Answer:
10 cards
Step-by-step explanation:
In order to find how many packs Joel needs to buy we need Make an equation
Equation = 5c + 15 = 65
where,
c = cards5c+15=65
Step 1: Subtract 15 from both sides.
5c+15−15=65−15
5c=50
Step 2: Divide both sides by 5.
5c/5 = 50/5
c=10
Therefore, Joel need to buy total of 10 cards in order to have at least 65 total cards
[tex]c=0.5q+0.5n;q=3,n=5[/tex]
The required solution of value of c is 4.
It is required to find the value of c.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.
Given:
The equation is
c=0.5q+0.5n
We have to find the value of c.
According to given question we have
By putting the value of q=3 and n=5 we have
c=0.5q+0.5n
c=0.5*3+0.5*5
By multiply with q=3 and n=5 and simplifying we get,
c=4
The result of the equation is 4.
Therefore, the required solution of value of c is 4.
Learn more details about equation here:
https://brainly.com/question/10413253
#SPJ1
3 checks for $500 and 2 bills for $2000 with $5000 what is the ending balance
The ending balance based on the information given will be $2000.
How to calculate the value?From the information, it was stated that there are 2 checks for $500 and 2 bills for $2000 with $5000.
It should be noted that bill is a expense and will be deducted.
This will be illustrated as:
= $5000 + (2 × $500) - (2 × $2000)
= $5000 + $1000 - $4000
= $2000
Therefore, the ending balance based on the information given will be $2000.
Learn more about ending balance on:
https://brainly.com/question/19156693
#SPJ1
Look at this link https://brainly.com/question/28634931 it goes to another question! 20 points that's all I have! look at the screenshots!
Answer: The answer for question 6 is 20, The answer for question 7 is 7,
The answer for question 9 is 72, and the answer for question 8 is 12
Step-by-step explanation: Here is how you solve question 6!
4(3+5)-3(6-2) (You multiply 4 within the parentheses and the same for 3.)
12+20-18+6
32-18+6
14+6
20
Here is how you solve question 7
6+1/4(12-8) I multiply 1/4 with 12 to get 3 and -8 to get -2
6+3-2
7
Here is how you solve question 8
8(7.3+3.7-8)/2 You multiply within the 8 parentheses
58.4+29.6-64/2
24/2
12
Here is how you solve question 9
6^2(3+5)/4 This time you do not multiply anything over!
36(8)/4 I multiplied 36 with 8 to get 288
288/4
72
Hope this Helped :D
Answer:
6.
4(3 + 5) - 3(6-2)
= 4(8) - 3(4)
= 32 - 12
= 20
7.
6 + 1/4(12 - 8)
= 6 + 1/4(4)
= 6 + 1
= 7
8.
8(7.3 + 3.7 - 8) ÷ 2
= 8(3) ÷ 2
= 24 ÷ 2
= 12
9.
(6^2(3+5)/4)
= (36(8)/4)
= 288/4
= 72
10.
8 + 5(4) - 3(2)
= 8 + 20 - 6
= 22
Identify two angles that are marked congruent to each other on the diagram below. (Diagram is not to scale.)
The angles that are marked congruent to each other on the diagram are : angle ZVY and angle ZYV
In this question, we need to identify two angles that are marked congruent to each other on the diagram.
We know that two angles are congruent means the measure of these angles is equal to each other.
These angles are identical to each other.
In given diagram we can observe that, angle ZVY and angle ZYV are identical.
This means, angle ZVY and angle ZYV are marked congruent to each other.
Therefore, two angles that are marked congruent to each other on the diagram are : angle ZVY and angle ZYV
Learn more about the congruent angles here:
https://brainly.com/question/2141762
#SPJ1
hexadecimal numbering system therefore uses 16 (sixteen) different digits with a combination of numbers from 0 through to 15. in other words, there are 16 possible digit symbols.however, there is a potential problem with
Hexadecimal numbering system includes zero via nine plus letters "A'' via "F"
Before I give an explanation for what Hexadecimal is, it is ideal that we recognize what base 10 number system is. Base 10 number system which is likewise referred to as the decimal number system has 10 digits that we rely from zero all the way through 9 (zero-nine). It is the usual numerical system that is used most often. If we took the bottom 10 numerical system and combined it with six more symbols, we usually get the hexadecimal number system. Thus, this indicates hex makes use of the usual zero-nine mixed with 6 digits taken from the alphabet A-F (A, B, C, D, E, and F). So in preference to representing the numbers 10 to 15, we use A-F to symbolize the decimal values 10-15. In quick we need to get some thing like (zero 1 2 three four five 6 7 eight nine) (A B C D E F).
Therefore, Hexadecimal numbering system includes zero via nine plus letters "A'' via "F"
Learn more about hexadecimal here:
brainly.com/question/12597251
#SPJ4
the length of a rectangle is 15 cm more than the width. a second rectangle whose perimeter is 72 cm is 5cm wideer but 2cm shorter than the first rectangle. what are the dimensios of each rectangle?
the dimensions of each rectangle is 72.
What is perimeter?In geometry, a shape's perimeter is referred to as its total length. The perimeter of a form is determined by adding up the lengths of all of its sides and edges. Linear measurements like centimeters, meters, inches, and feet are used to indicate its dimensions.
EXPLANATION :
The length of a rectangle is 15 cm more than its width.
L - W = 15
Compared to the first rectangle, which has a circumference of 72 cm, the second is 2 cm smaller and 5 cm wider.
2(L-2) + 2(W+5) = 72
Simplify to get 36 L + W + 3 and 36 L + W, which equals 33 by multiplying L - 2 + W + 5 by 2.
Here, combine the two equations and apply elimination.
L - W = 15 \sL + W = 33
Using the initial length, L 2L = 48 L = 24 cm, we may find W = 24 - 15 W = 9 cm, so removing W. Second rectangle width: initial width 24 - 2 = 22 cm; second rectangle length: 9 + 5 = 14 cm.
Calculate the second rectangle's perimeter using the following equation: 2(22) + 2(14) = 44 + 28 = 72
To know more about perimeter, visit;
https://brainly.com/question/9369181
#SPJ4
in the ambrose family, the ages of the three children are three consecutive even integers. if the age of the youngest child is represented by x 3, which expression represents the age of the oldest child?
The expression that represents the age of the oldest child is x +5
Consecutive integersIntegers are whole number and can be negative or positive. For instance, 1,2, 3, -5 are al integers.
Fractions cannot be an integers. From the question, we are told that the ages of the three children are three consecutive even integer. If the youngest child is represented by x + 3, the the others will be determine by simply adding 1 to each term
Middle child = x + 3 + 1
Middle child = x + 4
Oldest child = x + 4 + 1
Oldest child = x + 5
Hence the expression that represents the age of the oldest child is x +5
Learn more on consecutive integers here: https://brainly.com/question/841485
#SPJ1
The function g(x)=x² + 3px + (14p - 3), where p is an integer, has two equal roots.
a Find the value of p.
b For this value of p, solve the equation x² + 3px + (14p - 3)
a, The value of p is 6 and 2/9
b. After solving the equation x is equal to 9
a. If the roots of a quadratic ax² + bx = c = 0, are equal then the discriminant is zero express as
b² - 4ac = 0
W have given the equation x² + 3px + (14p - 3) = 0
Here, a = 1
b = 3p
c = 14p - 3
So, substitute the value and we get
⇒ (3p)² - 4(14p -3) = 0
⇒ 9p² - 56p + 12 = 0
⇒ 9p² - 2p - 54p + 12
⇒ p(9p - 2) -6(9p - 2)
⇒ (9p - 2)(p - 6)
⇒ p = 6, p = 2/9
b. Lets substitute p = x in x² + 3px + (14p - 3)
⇒ x² + 3(6)x + (14(6) - 3)
⇒ x² + 18x + (84 - 3)
⇒ x² + 18x + 81
⇒ x² + 9x + 9x + 81
⇒ x(x + 9) +9(x + 9)
⇒ (x + 9)(x + 0)
⇒ x = 9
Learn more about discriminant
https://brainly.com/question/24730520
#SPJ9
do any of yall know the questions
Answer:
In a election of municipality two candidates P and Q stood for the post of mayor and 35000 people were in voter list. Voters were supposed to cast for a single candidate .22000 people cast vote for P, 5500 people cast for Q and 1500 cast vote even for both. How many people didn't cast vote find it
determine whether the underlined numerical value is a parameter or a statistic. explain your reasoning. in a sample of 12000 students
The underlined part in the given case is a statistic.
What is a parameter and a statistic?A statistic is a number that describes a sample, whereasA parameter is a number that describes the entire population (such as the population mean) (e.g., sample mean).Now,
In a given sample of 12000 students, the underlined part is a statistic, because:
The data set of a sample of 12000 students is a sample, satisfying the definition of statistic.Hence, the underlined part is a statistic.
To learn more about parameter and statistic, refer to the link:https://brainly.com/question/13794992
#SPJ4
In february, marena traveled 7 times as many miles as in january. in march, she traveled 10 times as many miles as in january. over the past three months, she traveled a total of 6,264 miles. how many miles did she travel each month?
Distance travelled in January, February and March are 348 miles, 2436 miles and 3480 miles respectively.
What is a linear equation in one variable?Ax + b = 0, where a and b are two integers, and x is a variable, is an equation expressed in the form of linear equation with one variable. This equation has only one solution.
Let the miles travelled in January be x.
Miles travelled in February = 7x.
Miles travelled in March = 10x.
Total distance covered in three months = 6,264 miles.
Hence, the linear equation formed for given data will be:
X+7x+10x = 6264
18x = 6264
X=6264/18
X=348
So,
miles travelled in January = x
miles travelled in January = 348 miles.
Miles travelled in February = 7x
Miles travelled in February = 7*348
Miles travelled in February =2436 miles
Miles travelled in March = 10x
Miles travelled in March =1 0 * 348
Miles travelled in March=3480 miles
To learn more about linear equations, visit:
https://brainly.com/question/13738061
#SPJ4
a vineyard has 145 acres of chardonnay grapes. a particular soil supplement requires 5.50 gg for every square meter of vineyard. how many kilograms of the soil supplement are required for the entire vineyard? (recall that 1 km2
3230 kilograms of the soil supplement are required for the entire vineyard;
1 km = 1000 m = 10³ m
1 km² = 1000000 m² = 10⁶ m²
1 km² = 247 acres
1 kg = 1000 g;
A vineyard has 145 acres of Chardonnay grapes.
145 acres = 145/247 km²
= 0.587 km²
A particular soil supplement requires 5.50 grams for every square meter of vineyard.
1 km² requires = 5.5 × 10³ kg
145 acres requires = 0.587 × 5.5 × 10³ kg = 3230 kg;
An annual percentage rate is expressed as an hobby charge. It calculates what percentage of the major you will pay every year by using taking things inclusive of month-to-month bills under consideration. APR is also the annual rate of interest paid on investments without accounting for the compounding of interest within that year.
To learn more about percentage this, visit: https://brainly.com/question/1578028
#SPJ4
Solve the following quadratic equation: (8x+7)(x+1)=9
Answer:
[tex]x=\dfrac{1}{8}, \quad x=-2[/tex]
Step-by-step explanation:
Given equation:
[tex](8x+7)(x+1)=9[/tex]
Expand the brackets:
[tex]\implies 8x^2+15x+7=9[/tex]
Subtract 9 from both sides:
[tex]\implies 8x^2+15x+7-9=9-9[/tex]
Simplify:
[tex]\implies 8x^2+15x-2=0[/tex]
To factor a quadratic equation in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]:
[tex]\implies ac=8 \cdot -2=-16[/tex]
[tex]\implies b=15[/tex]
Therefore, the two numbers are: 16 and -1.
Rewrite [tex]b[/tex] as the sum of these two numbers:
[tex]\implies 8x^2+16x-x-2=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies 8x(x+2)-1(x+2)=0[/tex]
Factor out the common term (x + 2):
[tex]\implies (8x-1)(x+2)=0[/tex]
Apply the zero-product property:
[tex]\implies 8x-1=0 \implies x=\dfrac{1}{8}[/tex]
[tex]\implies x+2=0 \implies x=-2[/tex]
Therefore, the solutions to the given quadratic equation are:
[tex]x=\dfrac{1}{8}, \quad x=-2[/tex]
Learn more about factoring quadratic equations here:
https://brainly.com/question/27956741
https://brainly.com/question/27947331
Answer:
x = 1/8 (or) x = -2
Step-by-step explanation:
Now we have to,
→ solve the following quadratic equation.
Let's solve for quadratic equation,
→ (8x+7)(x+1) = 9
→ 8x² + 7x + 8x + 7 - 9
→ 8x² + 15x - 2
→ 8x² + 16x - x - 2
→ 8x(x + 2) - 1(x + 2)
→ (8x - 1)(x + 2)
→ x = 1/8 (or) x = -2
Hence, the solution is x = 1/8, -2.
Given: f ( x ) = 2x - 7 and g ( x ) = x 2 + 2x - 3, find f ( x ) + g ( x )
Answer:
2x^2+4x−13
Step-by-step explanation:
HELP ASAP
easy stuff
The relation between the linear and recursive functions are given as follows:
f(n) = -n < - > {-1,-2,-3,-4...}, where f(1) = 1 and f(n + 1) = f(n - 1) - 1 for n > 1.f(n) = 2n - 3 < - > {-1,1,3,5...}, where f(1) = -1 and f(n + 1) = f(n - 1) + 2 for n > 1.f(n) = -n + 5 < - > {4,3,2,1...}, where f(1) = 4 and f(n + 1) = f(n - 1) - 1 for n > 1.f(n) = 2n + 2 < - > {4,6,8,10...}, where f(1) = 4 and f(n + 1) = f(n - 1) + 2 for n > 1.What is a linear function and how does it relate to a recursive function?A linear function is modeled according to the following rule:
f(x) = mx + b
In which:
m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis, that is, when x = 0.Considering the concepts of a linear function, the recursive function is given as follows:
f(n) = f(n - 1) + m for n > 1. f(1) for n = 1. (numeric value of the linear function when x = 1).The linear function with first term -1 and slope -1 is given by:
f(n) = -n.
Hence:
f(n) = -n < - > {-1,-2,-3,-4...}, where f(1) = 1 and f(n + 1) = f(n - 1) - 1 for n > 1.
The linear function with first term -1 and slope 2 is given by:
f(n) = 2n - 3
Hence:
f(n) = 2n - 3 < - > {-1,1,3,5...}, where f(1) = -1 and f(n + 1) = f(n - 1) + 2 for n > 1.
The linear function with first term 4 and slope -1 is given by:
f(n) = -n + 5
Hence:
f(n) = -n + 5 < - > {4,3,2,1...}, where f(1) = 4 and f(n + 1) = f(n - 1) - 1 for n > 1.
The linear function with first term 4 and slope 2 is given by:
f(n) = 2n + 2
Hence:
f(n) = 2n + 2 < - > {4,6,8,10...}, where f(1) = 4 and f(n + 1) = f(n - 1) + 2 for n > 1.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
1. Yu Yan competes in a sprint triathlon. The race consists of three parts: a 0.5-mile swim, a
12.4-mile bike ride, and a 3.1-mile run.
a. Yu Yan completes the swim portion of the sprint triathlon in 25 minutes. What is her average
swimming speed in miles per minute?
The required average speed of the triathlon is 0.02 miles per minute.
Given that,
Total distance swim in the triathlon = 0.5 miles
Total time consumed to swim = 25 minutes
To determine the average speed of swimming in the triathlon.
Here,
Total time consumed to complete the swim portion of the triathlon = 25 minute
Distance swim = 0.5 miles
Speed of swim or average speed of swim = distance swim \time
= 0.5 / 25
= 0.02 miles / minute.
Thus, the required average speed of the triathlon is 0.02 miles per minute.
Learn more about speed here:
https://brainly.com/question/7359669
#SPJ1
Point e is on line segment DF given ef =16 and DF=19
In a line segment DF with point e somewhere on the line, ef = 16 and ed = 3.
We have given a line segment DF with a point e on the line segment
We have been informed that ef = 16 and DF = 19
We know that
⇒ DF = ed + ef
⇒ ed = DF - ef
= 19 - 16
= 3 units
What is line segment?
This line segment has two ends with defined lengths, A and B. This line segment's length is equal to the distance between its ends, A and B.
A line segment is hence a section or component of a line with two endpoints. A line segment, unlike a line, has a set length.
Measuring the length of a line segment can be done using either metric measurements, such as millimeters or centimeters, or conventional measurements, such as feet or inches.
Learn more about line segment
https://brainly.com/question/280216
#SPJ9
Full question
Point e is on line segment DF given ef =16 and DF=19. Find ed.
what dose 7/8 x 2/3 =
Answer:
14/24
Step-by-step explanation:
multiply 7 x 2 and 8 x 3
Answer:
Step-by-step explanation:
7/8 * 2/3
7 * 2 = 14
8 * 3 = 24
14/24 = 7/12
answer: 7/12
105 fans talked about their favorite anime 73 like Dragon Ball Z, 67 like Naruto Shippuden, 51
like One Piece, 42 like Dragon Ball Z and Naruto Shippuden, 38 Like Dragon Ball Z and One
Piece, 40 like Naruto Shippuden and One Piece, 29 like all three.
19. P(Dragon Ball Z or Naruto Shippuden)
20. P (Naruto Shippuden/Not DBZ)
21. P (One piece or Naruto Shippuden)
22. P (Dragon ball Z/Not One Piece)
23. What is the probability of students that like Dragon Ball Z and Naruto Shippuden?
24. What is the probability of students that like One Piece and do not like Naruto Shippuden?
We can make a 3 set venn diagram out of the given information as shown in the figure below. Based on the venn diagram, we can answer the questions.
19. P(Dragon Ball Z or Naruto Shippuden)
This can also be written as-
1 - P(only one piece)
P(only one piece) = 2/100
Thus, P(Dragon Ball Z or Naruto Shippuden) = 1- 2/100
= 98/100
= 0.98
20. P (Naruto Shippuden/Not DBZ)
Number of people who don't like Dragon ball z = 100 - 73
= 27
Number of people who like Naruto Shippuden but not Dragon ball z = 11 + 14
= 25
Thus, P (Naruto Shippuden/Not DBZ) = 25/27
= 0.92
21. P(One piece or Naruto Shippuden)
This can also be written as-
1 - P(only DBZ)
P(only DBZ) = 22/100
Thus, P(One piece or Naruto Shippuden) = 1- 22/100
= 78/100
= 0.78
22. P(Dragon ball Z/Not One Piece)
Number of people who don't like one piece = 100 - 51
= 49
Number of people who like Naruto Shippuden but not one piece = 14 + 13
= 27
Thus, P(Dragon ball Z/Not One Piece) = 27/49
= 0.55
23. Number of people who like both DBZ and Naruto Shippuden = 13 + 29
= 42
Thus, probability of students that like Dragon Ball Z and Naruto Shippuden = 42/100
= 0.42
24. Number of people who like one piece but not naruto = 51 - 29 - 11
= 11
Thus, the probability of students that like One Piece and do not like Naruto Shippuden = 11/100
= 0.11
Learn more about probability here-
https://brainly.com/question/24756209
#SPJ1
Match each group of numbers with the appropriate group name.
13, 0.781781...
a.
b.,1.5, -56.25
c. √5, 1.1,
d. 0.-€,0.975
e. √9,-4,892
[Choose]
Whole Numbers
Positive Numbers
Repeating Decimals
Improper Fractions
Numbers Between -1 and 1
Repeating Decimals
27
Answer:
A . 6822 just divede 420 to 32 then times 562 tk 911
Find the equation of the line which passes through (4,1) and is parallel to the line with equation 2y=x+1
Parallel to the line:
[tex]{\sf{2y = x + 1}}[/tex]
[tex]{\sf{y = \frac{x}{2} + \frac{1}{2 }}} [/tex]
Hence Slope:
[tex]{\sf{\large{\frac{1}{2}}}}[/tex]
The slope of line of which equation we need is parallel to the line given. Therefore, it's slope also is (m):
[tex]{\sf{\large{\frac{1}{2}}}} [/tex]
Also, the line passes through the points (4, 1)
Therefore by the formula of
[tex]{\sf{(y - y1) = m(x - x1)}}[/tex]
we have:
[tex]{\sf{(y - 1) = \frac{1}{2} (x - 4) }}[/tex]
[tex]{\sf{2y - 2 = x - 4}}[/tex]
[tex]{\sf{x - 4 - 2y + 2 = 0}}[/tex]
[tex]{\sf{\red{\boxed{\sf{x - 2y - 2 = 0}}}}}[/tex]
What is correct solution for this problem?
(x°) + (4x°) = 180°
Answer:hi how are you
Step-by-step explanation:
SECOND TIME ASK9INIG PLEASE HELP
EASY POINTS WILL GIVE BRAINLIST TO BEST ANSWER
What is the result of solving this equation for t ?
Mt – 5ab = nRT
explain!!
Answer:
t = nRT/M + 5ab/M
Step-by-step explanation:
I'm going to assume that the t and T are seperate variables.
basically all you have to do is isolate t by dividing each side with factors that do not contain the t
Graph the equation by plotting three
points. If all three are correct, the line
will appear.
-4y = x - 18
If three points (2,4), (6,3), (10,2) are correct, the line -4y = x - 18 will appear.
If all the three points are plotted correctly then the line obtained will be -4y = x - 18.
The form of equation of line is the slope intercept form of line. In this form of line, the line is represented with the slope of line and the intercept of the y axis.
By using the equation of the line, all the three correct points can be found out easily,
By assuming any three values of x, we can find the value of y.
1. Let us assume x = 2.
Putting value of x we get,
-4y = 2 - 18
-4y = -16
y = 4.
So, the first point is (2,4).
2. Let us assume x = 6.
Putting value of x we get,
-4y = 6-18
-4y = -12
y = 3.
So, the second point is (6,3).
3. Let us assume x = 10.
Putting value of x we get,
-4y = 10-18
-4y = -8
y = 2.
So, the third point is (10,2).
The three points to obtain the equation of line -4y = x -18, are (2,4), (6,3) and (10,2).
To know more about Slope-intercept form, visit,
https://brainly.com/question/1991439
#SPJ9
3. Robinsport and Titusville are 324 mi apart on a railroad line. Trains
leave each of these depots at the same time headed for the other depot.
One travels at 43 mi/h, the other at 38 mi/h. How long will it take for
the two trains to pass one another?
The time taken for the two trains to pass one another at 324 mi apart is 4 hours.
What is velocity ?
velocity is defined as rate of change of displacement d of the object with respect to rate of change in time t. In mathematics It is written as :
v = d/t
here it is given that :
Robinsport and Titusville trains are 324 mi apart on a railroad line that is distance between then is 324 mi.
also,
Trains leave each of these depots at the same time headed for the other depot and one travels at v₁ = 43 mi/h , the other at v₂ = 38 mi/h in opposite direction that is relative speed will get add-up that is :
Δv = v₁ - v₂
Δv = 43-(-38)
Δv = 81 mi/h
Now, the time taken for the two trains to pass one another is calculated :
Δv = d/t
81 = 324/t
t = 324/81
t = 4 hours
Therefore, the time taken for the two trains to pass one another is 4 hours.
Learn more about "velocity" here:
https://brainly.com/question/14236800
#SPJ1
What is the area? Please help!!
Answer:
7.2
Step-by-step explanation:
The area of a rectangle is calculated by multiplying its width and length.
The length is already given as 13 cm and the area is given as 93.6 cm.
Now, to find the width we will divide the area by length:
93.6 ÷ 13 = 7.2
nightclub management you have just opened a new nightclub, russ' techno pitstop, but are unsure of how high to set the cover charge (entrance fee). one week you charged $9 per guest and averaged 315 guests per night. the next week you charged $12 per guest and averaged 270 guests per night.
The answers to all the parts of the question are:
(A) q(p) = -15p + 300(B) R(p) = -15p² + 300p(C) C(p) = -30p + 1600(D.1) P(p) = -15p²+ 330p - 1600(D.2) p = $11(A) Before we begin, consider the cartesian plane, where the x-axis represents the cover charge and the y-axis represents the number of guests per night.
According to the previous information, we will find the following coordinates there: (9,165) (10,150).
Remember that the linear equation's slope-intercept form is y=mx+b, where m is the slope and b is the intercept.
The slope can be calculated using the following formula:
[tex]m=\frac{y^2-y^1}{x^2-x 1}[/tex]In this case, the first coordinate will be (9,165) and the second will be (10,150).
The order is irrelevant.
Finally, we get the same value for m.
So,
m = (150 - 165)/(10 - 9) = -15We now have the slope and two points. Find a linear demand equation using this formula and remember that the point-slope form of a line's equation is y - y1 = m(x - x1).
Any of two coordinates can be selected.
In this case, we will select the second one.
We can choose between two coordinates.
In this case, we'll go with the second option.
y-150=-15(x-10) ....... (1)Solve equation (1) for y:
y = -15x + 150 + 150y = -15x + 300We defined x as the cover charge (p) and y as the number of guests above (q).
As a result, rewrite equation 1.
q(p) = -15p + 300Its formula depicts the number of guests per night as a function of the cover charge.
(B) The nightly revenue can be calculated by multiplying the cover charge price by the number of guests.
So we simply multiply the equation 1 by p.
p × q(p) = p × (-15p +300)R(p) = -15p² + 300p ......(2)(C) To calculate the nightclub's cost function, multiply the cost of two non-alcoholic drinks by the number of guests (equation 1) and add nightly overheads.
C(p) = 2 × (-15p+300) + 1000C(p) = -30p + 600 + 1000C(p) = -30p + 1600(D) To calculate the profit in terms of the cover charge, subtract the nightly costs (equation 3) from the nightly revenue (equation 2).
P(p) = R(p)-C(p)P(p) = -15p² + 300p - (-30p + 1600)P(p) = -15p² + 300p+30p - 1600P(p) = -15p² + 330p - 1600We will use the first derivative test (y'(x)=0) to find an extremum point to determine the entrance fee we should charge for maximum profit.
P's first derivative should be computed (p)
P'(p) = -30p + 330 = 0
30p = 330
p = 330/30
p = $11
For maximum profit, the entrance fee should be p=$11 per guest.
Therefore, the answers to all the parts of the question are:
(A) q(p) = -15p + 300(B) R(p) = -15p² + 300p(C) C(p) = -30p + 1600(D.1) P(p) = -15p²+ 330p - 1600(D.2) p = $11Know more about equations here:
https://brainly.com/question/2972832
#SPJ4
The complete question is given below:
You have just opened a new nightclub, Russ' Techno Pitstop, but are unsure of how high to set the cover charge (entrance fee). One week you charged $9 per guest and averaged 165 guests per night. The next week you charged $10 per guest and averaged 150 guests per night.
(a) Find a linear demand equation showing the number of guests q per night as a function of the cover charge p. q(p) =
(b) Find the nightly revenue R as a function of the cover charge p. R(p) =
(c) The club will provide two free non-alcoholic drinks for each guest, costing the club $2 per head. In addition, the nightly overheads (rent, salaries, dancers, DJ, etc.) amount to $1,000. Find the cost C as a function of the cover charge p. C(p) =
(d) Now find the profit in terms of the cover charge p. P(p) =
Determine the entrance fee you should charge for a maximum profit. p = $ per guest.
Consider Sn = 1/2 + 1/4 + 1/8 + 1/16 +...+ 1/2^n a Find S1, S2, S3, S4 and S5 in fractional form b From A guess the formula for Sn c Find Sn using Sn= u1(1-r^n)/1-r d Comment on S, as n gets very large. e What is the relationship between the given diagram and d?
Part (a)
S1 = 1/2 since we only have one term, i.e. we aren't really summing anything here.
S2 = (1/2) + (1/4) = (2/4) + (1/4) = (2+1)/4 = 3/4
S3 = (1/2) + (1/4) + (1/8) = (4/8) + (2/8) + (1/8) = (4+2+1)/8 = 7/8
Or,
S3 = S2 + 1/8 = (3/4) + (1/8) = (6/8) + (1/8) = (6+1)/8 = 7/8
S4 = S3 + 1/16 = (7/8) + (1/16) = (14/16) + (1/16) = (14+1)/16 = 15/16
S5 = S4 + 1/32 = (15/16) + (1/32) = (30/32) + (1/32) = (30+1)/32 = 31/32
Here's the summary:
S1 = 1/2S2 = 3/4S3 = 7/8S4 = 15/16S5 = 31/32=============================================================
Part (b)
Through trial and error, the formula is
Sn = ( (2^n) -1 )/(2^n)
For example, if n = 4, then,
Sn = ( (2^n) -1 )/(2^n)
S4 = ( (2^4) -1 )/(2^4)
S4 = (16 - 1)/(16)
S4 = 15/16
=============================================================
Part (c)
u1 = first term = 1/2
r = common ratio = 1/2
Sn = u1*( 1 - r^n)/(1 - r)
Sn = (1/2)*( 1 - (1/2)^n )/(1 - 1/2)
Sn = (1/2)*( 1 - (1/2)^n )/(1/2)
Sn = 1 - (1/2)^n
Sn = 1 - 1/(2^n)
Sn = (2^n)/(2^n) - 1/(2^n)
Sn = ( (2^n) -1 )/(2^n)
This helps confirm the formula mentioned in part b
=============================================================
Part (d)
As n gets very large, Sn approaches 1
Examples:
n = 7 leads to S7 = 0.9921875n = 10 leads to S10 = 0.9990234375n = 12 leads to S12 = 0.999755859375n = 20 leads to S20 = 0.999999046325684Try out larger values of n and the Sn value should get closer to 1.
The reason why this works is because Sn = (x - 1)/x where x = 2^n
The (x-1)/x is equivalent to 1 - (1/x) and the 1/x approaches zero when x gets larger. The x gets larger as 2^n does.
The value of Sn itself will never equal 1 exactly. It simply gets closer and closer.
=============================================================
Part (e)
The diagram is missing, so I don't have enough info to be able to answer this.
Solve. 3x + 4y = 23
A. x = 23/4y / 2
B.x=23 - 4y/2
C. x = 23 - 4y/3
D. x = 2y
Answer:
C
Step-by-step explanation:
Find the 12th term of the arithmetic sequence -3x+8, 4x+5, 11x+2, ....
Please help me
Answer:
74x - 25.
Step-by-step explanation:
The common difference d
= 4x + 5 - (-3x + 8)
= 7x - 3
also:
11x + 2 - (4x + 5)
= 7x - 3.
First term a1 = -3x + 8
so, 12th term
= a1 + (n -1)d
= -3x + 8 + (12 - 1)(7x - 3)
= -3x + 8 + 11(7x - 3)
= -3x + 8 + 77x - 33
= 74x - 25.