The average total cost of manufacturing scented candles is given by the formula A(b) = C(b)/b = (250 + 3b)/b, where b is the number of candles manufactured.
Explanation:The concept of average total cost is key in the calculation. Given the function for total cost of the candles, C(b) = 250 + 3b, the average cost, A, can be calculated by dividing the total cost by the number of candles, b. Therefore, the function representing the average cost, A, in terms of b is given by A(b) = C(b)/b = (250 + 3b)/b. It's important to note that this function also signifies the 'economies of scale', stating as output number increases, the average cost falls.
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What Ticket prices will result in an income of $0?
100p-5p^2 = 0
Factor out 5p out of 100p and -5p^2:
5p(20) + 5p(-p) = 0
Factor:
5p(20-p)=0
Divide each term by 5:
p = 0
Set 20-p to 0 and solve for p:
p = 20
The answer is 0, 20
To find 27 x 600 just plus 27 + 27+ 27 + 27 + 27 + 27 = 162 then add the zeros in 600. That is the answer
The correct product of 27 and 600 is:
[tex]\[ \boxed{16200} \][/tex]
"The correct answer to find the product of 27 and 600 is not obtained by simply adding 27 six times and then appending zeros. The correct method to calculate 27 x 600 is as follows:
First, multiply 27 by 6 to get the hundreds place value correct:
[tex]\[ 27 \times 6 = 162 \][/tex]
Next, since we are multiplying by 600, we need to account for the additional zeros. Each zero represents a factor of 10, so we multiply 162 by 100 (since there are two zeros in 600):
[tex]\[ 162 \times 100 = 16200 \][/tex]
Therefore, the correct product of 27 and 600 is:
[tex]\[ \boxed{16200} \][/tex]
The method described in the question is incorrect because it does not properly account for the place value of the digits in the multiplication. When multiplying by a number with zeros, each zero represents a power of ten and must be considered in the multiplication process. The correct method involves multiplying the numbers and then adjusting the final product's place value by adding zeros according to the multiplier's zeros."
Janelle is at the movie theater and has $20 to spend.
She spends $8 on a ticket and wants to buy some snacks. Each snack costs $4.99.
How many snacks, x, can Janelle buy?
Inequality that represents this situation:
20≥8+4.99x
Drag each number to show if it is a solution to both the inequality and the problem situation, to the inequality only, or if it is not a solution.
Answer:
you minus 8 from 20 which will = to 12. Then you divide 12 by 4.99 and it equals to like 2.4 but you can't buy a .4 of a candy bar so have to round it down to 2
Step-by-step explanation:
Janelle can buy 2 snacks with her remaining budget after purchasing a movie ticket. The inequality 20 ">= 8" + 4.99x is satisfied with x=2, where each snack costs $4.99.
Janelle is at the movie theater with a budget of $20 to spend. After purchasing her movie ticket for $8, she wants to buy snacks with the remaining money. Since each snack costs $4.99, we can represent the situation with the following inequality:
20 ≥ 8 + 4.99x
To find out how many snacks, x, Janelle can buy, we subtract the cost of the movie ticket from her total budget:
$20 - $8 = $12
Now, we divide the remaining amount by the cost of one snack:
$12 / $4.99 ≈ 2.4
Since Janelle cannot buy a fraction of a snack, we round down to the nearest whole number. Thus, Janelle can buy 2 snacks with her remaining budget.
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!
Factor x^2 + 25 in the complex numbers.
A) (x + 5)(x - 5)
B) (x + 5)(x + 5)
C) (x + 5i)(x - 5i)
D) (x + 5i)(x + 5i)
[tex]x^2 + 25=\\\\x^2-(-25)=\\\\(x-\sqrt{-25})(x+\sqrt{-25})=\\\\(x-5i)(x+5i)[/tex]
What is 147.3 as a mixed number and what is 147.3 as a improper fraction
Madam Siti bought the same lengths of red and yellow ribbons. After she used 836 cm of the red ribbon, the length of the yellow ribbon was 5 times the length of the remaining red ribbon. What was the original total length of the two ribbons?
Answer: 1045 cm of red ribbon and 1045 cm of yellow ribbon
Step-by-step explanation:
Let R represent the amount red ribbon and Y represent the amouont of yellow ribbon.
bought the same lengths of red and yellow: R = Yafter used 286 of red, yellow is 5 times the remaining red; 5(R - 836) = YUse substitution method to solve:
5(R - 836) = R
5R - 4180 = R distributed 5 on the left side
4R - 4180 = 0 subtracted R from both sides
4R = 4180 added 4180 to both sides
R = 1045 divided both sides by 4
Answer:
Step-by-step explanation:
Determine which line is steeper. Explain your answer. What does it represent in this situation?
Answer:
I would say the Pennington line is steeper because the slope of the purple line is 2 and the other is 3/2 (don't know if they want slope or not) and it represents that it took 2.5 to three hours to travel 240 miles compared to the other one that takes four hours to travel the same distance. Hopefully that's right
Step-by-step explanation:
Answer:
the purple one is steeper
Step-by-step explanation:
bc i said so :) and it shows that it is
Based on a poll, 70% of internet users are more careful about personal information when using a public wi-fi hotspot. What is the probability that among three randomly selected internet users, at least one is more careful about personal information when using a public wi-fi hotspot? How is the result affected by the additional information that the survey subjects volunteered to respond?
The probability that at least one of the three randomly selected internet users is more careful about personal information when using a public wi-fi hotspot is 97.3%.
Explanation:To find the probability that at least one of the three randomly selected internet users is more careful about personal information when using a public wi-fi hotspot, we can calculate the probability of the complement event, which is the event that none of the users are more careful. Since the probability that an internet user is more careful is 70%, the probability that a user is not more careful is 1 - 70% = 30%. The probability of the complement event for all three users is (0.3)^3 = 0.027. Therefore, the probability that at least one user is more careful is 1 - 0.027 = 0.973, or 97.3%.
Additional information that the survey subjects volunteered to respond does not affect the calculation of the probability. The probability is based solely on the given percentage from the poll, which represents the proportion of internet users who are more careful about personal information when using a public wi-fi hotspot.
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The probability that at least one internet user is more careful about personal information when using a public wi-fi hotspot is 0.973.
Explanation:To find the probability that at least one person is more careful about personal information when using a public wi-fi hotspot, we can use the complement rule. The complement of at least one person being more careful is that no one is more careful. So, the probability that no one is more careful is 0.3 multiplied by 0.3 multiplied by 0.3 (since there are three internet users). Then we subtract this probability from 1 to find the probability that at least one person is more careful. So, the probability that at least one person is more careful is 1 - (0.3 x 0.3 x 0.3) = 0.973.
The additional information that the survey subjects volunteered to respond does not affect the result of the probability calculation. The probabilities are based on the initial survey results, and any additional information would be separate from those probabilities.
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A car needs fixing and abe can tfix it for $70 per hour with $130 part, but gabe can fix it for $80 an hour with a $40 part. How long will it take for both abe and gabe to cost the same amount?
answer is $560
that is lcm of 70&80
Factor the expression completely over the complex numbers.
x^4 + 10x^2 + 25
Enter your answer in the box
[tex]\displaystyle\\x^4+10x^2+25=\\\\=x^4+5x^2+5x^2+25=\\\\=(x^4+5x^2)+(5x^2+25)=\\\\=x^2(x^2+5)+5(x^2+5)=\\\\=(x^2+5)(x^2+5)=\\\\=\left(x^2+\left(\sqrt{5}\right)^2\right)\left(x^2+\left(\sqrt{5}\right)^2\right)=\\\\=\Big(x+i\sqrt{5}\Big)\Big(x-i\sqrt{5}\Big)\Big(x+i\sqrt{5}\Big)\Big(x-i\sqrt{5}\Big)=\\\\=\Big(x+i\sqrt{5}\Big)\Big(x+i\sqrt{5}\Big)\Big(x-i\sqrt{5}\Big)\Big(x-i\sqrt{5}\Big)=\\\\=\boxed{\Big(x+i\sqrt{5}\Big)^2\Big(x-i\sqrt{5}\Big)^2}[/tex]
Centroid: Find AD if HD=24.
To find segment AD given HD = 24 when H is the centroid, you would use the property of the centroid that divides medians in a 2:1 ratio. Since HD is the shorter part, multiply 24 by 2 to get AD = 48 units.
Explanation:You're asking how to find the length of segment AD given HD = 24 in a geometric context involving a centroid. To find AD, we must understand the properties of the centroid, which is the point where the three medians of a triangle intersect. A median connects a vertex of a triangle to the midpoint of the opposite side, and in every triangle, the centroid divides each median in a 2:1 ratio, with the longer segment being closest to the vertex.
Given that HD = 24 and D is the midpoint of AH (because H is the centroid), according to the centroid properties, the length of AD must be twice the length of HD. Therefore:
AD = 2 * HD
AD = 2 * 24
AD = 48
The length of segment AD is 48 units.
A rectangular piece of paper with length 27cm and width 12cm has two semicircles cut out of it, as shown below.
Find the area of the paper that remains. Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.
PLEASE SOMEONE HELP ME THANK YOU!!
Remark
I take it the semicircles cover the full width of the paper.
So the radius is 12/2 = 6 cm
Since there are two of them, the area = a full circle.
Step One
Find the area of the rectangle before the cuts were made.
Area = L * W
L = 27
W = 12
Area = 27 * 12 = 324 cm^2
Step Two
Find the area of the circle cut outs.
r = 6
Area = pi * r^2
Area = 3.14 * 6^2
Area = 3.14 * 36
Area = 113.04 cm^2
Step Three
Find the total area left
Total Area Left = rectangle - circle
Total Area Left = 324 - 113.04
Total Area left = 210.96 cm^2 Answer
How many four - digit numbers can be made from the numerals 7,6,5, and 3
4
12
24
There can be 24 unique four-digit numbers formed from the numerals 7, 6, 5, and 3, calculated by the factorial of 4 (4!).
The student asks how many four-digit numbers can be made from the numerals 7, 6, 5, and 3. These numbers can be arranged in a systematic way, and the total number of combinations can be calculated using permutations. The formula to calculate permutations without repetition is n! (n-factorial), where 'n' is the number of numerals to arrange.
In this case, we have 4 numerals, so the calculation would be 4! This equals to 4 × 3 × 2 × 1 = 24. Thus, there are 24 unique combinations when we arrange the numerals 7, 6, 5, and 3 into four-digit numbers without any repetitions.
solve the equation
12x + 6y = 24 for x
12x + 6y = 24
add -6 to both side
12x + 6y + -6y = 24 + -6y
Combine like terms:
6y + -6y = 0
12x + 0 = 24 + -6y
12x = 24 + -6y
Divide each side by '12'
x = 2 + -0.5y (your answer)
What is the slope of the line?
6x - 2y = 10
The slope of the Line is 3
What is the slope of a line?
Generally, the slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says (x1,y1) and (x2,y2) may be easily determined by finding the difference among the coordinates of the points. The slope is normally represented by the letter 'm'.
Conclusion: The slope is defined as the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run.
The general equation of a line having a slope is y = mx + c
we have to arrange the equation 6x - 2y = 10 in y = mx + c form
6x -2y = 10
2y = 6x - 10
y = 3x - 5
The slope of the line is represented by m, the value of m in equation y = 3x - 5 is 3
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amal solved the equation by completing the square.
x2−8x+14=0
Which equation shows one of the steps Jamal could have taken to complete the square?
x2−8x+16=−14+16
x2−8x+64=−14+64
x2−8x+16=−14
x2−8x+64=−14
Consider the given equation [tex]x^2-8x+14=0[/tex]
We will solve this equation by completing the square method.
Consider the coefficient of 'x', divide it by '2'. then adding and subtracting the square of this number in the given equation.
Coefficient of 'x' = -8
By dividing it by '2', we get -4
Taking the square of '-4' = 16
Adding and subtracting '16' from the given equation.
[tex]x^2-8x+14+16-16=0[/tex]
So, [tex]x^2-8x+16 = -14+16[/tex]
This equation shows one of the step used in solving the equation by completing the square method.
Therefore, option 1 is the correct answer.
For Jamal to solve the equation, [tex]x^2 - 8x + 14 = 0[/tex], by completing the square, one of the steps that could be taken is: A. [tex]\mathbf{x^2 - 8x + 16 = - 14 + 16}[/tex]
Jamal was given the equation, [tex]x^2 - 8x + 14 = 0[/tex], to solve by completing the square.
To do this, the first step would be to move the constant, 14 to the other side of the equation by subtracting 14 from both sides of the equation.
Thus:
[tex]x^2 - 8x + 14 - 14 = 0 -14\\\\x^2 - 8x = -14[/tex]
The next step to take is for Jamal to add the square of half of the coefficient of x to both sides of the equation.
Coefficient of 8x = 8Half of the coefficient of 8 is 4Square of 4 = 16Add 16 to both sides of the equation[tex]x^2 - 8x + 16 = - 14 + 16[/tex] (this tallies with the first option given).
Therefore, for Jamal to solve the equation, [tex]x^2 - 8x + 14 = 0[/tex], by completing the square, one of the steps that could be taken is: A. [tex]\mathbf{x^2 - 8x + 16 = - 14 + 16}[/tex]
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Grady marks down some $4.09 pens to $3.59 for a week and then marks them back up to $4.09. Find the percent of increase and the percent of decrease to the nearest tenth. Are the percents of change the same for both price changes? If not, which is a greater change
Answer:
Percentage decrease ( from $4.09 to $3.59) is 0.1% ( Rounded to nearest tenth)
Percentage increase (from $3.59 to 4.09) is 0.1% ( Rounded to nearest tenth)
Percentages are not same for the both price changes. As we can see from the calculations percentage change from $3.59 to $4.09 is higher.
Step-by-step explanation:
$4.09 has been changed to $3.59.
Percent change = [(Value after - Value before) / Value before]*100
=[tex]\frac{3.59-4.09}{4.09}*100[/tex]%
=[tex]\frac{-0.5}{4.09}*100[/tex]%
=[tex]-0.122249[/tex]%
=[tex]-0.1[/tex]% ( Rounded to nearest tenth)
Percentage decrease is 0.1% ( Rounded to nearest tenth)
Now lets calculate the percentage change from $3.59 to $4.09.
Percent change = [(Value after - Value before) / Value before]*100
=[tex]\frac{4.09-3.59}{3.59}*100[/tex]%
=[tex]\frac{0.5}{3.59}*100[/tex]%
=[tex]0.13927[/tex]%
=[tex]0.1[/tex]% ( Rounded to nearest tenth)
Percentage increase is 0.1% ( Rounded to nearest tenth)
Percentages are not same for the both price changes. As we can see from the calculations percentage change from $3.59 to $4.09 is higher.
This mathematical problem involves calculating percentages of increase and decrease, using the same technique to calculate both. The percentage decrease when the price was marked down from $4.09 to $3.59 is approximately 12.2%, while the percentage increase from $3.59 back to $4.09 is approximately 13.9%, making the percentages of change different for the two price shifts. The greatest change occurs with the increase back to the original price.
Explanation:The subject of this question is mathematics, specifically the calculation of percentage increases and decreases. To find the percentage decrease when the price was marked down from $4.09 to $3.59, we use the formula:
[(Old Price - New Price) / Old Price] x 100
[(4.09 - 3.59) / 4.09] x 100 ~ 12.2%
So the percentage decrease is around 12.2%. Now, to calculate the percentage increase from $3.59 back to $4.09, we use the same approach:
[(4.09 - 3.59) / 3.59] x 100 ~ 13.9%
This gives us a percentage increase of approximately 13.9%. Therefore, the percentage of change is not the same for both price changes. The greater change is seen with the increase back to the original price, which results in a larger percentage of 13.9% compared to the decrease of 12.2%.
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Your food bill was $80 at a restaurant. You left a tip of $ 16 . What percentage of the food bill did you leave for the tip?
Only had 10% of the t shirts he started with. If he has 25 t shirts
Ron bought 40 pen sets and sold 25. This year he bought 75 pen sets and sold 60. The absolute error each year was the same. Are the percent errors also the same? Explain using the solutions.
Absolute error is defined as the magnitude of the difference between the exact value and the approximation.
Here both the times, the error is 15.
40-25=15 and 75-60=15
No, the percent error is not same because the exact values are different and hence, the percent error is different.
Percent error value in 1st case is :
[tex]40-25=15[/tex]
error percent is= [tex]\frac{15}{40}\times100=37.5[/tex]%
Percent error value in 2nd case:
[tex]75-60=15[/tex]
error percent is=[tex]\frac{15}{75}\times100=20[/tex]%
Answer:
The percent error compares the absolute error
Step-by-step explanation:
Which graph appears to show a normal distribution ?
Look at the picture.
It are the examples of a normal distribution.
Answer: B.
help me with this please, anyone?
i DON;T KNOW MAYBE 10+9=21 is the correct answer. let me know if it right! hope u have a grate day
the last statement is true, that is
the table represents a function because each input has exactly one output assigned to it.
If a square has an area of 1255 sq yards, what is the length of one of the sides of this square?
Answer: 35.4 yards
Step-by-step explanation:
Area of a square = s²
1255 = s²
35.4 = s
T a: find a rational number that is between 5.2 and 5.5. Explain why it is rational. (2 points) part b: find an irrational number that is between 5.2 and 5.5. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth. (3 points)
5.3 is one rational number between 5.2 and 5.5.
It is a rational because it can be written as a fraction a/b where a and b are integers ( not = 0):-
5.3 = 53/100.
If a store advertised a sale that gave costumers a 1/4 discount, what is the fractions part of the original price that the the costumer will pay?
[tex]\frac{3}{4}[/tex]
the original price = 1 = [tex]\frac{1}{4}[/tex] + [tex]\frac{3}{4}[/tex]
the customer obtains a [tex]\frac{1}{4}[/tex] discount
and has to pay [tex]\frac{3}{4}[/tex] of the original price
43 ones times 3 tens equals how many hundreds
402 ÷ 19
≈ 400 ÷ 20
= 400 ÷ 10
÷ 2
=____÷ 2
Answer: 40
Step by step explanation
The _______ is asking what 400 ÷ 10 is
400 ÷ 10 = 40
a football team lost 3 yards on the first play and 6 yards on the second play how many total yards did they lose
All you have to do is combine the number of yards that they lost on the first play. The total yards lost is 9 yards.
The answer = 9 yardsPick any number. If that number is even, divide it by 2. If it's odd, multiply it by 3 and add 1. Now repeat the process with your new number. If you keep going, you'll eventually end up at 1. Every time.
4/2=2+1=3x3=9+1=10/2=5+1=6/2=3+1=4/2
That is pretty darn cool.
Create and solve a linear equation that represents the model, where squares and triangles are shown evenly balanced on a balance beam. Assume the weight of a square is 1 unit and the weight of a triangle is unknown.
Let the weight of triangle be x units. You are given that the weight of square is 1 unit.
1) On the left side of the balanced beam you can see 3 triangles and 5 squares. The weight on left side is 3·x+5·1=3x+5 units.
2) On the right side of the balanced beam you can see 2 triangles and 7 squares. The weight on right side is 2·x+7·1=2x+7 units.
3) If the whole system is balanced, then the weights on left and right sides are equal:
3x+5=2x+7.
Solve this equation:
3x-2x=7-5,
x=2 units.
Answer: option A