Answer:
Step-by-step explanation:
Hello!
The variable of interest is
Y: number of new leaves of Bromeliads grown under different types of fertilization.
Factor: Type of fertilizer
Treatments: 1. Nitrogen, 2. Phosphorus, 3. Both, 4. Neither (control group)
To compare these four groups you have to conduct an ANOVA
The hypotheses are:
H₀: μ₁= μ₂= μ₃= μ₄
H₁: At least one population mean is different from the others.
α: 0.05
a)
The degrees of freedom of the F-statistic are:
[tex]F_{I-1;N-I}= F_{4-1;31-4}= F_{3;27}[/tex]
I= number of treatments
N= total number of experimental units (in all groups)
b)
SSTreatments= 39.37
SSError= 72.18
MSTreatments= SStreatments/DfTreatments= 39.37/3= 13.12
MSError=SSError/DfError= 72.18/27= 2.67
[tex]F= \frac{MS_{Treatments}}{MS_{Error}} = \frac{13.12}{2.67} = 4.91[/tex]
c)
This test is one-tailed to the right and so is the p-value:
P(F₃;₂₇≥4.91)= 1 - P(F₃;₂₇<4.91)= 1 - 0.9925= 0.0075
d)
The decision rule using the p-value is:
If p-value ≤ α, reject the null hypothesis.
If p-value > α, do not reject the null hypothesis.
The p-value is less than α, the test is significant at 5% significance level.
"We have significant evidence at the 5% level that the means are not all the same."
I hope this helps!
A coat manufacturer puts 431 coats in a shipment. If they sent out 80 shipments, how many coats would they have sent out?
Answer:
80 shipments will be 80 * 431 = 34,480 coats.
Mackenzie investigated the relationship between the number of hours studying and the test score for some of the students in her class. She constructed the scatterplot below.Which statement is correct based on the scatterplot?
Answer: there is a relationship between study hours and test score. as the hours of studying increase, the test scores increase.
Answer:
C) There is a relationship between study hours and test score. As the hours of studying increase, the test scores increase.
Step-by-step explanation:
In the scatter plot, I can see that when the hours increase, so does the test scores. Thus, the answer is C
9. What is the scale factor of the dilation?
Answer:
D
Step-by-step explanation:
The scale factor is the ratio of the corresponding sides, image to original, that is
scale factor = [tex]\frac{P'S'}{PS}[/tex] = [tex]\frac{6}{3}[/tex] = 2 → D
Use the formula above to find the Celsius temperature equivalent to 185°F. A. 85°C B. 153°C C. 102°C D. 68°C
Answer: A. 85ᴼC
Step-by-step explanation:
0 degrees Celsius is at 32 degrees Fahrenheit.
100 degrees Celsius is at 212 degrees Fahrenheit.
212 - 32 = 180
180 / 100 = 1.8
So, every degree Celsius is 1.8 degrees Fahrenheit, starting at 32 of course.
1.8 * 85 = 153
153 + 32 = 185
Answer:
The correct answer is 85°C.
Step-by-step explanation:
I use the equation 9C = 5F - 160 to solve for temperatures.
Therefore, we just insert values for each variable except for the one that we want to solve for. In this case, we are doing Fahrenheit → Celsius, so we are solving for the unknown variable of C. We are given a value for F, 185°.
Therefore, just insert these into the equation and solve for C.
[tex]9C = 5(185)-160[/tex]
[tex]9C = 925 - 160[/tex]
[tex]9C = 765[/tex]
[tex]\frac{765}{9} = 85[/tex]
C = 85°C
For the following hypothesis test, determine the null and alternative hypotheses. Also, classify the hypothesis test as two tailed, left tailed, or right tailed. The mean local monthly bill for cell phone users in this country was $47.79 in 2001. A hypothesis test is to be performed to determine whether last year's mean local monthly bill for cell phone users has decreased from the 2001 mean of $47.79.
Answer:
The null and alternative hypothesis are:
[tex]H_0: \mu=47.79\\\\H_a:\mu< 47.79[/tex]
This is a left tailed test.
Step-by-step explanation:
A hypothesis test is to be performed to determine whether last year's mean local monthly bill for cell phone users has decreased from the 2001 mean of $47.79.
Then, the claim that will be expressed in the alternative hypothesis is that the monthly bill is lower than $47.79.
The null hypothesis will state that the monthly bill does not differ significantly from $47.79.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=47.79\\\\H_a:\mu< 47.79[/tex]
As we only want to test if its lower, we are interested only in the left tail of the distribution. We want to know if the test statistic is below the critical value to conclude if we have evidence for our claim. This is then a left tailed test.
A researcher wanted to see if giving a selective serotonin reuptake inhibitor (anti-depressant) would decrease the number of self-injurious behaviors (SIB’s) found in adolescents. They gave the anti-depressant to a group of 8 participants and counted the numbers of SIBs a person performed for a month after taking the drug for 6 months. Here are the number of SIB’S performed by the 8 people, 27, 25, 32, 40, 43, 37, 35, 38.
a. Find the mean variance, and standard deviation of this group.
b. Suppose the u=45, what is the z score?
c. What is the SEM for this particular group?
Answer:
a. The mean of the sample is M=35.
The variance of the sample is s^2=39.125.
The standard deviation of the sample is s=6.255.
b. z=-1.6
c. SEM = 2.212
Step-by-step explanation:
The mean of the sample is M=35.
The variance of the sample is s^2=39.125.
The standard deviation of the sample is s=6.255.
Sample mean
[tex]M=\dfrac{1}{8}\sum_{i=1}^{8}(27+25+32+40+43+37+35+38)\\\\\\ M=\dfrac{277}{8}=35[/tex]
Sample variance and standard deviation
[tex]s^2=\dfrac{1}{(n-1)}\sum_{i=1}^{8}(x_i-M)^2\\\\\\s^2=\dfrac{1}{7}\cdot [(27-(35))^2+(25-(35))^2+(32-(35))^2+(40-(35))^2+(43-(35))^2+(37-(35))^2+(35-(35))^2+(38-(35))^2]\\\\\\[/tex]
[tex]s^2=\dfrac{1}{7}\cdot [(58.141)+(92.641)+(6.891)+(28.891)+(70.141)+(5.64)+(0.14)+(11.39)]\\\\\ s^2=\dfrac{273.875}{7}=39.125\\\\\\s=\sqrt{39.125}=6.255[/tex]
b. If the population mean is 45, the z-score for M=35 would be:
[tex]z=\dfrac{M-\mu}{\sigma}=\dfrac{35-45}{6.255}=\dfrac{-10}{6.255}=-1.6[/tex]
c. The standard error of the mean (SEM) of this group is calculated as:
[tex]SEM=\dfrac{s}{\sqrt{n}}=\dfrac{6.255}{\sqrt{8}}=\dfrac{6.255}{2.828}=2.212[/tex]
After shopping, it took Manuel 87 seconds to push a shopping cart directly to his car. In one-
third of that time, Manuel had moved 58 meters at a constant velocity. What was the cart's
velocity?
Answer:
The carts velocity= 2m/s
Step-by-step explanation:
It took Manuel 87 seconds to push a shopping cart directly to his car.
One third of 87 = 87/3 = 29
In 29 seconds the carts moved 58 meter's.
The carts velocity = distance/time
The carts velocity = 58/29
The carts velocity= 2m/s
4. Calculate the volume of material used in making 100 ft of 4-in. type M, copper tubing.
Answer:
1443.3 in³ or 0.835 ft³
Step-by-step explanation:
Let's begin by listing out the given variables:
length (l) = 100 ft = 1200 in, nominal size = 4 in
From the copper tube of industry standard guide of the design and the installation of piping system, the dimension and physical characteristics of type M copper tubing of nominal size 4 inch is given as
Outer diameter (Do) = 4.125 in ⇒ ro = Do ÷ 2 = 2.0625 in, Inner diameter (Di) = 3.935 in ⇒ ri = Di ÷ 2 = 1.9675 in
calculate the volume of the pipe, we use the formula
V = π(ro² - ri²) * l
V = π(2.0625² - 1.9675²) * 1200
V = 1443.3 in³ or 0.835 ft³
Which of the x-values are solutions to both of the following inequalities? 60 > X and x > 57. Also, Please hurry I will give brainliest to whoever answers 1st.
Answer:
B
Step-by-step explanation:
x must be a number between 60 and 57 and those numbers are 58 or 59
60 is greater than 59, and 59 is greater than 57
Answer:
x = 59
Step-by-step explanation:
The number must be less than 60 from the first inequality and greater than 57 from the second inequality
so the integers allowed are 58,59
Any help would be greatly appreciated
Answer:
0.927
Step-by-step explanation:
Hope this helps.
Answer:
I think it would just be 0.927
Step-by-step explanation:
with 0.9267, 6 is in the thousandth spot. 2 is in the hundredth spot, and 9 is in the tenth spot. Since the number behind 6 is larger than five, you'd round your number 6 in the thousandth spot to a 7. Therefore, you should have 0.927.
The ideal mass for a piece of chocolate is 2.5 ounces. The actual mass for a production can vary by, at most, 0.08
ounces. Create an absolute value inequality and solve it to determine the range of chocolate masses.
9514 1404 393
Answer:
|m-2.5| ≤ 0.08
2.42 ≤ m ≤ 2.58
Step-by-step explanation:
The equation of interest is the one that says the positive difference from the ideal mass is at most 0.08 ounces:
|m -2.5| ≤ 0.08 . . . an absolute value inequality
The solution is found by solving the equivalent compound inequality:
-0.08 ≤ m -2.5 ≤ 0.08
2.42 ≤ m ≤ 2.58 . . . . the range of masses
You are planning a sample survey that involves selecting 11 of the 100 counties in North Carolina. Your sample will be a stratified sample consisting of the 6 most populous counties in the state and 5 counties randomly selected from the remaining 94 counties. Obtain your stratified sample from the US Census Bureau North Carolina county populations in this Excel file. The Excel worksheet has an alphabetical listing of all 100 North Carolina counties in column A and population estimates for July 1, 2011 and July 1, 2012 in columns D and E, respectively. We will use the population values for July 1, 2012 in column E. To simplify the selection of the 11 counties, we will order the counties according to their July 1, 2012 populations.Order the counties by July 1, 2012 population as follows:
Excel 2003
highlight the cell range A5:E105
in the Excel menu bar click on "Data"; in the drop-down menu click "Sort"
near the bottom of the Sort dialogue box click the radio button next to "Header row"
in the first "Sort by" window choose "2012" and make sure that the "Ascending" radio button is selected
click OK
Excel 2010 and Excel 2007
highlight the cell range A5:E105
Click the "Home" tab at the upper left of the Excel window
at the far right of the menu ribbon click on the "Sort and Filter" icon
In the drop-down menu click on "Custom Sort..."
In the upper right-hand corner of the Sort window make sure the box next to "My data has headers" has a check mark; if it does not have a check mark, click in the box to make a check mark appear.
In the Sort window, under Column, sort by "2012"
In the Sort window, under Sort On, choose "values"
In the Sort window, under Order, choose "A to Z"
Click OKThe counties should now be listed in increasing order according to their July 1, 2012 populations. Tyrell County should be listed first (in row 6) with July 1, 2012 population 4,338.
Question 1. Scroll down to the bottom of the worksheet to see the most populous counties. List below the 6 most populous counties and their populations. List the most populous county first and use commas in your population answers.
Answer: The answer is given below
Step-by-step explanation:
In statistics, a stratified sampling is a method of sampling that is gotten from a population that can be divided into subpopulations.
Based on th information provided in n the question, the 6 most populous counties and their populations are provided below
Mecklenburg County, North Carolina 969,031
Wake County, North Carolina 952,151
Guilford County, North Carolina 500,879
Forsyth County, North Carolina 358,137
Cumberland County, North Carolina 324,049
Durham County, North Carolina 279,64
find the arc length of a partial circle
Answer:
23.55 or [tex]\frac{15}{2}[/tex]π
Step-by-step explanation:
The arc is 75% of the full circumference, as the cut away angle is 90º.
To find the arc length, you multiply the ratio of the whole circle that remains by the circumference: [tex]\frac{270}{360}[/tex]×π×2(5)=[tex]\frac{15}{2}[/tex]π, or 23.55 if you round pi to 3.14.
Answer:
7.85
Step-by-step explanation:
Solve this by using the formula for arc length with central angle in degrees.
Do this by identifying the formula and plugging in the given values. The formula for arc length is [tex]arc length = 2\pi r (\frac{theta}{360} )[/tex] , where the theta is represented by the central angle and r is the radius
The radius is shown on the circle is 5 and the theta (angle in degrees) is 90, represented by the tiny square in the middle.
Plug it all into the formula. Your equation should now look like this: arc length = 2 (3.14 or [tex]\pi[/tex]) (5) ([tex]\frac{90}{360}[/tex])
Solve for arc length and enter your answer as a decimal or in terms of pi
y = mx + b is the slope-intercept form of a linear equation where m = slope and b = y-intercept.
Ax + By = C is the standard form of a linear equation.
Which expression gives the y-intercept of the line when the equation is in standard form?
A.-c/b
b.c/-b
c.c/a
d.c/b
Answer:
C/B
Step-by-step explanation:
Ax + By = C
Subtract Ax from each side
Ax -Ax+ By =-Ax+ C
By = -Ax +C
Divide each side by B
By/B = -A/Bx +C/B
y = -A/Bx +C/B
The y intercept is C/B
Five cards are drawn from a standard 52-card playing deck. A gambler has been dealt five cards—two aces, one king, one 3, and one 6. He discards the 3 and the 6 and is dealt two more cards. What is the probability that he ends up with a full house (3 cards of one kind, 2 cards of another kind)? (Round your answer to four decimal places.)
Answer:
The probability that he ends up with a full house is 0.0083.
Step-by-step explanation:
We are given that a gambler has been dealt five cards—two aces, one king, one 3, and one 6. He discards the 3 and the 6 and is dealt two more cards.
We have to find the probability that he ends up with a full house (3 cards of one kind, 2 cards of another kind).
We know that gambler will end up with a full house in two different ways (knowing that he has given two more cards);
If he is given with two kings.If he is given one king and one ace.Only in these two situations, he will end up with a full house.
Now, there are three kings and two aces left which means at the time of drawing cards from the deck, the available cards will be 47.
So, the ways in which we can draw two kings from available three kings is given by = [tex]\frac{^{3}C_2 }{^{47}C_2}[/tex] {∵ one king is already there}
= [tex]\frac{3!}{2! \times 1!}\times \frac{2! \times 45!}{47!}[/tex] {∵ [tex]^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }
= [tex]\frac{3}{1081}[/tex] = 0.0028
Similarly, the ways in which one king and one ace can be drawn from available 3 kings and 2 aces is given by = [tex]\frac{^{3}C_1 \times ^{2}C_1 }{^{47}C_2}[/tex]
= [tex]\frac{3!}{1! \times 2!}\times \frac{2!}{1! \times 1!} \times \frac{2! \times 45!}{47!}[/tex]
= [tex]\frac{6}{1081}[/tex] = 0.0055
Now, probability that he ends up with a full house = [tex]\frac{3}{1081} + \frac{6}{1081}[/tex]
= [tex]\frac{9}{1081}[/tex] = 0.0083.
Answer:
0.0083
Step-by-step explanation:
The gambler will have full house if he is dealt two kings or ace and a king.Now, there are 47 cards left in the deck and two which are aces and three are king.
The probability of these event are [tex]\frac{3C_2}{47C_2}[/tex]
and [tex]\frac{3C_1\times 2C_1}{47C_2}[/tex] respectively. So, the probability of a full house is given as:
[tex]\frac{3C_2}{47C_2}+\frac{3C_1\times 2C_1}{47C_2}[/tex]
=0.0083
The average of four numbers is 38, and the average of the first two numbers is 42, and the average of the last three numbers is 36. What is the second number?
Answer:
40
Step-by-step explanation:
let the numbers be a+b+c+d.
the average of 4 numbers is 38
; (a+b+c+d)/4 = 38
(a+b+c+d) = 152 ......equ1
the average of the first two numbers is 42
; (a+b)/2 = 42
(a+b) = 84 ...... equ2
the average of the last three numbers is 36
; (b+c+d)/3 = 36
(b+c+d) = 108 .....equ3
substitute equ3 into equ1
a + 108 = 152
a= 152 - 108
a = 44
input the value of a into equ2
44 + b = 84
b = 40
the second number is 40.
I hope this helps.
A road crew can pave 2/5 km in 1 1/2 hours.how many km of road can they pave in 10 hours?
Answer:
8/3 km
Step-by-step explanation:
we can represent the given information on a table:
Kilometers time (hours)
2/5 ⇔ 1 1/2
and since we want to know how many kilometers (x) will be paved on 10 hours:
Kilometers time (hours)
2/5 ⇔ 1 1/2
x ⇔ 10
The relationship these 3 numbers have can be described by using the rule of three, which is to multiply the cross quantities on the table (2/5 by 10) and then divide by the remaining amount (1 1/2):
x = [tex]\frac{2}{5}*10[/tex] ÷ [tex]1\frac{1}{2}[/tex]
x = [tex]\frac{20}{5}[/tex] ÷ [tex]1\frac{1}{2}[/tex]
we use [tex]1\frac{1}{2}=\frac{3}{2}[/tex]
x = [tex]\frac{20}{5}[/tex] ÷ [tex]\frac{3}{2}[/tex]
and we make the division:
x = [tex]\frac{20}{5}[/tex] ÷ [tex]\frac{3}{2}[/tex] = [tex]\frac{20*2}{5*3}=\frac{40}{15}[/tex]
we simplify the fraction by dividing the numerator and denominator both by 5, and we get the result:
x = [tex]\frac{8}{3}[/tex]
thus, in 10 hours the crew will pave 8/3 km. Which is about 2.66 km.
Determine the place value of the digit 4 in the number 12.0764
Answer:
ten-thousandths place
Step-by-step explanation:
You start by going to the right side of the decimal. The order is tenths, hundredths, thousandths, ten-thousandths.
What is Three-fourths divided by one-half?
Answer:
3/2
Step-by-step explanation:
(3/4) / (1/2) is equivalent to (3/4)*(2/1), or 6/4, or 3/2.
To divide by a fraction, invert the fraction and multiply instead.
Answer:
the answer is 1 and 1/2
A basket contains 8 green apples, 11 red apples, 5 nectarines, and 12 oranges. Mark randomly chooses a piece of fruit, eats it, then selects another. Find P(a green apple then a nectarine)
Answer:
3.17% probability of selecting first a green apple and then a nectarine.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
P(a green apple then a nectarine)
This is the probability of selecting first a green apple and then a nectarine.
Initially, there are 8+11+5+12 = 36 fruits, of which 8 are green apples. So 8/36 probability of choosing a green apple.
Now, there are 35 fruits, of which five are nectarines. So 5/35 probability of choosing a nectarine.
Then
[tex]p = \frac{8}{36}\times\frac{5}{35} = 0.0317[/tex]
3.17% probability of selecting first a green apple and then a nectarine.
Answer:
Step-by-step explanation:
Select the equivalent expression.
A, B or C?
Answer:
A
Step-by-step explanation:
The relevant rules of exponents are ...
(a^b)^c = a^(bc)
a^-b = 1/a^b
__
[tex]\left(\dfrac{2^{-10}}{4^2}\right)^7=\dfrac{2^{(-10)(7)}}{4^{(2)(7)}}=\dfrac{2^{-70}}{4^{14}}\\\\=\boxed{\dfrac{1}{2^{70}\cdot 4^{14}}}[/tex]
Explain how you could use the strategy solve a simpler problem to solve the equation 3/4x=3/10
Answer:
x = 0.4
Step-by-step explanation:
Let me rewrite it so it looks better:
[tex]\frac{3}{4} x=\frac{3}{10}[/tex]
The first way is to cross multiply.
30x = 12
x=0.4
The other way is to see that the two numerators are the same except for the x on the left side.
You can see the the denominators are 4 and 10.
You can create a proportion of 4 : 10 and apply it to the fractions.
You get that you have to multiply the left side by 0.4, so x = 0.4
Answer:
0.4
Step-by-step explanation:
Use the GCF and the distributive property to find the expression that is
equivalent to 36 + 60.
18 (2+4)
3(12 + 20)
6(6+10)
12 (3+5)
Answer:
[tex]D[/tex]
Step-by-step explanation:
[tex]36 + 60[/tex]
[tex]12(3)+12(5)[/tex]
[tex]12(3+5)[/tex]
Answer:
12( 3+5)
Step-by-step explanation:
Which of the following are valid names for the given triangle? Check all that
apply
T
A
A. ATAY
B. AMAY
C. AMAX
D. AAXM
Ε. ΔΧΜΑ
F. AXMT
Answer:
I think it's just E.
Step-by-step explanation:
When you name triangles, you would often put a Δ and then the letters of the 3 angles. The only answer that fits that criteria is E.
The valid name for the given triangle is ΔΧΜΑ.
What is a triangle?
A triangle is a 3-sided polygon that consists of three edges and 3 vertices. The most vital asset of a triangle is that the sum of the inner angles of a triangle is identical to a hundred and eighty tiers. This belonging is called the attitude sum property of the triangle.
What are the types of triangles?
equilateral, isosceles, scalene, right triangles.
Learn more about triangle here https://brainly.com/question/2938476
#SPJ2
Johnson has recently open his workshop at the main street of a major city in the North East. Johnson estimates about 20 cars arriving at his workshop for repairs everyday. Based on industry data, he estimates that 40% of the arrivals will agree to have the work repaired at his workshop. His average daily cost at the workshop is $1200. He expects to make a revenue of $200 for each car that is repaired. Johnson would like to know the following information:A) The probability that no car will arrive at his workshop for repair on a given day. B) The probability that he will have at least 4 cars to repair on a given day. C) The expected daily profit assuming that he is able to repair all the arriving cars in a day. D) Develop a probability distribution for this problem.
Answer:
a=0.000000002
b=0.95762
c=$2800
Step-by-step explanation:
Kindly check attached picture for other calculation and the Poisson Probability Distribution for the problem.
1. Considere as funções f e g, ambas com domínio Z, dadas por f(x) = x²- 2x e g(x) = x³-1. Associe as colunas e assinale a alternativa que apresenta a sequência correta: *
1 ponto
a) f (-2) ( )29
b) g(-2) ( )15/7
c) f(-1) + g(3) ( )8
d) f(5) : g(2) ( )-9
a) C, D, A, B
b) A, B, D, C
c) D, C, A, B
d) A, C, D, B
ajuuuuuda
Answer:
(A)C,D,A,B
Step-by-step explanation:
[tex]f(x) = x^2- 2x\\g(x) = x^3-1[/tex]
a)
[tex]f(-2) = (-2)^2- 2(-2)\\=4-(-4)\\=4+4\\=8$ (C)[/tex]
b)
[tex]g(-2) = (-2)^3-1\\\=-8-1\\=-9 $(D)[/tex]
c)
[tex]f(-1) = (-1)^2- 2(-1)=1+2=3\\g(3) = (3)^3-1=27-1=26\\f(-1) + g(3)=3+26\\=29$ (A)[/tex]
d) f(5) : g(2)
[tex]f(5) = (5)^2- 2(5)=25-10=15\\g(2) = (2)^3-1=8-1=7\\f(5) :g(2)=15/7$ (B)[/tex]
Base of building 180 meters
Step-by-step explanation:
please give me full question
If f(x) = 6x - 4, what is f(x) when x = 8?
2.
16
044
52
Answer:
44
Step-by-step explanation:
f(x) = 6x - 4
f(8) = 6(8) - 4
f(8) = 48 - 4
f(8)= 44
The value of homes sold in Hampton VA are normally distributed with a mean of $200,000
and a standard deviation of $10,000. If 1216 houses were sold in 2012, how many houses would
have a value greater than one standard deviation above the mean?
Answer:
[tex]X \sim N(200000,100000)[/tex]
Where [tex]\mu=200000[/tex] and [tex]\sigma=10000[/tex]
From the empirical rule we know that within one deviation from the mean we have 68% of the values so then 1 deviation above the mean we will have (100-68)/2 = 16% and then the number of houses that are greater than one deviation above the mean are:
[tex] Number = 1216*0.16 = 194.56[/tex]
And the answer woud be between 194 and 195 houses
Step-by-step explanation:
Let X the random variable that represent the value of homes in Hampton VA of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(200000,100000)[/tex]
Where [tex]\mu=200000[/tex] and [tex]\sigma=10000[/tex]
From the empirical rule we know that within one deviation from the mean we have 68% of the values so then 1 deviation above the mean we will have (100-68)/2 = 16% and then the number of houses that are greater than one deviation above the mean are:
[tex] Number = 1216*0.16 = 194.56[/tex]
And the answer woud be between 194 and 195 houses
The position function of a particle moving along a coordinate line is given, wheresis in feet andtis in seconds.
s(t)= t/t^2+4, t>=0
a. Find the velocity and acceleration functions.
b. Find the position, velocity, speed, and acceleration at time t=1.
c. At what times is the particle stopped?
d. When is the particle speeding up? Slowing down?
e. Find the total distance traveled by the particle from time t=0 to time t=5
Answer:
a) s = (4-t)/(t^2+4)^2, a(t) = (2t^3-24t)/(t^2+4)^3
b) s = 0.2ft, v = 0.12 ft/s, a = -0.176 ft/s^2
c) t = 2s
d) slowing down for t < 2, speeding up for t > 2
e) 0.327 ft
Step-by-step explanation:
The position function of a particle is given by:
[tex]s(t)=\frac{t}{t^2+4},\ \ \ t\geq 0[/tex] (1)
a) The velocity function is the derivative, in time, of the position function:
[tex]v(t)=\frac{ds}{dt}=\frac{(1)(t^2+4)-t(2t)}{(t^2+4)^2}=\frac{4-t^2}{(t^2+4)^2}[/tex] (2)
The acceleration is the derivative of the velocity:
[tex]a(t)=\frac{dv}{dt}=\frac{(-2t)(t^2+4t)^2-(4-t^2)2(t^2+4)(2t)}{(t^2+4)^4}\\\\a(t)=\frac{(-2t)(t^2+4)-4t(4-t^2)}{(t^2+4)^3}=\frac{2t^3-24t}{(t^2+4)^3}[/tex] (3)
b) For t = 1 you have:
[tex]s(1)=\frac{1}{1+4}=0.2\ ft\\\\v(1)=\frac{4-1}{(1+4)^2}=0.12\frac{ft}{s}\\\\a(1)=\frac{2-24}{(1+4)^3}=-0.176\frac{ft}{s^2}[/tex]
c) The particle stops for v(t)=0. Then you equal equation (2) to zero ans solve the equation for t:
[tex]v(t)=\frac{4-t^2}{(t^2+4)^2}=0\\\\4-t^2=0\\\\t=2[/tex]
For t = 2s the particle stops.
d) The second derivative evaluated in t=2 give us the concavity of the position function.
[tex]\frac{d^2s}{dt^2}=a(2)=\frac{2(2)^3-24(2)}{(2^2+4)^3}=-0.062<0[/tex]
Then, the concavity of the position function is negative. For t=2 there is a maximum. Before t=2 the particle is slowing down and after t=2 the particle is speeding up.
e) Due to particle goes and come back. You first calculate s for t=2, then calculate for t=5.
[tex]s(2)=\frac{2}{2^2+4}=0.25\ ft[/tex]
[tex]s(5)=\frac{5}{5^2+4}=0.172\ ft[/tex]
The particle travels 0.25 in the first 2 seconds. In the following three second the particle comes back to the 0.172\ ft. Then, in the second trajectory the particle travels:
0.25 - 0.127 = 0.077 ft
The total distance is the sum of the distance of the two trajectories:
s_total = 0.25 ft + 0.077 ft = 0.327 ft
