Two automobiles left simultaneously from cities A and B heading towards each other and met in 5 hours. The speed of the automobile that left city A was 10 km/hour less than the speed of the other automobile. If the first automobile had left city A 4 1/2 hours earlier than the other automobile left city B, then the two would have met 150 km away from B. Find the distance between A and B.

Answer: The first number is 2000 times greater than second number.

Step-by-step explanation:

Let the first number be 'x' and second number be 'y'

We are given:

x = [tex]8\times 10^{-3}[/tex]

y = [tex]4\times 10^{-6}[/tex]

To calculate the times, number 'x' is greater than number 'y', we divide the two numbers:

[tex]\frac{x}{y}=\frac{8\times 10^{-3}}{4\times 10^{-6}}\\\\\frac{x}{y}=2\times 10^3\\\\x=2000y[/tex]

Hence, the first number is 2000 times greater than second number.

The number [tex]8\times 10^{-3}[/tex] is [tex]2000[/tex] times grater than the number [tex]4\times 10^{-6}[/tex].

Given information:

The number [tex]8 \times 10^{-3}[/tex]

And number [tex]4\times 10^{-6}[/tex]

Now , consider the first number as [tex]x[/tex] and number second as [tex]y[/tex].

So, according to the information given in the question we can write as:

[tex]\frac{x}{y} =\frac{8\times 10^{-3}}{4\times 10^{-6}}[/tex]

[tex]\frac{x}{y} = 2\times 10^3\\x=2000y[/tex]

Hence, We can conclude that the number [tex]8\times 10^{-3}[/tex] is [tex]2000[/tex] times the number [tex]4\times 10^{-6}[/tex].

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Answer:

Part a) The amount of hardwood floor is [tex]480\ ft^{2}[/tex]

Part b) The amount of trim to buy is [tex]78\ ft[/tex]

Part c) The amount of paintable space is [tex]1,297\ ft^{2}[/tex]

Part d) The amount of paint needed is [tex]7.41\ gallons[/tex]

Step-by-step explanation:

Part a) You want to put down hard wood floors in your master bedroom. How much hard wood flooring would you need to buy?

Find the area of the floor

[tex]A=(10+5+3)(10+5+10)+(2+6+2)(3)[/tex]

[tex]A=(18)(25)+(10)(3)[/tex]    

[tex]A=480\ ft^{2}[/tex]

Part b) You also want to put a trim on the bottom of each wall, except in front of the french doors, sliding doors, or hallway. How much trim should you buy?  

step 1

Find the perimeter of the  master bedroom

[tex]P=2(25)+2(18)+2(3)[/tex]

[tex]P=50+36+6[/tex]

[tex]P=92\ ft[/tex]

step 2

Subtract the front of the french doors, sliding doors and hallway from the perimeter

[tex]92-(5+6+3)=78\ ft[/tex]

Part c) You want to paint your new bedroom. How much paintable space is there in the room?

step 1

Find the area of the ceiling

we know that

The area of the floor is equal to the area of the ceiling

so

The area of the ceiling is equal to [tex]A=480\ ft^{2}[/tex]

step 2

Find the area of the walls

Multiply the perimeter by the height

[tex]92*10=920\ ft^{2}[/tex]  

step 3

Subtract 73 square feet of surface that does not get painted (windows and sliding doors ) and the area of the hallway

The amount of paintable space is equal to

[tex]A=480+920-73-3(10)=1,297\ ft^{2}[/tex]

Part d) How many gallons of paint would you need to buy?

we know that

One gallon of paint covers 350 square feet

Multiply the area by two (because You want to put on two coats of paint on every paintable surface)

so

[tex]1,297*(2)=2,594\ ft^{2}[/tex]

using proportion

[tex]1/350=x/2,594[/tex]

[tex]x=2,594/350[/tex]

[tex]x=7.41\ gallons[/tex]

Answer:

Graph A

Basically a graph of a function will have no turns if linear, 1 turn if quadratic, 2 turns if cubic, and 3 terms if quartic.

Graph A has a small turn on its right side.

Step-by-step explanation:

I love the way this other guy explained it, basically you count the turns that it says. i.e quartic = 4, so 4 turns, so A in this case

This was so confusing and I've been learning it for over a week and never understood it but literally took me 2 seconds to read his answer and understand it perfectly

Answer: (a)  [tex]\dfrac{1}{7}[/tex]    (b)  [tex]\dfrac{12}{35}[/tex]

Step-by-step explanation:

Given: Number of white balls : 6

Number of red balls = 9

Total balls = 15

(a)  The probability that both balls are white is given by :-

[tex]\dfrac{^6C_2}{^{15}{C_2}}\\\\=\dfrac{\dfrac{6!}{2!(6-2)!}}{\dfrac{15!}{2!(15-2)!}}=\dfrac{1}{7}[/tex]

∴ The probability that both balls are white is  [tex]\dfrac{1}{7}[/tex] .

(b)  The probability that both balls are red is given by :-

[tex]\dfrac{^9C_2}{^{15}C_2}\\\\=\dfrac{\dfrac{9!}{2!(9-2)!}}{\dfrac{15!}{2!(15-2)!}}=\dfrac{12}{35}[/tex]

∴ The probability that both balls are red is [tex]\dfrac{12}{35}[/tex] .

Answer: Hello your in college please help me with my latest problem please :(

Step-by-step explanation:

Answer:

The correct answer option is C. [tex]\frac{y_4-y_3}{x_4-x_3} \times \frac{y_2-y_1}{x_2-x_1} = -1[/tex].

Step-by-step explanation:

We are given that two line segments AB and CD are formed from the points A ([tex](x_1, y_1)[/tex], B ([tex](x_2, y_2)[/tex], C ([tex](x_3, y_3)[/tex] and D ([tex](x_4, y_4)[/tex].

We are to determine which condition needs to be met in order to prove that AB is perpendicular to CD.

When slopes of two perpendicular lines are multiplied, they give a product of -1.

Hence option C. [tex]\frac{y_4-y_3}{x_4-x_3} \times \frac{y_2-y_1}{x_2-x_1} = -1[/tex] is the correct answer.

Answer:

We need to find how many number of equivalence relations are on the set {1,2,3}

A relation is an equivalence relation if it is reflexive, transitive and symmetric.

equivalence relation R on {1,2,3}

1.For reflexive, it must contain (1,1),(2,2),(3,3)

2.For transitive, it must satisfy: if (x,y)∈R then (y,x)∈R

3. For symmetric, it must satisfy: if (x,y)∈R,(y,z)∈R then (x,z)∈R

Since (1,1),(2,2),(3,3) must be there is R, (1,2),(2,1),(2,3),(3,2),(1,3),(3,1). By symmetry,

we just need to count the number of ways in which we can use the pairs (1,2),(2,3),(1,3) to construct equivalence relations.

This is because if (1,2) is in the relation then (2,1) must be there in the relation.

the relation will be an equivalence relation if we use none of these pairs (1,2),(2,3),(1,3) . There is only one such relation: {(1,1),(2,2),(3,3)}

we can have three possible equivalence relations:

{(1,1),(2,2),(3,3),(1,2),(2,1)}

{(1,1),(2,2),(3,3),(1,3),(3,1)}

{(1,1),(2,2),(3,3),(2,3),(3,2)}

Equivalence relations on a set satisfy conditions of reflexivity, symmetry, and transitivity. The Bell number counts the number of partitions, or equivalence relations, on a set. Hence, for the set {1, 2, 3}, there are five equivalence relations.

The subject of this question relates to equivalence relations on a set which is an important topic in discrete mathematics and set theory. In simple terms, an equivalence relation is a relation on a set that equates certain pair of elements. In your set {1, 2, 3}, an equivalence relation must meet three conditions: reflexivity (each number is equal to itself), symmetry (if 1 is related to 2, then 2 is related to 1), and transitivity (if 1 is related to 2 and 2 is related to 3, then 1 is related to 3).

To find the number of equivalence relations on a set, we refer to the Bell number. Bell numbers count the number of partitions of a set. For a set with 3 elements like yours, the third Bell number gives the number of equivalence relations, which is 5. Therefore, there are 5 equivalence relations on the set {1, 2, 3}.

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Answer:

  use a suitable calculator

Step-by-step explanation:

For finding values related to a normal probability distribution function, it is convenient to use a suitable calculator or spreadsheet. (See below)

___

If all you have is a z-table, you must calculate the corresponding z-value and look it up in the table.

  z = (X -µ)/σ = (56 -54)/8 = 1/4

You are interested in the area above z=1/4. The table in the second attachment gives the area between z=0 and z=1/4. So, the area of interest is the table value subtracted from 0.5 (the total area above z=0.):

  0.5000 -0.0987 = 0.4013

Answer:

Step-by-step explanation:

Anwer -1

Answer:

-1

Step-by-step explanation:

You could solve for x... or just plug those values in to see which would make the inequality true

Let's check x=3

-3(3-4)>6(3-1)

-3(-1)>6(2)

3>12  this is false  so not x cannot be 3

Let's check x=-1

-3(-1-4)>6(-1-1)

-3(-5)>6(-2)

15>-12 this is true so x can take on the value -1

Let's check x=7

-3(7-4)>6(7-1)

-3(3)>6(6)

-9>36 is false so x cannot be 7

Let's check x=2

-3(2-4)>6(2-1)

-3(-2)>6(1)

6>6 is false so x cannot be 2

Answer: 0.9713

Step-by-step explanation:

Given : Mean : [tex]\mu = 5.2\text{ day}[/tex]

Standard deviation : [tex]\sigma = 1.7\text{ days}[/tex]

The formula of z -score :-

[tex]z=\dfrac{X-\mu}{\sigma}[/tex]

At X = 2 days

[tex]z=\dfrac{2-5.2}{1.7}=-1.88235294118\approx-1.9[/tex]

Now, [tex]P(X>2)=1-P(X\leq2)[/tex]

[tex]=1-P(z<-1.9)=1- 0.0287166=0.9712834\approx0.9713[/tex]

Hence, the probability of spending more than 2 days in recovery = 0.9713

Answer:

There is a 98.54% probability of spending more than 2 days in recovery.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 5.7, \sigma = 1.7[/tex]

What is the probability of spending more than 2 days in recovery?

This probability is 1 subtracted by the pvalue of Z when X = 2. So:

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

[tex]Z = \frac{2 - 5.7}{1.7}[/tex]

[tex]Z = -2.18[/tex]

[tex]Z = -2.18[/tex] has a pvalue of 0.0146.

This means that there is a 1-0.0146 = 0.9854 = 98.54% probability of spending more than 2 days in recovery.

Answer: 0.0668

Step-by-step explanation:

Given: Mean : [tex]\mu=\text{4 min. 3 sec.=4.05 minutes}[/tex]

Standard deviation : [tex]\sigma = \text{2 seconds=0.033333 minutes }[/tex]

The formula to calculate z-score is given by :_

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x= 4 minutes  , we have

[tex]z=\dfrac{4-4.05}{0.03333}\approx-1.5[/tex]

The P-value = [tex]P(z\leq-1.5)=0.0668072\approx0.0668[/tex]

Hence, the probability that on a given run, the time will be 4 minutes or less = 0.0668

The probability that on a given run, the time will be 4 minutes or less is approximately 6.68%.

To find the probability that on a given run, the time will be 4 minutes or less, we need to calculate the z-score for 4 minutes and then use the standard normal distribution table to find the probability. The z-score can be calculated using the formula (x - mean) / standard deviation. In this case, the z-score is (4 - 4.05) / 0.0333333⋯ = -1.50. Looking up the z-score in the standard normal distribution table, we find that the probability is approximately 0.0668 or 6.68%.

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Answer:

the number to be expected is 1,000

Step-by-step explanation:

you multiply 100,000 by 1% which give you 1,000

Answer:   1000

Step-by-step explanation:

Given : The proportion of the defective widgets manufactured by XYZ corp= 1%

= 0.01   [we divide a percent by 100 to convert it into decimal to perform further calculations]

If the total number of widgets manufactured by XYZ = 100000

Then, the number of defective widgets is expected to be

(proportion of defective widgets) x (number of widgets manufactured by XYZ)

= 0.01 x 100000

= 1000

Hence, the number of defective widgets is expected to be 1000 .

Answer:

22 yd

Step-by-step explanation:

Length is four times its width   ----->    L=4W

area of rectangle is 196           ----->   196=LW

Plug L=4W into 196=LW giving you 196=(4W)W

Simplify a bit 196=4W^2

Divide both sides by 4:   196/4=W^2

Simplify a bit:   49=W^2

Square root both sides:  7 or -7=W

The width is 7 yd

The length is 4(7)=28 yd

Now its final part is for you to find the perimeter of this rectangle.  The rectangle is a 7 yd by 4 yd rectangle.

Double both then add.. 14+8=22 yd

Answer:

21 yd

Step-by-step explanation:

Length of a rectangle is four times its width =

L = 4 × w

The area of the rectangle is 196

L = 4W

A = L*W = 196

---

4W*W = 196

W*W = 196/4

W*W = 49

W = 7

L = 28

---

Answer:

P = 2(L + W)

P = 2(28 + 7)

P = 14 + 7

P = 21 yd

Answer: 0.8186

Step-by-step explanation:

Given: Mean : [tex]\mu=1.01\text{ inch}[/tex]

Standard deviation :  [tex]\sigma=0.003\text{ inch}[/tex]

Sample size :  [tex]n=9[/tex]

The formula to calculate z-score :-

[tex]z=\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

For x=1.009 inch

[tex]z=\dfrac{1.009-1.01}{\dfrac{0.003}{\sqrt{9}}}=-1[/tex]

For x=1.012 inch

[tex]z=\dfrac{1.012-1.01}{\dfrac{0.003}{\sqrt{9}}}=2[/tex]

Now, The p-value =[tex]P(-1<z<2)=P(2)-P(-1)=0.9772498-0.1586553=0.8185945\approx0.8186[/tex]

Hence, the required probability = 0.8186

Answer: [tex]P = \$\ 52[/tex]

Step-by-step explanation:

We have the equation [tex]P = 31 + 1.75w[/tex] where P represents the payment and w represents the amount of water used.

To calculate the monthly payment that corresponds to 12 units of water you must do [tex]w = 12[/tex] in the main equation and solve for the variable P.

[tex]P = 31 + 1.75w[/tex]

[tex]P = 31 + 1.75(12)[/tex]

[tex]P = 31 + 21[/tex]

[tex]P = 52[/tex]

Tuyet's payment for a month when 12 units of water are used is $52.

To find Tuyet's payment for a month when 12 units of water are used, we can substitute 12 for 'w' in the equation P = 31 + 1.75w and solve for P.

P = 31 + 1.75(12)

P = 31 + 21

P = 52

Therefore, Tuyet's payment for a month when 12 units of water are used is $52.

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Step-by-step explanation:

Well it is simple.If he was able to solve 400 problems in just 25 ' then how long would it take him to solve 100(1/4 of 400)?It would take him 6.25' to solve 100 problems(1/4 of 25).So if he had to do another 500 (because 1000 -500=500) it would take him 31.25' (5*6.25) to complete them.If you have any further questions please contact me.

Yours sincerely,

Manos

Answer: Third Option

[tex]f(t)=21,386[/tex]

Step-by-step explanation:

We know that the equation that models the number of trees in the forest is:

[tex]f(t)=\frac{32,000}{1+12.8e^{-0.065t}}[/tex]

Where t represents the time elapsed in years

To calculate the number of trees after 50 years substitute [tex]t = 50[/tex] in the equation

[tex]f(t)=\frac{32,000}{1+12.8e^{-0.065(50)}}[/tex]

[tex]f(t)=21,386[/tex]

Answer:

  x = 4

Step-by-step explanation:

Add 8 to both sides of the equation:

  6x -8 +8 = 16 +8

  6x = 24

Divide both sides of the equation by 6:

  6x/6 = 24/6

  x = 4

For this case we have the following equation:

[tex]6x-8 = 16[/tex]

We must find the value of the variable "x":

Adding 8 to both sides of the equation we have:

[tex]6x = 16 + 8\\6x = 24[/tex]

Dividing between 6 on both sides of the equation we have:

[tex]x = \frac {24} {6}\\x = 4[/tex]

Thus, the solution of the equation is[tex]x = 4[/tex]

Answer:

[tex]x = 4[/tex]

Answer:

It diverges to positive infinity  

Step-by-step explanation:

I see it was 4/(x-6)^3 not 4(x-6)^3... but still can't make out everything else.

[tex] \int_6^8 \frac{4}{(x-6)^3} dx [/tex]

The integrand does not exist at x=6.

[tex] \int_6^8 \frac{4}{(x-6)^3} dx [/tex]

[tex] \lim_{z \rightarrow 6^{+} } \int_z^8 4(x-6)^{-3} dx [/tex]

[tex] \lim_{z \rightarrow 6^{+} }\frac{4(x-6)^{-2}}{-2} |_z^8dx [/tex]

[tex] \lim_{z \rightarrow 6^{+} }[\frac{4(8-6)^{-2}}{-2} -\frac{4(z-6)^{-2}}{-2} ] [/tex]

[tex] \frac{1}{-2} - -\infty [/tex]

[tex] \infty [/tex]

So it diverges

Answer:

I could not properly read this but here was what I could make out

Step-by-step explanation:

Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.

LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)

home this helped ;)

Answer:

  sales are increasing at the rate of 6000 units per week

Step-by-step explanation:

Your demand equation appears to be ...

  4p³ +x² =38400

Then differentiation gives ...

  12p²·p' +2x·x' = 0

Solving for x', we get ...

  x' = -6p²·p'/x

Filling in the given values, we find the rate of change of sales to be ...

  x' = -6(20²)(-0.20/wk)/80 = 6/wk . . . . . in thousands of units/wk

Sales are increasing at the rate of 6000 units per week.

Answer with explanation:

It is given that,  for all real numbers x, if 2 x+1 is rational .

      When you will look at the expression ,2 x +1

⇒1 is rational

⇒2 x will be rational, because the expression , 2 x+1, is rational.

⇒2 x is rational, it means , x will be rational,because 2 is rational.

Some important rules considering rational and irrational

1.⇒Product of rational and rational is Rational.

2.⇒Product of Irrational and Rational is Irrational.

3.⇒Product of Irrational and Irrational may be irrational or rational.

≡2 x →is rational, 2 is rational number ,so x will be rational also.

If 2x+1 is rational, hence 2x is rational subtracting 1 which is also rational. Assuming 2x is expressible as a/b, then x is a/2b, again showing x is rational.

To prove that if 2x+1 is rational, then x must also be rational, we must understand the definition of rational numbers and basic properties of arithmetic operations involving rational numbers. A number is considered rational if it can be written as the quotient of two integers (where the denominator is not zero). Given that the sum of two rational numbers is also rational, if 2x+1 is rational, and we know that 1 is rational (since 1 can be written as 1/1), then 2x must be rational because rational minus rational yields a rational result.

Now, assuming 2x is rational, we can express it as a fraction [tex]\frac{a}{b}[/tex], with a and b being integers and b non-zero. Since the multiplication of a rational number by an integer is also rational, and knowing that 2 is an integer, we can then say that x, which is  [tex]\frac{a}{2b}[/tex], is also rational. This is because we can express the result of  [tex]\frac{a}{2b}[/tex] with integers in the numerator and the denominator.

You just put the expression in a calculator! We have

[tex]\dfrac{7}{2^6} = \dfrac{7}{64}=0.109375[/tex]

Answer:

  28 mi

Step-by-step explanation:

The cars are separating at the rate of 52 mi/h - 45 mi/h = 7 mi/h. Then after 4 hours, their separation distance will be ...

  (7 mi/h)(4 h) = 28 mi

The two cars will be 28 miles apart after 4 hours.

To find the distance between the two cars after 4 hours, we need to calculate the distance traveled by each car. The formula to find distance is speed multiplied by time. The first car travels at an average speed of 45 mph for 4 hours, so its distance traveled is 45 mph * 4 hours = 180 miles.

The second car travels at an average speed of 52 mph for 4 hours, so its distance traveled is 52 mph * 4 hours = 208 miles. Therefore, the two cars will be 208 miles - 180 miles = 28 miles apart after 4 hours.

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Answer:

The minimum amount in sales this month to meet her goal is [tex]\$5,714.29[/tex]

Step-by-step explanation:

Let

x----> amount in sales this month

we know that

[tex]7\%=7/100=0.07[/tex]

The inequality that represent this situation is equal to

[tex]2,500+0.07x\geq2,900[/tex]

Solve for x

Subtract 2,500 both sides

[tex]0.07x\geq2,900-2,500[/tex]

[tex]0.07x\geq400[/tex]

Divide by 0.07 both sides

[tex]x\geq400/0.07[/tex]

[tex]x\geq \$5,714.29[/tex]

therefore

The minimum amount in sales this month to meet her goal is [tex]\$5,714.29[/tex]

Step-by-step explanation:

The square root of 17 is 4.12. Minus one equals 3.12

The square root of 5 is 2.23.

pi+7 equals 10.142. Divided by five equals around 2.

so you end up with, 3.12, 2.23, and 2.1

Answer:

n = 1067

Step-by-step explanation:

Since nothing is known, we would assume that 50% of the computers use the new operating system.

So, standard error = 0.5/SQRT(n)

Z-value for a 95% CI = 1.9596

So, margin of error = 1.9596 x 0.5 / SQRT(n) = 0.03

So, n = 1067 (approx.)

This will be your approximate answer : n = 1067

Answer: 2401

Step-by-step explanation:

Formula to find the sample size is given by :-

[tex]n= p(1-p)(\dfrac{z_{\alpha/2}}{E})^2[/tex]

, where p = prior population proportion.

[tex]z_{\alpha/2}[/tex] = Two -tailed z-value for [tex]{\alpha[/tex]

E= Margin of error.

As per given , we have

Confidence level : [tex]1-\alpha=0.95[/tex]

⇒[tex]\alpha=1-0.95=0.05[/tex]

Two -tailed z-value for [tex]\alpha=0.05 : z_{\alpha/2}=1.96[/tex]

E= 2%=0.02

We assume that nothing is known about the percentage of computers with new operating systems.

Let us take p=0.5  [we take p= 0.5 if prior estimate of proportion is unknown.]

Required sample size will be :-

[tex]n= 0.5(1-0.5)(\dfrac{1.96}{0.02})^2\\\\ 0.25(98)^2=2401[/tex]

Hence, the number of computer must be surveyed = 2401

[tex]|\Omega|={_{16}C_5}=\dfrac{16!}{5!11!}=\dfrac{12\cdot13\cdot14\cdot15\cdot16}{120}=4368\\|A|={_{12}C_5}=\dfrac{12!}{5!7!}=\dfrac{8\cdot9\cdot10\cdot11\cdot12}{120}=792\\\\P(A)=\dfrac{792}{4368}=\dfrac{33}{182}\approx18\%[/tex]

The probability of the event is defined as the ratio of the number of cases favourable to an occurrence, and the further calculation can be defined as follows:

4 of the 16 modems are defective, while the remaining 12 are not.

P(accepting shipment) = P (all 5 modems work)

[tex]\bold{^{12}C_{5}}[/tex] methods could be used to choose 5 non-defective modems from a pool of 12 non-defective modems.

[tex]\to \bold{^{12}C_{5} = \frac{12!}{ (12 -5)! \times 5! }}[/tex]

             [tex]\bold{ = \frac{12!}{ 7! \times 5!}}\\\\\bold{ = \frac{12 \times 11 \times 10 \times 9 \times 8 \times 7!}{ 7! \times 5!}}\\\\\bold{ = \frac{12 \times 11 \times 10 \times 9 \times 8}{5 \times 4 \times 3 \times 2 \times 1}}\\\\\bold{ =11 \times 9 \times 8}\\\\\bold{=792}[/tex]

The total number of methods to choose 5 modems from a pool of 16 modems is [tex]\bold{^{16}C_{5}}[/tex].

[tex]\to \bold{^{16}C_{5} = \frac{16!}{ (16 -5)! \times 5! }}[/tex]

             [tex]\bold{ = \frac{16!}{ 11! \times 5!}}\\\\\bold{ = \frac{16 \times 15 \times 14 \times 13 \times 12 \times 11 !}{ 11! \times 5!}}\\\\\bold{ = \frac{16 \times 15 \times 14 \times 13 \times 12}{ 5!}}\\\\\bold{ = \frac{16 \times 15 \times 14 \times 13 \times 12}{ 5\times 4\times 3 \times 2 \times 1}}\\\\\bold{ = 8 \times 3 \times 14 \times 13 }\\\\\bold{ = 4368 }\\\\[/tex]

P(accepting shipment) = P(all 5 modems work):

[tex]= \bold{\frac{^{12}C_5}{ ^{16}C_{5}}}[/tex]

[tex]\bold{=\frac{792}{4368}}\\\\\bold{=0.18131}\\\\\bold{=0.18131 \times 100= 18.131 \approx 18.131\%}\\\\[/tex]

Therefore, the final answer is "18.131%".

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Answer: There are 26000 miles that will both be due at the same time.

Step-by-step explanation:

Since we have given that

Number of miles required by new vintage = 400

Number of miles if these services have must been performed by the dealer = 13000

We need to find the number of miles from now that will both be due at the same time.

We would use "LCM of 400 and 13000":

As we know that LCM of 400 and 13000 is 26000.

So, there are 26000 miles that will both be due at the same time.

Answer:

Step-by-step explanation:

n^2 is less than 2^n for n < 2 and for n > 4. The smallest size of n that is of interest is n=1. For that, n^2 = 1^1 = 1.

The n^2 algorithm will outperform the 2^n algorithm for n = 1. That problem size will take 1 day to solve.

_____

Please note that there are no algebraic methods for solving an inequality of the form x^2 < 2^x. We have solved it using a graphing calculator.

Final answer:

The smallest instance size where the n² days algorithm outperforms the 2n seconds algorithm is n=43200. However, it's not practical, as this size leads to a computation time of approximately 1.86496 × 10⁹ days for the first algorithm, showing that for any realistic value of n, the second algorithm is more efficient.

Explanation:

The student's question is about the comparison of the performance of two different algorithms. Specifically, the question asks at what size the algorithm, which takes n² days to solve an instance of size n, will outperform the 2n seconds algorithm.

To determine the smallest instance size at which the first algorithm outperforms the second, we must set the two times equal and solve for n. Let's denote the time taken by the first algorithm as T1 and the second algorithm as T2, where T1 = n² days and T2 = 2n seconds. We should convert both times to a common unit, which typically is seconds, as follows:

1 day = 24 hours = 86400 seconds

T1 in seconds: n²  times 86400 seconds/day

T2 is already in seconds: 2n seconds

Now equate the two to find the smallest n:

n²  times 86400 = 2n

n²  times 86400 / 2 = n

n = 86400 / 2 = 43200

Thus, the smallest instance size n is 43200. To find how long this instance takes to solve by the first algorithm:

T1 = 43200² days

T1 ≈ 1.86496 × 109 days

This is impractically large, indicating that for any realistic value of n, the second algorithm is more efficient.

Answer:

Probability that a randomly selected broiler weighs more than 1454 g is 0.3372 or 34% (approx.)

Step-by-step explanation:

Given:

Weights of Broilers are normally distributed.

Mean = 1387 g

Standard Deviation = 161 g

To find: Probability that a randomly selected broiler weighs more than 1454 g.

we have ,

[tex]Mean,\,\mu=1387[/tex]

[tex]Standard\,deviation,\,\sigma=161[/tex]

X = 1454

We use z-score to find this probability.

we know that

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

[tex]z=\frac{1454-1387}{161}=0.416=0.42[/tex]

P( z = 0.42 ) = 0.6628   (from z-score table)

Thus, P( X ≥ 1454 ) = P( z ≥ 0.42 ) = 1 - 0.6628 =  0.3372

Therefore, Probability that a randomly selected broiler weighs more than 1454 g is 0.3372 or 34% (approx.)