"suppose that the dollar cost of producing x radios is c(x) = 200 + 10 x - 0.2 x 2 . find the average cost per radio of producing the first 30 radios"
Final answer:
To find the average cost per radio of producing the first 30 radios, divide the total cost of producing the first 30 radios by 30. The average cost per radio is $10.67.
Explanation:
To find the average cost per radio of producing the first 30 radios, we need to divide the total cost of producing the first 30 radios by 30. The total cost function is given as c(x) = 200 + 10x - 0.2x^2, where x represents the number of radios produced. Plugging in x = 30 into the function, we get c(30) = 200 + 10(30) - 0.2(30^2) = 200 + 300 - 180 = 320.
Therefore, the total cost of producing the first 30 radios is $320. To find the average cost per radio, we divide the total cost by the number of radios: $320 / 30 = $10.67.
Factor the polynomial x^9-y^12
Which of the following is a solution for the inequality 2x < 9?
The number of people contacted at each level of a phone tree can be represented by f(x) = 3x, where x represents the level.
What is x when f(x) = 27?
Answer:
Option B is correct
x= 3, At level 3, 27 number of people contacted
Step-by-step explanation:
As per the given statement:
The number of people contacted at each level of a phone tree can be represented by:
[tex]f(x) = 3^x[/tex]
where, x represents the level.
We have to find the value of x when f(x) = 27.
⇒27 = 3^x
We can write 27 as:
[tex]27 = 3 \times 3 \times 3 = 3^3[/tex]
then;
[tex]3^3 = 3^x[/tex]
on comparing we have;
3 = x
or
x = 3
Therefore, the value of x is, 3.
Find the area of the region bounded by the parabola y=2x^2 , the tangent line to the parabola at (5,50), and the x-axis
The area of the region bounded by the parabola[tex]y=2x^2[/tex]angent line at (5,50), and the x-axis is found by integrating the function of the parabola, finding the x-intercept of the tangent line, and subtracting the area under the tangent line from the area under the parabola between x=0 and x=5.
Explanation:The area of the region bounded by the parabola , the tangent line at the point (5,50), and the x-axis can be found using integral calculus. First, we find the equation of the tangent line to the parabola at (5,50). The derivative of y with respect to x is given by [tex]y=2x^2[/tex]= 4x. At x=5, the slope of the tangent line is 20. Thus, the equation of the tangent line is y - 50 = 20(x - 5). To find the bounded area, we integrate the area under the parabola from the x-intercept of the tangent line to x=5, and subtract the area under the tangent line in the same interval.
Let's call the x-intercept of the tangent line x1. To find x1, we set the y-value of the tangent line equation to 0 and solve for x. The integration itself uses the antiderivative of which is [tex]2x^2,[/tex] and the antiderivative of the linear tangent line equation. Subtracting the integral of the tangent line from the integral of the parabola gives us the exact area under the parabola.
Simplify 72 - 81 - 10 + 4
Write the number 70,000,000+400,000+10,000+8,000+500+30+9 in word form and standard form
The standard form of the given expression is 70,418,539.
Given that, 70,000,000+400,000+10,000+8,000+500+30+9.
We need to write the given expanded form in word form and standard form.
What are word form and standard form?Standard form is the usual way of writing numbers. One example is 756. This is how we see numbers every day in the grocery, on our phones, on computers, etc.
Expanded form is breaking down the numbers in such a way that you see the value of each number. So, the expanded form of 756 is 700 + 50 + 6.
Word form is when you write a number the way that you read it. When you see the number 756, you write it as “seven hundred fifty-six”.
Now, standard form of the given expression is 70,418,539.
Word form of the given expression is sevety million, four hundred and eighteen thousand, five hundred and thirty nine.
Therefore, the standard form of the given expression is 70,418,539.
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The average time a boulder high varsity lacrosse player plays in a game is 30 minutes with a standard deviation of 7 minutes. nolan’s playing time in last week’s game against fairview was 48 minutes. (a) calculate the z-score for nolan’s playing time against fairview. (round your answer to 2 decimal places.)
Solving this problem is pretty straight forward.
We simply use the formula:
z-score = (x – u) / s
where,
x = sample value = 48 minutes
u = mean value = 30 minutes
s = standard deviation = 7 minutes
Therefore,
z-score = (48 minutes – 30 minutes) / 7 minutes
z-score = 2.57
Final answer:
To calculate Nolan's z-score for playing time against Fairview, use the given formula. Nolan's z-score for this game is 2.57.
Explanation:
A: To calculate the z-score for Nolan's playing time against Fairview, use the formula: z = (x - μ) / σ, where x is Nolan's playing time, μ is the average time, and σ is the standard deviation.
B: Substituting the values, z = (48 - 30) / 7 = 2.57. Therefore, Nolan's z-score for playing time against Fairview is 2.57.
you build four scale models of the Empire State Building. The smallest model is 3 centimeters tall. The height of each model is three times the height of the previous model.Write a power to represent the height of the tallest model.Then find the height.
how do you place each group of decimals in order from greatest to least 0.058, 0.0099, 0.105, 0.02999?
Seven less than four times a number is 35. Whats a number?
Please explain-a)7;b)21/2;c)-7;d)-21/2
4N-7 = 35
4N = 42
N = 42/4 = 10.5
10.5 = 21/2
B 21/2 is the answer
The graphs of the function FF (left, in blue) and GG (right, in red) are below. Let P(x)=F(x)G(x)P(x)=F(x)G(x) and Q(x)=F(x)/G(x).Q(x)=F(x)/G(x). Answer the following questions.
The problem involves understanding relationships between functions F(x) and G(x), achieved by creating new functions P(x) as their product and Q(x) as their quotient, and studying their behavior for different values of x.
Explanation:The subject of the question deals with understanding the relationship between two functions, F(x) and G(x), through creating new functions P(x) and Q(x). P(x) is defined as the product of F(x) and G(x), while Q(x) represents the division of F(x) by G(x).
One way to explore the nature of these new functions would be to take particular values of x, calculate the corresponding outputs for F and G, and then apply the definitions of P and Q. For instance, if F(1)=2 and G(1)=3, then P(1)=F(1)G(1)=2*3=6 and Q(1)=F(1)/G(1)=2/3. Through these examples we can get a grasp of how these functions behave. Comparing P(x) and Q(x) across a number of x-values also provides insight into their relative behavior and interplay.
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The total cost of a tie and a pair of of pants was$87.76. If the price of the tie was $5.64 less than the pair of pants, what was the price of the tie? Express your answer as a simplified fraction or a decimal rounded to two places.
Answer:788
Step-by-step explanation:
How many solutions does the equation have? 3+x=2–3x
free-falling body: h = -15t + 1/2at^2 + 5 (Solve for a)
When a body is said to be in a state of free fall, therefore this means that the only force associated with it is gravity. Gravity imposes an acceleration of about 9.81 m/s^2. Therefore we do not need to calculate for a, since a = g. (g = acceleration due to gravity)
a = 9.81 m/s^2
Sergio's internet provider charges its customers $9 per month plus 4¢ per minute of on-line usage. Sergio received a bill from the provider covering a period and was charged a total of $81.40. How many minutes did he spend on-line during that period? (Round to the nearest whole minute, if necessary.)
A number greater than 1000 who is prime factorization contains one prime number that does not repeat one prime number that repeat three times and one prime number that repeats twice
From examples 9 and 10, what is the connection between function notation to evaluate a function at certain values and ordered pair solutions of the function?
Function notation and ordered pair solutions of a function are closely connected. Function notation is a way to represent a function by its name and its input value, while an ordered pair solution of a function is a pair of numbers (x, y) such that y is the output of the function when x is the input.
To evaluate a function using function notation, we simply substitute the input value into the function's expression. For example, if the function is f(x) = x^2, then to evaluate f(2), we would substitute 2 into the function's expression:
f(2) = 2^2 = 4
This means that the ordered pair solution (2, 4) is a solution of the function f(x) = x^2.
In general, any ordered pair solution of a function can be evaluated using function notation. For example, if the function is g(x) = 2x + 1, and the ordered pair solution is (3, 7), then we can evaluate g(3) as follows:
g(3) = 2(3) + 1 = 6 + 1 = 7
This confirms that the ordered pair solution (3, 7) is a solution of the function g(x) = 2x + 1.
Conversely, any function value can be represented as an ordered pair solution of the function. For example, if the function is h(x) = x^3, and the function value is 8, then we can represent this as the ordered pair solution (2, 8), since h(2) = 8.
In general, any function value can be represented as an ordered pair solution of the function by writing the input value as the first coordinate and the function value as the second coordinate.
Therefore, function notation and ordered pair solutions of a function are closely connected. Function notation is a way to represent a function and its input value, while an ordered pair solution of a function is a pair of numbers (x, y) such that y is the output of the function when x is the input. Any function value can be evaluated using function notation, and any ordered pair solution of a function can be represented as a function value.
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The following question may be like this:
What is the connection between function notation to evaluate a function at certain values and ordered pair solutions of the function?
Which expression results when the change of base formula is applied to log4(x+2) ?
Answer:
Option A : [tex]\frac{log(x+2)}{log(4)}[/tex]
Step-by-step explanation:
Write the expression when the change of base formula is applied to log4(x+2
Given [tex]log_4(x+2)[/tex]
USe change of base formula
[tex]log_b(a)= \frac{log(a)}{log(b)}[/tex]
WE apply change of base formula for the given log
the base of log becomes the denominator .
Numerator becomes the x+2
[tex]log_4(x+2)= \frac{log(x+2)}{log(4)}[/tex]
option A is the correct answer
A disco ball is shaped like a sphere with a diameter of 16 inches. To the nearest square inch, what is the surface of the disco ball?
The surface area of the disco ball is approximately 804 square inches.
Explanation:To find the surface area of a sphere, we can use the formula: 4πr², where r is the radius of the sphere. Since the diameter of the disco ball is given as 16 inches, we can find the radius by dividing the diameter by 2. So, the radius will be 8 inches. Plugging this value into the formula, we get:
Surface area = 4π(8)² = 4π(64) = 256π inches². To the nearest square inch, the surface area of the disco ball is approximately 804 square inches.
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which of the following is the missing side length that completes Pythagorean triple below
1573 ÷ 7 equals
plzz help for my hw
A line passes through the point(4,-1) and (2,3). What is the slope of the line
-10d^4 e^3 f^5 ÷ 15d^2 e^2 f
Answer:
transcript
Step-by-step explanation:
dividing by a polinomial
need help with this
(450-210)/4+50=110
hope this helps
think about a real world example of where a wall meets the floor and where the same wall meets the ceiling. which term describes the edge of the floor and the edge of the ceiling?
A. Parallel line segments
B. Perpendicular line segments
C. Right angle
D. Acute angle
What is x in 6x=2x+40
What is 378×6 using place value with regrouping
243.875 round to the nearest hundred
compare 9x10^4 and 3x10^2
On comparison 9 x 10⁴ is a larger number than 3 x 10².
To compare 9 x 10⁴ and 3 x 10², we can compare the coefficients (9 and 3) and the powers of 10 (10⁴ and 10²) separately.
Comparing the coefficients: 9 vs. 3
The coefficient 9 is greater than the coefficient 3. Therefore, 9 x 10⁴ is greater than 3 x 10² in terms of the actual value of the numbers themselves.
Comparing the powers of 10: 10⁴ vs. 10²
The power of 10 in 10⁴ is greater than the power of 10 in 10². A larger power of 10 means the number has more zeros. In this case, 10⁴ has four zeros (10,000), while 10² has two zeros (100).
Since 10⁴ has more zeros than 10², it represents a larger value.
Combining both comparisons:
When comparing the entire numbers, 9 x 10⁴ is greater than 3 x 10². The larger coefficient (9) and the larger power of 10 (10⁴) contribute to its greater value.
In summary, 9 x 10⁴ is a larger number than 3 x 10².
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