The diameter of an electric cable is normally distributed, with a mean of 0.9 inch and a standard deviation of 0.02 inch. What is the probability that the diameter will exceed 0.92 inch? (You may need to use the standard normal distribution table. Round your answer to three decimal places.)

Answers

Answer 1

The probability that the diameter of the electric cable that is normally distributed will exceed 0.92 inch is 0.841

What is probability?

Probabilities are used to determine the chances, likelihood, possibilities of an event or collection of events

How to determine the probability?

The given parameters are:

Mean = 0.9

Standard deviation = 0.2

Calculate the z-score at x = 0.92 using

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

This gives

z = (0.92 - 0.9)/0.02

Evaluate the numerator; subtract 0.9 from 0.92

z = 0.02/0.02

Divide 0.02 by 0.02. This gives

z = 1

The probability is then represented as:

P(x > 0.92) = P(z > 1)

Next, we look up the value of the z table of probabilities

From the z table of probabilities, we have:

P(x > 0.92) = 0.841

Hence, the probability that the diameter of the electric cable that is normally distributed will exceed 0.92 inch is 0.841

Related Questions

Decide whether the conditions create a unique triangle, multiple triangles, or no triangle m∠A=65∘ m∠B=75∘ m∠C=40∘

Answers

Answer:

multiple triangles

Step-by-step explanation:

add the numbers up it adds to 180 which is the sum of a triangle and could create other triangles

Carter and Isabella run a carwash business. They split the revenue 50/50. They are deciding on if they should join forces with Carla's carwash. If they join with Carla, the combined carwash will make $2400 more per month, but they'll have to split revenue equally (33.3/33.3/33.3). On an average month, Carter and Isabella's carwash makes $6000. How much more or less would Carter or Isabella individually make if they merged with Carla's carwash?

Answers

we can see that when they join with Carla, Carter and Isabella will get $200 less (individually).

How much more or less would Carter or Isabella individually make if they merged with Carla's carwash?

When Carter and Isabella work together, they have a revenue of $6000, which is split in 50/50, so each one gets:

$6000/2 = $3000

Carter wins $3000 and Isabella wins $3000.

If they join with Carla, the revenue increases by $2400, so now the total revenue is:

$6000 + $2400 = $8400

And now they split it between 3, so each one gets:

$8400/3 = $2800

The difference of Carter's (Or Isabella's) part is:

$3000 - $2800 = $200

Then we can see that when they join with Carla, Carter and Isabella will get $200 less (individually).

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What is the value of pi (i need to unlock the safe because is an inhibitor there) DYING LIGHT 2

Answers

The number π (pi) is a mathematical constant which is equal to the ratio of a circle's circumference to its diameter. It has a value of π = 22/7

What is an equation?

An equation is an expression that shows the relationship between two or more variables and numbers.

The number π (pi) is a mathematical constant which is equal to the ratio of a circle's circumference to its diameter. It is given by:

π = 22/7

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Use the table to the right to answer the following question.
Compare the energy released by fission of 1 kilogram of element B to that released by burning 1 kilogram of element A.

Answers

The energy is compared based on the information given below.

How to illustrate the energy?

Energy released by burning 1 kilogram of element A = EA = 5.1 * (10)8

Energy released by fission of hydrogen in 1 kilogram of element B = EB = 1.3 * (10)10

Therefore,

Ratio = EB / EA = 1.3 * (10)10 / 5.1 * (10)8 = 25

Thus, the fission of 1 kg of element B releases 25 times as much energy as burning 1 kilogram of element A.

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The other part of the question:

Energy released by burning 1 kilogram of element A = 5.1 times 10 Superscript 8

Energy released by the fission of hydrogen in 1 kilogram of element B = 1.3 times 10 Superscript 10

You are building a ramp for your grandparent's house. The ramp will replace the steps that go
to their front door which is 3 feet off the ground. You want the ramp to start 10 ft from the
front door. How long will the ramp need to be?

Answers

Using right triangle, the length of the ramp is 10.44 ft.

How to find the length of the ramp using right triangle?

The situation forms a right angle triangle.

The length of the ramp is the hypotenuse side of the right triangle.

Therefore, using Pythagoras theorem,

c² = a² + b²

where

a and b are the other legsc is the hypotenuse side

Therefore,

c² = 10² + 3²

c² = 100 + 9

c = √109

c = 10.4403065089

c = 10.44 ft

Therefore, the length of the ramp is 10.44 ft.

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if f x is a linear function, f(-1)=3, and f(1)=5, find an equation for f(x)

Answers

The equation of f(x) is f(x) = x + 4

How to determine the equation?

The given parameters are

f(-1) = 3 and f(1) = 5

Start by calculating the slope (m) using:

[tex]m = \frac{f(1) - f(-1)}{1 - -1}[/tex]

This gives

[tex]m = \frac{5 - 3}{1 + 1}[/tex]

Evaluate

m = 1

The equation is then calculated as;

f(x) = m(x - x1) + f(-1)

This gives

f(x) = 1(x + 1) + 3

Expand

f(x) = x + 4

Hence, the equation of f(x) is f(x) = x + 4

Answers

Angles on straight line = 180

180 - 115 = 65

So, angle above 4 in the top corner is 65.

Co-interior angles add up to 180.

(180-65=115)

Thus, the value of 4 is 115 degrees.

Hope this helps!

8⁄9 ÷ 1⁄3 what is the answer please

Answers

Answer:

8/3

Step-by-step explanation:

8/9

use long division to convert 3/10 into decimals.

Answers

Answer:

3/10 as a decimal is expressed as 0.3.

Answer showing long division in attachment
.3 is the answer

A perimeter of a movie screen is 56 meters. the area is 171 square meters what are the dimensions of the screen

Answers

Using the formula for the perimeter and area of rectangle, the dimensions are: Length = 19 m; width = 9 m.

What is the Perimeter and Area of a Rectangular Shape?

Perimeter = 2(length + width)

Area = (length)(width).

Let x represent the length and y the width, therefore:

2(x + y) = 56 --> eqn. 1

xy = 171 --> eqn. 2

Rewrote eqn. 1

x + y = 56/2

x = 28 - y

Substitute x = (28 - y) into eqn. 2

171 = (28 - y)y

171 = 28y - y²

171 - 28y + y² = 0

y² - 28y + 171 = 0

Factorize

(y - 9)(y - 19)

y = 9 and y = 19

Therefore, the dimensions are: Length = 19 m; width = 9 m.

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Solve the following:
3 x 10³ - 7000
(8 × (−5)) + (4² +2²)
Give your answer in simplest form.
Enter can you help me solve this I was doing very good up to now

Answers

Answer:

3x(10x10x10): 3x(1000): 3000-7000: -4000. (8x(-5)): -40. (4x4) +(2x2): (16 +4): 20

Name the type of angle relationship. Set up the equation and solve for x.
Equation:
Solve: x :

Answers

Answer:

Same side interior angles

x=10

Step-by-step explanation:

The angles are same side interior angles

The add to 180 degrees

6x+10 + 110 = 180

Combine like terms

6x+120 =180

Subtract 120 from each side

6x = 180-120

6x= 60

Divide by 6

6x/6 = 60/6

x = 10

Answer:

Same-Side Interior Angles

Equation: 6x + 10 + 110 = 180

x = 10

Step-by-step explanation:

Hello!

The sum of the two given angles is 180°, as they are same-side interior angles.

Equation: 6x + 10 + 110 = 180

Solve for x6x + 10 + 110 = 1806x + 120 = 1806x = 60x = 10

The value of x is 10°.

A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180

Answers

The true options regarding the triangle diagram are;

m∠5 + m∠6 = 180°

m∠2+ m∠3 = m∠6

m∠2 + m∠3 + m∠5 = 180°

How to prove congruent angles?

We see the attached image showing ΔABC with Exterior angles as;

∠ 1 , ∠ 4 ,and ∠ 6

Now, the exterior angle property of triangles states that; An exterior angle of a triangle is equal to the sum of the opposite interior angles.

For Exterior ∠1 we have;

∠1 = ∠5 + ∠3 (Exterior angle Property of Triangle)

Similarly,

For Exterior ∠ 4 we have;

∠4 = ∠5 + ∠2 (Exterior angle Property of Triangle)

For Exterior ∠6 we have;

∠6 = ∠2 + ∠3 (Exterior angle Property of Triangle)

From Triangle Sum Property, we know that the sum of the measures of angles in a triangle is equal to 180°. Thus;

m∠2 + m∠3 + m∠5 = 180° (Triangle Sum Property)

Linear Pair of angles states that the measure of a straight angle is 180° and as such a linear pair of angles must add up to 180°. Thus;

m∠5 + m∠6 = 180° (Linear Pair)

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W
If 15 cans of food are needed for 7 campers for 2 days,
the number of cans needed for 4 campers for 7 days
is? (round up to nearest whole number)

Answers

Answer:

30 cans

Step-by-step explanation:

cross multiply

14x = 28 * 15

14x = 420

x = 420/14

x = 30 cans

Value of x after the statement "if P(x) then x 1" is executed where P(x): > 1

and x = 0 when the statement is reached:

Answers

The values of x after the statement are:

b) If x=1, then the statement P(1)="1>1" is false, and thus the value of x is equal to 1 after the statement "P(x) then x := 1".c) If x=2, then the statement P(2)="2>1" is true, and thus the value of x is equal to 1 after the statement "if P(x) then x := 1".

What is Discrete Mathematics?

This refers to the field of mathematics that studies mathematical structures and views them as discrete, rather than continuous and they include integers, statements, etc.

Therefore, if we consider the statement "if P(x) then x:=1" which is equivalent to "if x>1 then x:=1", then we can see that If x=1, then the statement P(1)="1>1" is false

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Find f−1(x) for f(x)=15+12x.

Answers

Answer:

[tex]\text{f}^{-1}(x)=\dfrac{x-15}{12}[/tex]

Step-by-step explanation:

[tex]\text{f}^{-1}(x)[/tex] is the notation for the inverse of a function.

The inverse of a function is a reflection in the line y = x.

Given function:

[tex]\text{f}(x)=15+12x[/tex]

To find the inverse of the given function:

Step 1

Replace f(x) with y to get an equation for y in terms of x:

[tex]\implies y=15+12x[/tex]

Step 2

Rearrange the equation to make x the subject:

[tex]\implies y-15=15+12x-15[/tex]

[tex]\implies y-15=12x[/tex]

[tex]\implies \dfrac{y-15}{12}=\dfrac{12x}{12}[/tex]

[tex]\implies x=\dfrac{y-15}{12}[/tex]

Step 3

Replace x with [tex]\text{f}^{-1}(x)[/tex] and y with x → this is the inverse function:

[tex]\implies \text{f}^{-1}(x)=\dfrac{x-15}{12}[/tex]

Step 4 (if necessary)

The domain of the function is the range of the inverse function.

The range of the function is the domain of the inverse function.

Therefore, as the domain and range of the given function are unrestricted, so too are the domain and the range of the inverse function:

Domain: (-∞, ∞) → all real numbersRange: (-∞, ∞) → all real numbers

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[tex]\\ \rm\leadsto y=15+12x[/tex]

Interchange x and y

[tex]\\ \rm\leadsto x=15+12y[/tex]

Solve for y

[tex]\\ \rm\leadsto 12y=x-15[/tex]

[tex]\\ \rm\leadsto y=\dfrac{x-15}{12}[/tex]

That's the inverse

In a stock of 12 blouses, 90 are sleeveless. How many percent of the stock are sleeveless?

Answers

75 percent of the stock are sleeveless

How to determine the percentage?

The given parameters are:

Blouse = 120

Sleeveless = 90

The percentage is calculated as:

Percentage = Sleeveless/Blouse * 100%

So, we have:

Percentage = 90/120* 100%

Evaluate the expression

Percentage = 75%

Hence, 75 percent of the stock are sleeveless

Answers

Answer:

Step-by-step explanation:

(-4(-1)-8)(3(2)^2+2=4-8×12+2

-4×14=-56

what two equal numbers add to the number 40

Answers

Answer:

3+37

11+29

17+23

20+20

Step-by-step explanation:

It's 20

(20+20 = 40)

Hope this helps!

spent a total of $5.58 for carrots, priced at $0.90 per pound. How many pounds of
carrots did Trina buy?

Answers

Answer:

6.2 pounds

Step-by-step explanation:

$5.58 / $.9 = 6.2 pounds of carrots bought

11) Find the mode of the data set.
O a.) 9
Ob.) 8
Oc.) 7
O d.) 6

Data:
5, 8, 12, 6, 7, 10, 14, 6, 13
4

Answers

4,5,6,6,7,8,10,12,13,14
Since 6 has the most occurring data, it is 6.

Answer:

Step-by-step explanation:

The mode is the number that is repeated the most in the data set. 6 is the only number that is repeated twice, so it is the mode.

Brainliest, please :)

Mary’s rectangular garden is 27 units long and 49 units wide. What is the perimeter?

Answers

Answer:

152 units

Step-by-step explanation:

Two sides of the rectangle are 27 units long and the other two sides are 49 units wide. You just add all the numbers up (27+27+49+49). When you do that, you get 152. I hope this helps!

What is the value of a?
O 5 units
05/
units
6 units
O 7 units

Answers

From the Δ YWZ we get c = 5 then the value of [tex]$a= 5 \frac{1}{3}[/tex].

How to estimate the value of a?

In the given Δ YWZ

WZ² = YW² + YZ²

c² = 4² + 3² = 16 + 9 = 25

c = 5

In the Δ XYW

b² = 4² + a²-----(1)

In the right-angle Δ WXZ

(a + 3)² = b² + c²

a² + 9 + 6a = b²+ c²

By putting the value of b² from (1)

a² + 9 + 6a = 16 + a² + 25

Simplifying the above equation, we get

6a + 9 = 41

6a = 41 - 9

6a = 32

[tex]$a = \frac{32}{6} = \frac{16}{3}[/tex]

[tex]$a= 5 \frac{1}{3}[/tex]

Therefore, the value of [tex]$a= 5 \frac{1}{3}[/tex].

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Solve for x.
BC = 2
CD =2x-6
BD X+2

Answers

Answer:

Step-by-step explanation:

Assuming C lies on segment BD, we know that by the segment addition postulate,

[tex]BC+CD=BD \\ \\ 2+2x-6=x+2 \\ \\ 2x-4=x+2 \\ \\ x=6[/tex]

The values of BC = 2, CD = 2x - 6 and BD = x + 2 then the value of x = 6.

How to find the value of x?

The algebraic expression should be any one of the conditions such as addition, subtraction, multiplication, and division.

In mathematics, an algebraic expression exists as an expression built up from integer constants, variables, and algebraic operations. For example, 3x² − 2xy + c exists as an algebraic expression.

To estimate the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to estimate the result.

Given: BC = 2, CD = 2x - 6 and BD = x + 2 then

BC+CD= BD

2+2x-6=x+2

Simplifying,

2x-4=x+2

Thus,

x=6

Therefore, the value of x = 6.

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Which of the following statements is TRUE about rectangle ABDC.

Answers

The statement that is TRUE of the rectangle is AB + BD > AD. Option A

Facts about the rectangle

WE have that a diagonal divides the rectangle into two equal triangles

line AD is the length of the diagonal

With the diagonal drawn, we have

AD = hypotenuse

AB and BD are the two other sides

From the Pythagorean theorem, we have that the square root of the square sum of the other two sides fives the hypotenuse. This mean that their sum is greater than the hypotenuse

Thus, the statement that is TRUE is AB + BD > AD. Option A

The complete question is;

Which of the following statements is TRUE about rectangle ABDC.

a. AB + BD > AD

b. AB + BD < AD

c. AB + BD = AD

d. (AB) (BD) = AD

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4. In the figure above ABCD is a parallelogram with
mLB = 60°, BC = XC = AZ = 4, XZ BC. What
is the perimeter of parallelogram ABCD?

Answers

Answer:

G. 24

Step-by-step explanation:

The perimeter of the figure is the sum of its side lengths. The given dimensions tell us all of the side lengths.

Analysis

Triangle BCX is given as an isosceles triangle with a base angle of 60° and side lengths of 4. Such a triangle is equilateral, so all side lengths will have a measure of 4.

The given information tells us all sides that appear parallel are parallel, so the figure consists of 4 equilateral triangles. Every short line segment has length 4.

Perimeter

The perimeter is the length of 6 short line segments, so is ...

P = 6×4 = 24

The perimeter of parallelogram ABCD is 24 units.

Diego Company manufactures one product that is sold for $70 per unit in two geographic regions—the East and West regions. The following information pertains to the company’s first year of operations in which it produced 53,000 units and sold 48,000 units.

Variable costs per unit:
Manufacturing:
Direct materials $ 21
Direct labor $ 10
Variable manufacturing overhead $ 2
Variable selling and administrative $ 4
Fixed costs per year:
Fixed manufacturing overhead $ 1,060,000
Fixed selling and administrative expense $ 557,000

The company sold 36,000 units in the East region and 12,000 units in the West region. It determined that $270,000 of its fixed selling and administrative expense is traceable to the West region, $220,000 is traceable to the East region, and the remaining $67,000 is a common fixed expense. The company will continue to incur the total amount of its fixed manufacturing overhead costs as long as it continues to produce any amount of its only product.

15. Assume the West region invests $43,000 in a new advertising campaign in Year 2 that increases its unit sales by 20%. If all else remains constant, what would be the profit impact of pursuing the advertising campaign?

Answers

The 53,000 units produced and the increase in sales of 50,400 - 48,000 = 2,400 units, give an impact (increase) in profit of $168,000

How can the impact in profit be found?

Price per unit = $70

Number of units produced = 53,000

Number of units sold = 48,000

Material cost per unit = $21

Labour cost per unit = $10

Manufacturing overhead = $2

Selling and administrative overhead = $4

Fixed cost = $1,060,000

Administrative expenses = $557,000

Advertising cost = $43,000

Percentage increase in sales = 20%

Number of units sold in Year 2 = 1.2 × 12,000 = 14,400

Total cost = 53000×(21+10+2+4) + 1,060,000 + 557,00 = 3,578,000

Total revenue in Year 1 = 70 × 48,000 = 3,360,000

Profit = Revenue - Cost

Profit in Year 1 = 3,360,000 - 3,578,000 = -218,000

Total revenue in Year 2 = 70 × (36,000+14,400) = 3,528,000

Profit in Year 2 = 3,528,000 - 3,578,000 = -50,000

The impact on the profit is therefore;

-50,000 - (-218,000) = 168,000

The profit impact is an increase in profit of $168,000

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How do I scale a landscape drawing that is half an acre

Answers

The steps to carry out scaling of a landscape drawing are; as detailed below

How to do landscape drawings?

The steps to carry out if we want to scale landscape drawings are;

1) Measure the half acre area that you want to draw.

2) Write down your notations. Convert the measurements to inches so you can draw your rendition on a piece of standard paper.

3) Scale the items by use of ratios. Set up your fraction as the length of the paper divided by the measured length.

4) Divide the fraction answer by the measured length and reduce the fraction by dividing the top and bottom by the fraction answer.

5) Scale everything you are going to draw accordingly.

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A room has a floor dimension of 30 feet by 50 feet. The height of the basement is 6 feet. What is the total area of all four walls?

Answers

Answer:

960 feet

Step-by-step explanation:

30×6=180

180×2=360

50×6=300

300×2=600

360+600=960

A rectangular waterbed is 8 ft long, 7 ft wide, and 1.5 ft tall. How many gallons of water are needed to fill the waterbed? Assume 1 gallon is 0.13 cu ft. Round to the nearest whole gallon.

Answers

646 gallons of water are needed to fill the waterbed

How to determine the gallons of water?

The dimensions are given as:

8 ft long, 7 ft wide, and 1.5 ft tall

The volume is calculated as:

Volume = Length * Width * Height

So, we have

V = 8 * 7 * 1.5 cubic feet

Evaluate

V = 84 cubic feet

1 gallon = 0.13 cubic feet

So, we have:

V = 84/0.13 gallon

Evaluate

V = 646 gallons

Hence, 646 gallons of water are needed to fill the waterbed