In order to calculate the exact closed form bound of the number of times function F is called in each code segment, we need to consider the number of times F is called in each line of code.
For COUNT1, line 3 calls F once, line 5 calls F n times, and line 7 calls F once more, for a total of n+2 calls.For COUNT2, line 4 calls F once, line 6 calls F n(n+1)/2 times, and line 7 calls F n(n-1)/2 times, for a total of n*(2n+1)/2 calls.For the initial call of F(n^2), the number of times F is called depends on the value of n. To calculate the exact number of calls for any value of n, we can use a recursive approach, starting from the top line of code and working our way down.
For example, for n=4, the initial call of F(16) will call F(4), which will then call F(1) four times, for a total of 5 calls. For n=8, the initial call of F(64) will call F(16), which will call F(4) four times and F(1) sixteen times, for a total of 20 calls.
Thus, for any value of n, the exact closed form bound of the number of times function F is called is given by the formula [1]:
F(n^2) + 4 * F(n/4) + 16 * F(n/16) + …Where the number of terms in the summation is equal to the number of times n is divided by 4 before it reaches 1.
For example, for n=16, the summation will have four terms (n=16, n=4, n=1), and for n=32, the summation will have five terms (n=32, n=8, n=2, n=1).
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Which BEST represents Positive Exponential Growth? (positive growth means growth with no reflections) Group of answer choices
y=3(1/5)^x
y=2(5/8)^x
y=2(8/5)^x
y=−3(1/5)^x
The answer choice which best represents the positive exponential growth as required from the task content is; y=2(8/5)^x.
Which answer choice represents a positive exponential growth?As evident from the standard form equation of exponential relations; we have that;
y = a (b)^x.
By convention, an exponential growth factor is one is which case, the multiplying factor, b is greater than 1.
On this notes the answer choice which represents a positive exponential growth as required is; y=2(8/5)^x.
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The multiplicative inverse of 1/16 ÷ 1/81 +-1/8
The Multiplicative inverse of 1/16 ÷ 1/81 +-1/8 is 16/79
What is multiplicative inverse?The multiplicative inverse of a number x is represented by x-1, which has the property that when multiplied by the original number, it has a value of 1. For instance, 2-1 is the multiplicative inverse of 2, as it meets the formula: 2 x 2-1 = 2 x 12 = 1. The reciprocal of a number is another name for it. A number that, when multiplied by a number x, produces the multiplicative identity 1, or 1/x or x1, is known as a multiplicative inverse or reciprocal in mathematics. B/a is the multiplicative inverse of the fraction a/b. Divide 1 by the real number to find its multiplicative inverse.Essentially a reciprocal, a multiplicative inverse is. The number that produces 1 when multiplied by the original number is known as the multiplicative inverse of that number.1/16 ÷ 1/81 + -1/8
1/16 ÷ 1/81 = 81/16
+ -1/8 = - 1/8
81/16 - 1/8
Then,
= 81/16 - 2/16
= (81 - 2)/16
= 79/16
Multiplicative inverse = 16/79
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Consider a situation that you might need to use your understanding of probability to make an informed decision.
What sorts of information would you collect?
How might you use what you have learned about probability to determine a course of action?
What are the possible benefits and limitations of this approach?
The information that we collects while finding probability is given below.
What is probability?
Probability denotes the likelihood of something happening. It is a mathematical discipline that deals with the occurrence of a random event. The value ranges from zero to one. Probability has been introduced in mathematics to predict the likelihood of occurrences occurring. Probability is defined as the degree to which something is likely to occur. This is the fundamental probability theory, which is also utilized in the probability distribution. To determine the likelihood of a particular event occurring, we must first determine the total number of possibilities.
Now,
Information that we need while calculating probability is :
Determine a single event with a single outcome .Identify the total number of outcomes that can occur.Divide the number of events by the number of possible outcomes.Information needed to find the probability of multiple events
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Which polygon is a convex heptagon?
Answer:
For a heptagon or other polygon to be classified as convex, the interior angles must total less than 180°. Any ordinary heptagon could be classified as a convex heptagon.
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Question 3
Elias ordered 6 books online for a total of $105. Each book cost the same. He applied a
$2 discount per book. What was the original cost of each book?
Let d represent the cost of each book, in dollars. Fill in the blanks to create an equation
to solve the problem:
(d-
The cost of each book was $
When purchasing 6 books online for a total of $105 and each costing the same, the starting cost of a book is $19.5.
what is unitary method ?The component technique is a way of problem-solving where you first calculate the cost of a single component, then multiply that value to get the answer. Simply expressed, a single product value is extracted from a specified multiple using the unit method. For instance, 40 pens will set you back 400 rupees, or $1.01. The method used to accomplish this might be standardized. a solitary nation. anything has a distinctive component. (Mathematics, Algebra) Its adjoint and counterpart are equivalent. (Linear Algebra, Academic Analysis, Mathematics of Matrix or Operators)
given
Step: Since the cost of all six books is $105 and they are all the same price. she paid $17.5 for each book, making
Therefore, the price she paid for the book was 17.5 + $2, which is its original price of 107 / 6 = 17.5.
When purchasing 6 books online for a total of $105 and each costing the same, the starting cost of a book is $19.5.
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Answer:
Step-by-step explanation:
u need to explain more to the question
A triangle has a 60° angle, and the two adjacent sides are 12 and "12 times the square root of 3". Find the radius of a circle with the same vertex as a center, if the arc in the triangle bisects the area of the triangle.
Answer:
To calculate the radius of the circle, you need to use the Law of Sines. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is the same for all three sides of the triangle. Therefore, in your triangle, the ratio of the length of the side opposite the 60° angle to the sine of the 60° angle is the same as the ratio of the length of the other two sides to their respective sines.
Let's call the two adjacent sides of the triangle a and b, respectively. The Law of Sines states that:
a/sin(60°) = b/sin(30°)
The length of side a is 12, and the length of side b is 12 times the square root of 3. This means that:
12/sin(60°) = (12√3)/sin(30°)
We can rearrange this equation to calculate the radius of the circle:
r = 12 * sin(30°) / sin(60°)
This gives us a radius of 12√3.
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Can anyone help? Currently stuck with this problem
A rectangle has width 4.1 and height 3.9 . What is the percentage error if an approximate value of 4 × 4 = 16 is used for the area of this rectangle?
Answer:
0.06254%
Step-by-step explanation:
You want the percentage error in using 4·4=16 as an estimate for the area of a rectangle that is 4.1 by 3.9.
Percentage errorThe percentage error is found using the formula ...
percent error = (estimate - actual)/actual × 100%
percent error = (16 -(4.1×3.9))/(4.1×3.9) × 100%
= (16 -15.99)/15.99 × 100% ≈ 0.06254%
Answer: The actual area of the rectangle is 4.1 * 3.9 = 16.09. The percentage error is calculated as follows:
(|actual value - approximate value| / actual value) * 100% = (|16.09 - 16| / 16.09) * 100% = 0.57%
So, the percentage error is 0.57%.
Step-by-step explanation:
1. What are the horizontal shift and vertical shift for the function below? Use complete sentences and explain your reasoning.
Answer:
Below
Step-by-step explanation:
The horizontal shift is 2 units to the LEFT because of the +2 added to x
The vertical shift is 3 DOWNWARD due to subtraction 3 from the first portion of the function.
When representing colors on a computer each color is represented by a number. There are
different scales for representing these colors. In 24 bit color, there are 16,777,216 possible
colors. The lowest color number is 0 and the highest is 16,777,215. In 16 bit color, there are
65,536 possible colors. The lowest number is 0 and the highest is 65,535. If you had the 16
bit color value 10,000 what would be its equivalent as a 24 bit color?
The equivalent of a 16-bit color value of 10,000 as a 24-bit color value would be 65280.
Explanation:
The 16-bit color value of 10,000 is represented by the number 10000 in decimal.
24-bit color uses 8 bits for each of the three color channels (red, green, and blue),
So, to convert a 16-bit color value to its equivalent 24-bit value, you would add leading zeros to fill out the remaining 8 bits in each color channel.
so in this case 10000 in binary is 10011100010000
so to convert it to 24 bit we add leading zeroes
00010011100010000
So the equivalent 24 bit color value is 65280.
Answer:
Below
Step-by-step explanation:
10 000 is the 10001 th color out of 65536 possible colors
(because '0' is a color)
10 001 is to 65 536 as 'x' is to 16 777 216
10 001 / 65 536 = x / 16 777 216
x = 2, 560,256 in 24 bit scheme
Find the best approximation to a solution of the following systems of equations. What the value for y? 2x+y=-5– 2 = 82x + 3y = 1 3 O-3 4 -4
The system of equations is inconsistent and has no solution.
Here's a step by step process to check for consistency:
2x + y = -5
82x + 3y = 1
Subtracting the first equation from the second gives us:
80x + 2y = 6, which can not be true for any values of x and y.
Therefore, the system of equations has no solution and no approximation of y can be made.
The arrangement of conditions gave doesn't have an answer, since it prompts clashing responses. Basically, when we plug in values for x, the conditions offer us two unique responses for y, and that implies there is definitely not a solitary point that fulfills the two conditions. This makes it difficult to track down an incentive for y that would make the two conditions right. It's like attempting to adjust two teeter-totters simultaneously with loads, yet the loads are different on each side, making it difficult to adjust the two sides. For this situation, there is no arrangement, so finding an incentive for y that works for the two equations is impractical.
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What is the area of this rectangle
Answer:
2400 cm^2
Step-by-step explanation:
Area of a rectangle is its Length X Breadth
so in this case,
Area = 24 x 100
= 2400 cm^2
A book Thandi is reading features totem poles from two regions in the Pacific Northwest.
The two-way table shows some of the animals carved in the totem poles and the
regions where the totem poles are located.
Thandi states that 20% of Alaskan totem poles featured in the book have eagles carved
in them. Use the drop-down menus to explain and correct Thandi's error.
Alaska
British
Columbia
Total
Eagle
5
7
12
Totem Poles
Y
Bear
3
2
5
Wolf
2
6
8
Click the arrows to choose an answer from each menu.
Thandi may have found the percent of the total totem poles that
have eagles and are in Alaska
eagles carved in them is Choose....
Total
10
15
25
The actual percent of Alaskan totem poles that have
According to the information in the graph, it can be inferred that Thandi is wrong because the eagle totems are not equivalent to 20% of the totems in Alaska.
How to find Thandi's error?To find the Thandi error we must perform the following mathematical operation.
5 + 3 + 2 + 10 = 20
20 / 100 = 0.2
0.2 * 20 = 4
According to the above, it can be inferred that the 5 totems represent more than 20% of the totems in Alaska, since 20% is equivalent to 4 totems. Actually, the 5 totems represent 25%.
Note: This question is incomplete. Here is the complete information:
graph attached
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please help me with math i’ll give you brainlist
Please help me with this question.
The solution of the given differential initial value problem is
y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6).
What is initial value problem?In multivariable calculus, an initial value problem is an ordinary differential equation together with an initial condition which specifies the value of the unknown function at a given point in the domain.Given is the initial value problem -
y''' + 10y'' + 25y' = 0
We can write the -
[tex]$25 \frac{d}{d x} y{\left(x \right)} + 10 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = 0$[/tex]
The given differential equation can be solved and written as -
y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6)
Therefore, the solution of the given differential initial value problem is
y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6).
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The product of any two counting numbers is divisible by 2.
Question content area bottom
Part 1
Choose the correct answer below.
A.
248, which is not divisible by 2.
B.
3515, which is not divisible by 2.
C.
3412, which is not divisible by 2.
D.
236, which is not divisible by 2.
Number which is not divisible by 2 = 3515
The correct option is B.
What is division?The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups.
Given,
Product of two numbers is divisible by 2.
Given products of numbers
248, 3515, 3412, 236
Numbers divisible by 2 should end with 2, 4, 6, 8, 0
3515 is the number that end with 5, not with 2, 4, 6, 8, 0.
Hence, 3515 is not divisible by 2.
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the following are final scores of an algebra class of 20 students in a high school: 79 74 42 88 81 64 98 78 85 53 77 66 76 52 80 60 77 90 86 77 find the q1 using r.
The first quartile of the final scores of an algebra class of 20 students is 65.5.
Given, the final scores of an algebra class of 20 students in a high school: 79 74 42 88 81 64 98 78 85 53 77 66 76 52 80 60 77 90 86 77.
We know that Q1 means the first quartile is called the .25 quartile and for n data points, there will be p quantiles which will occur at the position 1+(n−1)p ( p represents the quartile)
Here the sorted data is
42 52 53 60 64 66 74 76 77 77 77 78 79 80 81 85 86 88 90 98
Q1 position = 1+(n-1)p = 1+(20-1)(0.25) = 5.75
This is 3/4 of the way between the 5th and 6th number which is
= 64 + .75*(66-64)
= 65.5
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Translate the following sentence into and algebraic inequality
The quotient of a number, x, and nine is less than eight more than the product of five and the same number x
the answer is
x/9 < 8 + 5x
Write equations for the horizontal and vertical lines passing through the point (6, 1).
horizontal line:
vertical line:
Answer:
horizontal y=1
vertical x=6
Answer:
see below
Step-by-step explanation:
horizontal line:y=1 cause on this line y is always 1 regardless what x is
vertical line: x=6 cause on this line x is always 6 regardless what y is
the angle of elevation to the top of a building in new york is found to be 5 degrees from the ground at a distance of 2 miles from the base of the building. using this information, find the height of the building in feet. (hint: 1 mile
The height of the building will be 897.6 feet if the angle of elevation is 5 degree and distance is 2 miles.
The height, length of angle of elevation and the base of the triangle will form the right angled triangle. Thus, to find the height, we will use the formula -
tan theta = perpendicular ÷ base, where theta is the angle of elevation.
Now, keep the values in formula to find the height of the building.
height = tan 5 × 2
Keep the value of angle
height = 0.087 × 2
Performing multiplication on Right Hand Side of the equation
height = 0.17 mile
As per the known information, 1 mile = 5280 feet
So, 0.17 mile = 897.6 feet
Thus, the height of building is 897.6 feet.
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What is the measure of Arc CB?
84
60
90
67
Answer:
60°.
Step-by-step explanation:
1. DB is diametre, then
2. m∠BCD=90°, then
3. m∠BDC=m∠BCD-m∠CBD=90-60=30°, then
4. finally, Arc(CB)=2*m∠BDC=60°.
a recent study asked u.s. adults to name 10 historic events that occurred in their lifetime that have had the greatest impact on the country. the most frequently chosen answer was the september 11, 2001, terrorist attacks, which was included by 76% of the 2025 randomly selected u.s. adults. construct and interpret a 95% confidence interval for the proportion of all u.s. adults who would include the 9/11 attacks on their list of 10 historic events.
The confidence interval is (0.7414,0.7786) and the margin of error is 0.0186.
From the given data n=2025
[tex]\tilde{p}[/tex]=76%=0.76
Confidence Level =0.95
The sample proportion is a random variable: it varies from sample to sample in a way that cannot be predicted with certainty. Viewed as a random variable it will be written [tex]\tilde{p}[/tex].
[tex]$\widehat{p}=\frac{x}{n}$[/tex] (Sample Proportion)
[tex]$E=Z_{\alpha / 2} \times \sqrt{\frac{\rho(1-\bar{p})}{n}}$[/tex](Margin of Error)
[tex]$(\widehat{p}-E, \widehat{p}+E)$[/tex] (Confidence Interval)
Random Selection: This is satisfied as US adults are selected randomly.
- Less than 10% population: Adults are less than 10% of US adults. This condition is satisfied.
The [tex]$$n \bar{p}$[/tex] and [tex]$n(1-\tilde{p})$[/tex] must be[tex]$\geq 10$[/tex] : Here [tex]$n \widehat{p}[/tex]=2025×0.76=1539 [tex]\geq 10$[/tex]and [tex]$n(1-\hat{p})[/tex]=2025×(1-0.76) =486 [tex]\geq 10$[/tex] which is met. This condition is also satisfied.
All conditions are met.
Calculation
Confidence level is 0.95
Level of significance is a=0.05
[tex]$\mathrm{Z}_{\mathrm{c}}=\mathrm{Z}_{\mathrm{a} / 2}$[/tex] critical value=1.96
Margin of error is
[tex]$$E=1.96 \times \sqrt{\frac{0.76(1-0.76)}{2025}}$$[/tex]
Confidence interval is (0.76-0.0186,0.76+0.0186)
=(0.7414,0.7786)
E=0.0186
Therefore, the confidence interval is (0.7414,0.7786) and Margin of error is 0.0186
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Please help me with this
Extra points n
The Equation for the phrase is 2(x + 9) = x/2.
What is the equation?
An equation is a mathematical statement having two algebraic expressions each side of the "equal to (=)" sign. It shows that the expressions written on the left and right sides have an equal relationship. Any mathematical equation is not one if its statement has no "equal to" symbol. It will be considered as a phrase.
Given the expression 9 is half a number and two times the sum of a number,
The phrase begins, "two times the number and nine,"
The equation will be if the number is x.
2(x + 9)
The second phrase is only half as many as the first.
x/2
resulting equation is
2(x + 9) = x/2
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Show me your work!
Divide: 2 3/4 / 1 1/2
A) 1 2/3
B) 1 5/6
C) 1 1/4
D) 2 5/6
Answer:
[tex]B) 1\dfrac{5}{6}[/tex]
Step-by-step explanation:
Fraction division:Convert mixed fraction to improper fraction.
[tex]2\dfrac{3}{4}=\dfrac{11}{4}\\\\\\1\dfrac{1}{2}=\dfrac{3}{2}[/tex]
Use KCF method
Keep the first fraction.Change division to multiplication. Flip the second fraction.[tex]\sf \dfrac{11}{4} \ \div \ \dfrac{3}{2}=\dfrac{11}{4}*\dfrac{2}{3}[/tex]
[tex]\sf =\dfrac{11}{2*3}\\\\\\=\dfrac{11}{6}\\\\=1\dfrac{5}{6}[/tex]
3. i just graduated from school with $25,000 worth of debt. i want to know what my monthly payment is going to be. i was able to finance it over 7 years at 6%.
If i just graduated from school with $25,000 worth of debt. The monthly payment if you were able to finance it over 7 years at 6% is: $359.44.
How to find the monthly payment?Using the loan payment formula to find the monthly payment
Payment = Loan Amount× (Interest Rate / 12) / (1 - (1 + (Interest Rate / 12))^- (Number of Payments))
Plugging in the values:
Payment = $25,000× (0.06 / 12) / (1 - (1 + (0.06 / 12))^- (12 × 7))
Payment = $359.44
Therefore the monthly payment is $359.44.
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Use +, -, x and to write an equation which gives an answer of 7. Put in brackets if necessary. 4( )4( )4( )4( )4=7
PLEASE HELP
(10 points)
The equation that gives the answer as 7 is 4 (×) 4 (-) 4 (÷) 4 = 7.
What are mathematical operations?Subtraction and Addition
Many problems in everyday life can be resolved using addition and subtraction. Simply said, the mathematical terminology for "combining" and "taking away" are addition and subtraction. When we combine or increase, we are adding. We take away or decrease when we subtract.
Multiplication is another operation that shares the commutative characteristic. Similar to addition and subtraction, multiplication and division have opposing purposes. While division is intended to demonstrate the dividing or subdividing of a value into smaller groups, multiplication serves the purpose of representing numerous groups of a single value.
4 (×) 4 (-) 4 (÷) 4 = 7
Hence, the equation that gives the answer as 7 is 4 (×) 4 (-) 4 (÷) 4 = 7.
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A rectangular flag is 24 ft long and 18 ft wide. If a triangle is cut out of the center of the flag that has base of 7ft and a height of 14ft, what was is the remaining area of the flag?
The remaining area of the flag is 383 ft²
What is area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
Given that, a rectangular flag is 24 ft long and 18 ft wide. If a triangle is cut out of the center of the flag that has a base of 7ft and a height of 14ft, we need to find the remaining area of the flag,
To find the remaining area of the flag, we will subtract the area of triangle from the area of rectangle,
Area of a rectangle = length × width
Area of a triangle = 1/2 × base × height
Therefore,
The remaining area = 24 × 18 - 1/2 × 7 × 14
= 432 - 49
= 383 ft²
Hence, the remaining area of the flag is 383 ft²
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Please help me with this question.
We can see here that using a property of equality, we have:
The teacher's requirement that x be on the left side of the equals sign in the answer 5=x supported by mathematical principles. According to the symmetric property of equality, x = 5 equals x = 5, If x=5 equals 5 = x, so the two forms are equivalent.
What is property of equality?The properties of equality are mathematical rules that apply to any equation of the form a = b. There are several properties, including:
Reflexive property: a = a for any value of a.Symmetric property: if a = b, then b = a.Transitive property: if a = b and b = c, then a = c.Additive property: if a = b, then a + c = b + c.Multiplicative property: if a = b, then a * c = b * c.These properties allow us to manipulate and simplify equations, and to determine if two equations represent the same relationship between variables.
According to the Symmetric property of equality, x = 5 is equal to 5 = x. This property states that for any equation a = b, both sides can be exchanged to form the equation b = a. In this case, exchanging the sides of the equation x = 5 results in 5 = x, showing that both forms represent the same mathematical relationship.
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help meeeeeeeeeee!!! pleaseeee
Answer:
1/216
Step-by-step explanation:
(1/6)^3 is equal to 1/6 x 1/6 x 1/6 which is equal to 1x1x1/6x6x6.
You can simplify that, 1x1x1=1 and 6x6=36 and 36x6 is 216.
Therefore, the answer is 1/216.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{(\dfrac{1}{6})^3}[/tex]
[tex]\mathsf{= \dfrac{1}{6}\times\dfrac{1}{6}\times\dfrac{1}{6}}[/tex]
[tex]\mathsf{= \dfrac{1\times1\times1}{6\times6\times6}}[/tex]
[tex]\mathsf{= \dfrac{1\times1}{36\times6}}[/tex]
[tex]\mathsf{= \dfrac{1}{216}}[/tex]
[tex]\huge\text{Therefore your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{\dfrac{1}{216}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
an air conditioning system can circulate 530 cubic feet of air per minute. how much cubic yards of air can it circulate per minute?
Type your answer as decimal or integer
Answer:
below
Step-by-step explanation:
In a cubic yard there are 3 x 3 x 3 = 27 ft^3
540 ft^3 / 27 ft^3/yd^3 = 20 yd^3
Ariana is a songwriter who collects royalties on her songs
whenever they are played in a commercial or a movie. She
will earn $30 every time one of her songs is played in a
commercial and she will earn $110 every time one of her
songs is played in a movie. Ariana earned a total of $620
in royalties dn 10 commercials and movies. Write and
solve a system of equations to determine the number of
commercials and the number of movies on which her songs
were played.
number of commercials:
number of movies:
The songs played in movie is 4 and that of in commercial is 6
What is a system of equations?A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Given that, Ariana earns $30 every time one of her songs is played in a
commercial and she will earn $110 every time one of her songs is played in a movie. She in total earned $620 and in total 10 songs are played,
Let the songs played in movie be x and that of in commercial be y,
Therefore, establishing a system of equations to determine the number of commercials and the number of movies on which her songs were played.
x + y = 10
x = 10-y.....(i)
110x + 30y = 620......(ii)
Put eq(i) in eq(ii)
110(10-y) + 30y = 620
1100 - 110y + 30y = 620
80y = 480
y = 6
Put y = 6 in eq(i)
x = 10-6
x = 4
Hence, the songs played in movie is 4 and that of in commercial is 6
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