The time taken to complete a motorcycle race is normally distributed, with an average time (µ) of 2.5 hours and a standard deviation () of 0.5 hours.
What is the probability that a randomly selected cyclist will take at least 2.45 hours to complete the race?

Answers

Answer 1

Using the normal distribution, there is a 0.5398 = 53.98% probability that a randomly selected cyclist will take at least 2.45 hours to complete the race.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 2.5, \sigma = 0.5[/tex]

The probability that a randomly selected cyclist will take at least 2.45 hours to complete the race is one subtracted by the p-value of Z when X = 2.45, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2.45 - 2.5}{0.5}[/tex]

Z = -0.1

Z = -0.1 has a p-value of 0.4602.

1 - 0.4602 = 0.5398.

0.5398 = 53.98% probability that a randomly selected cyclist will take at least 2.45 hours to complete the race.

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Related Questions

The first shelf of one bookcase is 2 inches off the ground. The second shelf is 1’5” above the first the third shelf is 1’3” above the second and the fourth shelf is 1’2” above the third. The top shelf is 1’4” above the fourth how high off the ground is the top shelf.

Answers

answer: 5'6"

step by step: 1'5"+2"=1'7"+1'3"=3'0"+1'2"=4'2"+1'4"=5'6"

D
(x+2)(x+6)=0
In the problem shown, to conclude that x+2=0 orx+6=0, one must use the:
O zero product property
O division property
O transitive property
O multiplication property
H
OI

Answers

Answer:

zero product property

Step-by-step explanation:

To conclude that x+2=0 or x+6=0 from the equation (x+2)(x+6)=0, one must use the zero product property.

The zero product property states that if the product of two factors is equal to zero, then at least one of the factors must be equal to zero. In this case, if (x+2)(x+6)=0, it means that the product of (x+2) and (x+6) is zero. Therefore, we can conclude that either (x+2) = 0 or (x+6) = 0, based on the zero product property.

What is the value of x *
7+5x
47°

Answers

The answer is going to be 8

Answer: X = 8

Step-by-step explanation:

47 - 7 = 40

40 / 5 = 8

x = 8

A rectangle has an area of 114cm squared and a perimeter of 50 cm. What are its dimensions

Answers

Answer:

width = 6

length = 9

Step-by-step explanation:

Perimeter = 2(length + width) or P = 2(l + w)

2(l + w) = 50

l + w = 25

l = 25 - w

Area = length x width or A = lw

lw = 114

Substitute l = 25 - w into the lw = 114

(25 - w)w = 114

25w - w^2 = 114

-w^2 + 25w - 114 = 0

=> w^2 - 25w + 114 = 0

we have x = [-b ± √(b^2 - 4ac)] / 2a

w = [-(-25) ± √((-25)^2 - 4(1)(114)))] / 2(1)

w = [25 ± √(625 - 456)] / 2

w = [25 ± √(169)]/2

w = [25 ± 13]/2

w = [25 + 13]/2 = 38/2 = 14

or

w = [25 - 13]/2 = 12/2 = 6

if width = 14, length = 25 - 14 = 11

then area = 14 x 11 = 154, this is incorrect answer

if width = 6, length = 25 - 6 = 19

then area = 6 x 19 = 114, this is correct answer

Please help urgent thank you

Answers

If he wants an average of 84, he needs to get at least 93 points.

What score does he need to get in the next test?

Remember that the average value between 3 values A, B, and C is:

(A + B + C)/3

Here we know that the first two scores are 76 and 83 points, let's say that the third score is x, if we want to have an average of 84 or more, then we need to solve:

(76 + 83 + x)/3 = 84

159 + x = 252

x = 252 - 159

x = 93

So he needs to get at least 93 points in the next exam.

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What is the length of this circle?

Answers

The length of arc length s is 1152π² or 11358.26.

We have,

The arc length of a circle can be calculated using the formula:

Arc Length = 2πrθ/360

Where:

π is a mathematical constant approximately equal to 3.14159.

r is the radius of the circle.

θ is the central angle subtended by the arc, measured in degrees.

The arc length of a circle can be written as:

s = angles/360 x 2πr _______(1)

Now,

r = 4 cm

Angle = (2/5)π

Now,

Substitute in (1).
s = angles/360 x 2πr

s = (2/5)π/360 x 2π x 4

s = 2π x 72 x 2π x 4

s = 4π² x 288

s = 1152π²

or

s = 11358.26

Thus,

The length of arc length s is 1152π² or 11358.26.

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Find k so the product of the roots is -4 if 3x² + 5x + 3k = 0

Answers

Answer:

k = - 4

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 ) , then the product of the roots is [tex]\frac{c}{a}[/tex]

3x² + 5x + 3k = 0 ← is in standard form

with a = 3 and c = 3k , then

[tex]\frac{c}{a}[/tex] = - 4 , that is

[tex]\frac{3k}{3}[/tex] = - 4 ( multiply both sides by 3 to clear the fraction )

3k = - 12 ( divide both sides by 3 )

k = - 4

How many different ways can president, vice president, and secretary be chosen from a group of 24 individuals?

Answers

The number of ways to choose a president, vice president and secretary from a set of 24 individuals is given as follows:

12,144 ways.

What is the permutation formula?

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

The permutation formula is used when the order in which the elements are chosen is important, which is the case for this problem. The order is important as there are different roles, that is, president, vice president and secretary.

For this problem, 3 people are chosen from a set of 24, hence the number of ways is given as follows:

P(24,3) = 24!/21! = 12144.

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Cual es la sucesión aritmética de 3,8,13,18,23

Answers

Equation [1] : a(n) = 3 + (n - 1)5 represents the step where he made the mistake.

We have,

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have a student who used the explicit formula a[n] = 5+3(n-1) for the sequence 3,8,13,18,23,...to find the 12th term.

The given sequence is -

3 , 8 , 13 , 18 , 23, ..

Here -

d = 8 - 3 = 13 - 8 = 5

a = 3

a(n) = a + (n - 1)d      {for arithmetic sequence}

a(n) = 3 + (n - 1)5     ...Eq[1]

a(n) = 3 + 5n - 5

a(n) = 5n - 2

Therefore, Equation [1] : a(n) = 3 + (n - 1)5 represents the step where he made the mistake.

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complete question:

A student uses the explicit formula an= 5+3(n-1) for the sequence 3,8,13,18,23,...to find the 12th term. Explain the error the student made.

Which equation is the inverse of y = x² - 36?
Oy=± √√x +6
Oy=+√√x+36
O y=+√√x +36
Oy=+√√x²+36

Answers

Answer:

Step-by-step explanation:

Answer:   B y = ±[tex]\sqrt{x+36}[/tex]

Step-by-step explanation:

To find the inverse of any equation.  Switch the x and the y then solve for y.

y = x² - 36                      >switch variables

x = y² - 36                      >add 36 to both sides

x+36=y²                         >take square root of both sides

y = ±[tex]\sqrt{x+36}[/tex]  

B

evaluate 6a +4b -3c when a=4 , b=7 , and c=-2 (a) 26 (b) 16 (c) 46) (d) 58​

Answers

Answer:

(d) 58

Step-by-step explanation:

Let's start with the equation:

6a+4b-3c

Now, since we got the values of a, b, and c, we can just plug them into the equation:

6(4)+4(7)-3(-2)

24+28+6=58

So the answer is d) 58

A woodworker wants to build a jewelry box in the shape of a rectangular prism with a total volume of 61.3 cubic inches. The woodworker is going to use a very expensive exotic wood to build the box. He wants to choose the dimensions of the box so that the bases of the prism are squares and the box's surface area is minimized. What dimensions should he choose for the box? Round answers to 4 decimal places

Answers

Answer: the woodworker should choose the dimensions of the box to be approximately 3.825 inches by 3.825 inches by 1.603 inches, with a total surface area of approximately 33.512 square inches.

Step-by-step explanation:

Let the side length of the square base be x, and the height of the prism be h. Then the volume of the prism is:

V = x^2h

We're given that V = 61.3 cubic inches, so:

x^2h = 61.3

We want to minimize the surface area of the box, which consists of the area of the two square bases (2x^2) plus the area of the four rectangular faces (4xh). So the total surface area is:

A = 2x^2 + 4xh

We can solve the first equation for h:

h = 61.3/x^2

Substituting this into the equation for A, we get:

A = 2x^2 + 4x(61.3/x^2)

A = 2x^2 + 245.2/x

To minimize A, we take the derivative and set it equal to zero:

dA/dx = 4x - 245.2/x^2 = 0

4x = 245.2/x^2

x^3 = 61.3

x = (61.3)^(1/3)

x ≈ 3.825

So the length of each side of the square base should be approximately 3.825 inches. We can use the equation for h to find the height:

h = 61.3/x^2

h ≈ 1.603

So the height of the prism should be approximately 1.603 inches.

Therefore, the woodworker should choose the dimensions of the box to be approximately 3.825 inches by 3.825 inches by 1.603 inches, with a total surface area of approximately 33.512 square inches.

Which expressionis equivalent to 60m-2n6/5m-4n-2 for all values of m and n where the expression is defined?

Answers

The expression that is equivalent to [tex]\\\\\frac{60m^-2n^6\\}{5m^-4 n^-2}[/tex] for all values of m and n where the 5m-4n-2 expression is defined is [tex]12m^{2} n^{8}[/tex]

How can the expression be known?

In mathematics, an expression or mathematical expression  can be described as the finite combination of symbols which is been analyzed and  well-formed according by following some set of rules which could be varies base on the kind of the symbol as ll as the operation  that are involved in the expression and it s been done  depending on the context so that another expression can be gotten.

This is given as   [tex]\\\\\frac{60m^-2n^6\\}{5m^-4 n^-2}[/tex]

Then we have it defined by;  [tex]12m^{2} n^{8}[/tex]

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you and a friend have created a carnival game for your classmates. you plan to charge $1 for each time a student plays, and the payout for a win is $5. according to your calculations, the probability of a win is .05 what is your expected value for this game?​

Answers

Answer:

The expected value for this game is -$0.75, indicating that, on average, players would expect to lose $0.75 per game.

Step-by-step explanation:

Expected Value = (Probability of Winning * Payout for Win) - Cost of Playing

In this case:

Probability of Winning = 0.05

Payout for Win = $5

Cost of Playing = $1

Expected Value = (0.05 * $5) - $1

Expected Value = $0.25 - $1

Expected Value = -$0.75

Can someone help me? Write a rule for nth term of the arithmetic sequence with a1=7 and the common difference is 3

Answers

Answer:

[tex]a_n=3n+4[/tex]

Step-by-step explanation:

If the common difference is d=3 and the first term is a₁=7, then we can create an arithmetic sequence:

[tex]a_n=a_1+(n-1)d\\a_n=7+(n-1)(3)\\a_n=7+3n-3\\a_n=3n+4[/tex]

A student is establishing the A.A criterion for the similarity of triangles [MN and [QR. The student writes LMLN ~ ZQLR What other information can the student use to establish the AA criterion?

Answers

The other information can the student use to establish the AA criterion is Angle LMN congruent angle LQR or angle LMN congruent angle LRQ

The student can use the following information to establish the AA criterion:

Angle MLN congruent angle QLR (already given)Angle LMN congruent angle LQR or angle LMN congruent angle LRQ (either one will work)

These two angles correspond to the two angles in the other triangle (LQR or LRQ) that are not congruent to the angle already known to be congruent (angle QLR).

Therefore, the AA congruent for similarity can be congruent .

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factorise fully:

1) 2014² - 2013²

please explain and help​

Answers

4027


The rule of the “difference of two squares” says $$2014^2 - 2013^2 = (2014 +2013) * (2014 - 2013)$$

= (2014 +2013) * (2014 - 2013)
= 4027 * 1
= 4027

lin's family needs to travel 325 miles to reach her grandmother's house at 377 miles what percentage have they completed

Answers

Lin's family has completed approximately 86.15% of the total Distance to her grandmother's house.

The percentage of the distance Lin's family has completed, the ratio of the distance they have traveled to the total distance.

The distance traveled is 325 miles, and the total distance to Lin's grandmother's house is 377 miles.

To calculate the percentage, we can use the following formula:

Percentage = (Distance Traveled / Total Distance) * 100

Plugging in the values, we have:

Percentage = (325 / 377) * 100

          = 0.8615 * 100

          = 86.15

Therefore, Lin's family has completed approximately 86.15% of the total distance to her grandmother's house.

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In Algebra, a minus symbol [-] will represent two things, an operation of subtraction and a negative number, depending on where it's placed.
(a) True
(b) False​

Answers

Answer:

It is true that in algebra minus symbol represent two things

Step-by-step explanation:

And it is true that it depend on where it placed such as

8-2 this minus indicate the substraction of two terms

-3 this show that the number has negative quantity

when y is directly proportional to x. When x= 2.5, y=20. what is the value of y when x= 22?

Answers

If it’s proportional that means you can put it in a ratio
Y:X
20:2.5
8:1
176:22

Haru recorded how long his bus ride to school took for `16` days.



Here are the values of the quartiles.



About how many rides would you expect to be less than `6.5` minutes long?

Answers

The number of rides that one would expect to be less than `6.5` minutes long is 4 rides.

How to determine the number of rides

To determine the number of rides, we will first begin by classifying the quartiles. There are 4 quartiles that each constitute 25% of the ride timing.

The number of rides that one would expect to be less than 6.5 minutes can be gotten by finding 25% of 16, the total days recorded. This is 1/4 * 16 = 4. So, the number of rides that will be less than 6.5 minutes will be 4 rides.

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What is x? Because I don’t know g how to work it out

Answers

Answer:

45 degrees

Step-by-step explanation:

The 4 angles of a quadrilateral will add to 360.

We know 1 of them (angle B) is 90 degrees.

We can set up an equation to solve the others.

2x+3x+x+90 = 360

Now solve for x.

Start by combining the x terms together.

6x+90 = 360

6x = 360-90

6x = 270

(6x/6) = 270/6

x = 45 degrees

Check back to see if that makes sense and if the equation equals 360 when x is 45:

2x+3x+x+90 = 360

2(45)+3(45)+45+90=360.

8 +[13-(2+1] =
20
18
-3

Answers

Answer: false

Step-by-step explanation:

What is the value of i 20+1
1
-1
i
-i

Answers

the value of 20+1 should be one bc thats what it equals

Can someone please answer and provide an explanation for these problems?

Answers

The values of x for the tangent segments to the circles are: (25). x = 2 and (26). x = 4

What are the segments tangent to the circle

A theorem of tangents to a circle states that if from one exterior point, two tangents are drawn to a circle then they have equal tangent segments.

(25). 2x - 1 = x + 1 {equal tangent segments}

2x - x = 1 + 1 {collect like terms}

x = 2

(26). 2x - 4 = x {equal tangent segments}

2x - x = 4 {collect like terms}

x = 4

Therefore, the values of x for the tangent segments to the circles are: (25). x = 2 and (26). x = 4

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Suppose it is known that 879 of young Americans earn a hig of 1600 young Americans is selected.
a) Describe the distribution of the proportion of people in t high school diploma.
chool diploma. A random sample
same who have earned their
b) What is the probability that at least 88% of the sample of 1600 young Americans will have earned their high school diploma?

Answers

(a) The distribution of the proportion of people in t high school diploma = 0.0158.

(b)  the probability that at least 88% of the sample of 1600 young Americans will have earned their high school diploma is extremely small.

Given that,

(a) Based on the central limit theorem, the normal distribution may be used to approximate the fraction of persons in the sample who have a high school diploma.

The mean proportion of individuals in the population who have earned their high school diploma can be estimated as

⇒ 879/1600 = 0.5494.

The standard deviation can be estimated as the square root of (0.5494*(1-0.5494)/1600)

=0.0158

b) To find the probability that at least 88% of the sample of 1600 young Americans will have earned their high school diploma,

We need to use the normal distribution with a mean of 0.5494 and a standard deviation of 0.0158.

We can standardize the value of 88% to the corresponding z-score:

z = (0.88 - 0.5494) / 0.0158

  = 20.99

Using a standard normal distribution table or calculator, we find that the probability of a z-score this large or larger is essentially zero,

So the probability that at least 88% of the sample will have earned their high school diploma is extremely small.

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A square piece of sheet metal (24 in x 24 in)
is used to make an open box (no lid). Equal
squares are cut out of each corner, and the
edges are folded up to make the box.
What is the maximum volume, V, of the box?

Answers

The maximum volume of the box is 864 cubic inches.

Let side length of the square cut from each corner is x inches.

After cutting the squares from each corner, the remaining dimensions of the sheet metal will be:

Length: 24 - 2x inches

Width: 24 - 2x inches

Height: x inches

So, the volume of the box

V = (24 - 2x) (24 - 2x)  x

V = x(24 - 2x)²

To find the maximum volume, we can take the derivative of V with respect to x, set it to zero, and solve for x:

dV/dx = (24 - 2x)² - 2x(24 - 2x) = 0

4x² - 96x + 576 = 0

Solving the quadratic equation,

x = 6 and x = 12.

We can substitute x = 6 into the volume equation to find the maximum volume:

V = 6(24 - 2(6))²

V = 6(12)²

V = 6 x 144

V = 864 cubic inches

Therefore, the maximum volume of the box is 864 cubic inches.

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3. In a cooking class, Martin pours 500 milliliters
of broth into a pot. He then adds 1,500 milliliters
of water to the broth. How much total liquid is in
the pot?
A. 1 liter
B.
2 liters
C.
3 liters
D. 5 liters
C

Answers

Answer:The correct answer is C. 3 liters.

Step-by-step explanation:

To determine the total amount of liquid in the pot, we need to add the volume of the broth and the volume of the water.

The broth has a volume of 500 milliliters, and the water has a volume of 1,500 milliliters. Adding these together, we get:

500 mL + 1,500 mL = 2,000 mL

Since there are 1,000 milliliters in a liter, we can convert the volume to liters:

2,000 mL ÷ 1,000 = 2 liters

Therefore, the total amount of liquid in the pot is 2 liters.

The distribution of monthly charges for cellphone plans in the United States is approximately normal with a mean of $62 and a standard deviation of $18. What percentage of plans have charges that are less than $83.60?

Answers

About 88.49% of cellphone plans have charges that are less than $83.60.

How to determine the percentage of plans have charges that are less than $83.60?

To determine the percentage of plans that have charges less than $83.60, we need to find the z-score (z) using the given mean and standard deviation, and then look up the corresponding area under the normal distribution curve.

z = (x – μ) / σ

where x = 83.60, mean, μ =  62 and standard deviation, σ = 18

Thus, the z-score of $83.60 is:

z = (83.60 - 62) / 18 = 1.2

Using a standard normal distribution table, we can find that the area to the left of z = 1.20 is 0.8849 or 88.49% (check image attached).

Therefore, about 88.49% of cellphone plans have charges that are less than $83.60.

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AABC is similar to ADEF.
Find x.
D
A
6
B
8
PADEF = 60
[?]
X =

Answers

We can solve for x by equating the two ratios:

a/b = 6/8 = 3/4

We can conclude that x is equal to 3/4.

To find the value of x in the given scenario, where triangles AABC and ADEF are similar, we can use the concept of corresponding sides in similar triangles.

From the given information, we know that the lengths of sides AB and DE are in proportion with each other, as the triangles are similar. Let's denote the length of AB as a and the length of DE as b. Similarly, let's denote the length of BC as c and the length of EF as d.

Since the corresponding sides are in proportion, we can set up the following equation:

AB/DE = BC/EF

Substituting the given values, we have:

a/b = 6/8

To find the value of x, we need to determine the ratio of the corresponding side lengths. Dividing both sides of the equation by 6, we get:

a/6 = b/8

Cross-multiplying, we have:

8a = 6b

Now, we can solve for x by equating the two ratios:

a/b = 6/8 = 3/4

We can conclude that x is equal to 3/4.

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Can you solve the hcf of 20and 10 A plece of food is placed into a highly concentrated sait solution. After several days in the solution, what will happen to the salt concentration inside. he food? Multiple Cholice It will decrease becouse wiler enters the food If will increase becouse water ietves the food It wit increose because witer enters the food It wif dearene becmuse water ieares the food Chen Inc. accepted a two-year noninterest-bearing note for $605,000 on January 1, 2016. The note was accepted as payment for merchandise with a fair value of $500,000. The effective interest rate is 10%.1. The cash collection on December 31, 2017, would be recorded as:a)Cash605,000Discount on note receivable105,000Note receivable605,000Interest revenue105,000b)Cash605,000Note receivable500,000Discount on note receivable105,000c)Cash605,000Note receivable605,000d)Discount on note receivable55,000Cash605,000Note receivable605,000Interest revenue55,000 an lc circuit has an inductance of 20 mh and a capacitance of 5.0 pf. at time t = 0 the charge on the capacitor is 3.0 pc and the current is 7.0 ma. the total energy is: The equation 3x 2y = 0 represents a proportional relationship. What is the constant of proportionality? A) 3 2 B) 2 3 C) 2 3 D) 3 2. True/fase : type i topoisomerases are only found in prokaryotes. In which of the following phases of the systems development life cycle do developers identify the particular features and functions of a new system?A) system definitionB) requirement analysisC) component designD) implementation What changes did Deloitte make in the kinds of data it collects? What are some pros and cons of the changes? Which of the following statements do you use to get column values from a row in a cursor and store them in a series of variables?a.UPDATEc.FETCHb.OPENd.WHILE whats is the surface area of this rectangular prism? at ibm, there are five divisions: global technology services, global business services, software, systems and technology, and global financing. ibm utilizes a _____ structure. Based on her descriptions in "The Light of Gandhi's Lamp" how did growing up in apartheid-era South Africa affect Hilary Kromberg Inglis? Question 10 options: It showed her that armed resistance to injustice is wrong. It compelled her to join the fight for justice and equality. It made her fearful of those who sought to overturn the country's power structure. It pushed her to seek to emigrate to a country that treated its citizens with dignity An aqueous solution of KCl is colorless, KMnO4 is purple, and K2Cr2O7 is orange. What color would you expect of an aqueous solution of Na2Cr2O7? Explain. Give the corresponding snapshots of memory after each of the following set of statements has been executed.1.intx1;x1=3+4intx(1),z(5);x=__z=__z=z/++x;Nowz=__ A magnifying glass is placed a distant of 7.5 cm from an object and the image appears at 15 cm to the left of the lens. What is magnification?A. 2B. 0.5C. 22.5D. 7.5 Labor productivity is a major determinant of: a. the size of the labor force. b. the skill level of the labor force. c. the money supply. d. living standards. Marta browses online for some new coffee mugs, and then logs into her favorite social media site. She is surprised to see that ads for coffee mugs are following her to other sites. This is most likely a result of many researchers argue that older adults need a protein intake of up to Escribe un ensayo de tres hojas con el tema el aborto Given the following experimental data, find the rate law and the rate constant for the reaction: 2NO2(g) + F2(g) 2NO2F(g) Run 1 2 3 [NO2]. 0.0482 0.0120 0.0480 [F2]. 0.0318 0.0315 0.127 Initial Rate 1.9 x 10-3 4.69 x 10-4 7.57 x 10-3