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The required probability of the randomly selected steel rod with the average length greater than 206.1cm whose mean is 205.8cm and standard deviation is 0.5cm is equal to 0.0024012.

As given in the question,

Mean of the normally distributed steel rod ' μ '= 205.8cm

Standard deviation of the normally distributed steed rod 'σ ' = 0.5cm

Number of steel rod bundled together 'n' = 22

Randomly selected steel rods bundle the average length is greater than

'[tex]\bar {X}[/tex]' = 206.1cm

Required probability is given by :

P( [tex]\bar {X}[/tex] > 206.1 )

= P [([tex]\bar {X}[/tex] - μ )/ (σ/√n) > ( 206.1 - 205.8)/ (0.5/√22) ]

= P ( Z > (0.3/ 0.1064))

= P ( Z > 2.8195)

= P ( Z > 2.820)

= 0.0024012

Therefore, the probability of the randomly selected steel rod with the average length greater than 206.1cm is equal to 0.0024012.

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If the larger triangle has a perimeter of 62 feet, its area will be 120 square feet.

We know that the perimeter of the smaller triangle is 31 feet, which means that the sum of the lengths of its three sides is 31 feet. We also know that the area of the smaller triangle is 40 square feet. We can set up the following equation to calculate the length of each side of the smaller triangle:

Side 1 + Side 2 + Side 3 = 31

We can then use the formula for the area of a triangle, A = bh/2, to calculate the length of the base and height of the smaller triangle. Since we know the area is 40 square feet, we can set up the following equation:

40 = (b)(h)/2

We can then solve this equation for b and h. We know that b + h = 31, so we can set up the following equation and solve for h:

h = 31 - b

Now that we know b and h for the smaller triangle, we can use the same formula to calculate the area of the larger triangle. Since we know that the perimeter of the larger triangle is 62 feet, we can set up the following equation to calculate the length of each side of the larger triangle:

Side 1 + Side 2 + Side 3 = 62

We can then use the following formula to calculate the area of the larger triangle:

A = (b)(h)/2

We know that b + h = 62, so we can set up the following equation and solve for h:

h = 62 - b

Now that we know b and h for the larger triangle, we can plug those values into the area formula and calculate the area of the larger triangle. The area of the larger triangle is 120 square feet. Therefore, if the larger triangle has a perimeter of 62 feet, its area will be 120 square feet.

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The amount of money each waiter get in tip is 44 dollars.

In this question we have been given at the yum yum cafe the waiters combine their tips and divide the total by the number of waiters.

Today's tip total is 132 and three waiters are working.

We need to find the amount of money each waiter get in tip.

Let x dollers be the amount each waiter get in tip.

Total tip amount = 132

number of waiters = 3

By unitary method,

x = 132/3

x = 44 dollars

Therefore, each waiter get 44 dollars in tip.

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The value of material's resistance at 100 v voltage and at 2 A current is 50 Ω.

As per the data given in the question the value of Voltage is 100 v, Current is 2 A

Ohm’s law states that the current through a conductor between two points is directly proportional to the voltage across the two points.

This law is one of the most basic laws of electricity.

Ohm’s Law Formula:

Voltage = Current× Resistance

V = I × R

V = Voltage, I = Current and R = Resistance.

Using Ohm's Law we have to determine the value of R.

R is Resistance and has units of ohms, with symbol Ω.

V = I × R

At Voltage = 100 v, Current = 2 A

100 = 2 × R

R = [tex]\frac{100}{2}[/tex]

R = 50 Ω

Therefore the value of Resistance of material, R = 50 Ω

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FIGURE EX 31.38 is a current-versus-potential-difference graph for a material. What is the material's resistance?

Diagram attaches at the end of solution.

The amount  Trevor's family spent, in total, on shower water in the past month = 0.03 dollars per minute

In this question we have been given there are 6 people in Trevor's house.

There are 3 bathrooms in the house.

Each person showered for an average of 480 minutes and used an average 72 liters of shower water (over the entire month)

We need to find the amount of money Trevor's family spent, in total, on shower water in the past month.

By unitary method,

72 * 6 = 432 liters of shower water used by the entire family over the month

Each liter costs $0.2

so by unitary method,

the total amount paid:

A = 432 * 0.2

  =  86.4 dollars

Each person showered for an average of 480 minutes.

So, total minutes would be 6x480 = 2880 minutes.

So, the required amount would be,

86.4/2880 = 0.03 dollars  per minute

Therefore, Trevor's family paid $0.03 per minute on shower water.

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1.5 litres of water are released from the faucet per minute.

It is given to us that -

There is a one quart jar

Water from the kitchen faucet fills the 1-quart jar in 10 seconds.

We need to ascertain the faucet's flow rate in gallons per minute.

We know that -

1 quart = 0.25 gallon ---- (1)

We also know that -

1 minute = 60 seconds

=> 60 seconds = 1 minute

=> 10 seconds = 10/60 = 0.16 minutes ----- (2)

Now, the flow rate can be calculated as -

Flow rate = Amount of water filled/Time taken ----- (3)

Substituting the values from equation (1) and (2) in equation (3), we have -

Flow rate = Amount of water filled/Time taken

=> Flow rate = 1 quart water/10 seconds

=> Flow rate = 0.25 gallons/0.16 minutes

=> Flow rate = 1.5 gallons per minute

Therefore, the flow rate of water from the faucet is 1.5 gallons per minute.

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Answer: True. Renting is a great option for many people because it offers flexibility and affordability. Renting allows individuals to live in a desired location without the financial burden and commitment of owning a home. It also provides flexibility, as renters can easily move to a different location if their needs or circumstances change. Additionally, renting can be a more affordable option compared to owning a home, as it typically involves lower upfront costs and maintenance expenses. For these reasons, renting is a viable and attractive option for many people.

Step-by-step explanation:

Using the concept of percentage, the percentage of dolphins that knew the difference is 26%

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

The number of dolphins that knew the difference between strike and ball is given as 4 out of 15.

This can be represented in a fraction as 4 / 15

The percentage that knew the difference = (4 / 15) * 100

The percentage that knew the difference will be 0.26 * 100 = 26 %

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Answer:

Step-by-step explanation:

good luck lol

The equation to find the distance between the lions and giraffes is

x² = 121 + 256.

Option D is the correct answer.

Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

Hypotenuse = Distance between lion and giraffes = x

Distance between lions and monkeys = 11 feet

Distance between monkeys and giraffes = 16 feet

Applying the Pythagorean theorem.

x² = 11² + 16²

x² = 121 + 256

x² = 377

x = √(377)

x = 19.42

Thus,

The distance between lions and giraffes is 19.42 feet.

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Answer:B and D

Step-by-step explanation:

Using the concept of percentages the total earning of Cara can be found to be $4200.

Percentage is a number expressed as a fraction of 100. The % sign means to divide the number by 100.

Cara's earning = commission + basic salary

basic salary = $1800 (this is constant)

commission = 6% of $40000

= (6/100)*40000

= $2400

Cara's earning = 1800 + 2400

Hence, her earning is $4200

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Answer:

13.85$

Step-by-step explanation:

105$-8$=97$

97$/7$=13.85$

Answer: About $13.86

Step-by-step explanation: To find how much the cost of the forks is, we need to subtract the value of the lunch box from the total cost, because we don't need to find the value of the lunch box. So:

105 - 8 = 97

So, now since he bought 7 forks, we need to divide 7 by 97. So:

97 / 7 = 13.857142857142858

So, we need to round to the nearest cent. So, the 7 is greater than 5, so we round up. So, we have $13.86 each. So, check, we do:

13.86(7) + 8

97.02 + 8

= 105.02

This is the closest he can buy for each fork is ABOUT $13.86. I hope this helps ;)

Answer: 6 1/2. yards

Step-by-step explanation:    you have to add 1 1/3 + 5/6, which is 2 1/6. 2 1/6x3=6 1/2.  then thats your answer

Answer:

aproximantly 131.1701yen

Step-by-step explanation:

Answer:

15430 Japanese yen

Step-by-step explanation:

To find out how many Japanese yen you receive for 100 British pounds, we need to find the exchange rate between British pounds and Japanese yen in the table. From the table, we can see that the exchange rate between British pounds and Japanese yen is 154.43. Therefore, if you exchange 100 British pounds, you will receive 100 * 154.43 = 15430 Japanese yen.

Answer:

The coordinates of a point are a pair of numbers that define its exact location on a two-dimensional plane. Recall that the coordinate plane has two axes at right angles to each other, called the x and y-axis. The coordinates of a given point represent how far along each axis the point is located.

Answer:

The area of the compound shape is 5√10 cm²

Step-by-step explanation:

In the given shape, there is a rectangle and a right angle triangle.

i.e.,

Compund shape = Rectangle + Triangle

So,

Area of Compound Shape = Area of Rectangle + Area of Right Angle Triangle

Formula;

A = 2√5 × 2√2 cm

A = 4√10 cm²

Formula;

A = ½ × √2 × 2√5 cm

A = 1 × √2 × √5 cm

A = √10 cm²

Now,

Area of Compound Shape = Area of Rectangle + Area of Right Angle Triangle

A = 4√10 cm² + √10 cm²

A = 5√10 cm²

Thus, The area of the compound shape is 5√10 cm²

Answer:

Because when you divide 100 by 4 and 50 by 2, you will get the same value

Answer:

--------------------------------------

Given is the graph of an absolute value function.

It has no domain restrictions, so x can be any real number.

There is a restriction on its range, it has a minimum at y = 0 and the rest of the values are positive real numbers.

It is correctly described in option d).

Answer:

The smaller integer is greater than 1

Step-by-step explanation:

The integers are x and x+1

[tex]x + x + 1 < 3x \\ 2x + 1 < 3x \\ 2x - 2x + 1< 3x - 2x \\ 1< x [/tex]

Answer: x=(10-sqrt(128))/14=(5-4sqrt(2))/7=-0.094

Step-by-step explanation:  (7x2 -  10x) -  1  = 0

STEP

2

:

Trying to factor by splitting the middle term

2.1     Factoring  7x2-10x-1

The first term is,  7x2  its coefficient is  7 .

The middle term is,  -10x  its coefficient is  -10 .

The last term, "the constant", is  -1

Step-1 : Multiply the coefficient of the first term by the constant   7 • -1 = -7

Step-2 : Find two factors of  -7  whose sum equals the coefficient of the middle term, which is   -10 .

     -7    +    1    =    -6

     -1    +    7    =    6

Answer:

Divide 5 to both side.

Step-by-step explanation:

Original Equation:

[tex]5(x-3)=5[/tex]

2nd Equation:

[tex](x-3)=1[/tex]

Single Steps:

Divide 5 to both side on Original Equation to get 2nd Equation.

Answer:

3x is a single term

Step-by-step explanation:

The "3" is a coefficient. The "x" is the variable. is also a single term.

hope this helps

William ran for 48 minutes since Eliot ran for 8 miles in 40 fewer minutes than William. They were running at the same speed.

Eliot and William both went running and ran for 8 miles and 12 miles respectively. Eliot finished his 8 mile run in 40 fewer minutes than William. This means that if the two of them were running at the same speed, it would take William 40 minutes longer than Eliot to finish his 12 mile run. To calculate how long William ran for, we can add 40 minutes to the time it took Eliot to run 8 miles. Since Eliot ran 8 miles in 40 fewer minutes than William, this means that Eliot ran 8 miles in the amount of time that William ran 12 miles. The total time William ran for is therefore 8 miles plus 40 minutes, which is 48 minutes.

Eliot: 8 miles ÷ 40 minutes fewer

= 0.2 miles/minute

William: 12 miles ÷ (0.2 miles/minute x 40 minutes)

= 48 minutes

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The diameter of a bicycle wheel is 24 inches. Around the wheel, there are 32 spokes that are spaced 48 meters away from one another.

The diameter of a circle is the distance measured through its center. The radius of a circle is the distance from the center to any point on the edge. Diameter divided by radius equals two, or 2r=d. 2 r = d . The simplest place to start would be to use a ruler to measure the distance between the circle's outside edges starting from its very center. The diameter would be that.

The diameter of the circle is the measurement at issue. The distance between the circle's center and its periphery can be measured.

far apart is each spoke (distance) = radius = diameter / 2

distance = 24/2

distance = 12

Since a wheel has 4 parts. so, 12*4 =  48 m

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The dimensions of the rectangle are, length = 5 inch and width = 6 inch.

What is rectangle?

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. It can alternatively be explained in terms of an equiangular quadrilateral—a term that refers to a quadrilateral whose angles are all equal—or a parallelogram with a right angle. A square is an irregular shape with four equal sides.

Let, the length of a rectangle is  7 inches less than twice the width, w, of the rectangle.

Suppose,

width = w = x, then,

length = l = 2x - 7

Since the area of the rectangle is 30 square inches.

We know that.

Area of rectangle = length x width

                       30 = (2x - 7) x (x)

                       30 = 2x^2 - 7x

    2x^2 - 7x - 30 = 0

2x^2 - 12x + 5x - 30 = 0

2x(x - 6) + 5(x - 6) = 0

     (2x + 5)(x - 6) = 0

⇒ 2x + 5 = 0,     x - 6 = 0

⇒ x = -5/2,           x = 6

Since length is not negative.

Therefore, w = 6.

So, l = 2(6) - 7 = 12 - 7 = 5

Hence, the length is 5 inches and the width is 6 inches.

complete question

The length of a rectangle i 7 inche le than twice the width, w, of the rectangle. Find the dimenion if the area i 30 quare meter

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If Brandon does 14 hours at the grocery store and 13 hours at the nursery the the total working hours = 96 hours

And if Brandon does g hours at the grocery store and n hours at the nursery then total working hours = (5g + 2n) hours

In this question we ahve been given Brandon has two summer jobs. During the week he works in the grocery store, and on the weekend he works at a nursery.

He gets paid $15 per hour to work at the grocery store and $20 per hour to work at the nursery.

We need to find the total working hours if he does 14 hours at the grocery store and 13 hours at the nursery.

Also, we need to find total working hours if he does g hours at the grocery store and n hours at the nursery.

We know that the number of week days = 5 and the number of weekend days = 2

if he does 14 hours at the grocery store during 5 days, then by unitary method he will work for 14 * 5 = 70  hours

Similarly, if he does13 hours at the nursery for 2 days, this means by unitary method he is working for 13 * 2 = 26 hours

So, the total number hours of working during a week,

70 + 26 = 96 hours

Let he does g hours at the grocery store

During week days total working hours would be,

= number of weekdays * number of working hours

= 5 * g

= 5g

and n hours at the nursery.

= number of weekend days * number of working hours

= 2n

so, the total hours would be 5g + 2n

Therefore, a) the total hours does he work if he does 14 hours at the grocery store and 13 hours at the nursery = 96 hours

b) the total hours does he work if he does gg hours at the grocery store and nn hours at the nursery = (5g + 2n) hours

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Answer: 7%

Step-by-step explanation:

Take 6848 divided by 6400, then times 100 = 107%

Then take 107% - 100% = 7%

The sales tax percentage is 7%

To cut the standard error of the mean in half, the sample size must be increased by a factor of four.

Therefore, the answer is False.

The formula to determine the standard error of the mean is

SE = SD/ √n

where SD is the standard deviation

n is the sample size

Therefore the standard error of the mean is inversely proportional to the square root of the sample size. Thus in order to decrease the standard error of the mean to half, we should increase the sample size by a factor of 4.

SE' = SD/ √(4n)

SE' = SD/ 2n

SE' = SE/ 2

--The question is incomplete, answering to the question below--

"To cut the standard error of the mean in half, the sample size must be increased by a factor of two. True or False."

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