The average cost function for the given total cost function is AC(x) = 2,100/x + 4 - 0.0003x.
To find the average cost function C, we need to divide the total cost function C(x) by the quantity of output produced, which is represented by x.
The formula for average cost (AC) is:
AC(x) = C(x) / x
Plugging in the given values, we have:
AC(x) = (2,100 + 4x - 0.0003x2) / x
Simplifying this expression, we get:
AC(x) = 2,100/x + 4 - 0.0003x
Therefore, the average cost function C(x) is:
C(x) = 2,100/x + 4x - 0.0003x2
This function represents the average cost per unit of output, taking into account fixed costs (2,100) and variable costs (4x - 0.0003x) that increase as output increases.
It's important to note that the cost function C(x) is quadratic, which means that the average cost function C(x) will have a U-shaped curve.
This is because initially, as output increases, fixed costs are spread out over a larger quantity of output, leading to a decrease in average cost.
However, at a certain point, the increasing variable costs will outweigh the decreasing fixed costs, causing average cost to increase again.
Overall, knowing the average cost function can be useful for businesses to make decisions about pricing, production levels, and cost management strategies.
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In the figure, the angles are formed by a transversal and two parallel lines. Which angles seem to be congruent?
The angles are formed by a transversal and two parallel lines in the figure. By applying congruent angles and vertical opposite angle property, ∠1 ≅∠3 ≅ ∠5 ≅ ∠7; ∠2 ≅ ∠4 ≅ ∠6 ≅ ∠8. Therefore option B is correct.
Congruent angles are identical to each other and have the same measure. The angles formed by the transversal in corresponding corners are called corresponding angles and they are congruent.
Therefore, ∠1 ≅ ∠5, ∠3 ≅ ∠7----------(1)
At a vertex if two angles are opposite to each other, then they are vertically opposite angles, they are equal and congruent to each other.
Therefore, ∠1 ≅ ∠3, ∠5 ≅ ∠7----------(2)
Combining (1) and (2), we get:
∠1 ≅∠3 ≅ ∠5 ≅ ∠7
Similarly we can find,
∠2 ≅ ∠4 ≅ ∠6 ≅ ∠8.
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How to get the square root of a number?
Answer:
Step-by-step explanation:
What is the Formula for Calculating the Square Root of a Number? The square root of any number can be expressed using the formula: √y = y½. In other words, if a number has 1/2 as its exponent, it means we need to find the square root of the number.
In mathematics, the square root of a number is a value that, when multiplied by itself, gives the original number.
The square root of a number "a" is denoted by the symbol "√a" or "a^(1/2)." For example, the square root of 9 is 3 because 3 * 3 = 9.
Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to
the given statistics and confidence level. Round the margin of error to four decimal places
98% confidence; the sample size is 800. of which 40% are successes
The error E = ± 4.04 %
Sample data = ( p ).
success p = success percentage = 40 %
confidence interval CI = 98%
sample size n = 800
margin of error E:
The margin of error "E" for estimation of population proportion ( p ) is given by:
E = z - critical √(p(1-p)/n)
P ( Z < Z-critical ) = a/
a = 1 - CI
P ( Z < Z-critical ) = (1 - 0.98) / 2
P ( Z < Z-critical ) = 0.01
Z-critical = 2.33
The error E = ± 4.04 %
Thus, the correct answer is E=± 4.04 %
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Sam just bought a refrigerator for 1058. He paid 211.40 in a down payment and will pay the rest in 6 equal installments. How much does he need to pay for each installment?
The amount Sam needs to pay in each installment is $141.1
How much does he need to pay for each installment?From the question, we have the following parameters that can be used in our computation:
Cost of refrigerator = 1058
Down payment = 211.40
Number of equal installments = 6
Using the above as a guide, we have the following:
Each installment = (Cost of refrigerator - Down payment)/Number of equal installments
substitute the known values in the above equation, so, we have the following representation
Each installment = (1058 - 211.40)/6
Evaluate
Each installment = 141.1
Hence, the amount in each installment is $141.1
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When the sun is at its highest point in the sky, Hong goes to fly a kite in a flat field. He lets out 42.9 feet of string, and the spool of string is 3.4 feet above the ground. The shadow that the kite makes (directly below the kite on the ground) is 16.5 feet away from Hong. How high is the kite off the ground? Round your answer to two decimal places.
The height of the kite off the ground is approximately 17.87 feet rounded to two decimal places.
To solve the problem can use similar triangles.
Let's draw a diagram:
A
|\
| \
h | \ x
| \
|____\
d B
Point A represents the kite, point B represents the tip of the kite's shadow on the ground and point D represents the point directly below the spool of string on the ground.
The height of the kite represented by h.
The length of the string is 42.9 feet so the distance from point A to point D is also 42.9 feet.
The distance from point B to point D is 16.5 feet.
These two lengths to find the length of segment AB:
AB/AD = BD/AD
AB/42.9 = 16.5/42.9
AB = 16.5
So AB is 16.5 feet.
Now we can use the similar triangles to find h.
We have:
h/x = AB/AD
h/x = 16.5/42.9
h = x × 16.5/42.9
We need to find x.
The spool of string is 3.4 feet above the ground and we know that the kite is directly above the spool when it is at its highest point in the sky.
So the height of the kite above the ground is the same as the height of the spool above the ground plus the length of string that has been let out:
x = 3.4 + 42.9
= 46.3
Now we can substitute this value of x into the previous equation to find h:
h = 46.3 × 16.5/42.9
= 17.87
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PA HELP PO SA STATS TOPIC PO "RANDOM SAMPLING AND SAMPLING DISTRIBUTION" THANKYOU
1) Note that the population mean is 153.
2) there are 36 possible random samples of size two that can be selected from a population of nine.
How did we arrive at the above?1) Population Mean = (172 + 148 + 156 + 170 + 161 + 138 + 142 + 156 + 134) / 9
= 1377 / 9
Population Mean = 153
2) To get the number of possible random samples, we must use Combination whose equation is given as
nCr = n! / (r! (n-r)!)
nC2 = 9! / (2!(9-2)!)
= 9! / (2! 7!)
= (9 x 8 x 7!) / (2!7!)
= (9 x 8) / 2
= 36
Thus, the number of random samples that can be selected form a population of 9 is 36.
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Diana walks around a circular swimming pool of diameter 14 feet. What is the distance she has walked?
Step-by-step explanation:
She walks the entire CIRCUMFERENCE of the circle
circumference = pi X diameter
= pi X 14 ft = 43.98 ft = ~ 44 ft (rounded)
Can someone please help me? I need this fast and it’s really important that I get it right. Graph the function shown in the image.
Answer: attached in image, look at both
Step-by-step explanation:
In the following rectangle, AC = 2x + 7 and BD = 5x - 14. Solve for x.
A
D
2=
B
C
Answer:
7
Step-by-step explanation:
yw ;)
If n‖m, find m∠1 + m∠2.
Answer:
80°
Step-by-step explanation:
You want the sum of angles 1 and 2 in the attached figure where line m ║ line n.
Vertical anglesVertical angles are congruent. This means angle 1 is 60°, and the unnumbered angle in triangle ABC at vertex A is 20°.
Alternate interior anglesWhere a transversal crosses parallel lines, alternate interior angles are congruent. This means angle 2 is congruent with the unnumbered interior angle at A, which we know is 20°.
Angle 1 is 60° and angle 2 is 20°. Their sum is ...
∠1 +∠2 = 60° +20° = 80°
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The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 24
minutes of calls is $22.12, and the remaining credit after 63 minutes of calls is $17.44. What is the remaining credit after 91 minutes of calls?
The remaining credit after 91 minutes of calls is $16.76.
We are given that;
(24, 22.12) and (63, 17.44)
Now,
To find the slope and the y-intercept of the function. You can write your solution as:
Slope = (y2 - y1) / (x2 - x1) = (17.44 - 22.12) / (63 - 24) = -0.08 y-intercept = y - mx = 22.12 - (-0.08)(24) = 24.04 Equation: y = -0.08x + 24.04
To find the remaining credit after 91 minutes of calls, you need to substitute x = 91 in the equation and simplify. You can write your answer as:
y = -0.08(91) + 24.04 y = -7.28 + 24.04 y = 16.76
Therefore, by the intercept the answer will be $16.76.
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Given: Isosceles trapezoid ABCD with diagonals BD and AC Identify the missing reason in the proof.
The statement thet complete the proof of the congruent triangles is (a) SAS criterion
How to determine the statement thet complete the proof of the congruent trianglesFrom the question, we have the following parameters that can be used in our computation:
The incomplete proof
In the proof, we have
AD ≅ BC --- side length
DC ≅ DC --- side length
∠ADC ≅ ∠BCD -- angle
This means that the triangles are congruent by the SAS theorem
The SAS theorem is defined by "If two sides in one triangle are congruent to two sides in another triangle and the included angle in both are congruent, then the two triangles are congruent"
This means that they are congruent by the SAS congruent
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Answer: A. SAS criterion.
Step-by-step explanation: Angle : ∠ADC ≅ ∠BCD Side length : AD ≅ BC Side length : DC ≅ DC
Because of this △ADC ≅ △BCD by SAS criterion.
Dina draws marbles of the same size and shape out of a bag. The probability of randomly drawing a green marble is 30%. The probability of randomly drawing a yellow marble is 25%. What is the probability Dina will randomly draw a marble that is not green, replace it, then randomly draw a yellow marble? Enter your answer as a %.
After analysing the given data we conclude that the probability that Dina will randomly choose that is not green and change it and again randomly choose a marble that is yellow is 17.5%.
The given probability of Dina drawing a green marble is 30%. Then, the probability of her not drawing a green marble is 70%. It can be said that probability of her drawing a yellow marble is 25%. Hence, the probability of her not drawing a yellow marble is 75%.
The probability of Dina drawing a marble that is not green and then replacing it is
70% × 100% = 70%.
The probability of her then drawing a yellow marble is 25%. Therefore, the probability of Dina randomly drawing a marble that is not green, replace it, then randomly draw a yellow marble is
70% × 25% = 1750
1750× 100 = 17.5%.
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find lim x approaches 3
f(x) = x^2 - 2
f(x) = -3x + 15. x> 3
The value of the limit of the function f(x) = x² - 2 is 7.
The value of the limit of the function f(x) = -3x + 15 is -6.
We have,
To evaluate the limit as x approaches 3, we need to find the limit of function f(x) as x approaches 3 from both sides of 3.
First, let's evaluate the limit from the left side of 3:
lim x → 3⁻ f(x) = lim x → 3⁻ (x^2 - 2)
Substituting x = 3 - h (where h approaches zero) gives:
lim h → 0⁺ [(3 - h)^2 - 2]
= lim h → 0⁺ [9 - 6h + h^2 - 2]
= lim h → 0⁺ [h^2 - 6h + 7]
= 7
(since the limit of a quadratic function as h approaches zero is the constant term)
Next, let's evaluate the limit from the right side of 3:
lim x → 3⁺ f(x)
= lim x → 3⁺ (-3x + 15)
= -6
Since the limit from the left side is not equal to the limit from the right side, the limit of f(x) as x approaches 3 does not exist.
Thus,
The value of the limit of the function f(x) = x² - 2 is 7.
The value of the limit of the function f(x) = -3x + 15 is -6.
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solve the following for x 2log a x- log a(x-1) =log a(x-2)
The solution to the equation [tex]2log_a(x) - log_a(x-1) = log_a(x-2)[/tex] is
x = 2/3.
To solve the equation [tex]2log_a(x) - log_a(x-1) = log_a(x-2)[/tex] for x, We can employ algebraic manipulation and logarithmic characteristics.
Apply logarithmic properties.
Using the logarithmic property[tex]log_a(b) - log_a(c) = log_a(b/c),[/tex] we can rewrite the equation as:
[tex]log_a(x^2) - log_a(x-1) = log_a(x-2).[/tex]
Combine the logarithms.
Applying the logarithmic property [tex]log_a(b) - log_a(c) = log_a(b/c),[/tex] we can combine the logarithms on the left-hand side:
[tex]log_a[(x^2)/(x-1)] = log_a(x-2).[/tex]
Take the logarithms out.
We can do away with the logarithms because the base of the equation is the same.
[tex](x^2)/(x-1) = x-2.[/tex]
Streamline the equation.
We can eliminate the denominator and simplify the equation by multiplying both sides by (x-1):
[tex]x^2 = (x-2)(x-1).[/tex]
Expand and simplify.
Expanding the right-hand side, we have:
[tex]x^2 = x^2 - 3x + 2[/tex]
Rearrange the equation.
Rearranging the equation, we get:
0 = -3x + 2.
Do the x math.
We must isolate x on one side of the equation in order to find its value. Taking 2 away from both sides:
3x = 2.
Finally, divide both sides by 3:
x = 2/3.
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Xavier drew a map of an island using a scale in which 2 inches represents 50 feet. The length of the island is 400 feet. What is the length of the island on the map in inches?
Answer:
16 in
Step-by-step explanation:
50 ft x 12 in/ft = 600 in
Scale factor: 2 : 600 = 1 : 300
x = length of island on the map
400 ft = 4800 in
1/300 = x/4800
x = 4800/300 = 16 in
Solve A and B please
a. The standard deviation of the tuition is $150.
b. The shape of this distribution is a normal distribution, which is a bell-shaped curve.
How to calculate the value(a) The mean tuition is $100 per credit hour * 15 credit hours per semester + $150 lab fee = $1650 per semester.
The standard deviation of the tuition is l:
= ✓(100² + 150²) =
= ✓22500
= $150.
(b) The shape of this distribution is a normal distribution, which is a bell-shaped curve. The mean is the center of the distribution, and the standard deviation is the width of the distribution. The majority of the tuitions will be close to the mean, with fewer and fewer tuitions as you move further away from the mean.
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What is the answer to this expression?
3⋅10+3⋅5 ^2 +3 ?
Pls help
Will leave gd rating
Answer:
Step-by-step explanation:
PEMDAS (order in which to do operations)
P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction
there are no parentheses so skip that
5^2 is an exponent so do that first
3x10 + 3x5^2 + 3 --> 3 x 10 + 3 x 25 + 3
Next, do multiplication/division operations from left to right
3 x 10 + 3 x 25 + 3 --> 30 + 75 + 3
Finally, do the addition operations
30 + 75 + 3 = 108
final answer: 108
Calculator What is the area of a sector with a central angle of 40° and a radius of 16.7 ft? Use 3.14 for T and round your final answer to the nearest hundredth. Enter your answer as a decimal in the box. ft² B
The area of the sector is approximately 9.25 ft².
We have,
The formula for the area of a sector.
A = (θ/360°) × πr²
where A is the area of the sector, θ is the central angle in degrees, and r is the radius.
Substituting the given values.
A = (40°/360°) × 3.14 × (16.7 ft)²
A = 0.1111 × 3.14 × 278.89 ft²
A = 9.2465 ft²
Rounding to the nearest hundredth.
A ≈ 9.25 ft²
Therefore,
The area of the sector is approximately 9.25 ft².
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I will give brainliest and ratings if you get this correct
1. The product of MG is as follows;
[tex]\left[\begin{array}{ccc}1&k_1+9&4k_2+36 \\2t_1&k_1t_1-17&3k_2-19t_1-11\\t_2+1&k_1-4t_2+5&k_2t_2-8\end{array}\right][/tex]
2. The values are k₁ = -9, k₂ = -9, t₁ = 0 and t₂ = -1 given that G = M⁻¹
How do we find the product MG?Matrix M and matrix G are given as
M = [1, 4, 5; t₁, 3, -1; 1, t₂, 1] and
G = [2, k₁, -19; 1, -4, k₂; -1, 5, 11]
MG becomes
1×2 + 4×1 + 5×-1 1k₁+4×-4+ 5×5 1×-19+4k₂+5×11
t₁×2+3×1+-1×-1 t₁k₁+3×-4+-1×5 t₁×-19+3k₂+-1×11
1×2+t₂×1+1×-1 1k₁+t₂×-4+-1×5 1×-19+t₂k₂+1×11
=
1 k₁+9 4k₂+36
2t₁ k₁t₁-17 3k₂-19t₁-11
t₂+1 k₁-4t₂+5 k₂t₂-8
To solve G = M⁻¹ we know it is an identity matrix
I = | 1 0 0 |
| 0 1 0 |
| 0 0 1 |
We can equate the elements of MG and I to find the values of t₁, t₂, k₁, and k₂:
1 = 1, k₁+9 = 0, 4k₂+36 = 0
2t₁ = 0 k₁t₁-17 = 1 3k₂-19t₁-11 = 0
t₂+1 = 0 k₁-4t₂+5 = 0 k₂t₂-8 = 1
k₁+9 = 0 4k₂+36 = 0 2t₁ = 0 t₂+1 = 0
k₁ = -9 k₂ = -9 t₁ = 0 t₂ = -1
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Two systems of linear equations in two variables, x and y, are given.
System P:
(3x-10y=8
7x+2y=6
The two systems have the same solution..
What are the values of b and c?
b=
System T:
bx - 10 y + 10 y = 38
cx + 10 y = 30
=
C =
Answer:
Step-by-step explanation:
Select the correct answer.
Which expression is equivalent to the given expression?
(14x³y^-4) (4x^-5y^4)
OA. 56/x^2
OB. 56x^2y
OC. 56y/x^2
OD. 56x^2
please help i need the answer!!
Answer:
The correct answer is D. 56x^2.
Please Help! 13 points!
a) The first mistake that Fatima made was in the first step.
b) She incorrectly changed the place value of 0.02 in the subtraction operation.
c) Based on the correct subtraction operation and place value in step one, Fatima has 0.395 kilograms of rose petals left.
What is a place value?The place value shows the position of a digit in a number.
The right place values are essential for correct mathematical operations.
The quantity of rose petals that Fatima bought initially = 0.454 kilograms
The quantity of rose petals used for making rose water = 0.02 kilograms
The remaining quantity of rose petals = 0.434 (0.454 - 0.02)
The additional quantity of rose petals Fatima bought = 0.056
The quantity of rose petals used for making the second rose water = 0.095
The quantity of rose petals left = 0.395 (0.434 + 0.056 - 0.095)
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What is the break-even point? A graph has units on the x-axis, and cost (dollars) on the y-axis. 2 lines intersect at (11, 44). a. 11 units c. 3 units b. 44 units d. 6 units
The break-even point would be when the cost is equal to 44 dollars.
Option B is the correct answer.
We have,
The break-even point represents the point at which the cost equals the revenue or the point where there is no profit or loss.
Now,
In this case, if the graph represents the cost (dollars) on the y-axis and units on the x-axis, the break-even point occurs when the cost is equal to the revenue or total sales.
Given that two lines intersect at (11, 44),
The break-even point would be when the cost is equal to 44 dollars.
Thus,
The break-even point would be when the cost is equal to 44 dollars.
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12. In the figure, AB is a diameter, and ABL CD The figure is not drawn to scale.
If m AC-54°, what is m BD
(1 point)
0 36°
O 108
O 126°
O 144°
20 points
In the figure, AB is a diameter, and AB⊥CD, If m AC = 54°, BD is 36°. Option A
How do we calculate the line BD given the that AB is a diameter, and AB⊥CD?In a circle, a diameter divides it into two equal parts and forms a straight line that measures 180°.
Given that AB is a diameter = 180°.
AB is perpendicular to CD, therefore m∠AC + m∠BD = 90°.
Substituting m∠AC =54°, we get m∠BD + 54° = 90°.
Solving for m∠BD, we get 90° - 54° = 36°.
There BD is 36°.
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Refer to the painting.
110°
7x
Write an equation that can be used to find the value of x.
An equation that can be used to find the value of x include the following: 110° + 7x = 180°.
What is a supplementary angle?In Mathematics and Geometry, a supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees.
Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can reasonably infer and logically deduce that the sum of the given angles are supplementary angles:
110 + 7x = 180°
7x = 180° - 110°
7x = 70°
x = 70°/7
x = 10°
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
The table represents a quadratic function C(t).
t C(t)
−2 7
−1 4
0 3
1 4
2 7
What is the equation of C(t)?
C(t) = −(t − 3)2
C(t) = (t − 3)2
C(t) = −t2 + 3
C(t) = t2 + 3
The equation of the quadratic function C(t) is given as follows:
C(t) = t² + 3.
How to define the quadratic function given it's vertex?The quadratic function of vertex(h,k) is given by the rule presented as follows:
y = a(x - h)² + k
In which:
h is the x-coordinate of the vertex.k is the y-coordinate of the vertex.a is the leading coefficient.The vertex is the turning point of the function, where it changes from decreasing to increasing, or vice versa, hence:
(0,3).
Then:
y = at² + 3.
When x = 1, y = 4, hence the leading coefficient a is obtained as follows:
4 = a(1)² + 3
a = 1.
Hence the function is given as follows:
y = t² + 3.
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What is the range of the function y=−7x−5?
Step-by-step explanation:
"Range'' is the values of 'y' that a graph can have....there are no limits on this one
(-∞,+∞)
What is the surface area of the cylinder with height 8 cm and radius 4 cm? Round your answer to the nearest thousandth.
Answer:
301.59289cm²
Step-by-step explanation:
Theprofit(indollars)earnedbysellingwappletreesisrepresentedby w2 − 4w + 14. The profit (in dollars) earned by selling w pear trees is
represented by 2w + 10. Write a polynomial that represents how much more profit is earned by selling w apple trees than w pear trees.
[tex]w^2 - 6w + 4[/tex] is a polynomial that represents how much more profit is earned by selling w apple trees than w pear trees.
The profit earned by selling w pear trees is 2w + 10
To find the difference in profit, we need to subtract the profit earned by selling w pear trees from the profit earned by selling w apple trees:
[tex](w^2 - 4w + 14) - (2w + 10)[/tex]
Simplifying the expression:
[tex]w^2 - 6w + 4[/tex]
Therefore, the polynomial that represents how much more profit is earned by selling w apple trees than w pear trees is [tex]w^2 - 6w + 4[/tex].
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