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.
Dilate the figure by the scale factor. Then enter
the new coordinates.
A(-2,4)
K=3
B(4,-1)
A'([?],[])
B'([10
C'( 10 )
C(-1,-2)
Step-by-step explanation:
A'(-6, 12)
B'(12, -3)
C'(-3, -6)
For a statistics class project, a college student randomly samples 75 men who exercise at a gym regularly and 68 women who exercise at a gym regularly. The college tudent believes that on average men spend more time at the gym each week. The college student records the number of minutes each person exercises in a given week. The college student conducts a hypothesis test at the 5% significance level.
Use the summary statistics to conduct a hypothesis test in StatCrunch. (Open an empty StatCrunch spreadsheet. Choose Stat, T Stats, two sample, with Summary. Adjust the alternative hypothesis as necessary Two Sample T-Test
Sample n Mean Std. Dev.
Men 75 65.7 13.9
Women 68 64.8 9.6
What conclusion can you draw from the output?
i. The data provide sufficient evidence to reject the null hypothesis and to conclude that the mean amount of exercise (minutes) is greater for men than for women at this gym.
ii. The data provide sufficient evidence to conclude that there is no difference in the mean number of minutes exercised per week for men and women.
iii. The data do not provide sufficient evidence to conclude that the mean number of minutes exercised per week is larger for men than for women at this gym
Answer:
iii. The data do not provide sufficient evidence to conclude that the mean number of minutes exercised per week is larger for men than for women at this gym
Step-by-step explanation:
1) The hypotheses are
H0: u1 ≤ u2 against the claim Ha: u1 > u2
The men spend less or equal time than the women at the gym each week
vs
the men spend greater time than the women at the gym each week
2) The test statistic is
t= (x1`- x2`) / √ s1²/n1+ s2²/n2
t= 65.7- 64.8/√(13.9)²/75 + (9.6)²/68
t= 0.9/√2.57613 +1.35529
t=0.4539
and the degrees of freedom is
3) υ = [s₁²/n1 + s₂²/n2]²/ (s₁²/n1 )²/ n1-1 + (s₂²/n2)²/n2-1
=[(13.9)²/75 + (9.6)²/68]²/ [(13.9)²/75 ]² /74 + [ (9.6)²/68]²/67
= 139
The degrees of freedom is always rounded in this calculation
4) The Critical region is [1.656, ∞]
5) t-score is outside of the critical region, so there is not enough evidence to reject H₀.
iii. The data do not provide sufficient evidence to conclude that the mean number of minutes exercised per week is larger for men than for women at this gym
Please help me with this question
9514 1404 393
Answer:
(x, y) = (5, 2)
Step-by-step explanation:
Given:
LP = x
MP = 2y+3
NP = y+3
KP = 3x -8
KP = MP, LP = NP
Find:
x, y
Solution:
The given relations between the segment lengths let us write two equations:
KP = MP
3x -8 = 2y +3 ⇒ 3x -2y -11 = 0 [eq1]
LP = NP
x = y +3 ⇒ x -y -3 = 0 [eq2]
__
Subtracting 3 times [eq2] from [eq1] gives ...
(3x -2y -11) -3(x -y -3) = 0
y -2 = 0 . . . . . . . . simplify
y = 2 . . . . . . . . . . add 2
Substituting this value into [eq2] gives ...
x = 2 + 3 = 5
The values of x and y are ...
x = 5, y = 2
PLEASE HELP GUYS I’m being timed
The question is the base of the triangle, so we use the formula : b²=c²–a²
——————————————————————
[tex] {b}^{2} = \sqrt{c^{2} - {a}^{2} }[/tex]
[tex] {b}^{2} = \sqrt{ {16}^{2} - {8}^{2} } [/tex]
[tex] {b}^{2} = \sqrt{256 - 64} = \sqrt{192} [/tex]
[tex] \sqrt{192} =8 \sqrt{3} [/tex]
Please answer all correct for brainlest
Answer:
2. 2(7y-2)
3. -5-2x
4. 9+y
5. 5x-7
6. 3m+2
7. 8-9m
Step-by-step explanation:
collect like terms
A point with a positive x-coordinate and a negative y-coordinate is reflected over the y-axis.
Which sentence describes the coordinates of the new point?
The r-coordinate is positive, and the y-coordinate is negative.
The r-coordinate is negative, and the y-coordinate is negative.
The x-coordinate is positive, and the y-coordinate is positive.
The r-coordinate is negative, and the y-coordinate is positive.
Answer:
the x coordinate is negative and y coordinate is positive
Step-by-step explanation:
If anyone can help, it’d be appreciated! I’m so confused
Please help I am so confused and I would really appreciate it ♥️♥️
A line representing Car B would have a parallel slope if:
Answer:
you add an image
Step-by-step explanation:
Answer:
... if it had the same slope in the y=mx+b equation where m is the slope and x is just x and b is the y-intercept
Step-by-step explanation:
say Car A had the equation y=2x+3- Car B would also have to have be y=2x but the y intercept could be any value
Un camion se desplazo de punto "a" al punto "b" quien a cambiado de posicion?
a) El camión
b) los hombres parados en la rampa
[tex] \huge \underbrace \mathfrak \red{Respuesta}[/tex]
a) Para The Man The Truck ha cambiado de posición.
b) Para el camión, el hombre parado en la rampa ha cambiado de posición.
[tex] \bold\green{Entonces\: la}[/tex] [tex]\underline\bold\red{opción \:A}[/tex] [tex] \bold\green{ es\: correcto}[/tex]
Espero que esto te ayude ❤️PLEASE HELP IM BEING TIMED
Answer:
1
Step-by-step explanation:
Any number to the 0 power is equal to 1.
Hope that this helps!
Answer:
1 is correct
Any number that is raised to the power of 0 is 1, and any number that’s raised to the power of 1 is itself
The graph below shows Ariana's pay as a painter. How much does Ariana charge per painting?
Find the surface area of the figure below.
10 in
7 in.
4 in
Answer:
Surface Area = 2×(10×7 + 10×4 + 7×4) = 276 feet^2
Step-by-step explanation:
Hope this helps :)
y is directly proportional ( x+2)²
when x = 8 y= 250
find y when x = 4
Answer:
y=90 when x=4
Step-by-step explanation:
We are given that
[tex]y\propto (x+2)^2[/tex]
When x=8 and y=250
We have to find the value of y when x=4
[tex]y=k(x+2)^2[/tex]
Where k= Proportionality constant
Substitute the values
[tex]250=k(8+2)^2[/tex]
[tex]250=100k[/tex]
[tex]k=\frac{250}{100}[/tex]
[tex]k=5/2[/tex]
Now, substitute x=4 and k=5/2
Then, we get
[tex]y=\frac{5}{2}(4+2)^2[/tex]
[tex]y=\frac{5}{2}\times 36[/tex]
[tex]y=90[/tex]
Reflect (1,‐4) across the x‐axis what is the reflected ordered pair?
Answer:
(1,4)
Step-by-step explanation:
(1,-4) is over 1 and down negative 4 so reflected over the x-axis(the horizontal one) it would be four up so the answer is (1,4)
Answer: (1,4)
Step-by-step explanation:
The rule for reflecting over the X axis is to negate the value of the y-coordinate of each point, but leave the x-value the same. For example, when point P with coordinates (1,-4) is reflecting across the X axis and mapped onto point P', the coordinates of P' are (1,4)
Find the area of the figure. with 4in 8in 2in 10in
Answer:
24 in total
Step-by-step explanation:
The probability that a student is accepted to a prestigious college is 0.3. If 5 students from the same school apply, what is the probability that at most 4 are accepted
Answer:0.849185
Step-by-step explanation:
Binomial probability formula we will use:
[tex]$P(x)=\frac{n !}{x !(n-x) !} p^{x} q^{n-x}$[/tex]
where,
[tex]n=5$\\$\mathrm{P}$ (probability of success) $=0.3$\\q=1-p[/tex]
The computation of the probability will be :
[tex]$P(x \leq 2 ; 5,0.3)=P(x=0 ; 5,0.3)+P(x=1 ; 5,0.3)+P(x=2 ; 5,0.3)+P(x=3 ; 5,0.3)$\\$=\left[\frac{5 !}{5 !(5-0) !}(0.3)^{0}(1-0.3)^{5-0}\right]+\left[\frac{5 !}{5 !(5-1) !}(0.3)^{1}(1-0.3)^{5-1}\right]$$+\left[\frac{5 !}{5 !(5-2) !}(0.3)^{2}(1-0.3)^{5-2}\right]$$++\left[\frac{5 !}{5 !(5-3) !}(0.3)^{3}(1-0.3)^{5-3}\right]$$++\left[\frac{5 !}{5 !(5-4) !}(0.3)^{4}(1-0.3)^{5-4}\right]$\\$=0.1681+0.3601+0.3087+0.006615+0.00567$\\$\Rightarrow 0.849185$[/tex]
The probability that at most 4 are accepted = 0.849185
Help with volume all help is appreciated :)
Answer:
It would be 0.41 ft^3
Step-by-step explanation:
Alright, to start, lets get the volume of the entire cinder block and the holes within it.
1.31 * 0.66 * 0.66 ---> 0.5706...
Next with the holes, they are both 0.33 wide, 0.39 long, and just as tall at 0.66 feet.
0.33 * 0.39 * 0.66 ---> 0.0849...
Since there's two of them: 0.1698...
To finish it, subtract the hole volume from the total volume;
0.5806 - 0.1698 = 0.4108
Rounds to 0.41 ft^3
|x-4| if x>4
can you please help me
Answer: x - 4 without the absolute value bars surrounding it
=================================================
Explanation:
If x is larger than 4, then x-4 is positive. For example, if x = 5, then
x-4 = 5-4 = 1
So for cases when x > 4, the |x-4| and x-4 are the same identical expression. Try out more values of x to compare the two outputs. I recommend making a table with 3 columns. You'll have x in column 1, then |x-4| in column 2, and x-4 in column 3. You should find that the outputs for columns 2 and 3 are identical when x is larger than 4.
It's only when x < 4 is when |x-4| and x-4 differ. Instead we would say |x-4| = -(x-4). But we aren't focused on this case.
In short, when x > 4, we simply drop the absolute value bars to get the answer x - 4
4(-8x + 5) = -32.x - 26
solve the equation
Answer:
-46
Step-by-step explanation:
4(-8x + 5) = -32x - 26
-32x + 20 = -32x - 26
-32x + 32x = -26 - 20
x = -46
Answer:
-32x+20=-32x-26
20=-26
so unequal or undefined
hope this helps
have a good day :)
Step-by-step explanation:
Select the correct answer. What are the y-intercept and the slop of the line represented in the graph?
Answer:
B
Step-by-step explanation:
The line crossed the y axis at 4 and the slope is -2. you can do rise/ run to find the slope which is -2/1 or -2
chhering deposite rs. 40000 in a bank at the rate of 5% p.a. if he has to pay 5%of the total interest as tax for the bank how much will he get after 4 years
Answer: Rs 7600
Step-by-step explanation:
The interest will be calculated as:
= Principal × Rate × Time
= 40000 × 5% × 4
= 40000 × 0.05 × 4
= 8000
Since he has to pay 5% of the total interest as tax for the bank, the amount that he will he get after 4 years will be:
= 8000 - (5% × 8000)
= 8000 - (0.05 × 8000)
= 8000 - 400
= 7600
Therefore, he'll get Rs 7600
Can somebody help me with this
Answer:
0.04997916927
Step-by-step explanation:
Answer:
30 degrees
Step-by-step explanation:
arcsin(0.5) deg
= 30
NEED HELP ASAP!!!!
3/4 + (1/3 ÷ 1/6) - (-1/2)=?
A:1/4
B:1 1/4
C:3/4
D:2 1/4
⚠️NO LINKS OR I WILL REPORT⚠️
Answer:
anser is 3.24 or 3 and 1/4
Step-by-step explanation:
Answer:
3 1/4
Step-by-step explanation:
3/4+(1/3 ÷1/6)-(-1/2)=
3/4+(2)+1/2
3/4+5/2
3/4+10/4
13/4
3 1/4
Find the missing angle measurement.
Answer:
54°
Step-by-step explanation:
54°
Answer:
the missing angle is 54
Step-by-step explanation:
so first we need two triangle angles to get our measurement and we know straight lines add up to 180 so
180-123=57
57+69(other angle)=126
all triangle angles add up to 180 so subtract the two other angles to get your result
180-126=54
54 is your anwser
what is the vertex of the graph show Below?
Answer:
(-3, -2)
Step-by-step explanation:
"If the parabola opens up, the vertex represents the lowest point on the graph". By looking at the graph, we can see that the lowest point is (-3, -2).
someone please tell me this answer!!
en un rectnagulo de 17 cm de ancho y su diagonal mide 26 cm ¿cuanto mide el rectangulo de largo?
Answer:
[tex]x=19.67[/tex]cm
Step-by-step explanation:
Por Pitágoras,
[tex]x^{2} = 26^{2} - 17^{2} \\\\x^{2} = 676 - 289\\\\x^{2} =387\\\\x=\sqrt{387} \\\\x=19.67[/tex]
Jenny bought gallons of lemonade and milk for a banquet. A gallon of lemonade costs $5, and a gallon of milk costs $3. Jenny spent $120 and bought 32 total gallons. How many gallons of milk did Jenny buy?
Answer:
She Bought 40 Gallons of Milk
Step-by-step explanation:
Philip wants to buy a new video game system that costs
$349.99 including tax. Philip has $125.50 saved. If
Philip mows grass for $15.00 per yard, what is the least
amount of yards he could cut to purchase the new video
game system?
Answer:
I think the answer I think the answer would be 14