Sixty-five percent of employees make judgements about their co-workers based on the cleanliness of their desk. You randomly select 8 employees and ask them if they judge co-workers based on this criterion. The random variable is the number of employees who judge their co-workers by cleanliness. Which outcomes of this binomial distribution would be considered unusual? Sixty-five percent of employees make judgements about their co-workers based on the cleanliness of their desk. You randomly select 8 employees and ask them if they judge co-workers based on this criterion. The random variable is the number of employees who judge their co-workers by cleanliness. Which outcomes of this binomial distribution would be considered unusual?

Answers

Answer 1

Answer:

The outcomes of this binomial distribution that would be considered unusual is {0, 1, 2, 8}.

Step-by-step explanation:

The outcomes provided are:

(A) 0, 1, 2, 6, 7, 8

(B) 0, 1, 2, 7, 8

(C) 0, 1, 7, 8

(D) 0, 1, 2, 8

Solution:

The random variable X can be defined as the number of employees who judge their co-workers by cleanliness.

The probability of X is:

P (X) = 0.65

The number of employees selected is:

n = 8

An unusual outcome, in probability theory, has a probability of occurrence less than or equal to 0.05.

Since outcomes 0 and 1 are contained in all the options, we will check for X = 2.

Compute the value of P (X = 2) as follows:

[tex]P(X=2)={8\choose 2}(0.65)^{2}(0.35)^{8-2}[/tex]

                [tex]=28\times 0.4225\times 0.001838265625\\=0.02175\\\approx 0.022<0.05[/tex]

So X = 2 is unusual.

Similarly check for X = 6, 7 and 8.

P (X = 6) = 0.2587 > 0.05

X = 6 not unusual

P (X = 7) = 0.1373 > 0.05

X = 7 not unusual

P (X = 8) = 0.0319

X = 8 is unusual.

Thus, the outcomes of this binomial distribution that would be considered unusual is {0, 1, 2, 8}.


Related Questions

Please help I did the first 2 already.

Answers

The answer to C is 1.5 or 3/2

Since we know that 2x is equal to 3 because the solution is three and 3+3=6 then we divide 3 by 2 to get 3/2

Sofia ordered sushi for a company meeting. They change plans and increase how many people will be at the meeting, so they need at least 100100100 pieces of sushi in total. Sofia had already ordered and paid for 242424 pieces of sushi, so she needs to order additional sushi. The sushi comes in rolls, and each roll contains 121212 pieces and costs \$8$8dollar sign, 8. Let RRR represent the number of additional rolls that Sofia orders.

Answers

Answer:

Sofia will order 7 more rolls of sushi (84 pieces) and pay $56

Step-by-step explanation:

They need at least 100 pieces of sushi

Sofia had ordered and paid for 24 pieces of sushi already

Sushi comes in rolls

Each roll=12 pieces at $8

R=additional rolls that Sofia orders

Additional sushi= Needed sushi - ordered sushi

=100-24

=76 pieces of sushi

Each roll has 12 pieces

76/12=6.33

Sofia has to order in rolls

So, she will order 7 more rolls of sushi of 12 pieces each

12*7=84 pieces

Recall, that they needed at least 100 pieces, so the number of pieces could be more than 100

If Sofia orders 84 pieces + the already ordered 24 pieces

Total pieces=108 pieces

She has paid for 24 pieces (3 rolls) at $8 per roll

7 rolls=$8*7

=$56

♡ The Question/Task(s)! ♡

✦ || 1) Which inequality describes this scenario?

✦ || 2) What is the least amount of additional money Sofia can spend to get the sushi they need?

︶꒦︶꒷︶︶ʚ♡ɞ︶︶꒷︶꒦︶

♡ The Answer(s)! ♡

✦ || 1) The inequality is, "24 + 12R ≥ 100"!

✦ || 2) They need 56 Dollars!

I apologize if the answer is incorrect! ♡

︶꒦︶꒷︶︶ʚ♡ɞ︶︶꒷︶꒦︶

♡ The Step-By-Step Process! ♡

✦ || Sofia needs the sushi she's already ordered plus the additional sushi to be at least 100 pieces. We can represent this with an inequality whose structure looks something like this:

(sushi already ordered) + (additional sushi) [≤ or ≥] 100

Then, we can solve the inequality for R to find how many additional rolls Sofia needs to order. Sofia has already ordered and paid for 24 pieces. Each roll has 12 pieces, and R represents the number of additional rolls, so the number of additional pieces from these rolls is 12R. The number of pieces she's already ordered plus the additional pieces needs to be greater than or equal to 100 pieces. Since she can't order partial rolls, Sofia needs to reserve 7 additional rolls. And each roll costs $8, so ordering 7 additional rolls costs 7 ⋅ $8 = $56.

︶꒦︶꒷︶︶ʚ♡ɞ︶︶꒷︶꒦︶

♡ Tips! ♡

✦ || No Tips Provided!ヽ(>∀<☆)ノ

A landscaper is designing a wall of white bricks . The pattern consists of 130 white bricks in the bottom row , 110 white bricks in the second row , and 90 white bricks in the third row . How meany white bricks will the 6th row have

Answers

Answer:

30 Bricks in the 6th row

Step-by-step explanation:

i found the answer online

Answer:

b: 30

Step-by-step explanation:

took test

Please show your work. I will give brainliest to the right answer!

Answers

Answer:

[tex]y = \frac{1}{8}(x + 4)^2 + 4[/tex]

Step-by-step explanation:

Given:

Focus of parabola: (-4, 6)

Directrix: y = 2

Required:

Equation for the parabola

SOLUTION:

Using the formula, [tex] y = \frac{1}{2(b - k)}(x - a)^2 + \frac{1}{2}(b + k) [/tex] , the equation for the parabola can be derived.

Where,

a = -4

b = 6

k = 2

Plug these values into the equation formula

[tex] y = \frac{1}{2(6 - 2)}(x - (-4))^2 + \frac{1}{2}(6 + 2) [/tex]

[tex]y = \frac{1}{2(4)}(x + 4)^2 + \frac{1}{2}(8)[/tex]

[tex]y = \frac{1}{8}(x + 4)^2 + \frac{8}{2}[/tex]

[tex]y = \frac{1}{8}(x + 4)^2 + 4[/tex]

Kareem wants to find the number of hours the average sixth-grader at his school practices an instrument each week. Which is the best way Kareem can get a representative sample?

Answers

This question is incomplete because the options are missing; here is the complete question:

Kareem wants to find the number of hours the average sixth-grader at his school practices an instrument each week. Which is the best way Kareem can get a representative sample?

A. He can randomly survey 50 boys in the school.

B. He can survey 30 students in the school band.

C. He can randomly survey 50 6th graders in the school.

D. He can survey 20 friends from his neighborhood.

The correct answer is C. He can randomly survey 50 6th graders in the school.

Explanation:

A representative sample is a portion of a population that shows the characteristics of all the population. In this context, for a sample to be representative it needs to include only individuals of the population that is studied. Also, ideally, individuals should be selected randomly as this guarantees the sample is not influenced by the researcher. According to this, option C is the best as this is the only one that focuses on the target population (6th graders) and the sample is random, which contributes to the sample being objective and representing the behavior of 6th-graders.

Answer:

He can randomly survey 50 sixth-graders in the school.

Step-by-step explanation:

29. A painter leans a ladder against the side of a
house that is 3 feet from the base. If the top
of the ladder reaches 16 feet, how long is the
ladder ?

HELP! answer if you can!​

Answers

Answer:

16.2788 feet

Step-by-step explanation:

a²+b²=c²

3²+16²=c²

9+256=c²

265=c²

c=√265

c=16.2788 feet

If the ladder is 3 feet from the base of the house and the top is 16 feet from the base then the length of ladder is approximately 16.2788 feet long.

What is pythagoras theorem?

Pythagoras theorem says that in a right angled triangle the square of hypotenuse of triangle is equal to the sum of squares of base and perpendicular of that respective triangle.

[tex]H^{2} =P^{2} +B^{2}[/tex] where H is hypotenuse, P is perpendicular, B is base of triangle.

How to find length of ladder?

If a painter leans a ladder against a wall then it forms a right angled triangle so in this we will apply pythagoras theorem to find the length of ladder.

let the length of ladder be h so,

[tex]h^{2} =3^{2} +16^{2}[/tex]

[tex]h^{2} =9+256[/tex]

[tex]h^{2} =265[/tex]

h=[tex]\sqrt{265}[/tex]

h=16.2788 feet.

Hence the length of ladder is 16.2788 feet.

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6
PO
2. In school of 900 studonts, it was
found that 600 students participate
in singing 500 students
in dancing and 125
do not participate
in both the activities.
participate​

Answers

Answer:

[tex]B = 325[/tex]

Step-by-step explanation:

Given

Total = 900

Singing = 600

Dancing = 500

None = 125

Required

Determine the number of students that participate in both

Representing; Singing with S, Dancing with D, Both singing and dancing with B and None with N;

In Set Notation;

[tex]Total = (S - B) + (D - B) + N + B[/tex]

Substitute 900 for Total, 600 for S, 500 for D and 125 for N

[tex]900 = (600 - B) + (500 - B) + 125[/tex]

Open Brackets

[tex]900 = 600 - B + 500 - B + 125 + B[/tex]

Collect Like Terms

[tex]900 = 600 + 500 + 125 - B - B + B[/tex]

[tex]900 = 1225- B - B + B[/tex]

[tex]900 = 1225- B[/tex]

Collect Like Terms

[tex]900 - 1225 = -B[/tex]

[tex]-325 = -B[/tex]

Multiply both sides by -1

[tex]-1 * -325 = -B * -1[/tex]

[tex]325 = B[/tex]

Reorder

[tex]B = 325[/tex]

Hence, the number of students that do not participate in both is 325

Solve for x : 2^(x-5) . 5^(x-4) = 5​

Answers

Answer:

x = 5

Step-by-step explanation:

Notice that there is also a base 5 on the right hand side of the equation, therefore, let's move [tex]5^{x-4}[/tex] to the right by dividing both sides by it. and then re-writing the right hand side as 5 to a power:

[tex]2^{x-5}\,*\,5^{x-4}=5\\2^{x-5}=5/5^{x-4}\\2^{x-5}=5\,*\,5^{4-x}\\2^{x-5}=5^{5-x}[/tex]

Now apply log to both sides in order to lower the exponents (where the unknown resides):

[tex](x-5)\,log(2)=(5-x)\,log(5)[/tex]

Notice that when x = 5, this equation is true because it makes it the identity: 0 = 0

So, let's now examine what would be the solution of x is different from 5, and we can divide by (x - 5) both sides of the equation:

[tex]log(2)=\frac{5-x}{x-5} \,log(5)\\log(2)=-1\,\,log(5)\\log(2)=-log(5)[/tex]

which is an absurd because log(2) is [tex]\neq[/tex] from log(5)

Therefore our only solution is x=5

Answer:

if decimal  no solution

if multiply x =5

Step-by-step explanation:

If this is a decimal point

2^(x-5) . 5^(x-4) = 5

Rewriting .5 as 2 ^-1

2^(x-5)  2 ^ -1 ^(x-4) = 5

We know that a^ b^c = a^( b*c)

2^(x-5)  2 ^(-1*(x-4)) = 5

2^(x-5)  2 ^(-x+4) = 5

We know a^ b * a^ c = a^ ( b+c)

2^(x-5 +-x+4) = 5

2^(-1) = 5

This is not true so there is no solution

If it is multiply

2^(x-5)  * 5 ^(x-4) = 5

Divide each side by 5

2^(x-5)  * 5 ^(x-4) * 5^-1 = 5/5

We know that a^ b * a^c = a^ ( b+c)

2^(x-5)  * 5 ^(x-4 -1)  = 1

2^(x-5)  * 5 ^(x-5)  = 1

The exponents are the same, so we can multiply the bases

a^b * c*b = (ac) ^b

(2*5) ^ (x-5) = 1

10^ (x-5) = 1

We know that 1 = 10^0

10^ (x-5) = 10 ^0

The bases are the same so the exponents are the same

x-5 = 0

x=5


[tex] {x}^{3} - {x}^{2} \div x[/tex]

Answers

Answer

x(x^2 - 1)

Explanation

Order of Operations is BIDMAS

Therefore division before subtraction.

x^2 / x^1

Use law of indices where

x^m / x^n = x^m-n

So

x^2 / x^1 = x^2-1 = x^1 = x

x^3 - x is no possible as they aren’t like terms, However you can factorise to obtain

x(x^2 - 1)

The braking distance, D, of a car is directly proportional to the square of its speed, v. When d=5, v=10
Find d when v=70​

Answers

[tex] d \propto v^2[/tex]

$\implies d=kv^2$

substitute the given values, $5=k(10)^2\implies k=\frac1{20}$

now, $d=\frac{1}{20}\times( 70)^2=\frac{70\times70}{20}=245$

A big blunder from my side, now fixed!

Find the value of x. A. 53–√ m B. 241−−√ m C. 6 m D. 6+35–√ m

Answers

Answer:

x = 2√41 m

Step-by-step explanation:

Since the triangle is a right angled triangle we can use Pythagoras theorem to find the missing side x

Using Pythagoras theorem we have

a² = b² + c²

where a is the hypotenuse

From the question x is the hypotenuse

So we have

[tex] {x}^{2} = {8}^{2} + {10}^{2} [/tex][tex] {x}^{2} = 64 + 100[/tex][tex] {x}^{2} = 164[/tex]

Find the square root of both sides

We have the final answer as

x = 2√41 m

Hope this helps you

Answer:

2 sqrt(41) =c

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2

8^2 + 10^2 = c^2

64+ 100 = c^2

164 = c^2

take the square root of each side

sqrt(164) = sqrt(c^2)

sqrt(4*41) = c

2 sqrt(41) =c

the difference between y and 3/8 is 3/4. workout the possible values of y

Answers

Answer:

y-3/8 =3/4y=3/4-3/8y=3/8

Please give me the correct answer

Answers

Answer:

Step-by-step explanation:

slant height = l = 15 mm

radius = r = 7 mm

Surface area of cone = πr (l + r) square units

                                  = 3.14 * 7 *(15 + 7)

                                  = 3.14 * 7 * 22

                                 = 483.56 square mm

Please answer this question now in two minutes

Answers

Answer:

m∠C = 102°

Step-by-step explanation:

This diagram is a Quadrilateral inscribed in a circle

The first step is to determine what m∠B

is

The sum of opposite angles in an inscribed quadrilateral is equal to 180°

m∠D + m∠B = 180°

m∠B = 180° - m∠D

m∠B = 180° - 80°

m∠B = 100°

Second step is we proceed to determine the exterior angles of the circle

m∠ADC = 2 × m∠B

m∠ADC = 2 × 100°

m∠ADC = 200°

m∠ADC = m∠CD + m∠AD

m∠AD = m∠ADC - m∠CD

m∠AD = 200° - 116°

m∠AD = 84°

The third step is to determine m∠BAD

m∠BAD = m∠AD + m∠AB

m∠BAD = 84° + 120°

m∠BAD = 204°

The final step Is to determine what m∠C is

It is important to note that:

m∠BAD is Opposite m∠C

Hence

m∠C = 1/2 × m∠BAD

m∠C = 1/2 × 204

m∠C = 102°

Find the volume of the given shapes. Round to the nearest tenth if necessary.

Answers

Answer:

Step-by-step explanation:

5.

volume=l×w×h=8×6×7=336 mi³

6.

diameter=16 yd

radius=16/2=8 yd

[tex]volume=\frac{4}{3} \pi \times 8^3=\frac{2048}{3} \pi \approx 2144.67 \approx 2144.7 yd^3[/tex]

The time required to drive a fixed distance varies inversely as the speed. It takes 2 hr at a speed of 200 km/h to drive a fixed distance. How long will it take to drive the same distance at a speed of 80 km/h?

Answers

Answer:

5 hours

Step-by-step explanation:

From the question, we are told that:

Time required to drive a fixed distance varies inversely as the Speed

T ∝ 1/S

k = proportionality constant hence,

T =k × 1/S

T = k/S

Step 1

Find k

It takes 2 hr at a speed of 200 km/h to drive a fixed distance

T = 2 hours, S = 200km/h

T = k/S

2 = k / 200

k = 2 × 200

k = 400

Step 2

How long will it take to drive the same distance at a speed of 80 km/h?

S = 80km/h

T = k/S

k = 400

T = 400/80

T = 5

Therefore, it takes 5 hours to drive the same distance at a speed of 80km/hr

HHHHEEEEELLLLLPPPPPPP PLEASEEE ANSWER #1 AND #2

Answers

Answer:

37 = -3 + 5(k +6)

37 = -3 + 5k + 30

37 = 27 + 5k

10 = 5k

k = 2

-2 = -(w - 8)

-2 = -w + 8

-10 = -w

w = 10

Answer:

37=-3+5(k+6)                                            

37=-3+5k+30

37=27+5k

37-27=5k

5k=10

k=10/2

k=5

***********************************************************************************

-2= -(w-8)

-2=-w+8

-2-8=-w

-w=-10

w=10

the area of a trapezium is 14.7cmsquare. if the parallel sides are 5.3cm and 3.1cm long,find the perpendicular distance between them

Answers

The perpendicular distance of the trapezoid is 3.5 cm

How to determine the perpendicular distance?

The given parameters are:

Parallel sides = 5.3 cm and 3.1 cmArea = 14.7 square cm

The area of a trapezoid is:

Area = 0.5 * (Sum of parallel sides) * perpendicular distance

So, we have:

14.7 = 0.5 *(5.3 + 3.1) * perpendicular distance

Evaluate

Perpendicular distance = 3.5

Hence, the perpendicular distance of the trapezoid is 3.5 cm

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I WILL GIVE BRAINLIEST!
80 patients gave information about how long they waited to see the doctor.
1. Work out an estimate of the mean time that the patients waited.

2. The doctor says, “70% of our patients wait less than 30 minutes to be seen.” Is she correct?

Answers

Answer:

No, 68.75% waited less than 30mins

I don't really know about the other one, but i tried my best, soooo sorry

soz

Hope that helped!!! k

Solve for x: 3(x + 1) = -2(x - 1) + 6. (1 point)

Answers

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

x = 1

First: distribute 3(x+1)= -2(x-1)+6

3x+3=2(x-1)+6

Then you have too distribute again

3x+3=2(x-1)+6

3x+3= -2x+2+6

Third: add the numbers

3x+3= -2x+2+6

3x+3= -2x+8

Fourth: add the same term to both sides of the equation

3x+3= -2x+8

3x+3-3= -2x+8-3

Fifth: Simplify 3x= -2x+5

Sixth: add same term to both sides of the equation

3x= -2x+5

3x+2x= -2x+5+2x

Seventh: simplify again

5x =5

Eigth: divide both sides of the equation by the same term

5x=5

5x/5 =5/5

Last: Simplify

X=1

Need help ASAP!!!! THX

Answers

Answer:

C

Step-by-step explanation:

f(x) = x - 2

f(2) = (2) - 2

f(2) = 0

A + B are wrong cuz..

f(-2) = -2 - 2

f(-2) = -4


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


Answers

Answer:

[tex]\huge \boxed{x(x+3)}[/tex]

Step-by-step explanation:

[tex]2x+x^2 +x[/tex]

Combine like terms.

[tex]x^2 +(2x+x)[/tex]

[tex]x^2 +3x[/tex]

Factor out [tex]x[/tex] from the expression.

[tex]x(x+3)[/tex]

An agriculture company is testing a new product that is designed to make plants grow taller. This can be thought of as a hypothesis test with the following hypotheses.H0: The product does not change the height of the plant.Ha: The product makes the plant grow taller.Is the following an example of a type I or type II error?The sample suggests that the product makes the plant grow taller, but it actually does not change the height of the plant.a) Type Ib) Type II

Answers

Answer:

The error made here is a Type I error.

Step-by-step explanation:

A Type I error is the rejection of a null hypothesis (H₀) when indeed the null hypothesis is true. It is symbolized by α.

A Type II error is failing to discard a null hypothesis when indeed the null hypothesis is false. It is symbolized by β.

The hypothesis in this case is defined as follows:

H₀: The product does not change the height of the plant.

Hₐ: The product makes the plant grow taller.

The sample suggests that the product makes the plant grow taller, but it actually does not change the height of the plant.

So, the sample suggests to reject the null hypothesis when in fact the null hypothesis is true.

Thus, the error made here is a Type I error.

Sams building a suspension bridge for the playground at the elementary school I needed some chain-link and some rope he bought a total of 80 feet of materials and The chain-link cost two dollars per foot and the rope cost 1.50 per foot he spent a total of $135 how much of each did he buy

Answers

Answer:

Amount of material for chain link = 30 feet

Amount of material for rope = 50 feet

Step-by-step explanation:

Let the amount of chain link = X

The amount of rope be represented by Y

He bought a total of 80 feet of materials

Hence we have:

X + Y = 80 ....... Equation 1

Y = 80 - X

The chain-link cost two dollars per foot and the rope cost 1.50 per foot he spent a total of $135

X × $2 + Y × $1.50 = $135

2X + 1.5Y = 135 ......Equation 2

Substitute 80 - X for Y in Equation 2

2X + 1.5(80 - X) = 135

2X + 120 - 1.5X = 135

Collect like terms

2X - 1.5X = 135 - 120

0.5X = 15

X = 15/0.5

X = 30 feet

Substitute 30 feet for X in Equation 1

X + Y = 80 ....... Equation 1

30 + Y = 80

Y = 80 - 30

Y = 50 feet

Hence the amount of material he used for the chain link = 30 feet and the amount of material he used for the rope was = 50 feet

Given that ∆MTW ≅ ∆CAD, which angles are corresponding parts of the congruent triangles? ∠T ≅ ∠C ∠T ≅ ∠A ∠T ≅ ∠D

Answers

Answer:

∠T ≅ ∠A

Step-by-step explanation:

Since, ∆MTW ≅ ∆CAD

Therefore, ∠T ≅ ∠A (cpct)

The Three Stooges are having a pie eating contest. In 3 hours, Moe can eat 36 pies, Larry can eat 30, and Curly can eat 60. How many hours does it take them to eat 126 pies?

Answers

Answer:

3 hours

the information states in 3 hours they eat 36+30+60 = 126 pies.

Answer:

Altogether, the three stooges will consume 126 pies in three hours.

Step-by-step explanation:

1. In one hour, the three stooges can eat their total divided by three: Moe can eat 12 in one hour, Larry can eat 10 in one hour, and Curly can eat 20 in one hour. Therefore, the three stooges can eat 42 pies in one hour altogether. So, we have the equation 126 = 42h where h = the number of hours. Solving for 126 gives us 126/42 = h. h = 3. The three stooges can eat 126 pies in three hours.

A line passes through the point (–1,–2) and is perpendicular to the line with the equation y= –x – 1. What's the equation of the line?

Question 16 options:

A) 
y = x – 5

B) 
y = –x + 3

C) 
y = –x + 7

D) 
y = x – 1

Answers

Answer:

D) y = x - 1

Step-by-step explanation:

First we need the general equation of point slope form:

(y - y0) = m(x - x0)

Where y0 is the y coordinate and x0 is the x coordinate and m is the slope.

For the line to be perpendicular, we need the slope to be the negated opposite of the other equation.  So the negated opposite of -1 is 1.

So our m = 1, y0 = -2, and x0 = -1.  Now let's plug this into the equation and reform the equation into slope-intercept form

(y - (-2)) = 1 (x - (-1))

y + 2 = 1 (x + 1)

y + 2 = x + 1

y = x - 1

So the equation of the line that goes through the point (-1,-2) and is perpendicular to the line y = -x -1, is y = x - 1.

Cheers.

Answer:

B) y = -x - 3

Step-by-step explanation:

slope = -1

y = mx + b

-2 = -1(-1) + b

-3 = b

y = -x - 3

Which of the binomials below is a factor of this trinomial? URGENT!!!

Answers

Answer:

C

Step-by-step explanation:

10×-28=-280

35-8=27

35×(-8)=-280

10x²+27x-28

=10x²+(35-8) x-28

=10x²+35x-8x-28

=5x(2x+7)-4(2x+7)

=(2x+7)(5x-4)

Answer: C) 2x+7

=========================================================

Explanation:

One way we can factor is through use the of the quadratic formula.

Let [tex]10x^2+27x-28 = 0[/tex]

For now, the goal is to find the two roots of that equation.

Plug a = 10, b = 27, c = -28 into the quadratic formula

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(27)\pm\sqrt{(27)^2-4(10)(-28)}}{2(10)}\\\\x = \frac{-27\pm\sqrt{1849}}{20}\\\\x = \frac{-27\pm43}{20}\\\\x = \frac{-27+43}{20} \ \text{ or } \ x = \frac{-27-43}{20}\\\\x = \frac{16}{20} \ \text{ or } \ x = \frac{-70}{20}\\\\x = \frac{4}{5} \ \text{ or } \ x = -\frac{7}{2}\\\\[/tex]

The two roots are x = 4/5 and x = -7/2

For each root, rearrange the equation so we have 0 on the right hand side, and it's ideal to get rid of the fractions

x = 4/5

5x = 4

5x-4 = 0 gives us one factor

and

x = -7/2

2x = -7

2x+7 = 0 gives the other factor

The two factors are 5x-4 and 2x+7

Note how (5x-4)(2x+7) = 0 leads to the two separate equations of 5x-4 = 0 and 2x+7 = 0 due to the zero product property. Solving each individual equation leads to the two roots we found earlier.

Alternative methods to solve this problem are the AC factoring method (which leads to factor by grouping), using the box method, or you could use guess and check.

The average annual amount American households spend for daily transportation is $6312 (Money, August 2001). Assume that the amount spent is normally distributed.a. Suppose you learn that 5% of American households spend less than $1000 for dailytransportation. What is the standard deviation of the amount spent?b. What is the probability that a household spends between $4000 and $6000?c. What is the range of spending for the 3% of households with the highest daily transportationcost?

Answers

Answer:

(a) The standard deviation of the amount spent is $3229.18.

(b) The probability that a household spends between $4000 and $6000 is 0.2283.

(c) The range of spending for 3% of households with the highest daily transportation cost is $12382.86 or more.

Step-by-step explanation:

We are given that the average annual amount American households spend on daily transportation is $6312 (Money, August 2001). Assume that the amount spent is normally distributed.

(a) It is stated that 5% of American households spend less than $1000 for daily transportation.

Let X = the amount spent on daily transportation

The z-score probability distribution for the normal distribution is given by;

                          Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = average annual amount American households spend on daily transportation = $6,312

           [tex]\sigma[/tex] = standard deviation

Now, 5% of American households spend less than $1000 on daily transportation means that;

                      P(X < $1,000) = 0.05

                      P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{\$1000-\$6312}{\sigma}[/tex] ) = 0.05

                      P(Z < [tex]\frac{\$1000-\$6312}{\sigma}[/tex] ) = 0.05

In the z-table, the critical value of z which represents the area of below 5% is given as -1.645, this means;

                           [tex]\frac{\$1000-\$6312}{\sigma}=-1.645[/tex]                

                            [tex]\sigma=\frac{-\$5312}{-1.645}[/tex]  = 3229.18

So, the standard deviation of the amount spent is $3229.18.

(b) The probability that a household spends between $4000 and $6000 is given by = P($4000 < X < $6000)

      P($4000 < X < $6000) = P(X < $6000) - P(X [tex]\leq[/tex] $4000)

 P(X < $6000) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{\$6000-\$6312}{\$3229.18}[/tex] ) = P(Z < -0.09) = 1 - P(Z [tex]\leq[/tex] 0.09)

                                                            = 1 - 0.5359 = 0.4641

 P(X [tex]\leq[/tex] $4000) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{\$4000-\$6312}{\$3229.18}[/tex] ) = P(Z [tex]\leq[/tex] -0.72) = 1 - P(Z < 0.72)

                                                            = 1 - 0.7642 = 0.2358  

Therefore, P($4000 < X < $6000) = 0.4641 - 0.2358 = 0.2283.

(c) The range of spending for 3% of households with the highest daily transportation cost is given by;

                    P(X > x) = 0.03   {where x is the required range}

                    P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{x-\$6312}{3229.18}[/tex] ) = 0.03

                    P(Z > [tex]\frac{x-\$6312}{3229.18}[/tex] ) = 0.03

In the z-table, the critical value of z which represents the area of top 3% is given as 1.88, this means;

                           [tex]\frac{x-\$6312}{3229.18}=1.88[/tex]                

                         [tex]{x-\$6312}=1.88\times 3229.18[/tex]  

                          x = $6312 + 6070.86 = $12382.86

So, the range of spending for 3% of households with the highest daily transportation cost is $12382.86 or more.

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Answers

Answer:

the stone fell in the air for 7 sec and fell in the water for 5 sec

Answer:

Let time taken in air be 'a'

And the time taken in water be 'b'

a+b=12

Distance covered in air = 16a

′′′′′ ′′″″ water= 3b

16a + 3b = 127

Solve the two equations simultaneously

a= 7 secs

b= 5 secs

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