The values of a and n that make the equation[tex](ax^6)^(1/n) = 4x^2[/tex] true for all values of x are a = 4 and n = 3.
What are laws of exponents?The laws of exponents are rules for simplifying expressions with powers, including multiplying powers with the same base, dividing powers with the same base, and raising powers to a power.
The equation is [tex](ax^6)^(1/n) = 4x^2[/tex]. We want to find the values of a and n that make this equation true for all values of x.
We can begin by simplifying the equation using the laws of exponents:
[tex](ax^6)^(1/n) = 4x^2[/tex]
a[tex]ax^6/n = 4x^2[/tex]
Now we can solve for a and n by comparing the exponents of x on both sides of the equation:
The exponent of x on the left side is 6/n, and the exponent of x on the right side is 2. Therefore:
[tex]6/n = 2[/tex]
Multiplying both sides by n, we get:
6 = 2n
Dividing both sides by 2, we get:
n = 3
Now we can solve for a by substituting n = 3 into the equation and simplifying:
[tex]ax^6/3 = 4x^2\\ax^2 = 4x^2[/tex]
a = 4
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Jasper and Corey have saved up a total of $78. 0. Jasper has saved 6 dollars more than twice as much as Corey. How much Corey saved?
If Jasper and Corey have saved up a total of $78.0 and Jasper has saved 6 dollars more than twice as much as Corey, Corey has saved $24, for a total of $78.
Let's use C to represent the amount of money Corey has saved.
We know that Jasper has saved 6 dollars more than twice as much as Corey, so we can write an equation to represent this relationship:
J = 2C + 6
where J is the amount of money Jasper has saved.
We also know that the total amount of money saved by Jasper and Corey is $78, so we can write another equation to represent this:
J + C = 78
Now we can substitute the first equation into the second equation to get an equation with only one variable:
(2C + 6) + C = 78
Simplifying the equation, we get:
3C + 6 = 78
Subtracting 6 from both sides, we get:
3C = 72
Dividing both sides by 3, we get:
C = 24
Therefore, Corey has saved $24. We can use the first equation to find out how much Jasper has saved:
J = 2C + 6 = 2(24) + 6 = 54
So Jasper has saved $54.
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How do I get the percentage of numbers. Pls give examples
Answer:
divide by hundred
Step-by-step explanation:
example :
convert to percentage 300
300÷ 100= 3%
quesrion is 6q-12 =84 and the way
Answer:
16
Step-by-step explanation:
6q-12=84
6q=96
q=16
Answer:
q = 16
Step-by-step explanation:
First Step: Add 12 to both sides. giving you 96.
Second Step: Divide both sides by 6 giving you 16.
Solution: q = 16.
Let C(t) represent the dollar amount charged by a computer consultant to a client when they sign a contract t hours of work. the consultant gives a $4 discount to the client if the contract is increased by 10 hours. estimate the amount charged per hour when the client orders 80 hours of work if 70 hours of work cost a total of $4900
After answering the prοvided questiοn, we can cοnclude that Sο the equatiοn estimated amοunt charged per hοur when the client οrders 80 hοurs οf wοrk is $60.85.
What is equatiοn?In mathematics, an equatiοn is a statement that implies the unity οf twο traits. An equatiοn cοnsists οf twο sides separated because οf an analytical sοlutiοn (=). Fοr instance, the debate "2x + 3 = 9" asserts that the remark "2x + 3" equals the valuatiοn "9". The gοal οf sοlving equatiοns is tο determine the amοunt οr values οf the variable in the mοdel) that wοuld allοw the equatiοn tο really be true.
Fοrmulae can be simple οr cοmplex, regular οr nοnlinear, and cοntain οne οr mοre variables. Fοr example, in the equatiοn "x² + 2x - 3 = 0," the variable x is elevated tο the secοnd pοwer. Lines are used extensively in mathematics, including algebra, equatiοns, and geοmetry.
Let's start by using the given infοrmatiοn tο set up twο equatiοns:
C(70) = $4900
C(80) = C(70) - ($4/10) * 80
C(80) = C(70) - $32
C(80) = $4900 - $32
C(80) = $4868
$4868 / 80 = $60.85 per hοur
Sο the estimated amοunt charged per hοur when the client οrders 80 hοurs οf wοrk is $60.85.
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Answer each for 100 points
Step-by-step explanation:
1. 36g+9-5g=31g+9
2. 12x-4g+4x=16x-4g
3. 15h-6g
4. 2h-6g
5. 60g-20f
Answer:
31g+9, 16x-4g,15h-6g, 2h-6g, 20(3g-f)
Step-by-step explanation:
Q.1 9(4g+1)-5g=36g+9-5g
=31g+9
Q.2 4(3x-g)+4g=12x-4g+4x
=16x-4g
or 4(4x-g)
Q.3 3(5h-2g)=15h-6g
Q.4 2(h-3g)=2h-6g
Q.5 5(12g-4f)=60g-20f
or =20(3g-f)
On a school trip the ratio of staff to students is 1:10. All of the students are either from year 7 or 8. The ratio of y8 to y7 is 3:2. What fraction are y7?
The fraction of Year 7 students can be found by dividing y7 by the total number of students, which is 11 times the number of staff members; using the ratio of y8 to y7, we get y7/(11S) = 5/8.
Let's denote the number of staff members as S and the number of students as T. Since the ratio of staff to students is 1:10, we have:
S:T = 1:10
We can rewrite this as S = (1/11)T and T = 11S, where S is the number of staff members and T is the total number of students.
Let's denote the number of Year 7 students as y7 and the number of Year 8 students as y8. Since all students are either in Year 7 or Year 8, we have:
[tex]y7 + y8 = T[/tex]
Substituting T = 11S, we get:
[tex]y7 + y8 = 11S[/tex]
The ratio of y8 to y7 is 3:2, which means that:
[tex]y8:y7 = 3:2[/tex]
We can rewrite this as y8 = (3/5)y7. Substituting this expression into the equation y7 + y8 = 11S, we get:
[tex]y7 + (3/5)y7 = 11S[/tex]
Simplifying, we get:
[tex](8/5)y7 = 11S[/tex]
Dividing both sides by 11S, we get:
[tex]y7/(11S) = 5/8[/tex]
Therefore, the fraction of Year 7 students is 5/8.
The ratio of staff to students is 1:10, so S:T = 1:10, which can be rewritten as S = (1/11)T and T = 11S.
Let y7 and y8 be the number of Year 7 and Year 8 students, respectively. Then y7 + y8 = 11S.
The ratio of y8 to y7 is 3:2, so [tex]y8 = (3/5)y7[/tex].
Substituting [tex]y8 = (3/5)y7[/tex] into [tex]y7 + y8 = 11S[/tex], we get [tex](8/5)y7 = 11S[/tex].
Dividing both sides by 11S, we get [tex]y7/(11S) = 5/8[/tex].
Therefore, the fraction of Year 7 students is 5/8.
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How do you write 3.876 x 10^7 in standard form
Answer:
3.876 x 10^7 in standard form is 38,760,000.
Step-by-step explanation:
Answer:
38,760,000
Step-by-step explanation:
To write 3.876 x 10^7 in standard form, you need to move the decimal point to the left or right, depending on whether the exponent is positive or negative. In this case, the exponent is positive, so you need to move the decimal point 7 places to the right.
Starting with 3.876, move the decimal point to the right 7 places to get:
38,760,000
So 3.876 x 10^7 in standard form is 38,760,000.
Select all the conversions that are equivalent to the mass of a 6. 75 kilogram bowling ball
a. 67. 5 hg
b. 67. 5 dag
c. 6750 gram
d. 67500 cg
e. 6750000 mg
The mass of a 6.75 kg bowling ball is equivalent to 67.5 hg, 67.5 dag, 6750 g, 67500 cg, or 6750000 mg.
Mass is a measure of the amount of matter an object contains. The equation used to convert between mass units is:
Mass (m) = Mass (M) × Conversion Factor
For example, if we want to convert 6.75 kg to hg (hectograms), the formula and calculation would be:
m (hg) = M (kg) × 100
m (hg) = 6.75 kg × 100
m (hg) = 67.5 hg
Similarly, we can convert 6.75 kg to dag (decagrams) using the formula:
m (dag) = M (kg) × 10
m (dag) = 6.75 kg × 10
m (dag) = 67.5 dag
To convert 6.75 kg to g (grams), the formula and calculation are:
m (g) = M (kg) × 1000
m (g) = 6.75 kg × 1000
m (g) = 6750 g
We can also convert 6.75 kg to cg (centigrams) using the formula:
m (cg) = M (kg) × 10000
m (cg) = 6.75 kg × 10000
m (cg) = 67500 cg
Finally, to convert 6.75 kg to mg (milligrams), the formula and calculation are:
m (mg) = M (kg) × 1000000
m (mg) = 6.75 kg × 1000000
m (mg) = 6750000 mg
In conclusion, the mass of a 6.75 kg bowling ball can be equivalent to 67.5 hg, 67.5 dag, 6750 g, 67500 cg, or 6750000 mg.
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A baseball is roughly spherical with a radius of approximately 2.9 in. what is the approximate volume of a baseball to the nearest cubic inch?
Answer:
102 cubic inches
Step-by-step explanation:
The formula for a volume of a sphere is as follows:
[tex]V = \frac{4\pi r^2}{3}[/tex]
Hence, substituting r=2.9 into this equation,
[tex]\frac{4\pi (2.9)^3}{3}\\\\=\frac{4\pi (24.4)}{3}\\\\=102.160404[/tex]
Hence, the answer is 102 cubic inches.
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If you start a bank account with 15000 and your bank compound the interest monthly at an interest rate of 9% p. A. How much money do you have at the year's end assume that you do not add or withdraw any money to/from the account
At the end of 1 year, the amount in the account will be 16443.4. To sum up, compound interest is a type of interest calculated on the initial principal and the accumulated interest of the previous periods.
The formula for calculating compound interest is [tex]A = P (1 + r/n)^nt,[/tex]where A is the future value of the account, P is the principal amount, r is the interest rate, n is the number of times the interest is compounded per year and t is the number of years.In the given case, the principal amount is 15000, the interest rate is 9% per annum and the number of times the interest is compounded is 12. Therefore, the future value of the account at the end of 1 year will be[tex]A = 15000 (1 + (9/100)/12)^12x1 A = 15000 (1 + 0.0075)^12A = 15000 (1.0075)^12 A = 15000 x 1.0956A = 16443.4[/tex]Therefore, at the end of 1 year, the amount in the account will be 16443.4. . In the given case, the future value of the account at the end of 1 year will be 16443.4.Step 1:Calculate the monthly interest rate:Interest rate per month = [tex]9% / 12 = 0.75%[/tex],Step 2:Calculate the total amount at the end of the year:Total amount =[tex]15000 x (1 + 0.75%) ^ 12[/tex] Total amount = 15000 x 1.0975, Total amount =[tex]$16,462.50[/tex]
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at how many points does the graph of the function below intersect the x-axis? y=4x^2-9x+9
a. 1
b. 0
c. 2
To find the number of points at which the graph of the function intersects the x-axis, we need to find the roots of the equation:
4x^2 - 9x + 9 = 0
We can use the quadratic formula to find the roots:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
In this case, a = 4, b = -9, and c = 9, so:
x = (-(-9) ± sqrt((-9)^2 - 4(4)(9))) / 2(4)
x = (9 ± sqrt(81 - 144)) / 8
x = (9 ± sqrt(-63)) / 8
Since the discriminant is negative, the roots are complex and the graph does not intersect the x-axis. Therefore, the answer is b. 0.
How much television does the average American child watch per week?
A: 100 hours
B: 25 hours
C: 50 hours
D: 15 hours
Don’t answer if you don’t know.
Answer:
25 Hours
Step-by-step explanation:
True or false: f(x) represents a function.
f(x)
• A. False
• B. True
Answer:
• B. True
Step-by-step explanation:
Select all the equations that are equivalent to this equation.
1/4 (8x + 56) = 20
1; 56 + 8x = 80
2; 14 = 20 – 8x
3; 2x + 14 = 5
4: 2x = 6
5: x = 3
The equations equivalent to 1/4 (8x + 56) = 20 are
1. 56 + 8x = 80
2.14 = 20 - 8x
4.2x = 6
5. x = 3
What is an equation?An equation is a mathematical expression that shows the relationship between two variables.
Since we have the equation 1/4(8x + 56) = 20, and we want to find all the equations that are equivalent to it, we solve the equation.
So, we proceed as follows.
1/4(8x + 56) = 20
Expanding the brackets, we have
8x/4 + 56/4 = 20
2x + 14 = 20
Subtracting 14 from both sides, we have that
2x = 20 - 14
2x = 6
x = 6/2
x = 3
Also, in 1/4(8x + 56) = 20
Multiplying through by 4, we have that
8x + 56 = 80
2x + 14 = 20
Subtracting 2x from both sides, we have that
14 = 20 - 2x
So, the equations are
1. 56 + 8x = 80
2.14 = 20 - 8x
4.2x = 6
5. x = 3
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A day care facility is open six days a week. The number of childeren who attend each day are: 22, 23, 23, 24, 20, 8 Which is the most appropriate measure of center?
Answer:
To find an appropriate measure of center, we need to determine the typical or central value of the data. There are several measures of center, such as mean, median, and mode.
However, in this case, we need to consider the extreme value of 8, which is significantly lower than the rest of the values. This value may be an outlier, and including it in the calculation of the mean could skew the result.
Therefore, the most appropriate measure of center in this case would be the median, which is the middle value when the data set is ordered.
To find the median, we first need to order the data set:
8, 20, 22, 23, 23, 24
There are six values in the data set, so the median will be the average of the two middle values, which are 22 and 23.
Median = (22 + 23) / 2 = 22.5
Therefore, the most appropriate measure of center for this data set would be the median of 22.5.
i need help!! please help me out
Two shops, Waitroze and Budgins sell the same brand of cans of soup but with different offers. Calculate the price for one tin at each shop. Round your answer to the nearest penny. Write which shop is better value for money in the comment box.
Answer:
Step-by-step explanation:where are you ???
25 x __ = 36 + 12
sagot pls
Answer:
1.92
Step-by-step explanation:
25x = 36 + 12
25x = 48
x = 1.92
Let's check
25 x 1.92 = 36 + 12
48 = 48
So, 1.92 is the correct answer.
Factor 2x 2 - 9x - 11.
a.(2x - 11)(x + 1)
b.(2x + 11)(x - 1)
c.(2x - 11)(x - 1)
The factored form of the quadratic expression 2x² - 9x - 11 is: a. (2x - 11)(x + 1).
How to Factor a Polynomial Expression?To factor the quadratic expression 2x² - 9x - 11, we need to find two binomials that when multiplied together give us the original quadratic expression. Here are the steps to follow:
Step 1: Multiply the coefficient of the x² term (2) and the constant term (-11) to get -22.
Step 2: Find two numbers whose product is -22 and whose sum is the coefficient of the x term (-9). These numbers are -11 and 2.
Step 3: Rewrite the quadratic expression by splitting the x term into -11x + 2x, using the two numbers found in step 2:
2x² - 11x + 2x - 11
Step 4: Group the first two terms and the last two terms together and factor out the greatest common factor (GCF) of each group:
(2x² - 11x) + (2x - 11)
x(2x - 11) + (2x - 11)
Step 5: Factor out the common binomial factor of (2x - 11):
(2x - 11)(x + 1)
The answer is: a. (2x - 11)(x + 1)
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The diagonal of a square is 18in. Find the length of a side.
50 points in it for you plus a thanks, 5 star and brainliest
Answer:
length of a side is 3
Step-by-step explanation:
if it is a square, the sides are equal. The diagonal will divide the square into 2 isosceles right triangles with diagonal is the hypotenuse
Pythagorean theorem: c^2 = a^2 + b^2
since a = b in isosceles right triangle
c^2 = 2a^2
18 = 2a^2
a^2 = 18/2 = 9
a = √9 = 3
In the past month, Salma rented 1 video game and 7 DVDs. The rental price for the video game was $3.30. The rental price fo each DVD was $4.60. What is the total amount that Salma spent on video game and DVD rentals in the past month?
answer: 35.50
explanation; 4.60 x 7 = 32.20
( price for the 7 dvds )
+ 3.30
( video game price )
Please refer to the photo..
Identify the points that’s are in the solution set to the system of inequalities shown.
{y>= -3x+5
{3y>x+12
• (0,12)
• (-2,0)
•(-6,13)
•(1,6)
•(9,8)
•(-2,19)
•(8,3)
•(0,10
Answer:
• (0,12)
• (1,6)
• (9,8)
• (-2,19)
• (8,3)
Step-by-step explanation:
See the attached graph.
The two inequalities are graphed and the points that are solutions to both equations are all those in the purple area of the graph (the result of the red and blue solutions that overlap [= purple]). The individual points are added to find which points do, or do not, fall within the solution set of both inequalities:
• (0,12) Yes
• (-2,0) No
• (-6,13) No
• (1,6) Yes
• (9,8) Yes
• (-2,19) Yes
• (8,3) Yes
• (0,10) No
What must be true if the triangles are similar by SAS~?
Assign lengths and angle measures to the variables to demonstrate your reasoning.
What must be true for the triangles to be similar to each other by SAS is: y = z, and c/f = a/e, where y = z = 50°; c = 4, f = 3; a = 8; e = 6.
What is the SAS Similarity Theorem?SAS stands for "side-angle-side", which means that if two triangles have two pairs of corresponding sides that are proportional in length and the included angles between them are congruent, then the triangles are similar.
Therefore, for the triangles to be similar by SAS, we would have:
y = z, and
c/f = a/e
Assigning values, we would have:
y = z = 50°
c/f = 4/3
a/e = 8/6
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A cylindrical Paint storage tank is 8 feet high and has a radius of 3 feet. What is the maximum volume of Paint that can be stored in the
tank?
Answer:
Step-by-step explanation:
The maximum volume of paint that can be stored in the cylindrical tank occurs when it is completely filled. The formula for the volume of a cylinder is:
V = πr^2h
where V is the volume, r is the radius, and h is the height.
In this case, the height of the cylindrical tank is 8 feet and the radius is 3 feet. So we can substitute these values into the formula to get:
V = π(3^2)(8)
V = π(9)(8)
V = 72π
Therefore, the maximum volume of paint that can be stored in the tank is 72π cubic feet, which is approximately 226.2 cubic feet if we round to one decimal place.
In a given city, the probability it doesn’t rain is 0.75 and we find that 40 percent of people carry and umbrella when it’s not raining. What is the probability that a person is carrying an umbrella given that it’s not raining? Round your answer to at least 4 decimal places.
Given that it is not raining, there is a [tex]10.67[/tex]% probability that a man is holding an umbrella, or around [tex]0.1067[/tex].
Is probability simple or complex?As probabilistic arguments sometimes produce outcomes that appear contradictory or counterintuitive, probability is usually regarded as one of the most challenging topics of mathematics.
How do you teach students about probability?Probability is the likelihood that something will occur or the probability that something will happen. Probability is the measure of how probable it is that a coin will land heads up after being tossed into the air.
To find [tex]P(B|A)[/tex],
[tex]P(B|A) = P(A and B) / P(A)[/tex]
[tex]P(B|A) = P(A|B) * P(B) / P(A)[/tex]
Putting it all together,
[tex]P(A|B) = P(B|A) * P(A) / P(B)[/tex]
[tex]= [P(A|B) * P(B)] / P(A)[/tex]
[tex]= [P(A and B) / P(B)] * P(A) / P(A)[/tex]
[tex]= P(A and B) / P(B)[/tex]
Therefore,
[tex]P(B|A) = P(A and B) / P(A)[/tex]
[tex]= P(A) * P(B|A) / P(B)[/tex]
[tex]= 0.4 * (1 - 0.75) / 0.75[/tex]
[tex]= 0.1067[/tex]
So the probability that a person is carrying an umbrella given that it's not raining is approximately [tex]0.1067[/tex], or about [tex]10.67[/tex]%.
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Aubrey is flying a kite, holding her hands a distance of 2.5 feet above the ground and letting all the kite’s string play out. She measures the angle of elevation from her hand to the kite to be 25
∘
∘
. If the string from the kite to her hand is 150 feet long, how many feet is the kite above the ground? Round your answer to the nearest hundredth of a foot if necessary.
Using trigonometric ratio, the height of kite above the ground is approximately 65.90 feet.
What is trigonometric ratio?
Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios.
Distance of hand above the ground = 2.5 feet
String length form hand = 150 feet
Angle of elevation = 25°
We can use the sine function of trigonometric ratios to solve this problem.
The formula for sine function is -
sin θ = opposite / hypotenuse
Let's call the height of the kite above the ground "h".
Then we have -
sin (25°) = (h - 2.5) /150
0.42261 = (h - 2.5) /150
(h - 2.5) = 63.392
h = 65.892
Rounding to the nearest hundredth of a foot, we get -
h ≈ 65.90 feet
Therefore, the kite is about 65.90 feet above the ground.
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Find the exact value of x
The exact value of x is ±8√2. However, since x represents a length, the positive square root is the appropriate solution. Thus, x = 8√2.
Describe Triangle?A triangle is a two-dimensional geometric shape that is formed by three straight lines or segments that connect three non-collinear points. These points are called the vertices of the triangle, and the line segments are called its sides. The sides of a triangle may be of different lengths and can form different angles with each other.
Let the side of the triangle be AB, and let the perpendicular from C to AB divide AB into segments of length 4 and 16, with the shorter segment adjacent to A. Let the foot of the perpendicular be D. Then, we have:
AC = 4 + 16 = 20 (by the segment addition postulate)
AD = 4 (given)
CD = 16 (given)
By the Pythagorean theorem, we have:
AC² = AD² + CD²
Simplifying and substituting the values we have:
20² = 4² + 16²
400 = 16 + 256
400 = 272 + x² [where x is the height of the perpendicular]
Subtracting 272 from both sides, we get:
128 = x²
Taking the square root of both sides (since x cannot be negative), we get:
x = ±√128
Simplifying:
x = ±8√2
Therefore, the exact value of x is ±8√2. However, since x represents a length, the positive square root is the appropriate solution. Thus, x = 8√2.
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A). A small business woman has realized that for one of her products, if the price per unit is GH¢20 she can sell 300 units a day. On the other hand, if the price per unit is reduced to GH¢13, she can sell 440 units a day. From the accounting records, her accountant has estimated the fixed cost of production as GH₵2,000 with a variable cost per unit of GH¢10.
(i). Find an expression relating price and output assuming it is linear.
(ii). State the total cost function, assuming it is linear.
(iii) Advise the business woman on the level of production at which she will breakeven.
AN(10 marks)
AP(5 marks)
i) The expression relating price and output assuming it is linear is Price per unit = -20 × Number of units sold + c.
ii) The total cost function, assuming it is linear is 2000 + 10 × Number of units sold.
iii) The business woman need to produce 114 products to achieve breakeven.
(i) The expression relating price and output assuming it is linear can be written as:
Price per unit = m × Number of units sold + c
where m is the slope of the line and c is the y-intercept.
We can find the slope by using the two points (20, 300) and (13, 440):
m = (440 - 300) / (13 - 20) = 140 / (-7) = -20
So, the expression relating price and output is:
Price per unit = -20 × Number of units sold + c
(ii) The total cost function assuming it is linear can be written as:
Total cost = Fixed cost + Variable cost per unit × Number of units sold
Given that the fixed cost of production is GH₵2,000 with a variable cost per unit of GH¢10, the total cost function can be expressed as:
Total cost = 2000 + 10 × Number of units sold
(iii) To find the level of production at which the business woman will breakeven, we need to find the point at which the total cost equals the total revenue. Since the total revenue is simply the product of the price per unit and the number of units sold, we can set these two equations equal to each other:
Price per unit × Number of units sold = Total cost
Substituting the expressions we found in parts (i) and (ii), we get:
(-20 × Number of units sold + c) × Number of units sold = 2000 + 10 × Number of units sold
Simplifying and solving for the number of units sold, we get:
20 × Number of units sold^2 - 20c × Number of units sold - 2000 = 0
Using the quadratic formula, we get:
Number of units sold = (-(-20c) ± sqrt((-20c)^2 - 4 × 20 × (-2000))) / (2 × 20)
Simplifying, we get:
Number of units sold = (c + sqrt(c^2 + 2000)) / 2
Since we know that the business woman can sell 300 units a day at a price of GH¢20 and 440 units a day at a price of GH¢13, we can set up a system of equations to solve for the y-intercept, c:
-20 × 300 + c = 20c + 2000
-20 × 440 + c = 13c + 2000
Solving this system of equations, we get:
c = 2400/3 ≈ GH₵800
Therefore, the level of production at which the business woman will breakeven is:
Number of units sold = (800 + sqrt(800^2 + 2000)) / 2 ≈ 113.7 units
She should produce at least 114 units to breakeven.
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The double number line shows the number of children 1 adult supervises on a field trip.
Complete the table to show the same information as the double number line.
Adults Children
8
66
15
The double number line, along with the formula y = 8x + 58, can be used to determine the number of adults needed to supervise a given number of children on a field trip.
The double number line shows the relationship between the number of adults and the number of children they can supervise on a field trip. The table below represents the same relationship:
Adults Children
8 66
15 99
The formula used to calculate the number of children supervised by a given number of adults is y = 8x + 58, where y is the number of children and x is the number of adults. This formula can be derived by looking at the two points given in the table above. For 8 adults, the corresponding number of children is 66, so 66 = 8x + 58. Solving this equation yields x = 7, which means that 7 adults are needed to supervise 66 children. At 15 adults, the number of children goes up to 99, so 99 = 8x + 58. Solving this equation yields x = 11.25, which means that 11.25 adults are needed to supervise 99 children.
The equation can also be used to calculate the number of adults needed to supervise a given number of children. For example, if the field trip involves 45 children, the equation y = 8x + 58 can be used to calculate the number of adults needed. Substituting 45 for y yields 45 = 8x + 58, which when solved yields x = 5.625. This means that 5.625 adults are needed to supervise 45 children.
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Daniel says that more than half the students spent 2 1/2 hours or more on homework. Liz says more than half the students spent less than 2 1/2 hours on homework who is correct? explain
Daniel and Liz have conflicting claims about how much time students spend on homework.
Daniel claims that more than half of students spend 2 1/2 hours or more on homework, while Liz claims that more than half spend less than 2 1/2 hours. To determine who is correct, we must look at the actual data.
If, when we look at the data, we find that more than half the students spend 2 1/2 hours or more on homework, then Daniel is correct. Conversely, if more than half the students spend less than 2 1/2 hours on homework, then Liz is correct. It is important to note that the answer may depend on the sample size of the data we are looking at.
If the sample size is small, then it may be difficult to definitively answer the question. However, if the sample size is large, then it may be possible to provide a definite answer. In conclusion, to determine who is correct, we must look at the actual data. If the sample size is large enough, then it may be possible to definitively answer the question of who is correct.
Daniel says that more than half of the students spent 2.5 hours or more on homework, while Liz says more than half of the students spent less than 2.5 hours on homework. Liz's assertion is correct. So, Liz is correct since more than half of the students spent less than 2.5 hours on homework.
If Daniel were correct, the total percentage would be more than 100 percent, which is impossible since the total percentage is always 100 percent when the data set is of a limited population. The arithmetic mean of the time the students spend on their homework can be calculated using a statistical concept called a measure of central tendency.
The mean is used in this case. A measure of central tendency is a way of summarizing a data set using a single value that represents the entire collection of data in a condensed form. The mean is calculated by adding up all of the data and then dividing by the number of data points. To discover if the assertion that Liz is correct is accurate, more data is needed.
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