Mathematics College

Lenovo uses the​ zx-81 chip in some of its laptop computers. the prices for the chip during the last 12 months were as​ follows:                                                                                                              month price per chip month price per chip january ​$1.901.90 july ​$1.801.80 february ​$1.611.61 august ​$1.821.82 march ​$1.601.60 september ​$1.601.60 april ​$1.851.85 october ​$1.571.57 may ​$1.901.90 november ​$1.621.62 june ​$1.951.95 december ​$1.751.75 this exercise contains only part
d. with alphaα ​= 0.1 and the initial forecast for october of ​$1.831.83​, using exponential​ smoothing, the forecast for periods 11 and 12 is ​(round your responses to two decimal​ places): month oct nov dec forecast ​$1.831.83 1.801.80 1.791.79 with alphaα ​= 0.3 and the initial forecast for october of ​$1.761.76​, using exponential​ smoothing, the forecast for periods 11 and 12 is ​(round your responses to two decimal​ places): month oct nov dec forecast ​$1.761.76 1.701.70 1.681.68 with alphaα ​= 0.5 and the initial forecast for october of ​$1.721.72​, using exponential​ smoothing, the forecast for periods 11 and 12 is ​(round your responses to two decimal​ places): month oct nov dec forecast ​$1.721.72 1.651.65 1.631.63 based on the months of​ october, november, and​ december, the mean absolute deviation using exponential smoothing where alphaα ​= 0.1 and the initial forecast for octoberequals=​$1.831.83 is ​$ . 160.160 ​(round your response to three decimal​ places). based on the months of​ october, november, and​ december, the mean absolute deviation using exponential smoothing where alphaα ​= 0.3 and the initial forecast for octoberequals=​$1.761.76 is ​$ 0.1130.113 ​(round your response to three decimal​ places). based on the months of​ october, november, and​ december, the mean absolute deviation using exponential smoothing where alphaα ​= 0.5 and the initial forecast for octoberequals=​$1.721.72 is ​$ nothing ​(round your response to three decimal​ places).

Answers

Answer 1
Given the table below of the prices for the Lenovo zx-81 chip during the last 12 months

[tex]\begin{tabular} {|c|c|c|c|} Month&Price per Chip&Month&Price per Chip\\[1ex] January&\$1.90&July&\$1.80\\ February&\$1.61&August&\$1.83\\ March&\$1.60&September&\$1.60\\ April&\$1.85&October&\$1.57\\ May&\$1.90&November&\$1.62\\ June&\$1.95&December&\$1.75 \end{tabular}[/tex]

The forcast for a period [tex]F_{t+1}[/tex] is given by the formular

[tex]F_{t+1}=\alpha A_t+(1-\alpha)F_t[/tex]

where [tex]A_t[/tex] is the actual value for the preceding period and [tex]F_t[/tex] is the forcast for the preceding period.

Part 1A:
Given α ​= 0.1 and the initial forecast for october of ​$1.83, the actual value for october is $1.57.

Thus, the forecast for period 11 is given by:

[tex]F_{11}=\alpha A_{10}+(1-\alpha)F_{10} \\ \\ =0.1(1.57)+(1-0.1)(1.83) \\ \\ =0.157+0.9(1.83)=0.157+1.647 \\ \\ =1.804[/tex]

Therefore, the foreast for period 11 is $1.80


Part 1B:

Given α ​= 0.1 and the forecast for november of ​$1.80, the actual value for november is $1.62

Thus, the forecast for period 12 is given by:

[tex]F_{12}=\alpha A_{11}+(1-\alpha)F_{11} \\ \\ =0.1(1.62)+(1-0.1)(1.80) \\ \\ =0.162+0.9(1.80)=0.162+1.62 \\ \\ =1.782[/tex]

Therefore, the foreast for period 12 is $1.78



Part 2A:

Given α ​= 0.3 and the initial forecast for october of ​$1.76, the actual value for October is $1.57.

Thus, the forecast for period 11 is given by:

[tex]F_{11}=\alpha A_{10}+(1-\alpha)F_{10} \\ \\ =0.3(1.57)+(1-0.3)(1.76) \\ \\ =0.471+0.7(1.76)=0.471+1.232 \\ \\ =1.703[/tex]

Therefore, the foreast for period 11 is $1.70


Part 2B:

Given α ​= 0.3 and the forecast for November of ​$1.70, the actual value for november is $1.62

Thus, the forecast for period 12 is given by:

[tex]F_{12}=\alpha A_{11}+(1-\alpha)F_{11} \\ \\ =0.3(1.62)+(1-0.3)(1.70) \\ \\ =0.486+0.7(1.70)=0.486+1.19 \\ \\ =1.676[/tex]

Therefore, the foreast for period 12 is $1.68




Part 3A:

Given α ​= 0.5 and the initial forecast for october of ​$1.72, the actual value for October is $1.57.

Thus, the forecast for period 11 is given by:

[tex]F_{11}=\alpha A_{10}+(1-\alpha)F_{10} \\ \\ =0.5(1.57)+(1-0.5)(1.72) \\ \\ =0.785+0.5(1.72)=0.785+0.86 \\ \\ =1.645[/tex]

Therefore, the forecast for period 11 is $1.65


Part 3B:

Given α ​= 0.5 and the forecast for November of ​$1.65, the actual value for November is $1.62

Thus, the forecast for period 12 is given by:

[tex]F_{12}=\alpha A_{11}+(1-\alpha)F_{11} \\ \\ =0.5(1.62)+(1-0.5)(1.65) \\ \\ =0.81+0.5(1.65)=0.81+0.825 \\ \\ =1.635[/tex]

Therefore, the forecast for period 12 is $1.64



Part 4:

The mean absolute deviation of a forecast is given by the summation of the absolute values of the actual values minus the forecasted values all divided by the number of items.

Thus, given that the actual values of october, november and december are: $1.57, $1.62, $1.75

using α = 0.3, we obtained that the forcasted values of october, november and december are: $1.83, $1.80, $1.78

Thus, the mean absolute deviation is given by:

[tex] \frac{|1.57-1.83|+|1.62-1.80|+|1.75-1.78|}{3} = \frac{|-0.26|+|-0.18|+|-0.03|}{3} \\ \\ = \frac{0.26+0.18+0.03}{3} = \frac{0.47}{3} \approx0.16[/tex]

Therefore, the mean absolute deviation using exponential smoothing where α ​= 0.1 of October, November and December is given by: 0.157



Part 5:

The mean absolute deviation of a forecast is given by the summation of the absolute values of the actual values minus the forecasted values all divided by the number of items.

Thus, given that the actual values of october, november and december are: $1.57, $1.62, $1.75

using α = 0.3, we obtained that the forcasted values of october, november and december are: $1.76, $1.70, $1.68

Thus, the mean absolute deviation is given by:

[tex] \frac{|1.57-1.76|+|1.62-1.70|+|1.75-1.68|}{3} = \frac{|-0.17|+|-0.08|+|-0.07|}{3} \\ \\ = \frac{0.17+0.08+0.07}{3} = \frac{0.32}{3} \approx0.107[/tex]

Therefore, the mean absolute deviation using exponential smoothing where α ​= 0.3 of October, November and December is given by: 0.107




Part 6:

The mean absolute deviation of a forecast is given by the summation of the absolute values of the actual values minus the forecasted values all divided by the number of items.

Thus, given that the actual values of october, november and december are: $1.57, $1.62, $1.75

using α = 0.5, we obtained that the forcasted values of october, november and december are: $1.72, $1.65, $1.64

Thus, the mean absolute deviation is given by:

[tex] \frac{|1.57-1.72|+|1.62-1.65|+|1.75-1.64|}{3} = \frac{|-0.15|+|-0.03|+|0.11|}{3} \\ \\ = \frac{0.15+0.03+0.11}{3} = \frac{29}{3} \approx0.097[/tex]

Therefore, the mean absolute deviation using exponential smoothing where α ​= 0.5 of October, November and December is given by: 0.097

Related Questions

What pair of fractions is 0.8 between on a number line

Answers

0.8  has one decimal.. so... let's make it a fraction first, by using one zero with a one as denominator.

[tex]\bf 0.\underline{8}\implies \cfrac{08}{1\underline{0}}\impliedby \textit{one decimal, one zero, no dot} \\\\\\ \cfrac{8}{10}\implies \cfrac{4}{5} \qquad \qquad \qquad ......\cfrac{1}{5}..\cfrac{2}{5}..\cfrac{3}{5}..\boxed{\cfrac{4}{5}}..\cfrac{5}{5}..\cfrac{6}{5}..\cfrac{7}{5}......[/tex]

is between any of those, among many other fractions as well.

what is 11x-(6x-5)=40

Answers

+5
5x
45÷5
x=9
i guess lol 20 characters long annswer

Find the linear function such that f(1)=8 and f(5)=-4

Answers

f(1) = 8 is another way to say, x = 1, y = 8

f(5) = -4, is another way to say,  x = 5, y = -4

so, what's the equation of a line that passes through (1, 8) and (5, -4)

[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 1}}\quad ,&{{ 8}})\quad % (c,d) &({{ 5}}\quad ,&{{ -4}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-4-8}{5-1}\implies \cfrac{-12}{4}\implies -3[/tex]

[tex]\bf \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-8=-3(x-1) \\\\\\ y-8=-3x+3\implies y=-3x+3+8\implies y=-3x+11[/tex]

27x to second power-42x+12 if x=2

Answers

27x^2 - 42x + 12

If x = 2:

27(2)^2 - 42(2) + 12

= 27(4) - 84 + 12

= 108 - 72

= 36

What is the square root of 360 rounded to the nearest thousandth

Answers

The square root of 360 is 18.97

What are the necessary criteria for a line to be perpendicular to the given line and have the same y-intercept? The slope is and contains the point (0, 2). The slope is and contains the point (0, −2). The slope is and contains the point (0, 2). The slope is and contains the point (0, −2).

Answers

(-3,-4) (3, 0)
slope = (0 +4) / (3 + 3) = 4/6 = 2/3
perpendicular so slope = -3/2

line on graph
y = mx + b
0 = 2/3 (3) + b
0 = 2+ b
b = -2

y intercept (0,-2)

answer 
The slope is -3/2 and contains the point (0, −2). 

Answer: D.)The slope is Negative three-halves and contains the point (0, −2).

Step-by-step explanation:

i got it correct obviously oncrip

After working for 25 hours lammer made $375 after working 40 hours lammer made $600 predict how much will he make after 10 hours of work

Answers

25hr. 40h. 10hr

375$ 600$ x

25 . 40 . x = 1000
375 . 600 = 225000
225000÷1000
x = 225

Lammer will make $150 after working for 10 hours .

Calculating Earnings Based on Hours Worked

To predict how much Lammer will make after working 10 hours, we first need to determine his hourly wage. From the information given, we know:

After working 25 hours, Lammer made $375.After working 40 hours, Lammer made $600.

We can calculate his hourly wage as follows:

Hourly Wage = Total Earnings / Total Hours Worked

For both inputs, we observe:

$375 / 25 hours = $15 per hour$600 / 40 hours = $15 per hour

This indicates that Lammer's hourly wage is consistent at $15 per hour.

Now, to predict how much he will make after working 10 hours:

Earnings for 10 Hours of Work = Hourly Wage x Number of Hours

Earnings for 10 Hours = $15 x 10 = $150

Therefore, Lammer will make $150 after working 10 hours.

Calculate the rf value for the reactant b spot. estimate the ruler to the nearest tenth, report the answer using two significant figures.

Answers

1. Measure the distance the solvent front traveled from the baseline (m1). 2. Measure the distance the reactant b spot traveled (the center of the spot) (m2). 3. To determine the rf, divide (m2/m1). 4. Significant figures- use 2 so the answer should be written to the hundredths place as the spot will not travel farther than the solvent front.

Simplify the expression: Sqrt(16 − x^2)
as much as possible after substituting "4 sin x" for x.

Answers

[tex]\bf sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta)\\\\ -------------------------------\\\\ \sqrt{16-x^2}\implies \sqrt{16-[4sin(x)]^2}\implies \sqrt{16-[4^2sin^2(x)]} \\\\\\ \sqrt{16-16sin^2(x)}\implies \sqrt{16[1-sin^2(x)]}\implies \sqrt{16cos^2(x)} \\\\\\ \sqrt{4^2cos^2(x)}\implies \sqrt{[4cos(x)]^2}\implies 4cos(x)[/tex]

Final answer:

Simplify the expression √(16 − x²) by substituting x with '4 sin x' to get 4|cos x|. Use trigonometric identities to arrive at the simplified expression.

Explanation:

The expression to simplify is: √(16 − x²) after substituting '4 sin x' for x.

Step-by-step solution:

Replace x with 4 sin x in the expression: √(16 − (4 sin x)²)

Simplify: √(16 − 16 sin² x)

Apply trigonometric identity: √(16 cos² x) = 4|cos x|

The distance from NYC to Margate, New jersey on our route is 130 miles. Use the equation (d = 60t) to find t, the time needed to drive the distance.

Answers

Thanks for your question!

d = 60t

Since the distance is 130, let’s plug this in:

130 = 60t

Now let’s divide each side by 60 to get our answer:

130\6 = t

To do this equation properly, we need to convert this to mixed number:

t = 21 2/3

Hope this helps!

You want to get out of the sun and look for some shade. There are some trees by the side of the lake. You know you are just below 2 metres in height. 
Estimate the height of the tree in metres.

Answers

i would estimate it to be about 8 meters.


What is the solution to the inequality |x-4|<3

Answers

Unfold it and add 4.
  -3 < x-4 < 3
  1 < x < 7

Answer:

The solution of the given inequality  [tex]|x-4|<\:3\:[/tex] is [tex]1<x<7[/tex]

Step-by-step explanation:

Given inequality [tex]|x-4|<\:3\:[/tex]

We have to find the solution of the given inequality  [tex]|x-4|<\:3\:[/tex]

Using absolute rule, [tex]\mathrm{If}\:|u|\:<\:a,\:a>0\:\mathrm{then}\:-a\:<\:u\:<\:a[/tex], we have,

[tex]-3<x-4<3[/tex]

Rewrite as [tex]x-4<-3\quad \mathrm{and}\quad \:x-4<3[/tex]

Consider , [tex]x-4>-3[/tex]

Adding 4 both side, we have,

[tex]x-4+4>-3+4[/tex]

Simplify, we have,

[tex]x>1[/tex]

Consider , [tex]x-4<3[/tex]

Adding 4 both side, we have,

[tex]x-4+4<3+4[/tex]

Simplify, we have,

[tex]x<7[/tex]

Combining, we have,

[tex]1<x<7[/tex]

Thus, The solution of the given inequality  [tex]|x-4|<\:3\:[/tex] is [tex]1<x<7[/tex]

A restaurant advertises 256 types of nachos. how many topping ingredients must be available

Answers

Well, this depends on the number of topping ingredients you have for each serving of nachos. The general solution will be simply to add all the topping ingredients for each type. Assuming there is an average of 7 topping ingredients for every type, namely: cheese, fried beans, sour cream, onions, jalapeños, salsa, and guacamole. Hence,

Topping Ingredients = 7*256 = 1,792

Which angle pairs are supplementary? Check all that apply

Answers

Supplementary angles add up to 180 degrees, meaning they are straight lines.

B ∠4 and ∠3
C ∠4 and ∠5
E ∠3 and ∠6

The sum of two angles is equal to [tex]180^\circ[/tex] than the angle pairs are known as supplementary angles. Therefore, from the given diagram angle pairs [tex]\rm \angle 3\;and\;\angle6[/tex], [tex]\rm \angle 5\;and\;\angle6[/tex], [tex]\rm \angle 4\;and\;\angle5[/tex], [tex]\rm \angle 3\;and\;\angle4[/tex] and [tex]\rm \angle 7\;and\;\angle 8[/tex] are supplementary angles. So, the correct options are: B), C), and E).

Given :

[tex]\angle 3 = 90^\circ[/tex]

The sum of two angles is equal to [tex]180^\circ[/tex] than the angle pairs are known as supplementary angles.

From the diagram given in the question it can be clearly observe that if [tex]\angle 3 = 90^\circ[/tex] than [tex]\rm \angle 4,\;\angle 5,\;and\;\angle 6[/tex] are also equal to [tex]90^\circ[/tex].

Than according to the definition of supplementary angles:

[tex]\angle 3 +\angle6 = 180^\circ[/tex]

[tex]\angle 3 +\angle4 = 180^\circ[/tex]

[tex]\angle 4 +\angle5 = 180^\circ[/tex]

[tex]\angle 5 +\angle6 = 180^\circ[/tex]

[tex]\angle 7 +\angle8 = 180^\circ[/tex]

Therefore, angle pairs [tex]\rm \angle 3\;and\;\angle6[/tex], [tex]\rm \angle 5\;and\;\angle6[/tex], [tex]\rm \angle 4\;and\;\angle5[/tex], [tex]\rm \angle 3\;and\;\angle4[/tex] and [tex]\rm \angle 7\;and\;\angle 8[/tex] are supplementary angles.

For more information, refer the link given below:

https://brainly.com/question/19281924

A washer and a dryer cost $917 combined. The washer costs $67 more than the dryer. What is the cost of the dryer?

Answers

Final answer:

To find the cost of the dryer, set up equations based on the given information and solve for the dryer's cost, which results in the dryer being priced at $425.

Explanation:

To solve for the cost of the dryer in the given problem, we can create two equations based on the information provided. Let's denote the cost of the dryer as D and the cost of the washer as W. According to the problem, W = D + $67, and the combined cost of the washer and dryer is $917, so W + D = $917.

Substituting the first equation into the second, we have (D + $67) + D = $917. Simplifying this, we get 2D + $67 = $917. Subtracting $67 from both sides of the equation gives us 2D = $850. Finally, dividing both sides by 2, we find that D = $425.

Therefore, the cost of the dryer is $425.

Algebra 2 Slope questions

Answers

Slope equals the difference in y or difference in x, or rise over run.

1-1/-8-(-6)
0/-2
0

Final answer: A

A projectile is shot from a cannon. The fixed parameters are the acceleration of gravity,    g=9.8 m/sec2, and the muzzle velocity, v0=500 m/sec, at which the projectile leaves the cannon. The angle θ, in degrees, between the muzzle of the cannon and the ground can vary. The range of the projectile is
f(θ)=vo^2/g sin πθ/90=25510 sin πθ/90 meters.

Answers

The range at θ = 10⁰ is 155.4 meters.

What is a projectile?

A projectile is an object thrown or projected into the air, subject to gravity, following a curved trajectory.

Given that

v₀ = 500m/s

g = 9.8 m/s²

θ = 10⁰

Substitute into the function

f(θ)=v₀²/g sin πθ/90=25510 sin πθ/90 meters.

f(θ)= 25510sin πθ/90

= 25510sin10π/90

= 25510sinπ/9

= 25510sin(3.142/9)

= 25510sin(0.349)

= 25510 * 0.00609

= 155.4 m

The range at θ = 10⁰ is 155.4 meters.

Complete question

Final answer:

The greater the initial velocity of a projectile, the greater the range, with the maximum range achieved at a 45° angle in the absence of air resistance.

Explanation:

The initial velocity of a projectile has a significant impact on its range. Specifically, the greater the initial speed, ℓ0, the greater the range. The formula for range R on level ground, neglecting air resistance, is given by R = (v0²/g) sin(2θ), where θ is the launch angle, v0 is the initial velocity, and g is the acceleration due to gravity. The maximum range is reached when the launch angle is 45°. With air resistance, the optimal angle decreases to roughly 38°. Additionally, for every angle other than the optimal, there are two different angles that yield the same range, and their sum totals 90°.

greatest common factor for 8x and 40

Answers

The GCF of 8x and 40 is 8

40 | 2
20 | 2
10 | 2
  5 | 5
  1 


8 | 2
4 | 2
2 | 2
1

40 = 2³ * 5
8 = 2³

We take only common factors with lowest exponent.

So 2³ = 8

Need answer to number six in this photo

Answers

The equations for both runners are:

a(t) = -600 + 225tb(t) = 200t

If you equate them, you get -600 + 225t = 200t, which you can simplify to t=24. This means that 

a(24)=b(24)=4800

So ana wins; she catches up at 4800m after 24 minutes, which is well before the end of the part.

will give BRAINEST

A function has a constant halving time. What type of function does this represent?

Answers

Answer:

Exponential decay

Step-by-step explanation:

The function which has a constant halving time represents the exponential decay or negative growth curve type of function.

What is exponential decay?

When the value of one variable of the function is decreased with increase in the number of other variable, then it is called the exponential decay function with constant exponential coefficient.'

It can be given as,

[tex]f(x)=ab^x[/tex]

Here, a is the exponential coefficient.

A function which has a constant halving time is,

[tex]A(t)=A_o\left(\dfrac{1}{2}\right)^{t/h}[/tex]

Here, Ao is the initial time, t is time and h is halving time. This is an exponential decay function.

The function which has a constant halving time represents the exponential decay or negative growth curve type of function.

Learn more about the exponential decay here;

https://brainly.com/question/24077767

#SPJ2

Is 9760-5,220 more or less then 4,000

Answers

It's more than 4,000

Answer:

9760-5220 is more than 4000.

Step-by-step explanation:

Consider the provided numbers.

We need to find 9760-5220 is more or less than 4000.

Subtract the numbers as shown.

 9760

-5220

4540

Now compare the number 4540 and 4000

By comparing it can be concluded that the number 4540 is greater than 4000.

Hence, 9760-5220 is more than 4000.

use rounding or compatible numbers to estimate the sum 171+ 727

Answers

171 + 727 = 898.

We can round it off to 900.
Hello There!

171 becomes 170
727 becomes 730
170 + 730 = 900.

Hope This Helps You!
Good Luck :)

A car travels at 65 miles per hours. Going through construction it travels at 3/5 this speed. Write this fraction as a decimal and find the speed.

Answers

3/5 = 6/10 = 0.6
0.6×65=39
Car travels 39 miles per hour through construction.

Find n(A) for A={0,1,2,3,...,2000}

Answers

There are 2001 items in that set.

So n(A) = 2001

We can individually count them all out, which is very slow and tedious, or we can use the formula
n-m+1

where,
m = starting value
n = ending value

In this case,
m = 0
n = 2000
So,
n-m+1 = 2000-0+1 = 2001

This formula only works if we increase the number by 1 each time (eg: 6, 7, 8, etc)

Final answer:

To find n(A), we count the elements in the set A={0,1,2,3,...,2000} which form an arithmetic sequence. By applying the formula for the number of terms in an arithmetic sequence, we find that n(A) = 2001.

Explanation:

To find n(A), which represents the number of elements in set A, we simply count the elements listed in the given set A={0,1,2,3,...,2000}. These elements form an arithmetic sequence starting from 0 and ending at 2000 with a common difference of 1 between each consecutive number.

The formula for the number of terms n in an arithmetic sequence is given by:

n = (last term - first term) / (common difference) + 1

Applying the formula to our set A:

n = (2000 - 0) / 1 + 1 = 2000 + 1 = 2001

Therefore, n(A) = 2001.

Sergio's internet provider charges its customers $9 per month plus 4¢ per minute of on-line usage. Sergio received a bill from the provider covering a period and was charged a total of $81.40. How many minutes did he spend on-line during that period? (Round to the nearest whole minute, if necessary.)

Answers

9 + 0.04m = 81.40
0.04m = 81.40 - 9
0.04m = 72.40
m = 72.40 / 0.04
m = 1810 minutes <==

an insurance company sells a policy that pays $50,000.00 in case of accidental death. According to company figures, the rate of accidental death is 47 per 100,000 each year. What annual premium should the company charge for this coverage?

Answers

Answer: $23..50 see attachment for the explanation.  

Emelina wrote the equation of a line in point-slope form as shown below. (y+4)=3(x+2) What is Emelina’s equation in slope-intercept form?

Answers

y + 4 = 3(x + 2)
y + 4 = 3x + 6
y = 3x + 6 - 4
y = 3x + 2 <=== slope intercept form

Answer:

[tex]y=3x+2[/tex]

Step-by-step explanation:

We are given equation as

[tex](y+4)=3(x+2)[/tex]

Since, we have to write equation in slope-intercept form

so, we can use slope-intercept formula

[tex]y=mx+b[/tex]

where m is a slope

b is y-intercept

so, we can write our equation in this form

[tex](y+4)=3(x+2)[/tex]

Distribute 3

[tex]y+4=3\times x+3\times 2[/tex]

[tex]y+4=3x+6[/tex]

Subtract both sides by 4

[tex]y+4-4=3x+6-4[/tex]

[tex]y+4-4=3x+6-4[/tex]

[tex]y=3x+2[/tex]

So, slope-intercept form of equation is

[tex]y=3x+2[/tex]


In this problem, y = c1ex + c2e−x is a two-parameter family of solutions of the second-order de y'' − y = 0. find a solution of the second-order ivp consisting of this differential equation and the given initial conditions. y(0) = 1, y'(0)= 8

Answers

y(1) = 0 y'(1) = e y" = c1ex + c2e-x y' = c1ex - c2e-x for solving c1, 0 = c1e1 + c2e-1 this implies that c1 = - (c2/e2) and to solve c2 e1 = (-c2e-2)e1 - c2e-1 e1 = (-2c2e-1) c2= - (e1/2e-1) = - (e2/2) c1 = - (c2/e2) = (e2/2e2) Therefore y =(e2/2e2)ex - (e2/2)e-x

A restaurant used 9.5 ounces of cheese to make 5 slices of pizza. If each slice had the same amount of cheese, how much cheese was on each slice?

Answers

1.9 ounces on each slice

For a population, the mean is 19.4 and the standard deviation is 5.8. Compare the mean and standard deviation of the following random samples to the population parameters.

25, 32, 16, 12, 11, 38, 22, 21, 19, 20


Answers

Answer:

The mean of sample (21.6) is greater than population mean and the standard deviation of sample (8.4) is also greater than population standard deviation.

Both values, mean and std are greater than corresponding population values. This means, that our sample overestimates or is skewed to the right in the values of population. Also each specific value is farther apart from the mean so variation is much bigger in our sample than in our population.

Step-by-step explanation:

To calculate the mean, we estimate the avergage of the data as

Mean = Sum(data)/n

Where n is the number of observations of sample. We have;

(25 + 32 +  16 + 12 + 11 + 38 + 22 + 21  + 19 + 20)/10 = 21.6

The standard deviation is the square root of variance. Variance is sum of the deviation of each data point to the sample mean.

Variance = sum i= 1 to n (Xi-xmean)/(n-1)

Where n = 10 the # of observations and xi is each specific data point.

If you calculate it in Excel or or by hand you obtain:

Variance = sum i= 1 to n (Xi-21.6)/(10-1) = 8.4

Both values, mean and std are greater than corresponding population values. This means, that our sample overestimates or is skewed to the right in the values of population. Also each specific value is farther apart from the mean so variation is much bigger in our sample than in our population.

Answer:

The mean of the random samples (21.6) is greater than population´s mean (19.4) and the STD of the random samples (7.96) is greater than population´s STD (5.8)

Step-by-step explanation:

To calculate the mean of the random samples, we find the average value of the data set

[tex]Mean=\frac{(\sum_{i=0}^{n}{a_i})}{n}\\[/tex]

Where a is an element of the random example and n is the number of elements in the sample, as follows

Mean = (25+32+16+12+11+38+22+21+19+20)*(1/10) = 21.6

To calculate the STD (Standard Deviation) we need to know the variance, because

[tex]STD=\sqrt{var}[/tex]

The variance is determined as the sum of the deviation from one element of the data to the mean squared, all divided by n as below.

[tex]Var=(\sum_{i=1}^{n}{(a_{i}-Mean)^{2})/n[/tex]

If you calculate this by calculator or with a computer, you should get Var=63.44

And with that value, STD=7.96≈8

Therefore, by comparison, both Mean and STD of the random sample are greater than the population´s parameter

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