Answer: slope is -1/3 and the y intercept is -7
Step-by-step explanation:
You invest $15,000 to start a hot dog stand at the local sports complex. It costs you $.65 to produce each hot dog. How many hot dogs must you sell before your average cost per hot dog is $1.15?
The answer should be 30,000. I just do not understand how to get to it.
Thank you in advance!
Answer:
Below is the procedure to find the answer: 30,000 hot dogs.
Explanation:
The average cost is found dividing the total cost by the number of hot dogs:
[tex]Average\text{ }cost=Total\text{ }cost/Number\text{ }of\text{ }hot\text{ }dogs[/tex]
The total cost is the the sum of amount that you invest plus the product of the cost of producing each hot dog times the number of hot dogs:
[tex]Total\text{ }cost=investment+Number\text{ }of\text{ }hot\text{ }dogs\times cost\text{ }to\text{ }produce\text{ }each\text{ }hot\text{ }dog[/tex]
Substitute the values:[tex]Total\text{ }cost=15,000+0.65x\\ \\ Averate\text{ }cost=(15,000+0.65x)/x=1.15[/tex]
Where x is the number of hot dogs.
Solve for x from the equation:[tex](15,000+0.65x)/x=1.15\\ \\ 15,000+0.65x=1.15x\\ \\ 15,000=1.15x-0.65x\\ \\ 15,000=0.5x\\ \\ 15,000/0.5=x\\ \\ 30,000=x\\ \\ x=30,000[/tex]
Which shows you how you can find that the answer is 30,000 hot dogs.
Final answer:
To find the number of hot dogs needed to achieve an average cost of $1.15, including a fixed investment of $15,000 and a variable cost of $.65 per hot dog, the calculation reveals that 30,000 hot dogs must be sold to reach this target.
Explanation:
The question asks how many hot dogs must be sold before the average cost per hot dog is $1.15, given an initial investment of $15,000 and a production cost of $.65 per hot dog. To find the break-even point in terms of units sold to reach the target average cost, we use the formula to calculate average cost: Average Cost = (Fixed Costs + Variable Costs) / Quantity. Here, the fixed cost is the initial investment of $15,000, and the variable cost is $.65 per hot dog.
To find the number of hot dogs needed to achieve an average cost of $1.15, we set up the equation: $1.15 = ($15,000 + $.65Q) / Q. Solving for Q gives us 30,000 hot dogs as the break-even point where the average cost per hot dog would be $1.15.
This calculation allows the business owner to understand how many units need to be sold to overcome the initial investment and start making a profit on each hot dog sold at or above $1.15.
Can someone please help me with this also
Answer:
Step-by-step explanation:
each is divided into 8 sections.
So1 1/2 =1 1*4/2*4 =1 4/8 . plot in the 4 th point after 1
2 3/4
3*2/4*2 = 6/8
2 3/4 = 2 6/8. so plot in the 6th point after 2
Which of the following options could represent a possible set of interior angles of a triangle?
60°, 150° and 150°
15°, 35°, and 40°
35°, 65°, and 80°
45°, 105°, and 120°
Answer:
35+65+80=180
Step-by-step explanation:
the total interior angle of a triangle is 180
Answer:
its the third answer
[tex]35 \: \: 65 \: \: 80[/tex]
Step-by-step explanation:
because the addition of a interior angles has to be 180.'
when would you use a negative number to describe a real world amount? Give an example.
Answer:
Debt
Step-by-step explanation:
Let's say someone uses debit instead of credit and they don't have any money in their account. If used multiple times you could potentially end up owing the bank (be in debt) .
Negative numbers are used in real-world contexts to describe temperatures below zero, financial debts, or elevations below sea level, helping to clearly indicate quantities that are less than a referenced zero point.
You would use a negative number to describe a real-world amount when talking about temperatures below zero, debts, or elevations below sea level, among other scenarios. For example, if the temperature is 5 degrees below zero, it could be represented as -5°C. This indicates that it is 5 degrees colder than the point at which water freezes (0°C). Another example is financial: if you owe $100, you could represent your account balance as -$100, indicating a debt. Similarly, a town located 100 meters below sea level could have its elevation represented as -100 meters.
These examples show how negative numbers can effectively convey quantities less than zero in various real-world contexts, providing a clear understanding of situations where values are lacking or in deficit compared to a reference point.
What is the area of this trapezoid? 86 in² 112 in² 148 in² 184 in² Trapezoid A B C D with parallel sides D C and A B. Point F and E are on side D C. Point F is connected to point A by a dotted segment. Point E is connected to point B by a dotted segment. A B E F is a rectangle. D F is 3 inches. E C is 6 inches. E B is 8 inches. A B is 14 inches.
Option C: [tex]$148 \mathrm{in}^{2}$[/tex] is the area of the trapezoid.
Explanation:
The image of the trapezoid having these descriptions is attached below:
Now, we shall determine the area of the trapezoid using the formula,
[tex]$A=\frac{a+b}{2} h$[/tex] where a and b are the base of the trapezoid and h is the height of the trapezoid.
Thus, we shall find the value of a and b from the diagram given below.
[tex]a= AB=14in[/tex]
[tex]b=DC\\b=DF+FE+EC\\b=3+14+6\\b=23in[/tex]
It is given that the height of the trapezoid [tex]h=8in[/tex]
Thus, substituting the values of a,b and h in the formula [tex]$A=\frac{a+b}{2} h$[/tex], we get,
[tex]A=\frac{14+23}{2}(8)\\ A=\frac{37}{2} (8)\\A=148in^2[/tex]
Thus, the area of the trapezoid is [tex]$148 \mathrm{in}^{2}$[/tex]
Hence, Option C is the correct answer.
At the beginning of the year,
Shelby could run 2 miles. Now
she can run 3.5 miles. What is
the percent increase in the
distance she can run?
Answer:
175% increase
Step-by-step explanation:
(3.5 / 2) * 100 = 175%
What number represents an elevation of 80 feet below sea level
Answer:
-80
Step-by-step explanation:
The answer is -80 because 80 feet below sea level would be a negative number. So you just add a negative sign to 80 and voila! You get the answer. Your welcome, by the way!
Elevation 80 feet below sea level can be represented by the negative number -80 in mathematics. This is because negative numbers are used to represent depths or locations below sea level.
Explanation:In mathematics, when we talk about locations below sea level, we represent them with negative numbers. So, an elevation of 80 feet below sea level will be represented as -80. This numerical representation helps us have an accurate and easy understanding of above and below sea level elevations. Such as, 0 represents sea level, positive numbers represent elevations above sea level, and negative numbers represent depths below sea level.
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Y = -1/3 x + 2
Y= x + 2
What is the solution to the system of equations?
A. (0, 2)
B. (2, 0)
C. (-1, 3)
D. (0, -2)
Answer:
X = 0
Y = 2
so Option A (0,2) IS CORRECT
Step-by-step explanation:
Y = -1/3 x + 2 equation 1
Y = x+ 2 equation 2
from equation 2 we have
y = x+ 2 Put in equation 1
x + 2 = -1/3 x + 2
x +1/3x = 2 -2
0.67 x = 0
X = 0
so put x =0 in equation 2 then we have
y = x +2
Y = 0+ 2
Y = 2
How is selective boarding school will only admit students who plays at least 2 .5 standard deviation above the mean on a standardized test that has a mean of 100 and a standard deviation of 24. What is the minimum score that an applicant must make on the test to be accepted?
Answer:
I'd don't now
Step-by-step explanation:
ok am sorry
Tickets for a school carnival cost 10$ for adult and 5 for children. last Saturday carnival sold 170 tickets worth a total of $1200 . How many adults and childeren attended the carnival
70 adults and 100 children attended the carnival.
Step-by-step explanation:
Given,
Cost of each adult ticket = $10
Cost of each child ticket = $5
Total tickets sold = 170
Total revenue generated = $1200
Let,
Number of adults = x
Number of children = y
According to given statement;
x+y=170 Eqn 1
10x+5y=1200 Eqn 2
Multiplying Eqn 1 by 10
[tex]10(x+y=170)\\10x+10y=1700\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 2 from Eqn 3
[tex](10x+10y)-(10x+5y)=1700-1200\\10x+10y-10x-5y=500\\5y=500[/tex]
Dividing both sides by 5
[tex]\frac{5y}{5}=\frac{500}{5}\\y=100[/tex]
Putting y=100 in Eqn 1
[tex]x+100=170\\x=170-100\\x=70[/tex]
70 adults and 100 children attended the carnival.
Keywords: linear equation, elimination method
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simpilfy -19+4k-15k+k-9
Answer:
-10k-28
Step-by-step explanation:
-19+4k-15k+k-9
-28-11k+k
-10k-28
Answer:
12k+ -10
im not truely sure if this is correct... but i went off my knowlage
Find the equation for the circle with center (4,-5) and passing through (5,-4)
Answer:
(x -4)^2 +(y +5)^2 = 2
Step-by-step explanation:
The equation of a circle centered at (h, k) through point (p, q) is ...
(x -h)^2 +(y -k)^2 = (p -h)^2 +(q -k)^2
Filling in your given numbers gives ...
(x -4)^2 +(y +5)^2 = (5-4)^2 +(-4+5)^2
(x -4)^2 +(y -5)^2 = 2
The equation of the circle is (x - 4)² + (y + 5)² = 2.
The center of the circle is (4, -5). The circle passes through the point (5, -4).
The general formula for the equation of a circle is: (x - h)² + (y - k)² = r² where (h, k) is the center of the circle and r is the radius.
The radius is the distance between the center (4, -5) and the point (5, -4).
Use the distance formula: Distance = √ [(x2 - x1)² + (y2 - y1)²]
Distance = √ [(5 - 4)² + (-4 - (-5))²]
Distance = √ [(1)² + (1)²]
Distance = √ [1 + 1]
Distance = √ [2]
So, the radius r = √ [2].
Substitute the center (4, -5) and radius √ [2] into the circle equation: (x - 4)² + (y + 5)² = (√ [2])² (x - 4)² + (y + 5)² = 2
one number is 6 more than another. the sum of the numbers is 30. find the numbers.
To find the numbers, we can set up a system of equations and solve for the variables.
Explanation:Let's represent the numbers as x and y. According to the problem, one number is 6 more than the other. This can be written as:
x = y + 6
The sum of the numbers is 30. This can be written as:
x + y = 30
We can solve this system of equations by substituting the value of x from the first equation into the second equation:
(y + 6) + y = 30
Combining like terms:
2y + 6 = 30
Subtracting 6 from both sides:
2y = 24
Dividing by 2:
y = 12
Now, we can substitute the value of y back into the first equation to find the value of x:
x = 12 + 6
x = 18
Therefore, the two numbers are 12 and 18.
Solve the following system of equations by using the method of your choice
3x-y=-28
-5x-4y=-10
Answer:
(x, y) =(-6,4)
Step-by-step explanation:
3x-y=-28
-5x-4y=-10
y=3x+28
-5x-4(3x+28)=-10
y=3x+28
-5x-12x-112=-10
y=3x+28
-17x=-10+112
y=3x+28
-17x=102
y=3x+28
x=102/(-17)
y=3x+28
x=-6
y=3*(-6)+28
x=-6
y=-24+28
x=-6
y=4
x=-6
(x,y)=(-6,4)
Find the minimum value of the
parabola
y = x2 − 4x − 5 .
Answer:
-2x-5
Step-by-step explanation:
what is 6times40///////////////////////
Answer:
the answer is 240
Answer:
240
Step-by-step explanation:
i used a calculator
Write two fractions that are equivalent to 5
Answer:
5/1, 25/5
Step-by-step explanation:
Show how to add 24+9 by making 10s
If you add 10 and then subtract 1, you get the same result as if you just added 9.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
+ Addition operation: Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
We have to add 24+9 by making 10s.
As per the given question, the required solution would be as:
24 + 10 - 1 = 33
Therefore, if you add 10 and then subtract 1, you get the same result as if you just added 9.
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Final answer:
To add 24 and 9 using tens, break 9 into 6 and 3, add 6 to 24 to get 30, and then add the remaining 3 to reach 33.
Explanation:
To add 24 and 9 by making 10s, you can first break down the number 9 into 6 and 3.
Add 6 to 24 to make a round number, which is 30.
Now you have made a '10' because 30 is a multiple of 10.
Next, add the remaining 3 to get 33.
So, 24 + 9 = 33.
A particular bacterial colony doubles its population every 15 hours. A scientist running an experiment is starting with 100
bacteria cells. She expects the number of cells to be given by the formula, where t is the number of hours since the
experiment started.
C = 100 (2 ^t/15)
After how many hours would the scientist expect to have 300 bacteria cells?
Give your answer to the nearest hour.
A) 2 hours
B) 24 hours
C) 1,048,557 hours
D) 104,857,699 hours
Answer:
d
Step-by-step explanation:
Answer:
24 hours
24 hours is the solution to 300=10(2)^t/15
Which expression is equivalent to 7/2h-3(5h-1/2)?
Answer:
-23/2h+3/2
Step-by-step explanation:
7/2h-3(5h-1/2)
7/2h-15h+3/2
7/2h-30/2h+3/2
-23/2h+3/2
Answer:
(-23h+3)/2
Step-by-step explanation:
7/2h-3(5h-1/2)=
7/2h-3*5h+3*1/2=
7/2h-15h+3/2=
7/2h-30/2h+3/2=
-23/2h+3/2 or
(-23h+3)/2
Evaluate (3x-1) + 2 when x = 5
Answer:
16
Step-by-step explanation:
(3x - 1) + 2
(3(5) - 1) + 2
(15 - 1) + 2
14 + 2
16
Answer:
16
Step-by-step explanation:
Start by plugging in 5 for x in the equation.
(3 x 5 - 1) + 2
Next do the multiplication.
15 - 1 + 2
Add and subtract.
16
You have your answer.
Hope this helped.
calculus 1 limits and derivatives chapter help. delta and epsilon proof
Answer:
[tex]\delta=\frac{\epsilon}{3}[/tex]
The proof is in the explanation.
Step-by-step explanation:
Compare [tex]\lim_{x\rightarrow 7}(3x-2)=19[/tex] to [tex]\lim_{x\rightarrow a}f(x)=L[/tex].
We want to find [tex]\delta[/tex] such that whenever [tex]0<|x-a|<\delta[/tex] we have [tex]|f(x)-L|<\epsilon[/tex].
We want to find [tex]\delta[/tex] such that whenever [tex]0<|x-7|<\delta[/tex] we have [tex]|3x-2-19|<\epsilon[/tex].
[tex]|3x-2-19|<\epsilon[/tex]
Simplify:
[tex]|3x-21|<\epsilon[/tex]
Factor on left side inside the | |:
[tex]|3(x-7)|<\epsilon[/tex]
|ab|=|a||b|:
[tex]|3||x-7|<\epsilon[/tex]
|3|=3:
[tex]3|x-7|<\epsilon[/tex]
Divide both sides by 3:
[tex]|x-7|<\frac{\epsilon}{3}[/tex]
So we will need to choose [tex]\delta=\frac{\epsilon}{3}[/tex].
We want to prove there exists a [tex]\delta[/tex] such that whenever [tex]0<|x-7|<\delta[/tex] we have [tex]|f(x)-L|<\epsilon[/tex].
Proof:
Let [tex]\epsilon>0[/tex]. We will choose [tex]\delta=\frac{\epsilon}{3}[/tex] such that [tex]0<|x-7|<\delta[/tex] will give us [tex]|f(x)-L|<\epsilon[/tex].
[tex]|f(x)-L|=|(3x-2)-19|[/tex]
[tex]=|3x-21|[/tex]
[tex]=|3||x-7|[/tex]
[tex] =3|x-7|<3\delta=3\frac{\epsilon}{3}=\epsilon[/tex].
Therefore, we have for all [tex]\epsilon>0[/tex], [tex]\delta=\frac{\epsilon}{3}[/tex] is the number that satisfies the definition.
Which choice is equivalent to the expression below ?
The answer is B, 7i.
sqrt(-49)
Pull out an i.
i*sqrt(49)
Take the square root to get 7i.
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how do you solve 17- ||-16|-9|
Evaluate the inside absolute values first:
17-|16*9|
17-|144|
17-144
-127
Hope this helped!
What is 245 and 7/50 in decimal form
Answer:
245=2.45
7/50=0.14
Step-by-step explanation:
divide by 100
USE MATHAWAY DOT COM!!
-8|4k-10|=-48 okay y'all can you help me out with this?
Answer:
k = 4
Step-by-step explanation:
-8|4k-10|=-48
|4k-10|=-48/-8
|4k-10|= 6
4k = 6+10
4k = 16
k = 4
What is the value of the expression below?
(9-3)+4(6-7)
-7
-1
7
20
Final answer:
The expression (9-3)+4(6-7)-7 is calculated following PEMDAS, resulting in a value of -5 after simplifying the operations within the expression.
Explanation:
The value of the expression (9-3)+4(6-7)-7-1720 seems to have a typo, and it should probably read (9-3)+4(6-7)-7. To evaluate this expression, you follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
First, calculate the parentheses: (9-3) = 6 and (6-7) = -1.
Next, perform the multiplication: 4 * (-1) = -4.
Finally, add and subtract from left to right: 6 + (-4) - 7 = 6 - 4 - 7 = 2 - 7 = -5.
The value of the expression is -5.
ƒ(x) = 18x + 8, find x when ƒ(x) = 14.
Answer:
Step-by-step explanation:
18x+8=14
18x=6
x=1/3
When ƒ(x) is equal to 14, the value of x is 1/3.
To find the value of x when f(x) is equal to 14, we can set up the equation:
f(x) = 18x + 8
We know that f(x) is equal to 14, so we substitute that into the equation:
14 = 18x + 8
We isolate the variable x by subtracting 8 from both sides of the equation:
14 - 8 = 18x
6 = 18x
To solve for x, we divide both sides of the equation by 18:
6/18 = x
1/3 = x
Therefore, when f(x) is equal to 14, the value of x is 1/3.
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How would you solve 8(6-k)+2k ≥-15-(-3k) ( please show each step)
Answer:
Step-by-step explanation:
8(6-k)+2k ≥-15-(-3k)
Opening bracket
48 - 8k + 2k ≥ -15 + 3k
-8k - 3k + 2k ≥ -15 - 48
-9k ≥ -63
k ≤ -63/-9
k ≤ 7
Answer:
k ≤ 7
Step-by-step explanation:
8 (6 - k) + 2k ≥ - 15 -(-3k)
Let's simplify this by solving each side.
First side:
8 (6 - k) + 2k ≥ - 15 -(-3k)
48 - 8k + 2k ≥ - 15 -(-3k)
48 - 6k ≥ - 15 -(-3k)
Second side:
48 - 6k ≥ - 15 -(-3k)
48 - 6k ≥ -15 + 3k
DONE SIMPLIFYING!
Now solve for "k" algebraically (transitions are in bold):
48 - 6k ≥ -15 + 3k
-6k ≥ -15 - 48 + 3k
-6k ≥ -63 + 3k
-6k - 3k ≥ -63
-9k ≥ -63
-k ≥ -63 ÷ 9
-k ≥ -7
k ≤ 7
QUESTION 10
The park manager wants to conduct a survey to determine how people like the park facilities. Which would give her the most representative sample for the survey?
conducting the survey at the softball diamond
conducting the survey at a shopping mall
conducting the survey as visitors leave the park
conducting the survey at the playground
conducting the survey as visitors leave the park
The park manager wants to figure out how people like the park so she will conduct the survey as people leave the park.
Final answer:
The most representative sample for a survey on park facilities satisfaction would be obtained by conducting the survey as visitors leave the park, ensuring a broad and unbiased cross-section of park users are included.
Explanation:
The question asks which method would provide the most representative sample for a survey about how people like the park facilities. The most representative sample would be achieved by conducting the survey as visitors leave the park. This method ensures a wide cross-section of park users are surveyed, capturing various interests and usage patterns of the park facilities, from those who come for leisure activities at the softball diamond or playground to those seeking quiet contemplation or exercise.
Conducting the survey in other locations like a shopping mall or specific areas within the park, such as the softball diamond or playground, would likely bias the results. Surveying at a shopping mall doesn't guarantee participants have visited or are familiar with the park, and focusing solely on one area within the park would not capture the diverse usage and opinions of all park visitors. Therefore, surveying as visitors leave the park is the most inclusive and unbiased approach to understanding how the facilities meet the needs of the community.