Answer:
The total cost function is C (x) = 15x + 100 and the cost of a banquet for 20 guests is $ 400
Step-by-step explanation:
Let's suppose,
X: Number of guests
C (x) = total cost
CF (x) = fixed cost
CV (x) = variable cost
C (x) = CV (x) + CF (x)
For the situation presented,
CF (x) = 100
CV (x) = 15x
With this information, the function that provides the total cost is given by the expression:
C (x) = 15x + 100.
When there are 20 guests, the total cost of the banquet is:
C (20) = 15 (20) + 100 = 300 + 100 = 400
Conclusion: The total cost function is C (x) = 15x + 100 and the cost of a banquet for 20 guests is $ 400
Find the GFC of 56 and 84. A factor tree for 84 is given below. The GCF of 84 and 56 is .
The greatest common factor of the given numbers is 4.
The given numbers are 56 and 84.
The GCF (Greatest Common Factor) of two or more numbers is the greatest number among all the common factors of the given numbers.
Here, the factors of given numbers are
56 = 2×2×2×7
84 = 2×2×3×7
Now, the common factors from the above factorization is 2×2
= 4
Therefore, the greatest common factor of the given numbers is 4.
To learn more about the greatest common factor visit:
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Starting at home, Jessica traveled uphill to the grocery store for 18 minutes at just 20 mph. She then traveled back home along the same path downhill at a speed of 60 mph.
What is her average speed for the entire trip from home to the grocery store and back?
the lines shown below are perpendicular. if the green line has a slope of 1/7, what is the slope of the red line?
Answer: it's -7
Step-by-step explanation:
Answer:
Therefore, the slope of the red line must be -7
Step-by-step explanation:
If the two lines are said to be perpendicular each other, then the multiplicative of their slope is -1.
Let "m1" be the slope a line and "m2" be the slope of the perpendicular line.
So, m1*m2 = -1
Here, let's take "m1" be the slope of the green line and "m2" be the slope of the red line.
They said to be perpendicular to each other.
So, m1*m2 = -1
Given: m1 = 1/7
NOw plug in m1 = 1/7 in the above statement, we get
1/7 *m2 = -1
Let's find the value of m2, multiply both sides by the reciprocal of 1/7
The reciprocal of 1/7 is 7.
7*1/7*m2 = -1*7
7/7.m2 = -7
m2 = -7
Therefore, the slope of the red line must be -7
Elevator 1 moved up 15 feet from the ground level. Its position is labeled as +15. Elevator 2 moved down 6 feet from the ground level. Its position is labeled as _____. (Use the hyphen for negative such as -1)
Answer:
-6
Step-by-step explanation:
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What are the solution(s) of –x2 + 2x + 3 = x2 – 2x + 3?
a. 1 and 3
b. 0 and 2
c. 0
d. 3
HURRY IM BEING TIMED!!
Answer:
Step-by-step explanation:
Given: –x² + 2x + 3 = x² – 2x + 3 .
To find: What are the solution(s) .
Solution: we have given that
–x² + 2x + 3 = x² – 2x + 3 .
On subtracting both side by x² .
-2x² + 2x + 3 = x² - x² - 2x + 3
-2x² + 2x + 3 = -2x +3
On Addition both side by 2x .
-2x² + 2x + 2x + 3 =-2x +2x +3
-2x² + 4x + 3 = 3
On subtracting both side by -3 .
-2x² + 4x + 3 -3 = 3 - 3
-2x² + 4x = 0
Taking common 2x .
2x (- x +2 ) =0 .
On grouping .
2x= 0
so x= 0
Now , -x +2 =0 .
-x = -2 .
On dividing by -1
x= 2
Therefore , option B is 0 and 2 .
Holly earns $30 for babysitting 5 hours. She earns $28 when she does chores for 4 hours. Which compares the unit rates?
The rate of earning money for both activities will be calculated by dividing the amount earned by the total time spent for each of the activity.
Babysitting: rate = ($30 / 5 hours ) = $6 / hour
Doing chores: rate = ($28 / 4 hours) = $7 / hour
Thus, Holly is able to earn money faster when doing the chores compared to when she do the babysitting if she work for the same amount of time for each.
Answer:
The unit rate for doing chores is $1 more than the unit rate for babysitting.
Step-by-step explanation:
30 divided by 5=6 So that means it was six dollars for babysitting.
28 divided by four=7 So that means it was seven dollars for babysitting.
An item has a listed price of $80. If the sales tax rate is 6% , how much is the sales tax (in dollars)?
6% = 0.06
80 x 0.06 = 4.80
the tax is $4.80
Stumped on how to solve this one! The numbers just aren't making sense to me
30=3/5
so 10 miles = 1/5 on the map
there re 5/5 per inch, so 4 inches = 4*5 = 20/5
20*10 = 200
so they are 200 miles apart
A store sells cooking oil of two different brands in bottles of the same size. The table below and the equation each show the price (y) in dollars of different numbers of bottles of oil (x)
Brand A
Number of bottles (x).
2
3
4
5
Price (dollars) y
22
33
44
55
Brand B:
Y=17x
How many dollars more is the price of 8 bottles of Brand B than the price of 8 bottles of Brand A oil?
The number of dollars more is the price of 8 bottles of Brand B than the price of 8 bottles of Brand A oil is:
$ 48
Step-by-step explanation:Brand A--
Number of bottles (x) Price (dollars) y
2 22
3 33
4 44
5 55
The function that represents the relation between the price of the bottles and the number of bottles is:
y=11x
Brand B--
Also, the price of the bottles depending on the number of bottles is:
Y=17x
According to Brand A the price of 8 bottles is: y=11×8=$ 88
and according to Brand B the price of 8 bottles is: y=17×8= $ 136
Also, the difference in the price of Brand B to that of Brand A for 8 bottles is:
$ 136-$ 88
= $ 48
Of the 8760 hours in a year, one television was on for
1752 hours. What percent is this?
Roman mixes 12 liters of 8% acid solution with a 20% acid solution, which results in a 16% acid solution. Find the number of liters of 20% acid solution in the new mixture. Construct a table to organize the information, and show all of your work to solve the problem
What is the relationship between 8.76 x 10^6 and 8.76 x 10^2
s the work shown below correct? Explain your answer. (11 + 2i ) – (3 – 10i ) = 11 + 2i – 3 – 10i = (11 – 3) + (2i – 10i) = 8 – 8i
Answer:
Given that: [tex](11+2i)-(3-10i)[/tex]
Remove the parentheses, we have;
[tex]11+2i-3+10i[/tex]
Like terms are those terms which have same variables to the same power.
Combine like terms of a constant variable;
[tex](11-3) +2i+10i[/tex]
Similarly, combine like terms of imaginary part, we have;
[tex](11-3) +(2i+10i)[/tex]
Simplify:
[tex]8 +(12i)[/tex]
or
[tex]8+12i[/tex]
Therefore, the correct solution of [tex](11+2i)-(3-10i)[/tex] = [tex]8+12i[/tex]
-4(2x-6)=-(4x-9)-2x+3
C+1/c-2 = 4/7 please show how you got the answer which is 5
What is the answer to 6,007,200 in exspanded form
The number 6,007,200 in expanded form is written as 6,000,000 + 7,000 + 200, breaking down the number by each digit's place value.
To write the number 6,007,200 in expanded form, we break it down based on the place value of each digit. Here is how you would write it:
Identify the value of each digit in the number.
Starting from the left, write each digit multiplied by its place value.
Add each of these values together.
Applying this to the number 6,007,200, we get:
6,000,000 (6 millions) + 7,000 (7 thousands) + 200 (2 hundreds)
Therefore, the expanded form of 6,007,200 is:
6,000,000 + 7,000 + 200
A man owned 5/8 of an interest in a house. He sold 1/5 of his interest, at a cost for $1000. What is the total value of the house? Explain how u solved it.
For which pair of numbers is the greatest common factor 8
Sydney applied the steps below to find the product of (3.1)(–1.6).
Step 1: (3.1)(–1.6) = (–1.6)(3.1)
Step 2: = _______________
Step 3: = (–4.8) + (–0.16)
Step 4: = –4.96
Which expression correctly fills in the blank in Step 2?
(1.6)(3) – (1.6)(0.1)
(–1)(3) + (–0.6)(0.1)
(1)(3) – (0.6)(0.1)
(–1.6)(3) + (–1.6)(0.1
Answer with explanation:
We have to find the product of
⇒(3.1)× (-1.6)
Step 1:→ (3.1)(–1.6) = (–1.6)(3.1)
Step 2: = -1.6×(3 + 0.1)=(-1.6) ×3 + (-1.6)×(0.1)→→We have used Distributive property of addition with respect to Multiplication, which is , a × (b + c)=a×b + a × c
Step 3: = (–4.8) + (–0.16)
Step 4: = –4.96
The expression which correctly fills the blank is:
Option D: →→ (–1.6)(3) + (–1.6)(0.1)
a whole number is a perfect square if its square root is an integer true or false
Rewrite 256 in exponential form using 2 as the base
given that there are eight ounces in a cup and four cups in a quart, which quantity below is equal to 128 ounces
256 ounces 64 ounces 18 cups 4 quarts
Answer:
4 quarts i had this question on a test and got it right
Step-by-step explanation:
128 ounces is equal to 4 quarts.
To solve this, we need to convert the amount given in ounces to quarts.
Step-by-Step Solution:
There are 8 ounces in a cup.There are 4 cups in a quart.Therefore, there are 8 ounces/cup × 4 cups/quart = 32 ounces in a quart.To find out how many quarts are in 128 ounces, divide 128 by 32: 128 ounces / 32 ounces per quart = 4 quarts.So, the quantity equal to 128 ounces is 4 quarts.
The other options: 256 ounces and 64 ounces are obviously not equal to 128 ounces since 256≠ 128≠ 64
and, 18 cups =18×8= 144 ounces ≠ 128 ounces.
Determine two pairs of polar coordinates for the point (4, -4) with 0° ≤ θ < 360°.
Answer:
(4 square root 2, 315°), (-4 square root 2, 135°)
Step-by-step explanation:
First right answer gets brain
Help pleasee i am beggin
Carina spent a total of $5.27 buying a pineapple for $3.40 and several pounds of tomatoes that were on sale for $0.85 per pound. To determine the number of pounds of tomatoes that she bought, x, Carina wrote and solved the equation as shown below.
Answer:
pretty sure its B.
Step-by-step explanation:
Find the value of the expression m4 - m3 - 2m2 + 10m + 15 when m = -3.
(1-sec x)/(1-cos x) = -sec x
I got up to this:
(cos x - 1)/ (cos x(1 - cos x)
Can you help me verify the following identity?
We are given the trigonometric equation:
(1 - sec x) / (1 - cos x) = - sec x
Since the left side has more terms, then let us work on that side to make it exactly like the right side.
We know that sec = 1 / cos, therefore:
(1 – 1 / cos x) / (1 – cos x) = - sec x
[(cos x – 1) / cos x] / (1 – cos x) = - sec x
[- (1 – cos x) / cos x] / (1 – cos x) = - sec x
Cancelling out the term (1 – cos x):
- 1 / cos x = - sec x
- sec x = - sec x
PROVEN!
An equilateral triangle has a perimeter of 15x3 + 33x5 feet. What is the length of each side? x3 feet
The equation below shows the relationship between the temperature in degrees Celsius, C, and degrees Fahrenheit, F:
F = 9 over 5 C + 32
Which of the following formulas correctly solves for C?
A) C = 5F − 32 over 9
B) C = 5 F over 9 − 32
C) C = 9 over 5 (F − 32)
D) C = 5 over 9 (F − 32)
it is the last option C=5/9(F-32)
Answer:
option (D) is correct.
formula that solves for C is [tex]C=\frac{5(F-32)}{9}[/tex]
Step-by-step explanation:
Given : the relationship between the temperature in degrees Celsius, C, and degrees Fahrenheit, F as , [tex]F=\frac{9}{5}C+32[/tex]
We have to find the correct formula that solve for C,
Consider the given formula,
[tex]F=\frac{9}{5}C+32[/tex]
We have to find formula for C,
Thus, first subtract 32 both side, we get,
[tex]F-32=\frac{9}{5}C[/tex]
Now, multiply 5 both side, we get,
[tex]5(F-32)={9}C[/tex]
Now , divide both side by 9, we get,
[tex]\frac{5(F-32)}{9}=C[/tex]
Thus, formula that solves for C is [tex]C=\frac{5(F-32)}{9}[/tex]
Thus, option (D) is correct.