Answer:
a) The model for the sales of Garmin is represented by [tex]S(t) = -\frac{81}{2500}\cdot t^{3} + \frac{267}{250}\cdot t^{2} - 11.9\cdot t + 47.112[/tex].
b) The average sales of Garmin from 2008 through 2013 were $ 2.5 billion.
Step-by-step explanation:
a) The model for the sales of Garmin is obtained by integration:
[tex]S(t) = -0.0972\int {t^{2}} \, dt + 2.136\int {t}\,dt -11.9 \int\,dt[/tex]
[tex]S(t) = -\frac{81}{2500}\cdot t^{3} + \frac{267}{250}\cdot t^{2} - 11.9\cdot t + C[/tex] (1)
Where [tex]C[/tex] is the integration constant.
If we know that [tex]t = 9[/tex] and [tex]S(t) = 2.9[/tex], then the model for the sales of Garmin is:
[tex]-\frac{81}{2500} \cdot 9^{3} + \frac{267}{250}\cdot 9^{2}-11.9\cdot (9) + C = 2.9[/tex]
[tex]C = 47.112[/tex]
The model for the sales of Garmin is represented by [tex]S(t) = -\frac{81}{2500}\cdot t^{3} + \frac{267}{250}\cdot t^{2} - 11.9\cdot t + 47.112[/tex].
b) The average sales of the Garmin from 2008 through 2013 ([tex]\bar{S}[/tex]) is determined by the integral form of the definition of average, this is:
[tex]\bar{S} = \frac{1}{13 - 8} \cdot \int\limits^{13}_{8} {S(t)} \, dt[/tex] (2)
[tex]\bar S = \frac{1}{5}\cdot \int\limits^{13}_{8} {\left[-\frac{81}{2500}\cdot t^{3} + \frac{267}{250}\cdot t^{2}-11.9\cdot t + 47.112 \right]} \, dt[/tex]
[tex]\bar S = \frac{1}{5}\cdot \left[-\frac{81}{10000}\cdot (13^{4}-8^{4}) +\frac{89}{250}\cdot (13^{3}-8^{3}) -\frac{119}{20}\cdot (13^{2}-8^{2}) +47.112\cdot (13-8) \right][/tex][tex]\bar{S} = \frac{1}{5}\cdot (-198.167+599.86-624.75+235.56)[/tex]
[tex]\bar{S} = 2.5[/tex]
The average sales of Garmin from 2008 through 2013 were $ 2.5 billion.
Solve for (0,2π]
2cos ß * sin ß = cos ß
Given :
An equation, 2cos ß sin ß = cos ß .
To Find :
The value for above equation in (0, 2π ] .
Solution :
Now, 2cos ß sin ß = cos ß
2 sin ß = 1
sin ß = 1/2
We know, sin ß = sin (π/6) or sin ß = sin (5π/6) in ( 0, 2π ] .
Therefore,
[tex]\beta = \dfrac{\pi}{6}\ or\ \beta = \dfrac{5\pi}{6}[/tex]
Hence, this is the required solution.
Please help!!! Here’s a picture of my question
Answer:
option no. D
Step-by-step explanation:
i+34j+14k
hope it helps
If a vehicle to school and 72 mph how many feet does vehicle travel in one second
Answer:
The vehicle travels 105.6 feet in one second.
Step-by-step explanation:
This question is solved by proportions.
72 mph
One hour has 3600 seconds.
Each mile has 5280 ft.
So in 3600 seconds, the vehicle travels 5280*72 = 380160 feet. In one second, how many feet?
3600 seconds - 380160 feet
1 seconds - x feet
Applying cross multiplication:
[tex]3600x = 380160[/tex]
[tex]x = \frac{380160}{3600}[/tex]
[tex]x = 105.6[/tex]
The vehicle travels 105.6 feet in one second.
convert 495.05 to fraction
Answer:
9901 / 2000
Step-by-step explanation:
might be wrong
Help me PLEASEEEEEEEEEEEEE
Answer:
B, C, D.
Step-by-step explanation:
These are all statistical questions since these can be answered by collecting data that vary.
1.
What is the range of this data set?
07, 43, 9, 35, 38, 13, 24, 41
36
35
24
26
43-7= 36
Range is highest number minus smallest number
Which equation is the inverse of y = x2 + 16?
O y = x2 – 16
y=+√x - 16
y=+NX-16
y = x2 - 4
Hi there!
[tex]\large\boxed{y = \pm \sqrt{x - 16}}[/tex]
To solve for the inverse, swap the x and y variables:
x = y² + 16
Isolate for y by subtracting both sides by 16:
x - 16 = y²
Square root both sides:
√(x - 16) = y
Add the plus/minus sign:
y = ±√(x - 16)
Answer:
c
Step-by-step explanation:
I need help with this question
Somebody help me plzzz....
Answer:
1. 1 cm
2. 7 and 2/16 (or 1/8) inches
Step-by-step explanation:
2. The distance from each small line on a ruler is 1/16 of an inch.
-2x^2+6x+1=-3x^2 solve to the nearest tenth
Step-by-step explanation:
The given equation is :
[tex]-2x^2+6x+1=-3x^2[/tex]
Taking all the terms to one side of the equation i.e.
[tex]-2x^2+6x+1+3x^2=0\\\\x^2+6x+1=0[/tex]
It is a quadratic equation of the form [tex]ax^2+bx+c=0[/tex] whose solution is given by :
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Here, a = 1, b = 6 and c = 1
Put all the values,
[tex]x=\dfrac{-6\pm \sqrt{6^2-4(1)(1)}}{2(1)}\\\\x=-0.171\ and\ x=-5.82[/tex]
Hence, this is the required solution.
A right triangle (90) has a one angle that measures 35 degrees. What is the measure of the third angle?
A. 90 degrees
B. 145 degrees
C. 55 degrees
D. 180 degrees
Answer:
55°
Step-by-step explanation:
triangle= 180°
third angle= 180-90-35
= 55°
DNA contains the genetic code of an organism. The length of a DNA strand is about 10-7 meter. Which of the following represents the length of the DNA strand as a decimal?
Step-by-step explanation:
Write each decimal using a negative exponent. ... DNA contains the genetic code of an organism. ... meter. Which of the following represents the length of the DNA strand as a decimal?
please give answer would be cool
+
Step-by-step explanation:
38 to 18 m square / videos 400
sum of the two angle is equal to 90 degree the ratio of measure of these is 4:5 I what are the measures of these two angle
9x =90
x=90/9
=10
4×10= 40
5×10=50
what is the area of this figure
Answer:
A=162.56in^2
Step-by-step explanation:
make sure u separate the different shapes
halps pleasessssssssss
Answer:
SAS. ( side, angle, side)
in option 2nd
Answer:
False
SAS = This stands for Side Angle Side congruency theorem
Step-by-step explanation:
Question 1.)
If any of the 2 angles of any triangle is congruent to any of the 2 angles of the other triangle, then this would be true. Let's find the measure of ∠R and ∠G:
=> ∠G = 180 - (98 + 30)
∠G = 52
=> ∠R = 180 - (98 + 26)
∠R = 56
Now we know that Angles of ΔHIG are 30, 98, and 52, and Angles of ΔSQR are 26, 98, and 56. 2 angles of 1 triangle are not congruent 2 angles of the other triangle, therefore the triangles aren't congruent.
Question 2.)
SAS congruency is used since an angle and it's 2 adjacent sides are given for each triangle.
Hope this helps!
I need to know the answer for this so please help
Answer:
there is not solution the the equation (graph)
Step-by-step explanation:
when the lines are parallel and do not intersect they is no solution.
HELPPP HELPPP HELPPP!!!!
Answer:
Step-by-step explanation:
area =8*4 cm
=32 cm^2
Answer:
area of the figure=8×4
=32 cm²
76% of the grade 5 pupils are girls.Express 76% as decimal.
a.0.076
b.0.76
c.7.6
d.76.0
Express 76% as decimal is 0,76
76/100 = 0,76
(help) what type of triangle is shown below
atlas isttg dont ttake this down its a question and u have no right to
Answer:
13/16
Step-by-step explanation:
The equation of a function
y = 2/3x+1/3 find the value of y
when x = -3
when x = 1 1/2
Answer:
[tex]y = \frac{-5}{3}\\\\y = \frac {4}{3}[/tex]
Step-by-step explanation:
[tex]y = \frac{2}{3} x + \frac{1}{3}\\\\when \ x = -3 \\\\y = \frac{2}{3}(-3) + \frac{1}{3} = -2 + \frac{1}{3} = \frac{-6 + 1}{3}= \frac{-5}{3} \\\\When \ x = 1 \frac{1}{2} = \frac{3}{2}\\\\y = \frac{2}{3} \times \frac{3}{2} + \frac{1}{3} = 1+ \frac{1}{3} = \frac{3 + 1}{3}= \frac{4}{3} \\\\[/tex]
what is the perimeter of this given figure
pahelp po. thank you
Answer:
14 units
Step-by-step explanation:
Side length of each square is 1 unit.
So, sum of the lengths of all the border edges = 14 units
Thus, the Perimeter of the figure = 14 units
In a dark room, the pupil of a human eye grows to a diameter of about 3.2 x 10 inches. It
bright light, the pupil shrinks to a diameter of about 8 x 10 inches. How much greater is
the pupil's diameter in a dark room than in bright light?
Answer: the answer is 48 inches
Step-by-step explanation:
what is the value of side EC ?
Answer:
EC = 28'
Step-by-step explanation:
Since ∆KAR ~ ∆ENC, therefore, their corresponding side lengths will be proportional to each other.
By implication, we have:
EN/KA = EC/KR
EN = 96'
KA = 24'
EC = ?
KR = 7'
Thus:
96/24 = EC/7
Cross multiply
EC*24 = 7*96
EC*24 = 672
Divide both sides by 24
EC = 672/24
EC = 28'
g A radio station’s poll found that 68% of the respondents in a random sample of listeners plan to see a live music show in the next month. A 95% confidence interval for the population proportion was 0.68 ± 0.04. What is the correct interpretation of the 95% confidence interval? We can be 95% confident that 68% of all listeners will see a live music show in the next month. There is a 95% probability that between 64% and 72% of the listeners will see a live music show in the next month. There is a 5% chance that less than 64% or more than 72% of listeners will see a live music show in the next month. We can be 95% confident that the true proportion of listeners who will see a live music show in the next month is between 64% and 72%. If we repeatedly took samples of the same size from listeners of this radio station, approximately 95% of those samples would have between 64% and 72% of the sample going to see a live music show in the next month.
Answer:
We can be 95% confident that the true proportion of listeners who will see a live music show in the next month is between 64% and 72%.
Step-by-step explanation:
x% confidence interval:
A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.
A 95% confidence interval for the population proportion was 0.68 ± 0.04.
We are 95% sure that the true population proportion is between 0.68 - 0.04 = 0.64 and 0.68 + 0.04 = 0.72.
Thus, the correct answer is:
We can be 95% confident that the true proportion of listeners who will see a live music show in the next month is between 64% and 72%.
Please help me out I don’t understand this.
The area (A) of a trapezoid is calculated as follows:
A = 1/2 * sum of the parallel sides * height
In this case:
A = 1/2 * (23 + 5) * 12 = 168 yd^2.
Answer: it’s 168
Step-by-step explanation:
What does the digit 8 represent in 687, 413?
Answer:
80,000
hope this helps
have a good day :)
Step-by-step explanation:
Answer:
Hundreths
Step-by-step explanation:
Given this graph of average giveaway, what is the best estimate for the expected giveaway value of this game?
graph
A. $1.70
B. $2.50
C. $3.00
D. $3.80
Answer:
ans c hope it helps u take care have a nice day
Anybody Know? It’s just a SOLVE FOR X
Answer:
Hello! answer: 10
Step-by-step explanation:
x = 10 because...
10 × 3 = 30 30 + 5 = 35 35 + 55 + 90 = 180 therefore x = 10 hope that helps!