If p varies directly as r square p =3.2 when r=4 find the value of p when r=6.5
Answers
Answer:
I hope this is right :)..
Related Questions
A monument casts a shadow 28.7 feet long. a man who is 6 feet tall casts a shadow 8.2 feet long. the triangle drawn with the monument and its shadow is similar to the triangle drawn with the man and his shadow. how tall is the monument? *complete the statement by providing the correct answer in number form.
Answers
The information presented states that perhaps the sculpture is 21 feet in height.
What exactly is a triangle?A closed, two-dimensional triangle has three sides, three angles, and three vertices. A polygon also includes a triangle. Triangle ABC is shown in the image above. A triangle through one obtuse angle (more than 90°) and several acute angles is known as an obtuse trio (or obtuse-angled triangle). No Riemann triangle can contain more than one obscure angle because in Euclidean geometry, a rectangle angles must add up to 180°.
AB/DE = BC/EF
f/6 = 28.7/8.2
=> f/6 = 3.5
=> f = 3.5 *6 = 21 ft
Consequently, the memorial is 21 feet tall.
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The complete question is-
A monument casts a shadow 28. 7 feet long. A man who is 6 feet tall casts a shadow 8. 2 feet long. The triangle drawn with the monument and its shadow is similar to the triangle drawn with the man and his shadow. How tall is the monument? Complete the statement by providing the correct answer in number form.
One coin in a collection of 16 coins has two heads, the rest being fair coins with a head and a tail each. A coin is chosen at random from the collection and tossed four times, coming up with a head on each of the four tosses. What is the probability that the chosen coin is the two-headed one?
my work:
bayes' theorem. Bayes' theorem states that:
P(A|B) = P(B|A) * P(A) / P(B)
where A is the event that the chosen coin is the two-headed one, B is the event that the coin comes up heads on all four tosses, P(A|B) is the probability of A given B, P(B|A) is the probability of B given A, P(A) is the prior probability of A, and P(B) is the total probability of B.
in this case, P(A) is the probability that the chosen coin is the two-headed one out of the collection of 16 coins, which is 1/16. P(B|A) is the probability that the two-headed coin comes up heads on all four tosses, which is 1. P(B) is the total probability that the coin comes up heads on all four tosses, which can be found by considering all possible coins:
P(B) = (1/16) * 1 + (15/16) * (1/2)^4
P(A|B) = P(B|A) * P(A) / P(B) = 1 * (1/16) / P(B)
so the probability that the chosen coin is the two-headed one given that it comes up heads on all four tosses is (1/16) / P(B)
is it 1/16
Answers
The probability that the chosen coin is the two-headed one will be 1/16.
How to calculate the probabilityIt should be noted that probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events.
In this situation, one coin in a collection of 16 coins has two heads, the rest being fair coins with a head and a tail each.
When a coin is chosen at random from the collection and tossed four times, coming up with a head on each of the four tosses, the probability that the chosen coin is the two-headed one will be:
= Number of two headed coins / Total coins
= 1/16
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Which is bigger feet or miles?
Answers
Answer:
1 mile is about 1.6 km
1 feet is 30cm.
Safe to say a mile is bigger.
Answer:
Miles are bigger than feet.
Step-by-step explanation:
In 1 mile, there are 5,280 feet. So miles would be 5,280 times bigger than feet.
Given the function y=|x+1|. State the domain over which the function is increasing.
Answers
Let’s take a look at what this function looks like when graphed, so we can better understand the nature of the domain. If you graph y=|x+1|, you will end up with a “V”
We can see that the domain of this function is all real numbers, as the function is defined over all real numbers.
Now, let’s examine the behavior of the function in this domain. We see that the function is increasing over certain regions of the domain. Specifically, the function is increasing when x is less than -1 and when x is greater than -1. This can be seen clearly in the graph, as the “V” shape shows that the function increases on either side of the point where x=-1.
So, to summarize, we can say that the domain of the function y=|x+1| is all real numbers, and that within this domain, the function is increasing when x is less than -1 and greater than -1.
Eliud was running 125 miles per week. Now, he’s running 20% more miles per week.
b) How many miles is Eliud running per week? Write and solve an equation to determine how many miles Eliud is now running per week, r.
Answers
Answer:
125 miles per week
Step-by-step explanation:
He is running: 100 x (100 + 20)% = 100 x 120% = 100 x 6/5 = 125 miles
He is running 125 miles per week
=> r = 125 miles
A map has a scale of 1 : 500.
Martha measures a distance of
5 cm on the map. What actual
distance in m does this
correspond to?
Answers
Answer: it is 0.05 m
HELP FOR BRAINLIEST! I NEED IT ASAP
Answers
Answer:
$17.08
Step-by-step explanation:
Ok, so we know it takes 61-23 = 38 minutes of call to change the credit from $22.24 to $17.68.
Basically, it takes 43 minutes to lose 22.24 - 17.68 = $4.56
38 minutes - $4.56
5 minutes - $4.56 x 5 /38 = 0.6
I took 5 minutes because 5 + 61 = 66
Now, we know it takes 61 minutes for the person to have $17.68 remaining.
So, if we had 5 minutes, it becomes 17.68 - 0.6 = $17.08 remaining.
Pls mark as brainliest if possible. Cheers
Pleaseeee help this is due today
Answers
Answer:
Its 24ft
Step-by-step explanation:
Andrew drove 135 miles in 3 hours. If he drove at a constant rate, how far did he travel each hour?
Answers
Answer:
45 miles per hour is the answer. The unit rate (r) is calculated by dividing the number of miles (d) by the number of hours (t): r = d/t. We know that d equals 135 miles and t equals 3 hours. The unit rate is thus r = 135 miles/3 hours. r is equal to 135/3 miles per hour. r equals 45 miles per hour. 45 miles per hour is the unit rate. I hope this was helpful. Please let me know if you require any extra assistance!
Step-by-step explanation:
1000 kg of limestone is subjected to intense heat and high pressure to form marble. all but one of the statements applies to the formation of the marble.
a) marble is a metamorphic rock.
b) about 1000 kg of marble is produced.
c) marble is formed by recrystalization.
d) marble is formed close to earth's surface.
Answers
1000 kg of limestone is subjected to intense heat and high pressure to form marble. So, the statement "about 1000 kg of marble is produced" is applies to the formation of the marble. Hence, option b is correct.
When limestone is subjected to the heat and pressure of metamorphism, marble is created as a metamorphic rock. Calcite (CaCO3) makes up the majority of its composition, but it also frequently includes other minerals such clay, mica, quartz, pyrite, iron oxides, and graphite.
When limestone undergoes a process known as metamorphism, which involves heat and tremendous pressure, marble is created. The marble's interconnecting calcite crystals are created when the calcite limestone recrystallizes after metamorphism.
Hence, 1000 kg of limestone is subjected to intense heat and high pressure to form marble. So, the statement "about 1000 kg of marble is produced" is applies to the formation of the marble. Hence, option b is correct.
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paula is making hot apple cider using apple juice and cinnamon candy. her recipe calls for 0.5 cups of cinnamon candy for every 2 pints of apple juice. how many pints of apple juice does she need for 2 cups of cinnamon candy?
Answers
On solving the provided question, we can say that by unitary method 8 pints of apple juice does she need for 2 cups of cinnamon candy
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
Paula is brewing hot apple cider with cinnamon caramel and apple juice.
her recipe calls for = 0.5 cups of cinnamon
candy for every = 2 pints of apple juice
she need for 2 cups of cinnamon candy are -
for 1 = she need 2/0.5
for 2 = she needs 2/0.5 * 2 = 8
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tudents were surveyed on the number of siblings they have. the following probability model was created from the results. a 2-column table with 5 rows. column 1 is labeled number of siblings with entries 0, 1, 2, 3, 4 or more. column 2 is labeled probability with entries 0.223, 0.532, 0.121, 0.085, 0.039. what is the probability that a randomly selected student has at least 2 siblings? enter your answer as a decimal rounded to the thousandths place. p(at least 2 siblings)
Answers
The probability of a randomly selected student having at least two siblings is 0.160, which is equal to 0.160 when rounded to the thousandths place.
The probability of a randomly selected student having at least two siblings can be calculated by adding the probabilities of having two and three or more siblings.
Using the given probabilities, the calculation is as follows:
P(at least 2 siblings) = P(2 siblings) + P(3 or more siblings)
= 0.121 + 0.039
= 0.160
Therefore, the probability of a randomly selected student having at least two siblings is 0.160, which is equal to 0.160 when rounded to the thousandths place.
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find the curvature of r(t) = 7t, t2, t3 at the point (7, 1, 1).
Answers
Therefore ,as a result, the answer to the given circle problem is
√ 1996/(√ 62)3 =0.0915, which is the curvature.
A circle is what?A circle is created in the plane by each point that is a specific distance from another point (center). Thus, it is a curve made up of points that are separated from one another by a defined distance in the plane. Additionally, it is rotationally symmetric the about center at every angle. Every pair of endpoints in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle. Additionally, it is rotationally equal about the center at every angle.
Here,
Given: (7, 2t, 3t2) r'(t)
r''(t)= (0, 2, 6t) (0, 2, 6t)
r(t) x r(t) = (6t2, -42t, 14)
(36t4 + 1764t2 + 196) = sqrt (r'(t) x r"(t)
|r'(t)|= sqrt (49 + 4 T 2 + 9 T 4)
We know that t = 1 at (7,1,1), therefore sqrt (36 + 1764 + 196) = sqrt 1996 |r'(t)| = √ (49 + 4 + 9) = √ 62.
The curvature is then equal as√ 1996/(√ 62)3 =0.0915
Therefore ,as a result, the answer to the given circle problem is √ 1996/(√ 62)3 =0.0915, which is the curvature.
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two friends are playing with water balloons. they each start at the bucket of balloons and walk in opposite directions before tossing their balloons at each other. joy walked 12 steps forward, and shaunte walked 8 steps backwards. which expression correctly represents the distance between the friends?
Answers
The correct expression that represents the distance between the friends is 4 steps.
To calculate this
Joy walked 12 steps forward and Shaunte walked 8 steps backward. To find the distance between the two friends, we can add the number of steps they each took, so the expression would be:
12 + (-8) = 12 - 8 = 4
So the correct expression that represents the distance between the friends is 4 steps.
Note that the negative sign in front of Shaunte's steps indicates that she walked backward, and the positive sign in front of Joy's steps indicates that she walked forwards.
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a cylinder has a diameter of 8 cm and a height of 6 cm. what is the volume of the cylinder? use 3.14 for pi, and round your answer to the nearest hundredth. 75.36 cm3 150.72 cm3 301.44 cm3 1,205.76 cm3
Answers
The volume of the cylinder is 301.44 cm³. We use the radius that is half of diameter length in the formula for the volume of a cylinder.
What is the volume of a cylinder?The formula for the volume of a cylinder is
V = πr²h
Where
V = volumer = radius of cylinderh = height of cylinderA cylinder has
Diameter, d = 8 cmHeight, h = 6 cmUsing π = 3.14, find the volume of the cylinder!
We find the radius of the cylinder.
r = ½d
r = ½(8) cm
r = 4 cm
The volume of the cylinder would be
V = πr²h
V = (3.14)(4)²(6)
V = 18.84 (16)
V = 301.44 cm³
Hence, the volume of a cylinder with the diameter of 8 cm and height of 6 cm is 301.44 cm³.
The correct option is (c).
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Answer:
301.44
Step-by-step explanation:
v=3.14 times radius squared times height
Diameter is the radius times 2
8 the diameter divided by 2 is 4
replace those
v=(3.14)4^2(6)
final answer is 301.44
Your family drives 52.2 miles in one hour. How far does your family drive in 1.5 hours?
Answers
Answer:
78.3 miles
Step-by-step explanation:
Your family drives 52.2 miles in one hour. How far does your family drive in 1.5 hours?
52.2 : 1 = x : 1.5
x = 52.2 × 1.5 : 1
78.3 miles
hello! please help me find the x & y intercepts, domain & range, relative minimum & maximum, increasing & decreasing intervals, and positive & negative intervals.. thank you :)
Answers
Solve the equation y = f(x) to determine the values of the independent variable x and obtain the domain.
How do you find the domain and range of X and Y?We can easily identify the values of the independent variable x and the domain by solving the equation y = f(x). The range may then be found by solving for x.
For a relation, the domain and range are defined as sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively. For instance, if the relationship is R = (1, 2), (2, 2), (3, 3), and (4, 3), then
The collection of all x-coordinates with values 1, 2, 3, and 4 is known as the domain.Range is the set of all y-coordinates with values of 2, 3.
The elements that make up a function are its domain and range. A function's domain is the set of all potential input values, while its range is the range of possible output values. Range, Function, and Domain.
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3= blank +1/2+2/2+1/2
Answers
Answer:
3 = 1 + 1/2 + 2/2 + 1/2
The blank number is:
1
Step-by-step explanation:
2/2 = 1
1/2 + 1/2 = 2/2
3 = a + 1/2 + 2/2 + 1/2
3 = a + 1 + 1
3 = a + 2
3 - 2 = a
a = 1
I can't remember how to solve for inequalities or graph them, can someone help me? (This is a repost with a picture instead)
Answers
Answer:
see below
Step-by-step explanation:
1. -2/3x [tex]\geq[/tex] 7
first, we need to divide -2/3 from x and 7 to get x alone, we also need to flip the inequality sign since we are dividing by a negative
x [tex]\leq[/tex] 21/2
or x [tex]\leq[/tex] 10 1/2
2. 32 > 23 - x
first, rearrange the inequality
32 + x > 23
subtract 32 from both sides
x > -9
3. 2 (x + 6) < 10
divide both sides by 2
x + 6 < 5
subtract 6 from both sides
x < -1
4. 15 - 4x [tex]\leq[/tex] 3x - 6
rearrange the equation
-4x + 3x [tex]\leq[/tex] - 15 - 6
-7x [tex]\leq[/tex] - 21
multiply both sides by -1 and reverse the inequality sign
7x [tex]\geq[/tex] 21
divide both by 7
x [tex]\geq[/tex] 3
im super sorry but im not sure how to help you with the graphing :(
at what point do the curves r1(t) = t, 2 − t, 35 + t2 and r2(s) = 7 − s, s − 5, s2 intersect?
Answers
The curves r1(t) = t, 2 − t, 35 + t2 and r2(s) = 7 − s, s − 5, s2 intersect at the point (2.5, -2.5).
What is equation?An equation is a mathematical statement that asserts the equality of two expressions. It is usually written with an equals sign (=) and expresses the relationships between different variables and constants. Equations are often used to model or describe physical, biological, and chemical phenomena and relationships.
This can be seen by solving the system of equations formed by equating the two curves:
t = 7 − s
2 − t = s − 5
35 + t2 = s2
Solving the first two equations for t and s yields t = 7 − s and s = 2 − t. Plugging these equations into the third equation yields:
35 + (7 − s)2 = s2
By rearranging terms and solving, this equation can be solved for s, which yields s = 2.5. Plugging this value back into the first two equations yields t = 7 − 2.5 = 4.5 and s = 2 − 4.5 = -2.5. Thus, the two curves intersect at the point (2.5, -2.5).
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If m < 1 equals (6x + 3) and m < 2 equals 117 what is the value of x
Answers
The value of x is 19.
What is the slope intercept?
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line. An example of a linear equation is y=mx + b.
We can start by using the information given in the problem to set up an equation. We know that:
m < 1 = 6x + 3
m < 2 = 117
We are also given that m < 1 and m < 2 represent different values.
Now we can substitute the second equation into the first equation:
6x + 3 = 117
To solve for x, we can subtract 3 from both sides:
6x = 114
Finally, we can divide both sides by 6:
x = 19
Hence, the value of x is 19.
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Need help with this...
Answers
Find the slope of the graphed line please help asap I'll give brainliest answer pleasee
Answers
Ur answer would be “the slope is 1/4” :)
Choose the letter of the expression listed on the right that completes each step to show how to use the power and product properties of logarithms to prove that the quotient property is true for logb x y . logb x y = = = =
Answers
By using the logarithmic properties we can probe that,
(a) [tex]$\log _b \frac{x}{y}=\log _b x+\log _b y^{-1}$[/tex]
(b) [tex]$\log _b \frac{x}{y}=\log _b x-\log _b y$[/tex]
What is a logarithm?The logarithm is exponentiation's opposite function In mathematics. This means that the exponent which [tex]$b$[/tex] must be realized To produce a number [tex]$x$[/tex] is the logarithm of [tex]$x$[/tex] the base [tex]$b$[/tex]. For Instance, because[tex]$1000=10^{\wedge} 3$, Its logarlthm In base 10 is 3 , or $\log 10=3$.[/tex]
Given: [tex]$\log _b \frac{x}{y}$[/tex]
We have to prove,
(a) [tex]$\log _b \frac{x}{y}=\log _b x+\log _b y^{-1}$[/tex]
(b) [tex]$\log _b \frac{x}{y}=\log _b x-\log _b y$[/tex]
(a) Consider, [tex]$\log _b \frac{x}{y}=\log _a x+\log _b y^{-1}$[/tex]
L. H. S [tex]$=\log _b \frac{x}{y}$[/tex]
Using the Identity: [tex]$\frac{1}{\nu}=y^{-1}$[/tex]
L.H.S [tex]$=\log _b x y^{-1}$[/tex]
Using Identity: [tex]$\log _b m n=\log _b m+\log _b n$[/tex]
[tex]$$\Rightarrow \text { L.H.S }=\log _b x+\log _b y^{-1}$$[/tex]
Hence, L.H.S = R.H.S
(b) Consider [tex]$\log _b \frac{x}{y}=\log _b x-\log _b y$[/tex]
L.H.S [tex]$=\log _b \frac{x}{y}$[/tex]
Using the Identity
[tex]$$\begin{aligned}& \log _b \frac{m}{n}=\log _b m-\log _b n \\& \Rightarrow \text { L.H.S }=\log _b x-\log _b y \\& \text { L.H.S = R.H.S }\end{aligned}$$[/tex]
Hence, proved.
Hence, by using the logarithmic properties we can probe that,
(a) [tex]$\log _b \frac{x}{y}=\log _h x+\log _b y^{-1}$[/tex]
(b) [tex]$\log _b \frac{x}{y}=\log _b x-\log _b y$[/tex]
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Answer:
=C
=A
=D
=B
Step-by-step explanation:
Correct on Edge
Mr. Weinstein has a savings account with a balance of $19,211.34. It pays 4% interest compounded daily.
a. What is his ending balance after three years, if no other deposits or withdrawals are made?
b. How much interest does he earn over the three years?
Answers
assuming a year is 365 days
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$19211.34\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{daily, thus 365} \end{array}\dotfill &365\\ t=years\dotfill &3 \end{cases}[/tex]
[tex]A = 19211.34\left(1+\frac{0.04}{365}\right)^{365\cdot 3} \implies \stackrel{balance}{\boxed{A \approx 21660.58}}~\hfill \underset{interest}{\stackrel{21660.58~~ - ~~19211.34}{\boxed{\approx 2449.24}}}[/tex]
14. money a pancake breakfast fundraiser served 400 people and charged $5
for adults and $3.50 for children. use x to represent the number of adults
served and write an expression to show how much money was raised. then
simplify the expression.
Answers
A = 1.5x + 1400 is the equation for how much money was raised.
What is an equation ?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation.
The "=" sign and terms on both sides must always be present when writing an equation. both parties.
According to our question-
Let's stand in for
Adults = x, number of them
children = y is the number.
The total amount raised equals A
In the query, it is stated that:
400 people were fed during a pancake breakfast fundraiser that cost $5 for adults and $3.50 for kids.
Consequently, x + y = 400. Formula 1: y = 400 - x
Hence:
A is equal to $5 x and $3.50 y.
Where A = 5x + 3.50 and y = 400 - x (400 - x)
A = 5x + 1400 - 3.50x A = 1.5x + 1400
The formula for calculating how much money was raised is as follows:
A = 1.5x + 1400
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Here are two spinners.
6
spinner a
spinner b
3
spinner a
2
2
4
6
the two arrows are spun and the score is obtained
ows are
ng the t by multiplying the two numbers.
a) complete the possibility space.
1
3
spinner b
3
12
e the pe
un
10
5
b) what is the probability of scoring a total of 6?
10
c) what is the probability of scoring a total greater than 10?
me probability of scoring a total of 7
Answers
The probability of scoring a total of 6 is 1/36 and the probability of scoring a total greater than 10 is 25/36.
a) The possibility space for two spinners is all the possible combinations of numbers that the two spinners can produce. The possibilities for spinner A are 1, 2, 3, 4, 5, and 6, and for spinner B are also 1, 2, 3, 4, 5, and 6. Therefore, the possibility space is 1x1, 1x2, 1x3, 1x4, 1x5, 1x6, 2x1, 2x2, 2x3, 2x4, 2x5, 2x6, 3x1, 3x2, 3x3, 3x4, 3x5, 3x6, 4x1, 4x2, 4x3, 4x4, 4x5, 4x6, 5x1, 5x2, 5x3, 5x4, 5x5, 5x6, and 6x1, 6x2, 6x3, 6x4, 6x5, 6x6.
b) The probability of scoring a total of 6 is 1/36, since there is only one possibility (3x2) that produces a score of 6.
c) The probability of scoring a total greater than 10 is 25/36, since there are 25 combinations of numbers (4x3, 4x4, 4x5, 4x6, 5x2, 5x3, 5x4, 5x5, 5x6, 6x1, 6x2, 6x3, 6x4, 6x5, 6x6) that produce a score greater than 10.
The possibility space for two spinners is all the possible combinations of numbers that the two spinners can produce, which is 1x1, 1x2, 1x3, 1x4, 1x5, 1x6, 2x1, 2x2, 2x3, 2x4, 2x5, 2x6, 3x1, 3x2, 3x3, 3x4, 3x5, 3x6, 4x1, 4x2, 4x3, 4x4, 4x5, 4x6, 5x1, 5x2, 5x3, 5x4, 5x5, 5x6, and 6x1, 6x2, 6x3, 6x4, 6x5, 6x6. The probability of scoring a total of 6 is 1/36 and the probability of scoring a total greater than 10 is 25/36.
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There is 5 mg in 2.5 mL how many milligrams are in 7 mL
Answers
Answer: 14 mg
Step-by-step explanation:
5 mg/2.5 mL = 2 mg per mL
2 mg * 7 mL = 14 mg
Answer:
there are 14 milligrams in 7 mL.
Step-by-step explanation:
to find the number of milligrams in 7 mL, you can use the proportion:
(5 mg) / (2.5 mL) = (x mg) / (7 mL)
Where x is the number of milligrams in 7 mL. To solve for x, you can cross-multiply and divide:
(5 mg) * (7 mL) = (2.5 mL) * (x mg)
x = (5 mg) * (7 mL) / (2.5 mL)
x = 14 mg
0) A half-marathon is roughly 13.1 miles long. Which equation could be used to determine the time, t it takes to run a marathon as a function of the average speed, s, of the runner where t is in hours and s is in miles per hour?A) t = 13.sB) t = 13.1/sC) t= 13.1 - 13.1sD) t= 13.1s - S/13.1
Answers
The formula distance = speed x time must be used to calculate the duration of a marathon as a function of the runner's average speed.
1: List the known data. For example, a marathon is 13.1 miles long, and an average runner moves at s miles per hour.
2 :Rearrange the equation to solve for time in Step 2: Time = Speed/Distance
3: Enter the known numbers for distance and speed into the equation: time = 13.1 miles per second.
4: If necessary, simplify the equation. The units of miles will cancel out because the time is measured in hours and the speed in miles per hour, therefore the ultimate unit of time will be hours.
The final answer is t = 13.1/s, which expresses the duration of a marathon (in hours) as a function of the runner's average speed (in miles per hour).
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Find the 95% confidence interval for the standard deviation of the lengths of pipes if a sample of 21 pipes has a standard deviation of 14.6 inches. Show each step.
Answers
The 95% confidence interval for the standard deviation of the lengths of pipes is (10.2, 25.6)
given that
95% confidence interval for the standard deviation of the lengths of pipes
a sample of 21 pipes
standard deviation of 14.6 inches
chi-squared(1 - a/2) < or = (n-1)s^2/(std. dev.)^2 < or = chi-squared(a/2)
in the above
a is alpha
std is standard deviation
a = (1-95/100) = 1 - 0.95 = 0.05
then, degree of freedom = 21 - 1 = 20
chi-squared(0.975) = 20.5
chi-squared(0.025) = 3.25
chi-squared for 20.5 = (21-1)×[tex](14.6)^{2}[/tex] / 20.5 = 103.98
chi - squared for 3.25 = (21-1)×[tex](14.6)^{2}[/tex] / 3.25 = 655.8
we need to square-root of the above values
chi-squared for 20.5 = [tex]\sqrt{103.98}[/tex] = 10.2
chi - squared for 3.25 = [tex]\sqrt{655.8}[/tex] = 25.6
the 95% confidence interval for the standard deviation of the lengths of pipes is (10.2, 25.6)
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