Answer:
(r - c)(5) is the amount of profit generated by the George's store 5 months after it has been open.The total amount of profit 5 months after the store has been open is $5,400.Step-by-step explanation:
Given functions:
[tex]r(x)=x^2+5x+14[/tex]
[tex]c(x)=x^2-4x+5[/tex]
where:
r(x) is the store's revenue each month (in hundreds of dollars).c(x) is the store's expenses each month (in hundreds of dollars).x is the number of months since the store has been open.Profit is calculated by subtracting expenses from revenue.
Therefore, the composite function for profit is:
r(x) - c(x) = (r - c)(x)Since x represents the number of months the store has been open:
(r - c)(5) is the amount of profit generated by the George's store 5 months after it has been open.
To calculate the total amount of profit in the first 5 months, substitute x = 5 into the composite function:
[tex]\begin{aligned}\implies (r-c)(5)&=r(5)-c(5)\\&=(5^2+5(5)+14)-(5^2-4(5)+5)\\&=(25+25+14)-(25-20+5)\\&=(50+14)-(5+5)\\&=64-10\\&=54\end{aligned}[/tex]
Since the revenue and expenses functions are measured in hundred of dollars, so too is the profit function. Therefore, the amount of profit generated in 5 months is $5,400.
A headphone set that normally sells for $84 is marked down by 27%. What is the sale price?
Answer:
The answer is $61.32
QUESTION 1
Consider the following argument: Either there is a massive, multi-million dollar conspiracy at work, or else the electorate
have decided that Senator Wiggins is the best candidate for the position. The electorate have decided that Senator
Wiggins is the best candidate for the position. So, there is not a massive, multi-million dollar conspiracy at work. What is
the logical form of this argument?
O a. Modus Tollens
b. Disjunctive Syllogism
O c. Affirming the consequent
O d. Affirming a disjunct
Oe. Modus Ponens
Since the electorate have decided that Senator Wiggins is the best candidate for the position. The logical form of this argument is option b. Disjunctive Syllogism
What is Disjunctive Syllogism?The argument is presented in the form of a disjunctive syllogism, which involves a logical form that states that either one of two alternatives must be true, and one of them has been found to be true; therefore, the other must be false.
In this case, the two alternatives are:
There is a massive, multi-million dollar conspiracy at work.The electorate have decided that Senator Wiggins is the best candidate for the position.The argument concludes that the second alternative is true, which means that the first alternative must be false. Therefore, the argument logically deduces that there is not a massive, multi-million dollar conspiracy at work.Thus, the logical form of the argument is:
Either A or B.
Not A.
Therefore, B.
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The principal P is borrowed at a simple interest rate r for a period of time t. Find the loan's future value A, or the total amount due at time t.
P=$1000, r=5.0%, t=6 months
Step-by-step explanation:
To calculate the future value of a loan with simple interest, we can use the formula:
A = P(1 + rt)
where A is the future value or total amount due, P is the principal, r is the interest rate, and t is the time period in years.
In this case, we have:
P = $1000
r = 5.0% = 0.05 (expressed as a decimal)
t = 6 months = 0.5 years (since there are 12 months in a year)
Plugging these values into the formula, we get:
A = $1000(1 + 0.05 x 0.5)
A = $1000(1.025)
A = $1025
Therefore, the future value or total amount due on the loan after 6 months is $1025.
Which graph represents a function with direct variation? A coordinate plane with a line passing through (negative 4, 0) and (0, negative 2). A coordinate plane with a line passing through (negative 5, 4) and (0, 3). A coordinate plane with a line passing through (negative 4, negative 6) and (0, 3). A coordinate plane with a line passing through (negative 1, negative 4), (0, 0) and (1, 4). Mark this and return
We can state this by responding to the provided question A direct function variation function is represented by the graph of this equation, which is a straight line going through the points (0, -2) and (-4, 0).
what is function?Mathematicians research numbers, their variants, equations, associated structures, forms, and possible configurations of these. The word "function" describes the connection between a group of inputs, each of which has a corresponding output. A function is a connection between inputs and outputs where each input results in a single, distinct outcome. Each function has a domain, codomain, or scope assigned to it. Functions are usually denoted by the letter f. (x). An x is entered. On functions, one-to-one capabilities, so multiple capabilities, in capabilities, and on functions are the four main categories of accessible functions.
The coordinate plane with a line crossing between (0, -2) and (-2) is the graph that illustrates a function with direct variation (-4, 0).
If m is the line's slope and (x1, y1) is a point on the line, [tex]y - y1 = m(x - x1).[/tex]
The line's slope is as follows:
[tex]m = (y2 - y1)/(x2 - x1) = (-2 - 0)/(0 - (-4)) = 1/2[/tex]
The equation of the line going through (0, -2) and (-4, 0), expressed in point-slope form, is:
[tex]y - (-2) = 1/2(x - 0) (x - 0)[/tex]
When we simplify the equation, we obtain:
[tex]y = 1/2x - 2[/tex]
A direct variation function is represented by the graph of this equation, which is a straight line going through the points (0, -2) and (-4, 0).
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(4a^-2)^-1/2 simplify
Answer: To simplify the expression, we can apply the exponent rule for powers of powers which states that to raise a power to another power, we multiply the exponents.
So,
(4a^(-2))^(-1/2) = 4a^(-2 * (-1/2)) = 4a^(1) = 4a
Therefore, (4a^-2)^-1/2 simplifies to 4a.
Step-by-step explanation:
Parallelogram ABCD has vertices A(0,0), B(2,4), C(x, y) and D(5,0).
What are the coordinates of point C?
Tge coordinates of point c is - 3 and 1
Answer: The fourth vertex is D(8, 0)
A spectrophotometer used for measuring CO concentration [ppm (parts per million) by volume] is checked for accuracy by taking readings on a manufactured gas (called span gas) in which the CO concentration is very precisely controlled at 70 ppm. If the readings suggest that the spectrophotometer is not working properly, it will have to be recalibrated. Assume that if it is properly calibrated, measured concentration for span gas samples is normally distributed. On the basis of the six readings - 85, 77, 82, 68, 72 and 69 - is recalibration necessary? Carry out a test of the relevant hypotheses and report the P-value.
The p value is calculated as 0.116
How to solve for the p valueNull u = 70
alternate u ≠ 70
The alternate is a two tailed test
the test statistic calculation
t = x - u / s/√n
x = 85 + 77 + 82 + 68 + 72 + 69 / 6
= 75.5
standard deviation s = [tex]\sqrt{\frac{(85- 75.5)^2+(77- 75.5)^2+...(69- 75.5)^2}{6-1} }[/tex]
= 7.01
Test stat = (75.5 - 70) / 7.01/√6
= 1.92
degree of freedom = 6 - 1 = 5
this is 2 tailed
p value using excel = tdist( 1.8, 5 , 2)
= 0.116
We fail to reject the null hypothesis because it is greater than the level of significance
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7.
The list below shows Wendy's bowling scores in her last five games.
112, 123, 136, 145, 159
Which measure of data best describes how much these bowling scores varied?
A Mean
B Median
C Mode
D Range
Answer:
Step-by-step explanation:
the range would be the answer as it shows the top and the bottom score.
3. What is the solution of the equation −4(n+5)=−32 - 4 ( n + 5 ) = - 32 ? −13 - 13 −12 - 12 3 3 13
The solution of the given equation -4(n+5)=-32 is n=3.
What is equations ?
An equation is a mathematical statement that shows that two expressions are equal. It contains an equals sign (=) between two expressions. The expressions on both sides of the equals sign have the same value. Equations are used to solve problems in mathematics and science.
To solve the equation, we need to isolate the variable n.
-4(n+5) = -32
Distribute -4 on the left side of the equation:
-4n - 20 = -32
Add 20 to both sides of the equation:
-4n = -12
Divide both sides by -4:
n = 3
Therefore, the solution of the given equation -4(n+5)=-32 is n=3.
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he diameter of a circle is 18 feet. What is the circle's area?
Answer:
Step-by-step explanation:
[tex]A=\pi r^2\\[/tex]
[tex]=\pi \times 9^2[/tex] (radius = 9 feet)
[tex]=81\pi[/tex]
[tex]\approx 254.47[/tex] feet
Given the following table with selected values of f (x) and g(x), evaluate f (g(2)).
x –5 –4 –1 2 4 7
f (x) 0 2 7 –1 –6 –4
g(x) –8 –1 2 4 7 1
–4
2
4
–6
The value of f(g(2)) from the given table is -6.
What are functions?a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences. Expressions of well-known functions can be found in many frequently used mathematical formulas. For instance, the calculation for a circle's area
Given that,
x –5 –4 –1 2 4 7
f (x) 0 2 7 –1 –6 –4
g(x) –8 –1 2 4 7 1
The value of g(2) = 4
The value of f(g(2)) = f(4) = -6
Hence, the value of f(g(2)) from the given table is -6.
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A radioactive element has a half-life of 34 years. How long will it take for 21% of a sample to remain after decay begins? Round your answer to the nearest year.
The number of years for 21% to remain is 78years
What is half life?The time required for half of the original population of radioactive atoms to decay is called the half-life.
half life = 0.693/decay constant
decay constant = 0.693/34
= 0.02
21% of N(o) = 21N(o)/100 = N(y)
from the formula
N(t) = Noe^-kt
21N(o)/100 = Noe^-kt
21N(o)=100 Noe^-kt
divide bother sides by N(o)
21 = 100e^-kt
e^-kt = 21/100
e^-kt = 0.21
-0.02 t= ln0.21
-0.02 t= -1.56t
t = 1.56/0.02
t = 78years
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Help me do this thing for a math project
Answer:10
Step-by-step explanation:3x2=6 and 4x1=4 4+6=10
Answer:
See below
Step-by-step explanation:
Perimeter = (7x2) + (2x2) = 18
Area (L x W) = Square + rectangle
= (3x2) + (4x1) = 6 + 4 = 10
graph system of equations to determine solution
y=1/2x+3
2y=x+6
The system of linear equation has infinitely number of solutions
What is the graph of system of linear equationThe collection of all ordered pairs that concurrently fulfill both equations makes up the graph of a system of linear equations. It is the collection of all points that are the solutions to both equations, in other words.
The system of linear equations in this issue is stated as
y = 1/2x + 3...eq(i)
2y = x + 6...eq (ii)
The graph demonstrates that the system has an infinite number of solutions and that both lines cross one another. This demonstrates that the system is intractable.
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PLEASE HELP WILL GIVE BRAINLISET POINTS !!
Answer:
Step-by-step explanation:
37
Fill in the sentence below with the description that most specifically applies to the quadrilateral below.
The answer to the given problem can be stated as, "The quadrilateral is most specifically a square because all of its sides are equal and angles are right angle."
What is a square?A square is type of rectangle of which all sides are equal.
The diagonals of a square are perpendicular bisector of each other.
The given diagram of the quadrilateral clearly shows the following information,
All the angles of the quadrilateral are equal to right angle,
And, all of its sides are equal.
The given information matches with the property of a square which implies that the given quadrilateral is a square.
Hence, the given quadrilateral is a square.
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Answer:
Rhombus.All sides are congruent.Step-by-step explanation:
We need to identify the quadrilaterals given in the question.
For first image , we can see that;
All sides are equal .Opposite angles are equal.These are the properties of rhombus in which all sides and opposite angles are equal.
Hence in the first image quadrilateral is a " Rhombus" .
[tex]\rule{200}2[/tex]
In the second image , the most appropriate option is all sides are equal , as in rhombus all sides are congruent.
2x+6 in distributive property then into a expression
Answer:
2(x+3)
Step by Step:
2(x)=2x
2(3)=6
2x+6=2(x+3)
2(x)+2(3) =2 (x+3)
can someone help me with this problem please
here is the picture is just one
What is Function?
Function is the relationship between inputs where each input is related to exactly one output. It is a special relationship among the inputs (i.e. the domain) and their outputs (known as the codomain) where each input has exactly one output, and the output can be traced back to its input.
"y is a function of x" (denoted y = f(x)) means that y varies according to whatever value x takes on.
How to determine
Where F(x) = 2x^4 + x^2 - 10x + 1
So, to calculate f(-10)
f(x) = y
Where x = -10
f(-10) = 2(-10)^4 + (-10)^2 -10(-10) + 1
f(-10) = 2(10000) + 100 + 100 + 1
f(-10) = 20000 + 100 + 100 + 1
f(-10) = 20201
For f(2),
f(x) = y
Where x = 2
f(2) = 2(2)^4 +2^2 -10(2) + 1
f(2) = 2(16) + 4 -20 + 1
f(2) = 32 + 4 -20 + 1
f(2) = 17
For f(3)
f(x) = y
Where x = 3
f(3) = 2(3)^4 + 3^2 -10(3) + 1
f(3) = 2(81) + 9 -30 + 1
f(3) = 162 + 9 - 30 + 1
f(3) = 142
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Compare the function g(x) = 3/x-2 +5 to the parent function f(x)= 1/x please describe how the function has been transformed from the parent function.
The function g(x) = 3/(x-2) + 5 is a transformation of the parent function f(x) = 1/x with a horizontal shift of 2 units to the right, a vertical stretch by a factor of 3, and a vertical shift of 5 units up.
What is the transformation of the functionThe function g(x) = 3/(x-2) + 5 is a transformation of the parent function f(x) = 1/x.
Here are the transformations that were applied to f(x) to obtain g(x):
1. Horizontal shift: The denominator of f(x) is x, which means that the vertical asymptote is at x = 0. By subtracting 2 from x in the denominator of g(x), we are shifting the vertical asymptote to x = 2. This is a horizontal shift of 2 units to the right.
2. Vertical stretch: The coefficient 3 in front of the fraction means that the function is stretched vertically by a factor of 3 compared to f(x). This means that the distance between the horizontal asymptotes (which are at y = 0 for f(x) and y = 5 for g(x)) is three times larger for g(x) than for f(x).
3. Vertical shift: The constant 5 added to the fraction means that the entire function is shifted vertically by 5 units compared to f(x). This means that the horizontal asymptote of g(x) is at y = 5 instead of y = 0.
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The mean of the following data values is 36.
19, 23, 35, 41, 42
Answer:
To find the mean of a set of data, we need to sum up all the values in the set and divide by the number of values.
Sum of the data values = 19 + 23 + 35 + 41 + 42 = 160
Number of data values = 5
Mean = Sum of data values / Number of data values = 160 / 5 = 32
However, we are given that the mean is 36. Since the calculated mean is lower than the given mean, it means that we are missing a value that is higher than the other values in the set.
Let's call this missing value x. Then, we have:
(19 + 23 + 35 + 41 + 42 + x) / 6 = 36
Multiplying both sides by 6, we get:
19 + 23 + 35 + 41 + 42 + x = 216
Simplifying the left-hand side, we get:
160 + x = 216
Subtracting 160 from both sides, we get:
x = 56
Therefore, the missing value is 56, and the complete data set is:
19, 23, 35, 41, 42, 56
Now, we can calculate the mean as:
Mean = (19 + 23 + 35 + 41 + 42 + 56) / 6 = 216 / 6 = 36
So, the mean of the data values is indeed 36.
Answer:
32
Step-by-step explanation:
To find the mean of a set of numbers, we add up all the numbers and then divide by the total number of values.
Adding up the values:
19 + 23 + 35 + 41 + 42 = 160
We have a total of 5 values, so we divide the sum by 5:
160 / 5 = 32
Therefore, the mean of the given data values is 32, not 36.
whats the square root of 9
Answer: 3
Step-by-step explanation:
What number a is 24% of 25?
Answer: 24 percent of 25 is 6.
Step-by-step explanation: The output of 24 percent of 25 is 6. To obtain this answer, we multiply 0.24 by 25.
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options.
x2 + (y – 3)2 = 36
x2 + (y – 5)2 = 6
(x – 4)² + y² = 36
(x + 6)² + y² = 144
x2 + (y + 8)2 = 36
Since the center of the circle lies on the y-axis, the x-coordinate of the center must be 0.
Also, since the diameter of the circle is 12 units, the radius is half of that, or 6 units.
Using the standard form of the equation of a circle, which is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius, we can substitute the values we know and simplify the equations to see which ones match.
The equations that represent circles with a diameter of 12 units and a center that lies on the y-axis are:
x^2 + (y - 6)^2 = 36 (center is at (0, 6))
x^2 + (y + 6)^2 = 36 (center is at (0, -6))
Therefore, the two options that represent the circles with the given properties are:
x^2 + (y - 6)^2 = 36 and x^2 + (y + 6)^2 = 36.
Find the value of x.
Answer:
Step-by-step explanation:
Angle sum of a triangle = 180°. So we get:
[tex]62+69+(4x+5)=180[/tex]
[tex]136+4x=180[/tex]
[tex]4x=44[/tex]
[tex]x=11[/tex]°
Answer:
x = 11
Step-by-step explanation:
We know that the sum of the interior angles in a triangle is added up to 180°.
Accordingly,
62 + 69 + 4x + 5 = 180
Combine like terms.
136 + 4x = 180
Subtract 136 from both sides.
4x = 180 - 136
4x = 44
Divide both sides by 4.
x = 11
find ratio of speed of car 15 km/hr and speed of cycle 30km/hr
Write the equation of the line that is perpendicular to y = -1/6x-2 and passes through the point (-2,-1)
Therefore , the solution of the given problem of equation comes out to be y = 6x + 11.
How do equations work?Mathematical formulas frequently use the same letter to try to impose uniformity between two claims. Many variable academic numbers are shown to be equal using mathematical equations, also known as assertions. The normalise divides 12 and b + 6 into two parts using the result y + 6 = 12 as an illustration. It is possible to determine the connection between each sign component and the number of lines. The significance of a symbol usually contradicts itself.
Here,
In slope-intercept form, the provided equation y = -1/6x - 2 has a slope of -1/6. Consequently, this line's perpendicular inclination is as follows:
=> m2 = -(1/-1/6) = 6
Now that we know the desired line's slope and the spot through which it passes (-2, -1). To determine the solution of a linear equation, we can use its point-slope form:
=> y - y1 = m(x - x1) (x - x1)
where m is the slope 6 and (x1, y1) is the position (-2, -1). By replacing these numbers, we obtain:
=> y + 1 = 6(x + 2) y + 1
=> 6x + 12 y + 1
=> 6x + 11 y - (-1)
=> 6(x - (-2))
As a result, the equation for the line passing through the position (-2, -1) and perpendicular to y = -1/6x - 2 is y = 6x + 11.
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Calculate the cash discount and the net amount due the transaction (in $).
The cash discount is $353.20 and the net amount due is $17,306.80.
What are the purchase terms?Conditions of sale are the rules that govern a business transaction, including the cost, the method of payment, the delivery, and any other pertinent information. Normally, they are specified in a sales contract or invoice and acknowledged in advance of the transaction. The conditions of sale might alter based on the type of products or services being exchanged, the volume and complexity of the deal, and other elements.
We know that,
Cash discount = amount x discount rate
Net amount due = amount - cash discount
For 2/10:
Cash discount = $17,660 x 2% = $353.20
Net amount due = $17,660 - $353.20 = $17,306.80
Hence, the cash discount is $353.20 and the net amount due is $17,306.80.
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Which expression is the simplest form of 223-22 + 3 (23 - 422)?
O A. 23 - 13x2
O B. 523 - 1322
О c. 323 - 1222
O D. 523 - 522
The simplification value of the expression is,
⇒ 5x³ - 12x²
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 2x³ - x² + 3 (x³ - 4x²)
Now, We can simplify the expression as;
⇒ 2x³ - x² + 3 (x³ - 4x²)
⇒ 2x³ - x² + 3x³ - 12x²
⇒ 5x³ - 12x²
Thus, The simplification value of the expression is,
⇒ 5x³ - 12x²
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A lab technician draws a sample of blood. A cubic millimeter of the blood contains 22^5 red blood cells and 22^3 white blood cells. How many times more red blood cells are there than white blood cells?
There are 484 times more red blood cells than white blood cells in a cubic millimeter of blood.
What is proportionality?the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.
Given, A lab technician draws a sample of blood.
A cubic millimeter of blood contains 22⁵ red blood cells and 22³ white blood cells.
The number of red blood cells in a cubic millimeter of blood is 22⁵,
and the number of white blood cells in the same volume is 22³.
To find out how many times more red blood cells there are than white blood cells, we need to divide the number of red blood cells by the number of white blood cells:
22⁵ / 22³ = 22⁵⁻³ = 22² = 484
Therefore, there are 484 times more red blood cells than white blood cells in a cubic millimeter of blood.
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Consider the function graphed to the right.
The function is increasing on (4, 6).
The function is decreasing on (- 6, - 2).
The function is constant on (-2, 4).
The domain of the function is, (- 6, 6).
The range of the function is, (- 3, 1).
What is increasing and decreasing functions?A function f(x) is said to be increasing if the increase in the independent variable results in an increase in the dependent variable.
A function f(x) is said to be increasing if the increase in the independent variable results in a decrease in the dependent variable.
The function is increasing on the intervals (4, 6).
The function is decreasing on the interval (- 6, - 2).
The function is constant on the interval (-2, 4).
The domain of the function is, (- 6, 6).
The range of the function is, (- 3, 1).
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