Trucks in a delivery fleet travel a mean of 120 miles per day with a standard deviation of 23 miles per day. The mileage per day is distributed normally. Find the probability that a truck drives less than 159 miles in a day. Round your answer to four decimal places.

Answers

Answer 1

Answer:

the probability that a truck drives less than 159 miles in a day = 0.9374

Step-by-step explanation:

Given;

mean of the truck's speed, (m) = 120 miles per day

standard deviation, d = 23 miles per day

If the mileage per day is normally distributed, we use the following conceptual method to determine the probability of less than 159 miles per day;

1 standard deviation above the mean = m + d, = 120 + 23 = 143

2 standard deviation above the mean = m + 2d, = 120 + 46 = 166

159 is below 2 standard deviation above the mean but greater than 1 standard deviation above the mean.

For normal districution, 1 standard deviation above the mean = 84 percentile

Also, 2 standard deviation above the mean = 98 percentile

143 --------> 84%

159 ---------> x

166 --------- 98%

[tex]\frac{159-143}{166-143} = \frac{x-84}{98-84} \\\\\frac{16}{23} = \frac{x-84}{14} \\\\23(x-84) = 224\\\\x-84 = 9.7391\\\\x = 93.7391\ \%[/tex]

Therefore, the probability that a truck drives less than 159 miles in a day = 0.9374


Related Questions

Not sure how to do this

Answers

Answer:
Scale factor of 2

Explanation:
I compared the lengths of AC to DF. AC is one unit long, whereas DF is two units long, so DF is dilated by a scale factor of 2.

the length of a rectangle is twice its width the perimeter is 48 cm what are the dimensions of the rectangle

Answers

Answer:

The length=16cm and the width=8cm.

Step-by-step explanation:

Given that the length is twice the breadth or width of the rectangle

Let's assume that the breadth of the rectangle is x.

Thus the length is 2x.

Given perimeter=48cm

The formula for the perimeter of a rectangle is 2(l+b) where l is length and b is breadth.

2(x+2x)=48

(3x)=48/2

3x=24

x=8cm

2x=16cm

Step-by-step explanation:

length=2x

width=x

2x+x+2x+x=48

6x=48

6x÷6=48÷6

x=8

length=16

width=8

Find the exact length of the curve. x=et+e−t, y=5−2t, 0≤t≤2 For a curve given by parametric equations x=f(t) and y=g(t), arc length is given by

Answers

The length of a curve C parameterized by a vector function r(t) = x(t) i + y(t) j over an interval a ≤ t ≤ b is

[tex]\displaystyle\int_C\mathrm ds = \int_a^b \sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2} \,\mathrm dt[/tex]

In this case, we have

x(t) = exp(t ) + exp(-t )   ==>   dx/dt = exp(t ) - exp(-t )

y(t) = 5 - 2t   ==>   dy/dt = -2

and [a, b] = [0, 2]. The length of the curve is then

[tex]\displaystyle\int_0^2 \sqrt{\left(e^t-e^{-t}\right)^2+(-2)^2} \,\mathrm dt = \int_0^2 \sqrt{e^{2t}-2+e^{-2t}+4}\,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^2 \sqrt{e^{2t}+2+e^{-2t}} \,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^2\sqrt{\left(e^t+e^{-t}\right)^2} \,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^2\left(e^t+e^{-t}\right)\,\mathrm dt[/tex]

[tex]=\left(e^t-e^{-t}\right)\bigg|_0^2 = \left(e^2-e^{-2}\right)-\left(e^0-e^{-0}\right) = \boxed{e^2-\frac1{e^2}}[/tex]

The exact length of the curve when the parametric equations are x = f(t) and y = g(t) is given below.

[tex]e^2 -\dfrac{1}{e^2 }[/tex]

What is integration?

It is the reverse of differentiation.

The parametric equations are given below.

[tex]\rm x=e^t+e^{-t}, \ \ 0\leq t\leq 2\\\\y=5-2t, \ \ \ \ \ 0\leq t\leq 2[/tex]

Then the arc length of the curve will be given as

[tex]\int _0^2 \sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dx})^2}[/tex]

Then we have

[tex]\rm \dfrac{dx}{dt} = e^t-e^{-t}\\\\ \dfrac{dy}{dt} = -2[/tex]

Then

[tex]\rightarrow \int _0^2 \sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dx})^2}\ \ dt\\\\\rightarrow \int _0^2 \sqrt{(e^t-e^{-t})^2 + (-2)^2} \ dt\\\\\rightarrow \int _0^2 \sqrt{(e^t+e^{-t})^2} \ dt\\\\\rightarrow \int _0^2 (e^t+e^{-t}) \ dt\\\\\rightarrow (e^2-e^{-2}) \\\\\rightarrow e^2 - \dfrac{1}{e^2}[/tex]

More about the integration link is given below.

https://brainly.com/question/18651211

What is the common difference in this sequence: 3, 11, 19, 27,35?
1
ОА.1/8
O B. 3
O C. 8
O D. 12

Answers

Answer:

8

Step-by-step explanation:

To determine the common difference, take the second term and subtract the first term

11-3 = 8

Check with the other terms in the sequence

19-11= 8

27-19 = 8

35-27=8

The common difference is 8

Answer:

C. 8

Step-by-step explanation:

There is a common difference between them and that’s 8.

3 + 8 = 11

11 + 8 = 19

19 + 8 = 27

27 + 8 = 35

Зу = -2 - 6
3y = 2z - 6

Answers

Answer:

y = -8/3, z = -1

Rubin grew 9 tomatoes with 6 seed packs. How many seed packs does Rubin need to have a total of 21 tomatoes in his garden?

Answers

Answer: 14 seed packs

Step-by-step explanation:

You'd divide the 9 tomatoes by the 6 seed packs that were necessary to grow them, resulting in 1.5 tomatoes per seed pack. Divide 21 by this 1.5 to find the number of seed packs needed to grow 21 tomatoes, which would be 14.

I need help with this​

Answers

bing jhwwjwiwisisuwuwywywywfsfsahajai

a soft drink vendor at a popular beach analyzes his sales recods and finds that if he sells x cans of soda pop in one day, his profit (in dollars) is given by

Answers

Complete Question:

A soft-drink vendor at a popular beach analyzes his sales records, and finds that if he sells x cans of soda pop in one day, his profit (in dollars) is given by P(x) = -0.001x² + 3x - 1800.

a. What is his maximum profit per day?

b. How many cans must be sold in order to obtain the maximum profit?

Answer:

a. $450

b. 1500 cans

Step-by-step explanation:

Given the following quadratic function;

P(x) = -0.001x² + 3x - 1800  ......equation 1

a. To find his maximum profit per day;

Since P(x) is a quadratic equation, P(x) would be maximum when [tex] x = \frac {-b}{2a} [/tex]

Note : the standard form of a quadratic equation is ax² + bx + c = 0  ......equation 2

Comparing eqn 1 and eqn 2, we have;

a = -0.001, b = 3 and c = -1800

Now, we determine the maximum profit;

[tex] x = \frac {-b}{2a} [/tex]

Substituting the values, we have;

[tex] x = \frac {-3}{2*(-0.001)} [/tex]

Cancelling out the negative signs, we have;

[tex] x = \frac {3}{2*0.001} [/tex]

[tex] x = \frac {3}{0.002} [/tex]

x at maximum = 1500

Substituting the value of "x" into equation 1;

P(1500) = -0.001 * 1500² + 3(1500) - 1800

P(1500) = -0.001 * 2250000 + 4500 - 1800

P(1500) = -2250 + 2700

P(1500) = $450

b. Therefore, the soft-drink vendor must sell 1500 cans in order to obtain the maximum profit.

A solid oblique pyramid has a square base with edges measuring x cm. The height of the pyramid is (x + 2) cm.

A solid oblique pyramid has a square base with edges measuring x centimeters. The height is (x + 2) centimeters.

Which expression represents the volume of the pyramid?

StartFraction x cubed + 2 x squared Over 3 EndFraction cm3
StartFraction x squared + 2 x squared Over 2 EndFraction cm3
StartFraction x cubed Over 3 EndFraction cm3
StartFraction x cubed + 2 x squared Over 2 EndFraction cm3

Answers

Answer:

Hello,

Answer A StartFraction x cubed + 2 x squared Over 3 EndFraction cm3

Step-by-step explanation:

[tex]V=x^2*\dfrac{x+2}{3} \\\\\boxed{V=\dfrac{x^3+2x^2}{3} }\\[/tex]

the third of the sum of the cube of x and double of the square of x ( cm³)

The Volume of pyramid with a square base of side x cm and height of (x + 2) cm is (x³ + 2x²) / 3

What is volume?

Volume is the amount of space occupied by a three dimensional shape or object.

Area of the square base = x * x = x² cm²

Volume of pyramid = (1/3) * area of base * height = (1/3) * x² * (x + 2)

Volume of pyramid = (x³ + 2x²) / 3

The Volume of pyramid with a square base of side x cm and height of (x + 2) cm is (x³ + 2x²) / 3

Find out more on volume at: https://brainly.com/question/12410983

15
Simplify
a
25
O A. a3
O B. a10
O c. a-10
O D. a-3

Answers

Answer:

B is the correct answer of your question.

I HOPE I HELP YOU....

can someone help me out with this question??? ​

Answers

Answer:

a

Step-by-step explanation:

Miller's Steakhouse offers 8 side dishes, 5 types of steak, and 4 toppings. How many different smothered steak dinners can be made if a smothered steak dinner consists of the customer's choice of steak served with 3 different toppings and 3 different side dishes?

Answers

Answer:

1120

Step-by-step explanation:

To find the possible number of steak dinners, you would multiply the number of choices for each part of the dinner. You would used combinations instead of permutations since the order of the toppings chosen or side dishes chosen do not matter. There are 5 choose 1 choices for types of steak, which is just 5. There are 8 choose 3 choices for side dishes, which is 56. There are 4 choose 3 choices for toppings, which is 4. 5*56*4 is 1120, so there are 1120 possible steak dinners.

HELP PLZ<3

An international company has 28,300 employees in one country. If this represents 34.1% of the company's employees, how many employees does it have in
total?
Round your answer to the nearest whole number.

Answers

Answer:

82991 employees

Step-by-step explanation:

One way to solve this would be to solve for 1% of the company's employees and use that value to solve for 100% (100%=the whole part, or the total). We know that

28300 = 34.1%

If we divide a number by itself, it turns into 1. Dividing both sides by 34.1, we get

829.912 = 1%

Then, we know that anything multiplied by 1 is equal to itself. We want to figure out 100%, or the whole part, so we can multiply both sides by 100 to get

100% = 82991

If there is a 65% chance you will make a free throw, what percent of the
time you will miss? *

Answers

Given:

There is a 65% chance you will make a free throw.

To find:

The percent of the time you will miss.

Solution:

If p is the percent of success and q is the percent of failure, then

[tex]p+q=100\%[/tex]

[tex]q=100\%-p[/tex]         ...(i)

It is given that there is a 65% chance you will make a free throw. It means the percent of success is 65%. We need to find the percent of the time you will miss.  It means we have to find the percent of failure.

Substituting p=65% in (i), we get

[tex]q=100\%-65\%[/tex]

[tex]q=35\%[/tex]

Therefore, there is a 35% chance you will miss the free throw.

Josue leans a 26-foot ladder against a wall so that it forms an
angle of 80° with the ground. How high up the wall does the
ladder reach? Round your answer to the nearest hundredth of a
foot if necessary.

Answers

Answer:

25.61 feet

Step-by-step explanation:

First, we can draw a picture (see attached picture). With the wall representing the rightmost line, and the ground representing the bottom line, the ladder (the hypotenuse) forms a 80 degree angle with the ground and the wall and ground form a 90 degree angle.

Without solving for other angles, we know one angle and the hypotenuse, and want to find the opposite side of the angle.

One formula that encompasses this is sin(x) = opposite/hypotenuse, with x being 80 degrees and the hypotenuse being 26 feet. We thus have

sin(80°) = opposite / 26 feet

multiply both sides by 26 feet

sin(80°) * 26 feet = opposite

= 25.61 feet as the height of the wall the ladder reaches

The height of the wall does the ladder reach to the nearest hundredth of the foot is 25.61 feet.

What is a right-angle triangle?

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function. The Pythagoras is the sum of the square of two sides is equal to the square of the longest side.

Josue leans a 26 feet ladder against a wall so that it forms an angle of 80° with the ground.

The condition is shown in the diagram.

Then the height of the wall will be

[tex]\rm \dfrac{h }{26 } = sin 80 \\\\h \ \ = 26 \times sin 80\\\\h \ \ = 25.61 \ ft[/tex]

More about the right-angle triangle link is given below.

https://brainly.com/question/3770177

For a standard normal distribution, find:

P(z > -1.6)
Express the probability as a decimal rounded to 4 decimal places.

Answers

Answer:

P(z > -1.76) = 1 - P(z < -1.76) = 1 - 0.0392 = 0.960

What is the value of x in the equation
-%y = 30, when y = 15?

Answers

Answer:

x not given

therefore no answer for x

The travel time on a section of a Long Island Expressway (LIE) is normally distributed with a mean of 80 seconds and a standard deviation of 6 seconds. What travel time separates the top 2.5% of the travel times from the rest

Answers

Answer:

The travel time that separates the top 2.5% of the travel times from the rest is of 91.76 seconds.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 80 seconds and a standard deviation of 6 seconds.

This means that [tex]\mu = 80, \sigma = 6[/tex]

What travel time separates the top 2.5% of the travel times from the rest?

This is the 100 - 2.5 = 97.5th percentile, which is X when Z has a p-value of 0.975, so X when Z = 1.96.

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

[tex]1.96 = \frac{X - 80}{6}[/tex]

[tex]X - 80 = 6*1.96[/tex]

[tex]X = 91.76[/tex]

The travel time that separates the top 2.5% of the travel times from the rest is of 91.76 seconds.

Given the exchange rate as K1: HK$1.353, calculate Hong Kong dollar equivalent of K70

Answers

Answer:

The Hong Kong dollar equivalent of K70 is HK $ 94.71.

Step-by-step explanation:

Given the exchange rate as K1: HK $ 1,353, to calculate Hong Kong dollar equivalent of K70 the following calculation must be performed:

1,353 x 70 = X

94.71 = X

Therefore, the Hong Kong dollar equivalent of K70 is HK $ 94.71.

Answer this please~!!!!

Answers

Answer:

12

Step-by-step explanation:

113.04=3.14 x 3^2 x h/3

WILL MAKE BRAINLIEST

Answers

Answer:

x=3

Step-by-step explanation:

The ratios need to be the same

AB             CB

---------- = ----------

AD             ED

3           x

-----  = ---------

3+9       12

3           x

-----  = ---------

12          12

X must equal 3

f(x) = 2x2 + 4x - 5
g(x) = 6x3 – 2x2 + 3
Find (f + g)(x).

Answers

Answer:

4x-5=4x-5

(f+g) (x)=6x³+3

Step-by-step explanation:

What is the value of the expression 10(6 + 5)² when b = 3?

Answers

10(3+5)^2

10(8)^2

10(64)

=640

Combine the expressions below

4x+(-2x)+6+(-9)

Answers

=4x-2x=2x

=6-9=-3

=2x-3

Assume that in the absence of immigration and emigration, the growth of a country's population P(t) satisfies dP/dt = kP for some constant k > 0.

a. Determine a differential equation governing the growing population P(t) of the country when individuals are allowed to immigrate into the country at a constant rate r > 0.
b. What is the differential equation for the population P(t) of the country when individuals are allowed to emigrate at a constant rate r > 0?

Answers

Answer:

[tex](a)\ \frac{dP}{dt} = kP + r[/tex]

[tex](b)\ \frac{dP}{dt} = kP - r[/tex]

Step-by-step explanation:

Given

[tex]\frac{dP}{dt} = kP[/tex]

Solving (a): Differential equation for immigration where [tex]r > 0[/tex]

We have:

[tex]\frac{dP}{dt} = kP[/tex]

Make dP the subject

[tex]dP =kP \cdot dt[/tex]

From the question, we understand that: [tex]r > 0[/tex]. This means that

[tex]dP =kP \cdot dt + r \cdot dt[/tex] --- i.e. the population will increase with time

Divide both sides by dt

[tex]\frac{dP}{dt} = kP + r[/tex]

Solving (b): Differential equation for emigration where [tex]r > 0[/tex]

We have:

[tex]\frac{dP}{dt} = kP[/tex]

Make dP the subject

[tex]dP =kP \cdot dt[/tex]

From the question, we understand that: [tex]r > 0[/tex]. This means that

[tex]dP =kP \cdot dt - r \cdot dt[/tex] --- i.e. the population will decrease with time

Divide both sides by dt

[tex]\frac{dP}{dt} = kP - r[/tex]

Find x on this triangle

Answers

Answer:

3 sqrt(3) =x

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj / hyp

cos 30 = x/6

6 cos 30 = x

6 ( sqrt(3)/2) = x

3 sqrt(3) =x

Coefficient of y in the equation: 3(2x -1/3y) = 0 is equal to a) 3 b) 1 c)-3 d)-1

Answers

Answer:

d is the right answer because the coefficient of y is 3*(-1/3) which results -1 so d is the right answer

The coefficient of y in the given equation is 1. Therefore, option B is the correct answer.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is 3(2x -1/3y)=0.

Now, 6x-1/y=0

A numerical or constant quantity placed before and multiplying the variable in an algebraic expression.

Here, coefficient of y is 1.

Therefore, option B is the correct answer.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ2

Hii guys if you have time plz help me

Answers

Answer:

[tex]5 {x}^{2} + 21 + 5x[/tex]

Step-by-step explanation:

TOTAL AMOUNT earned = Tim money + Melina money

[tex]5 {x}^{2} - 4x + 8 + (9x + 13)[/tex]

[tex] = 5 {x}^{2} - 4x + 8 + 9x + 13[/tex]

[tex] = 5 {x}^{2} + 21 + 5x[/tex]

In the picture the exponent says 5/3

Answers

Answer:

the answer is B

Step-by-step explanation:

[tex] {{ (- 2)}^{3}}^{5 \div 3} = { ( - 2)}^{5} = - 32[/tex]

write -8 form of 2 on up and complete other steps

wrote the terms below.

–8, –4, 0, 4, 8, 12

What do these terms represent?
an arithmetic series
an arithmetic sequence
a geometric series
a geometric sequence

Answers

Answer:

an arithmetic sequence

Step-by-step explanation:

an arithmetic series is wrong also heres an example i found of an arithmetic sequence

The terms in the given sequence represents an arithmetic sequence.

What is Arithmetic Sequence?

Arithmetic sequence is a sequence of numbers where the numbers are arranged ion a definite order such that the difference of two consecutive numbers is a constant. This constant of difference is called common difference which is commonly denoted by the letter 'd'.

Given sequence of numbers is,

-8, -4, 0, 4, 8, 12, ......

We have to find which sequence does it represent.

This is not a series since they are not represented as the sum.

If the sequence is a geometric sequence, then the ratio of consecutive numbers will be same.

If it is arithmetic sequence, then the difference of consecutive numbers will be same.

Here, ratio is not same.

Difference are same.

-4 - -8 = 4, 0 - -4 = 4, 4 - 0 = 4, 8 - 4 = 4, ........

Common difference is 4.

Hence it is an arithmetic sequence.

Learn more about arithmetic Sequence here :

https://brainly.com/question/15412619

#SPJ3

Other Questions
8 A test rocket is fired and follows a path described by y = 0.1x(200 x). The height is y metres aboveground and x is the horizontal distance in metres.How far does the rocket travel horizontally?b How high does the rocket reach mid-flight? The dehumanizing aspects of the slave system were seen in which of the following? Select all correct responses.The threat and anticipation of punishmentHumiliationBrandingMutilationWhipping You are considering the purchase of a machine out of your evaluation among four new ones. They have differing initial and ongoing costs and differing lives. Whichever machine is purchased will be replaced at the end of its useful life. Under such circumstances, you should choose the machine to purchase based on the ___________________. (4y) (3y)Please help me Why does scattering of light occur ? HELP Describe one main ideas that walt whitman and Henry David have in common (read the picture for full question ) Throughout Act 2 it is implied that Eliza values herself and has self-respect. All of the following provides evidence for that conclusion except...she is suspicious of Higgins offer and his wager with Pickeringshe has put ostrich feathers in her cap and tried to clean her coatshe claims that despite not having a mom she is a good girlshe stays when Higgins offers her chocolate and taxi rides 9.2% written as a decimal is A tank is filled at a constant rate. 10 minutes after filling is started, the tank contains 4.8L of water. After 35 minutes the tank contains 7.3L of water. a. Find the rate at which the tank is being filled?b. Find the initial volume of fluid in the tank and express it as a function in terms of V and t.c. Find how long it takes to filled, if the tank has a maximum capacity of 60L? 20. simplify each of the following: see the above pictureand get 40 points During the data transmission there are chances that the data bits in the frame might get corrupted. This will require the sender to re-transmit the frame and hence it will increase the re-transmission overhead. By considering the scenarios given below, you have to choose whether the packets should be encapsulated in a single frame or multiple frames in order to minimize the re-transmission overhead.Justify your answer with one valid reason for both the scenarios given below.Scenario A: Suppose you are using a network which is very prone to errors.Scenario B: Suppose you are using a network with high reliability and accuracy. 13. Is the word LAWYER in the following sentence a predicate nominative or apredicate adjective?My sister became a lawyer after years of study. a colleague needs to move a 500 pound object that's on a lever. the fulcrum is 6 inches from the object. If your colleague weighs 180 pounds how far will your colleague need to be from the fulcrum to move the object? Use the formula B = (P x A) W, and round your answer to two decimal places. If two angles are complementary, find the measure of each of angle. Greg has a list of payments for goods brought every month for the years 2009,2010,2011, and 2012. He needs information from only the last three years. He can filter this by clicking on find a number which is when added to it's square the sum will be 72. demonstrated the knowledge of control ventilation 100 points for you if you help me While in a department store, a man picked up a sweater and slipped it under his shirt. The man then started for the door. A woman, who also was shopping in the store, saw the man take the sweater. The woman grabbed a baseball bat from the sporting goods aisle and chased the man into the parking lot. The woman began swinging the bat at the man's head, hoping to knock him out and thus prevent the theft. The man pulled a knife from his pocket and stabbed the woman, killing her. The man was arrested and charged with murder. At trial, will the man most likely be found guilty What's a third reaction? (Chemistry)