The rate of decrease in the revenue reduces each year, resulting in an
approximate quadratic equation model that is concave upwards.
The variables are;
x = Number of years since 2,000
y = Revenue for physically recorded music in millions of dollars
Find out -
To model the decline using a quadratic equation.
The general form of the quadratic equation is; y = a·x² + b·x + c
When y = 5547, x = 8
We get;
5547 = a·8² + b·8 + c = 64·a + 8·b + c
5547 = 64·a + 8·b + c...(1)
When y = 3113, x = 11
We get;
3113 = a·11² + b·11 + c = 121·a + 11·b + c
3113 = 121·a + 11·b + c...(2)
When y = 2056, x = 14
We get;
2056 = a·14² + b·14 + c = 196·a + 14·b + c
2056 = 196·a + 14·b + c...(3)
Subtracting equation (2) from equation (1) gives;
5547 - 3113 = 64·a + 8·b + c - (121·a + 11·b + c) = -57·a - 3·b
2434 = -57·a - 3·b...(4)
Subtracting equation (3) from equation (2) gives;
3113 - 2056 = 121·a + 11·b + c - (196·a + 14·b + c) = -75·a - 3·b
1057 = -75·a - 3·b...(5)
Subtracting equation (5) from equation (4) gives;
2434 - 1057 = -57·a - 3·b - (-75·a - 3·b) = 18·a
1377 = 18·a
a = 76.5
From, equation (4), 2434 = -57·a - 3·b, we have;
2434 = -57 × 76.5 - 3·b
Therefore;
b = -2264.8
From equation (1), we get;
5547 = 64 × 76.5 + 8×(-2264.8) + c
Therefore;
c = 5547 - (64 × 76.5 + 8×(-2264.8)) = 18769.
c = 18769.
Therefore, the quadratic model is;
Verifying, we have in year 2012, x = 12
y = 76.5×12² - 2264.8×12 + 18769. = 2607.74
Thus ,the completed table and comparison of the predicted physical revenue and actual values is presented in the attachment;
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Perform the operation. Enter your answer in scientific notation.
3.8 x10^*3 + 7.1 x 10^*4=
Answer:
7.48 X 10^4
Step-by-step explanation:
Hope it helps!!
An icecream shop has 10 flavors. One can choose 4 different
flavors. What is the total number of possible flavor
combinations?
a.
252
b.
462
c.
120
d.
330
e.
210
2.
An ice cream shop has 10 flavors and one can choose 4 different flavors. The question asks for the total number of possible flavor combinations.Therefore, we need to find the number of ways in which 4 flavors can be chosen from 10 flavors.
In such cases where order does not matter and repetitions are not allowed, we can use the formula for combinations which is as follows:C(n, r) = n! / (r! (n - r)!)Where n is the total number of items, r is the number of items being chosen at a time and ! represents the factorial function.
Using this formula we can find the total number of possible flavor combinations. Substituting the values in the above formula, we get:C(10, 4) = 10! / (4! (10 - 4)!)C(10, 4) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)C(10, 4) = 210Hence, there are 210 possible flavor combinations when one can choose 4 different flavors
.Explanation:The formula to be used for this type of question is combination. Combination is the method of selecting objects from a set, typically without replacement (without putting the same item back into the set) and where order does not matter. The formula for combination is given by C(n,r)=n!/(r!(n-r)!).
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My penMath The area of a triangle can be found using the formula: Area = 1/2 · base · height. Find the area of the triangle pictured below, where the measurements are given in meters (m) 2 m 10 m
Answer:
The area of the given triangle is 10 sq meters
Explanation:
The area of a triangle is given by the formula:
Area = 1/2 base . height
Given that the triangle has base = 10m, and height = 2m
Area = 1/2 * 10 * 2
= 10 square meters
The black part of each graph represents the solution.
Answer:
x≤ -2
Step-by-step explanation:
we want black part, so we know it's going to be to the left of -2.
the black dot at -2 means we include -2. if it was just an unfilled dot (circle) we exclude -2 (ie it would just be ( < -2)
so answer is x≤ -2
If the dicounted price i $328, what i the original price if there wa a 40% dicount?
The Original Price = 547
What is Original Price?
The complete cost of purchasing an asset is known as the original cost. When calculating an asset's original cost, all of the costs associated with buying and using the asset are taken into account.
Given,
Discounted Price = $328
Discount = 40%
Let original price be 100% as the percentage
Then 100% - 40% = 60%
= $328 is 60% of what number?
let what no be x
= $ 328 = 0.60*x
= $ 328 / 0.60 = 0.60/0.60 n
n = $ 328/0.60
n = 547
So, the original Price will be 547
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Jessie has 8 more pencils than Dylan. Together they have a total of 18 pencils. How many pencils does Dylan have?
Answer:
10 pencils
Step-by-step explanation:
If they have 18 total pencils. Then 18-8=10. Just remember to just subtract ok? Study this it's very easy.
Answer: 5
Step-by-step explanation:
Together they have 18.
Jesse has 8 MORE, which means Dylan has 5.
PLEASE HELP WILL GIVE BRAINLIEST DO NUMBER 8
Answer:
Step-by-step explanation:
Answer:
the equation of yours is wrong. the equation would be y=1/3x.
Step-by-step explanation:
here's the graph. hope it helps.
what is 11 to the power of 8 over 11 to the power of 4 equivalent to
Answer:
14,641.
Step-by-step explanation:
214,358,881 ÷ 14,641 = 14,641.
Please answer quick thanks
Answer:
140
Step-by-step explanation:
They are the same on both sides
:)Hope you enjoy this:)7+5-3*2(6*7)/4
• convert the above specified infix expression into
postfix expression
• Evaluate the resulted postfix expression
• convert the specified infix expression into prefix
expres
The postfix expression of "7+5-3*2(6*7)/4" is "7 5 + 3 2 * 6 7 * 2 * - 4 /". Evaluating the postfix expression gives the result of the expression. The prefix expression for the given infix expression is "/ - + 7 5 * 3 * 2 ( * 6 7 ) 4".
To convert the infix expression "7+5-3*2(6*7)/4" into postfix expression, we follow the rules of operator precedence and associativity. The postfix expression is obtained by placing operators after their operands.
The postfix expression for the given infix expression is:
"7 5 + 3 2 * 6 7 * 2 * - 4 /"
To evaluate the postfix expression, we use a stack data structure. We scan the postfix expression from left to right and perform the corresponding operations.
Starting with an empty stack, we encounter the operands "7" and "5". We push them onto the stack. Then we encounter the operator "+", so we pop the last two operands from the stack (5 and 7), perform the addition operation (7 + 5 = 12), and push the result back onto the stack.
We continue this process for the remaining operators and operands in the postfix expression. Finally, after evaluating the entire expression, the result left on the stack is the final answer.
To convert the infix expression into prefix expression, we follow similar rules but scan the expression from right to left. The prefix expression is obtained by placing operators before their operands.
The prefix expression for the given infix expression is:
"/ - + 7 5 * 3 * 2 ( * 6 7 ) 4"
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Match the value to the correct image. Not all values will be used.
Find the approximate surface area of each right regular prism.
The approximate surface areas of corresponding prisms are listed below:
A = 108 units²A = 229 units²A = 454 units²How to match given surface areas with given figuresThe surface area of the each figure (\(A\)), in square units, is equal to the sum of the surface area of the two bases (\(A_{b}\)), in square units, and the surface areas of the lateral sides (\(A_{l}\)), in square units. Since bases are regular polygons, base surface area can be determined by this expression:
\(A_{b} = \frac{l^{2}\cdot n }{4\cdot \tan \frac{180}{n} }\) (1)
Where:
l - Side length, in unitsn - Number of sidesThe area of one lateral side is expressed by this expression:
\(A_{l} =h\cdot l\) (2)
Where h is the height of the rectangle, in units.
The total surface area is defined by the following formula:
\(A = 2\cdot A_{b} + n\cdot A_{l}\) (3)
Now we proceed to calculate each surface area:
Case I (\(l = 2\), \(n = 6\), \(h = 9\))\(A = 2\cdot \left[\frac{2^{2}\cdot (6)}{4\cdot \tan \left(\frac{180}{6} \right)} \right]+6\cdot (2)\cdot (9)\)
A = 108.136 units²
Case II (\(l = 4\sqrt{3}\), \(n = 3\), \(h = 9\))\(A = 2\cdot \left[\frac{(4\sqrt{3})^{2}\cdot (3)}{4\cdot \tan \left(\frac{180}{3} \right)} \right]+3\cdot (4\sqrt{3})\cdot (9)\)
A = 228.631 units²
Case III (\(l = 6\), \(n = 5\), \(h = 11\))\(A = 2\cdot \left[\frac{6^{2}\cdot (5)}{4\cdot \tan \left(\frac{180}{5} \right)} \right]+5\cdot (6)\cdot (11)\)
A = 453.874 units²
The approximate surface areas of corresponding prisms are listed below:
A = 108 units²A = 229 units²A = 454 units²To learn more on surface areas, we kindly invite to check this verified question: https://brainly.com/question/2835293
Answer:
Look at the picture
Let A = {2,4,6,8,10,12} B = {3,6,9,12,15,18} C = {0,6,12,18} Find C-A. none of the choices {2,3,4,6,8,9,10,12} O {2,4,8,10) {0,18}
the correct choice is {0, 18}. These elements are unique to set C and do not appear in set A.
To find the set difference C - A, we need to remove all elements from A that are also present in C. Let's examine the sets:
C = {0, 6, 12, 18}
A = {2, 4, 6, 8, 10, 12}
We compare each element of A with the elements of C. If an element from A is found in C, we exclude it from the result. After the comparison, we find that the elements 2, 4, 8, 10 are not present in C.
Thus, the set difference C - A is {0, 18}, as these are the elements that remain in C after removing the common elements with A.
Therefore, the correct choice is {0, 18}. These elements are unique to set C and do not appear in set A.
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Find the total amount
$17,600 at 16% compounded
quarterly for 2 years
Answer:
57,700.10
Step-by-step explanation:
To solve, we use the equation \(17,600(1.16)^8\)
we set it to the power of 8, since it is compounding quarterly this means it compounds 4 times a year, and since there is 2 years, we get 8 compounds.
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Hannah made four withdrawals of $20 from her checking account. She also
wrote a check for $215. By how much did the amount in her checking account
change?
(Show answer )
1) A bakery used one-sixth of a bag of chocolate chips to make 8 batches of cookies. How
much of the bag did they use for each batch?
Answer:
Step-by-step explanation:
1/6 ÷ 8
1/6 × 1/8
1/48
for each batch
Which region represents the solution to the given system of inequalities?
{+3y < -3
{ x > 3
Step-by-step explanation:
the answer is in the above image
use the app DESMOS it helps in drawing graphs like this
Indicate the level of measurement for the data set described. Number of classes taken in a semester by each student at a college Answer :a. Nominal b. Ordinal c. Interval d. Ratio
The correct answer is option c. Interval. The level of measurement for the data set described is Interval.
This is so because the data set calculates each student's enrollment in classes during the course of a semester at a particular college.
Numerical information that is measured on a scale with evenly spaced intervals but lacks an absolute zero point is called interval data.
The numerical values themselves do not reflect quantities or have any absolute value, but the intervals between them all have the same size.
The interval between 3 classes and 4 classes, for instance, would be the same as the interval between 8 classes and 9 classes if the data set were measuring the number of classes each student took in a semester, but 3 classes and 8 classes do not have any such absolute value.
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the number of students who bike to school is 5% of the number of students who walk. how many students bike to school
Steps for sloving 6(4x-3)=30 are shown
6(4x-3)=30 oringal equation
24x-18=30 step 1
24x-18+18=30+18 step 2
24x=48 step 3
24x=48
24 24 step 4
x=2
which of these are not a part of the solution?
Answer:
da part wich iznot in da solution iz step 4
Angle Sum Theorem
y = ?
Answer:
140°
Step-by-step explanation:
The exterior angle is equal to the sum of the 2 remote interior angles. (The 2 angles farthest from the angle on the outside of the triangle)
20 + 120 = 140
Answer:
y= 140
Step-by-step explanation:
first you find x by using the sum of angles in a triangle(180-120-20). so x is 40.and then you do 180-40 ( adjustment angles on a straight line. let me know if it makes sense.
Traveling south along the 180 °from 5° N to 5° S approximately how many nautical miles will you cover? A. 600 B. 300 C. 690 D. 345
The correct answer is A. 600 nautical miles is not the distance you will cover when traveling south along the 180° longitude from 5°N to 5°S. The correct distance is 0 nautical miles since the points are on the same line of longitude.
The distance traveled along a line of longitude can be calculated using the formula:
Distance = (Latitude 1 - Latitude 2) * (111.32 km per degree of latitude) / (1.852 km per nautical mile)
Given:
Latitude 1 = 5°N
Latitude 2 = 5°S
Substituting the values into the formula:
Distance = (5°N - 5°S) * (111.32 km/°) / (1.852 km/nm)
Converting the difference in latitude from degrees to minutes (1° = 60 minutes):
Distance = (0 minutes) * (111.32 km/°) / (1.852 km/nm)
Simplifying the equation:
Distance = 0 * 60 * (111.32 km/°) / (1.852 km/nm)
Distance = 0 nm
Therefore, traveling south along the 180° longitude from 5°N to 5°S, you will cover approximately 0 nautical miles.
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Use your birthday month and day only, and find the sum and the product and the difference, and quotient.
month is 3 and day is 11
Answer:
sum 14, difference -8, product 33, quotient 3/11
Step-by-step explanation:
Sum: add
3 + 11 = 14
Difference: subtract
3 - 11 = -8
Product: multiply
3 * 11 = 33
and quotient: divide
3 / 11
(we can leave it like this as a fraction)
21.(03.02)
If f(x) = 7x – 1, what does f(12) represent?
Answer:
83
Step-by-step explanation:
f(x) = 7x - 1
Put x as 12.
f(12) = 7(12) - 1
f(12) = 84 - 1
f(12) = 83
3. Find the measure of Arc BED. *
O 180 degrees
O142 degrees
O218 degrees
O 72 degrees
The measure of arc BED is:
180 degrees
How to find the measure of Arc BED?The arc of a circle is the segment or part of the circumference of a circle. The measure of an arc is the angle at which the arc is subtended.
You will notice that AD is the diameter of the circle.
Since the measure of arc CD is 90°.
Thus, the measure of arc AB is:
90 - 52 = 38°
Arc ED = arc AB (vertically opposite angles are equal)
Therefore, the measure of Arc BED will be:
Arc BED = Arc BC + arc CD + arc ED
Arc BED = 52° + 90° + 38°
Arc BED = 180°
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2^{2x}-5\cdot2^{x}+4=0
This is a polynomial in \(2^x\) that can be factorized:
\(2^{2x}-5\cdot2^x+4 = 0\)
\(\left(2^x\right)^2-5\cdot2^x+4=0\)
\(\left(2^x-4\right)\left(2^x-1\right)=0\)
\(2^x-4=0\text{ or }2^x-1=0\)
\(2^x=4\text{ or }2^x=1\)
Since 4 = 2² and 1 = 2⁰, you get the two solutions x = 2 and x = 0.
amelia rented a dvd and it was due to be returned on 26 novmeber
Answer:
Step-by-step explanation:
PLS HELP ASAP...Im lost
Answer:
With what, I don't see anything?
How do you convert 54 Celsius to Fahrenheit?
After converting from Celsius to Fahrenheit , we will get 54 Celsius is equivalent to 129.2 Fahrenheit.
To convert Celsius to Fahrenheit, you can use the following formula:
°F = (°C x 9/5) + 32
In this case, to convert 54 Celsius to Fahrenheit, we can substitute 54 for °C in the formula:
°F = (54 x 9/5) + 32
Simplifying this expression, we can first perform the multiplication and division:
°F = (97.2) + 32
Then we can add 97.2 and 32 to get the final answer:
°F = 129.2
It's worth noting that the Celsius and Fahrenheit scales are both used to measure temperature, but they have different starting points and different degrees of scale. Celsius is based on the freezing and boiling points of water, where 0 degrees Celsius is the freezing point and 100 degrees Celsius is the boiling point at sea level.
Fahrenheit, on the other hand, is based on a system of degrees devised by Gabriel Fahrenheit, with 32 degrees being the freezing point and 212 degrees being the boiling point at sea level.
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In the data set below, what are the lower quartile, the median, and the upper quartile?
1235588
lower quartile =
median = 5
upper quartile =
The lower quartile is 2, the median is 5 and the upper quartile is 8.
What are quartiles?
The values that divide a list of numerical data into three quarters are known as quartiles.
We are given a data set as 1, 2, 3, 5, 5, 8, 8
From this, we get the median as 5 as median is the middle number of the data set.
We know that lower quartile is the median of the lower half of the data.
So, lower quartile is 2.
Upper quartile is the median of the upper half of the data.
So, upper quartile is 8.
Hence, the lower quartile is 2, the median is 5 and the upper quartile is 8.
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How many elementary events are in the sample space of the experiment of rolling three fair coins? O2 09 O 8 6