.5

Step-by-step explanation:

25=10h

25/10=2.5

35h + 25 = 45h

h = 2.5

Help help help help help help pls

Answers

Answer:

a.) 36

b.) 18

c.) 27

Step-by-step explanation:

Find 83 1/3 % of 384

Answers

Answer:

319.872

Step-by-step explanation:

319.872 / 384 = 83 1/3 / 100

Final Answer: [tex]320[/tex]

Steps/Reasons/Explanation:

Question: Find [tex]83\frac{1}{3}[/tex]% of [tex]384[/tex].

Step 1: Convert mixed fraction into improper fraction.

[tex]\frac{250}{3}[/tex]

Step 2: Multiply [tex]\frac{250}{3 * 100}[/tex] with [tex]384[/tex].

[tex]\frac{96000}{300}[/tex]

Step 3: Simplify

[tex]320[/tex]

~I hope I helped you :)~

What is the slope of the graph of y = 14x + 19?​

Answers

14x is the slope meaning it goes up 14 and over 1

What is the area of a hexagon with a side length of 10? it also has a rectangle in it with other measurements but the question is asking for the area of the hectagon.

Answers

Answer:

there is a formula for a hexagon ..  it's

Area = 3[tex]\sqrt{3\\}[/tex]/2 * [tex]length^{2}[/tex]

where length is the length of one side, assuming all sides are equal

Step-by-step explanation:

3*[tex]\sqrt{3}[/tex]/2= 7.348469228.........

since the length is 10...   the length squared is 100

then the total area of the hexagon is 734.8469228...... [tex]units^{2}[/tex].. what ever they are

if you want to work with some concepts.. you could also say that a hexagon is just a box with the corners cut off and the triangles that are missing are the equilateral right triangles with a hypotenuse of 10 .  and since 2 pieces of those triangles make a square.. you can subtract two squares of that size from the bigger box that the hexagon fits into.  this is a long way to figure this out but might be good for trigonometry practice   :)

it will also be 734.8463288.....  see if you can work that out :)

which number line correctly graphs the numbers in the list?​

Answers

Answer:

the first option

Step-by-step explanation:

Prove that for any natural value of n the value of the expression (n+2)^2-(n-2)^2 is a multiple of 8.

Answers

Answer:

We have the expression:

(n + 2)^2 - (n - 2)^2

Let´s break the parentheses:

(n + 2)^2 = n^2 + 4*n + 4

(n - 2)^2 = n^2 - 4n + 4

Then:

(n + 2)^2  - (n - 2)^2 = (n^2 + 4*n + 4) - (n^2 - 4n + 4) =

                                 = (n^2 - n^2) + (4 - 4) + (4n - (-4n)) = 4n - (-4n) = 8*n

Then for any natural value of n, 8*n will be a multiple of 8.

Sam says that the length of diagonal SQ is two times the length of diagonal OM.

Is Sam correct? Justify your answer and show all your work. Your work should state the theorem you used to find the lengths of the diagonals.

Answers

Answer:

Sam is wrong.

Step-by-step explanation:

A diagonal of square or rectangle is equals to hypotenuse of a triangle. So you can apply Pythagoras Theorem to solve it :

Given that QS is 17.9 and OM is 11.3. So SQ is not 2 times greater than OM.

Solve for x:abx²-(a⁴+b⁴)x+a³b³=0

Answers

Step-by-step explanation:

abx² - (a⁴ + b⁴)x + (a³b³) = 0

(ax - b³)(bx - a³) = 0

Therefore x = b³/a or x = a³/b.

Suppose that Gx=f(x+11). Which statement correctly describes the graph? please hurry!

Answers

Given:

[tex]g(x)=f(x+11)[/tex]

To find:

The correct statement for the given transformation.

Solution:

The translation is defined as

[tex]g(x)=f(x+a)+b[/tex]                .... (1)

Where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

We have,

[tex]g(x)=f(x+11)[/tex]            ... (2)

On comparing (1) and (2), we get

[tex]a=11>0[/tex]

So, the graph of f(x) translated 11 units to the left.

Therefore, the correct option is A.

Which equation should you solve to find x?

Answers

D
Cosine= adjacent / hypotenuse

You buy some 300-yen pieces of cake and some 350 yen pieces of cake. If you buy 10 pieces of cake and pay 3300 yen, how many of each kind did you buy?

Answers

Answer:

The number of:

300- yen cakes = x = 4

350 - yen cakes = y = 6

Step-by-step explanation:

Let the number of:

300- yen cakes = x

350 - yen cakes = y

You buy some 300-yen pieces of cake and some 350 yen pieces of cake. If you buy 10 pieces of cake and pay 3300 yen, how many of each kind did you buy?

Hence, our system of equations derived from the question is:

x + y= 10 ..... Equation 1

x = 10 - y

300x + 350y = 3300 yen... Equation 2

Substitute 10 - y for x in Equation 2

Hence:

300(10 - y) + 350y = 3300

3000 - 300y + 350y = 3300

- 300y + 350y = 3300 - 3000

50y = 300

y = 300/50

y = 6

x = 10 - y

Substitute 6 for y

x = 10 - 6

x = 4

Therefore, the number of:

300- yen cakes = x = 4

350 - yen cakes = y = 6

Suppose that 8,000 is placed in an account that pays 17% interest compounded each year assume that no withdraws are made from the account

Answers

Step-by-step explanation:

gakamajs8skwzaHzk

bak*ywnJz8s


Can you please help me with the question.

Answers

Answer:

Step-by-step explanation:

A. 40:80

B: 80/40

C; 40: 120

D: 80:120 ;)

Factorise
48x^3-27x

Answers

the answer is 3x(4x+3)(4x-3)

What is the value of StartFraction negative 3 (7 + 5) over 3 squared EndFraction + 9 (2)? –6 –2 14 22 Please help timed test??????

Answers

Answer:

your dad left to get the milk

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

i took the test on edge 2021

What is the equation of the line that has a slope of -3 and passes through the point (-2, 4)?
O y = -3x - 2
y=-3x
ООО
y=-3x - 4
y = -3x + 4
O y=-3x + 2

Answers

Y = -3x + b
Plug in points
4 = -3(-2) + b
4 = 6 + b, b = -2
Solution: y = -3x - 2

This my homework and I'm bad at math if you can take the time please help me out f(x)= (x-5)to the power of 2 +12

I need the vertex
Axis of symmetry
Domain
Range

Answers

Answer:

Vertex: (5,12)

Axis of Symmetry: x=5

Domain: (-infinity, +infinity)

Range: [12, +infinity)

Step-by-step explanation:

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