Remember that to model this kind of problems, we can use the equation of a straight line
[tex]y=mx+b[/tex]Where:
• b, are the fixed costs
,• x ,represents what varies
,• m, is the cost of what varies
1. Therefore, using the data provided, we can model the cost of production with a function where:
• x ,is the numbers of CD's produced
,• C, is the cost of producing those CD's
[tex]C=8x+30000[/tex]2. To model the revenue, we'll have to take into account that every CD sells at $68. Therefore, the money collected by selling the x CD's produced is:
[tex]R=63x[/tex]Where:
• x ,its the number of CD's produced and sold
,• R, is the total revenue
3. To get the profit, we'll have to substract the production cost to the money collected by the sale. Remember we already have two expressions, in terms of x, that describe both situations. Therefore,
[tex]\begin{gathered} P=R-C \\ \rightarrow P=63x-(8x+30000)\rightarrow P=63x-8x-30000 \\ \rightarrow P=55x-30000 \end{gathered}[/tex]Where:
• x ,its the number of CD's produced and sold
,• P, is the total revenue
4. In order to break even, the revenue (R) has to be equal to the cost of production (C), Thus,
[tex]\begin{gathered} R=C\rightarrow63x=8x+30000 \\ \rightarrow63x-8x=30000 \\ \rightarrow55x=30000\rightarrow x=\frac{30000}{55} \\ x=545.5 \\ \text{Rounding to closest integer,} \\ x=546 \end{gathered}[/tex]Therefore, 546 CD's would have to be produced to break even.
Find the average rate of change of his annual salary between 2017 and 2020
We were told that the salary, t years after 2015 is given by the function,
S(t) = 3100t + 56000
When considering 2017, the number of years, t from 2015 is 2017 - 2015 = 2
We would substitute t = 2 into the function and find S(2)
Thus,
S(2) = 3100 x 2 + 56000 = 6200 + 56000 = 62200
When considering 2020, the number of years, t from 2015 is 2020 - 2015 = 5
We would substitute t = 2 into the function and find S(2)
Thus,
S(5) = 3100 x 5 + 56000 = 15500 + 56000 = 71500
Thus, we can say that
when
x1 = 2, y1 = 62200
when x2 = 5, y2 = 71500
Recall,
slope or average rate of change = (y2 - y1)/(x2 - x1)
average rate of change = (71500 - 62200)/(5 - 2) = 9300/3
average rate of change = 3100
The last option is correct
3 What is the range of the function shown
in the graph?
Answer:
D y < 8
Step-by-step explanation:
the range is the interval or set of all valid y (functional result) values.
we can see the y values start at +8, and as the curve is only going down, clearly endlessly, every value smaller than 8 is valid.
8 itself is the be excluded, as there is a hollow point (a filled point would indicate "include").
and therefore we cannot say y <= 8.
we have to use y < 8.
Evaluate the inverse when y=4. Show all of your work.
The inverse of the function y = 4ˣ is f⁻¹(x) = ㏑x / ㏑4.
What is termed as the inverse of the function?An inverse function, also known as an anti function, is a function that can be reversed into another function. Simply put, if any function "f" takes x to y, then its inverse will take y to x. The inverse function is signified by f-1 or F-1 if the function is signified by 'f' or 'F'. Here, (-1) should not be confused with exponent or reciprocal.For the given question;
The function is given as;
y=4ˣ
Interchange the variables of the function.
x = 4∧y
Taking log both side.
㏑ x = ㏑(4∧y)
Using the power rule of log function.
㏑ x = y㏑(4)
y = ㏑ x/㏑(4)
Now, replace y with f⁻¹(x).
f⁻¹(x) = ㏑ x/㏑(4)
Thus, the inverse of the function y = 4ˣ is found to be f⁻¹(x) = ㏑x / ㏑4.
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The correct question is-
Evaluate the inverse when y=4ˣ. Show all of your work.
What is the measure of C?
Please show your work if you want to be brainiest!
The measure of ∠C in the given triangle is 58°.
According to the question,
We have the following information:
ACD is a triangle where we have BD as an altitude on the side AC.
Now, we know that the altitude on any side makes an angle of 90° or in other words, it can be said that it makes a right angle.
Now, we have two right-angled triangle: ABD and CBD.
We have ∠ADB = 32°.
Now, ∠CDB will also be equal to 32° because the altitude bisects the angle (in two equal parts).
We know that the sum of the three angles in a triangle is 180°.
In ΔCBD, we have:
∠B + ∠C + ∠CDB = 180°
90° + ∠C + 32° = 180°
∠C + 122° = 180°
∠C = (180-122)°
(Moving 122 from the left hand side to right hand side will result in the change of sign.)
∠C = 58°
Hence, the measurement of ∠C in the given triangle is 58°.
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The length of a piece of paper is 11 inches. What is the length of the paper in
centimeters?
(1 inch = 2.5 centimeters).
Answer:
Length in inches → 11
1 inch = 2.5 centimeters
Length in Centimetres → 11 × 2.5 → 27.5 cm
A line passes through the points (–3, –4) and (6, 2).
A coordinate plane.
What is the x-intercept of this line?
Answer:
x intercept is -3
Step-by-step explanation:
We need to find the equation for the line First we find the slope m = (y2-y1)/(x2-x1) = (2- -4)/(6- -3) = (2+4)/(6+3) =6/9 = 2/3 The we can write the equation y= mx+b y = 2/3x +b We can substitute in (6,2) 2 = 2/3(6) +b 2 =4+b Subtract 4 from each side 2-4 =b b =-2 y = 2/3 x-2 We want to find the x intercept, so set y =0 and solve for x 0 = 2/3x -2 Add 2 to each side 0-2 = 2/3x Multiply each side by 3/2 to isolate x -2 *3/2 = 2/3x * 3/2 -3 =x The x intercept is -3
You start at (2, -5). You move up 5 units and right 3 units. Where do you end?
the answer would be (0,5)
Find the measure of
Answer: 93°
Step-by-step explanation:
[tex]\angle A \ and\ \angle B\ are\ vertical\ angles.\ Hence,\ \angle A \ = \ \angle B\\\\2x+19=3x-18\\\\2x+19+18=3x-18+18\\\\2x+37=3x\\\\2x+37-2x=3x-2x\\\\37=x\\\\Thus,\ x=37\\\\m\angle A=(2(37)+19)^0\\\\m\angle A=(74+19)^0\\\\m\angle A=93^0\\\\[/tex]
Model Real Life A healthcare worker
has 3 shifts each week. The route from
her house to the hospital is 9.9 miles
and the route back to her house is
10.5 miles. About how far does she
travel for work each week?
She travels 61.2 miles for work each week.
What is addition?Addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.
We have been given that the healthcare worker has 3 shifts each week. The route from her house to the hospital is 9.9 miles and the route back to her house is 10.5 miles.
The distance from her house to the hospital = 9.9 miles
The distance back to her house = 10.5 miles.
The total distance travel in one shift = 9.9 + 10.5 = 20.4 miles
The total distance travel in 3 shift = 3 x 20.4 = 61.2 miles
Hence, She travels 61.2 miles for work each week.
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The janitor at a school discovered a leak in a pipe. The janitor found that it was leaking at a rate of 14 fl oz per hour. How fast was the pipe leaking in gallons per day?
Answer:
6.5625 gal per hour
Step-by-step explanation:
Since there are 60 minutes per hour, we need to multiply 14 by 60 to change per minute into per hour. Combining these: 14 fl oz / min x (1 gal / 128 fl oz) x (60 min / hr) = 6.5625 gal per hour. Written as a mixed fraction: 6 9/16 gal per hour.
Which equation does not represent a linear function?
a. y = 8x
by = ½x+2
c. y=0.5x - 1
d. y = 2x³
Answer:
d. y= 2x³
Step-by-step explanation:
All of the other equations represent linear functions, and are in the form y = mx + b. D on the other hand contains an exponent, making it a non-linear (in this case cubic) function.
a total of tickets were sold for the school play. they were either adult tickets or student tickets. there were 53 more student tickets sold than adult tickets. how many adult tickets were sold?
Total 250 adult tickets are sold.
Let a = number of adult tickets sold
Let s = number of student tickets sold
a + s = 553
s = a + 53
From above equations;
a + a + 53 = 553
2a = 553 - 53
2a = 500
a = 250
Total 250 adult tickets are sold.
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Elizabeth Oliver sells luxury cars. She earns a 4 percent straight commission. Lastmonth her sales totaled $128,000. What was her commission?
$128,000 represents 100%
To find how much is 4% we can use the next proportion:
[tex]\frac{128,000\text{ \$}}{x\text{ \$}}=\frac{100\text{ \%}}{4\text{ \%}}[/tex]Solving for x:
[tex]\begin{gathered} 128,000\cdot4=100\cdot x \\ \frac{512,000}{100}=x \\ 5,120=x \end{gathered}[/tex]Her commission is $5,120
1/2 x - 2 = x - 4
answersss??
A recent math test had an average score of 75, with a standard deviation of 10. What percentage of people scored an 85 or higher?16%34%50%, 13.5%
Answer:
16%.
Explanation:
In a recent math test:
• The average score = 75
,• Standard Deviation = 10
To find: The percentage of people who scored an 85 or higher, P(X>85).
First, find the z-score when X=85.
[tex]z-score=\frac{X-\mu}{\sigma}[/tex]Substitute the given values:
[tex]z=\frac{85-75}{10}=\frac{10}{10}=1[/tex]The people who scored an 85 or higher are 1 standard deviation away from the mean.
[tex]13.5\%+2.35\%+0.15\%=16\%[/tex]The percentage of people who scored an 85 or higher is 16%.
In Central city, there are 29,791 registered voters and 93 voting centers. Each voting centers serves about _____ of the city's population, what's the answer?
If in Central city, there are 29791 registered voters and 93 voting centers, then each voting centers serves about 320 of the city population.
Total number of registered voters in Central city = 29791 voters
Total number of voting centers = 93 voting centers
The number of population serves by each center = Total number of registered voters in Central city ÷ Total number of voting centers
Substitute the values in the equation
The number of population serves by each center = 29791/93
= 320.33
≈ 320
Hence, If in Central city, there are 29791 registered voters and 93 voting centers, then each voting centers serves about 320 of the city population.
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A virtual environment created by game engine renders non-character objects
more efficiently than it renders characters. If the assumption is that 72
percent of objects must be devoted to non-character objects and this reset
cache is set at 67 non-character objects, how many objects can be
characters before the cache resets?
Answer:18
Step-by-step explanation:
Elisa gets a tax free allowance of $6000 and pays tax at 25% on the next $20 000. She pays tax at a rate of 30% on the rest. If she earns $72000 per year, how much tax must she pay?
Find the velocity of the car at the end of a drag race. Round to the nearest whole number.
Answer:
183 miles per hour.
Explanation:
The estimated velocity(v) at the end of a drag race is modeled using the formula below:
[tex]v=234\sqrt[3]{\frac{p}{w}}[/tex]Given:
• The horsepower, p = 1311
,• The weight (in pounds), w = 2744 pounds.
Substitute into the formula above:
[tex]\begin{gathered} v=234\sqrt[3]{\frac{1311}{2744}}=182.9 \\ v\approx183\text{ miles per hour} \end{gathered}[/tex]The velocity is approximately 183 miles per hour.
If there are 16 successful outcomes in a sample with a size of 50, what is the
sample proportion?
OA. 0.55
OB. 0.16
OC. 0.34
OD. 0.32
The sample proportion is option(d) i.e, 0.32
What is Proportion?
A proportion is an equation in which two ratios are set equal to each other.
Given,
Number of successful outcomes = 16
Total number of outcomes = 50
The sample proportion =
Number of successful outcomes / Total number of outcomes
Sample proportion = 16 / 50
= 0.32
Hence, the sample proportion is option(d) i.e, 0.32
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Write an expression for the calculation triple 4 and then add 6 times 6
Answer:
4x3+6x6=48
Step-by-step explanation:
PEMDAS
4x3=12
6x6=36
12+36=48
therefore, the answer is 48
A garden store sells two types of potted palm trees. The Mediterranean palms sell for $150 each, and the palmetto palms sell for $125 each, including tax. The store wants to sell a total of at least 15 of the plants each day and have total sales of at least $2,000. Which of these systems of inequalities can be used to determine x, the number of Mediterranean palms, and y, the number of palmetto palms, that must be sold?
The system of inequalities that can be used to determine the number of each type of plant to be sold are :
x + y ≥ 15
$150x + $125y ≥ $2000
What are the system of inequalities?The first step is to determine the inequality signs that would be used in the system of inequalities:
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
The inequality sign that would be used is the greater than or equal to sign, ≥.
Two system of inequalities would be formed using the information provided in the question. The form of the system of inequalities would be:
number of Mediterranean palms sold + number of palmetto sold ≥ least number of plants
(number of Mediterranean palms sold x cost of Mediterranean palms) + (number of palmetto sold x cost of palmetto sold ≥ least number of sales
x + y ≥ 15
$150x + $125y ≥ $2000
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3.2+2(-1.5)-3.4
(pls solve by doing the order of operations)
(step by step pls)
AS per the order of operations, the value of the expression 3.2+2(-1.5)-3.4 is -3.2
Order of operations:
Order of operations states the rule that tells the correct sequence of steps for evaluating a math expression.
The order using PEMDAS:
Parentheses,
Exponents,
Multiplication and Division (from left to right),
Addition and Subtraction (from left to right).
Given,
Here we have the expression. 3.2+2(-1.5)-3.4
Now, we have to use the order of operations concept in order to solve it.
The highest priority for the order of operation is brackets and the next priority is for division and multiplication,
So, here we have to solve those things first, then we get,
=> 3.2 + (-3) - 3.4
We know that (+) x (-) = -, so, the expression is rewritten as,
=> 3.2 - 3 - 3.4
The next priority is for addition and subtraction,
So, the result is,
=> 3.2 - 6.4
=> -3.2
Therefore, the resulting number is -3.2
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Solve for x: -3x-6= -7x+34
Answer:
x = 10
Step-by-step explanation:
-3x - 6 = -7x + 34
+7x
4x - 6 = 34
+6
4x = 40
/4
x = 10
Answer:
x = 10
Step-by-step explanation:
-3x - 6 = -7x + 34 Add 7x to both sides
4x - 6 = 34 Add 6 to both sides
4x = 40 Divide both sides by 4
x = 10
please help to find the value of x and explain how to get it in simple terms.
SOLUTION
From the image above
[tex]\begin{gathered} z^2=6^2+3^2\ldots\text{ by pythagora's rule } \\ z^2=36+9 \\ z^2=45 \\ z=\sqrt[]{45} \end{gathered}[/tex]Considering the bigger right angle triangle,
[tex](3+x)^2=y^2+45[/tex]We can obtain the expression of y from the smaller right angle triangle,
Using pythagora's rule, we have
[tex]y^2=6^2+x^2[/tex]Then, recall
[tex](3+x)^2=y^2+45[/tex]Substite the expression for y², we have
[tex](3+x)^2=6^2+x^2+45[/tex]Expand the paranthesis, we have
[tex]\begin{gathered} 9+6x+x^2=x^2+36+45 \\ \text{Subtract x}^2from\text{ both sides } \\ 9+6x=36+45 \\ \end{gathered}[/tex]subtract 9 from both sides, we have
[tex]\begin{gathered} 6x+9-9=81-9 \\ 6x=72 \end{gathered}[/tex]Divide both sides by 6, we obtain
[tex]\begin{gathered} \frac{6x}{6}=\frac{72}{6} \\ \text{Then} \\ x=12 \end{gathered}[/tex]Therefore
Answer: x= 12
( f - 12) + Pf decreased by the sum of 12 and p is it correct?
The sum of 12 and P can be written as 12 + P
Then, f decreased by the sum of 12 and P can be written as:
f - (12 + P)
Answer: it isn't correct, the correct answer is f - (12 + P)
Find the mean of the data in the dot plot below.
Answer:
There is no dot plot below
Step-by-step explanation:
please help please please please please please please please please please please please please please please please please please please please please please please please please please please please please please please please please please please please
part 1 of the question is asking us to evaluate expressions to the power of 2. To do that let's remember the following:
[tex]a^2=a\times a[/tex]Ther is, when a number is elevated to second power it means we have to multiply that number by itself. For example:
[tex]\begin{gathered} 1^2=1\times1=1 \\ 2^2=2\times2=4 \\ 3^2=3\times3=9 \end{gathered}[/tex]In the second part of this question, we are asked to evaluate the square root of a number. Let's remember that the square root is the inverse operation of elevating a number to the second power. That is if we have:
[tex]\sqrt[]{a}=b[/tex]it means:
[tex]b^2=b\times b=a[/tex]For example:
[tex]\begin{gathered} \sqrt[]{1}=1 \\ \sqrt[]{4}=2 \\ \sqrt[]{9}=3 \end{gathered}[/tex]The third part of the questions asks us to solve for "x" the following equation:
[tex]x^2=9[/tex]To do that we take square root on both sides:
[tex]\sqrt[]{x^2}=\sqrt[]{9}[/tex]Since the square root of a number to the second power is the same number and the square root of 9 is 3, we get:
[tex]x=3[/tex]Match each equation to one of the lines
5x + 3y = 20
The graph of the linear function 5x + 3y = 20 is given at the end of the answer.
How to graph a linear function?To build the graph of a linear function, we identify two points on the line, and then plot a line passing through them.
In this problem, the function is:
5x + 3y = 20.
The points that we are going to choose are the intercepts. The x-intercept is the value of x when y = 0, hence:
5x = 20
x = 20/5
x = 4.
Meaning that point (4,0) is on the graph of the function.
The y-intercept is the value of y when x = 0, hence:
3y = 20
y = 20/3
y = 6.67.
Meaning that point (0, 6.67) is on the graph of the function.
The graph is plotted with a line passing through the points (4,0) and (0, 6.67).
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Amira is younger than Marques. Their ages are consecutive integers. Find Amira's age if the sum of Amira's age and 2 times Marques's age is 38.
Amira's age is 12 years when Amira is younger than Marques and their ages are consecutive integers and the sum of Amira's age and 2 times Marques's age is 38.
According to the question,
We have the following information:
Amira is younger than Marques.
Their ages are consecutive integers.
The sum of Amira's age and 2 times Marques's age is 38.
Now, let's take Amira's age to be x years.
Then, Marques's age will be (x+1) years.
So, we have:
x + 2(x+1) = 38
x + 2x + 2 = 38
3x+2 = 38
3x = 38-2 (Moving 2 from the left hand side to the right hand side will result in the change of the sign from plus to minus.)
3x = 36
x = 36/3
x = 12 years
Hence, Amira's age is 12 years.
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