The Cool Company determines that the supply function for its basic air conditioning unit is S(p) = 40 + 0.008p3 and that its demand function is D(p) = 200 - 0.16p2, where p is the price. Determine the price for which the supply equals the demand.
We are given the functions:
S (p) = 40 + 0.008 p^3 ---> 1
D (p) = 200 – 0.16 p^2 ---> 2
T o find for the price in which the price of supply equals demand, all we have to do is to equate the two equations, equation 1 and 2, and calculate for the value of p, therefore:
S (p) = D (p)
40 + 0.008 p^3 = 200 – 0.16 p^2
0.008 p^3 + 0.16 p^2 = 160
p^3 + 20 p^2 = 20,000
p^3 + 20 p^2 – 20,000 = 0
Calculating for the roots using the calculator gives us:
p = 21.86, -20.93±21.84i
Since price cannot be imaginary therefore:
p = 21.86
PLZ HELP I NEED THIS ASAP!!!
An 11-gram sample of a substance that is used to treat thyroid disorders has a k-value of 0.125. Find the substance's half-life in says, round to the nearest tenth.
How do i take the square root of a number?
Final answer:
To take the square root of a number, use the square root function on a calculator or raise the number to the power of 0.5. For higher roots, like fourth roots, raise to the power of 0.25, or take the square root twice. Adjust exponentials before taking roots and estimate if a calculator is not available.
Explanation:
To take the square root of a number, you can perform this operation either by using a calculator or through manual calculations. If you're using a calculator, simply use the square root function, which is usually represented by a radical sign (√) or sometimes as a button labeled 'sqrt'. However, when dealing with equations or expressions where the variable is raised to a power, such as , you will need to take the fourth root to solve for T. This is equivalent to raising the number to the 0.25 power (since 1/4 is equivalent to the fourth root). You can verify this method by checking that the square root of a number is the same as that number raised to the 0.5 power.
In case you are working with exponentials, remember to adjust the exponent so it's evenly divisible by 2 before extracting the square root. If the number is written in scientific notation, extract the square root of the coefficient and halve the exponent. For example, taking the square root of 1 x 104 would be 1 x 102 since the square root of 1 is 1 and half of 4 is 2.
When you lack a calculator, estimating roots, such as cube roots or higher, can be done with a rough mental approximation. For instance, to find the cube root of 87, you know that the cube root of 64 (which is 4) is too small and the cube root of 125 (which is 5) is too big, so you can start by guessing around 4.3. With trial, error, and adjustments, you can find a more accurate result.
Identify the 25th term of the arithmetic sequence 2,1 (3 / 5), 1 ( 1 / 5) ... (2 points)
The 25th term of the arithmetic sequence is -31.6.
Looking at the sequence:
- First term [tex]\( a_1 = 2 \)[/tex]
- Second term [tex]\( a_2 = 1 \left( \frac{3}{5} \right) = \frac{3}{5} \)[/tex]
- Third term [tex]\( a_3 = 1 \left( \frac{1}{5} \right) = \frac{1}{5} \)[/tex]
Calculate the common difference d:
[tex]\[ d = a_2 - a_1 = \frac{3}{5} - 2 = \frac{3}{5} - \frac{10}{5} = -\frac{7}{5} \][/tex]
Now that we have [tex]\( d = -\frac{7}{5} \)[/tex], we can find the general term [tex]\( a_n \)[/tex] of the arithmetic sequence:
[tex]\[ a_n = a_1 + (n-1)d \][/tex]
Substitute [tex]\( a_1 = 2 \)[/tex] and [tex]\( d = -\frac{7}{5} \)[/tex]:
[tex]\[ a_n = 2 + (n-1) \left( -\frac{7}{5} \right) \]\[ a_n = 2 - \frac{7(n-1)}{5} \]\[ a_n = 2 - \frac{7n - 7}{5} \]\[ a_n = \frac{10 - 7n + 7}{5} \]\[ a_n = \frac{17 - 7n}{5} \][/tex]
Now, find [tex]\( a_{25} \)[/tex]:
[tex]\[ a_{25} = \frac{17 - 7 \cdot 25}{5} \]\[ a_{25} = \frac{17 - 175}{5} \]\[ a_{25} = \frac{-158}{5} \]\[ a_{25} = -31.6 \][/tex]
Abel and Zöe’s grandparents opened a savings account for an equal amount upon the birth of each child. Now, the values of their accounts could be found by the following expressions, where t represents the years since 2011.
Abel: y = 1266.77(1.03)t
Zöe: y = 1159.27(1.03)t
Based upon this information, find the difference in the children’s ages.
Abel is ___ years older than Zöe.
Suggestions: Find the ratio 1266.77/1159.26. What does that ratio represent in terms of powers of 1.03? You also can graph both equations and figure out the shift.
Answer:
Abel is 3 years older than Zöe.
Step-by-step explanation:
Abel and Zöe’s grandparents opened a savings account for an equal amount upon the birth of each child. Now, the values of their accounts could be found by the following expressions, where t represents the years since 2011.
Abel: y = 1266.77(1.03)^t
Zöe: y = 1159.27(1.03)^t
To find the difference in children's ages first we take ratio of 1266.77/1159.26
Ratio of 1266.77/1159.26= 1.09
now we write ratio in terms of powers of 1.03
1.03^t = 1.09
Take ln on both sides
t ln(1.03) = ln(1.09)
Divide both sides by ln(1.03)
t= 3
Abel is 3 years older than Zöe.
what is the solution to the equipment 3x+2(x-9)= 8x +x -14
David is making his own strawberry yogurt. In his mixture, the number of strawberries is proportional to the amount of milk in cups david uses 2 1/2cups of milk for every 14 strawberries. If david uses 203 strawberries, how much milk will he need?
Which iniquality is represented by the graph? If you can do the top ones thanks too:) please show work if there is any:)
If 3x+y=14, and x and y are positive integers, all of the following could be the value of x+y EXCEPT? This is an sat question and it is bothering my mind, does anyone understand this? The answer choices are: A) 4 C) 8
The sum of x and y that cannot be obtained from the equation 3x + y = 14 is 8.
Explanation:The question asks for the sum of x and y that could not be obtained from the equation 3x + y = 14. To find the possible values of x and y, we need to consider different combinations of positive integers that satisfy the equation. If we test the answer choices, we can see that the sum of x and y cannot be equal to 8. Therefore, the correct answer is C) 8.
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Lines are cut by transversal such that the alternate interior angles have measures of 3X +17 X +53°
in circle p what is the measure of arc ab
Three-Fourths of the student body attended the pep-rally. If there were 1230 students at the pep rally, how many students are there in all?
To find the total number of students, set up a proportion and solve for x. The total number of students is 1640.
Explanation:To find the total number of students, we can set up a proportion using the information given. If three-fourths of the student body attended the pep-rally, that means three-fourths of the total number of students is equal to 1230. Let's let x represent the total number of students. Then, we can write the proportion as:
3/4 = 1230/x
Now, to solve for x, we can cross multiply:
3x = 4 x 1230
Dividing both sides by 3:
x = 4 x 1230 / 3
Calculating the expression on the right side of the equation:
x = 4920 / 3
Finally, divide 4920 by 3 to get:
x = 1640
So, there are 1640 students in total.
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From their location in the diagram, what are two possible values for n and m?
Answer:
n = [tex]3\frac{1}{4}[/tex] and m = [tex]2\pi[/tex]
Step-by-step explanation:
From the given figure we have,
'n' belongs to rational numbers but it is not an integer.
'm' belongs to irrational numbers.
Now, we look at the options,
a) n = [tex]\frac{1}{3}[/tex] , m = [tex]\sqrt{4}[/tex] = 2 is wrong as m is not a rational.
b) n = [tex]3\frac{1}{4}[/tex] and m = [tex]2\pi[/tex] is correct
c) m = [tex]\sqrt{3}[/tex] , n = [tex]\frac{4}{2}[/tex] = 2 is wrong as n is not an integer
d) m = [tex]\frac{\pi }{2}[/tex] , n = [tex]\sqrt{6}[/tex] is wrong as n is not an irrational number.
The two possible values of n and m are ; n = 3¼ and m = 2π
From the rules given;
n = rational number m = irrationalEvaluating the numbers given ; rational numbers can be whole numbers or fractions which can be expressed in form a/b where b ≠0.
All π values are irrational .
From the option, the value pairs which meets the requirements are ;
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The figure shows two parallel lines AB and DE cut by the transversals AE and BD:
Which statement best explains the relationship between Triangle ABC and Triangle EDC ?
A. Triangle ABC is similar to triangle EDC , because m∠2 = m∠6 and m∠1 = m∠5
B. Triangle ABC is similar to triangle EDC , because m∠3 = m∠6 and m∠1 = m∠4
C. Triangle ABC is congruent to triangle EDC , because m∠3 = m∠4 and m∠1 = m∠5
D. Triangle ABC is congruent to triangle EDC , because m∠3 = m∠6 and m∠1 = m∠4
A rectangle is placed around a semicircle as shown below. The length of the rectangle is 6cm . Find the area of the shaded region. Use the value 3.14 for π , and do not round your answer. Be sure to include the correct unit in your answer.
In the diagram, diameter AC¯¯¯¯¯ intersects chord BD¯¯¯¯¯ at point E such that AE = 2.5 units and BE = 3.4 units. Point O is the center of the circle, and the radius of the circle is 5 units. What is the approximate length of DE¯¯¯¯¯?
A. 5.5
B. 4.5 units
C. 6.0 units
D. 5.0 units
Answer:
(A) 5.5 units
Step-by-step explanation:
Given: Diameter AC intersects chord BD at point E such that AE = 2.5 units and DE = 3.4 units. Point O is the center of the circle, and the radius of the circle is 5 units. we have to find the approximate length of BE.
Now, CE=CO+OE=5+(OA-AE)=5+2.5=7.5 units.
Now, by Intersecting Chord Theorem which states that when two chords intersect each other inside a circle then the products of their segments are equal.
Thus, [tex]CE{\times}AE=BE{\times}DE[/tex]
Substituting the given values, we get
[tex]7.5{\times}2.5=3.4{\times}DE[/tex]
[tex]\frac{7.5{\times}2.5}{3.4}=DE[/tex]
[tex]5.541=DE[/tex]
[tex]DE[/tex]≈[tex]5.5{\text{units}[/tex]
therefore, the measure of DE is 5.5 units.
Hence, option A is correct.
Which number is the largest? 7.2 ⋅ 10−6, 3.09 ⋅ 103, 2.04 ⋅ 104, 5 ⋅ 103
7.2 ⋅ 10−6
3.09 ⋅ 103
2.04 ⋅ 104
5 ⋅ 103
Answer:
Option 3 - [tex]2.04\times 10^4[/tex]
Step-by-step explanation:
Given : Numbers [tex]7.2\times 10^{-6}[/tex] , [tex]3.09\times 10^3[/tex][tex]2.04\times 10^4[/tex] and [tex]5\times 10^3[/tex]
To find : Which number is largest ?
Solution :
We solve all number in standard form,
1) [tex]7.2\times 10^{-6}=\frac{72}{10}\times \frac{1}{1000000}[/tex]
[tex]7.2\times 10^{-6}=0.0000072[/tex]
2) [tex]3.09\times 10^3=\frac{309}{100}\times 1000[/tex]
[tex]3.09\times 10^3=3090[/tex]
3) [tex]2.04\times 10^4=\frac{204}{100}\times 10000[/tex]
[tex]2.04\times 10^4=20400[/tex]
4) [tex]5\times 10^3=5\times 1000[/tex]
[tex]5\times 10^3=5000[/tex]
The decimal number is the least number among all.
The five digit number is the greatest number among all.
So, 20400 is the greatest number.
Which means [tex]2.04\times 10^4[/tex] is the largest number.
Therefore, Option 3 is correct.
If you start with a number, add 5, then multiply by 7, the result is 133. what was the original number
Find all real numbers X such that 6x-21<=-3 AND 14x+11>=-17
What is x: 3.7x-1.2=58
Answer:
x = 16
Step-by-step explanation:
Add 1.2 to both sides, then divide by the coefficient of x.
3.7x = 59.2
x = 59.2/3.7 = 16
The value of x is 16.
Help please?? If you deposit $750 in an account that pays 8% annual interest compounded continuously, what will the balance be after five years?
The balance in your account after five years will be approximately $1,118.85.
Step 1: Understand Continuous Compounding
In continuous compounding, interest is earned not only on the initial principal amount but also on the accumulated interest over time. This means interest is calculated continuously throughout the year, leading to a slightly higher final balance compared to simple interest.
Step 2: Formula for Continuous Compounding
The formula for continuous compounding to find the future value (balance) after t years is:
A = P * e^(r*t)
where:
A = Final amount (balance after t years)P = Principal amount (initial deposit - $750)e = Euler's number (approximately 2.71828)r = Annual interest rate (as a decimal - convert 8% to 0.08)t = Time in years (5 years)Step 3: Apply the Formula
Now that we have the formula and values, let's plug them in:A = $750 * e^(0.08 * 5)Step 4: Calculate the Final Balance
You can use a calculator to evaluate the expression.
A ≈ $750 * e^(0.4) ≈ $750 * 1.4918
Step 5: Round the Answer (Optional)
Depending on the desired level of precision, you can round the answer to two decimal places:
A ≈ $1118.85 (rounded to two decimal places)
Part A: Factor 3x2c2 + 2xc2 − 1c2. Show your work. (4 points)
Part B: Factor x2 − 2x + 1. Show your work. (3 points)
Part C: Factor x2 − 64. Show your work. (3 points)
plz help!!!!!!!!!!!!!!! thanks!!!!!!!!!!
Geneva wants to put fencing around her rectangular flower bed. The width of her flower bed is 2/3 the length. The perimeter of the flower bed is 20 feet. What are the dimensions of her flower bed?
The dimensions of her rectangular flower bed will be 4 feet by 6 feet.
What is the perimeter of the rectangle?Let W be the rectangle's width and L its length.
The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be
Perimeter of the rectangle = 2(L + W) units
Geneva needs to put fencing around her rectangular bloom bed. The width of her bloom bed is 2/3 the length.
W = (2/3)L
3W = 2L
The perimeter of the bloom bed is 20 feet. Then we have
2(L + W) = 20
2L + 2W = 20
3W + 2W = 20
5W = 20
W = 4 feet
Then the length of the rectangle is given as,
2L = 3 x 4
L = 6 feet
The dimensions of her rectangular flower bed will be 4 feet by 6 feet.
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Aly is looking for a new car. She has test-driven two cars but can only purchase one. The probability that she will purchase car A is 0.47 and the probability that she will purchase car B is 0.35. What is the probability that she will not purchase either car A or car B? 0.12 0.41 0.82 0.18
The probability that Aly won't purchase either car A or car B is 0.18. This is calculated by subtracting the combined probability of purchasing either car from 1.
Explanation:The question pertains to the concept of probability, which can be defined as a measure of the likelihood that a given event will occur. In this case, Aly is deciding between two cars to purchase (Car A and Car B). The probability that she will purchase car A is 0.47 and the probability that she will purchase car B is 0.35. These probabilities might have been estimated based on Aly's preferences, past behavior, or other relevant factors.
Since probabilities add up to 1, we can calculate the probability that Aly won't purchase either car A or car B by subtracting the sum of the probabilities of buying car A and car B from 1. So, we do 1 - (0.47 + 0.35) = 0.18. Therefore, the probability that she will not purchase either car A or car B is 0.18.
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What is the equation of the blue graph?
Malcolm makes $11.78 per hour working at a restaurant, including tips. He works seven days a week. How much money does Malcolm make per week if he works 6 hours each day?
11.78*6 = 70.68 per day
70.68*7 = 494.76 per week
given the following right triangle, what is the measure of angle B
need the arctan of the 2 lengths given
9/12 reduces to 3/4
arctan on the calculator is tan^-1
arctan(3/4) = 36.86989 degrees
round off the answer as needed
your class sponsors a benefit concert and the tickets at $8 each.Jordan sells 12 tickets,Andy 16,Morgan 17,and Pat 13.Compute the total revenue brought in by these four persons.
Is the following relation a function?
X Y
6 ----> -1
-1 ----> 2
4 ----> 3
0 ----> 3
Yes or No (both 4 and 0 are pointing to 3)
Answer: Yes, it is definitely a function. Although one might say that it is not a one to one or injective function because of the presence of (-1,-2) and (6,-2).. The correct option among the two options that are given in the question is the second option. I hope that this is the answer that has actually come to your desired help
Step-by-step explanation: I took the test on FLVS
What is the sum of an 8-term geometric series if the first term is -11, the last term is 859,375, and the common ratio is -5?
the sum of an 8-term geometric series if the first term is -11, the last term is 859,375, and the common ratio is -5 is 716144
Given that,
What is the sum of an 8-term geometric series if the first term is -11, the last term is 859,375, and the common ratio is -5 is to be determined.
Arithmetic progression is the series of numbers that have common differences between adjacent
What is geometric progression?Geometric progression is a sequence of series whose ratio with adjacent values remains the same.
the formula of the sum of the 1st nth term in a Geometric Progression:
[tex]Sum = a_1(1-r^n)/(1-r) \\Sum = -11(1 - (-5)^8)/(1+5)\\sum = -11(1 - 390625)(6)\\Sum = 716144[/tex]
Thus, the required sum of the 8-term geometric series is 716,144.
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