Calculate the gradient of the line 2y =8x+4
Answer:
m=4
2y/2=y
8x/2=4x
4/2=2
so
y=4x+4
The rate of change in sales for Garmin from 2008 through 2013 can be modeled by
dS/dT = -0.0972t^2 + 2.136t -11.9
where S is the sales (in billions of dollars) and is the time in years, with t = 8 corresponding to 2008. In 2009, the sales for Garmin were $2.9 billion.
A. Find the model for the sales of Garmin.
B. What were the average sales of Garmin from 2008 through 2013?
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.
A toy manufacturer wants to know how many new toys children buy each year. A sample of 686686 children was taken to study their purchasing habits. Construct the 85%85% confidence interval for the mean number of toys purchased each year if the sample mean was found to be 6.86.8. Assume that the population standard deviation is 2.12.1. Round your answers to one decimal place.
Answer:
The 85% confidence interval for the mean number of toys purchased each year is (6.7, 6.9).
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.85}{2} = 0.075[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.075 = 0.925[/tex], so Z = 1.44.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.44\frac{2.1}{\sqrt{686}} = 0.1[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 6.8 - 0.1 = 6.7
The upper end of the interval is the sample mean added to M. So it is 6.8 + 0.1 = 6.9
The 85% confidence interval for the mean number of toys purchased each year is (6.7, 6.9).
Find the volume of x?
I will mark BRAINLIEST
Answer:
[tex]x=73[/tex]
Quadrilateral is shown in the coordinate plane below.
Draw an image of quadrilateral on the coordinate plane reflected over the y-axis.
Answer:
A'(6, 2), B'(6, 5), C'(3, 6) and D'(2, 1)
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
If a point A(x, y) is reflected over the y axis, the new point is at A'(-x, y).
From the document attached, the vertices of the quadrilateral is at A(-6, 2), B(-6, 5), C(-3, 6) and D(-2, 1). Hence if quadrilateral ABCD is reflected over the y axis, the new point is at A'(6, 2), B'(6, 5), C'(3, 6) and D'(2, 1).
Which graph best represents an exponential function?
O A.
O B.
C.
D.
Answer:
B
Step-by-step explanation:
that's how exponential functions are shaped
A cook needs 42 pieces of tomato for salads The cook has 4 tomatoes He cuts each tomato into 6 pieces
chipo set out from a on a bearing of 130 to town b ,she then boardef a bus from town b another town c on a bearing of 030 directly east of a. calculate the bearing of town a from her new position
Answer:
emm who exactly is chipo bcause i literally have no idea
Find the range of the data.
Answer:
7.3
Step-by-step explanation:
Biggest value = 8.9
smallest value = 1.6
range = 8.9-1.6 = 7.3
Step-by-step explanation:
range=highest number - lowest number
= 8.9 - 1.6
=7.3
In a clinical test with 2161 subjects, 1214 showed improvement from the treatment. Find the margin of error for the 95% confidence interval used to estimate the population proportion.
Answer:
The margin of error for the 95% confidence interval used to estimate the population proportion is of 0.0209.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In a clinical test with 2161 subjects, 1214 showed improvement from the treatment.
This means that [tex]n = 2161, \pi = \frac{1214}{2161} = 0.5618[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
Margin of error:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 1.96\sqrt{\frac{0.5618*0.4382}{2161}}[/tex]
[tex]M = 0.0209[/tex]
The margin of error for the 95% confidence interval used to estimate the population proportion is of 0.0209.
solve each problem part 2a. NO LINKS!!!!
Answers:
Problem 14) There are 1093 different ice creams possible.Problem 15) There are 120 ways to pick the reading list.Problem 16) We have 1365 combinations.Problem 17) There are 315 different combos of cars possible.Problem 18) You can go on 21,700 different combinations of rides.==================================================
Explanations:
Problem 14
There are n = 10 toppings to choose from.
If you order r = 0 toppings, then there is nCr = 13C0 = 1 way to do this.
Use the combination formula nCr = (n!)/(r!*(n-r)!)
If you order r = 1 topping, then there are 13C1 = 13 ways to do this.
If r = 2, then we have 13C2 = 78 different combos
If r = 3, then 13C3 = 286
If r = 4, then 13C4 = 715
Add up those subtotals: 1+13+78+286+715 = 1093
Note the use of nCr instead of nPr. The order of toppings doesn't matter.
-----------------
Problem 15
Again order doesn't matter. We have n = 10 books to pick from and r = 3 selections to make.
nCr = (n!)/(r!*(n-r)!)
10C3 = (10!)/(3!*(10-3)!)
10C3 = (10*9*8*7!)/(3!*7!)
10C3 = (10*9*8)/(3!)
10C3 = (10*9*8)/(3*2*1)
10C3 = (720)/(6)
10C3 = 120
There are 120 different ways to pick the three books (from a pool of ten).
-----------------
Problem 16
Follow the same steps as problem 15. This time you'll have n = 15 and r = 4. The answer you should get is 1365
Or you could follow these steps below:
We have 15*14*13*12 = 32,760 permutations and 4! = 24 different ways to arrange any group of 4, so we have (32,760)/(24) = 1365 combinations.
nCr = (nPr)/(r!)
-----------------
Problem 17
There are 7C1 = 7 ways to pick the color and 10C2 = 45 ways to pick the two options. Therefore, there are 7*45 = 315 different cars possible.
-----------------
Problem 18
"At least 15" means "15 or more".
If you ride on r = 15 rides, out of n = 20 total, then we have nCr = 20C15 = 15504 different combinations. If you ride on r = 16 rides, out of n = 20 total, then we have nCr = 20C16 = 4845 different combinations. If you ride on r = 17 rides, out of n = 20 total, then we have nCr = 20C17 = 1140 different combinations. If you ride on r = 18 rides, out of n = 20 total, then we have nCr = 20C18 = 190 different combinations. If you ride on r = 19 rides, out of n = 20 total, then we have nCr = 20C19 = 20 different combinations. If you ride on r = 20 rides, out of n = 20 total, then we have nCr = 20C20 = 1 combo onlyAdd up the subtotals to get
15504+4845+1140+190+20+1 = 21,700
Funny Question :
What is 1 + 1?
Answer:
2
Step-by-step explanation add 1+1
How fast would you reach the water if you jump off a cliff using the formula: h(t)= -16t +8t+ 24?
Answer:
I don’t know if this is correct
Step-by-step explanation:
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]
How to find the value of x round to the nearest tenth for a triangle if one side is 15ft and the other is 13ft
Answer:
C = 19.9 ft
Step-by-step explanation:
Your question isn't properly constructed. However, I'll attempt in providing a possible way of finding one of the sides of a given triangle.
Generally, the Pythagorean theorem is used to find the side of a triangle when two of its sides are known or provided.
Assuming the following data;
Let the length of sides of the triangle be;
Opposite side = a = 15 ft
Adjacent side = b = 13 ft
Hypotenuse side = c
From Pythagorean theorem;
Mathematically, Pythagorean theorem is given by the formula;
C² = a² + b²
C² = 15² + 13²
C² = 225 + 169
C² = 394
Taking the square root of both sides, we have;
C = √394
C = 19.9 ft
please do both of them THANK YOU
Answer:
4(3+x)
4x+12
Step-by-step explanation:
Hi there! I am Mizuki, and I'm just answering lol
Anyways, the answer for the first problem is 12 + 4x = 44
The answer for the second problem is 8
Work:
12 + 4x = 44
4x = 32
x = 8
I REALLY NEED HELP PLS I NEED THIS DONE TODAY!!! JUST LOOK AT THE PICTURE!!!
Answer:
147 sq meters
Step-by-step explanation:
To find the area of a trapezoid, use the formula ( (a+b)/2 ) x h, where a is base value 1 and b is base value 2. Plugging it all in : ( (4+17)/2 ) = 10.5 x 14 = 147 sq meters.
Answer: the answer is 147 square meters.
Step-by-step explanation:
formula: (a+b)/2 * h
bases are a and b: 4 and 17 meters.
h =14 meters
Plug numbers in (4+7)/2*14
solve and you get 147 square meters as answer
A 12 ft. ladder is leaning against a house. The ladder makes a 60° angle with the ground. Use special right triangles to find how far up the building the ladder will reach.
Given:
The length of the ladder = 12 ft
The angle of ladder with ground = 60 degrees
To find:
How far up the building the ladder will reach.
Solution:
Using the given information draw a figure as shown below.
We need to find the vertical distance between the top of ladder and the ground.
Let x be the required distance.
In a right angle triangle,
[tex]\sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]
In the below triangle ABC,
[tex]\sin A=\dfrac{BC}{AC}[/tex]
[tex]\sin 60^\circ=\dfrac{x}{12}[/tex]
[tex]\dfrac{\sqrt{3}}{2}=\dfrac{x}{12}[/tex]
Multiply both sides by 12.
[tex]\dfrac{\sqrt{3}}{2}\times 12=x[/tex]
[tex]6\sqrt{3}=x[/tex]
Therefore, the ladder will reach [tex]6\sqrt{3}[/tex] ft far up the building.
Instructor Vallejo is trying to figure out the percentage of students that still listen to The Doors. Instructor Vallejo
is pretty out of touch, so he doesn't have a prior percentage of students who listen to The Doors that he can use.
How many students should instructor Vallejo sample if he wants to be within 11% of the actual percentage of
students who listen to The Doors with a 82% confidence level.
Answer:
N=115
Step-by-step explanation:
n=.25(2.5715/.12)^2 =114.8 so round up to 115. Hope that help you
Assume the random variable X is normally distributed with mean μ=50 and standard deviation σ=7. Find the 81st percentile.
Answer:
[tex]P(81)=56.16[/tex]
Step-by-step explanation:
From the question we are told that:
Mean [tex]\mu=50[/tex]
Standard Deviation [tex]\sigma=7[/tex]
Percentile 81st
Generally Probability of 81st Percentile
[tex]P(Z<x)=81\%[/tex]
Using Standard normal Table
[tex]P(Z<0.88)=81\%[/tex]
Therefore the 81st percentile is given as
[tex]P(81)=z*\sigma *\mu[/tex]
[tex]P(81)=0.88*7*50[/tex]
[tex]P(81)=56.16[/tex]
From her home, Adriana would have to walk due north to get to her friend Gavin's house and due east to get to her friend Zach's house. It is 3 miles from Adriana's house to Zach's house and a straight-line distance of 5 miles from Gavin's house to Zach's house. How far is Adriana's house from Gavin's house?'
Answer:
4 miles.
Step by step explanation
MEAN: 14,12,17,
ASAP!:((
Answer:
hello there! I am mizuki, and I'll be helping you with this problem.
Mean is the average in numbers by the way!
Anyways, the answer is about 14.3
or...
14 1/3
Step-by-step explanation:
14 + 12 + 17 = 43
43 ÷ 3 = 14.333333...
1. Given f(x) = x2 – X and g(x) = 3x + 2, find f(g(2))
Answer:
56
Step-by-step explanation:
g(2) = 3(2) + 2
= 6 + 2
= 8
f(8) = 8^2 - 8
= 64 - 8
= 56
In each figure below find m∠1 and m∠2, if a||b. Show your work with statements.
m<1=130°[alternate angle are equal again]
m<1+m<2180°[linear pair]
m<2=180°-130°
====================================
If you have any questions feel free to ask me^^
Have a nice and great day!
Cayler#PilipinasAngBayanKo
An equilateral triangle has on vertex at the origin, another on the x-axis, and the third in the quadrant. find the slope of each side
Answer:
0, - 1.732 , 1.732
Step-by-step explanation:
The slope of the line is the angle of the tangent from the positive X axis in counter clock wise direction.
The slope of line AB is
tan 180 = 0
The slope of line BC is
tan 300 = - 1.732
The sloe of line AC is
tan 240 = 1.732
Convert the following angle from degrees to radians. Express your answer in simplest
form.
255°
Answer:
(17/12)π radians
Step-by-step explanation:
π radians = 180º
255 * (π/180) = (17/12)π
I’m confused. Can someone help? Please and thank you so much!
Answer:
Root of 65
Step-by-step explanation:
8^2 is equal to 64, so the sqrt of 64 would equal 8 exactly. The question is asking for which of the sqrts would be closest to 8, so sqrt of 65 is the number that is closest to 64, so it is the answer.
Answer:
[tex] \sqrt{65} [/tex]
as
[tex] \sqrt{64} = 8[/tex]
so it's the closest value to 8
and also
[tex] \sqrt{65} = 8.06[/tex]
via calculator
I think it’s 99 but I’m not sure. Can anyone confirm or deny or explain so I can be sure? thank you!
Answer:
Yeah its B or 99
Step-by-step explanation:
This problem is easy to solve even without a calculator. Simply 10 times 10 would be 100 (since its asking for square root) and the closest number to 100 would be 99 and the square root of 99 is around 9.94.
Find the area please
Answer:
[tex]area = \frac{1}{2} \times 11 \times 18 \\ = 99 \: {ft}^{2} [/tex]
For the equation 3(7 + x) = 3x + k, which value of k will create an equation with Infinity many solutions a) 7 b) 21 c) 10 d) 3
Answer:
21
Step-by-step explanation:
We have to create an identity
3x + 21 = 3x + k
if we substitute k with 21 we have
3x + 21 = 3x + 21
that is an identity so it’s true for every value of x