When some software companies develop software, they do it with "planned obsolescence"
in mind. This means that they plan on the sale of the software to rise, hit a point of
maximum sales, then drop and eventually stop when they release a newer version of the
software. Suppose a graph of the curve showing the number of sales over time can be
modeled with a parabola and that the company plans on the "life span" of its product to be
6 months, with maximum sales reaching 1.5 million units. Write an equation that models
this situation.
Answers
The equation of the parabola that models the given situation is y = [tex]\frac{-1}{6}(x-3)^{2}[/tex] + 1.5.
Define parabola and its types.A parabola is a roughly U-shaped mirror-symmetrical plane curve. It corresponds to a number of seemingly unrelated mathematical descriptions that all define the same curves.
To represent a parabola algebraically in the coordinate plane, the standard equation of a parabola is used. The general equation of the parabola is given by y = [tex]a(x-h)^{2}[/tex]+ k or x = [tex]a(y-k)^2[/tex] +h, where (h,k) denotes the vertex. A regular parabola's standard equation is [tex]y^2[/tex] = 4ax.
Now, the equation of parabola for the given situation is calculated as:
y = [tex]a(x-3)^2[/tex]+ 1.5
Now, put the value of x = 0 and y = 0.
0 = [tex]a(0-3)^2[/tex]+ 1.5
0 = 9a + 1.5
-9a = 1.5
a = - 1.5/9
a = -1/6
Now, put the value of a in equation y = [tex]a(x-3)^2[/tex]+ 1.5 to obtain:
y = [tex]\frac{-1}{6}(x-3)^{2}[/tex] + 1.5.
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Related Questions
What is the slope of segment AB?
Answers
answer:
3/8
explanation:
(m/n)
count units from point a and b vertically, that is m.
count units from point a and b horizontally, that is n.
A gardener is planting flowers and would like for them to be in even rows. he has 24 rose bushes and 28 tulips. what is the greatest number of plants he can have in each row to keep the rose bushes and tulips in their own rows?
Answers
The required solution is,
1. Gardner can put a maximum of 4 flowers in each row
2. At 150 minutes both the student will meet each other
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
1. For the planting of trees in even rows,
The greatest number of plants he can have in each row to keep the rose bushes and tulips in their own rows,
Taking HCF of number of plants 24 and 28
HCF of 24 and 28 is 4
Thus, Gardner can put a maximum of 4 flowers in each row.
2.
Time taken by the first student to complete one lap is 25 minutes,
So,
1 lap = 25 minute
1 minute = 1 / 25 lap
For the second student,
1 lap = 30 minute
1 minute = 1/30 lap
At time x minute both will meet each other,
x/25 -x/30 = 1
5x/750 = 1
x = 750/5
x = 150 minute
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Answer:
4
Step-by-step explanation:
The length of each side of the base of a regular octagonal prism is 6 inches, and the height is 11 inches. Find the lateral area.
Answers
The lateral area of the regular octogonal prism is 528 square inches.
How to determine the lateral area of a regular octogonal prism
Regular octogonal prisms has two regular octogonal base sides and eight rectangular lateral sides. In this problem we must look for the sum of the areas of the eight rectangular lateral sides, where each area is equal to the product of base side (l) and height (h), both in inches. Then,
A = l · h
A = (6 in) · (11 in)
A = 66 in²
A' = 8 · A
A' = 8 · (66 in²)
A' = 528 in²
The lateral area of the regular octogonal prism is 528 square inches.
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lincoln high wants to estimate the number of seniors who plan to go to a 4-year college. answer the following.
Answers
(1) Option A (25 glee club members are randomly selected; 16 plan to go to a 4-year college.) would probably best represent the entire population of seniors.
(2) 416 seniors would be planning to attend a four-year university, by unitary method.
What is unitary method?A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.
Now,
(1) Since Option A has a larger fraction ([tex]\frac{16}{25} > \frac{14}{25} > \frac{13}{25}[/tex]), it is probably the only one that best represents the majority of the people.
(2) As seen from Part (1),
Out of 650 seniors, around 416 will go to a 4-year college as, by unitary method:
For every 25 members, 16 plan to go to 4-year college
For every 650 members, [tex]\frac{16}{25}(650)=416[/tex] will plan to go to 4-year college.
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(COMPLETE QUESTION:
Lincoln High wants to estimate the number of seniors who plan to go to a 4-year college. 1) Which of the following surveys probably would best represent the entire population of seniors? a) 25 glee club members are randomly selected; 16 plan to go to a 4-year college. b) 25 honor roll students are randomly selected from the senior class; 14 plan to go to a 4-year college. c) 25 seniors are randomly selected; 13 plan to go to a 4-year college. 2) There are 650 seniors at Lincoln High. Using your answer from part (a), estimate the number of seniors who plan to go to a 4-year college.)
O Caden is paid 6.5% commission on his
sales or a salary of $185, whichever is
higher. Find his earnings if his sales are
$3.790.
Answers
Answer:
Do you have a picture or anything to show the problem? I am having a hard time understanding what you have wrote.
Step-by-step explanation:
The length and width of a rectangle are consecutive odd integers. The perimeter is 120 120 meters. Find the length and width
Answers
Answer: Width= 29 meters & Length= 31 meters
Step-by-step explanation:
Let, width= x and Length= x+2
Perimeter= 120 meters
Now, 2{x+(x+2)}= 120
⇒ x= 29
Width= 29 meters
Length= 31 meters
w + 5w + 4 = 3(2w − 1)
Answers
Answer:
my result is 0 = -7 It has no solutions though since it is a contradiction
w + 5w + 4 = 3(2w - 1)
Now, let’s combine like terms:
6w + 4 = 3(2w - 1)
Now, let’s distribute:
6w + 4 = 6w - 3
Our next step is to isolate the variable on the left side. To do so, we can subtract 4 from both sides:
6w + (4 - 4) = 6w - 3 - 4
Now, we can simplify:
6w = 6w - 7
Let’s subtract 6 from all sides:
6w - 6w = 6w - 7 - 6w
0 = 0 - 7
0 = -7
This expression has no solutions; 0 will never equal -7. Hence, we have no solutions.
f(x)=−x
2
+8x+14
\text{Find }f(-8)
Find f(−8)
Answers
The value of the function f(-8) if f(x) = -x^2 +8x + 4 is f(-8) = -124
How to evaluate the function?The equation of the function is given as
f(x) = -x^2 +8x + 4
The expression f(-8) means that x = -8
So, we have:
f(-8) = -(-8)^2 + 8(-8) + 4
Evaluate the exponent and the product
f(-8) = -64 - 64 + 4
Evaluate the sum and the difference
f(-8) = -124
Hence, the value of the function f(-8) if f(x) = -x^2 +8x + 4 is f(-8) = -124
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What is the slope of the line represented by the equation y = x-31
3?
O-3
10 - 1/2
5
O 3
Answers
Answer:
slope = 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = x - 31 ← is in slope- intercept form
with slope m = 1
the arithmetic sequence 1, .25, blank, -1.25, blank
Answers
The complete arithmetic sequence is 1, .25, -0.5, -1.25, -2
How to complete the arithmetic sequence?The arithmetic sequence is given as:
1, .25, blank, -1.25, blank
Replace the blanks in the arithmetic sequence with x and y
So, we have:
1, .25, x, -1.25, y
An arithmetic sequence has a common difference (d)
The common difference is calculated using
d = T2 - T1
So, we have
d = 0.25 - 1
d = x - 0.25
d = y + 1.25
Substitute d = x - 0.25 in d = 0.25 - 1
x - 0.25 = 0.25 - 1
This gives
x = 0.25 + 0.25 - 1
Evaluate the sum
x = -0.5
Substitute d = 0.25 - 1 in d = y + 1.25
0.25 - 1 = y + 1.25
This gives
y = 0.25 - 1 - 1.25
Evaluate
y = -2
Hence, the complete arithmetic sequence is 1, .25, -0.5, -1.25, -2
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a car is moving at a rate of 65 miles per hour, and the diameter of its wheels is 2 feet. (a) find the number of revolutions per minute the wheels are rotating.
Answers
The revolution per minutes of the wheels rotation is 912 rev/ min
How to determine the number of revolutionsGiven the parameters;
Velocity = 65 miles per hourDiameter = 2 feetConvert the velocity
[tex]v = 65mph = 65 mil/h - (1609m/mil0/(3600s/h)[/tex]
v = 29. 1 m/s
Let's find the circumference
Circumference = 2 π r
radius = diameter/ 2 = 0. 6096 meters/ 2 = 0. 30 meters
Circumference= 2 × 3. 142 × 0. 30 = 1. 915
Number of revolutions = 29. 1/ 1. 915 = 15.2 rev/ sec
Let's convert to rev/ min
= 15. 2 × 60
= 912 rev/ min
Thus, the revolution per minutes of the wheels rotation is 912 rev/ min
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How did the values compare the greatest 1/4 -1 1/4 -2 1/4 -1 3/4 -2 1/4
Answers
The values compared to the greatest :
-2 1/4,-1 1/4,-1 3/4, 1/4
Comparing and ordering fractions is an essential part of developing a sense of numbers. This is also an essential skill to have when facing practical questions, such as:
"Would you like to have {\displaystyle {\frac{3}{4}}}{\frac{3}{4 }} d 'a pizza does not, or {\displaystyle {\frac{6}{7}}}{\frac{6}{7}} of a pizza?" There are several ways to compare and order fractions. If you have a calculator, the fastest way is to convert fractions to decimals. If you don't have a calculator, you can make comparisons easily by finding a common denominator or simply using your reasoning skills and what you already know about fractions.
In this way, the given fractions are compared from largest to smallest
-2 1/4,-1 1/4,-1 3/4, 1/4
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If two adjacent angles of a parallelogram are (5x-5) and (10x+35),then find the ratio of these angle’s
Answers
Answer:
Ratio= 45/135 = 1/3 = 1:3
Step-by-step explanation:
Look at the attachment
Question 2 (2 points)
Charles is paid $3.75 per hour plus time and a half on holidays and makes an average of 15% tips on his food sales as a server at the local
seafood restaurant.
This is modeled by the expression 3.75(x) +3.75(1.5)(y) +0.15(z).
What is Charles' gross pay if he worked 25 regular hours and 5 holiday hours and had $1,915 in food sales?
O a
Ob
Oc
Od
$121.88
$399.75
$409.13
$446.63
Answers
Considering the function for his salary, his gross pay is of $409.13.
What is the function for his gross pay?His gross pay is modeled by the following function:
P(x,y,z) = 3.75x + 3.75(1.5)y + 0.15z.
In which:
x is the number of regular hours.y is the number of holiday hours.z is his earnings in food sales.For this problem, the parameters are given as follows:
x = 25, y = 5, z = 1915.
Hence his pay is given by:
P(25,5,1915) = 3.75(25) + 3.75(1.5)(5) + 0.15(1915) = $409.13.
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The length and width of a rectangle are consecutive odd integers. The perimeter of the rectangle is 80 centimeters. Find the length and width of the rectangle.
Answers
The length and width of the rectangle are 21cm and 19cm.
How to calculate the value?Let the dimensions be represented by x and x+2.
The perimeter of a rectangle is:
= 2(length + width)
= 2(x + x+2) = 80
2x + 2x + 4 = 80
4x + 4 = 80
4x = 80 - 4
4x = 76
Divide
x = 76/4
x = 19
Therefore, the second number will be:
= 19 + 2 = 21
The numbers are 19 and 21.
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Perform the following operation
and express the answer in
scientific notation.
4.3x1027.0×10²
[?]×10]
Answers
Answer:
[tex]4.4161 \times 10 ^{2} [/tex]
[tex]4.3 \times 1027 \times 10 { \\ \\ }^{2} [/tex]
[tex]4416.1 \times 10^{2} [/tex]
[tex]4.4161 \times 10 ^{2} [/tex]
-4 1/3 divided by 2 1/5
Answers
Answer: -1.9696969696969696969696
Step-by-step explanation:
Answer:
Exact form: -65/33
Decimal form: -1.96
Mixed number: - 1 32/33
Step-by-step explanation:
Bro help me this is 100 points
Answers
Answer: 145 minutes ==> 3rd option
Step-by-step explanation:
2*(45-10)+3*(30-5)=
2*35+3*25=
70+75=145 minutes ==> 3rd option
Answer:
145
Step-by-step explanation:
45 × 2 = 90
10 × 2 = 20
90 - 20 = 70
70
30 × 3 = 90
5 × 3 = 15
90 - 15 = 75
75
70 + 75 = 145
145
on a number line, suppose point e has a coordinate of , and eg. what are the possible coordinates of point g? question content area bottom part 1 the possible coordinates for g are
Answers
The possible coordinates of point G on this number line are either -10 or 14.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.
Given the following data:
E = 2.
EG = 12.
On this number line, the coordinate of EG is given by this mathematical expression:
EG = |E - G|
Substituting the given parameters into the expression, we have;
12 = |2 - G|
2 - G = ±12
G = 2 ± 12
Simplifying and evaluating the above expression, we have:
G = 2 + 12
G = 14.
OR
G = 2 - 12
G = -10
Therefore, the possible coordinates of point G on this number line are either -10 or 14.
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Complete Question:
On a number line, suppose point E has a coordinate of 2, and EG= 12. what are the possible coordinates of point G?
the lengths of plate glass parts are measured to the nearest tenth of a millimeter. the lengths are uniformly distributed with values at every tenth of a millimeter starting at 590.1, and continuing through 590.9. determine the mean and variance of the lengths. (a) mean round your answer to two decimal places (e.g. 98.76). (b) variance round your answer to three decimal places (e.g. 98.765)
Answers
The mean and variance of the lengths are 590. 50 and 0. 075 respectively
How to determine the valuesGiven that the lengths are;
590.1, 590. 2, 590. 3, 590. 4, 590. 5, 590. 6, 590. 7 , 590. 8, 590. 9
Mean = sum of terms/ number of terms
Mean = 590.1 + 590. 2 + 590. 3 + 590. 4 + 590. 5 + 590. 6 + 590. 7 + 590. 8 + 590. 9/ 9
Find the sum of the numerator
Mean = 5314. 5/ 9
Mean = 590. 500
Variance = sum of the distances from the mean/ total number - 1
Variance = (590. 1 - 590. 5)² + (590. 2 - 590. 5)² + (590. 3 - 590. 5)² + (590. 4 - 590. 5)² + (590. 5 - 590. 5)² + (590. 6 - 590. 5)² + (590. 7 - 590. 5)² + (590. 8 - 590. 5)² + (590. 9 - 590. 5)² ÷ 9 - 1
Variance = 0. 16 + 0. 09 + 0. 04 + 0. 01 + 0 + 0. 01 + 0. 04 + 0. 09 + 0. 016 ÷8
Variance = 0. 6/ 8
Variance = 0. 075
Thus, the mean and variance of the lengths are 590. 50 and 0. 075 respectively
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The ninth-grade teachers at Lincoln High School are buying ice cream for an end-of-year ice
cream social. They estimate the 160 students will eat about 2 scoops of ice cream each. If
the average scoop of ice cream is 0.5 cups, how many gallons of ice cream should the
teachers buy?
Hint: There are 16 cups in 1 gallon.
Write your answer as a whole number, decimal, or simplified fraction. Do not round.
Answers
The teacher should buy 10 gallons of ice cream.
The total number of students is 160.The estimated number of scoops for each student is 2.The total number of scoops of ice cream required is the product of the total number of students and the estimated number of scoops per student.The total number of scoops of ice cream required is 160*2.The total number of scoops of ice cream required is 320.The number of cups filled by an average scoop of ice cream is 0.5.The total number of cups needed to accommodate 320 scoops of ice cream is 0.5*320.The total number of cups needed to accommodate 320 scoops of ice cream is 160.The number of gallons in 16 cups is 1.The number of gallons in 1 cup is 1/16.The number of gallons in 160 cups is 160*(1/16).The total number of gallons is 10.To learn more about numbers, visit :
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Answer:
The answer is 10
Step-by-step explanation:
Help me I’m giving brainiest
Answers
Distribute 2 through the parentheses
Move the variable to the left-hand side and change its sign
Collect like terms
Divide both sides by -4
ANSWER ( x= -2)
Answer:
x = - 2
Step-by-step explanation:
x - 3x = 2(4+x)
-2x = 2*4 + 2x
-2x = 8 + 2x
-2x - 2x = 8
-4x = 8
x = 8/-4
x = -2
Check:
-2 - (3*-2) = 2(4+(-2))
-2 - (-6) = 2(2)
-2 + 6 = 4
“What is the geometric relationship between the labels angles? What is the relationship of their measures? Then use the relationship to write an equation and solve for x!”
Answers
Using complementary and supplementary angles, we have that:
c. The angles are complementary, hence the equation is 4x - 3 + 2x + 1 = 90 and the solution is x = 15.33.
d. The angles are supplementary, hence the equation is 43x + 16 + 110 = 180 and the solution is x = 18.
What are complementary angles?When the measures of two angles add to 90º, the angles are complementary.
This is the case in item c, hence:
4x - 3 + 2x + 1 = 90
6x = 92
x = 92/6
x = 15.33.
What are supplementary angles?When the measures of two angles add to 180º, the angles are supplementary.
This is the case in item d, hence:
3x + 16 + 110 = 180.
3x = 54
x = 54/3
x = 18.
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a set of 25 square blocks is arranged into a $5 \times 5$ square. how many different combinations of 3 blocks can be selected from that set so that no two are in the same row or column? (a) 100 (b) 125 (c) 600 (d) 2300 (e) 3600
Answers
A set of 25 blocks are arranged into 5×5 square, different combination of 3 blocks such that no two are in same column or row is 3600.
As given,
Set of 25 blocks arranged into 5×5 square.
Arrange 3 blocks
Delete column and row belong to filled block
Possibility for
First block =25 ways
Second block=16 ways
Third block =9 ways
Total ways =25×16×9
=3600
Therefore, set of 25 blocks are arranged into 5×5 square, different combination of 3 blocks such that no two are in same column or row is 3600.
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A rectangular pool is 9 meters wide and 11 meters long. If you swim diagonally from one corner to the other, how many meters will you swim? Approximate the answer to the nearest tenth.
A: 1.4 meters
B: 4.3 meters
C: 6.3 meters
D: 14.2 meters
Answers
The answer choice which represents the length to swim diagonally and expressed to the nearest tenth as required in the task content is; Choice D; 14.2 meters.
What is the length to swim diagonally in the rectangle as described in the task content?It follows from the task content that the pool in discuss is rectangular and hence, the diagonal of the rectangle makes a right triangle with two perpendicular sides of the rectangle.
Hence, from Pythagoras theorem; we have;
hyp² = opp² + adj²
Hence,
D² = 9² + 11²
D² = 81 + 121
D² = 202
D = √202
D = 14.2 rounded to the nearest tenth.
Therefore, The answer choice which represents the length to swim diagonally and expressed to the nearest tenth as required in the task content is; 14.2 meters.
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Write an expression to represent Vivian's change in elevation from -9.6 feet at the bottom of the Ferris wheel to 12.3 feet at the top.
Answers
The change in the elevation from the bottom of the Ferris is 21.9 feet.
What is defined as the change in elevation?Elevation change refers to the difference in elevation between the beginning and end of your route.
Given that the distance travelled by Vivian just at bottom of the elevation is -9.6 feet.
The distance traveled by Vivian at the top of the elevation is 12.3 feet.
Vivian's shift in elevation would be expressed as the difference between the elevations at the bottom and top.
Let Ei be the initial elevation of -9.6 feet.
Ef = 12.3 feet as the final elevation
Change in elevation;
ΔE = Ef - Ei
ΔE = 12.3 - (-9.6)
ΔE = 12.3 + 9.6
ΔE = 21.9 feet
Therefore, the change in the elevation is found to be 21.9 feet.
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5×62+6×33-68 (help pls I need it
Answers
Answer:
440
Step-by-step explanation:
To do this problem, you have to follow the PEMDAS order.
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
We have to do 5x62 first, which is 310. Next, we multiply 6 and 33, which gets us 198. Then, we add 310 to 198, which is 508. Finally, we subtract 68 from 508 to get 440.
Hope this helps!
Have a wonderful day! :D
First multiple 62x5 by using calculator then add that total with 6 then multiple with the result u got by 33 then subtract-that total with 68. And u will get answer 440
3. juan lies on the ground 45 feet from his tent. the tent is 400 feet from the base of a tall cliff. both the top of the tent and the top of the cliff are in his line of sight. if juan's tent is 10 feet tall, how tall is the cliff?
Answers
The cliff is 98.89 feet tall.
In the attached diagram, we can there are two triangles forming. Small triangle involves Juan and tent and larger triangle involves Juan and cliff. As per the known fact, tan theta = perpendicular ÷ base. So, tan theta will be common for both the triangles. Hence, relating the components of tan theta, of both the triangles.
Smaller triangle :
tan theta = 10/45
Larger triangle :
tan theta = h/(400 + 45)
tan theta = h/445
Relating both the triangles as follows -
10/45 = h/445
Performing cross multiplication
10×445 = h×45
h = 4450÷45
h = 98.89 feet
Hence, the cliff is 98.89 feet tall.
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write the slope-intercept form of the line described
11) through: (5,5), parallel to y = 8/5x + 5
Answers
Answer:
y=8/5x-3
Step-by-step explanation:
y-5=8/5(x-5)
y-5=8/5*x-8/5*5
y-5=8/5x-(8*5/5)
y-5=8/5x-(40/5)
y-5=8/5x-8
+5 +5
y=8/5x-3
Hope this helps.
QUESTION 11:
Consider the graphed function. Based on its end behavior, which of the following could be its equation? (photo attached below):
A) f (x)= x^3 + 6x^2-5x
B) f (x)= -x^4 +6x^3 - 5x^2
C) f (x)= x^4 +6x^3-5x^2
D) f (x)= -x^3+ 6x^2-5x
QUESTION 12:
Divide x2 by x – 1. What is the value of the remainder?
A) 0
B) 1
C) -1
D) 2