Please answer this correctly I want helping hand people to answer this correctly
Answers
Answer:
w = 36
Step-by-step explanation:
You can make a ratio 98 : 84 = 42 : w
[tex]\frac{49}{42}=\frac{42}{w}[/tex]
49w = 1764
w = 36
Related Questions
Identify the correct box-and-whisker plot of the given data. Then identify the interquartile range.
{6, 8, 12, 5, 3, 11, 7, 1, 6} PLEASE HELP
Answers
Answer:
Interquartile range IQR = 5.5
Step-by-step explanation:
Interquartile range IQR = third quartile Q3 - first quartile Q1
IQR = Q3 - Q1 ........1
arranging the data in ascending order;
1,3,5,6,6,7,8,11,12
The median of the data is the 5th number which is 6
Separating the data into two halves;
(1,3,5,6,),6,(7,8,11,12)
The first quartile Q1 is; (the median of the first half)
Q1 = (3+5)/2 = 4
The third quartile Q3 is; (the median of the second half)
Q3 = (8+11)/2 = 9.5
The interquartile range IQR can be derived using equation 1;
IQR = Q3 - Q1 = 9.5 - 4
IQR = 5.5
Please answer this correctly
Answers
Answer:
20.7 miles
Step-by-step explanation:
[tex]2(5.4)+2t=52.2 \\\\10.8+2t=52.2 \\\\2t=41.4 \\\\t=20.7[/tex]
Hope this helps!
Given:
Breadth = 5.4 milesLength = tPerimeter = 52.2 milesTo find out:
Find the value of t ?
Formula used:
Perimeter = 2 ( length + Breadth )
Solution:
We know that,
Perimeter = 2 ( length + Breadth )
☆ Substituting the values in the above formula,we get
=> 52.2 = 2 ( 5.4 + t )
=> 52.2 = 10.8 + 2t
=> 2t = 52.2 - 10.8
=> 2t = 41.4
=> t = 41.4/2
=> t = 20.7
Suppose a researcher is estimating the proportion of trees showing signs of disease in a local forest. They randomly sample 150 trees and find that 25 of them show signs of disease. Calculate the 95% confidence interval for p, the proportion of all trees in the forest showing signs of disease.
Answers
Answer:
[tex]0.167 - 1.96 \sqrt{\frac{0.167(1-0.167)}{150}}=0.107[/tex]
[tex]0.167 + 1.96 \sqrt{\frac{0.167(1-0.167)}{150}}=0.227[/tex]
And the 95% confidence interval would be given (0.107;0.227).
Step-by-step explanation:
Information given
[tex]X= 25[/tex] number of trees with signs of disease
[tex] n= 150[/tex] the sample selected
[tex]\hat p=\frac{25}{150}= 0.167[/tex] the proportion of trees with signs of disease
The confidence interval for the true proportion would be given by this formula
[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
For the 95% confidence interval the significance is [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2=0.025[/tex], and the critical value would be
[tex]z_{\alpha/2}=1.96[/tex]
And replacing we got:
[tex]0.167 - 1.96 \sqrt{\frac{0.167(1-0.167)}{150}}=0.107[/tex]
[tex]0.167 + 1.96 \sqrt{\frac{0.167(1-0.167)}{150}}=0.227[/tex]
And the 95% confidence interval would be given (0.107;0.227).
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
Answers
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
Measurements of the sodium content in samples of two brands of chocolate bar yield the following results (in grams):Brand A: 34.36 31.26 37.36 28.52 33.14 32.74 34.34 34.33 34.95Brand B: 41.08 38.22 39.59 38.82 36.24 37.73 35.03 39.22 34.13 34.33 34.98 29.64 40.60 Let formula415.mml represent the population mean for Brand B and let formula417.mml represent the population mean for Brand A.Find a 98% confidence interval for the difference formula419.mml. Round down the degrees of freedom to the nearest integer and round the answers to three decimal places.
Answers
Answer:
Step-by-step explanation:
For brand A,
Mean, x1 = (34.36 + 31.26 + 37.36 + 28.52 + 33.14 + 32.74 + 34.34 + 34.33 + 34.95)/9 = 33.44
standard deviation, s1 = √(summation(x - mean)²/n
Summation(x - mean)² = (34.36 - 33.44)^2 + (31.26 - 33.44)^2 + (37.36 - 33.44)^2 + (28.52 - 33.44)^2 + (33.14 - 33.44)^2 + (32.74 - 33.44)^2 + (34.34 - 33.44)^2 + (34.33 - 33.44)^2 + (34.95 - 33.44)^2 = 49.6338
Standard deviation = √(49.6338/9
s1 = 2.35
For brand B,
Mean, x2 = (41.08 + 38.22 + 39.59 + 38.82 + 36.24 + 37.73 + 35.03 + 39.22 + 34.13 + 34.33 + 34.98 + 29.64 + 40.60 )/13 = 36.89
Summation(x - mean)² = (41.08 - 36.89)^2 + (38.22 - 36.89)^2 + (39.59 - 36.89)^2 + (38.82 - 36.89)^2 + (36.24 - 36.89)^2 + (37.73 - 36.89)^2 + (35.03 - 36.89)^2 + (39.22 - 36.89)^2 + (34.13 - 36.89)^2 + (34.33 - 36.89)^2 + (34.98 - 36.89)^2 + (29.64 - 36.89)^2 + (40.60 - 36.89)^2 = 124.5024
Standard deviation = √(124.5024/13
s2 = 3.09
The formula for determining the confidence interval for the difference of two population means is expressed as
Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
For a 98% confidence interval, we would determine the z score from the t distribution table because the number of samples are small.
Degree of freedom =
(n1 - 1) + (n2 - 1) = (9 - 1) + (13 - 1) = 20
z = 2.528
x1 - x2 = 33.44 - 36.89 = - 3.45
Margin of error = z√(s1²/n1 + s2²/n2) = 2.528√(2.35²/9 + 3.09²/13) = 2.935
The 98% confidence interval is
- 3.45 ± 2.935
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?
Answers
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
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
Answers
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
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.
Answers
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.
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?
Answers
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?
Answers
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.
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?
Answers
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
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
Answers
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]
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.
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
What is Three-fourths divided by one-half?
Answers
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 coat manufacturer puts 431 coats in a shipment. If they sent out 80 shipments, how many coats would they have sent out?
Answers
Answer:
80 shipments will be 80 * 431 = 34,480 coats.
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)
Answers
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:
Any help would be greatly appreciated
Answers
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.
Answers
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
A population has a standard deviation of 5.5. What is the standard error of the sampling distribution if the sample size is 81?
Answers
Answer:
[tex]\sigma = 5.5[/tex]
And we have a sample size of n =81. We want to estimate the standard error of the sampling distribution [tex]\bar X[/tex] and for this case we know that the distribution is given by:
[tex] \bar X \sim N(\mu ,\frac{\sigma}{\sqrt{n}})[/tex]
And the standard error would be:
[tex]\sigma_{\bar x}= \frac{\sigma}{\sqrt{n}}[/tex]
And replacing we got:
[tex]\sigma_{\bar x}=\frac{5.5}{\sqrt{81}}= 0.611[/tex]
Step-by-step explanation:
For this case we know the population deviation given by:
[tex]\sigma = 5.5[/tex]
And we have a sample size of n =81. We want to estimate the standard error of the sampling distribution [tex]\bar X[/tex] and for this case we know that the distribution is given by:
[tex] \bar X \sim N(\mu ,\frac{\sigma}{\sqrt{n}})[/tex]
And the standard error would be:
[tex]\sigma_{\bar x}= \frac{\sigma}{\sqrt{n}}[/tex]
And replacing we got:
[tex]\sigma_{\bar x}=\frac{5.5}{\sqrt{81}}= 0.611[/tex]
What is the slope of the line described by the equation below?
y= 10x + 2
A. -10
B. 10
C. 2
O D. -2
Answers
Answer:
B because when you compare y= mx+ c where M is the slope or gradient
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.
Answers
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.
Determine the place value of the digit 4 in the number 12.0764
Answers
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.
Explain how you could use the strategy solve a simpler problem to solve the equation 3/4x=3/10
Answers
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:
Find the least common denominator for these fractions. 5/7 and 4/6
Answers
Answer: 21 is the least common denominator
Step-by-step explanation:
The least common denominator of 7 and 6 is 42, but will be simplified.
The fractions would turn into 30/42 and 28/42.
Now simplify.
15/21 and 14/21
This cannot be simplified any further without losing the common denominator
Answer:
The least common denominator is 21.
Step-by-step explanation:
Put the fractions out of a denominator of 42
5/7 = 30/42 4/6 = 28/42
Divide both fractions by 2
35/42 = 15/21 4/6 = 14/21
4. Calculate the volume of material used in making 100 ft of 4-in. type M, copper tubing.
Answers
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
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?
Answers
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
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
Answers
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
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
Answers
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
Matt paid $6.65 to download 7 song . What is the unit rate
Answers
Answer:
$0.95 per song.
Step-by-step explanation:
If it is $6.65 for 7 songs, divide that cost by the number of songs and you get the unit rate. Hope this helps!
If f(x) = 6x - 4, what is f(x) when x = 8?
2.
16
044
52
Answers
Answer:
44
Step-by-step explanation:
f(x) = 6x - 4
f(8) = 6(8) - 4
f(8) = 48 - 4
f(8)= 44
