The break-even point can be determined by setting the net sales per hour equal to the total cost per hour. The equation to solve for the break-even point is $200x = $1,320x. By dividing both sides of the equation by $1,320, we can find the value of x, which represents the number of hours per month the store needs to be open to break even.
Explanation:To determine the break-even point, we need to find the number of hours per month the store needs to be open in order to cover all its costs. The total cost for each hour the store is open is the sum of the rent and the employee salary. So, the total cost per hour is $1,200 + $120 = $1,320. The break-even point is reached when the net sales per hour equals the total cost per hour:
Net sales per hour = Total cost per hour
In this case, the net sales per hour is $200, so we can set up the equation:
$200x = $1,320x
where x represents the number of hours per month the store is open. By dividing both sides of the equation by $1,320, we can solve for x:
$200 = $1,320x / $1,320
$200 / $1,320 = x
x = 0.1515...
So, the break-even point is approximately 0.1515... hours per month, or about 9.09 minutes per month.
What system of linear inequalities is shown on the graph?
Answer:
[tex]3y-x<6[/tex]
[tex]2x+y\leq2[/tex]
Step-by-step explanation:
Equation of line that passes two points (a,b) and (c,d) :
[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]
Dotted line passes through (0,2) and (-3,1).
Equation of Dotted line :
[tex](y-2)=\dfrac{1-2}{-3-0}(x-0)[/tex]
[tex](y-2)=\dfrac{-1}{-3}x[/tex]
[tex]3(y-2)=x[/tex]
[tex]3y-6=x[/tex]
[tex]3y-x=6[/tex]
Inequality for dotted line (values on line is not included for dotted)
[tex]3y-x<6[/tex] (shaded below )
Solid line passes through (0,2) and (1,0)
[tex](y-2)=\dfrac{0-2}{1-0}(x-0)[/tex]
[tex]y-2=-2x[/tex]
[tex]2x+y=2[/tex]
Inequality for dotted line (values on line is included for solid line)
[tex]2x+y\leq2[/tex] (shaded leftwards )
∴ System of linear inequalities is shown on the graph:
[tex]3y-x<6[/tex]
[tex]2x+y\leq2[/tex]
Evaluate the expression when y = 4. 5 + y + 8 A. 72 B. 21 C. 17 D. 13
Answer: its c
Step-by-step explanation:
5+4=9 9+8=17
Suppose that α and β are the angles of a triangle. It is known that: 58°≤α≤59° and 102°≤β≤103°. Find the possible values of the third angle.
he was right, the answer is just flipped, so it's 18≤x≤20
Our galaxy the Milky Way has a diameter of about 1•^10
mathematicssssssssssss bruhhhhhh
how to factor polynomial 48a2b2-12ab
Boxes that are 12 inches tall are being stacked next to boxes that are 18 inches tall. What is the shortest height at which the two stacks will be the same height
The two stacks will be the same height when stacked to a height of 6 inches.
Explanation:To find the shortest height at which two stacks of boxes, one measuring 12 inches tall and the other measuring 18 inches tall, will be the same height, we need to find the least common multiple (LCM) of the two heights. Since 12 and 18 are both divisible by 6, the LCM is 6 inches. Therefore, the two stacks will be the same height when stacked to a height of 6 inches.
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The table shows the shipping costs for items of different values.
Which best describes the strength of the model?
a weak positive correlation
a strong positive correlation
a weak negative correlation
a strong negative correlation
Answer:
A strong positive correlation
Step-by-step explanation:
Since the dependent variable increases as the independent variable increases, this is a positive correlation.
Plotting these points, we can see that they form a nearly straight line. This makes it a strong correlation.
A strong positive correlation best describes the strength of the given model. So, option B is correct.
What is the correlation coefficient?The correlation coefficient is used to measure the strong relationship between the two variables.
The formula for the correlation coefficient
[tex]r= \frac{n(\sum xy)-(\sum x)(\sum y)} {\sqrt{ {[n\sum x^2-(x)^2] [n\sum y^2-(\sum y)^2]}}}[/tex]
We need to calculate the correlation coefficient and then make a conclusion about its value.
Form a table as shown where x is the cost of items and y is the shipping cost. The table becomes
x y XY x² y²
25 5.99 149.8 625 35.9
45 8.99 404.6 2025 80.8
50 8.99 449.5 2500 80.8
70 10.99 769.3 4900 120.8
190 34.96 1773.2 10050 318.3
The formula for the correlation coefficient
[tex]r= \frac{n(\sum xy)-(\sum x)(\sum y)} {\sqrt{ {[n\sum x^2-(x)^2] [n\sum y^2-(\sum y)^2]}}}[/tex]
where n=4
[tex]= \frac{ 4(1773.2)-(190)(34.96)} {\sqrt{{[4(10050)-190^2] [4(318.3)-34.96^2]}} }[/tex]
r[tex]=\frac{450}{4100\times51}[/tex]
r = 450 / √209100
r = 450/457.3
r = 0.98409
Thus, The value of r indicates a stronger positive correlation.
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Hailey paid $13 dollars for 1 3/7 kg of sliced salami.
Answer:
$9.1 per kg of sliced salami.
Step-by-step explanation:
We are supposed to find unit rate for the given scenario.
Hailey paid $13 dollars for 1 3/7 kg of sliced salami.
To find unit rate, we will divide total price by total weight.
[tex]\text{Unit rate}=\$13\div 1\frac{3}{7}\text{ kg}[/tex]
Convert mixed fraction to improper fraction:
[tex]\text{Unit rate}=\$13\div \frac{10}{7}\text{ kg}[/tex]
Convert to division problem by flipping the fraction as:
[tex]\text{Unit rate}=\$13\times\frac{7}{10}\text{ kg}[/tex]
[tex]\text{Unit rate}=\frac{\$13\times7}{10\text{ kg}}[/tex]
[tex]\text{Unit rate}=\frac{\$91}{10\text{ kg}}[/tex]
[tex]\text{Unit rate}=\frac{\$9.1}{\text{ kg}}[/tex]
Therefore, unit rate is $9.1 per kg of sliced salami.
One of your friends gives you $10 for a charity walkathon. Another friend gives you an amount per mile. After 5 miles, you have raised $13.50 total. Write an equation that represents the amount y of money you have raised after x miles.
The initial amount given is $10, this represents a constant
Now another friends is willing to give an amount which is not fixed, hence it is dependent on the amount if miles we walk
Let this variable amount be x
We have walks 5 miles in total
We have raid is 13.5 total amount
Therefore he expression to represent the total amount we have made is given as
10+5x= 13.50
Let us solve for x
subtract 10 from both sides we have
5x= 13.5-10
5x= 3.50
divide both sides by 5 we have
x = 3.5/5
x= 0.7
Hence our friend gives us $0.7 per mile
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The capacity of Jose vase is 2,419 milliliters of water he poured 1 liter 299 milliliters of water into the empty vase then he ,added 398 milliliters.how much more water will the vase hold ?
Point A is located at negative 5 over 8 and point B is located at negative 2 over 8 . What is the distance between points A and B? (1 point)
negative 5 over 8 minus negative 2 over 8 = negative 3 over 8 ; therefore, the distance from A to B is absolute value of negative 3 over 8 equals 3 over 8 units
negative 5 over 8 minus negative 2 over 8 = negative 3 over 8 ; therefore, the distance from A to B is absolute value of negative 3 over 8 equals negative 3 over 8 units
negative 5 over 8 plus negative 2 over 8 = negative 7 over 8 ; therefore, the distance from A to B is absolute value of negative 7 over 8 equals 7 over 8 units
negative 5 over 8 plus negative 2 over 8 = negative 7 over 8 ; therefore, the distance from A to B is absolute value of negative 7 over 8 equals negative 7 over 8 units
The Temperature in Indianapolis was -4°F at 7 AM the temperature rose 3°F by noon what was the temperature at noon use a number line to find the answer
Determine the correct scientific notation form of the number. 0.00000000165
Which graph models the equation -2x + 4y = -8?
If one-third of a number is greater than five less than twice the number, which of the following is true? x < 3, x > -3, x > -3/5, x < 3/5
Answer: The correct option is
(A) x < 3.
Step-by-step explanation: Given that one-third of a number is greater than five less than twice the number.
We are to select the inequality that is TRUE.
Let the required number be represented by x.
Then, according to the given information,we have
[tex]\dfrac{1}{3}x>2x-5\\\\\\\Rightarrow x>3(2x-5)\\\\\Rightarrow x>6x-15\\\\\Rightarrow x-6x>-15\\\\\Rightarrow -5x>-15\\\\\Rightarrow 5x<15~~~~~~~~~~[\textup{since }-a>-b~~~\Rightarrow a<b]\\\\\Rightarrow x<\dfrac{15}{5}\\\\\Rightarrow x<3.[/tex]
Thus, the true statement is x < 3.
Option (A) is CORRECT.
What is 4/5 of 10/13 in fractions.
Color count on facts
answer a and b...............
Do the fractions 6/7 and 16/25 convert to repeating or terminating decimal numbers
Answer:
reapeating and terminating
Step-by-step explanation:
Find a degree 3 polynomial having zeros -8, 1 and 8 and the coefficient of x^3 equal 1
Florida is 65,754.59 square miles what is the area of Florida rounded to the nearest tenth
The Area of Florida is 65,754.6
What is rounding a number to some specific place?Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.
Given that Florida is 65,754.59 square miles
rounding this nearest to tenth will be 65,754.6 square miles
Therefore, Area of Florida is 65,754.6 square miles
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Determine the correct scientific notation form of the number. 3,708,000,000\
A)
3.708 x 106
B)
3.708 x 109
C)
37.08 x 106
D)
37.08 x 108
The scientific notation of the given number is 3.708 × [tex]10^9[/tex]. Therefore, option B is the correct answer.
The given number is 3,708,000,000.
What is scientific notation?Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.
If the given number is multiples of 10 then the decimal point has to move to the left, and the power of 10 will be positive.
Now, 3,708,000,000 can be written in scientific notation as 3.708 × [tex]10^9[/tex].
The scientific notation of the given number is 3.708 × [tex]10^9[/tex]. Therefore, option B is the correct answer.
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About how much greater is 165760 than 14090
What is the equation of the linear function represented by the table?
Graph:
x y
–5 14
–2 11
1 8
4 5
Answer:
a y= -x+9
Step-by-step explanation:
write the equation for the transformation of the graph of y=f(x). use the form f(x)=a(x-h)+k. 13. translated 2 units left and 7 units down. 14. translated 5 units right, 2 units up, and stretched by a factor of 3.
The equations of the graph after respective transformations are;
13) f(x) = a(x + 2) - 7
14) f(x) = 3(x - 5) + 2
13) In transformations, when we translate a function to the left, it means we will add the number of units it is translated to the left to f(x).
Thus, if we translate 2 units to the left, then using the form f(x) = a(x - h) + k, we will have;
f(x) = a(x + 2) + k
This is because;
h = horizontal shift
k = the vertical shift
a = the factor of stretch.
Now, we are told that it is translated 7 units down.
Downward translation denotes subtraction. Thus, k = -7 and our final translated function is;
f(x) = a(x + 2) - 7
14) Using the same concept above;
Translation of 5 units to the left means h = -5
Also, translation of 2 units up means that k = +2
Stretching by a factor of 3 means that a = 3.
Thus, from the form; f(x) = a(x + h) + k, we have;
f(x) = 3(x - 5) + 2
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Ben is showing his work in simplifying (3.9 − 9.4) − 0.6 + 6.1. Identify any error in his work or reasoning.
Step 1: (3.9 − 9.4) − 0.6 + 6.1
Step 2: 3.9 + (−9.4 − 0.6) + 6.1 (associative property) Step 3: 3.9 − 10 + 6.1
Step 4: 3.9 + 6.1 − 10 (identity property)
Step 5: 10 − 10 = 0
A. He wrote identity instead of commutative in step 4.
B. He wrote associative instead of commutative in step 2.
C. He wrote identity instead of distributive in step 4.
D. He wrote associative instead of distributive in step 2.
Answer:
A.He wrote identity property instead of commutative in step 4.
Step-by-step explanation:
We are given that
Ben is showing his work in simplifying (3.9-9.4)-0.6+6.1
We have to identify error made by Ben in his work
Step 1. (3.9-9.4)-0.6+6.1
Step 2.3.9+(-9.4-0.6)+6.1
Reason: Using associative property of addition
[tex](a+b)+c=a+(b+c)[/tex]
Step 3.3.9-10+6.1
Step 4.3.9+6.1-10
Reason: Using commutative property of addition
[tex]a+b=b+a[/tex]
Step 5.10-10=0
Therefore, he makes an error in step 4.he wrote identity property instead of commutative property of addition.
Hence, option A is true.
Answer: A.He wrote identity property instead of commutative in step 4.
Which point represents the fraction 7/10???
J
K
L
or
M
TYSM <33333333 :DDDDDDDD
Samantha is painting the outside shape of a rectangular prism. It’s length is 18 centimeters, it’s width is 6 centimeters, and its height is 3 centimeters. What is the surface area of the box in square centimeters?
describe the transformation of the parent function f(x)=x^2 to 1/2 (x+1)^2-5