Finite population is treated as an infinite when Finite population is treated as an infinite when ____ is ____ a. np, >5 b. n/N, = .05 c. n(1-P), >5 d. n/N, < or = .05

The probability that the average number of hours of overtime worked last month by a random sample of 140 employees in the city exceeds 20 hours is approximately 0.9564, or 95.64%.

To find the probability that the average number of hours of overtime worked by a random sample of 140 employees exceeds 20 hours, we can use the Central Limit Theorem (CLT). The CLT states that for a large enough sample size, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution.

Given that the population mean is 18.9 hours and the population standard deviation is 7.8 hours, we can calculate the standard error of the mean using the formula: standard error = population standard deviation / sqrt(sample size).

For this problem, the sample size is 140, so the standard error is 7.8 / sqrt(140) ≈ 0.659.

To calculate the probability, we need to standardize the sample mean using the z-score formula: z = (sample mean - population mean) / standard error.

In this case, the sample mean is 20 hours, the population mean is 18.9 hours, and the standard error is 0.659. Plugging these values into the formula, we get z = (20 - 18.9) / 0.659 ≈ 1.71.

Now, we can use a standard normal distribution table or calculator to find the probability associated with a z-score of 1.71. Looking up this value in the table, we find that the probability is approximately 0.9564.

Therefore, the probability that the average number of hours of overtime worked last month by a random sample of 140 employees in the city exceeds 20 hours is approximately 0.9564, or 95.64%.

Here's a sketch to visualize the calculation:

                  |

                  |

                  |

                  |       **

                  |      *  *

                  |     *    *

                  |    *      *

                  |   *        *

                  |  *          *

                  | *            *

-------------------|--------------------------

      18.9        |       20

The area under the curve to the right of 20 represents the probability we're interested in, which is approximately 0.9564 or 95.64%.

for more such questions on probability visit:

https://brainly.com/question/251701

#SPJ8

(a) f(g(x)) = 2x - 9

(b) g(f(x)) = -2x + 18

(c) Yes, the functions f and g are inverses of each other.

(a) To find f(g(x)), we substitute g(x) into the function f(x). We have g(x) = -(x - 9), so:

f(g(x)) = -2(g(x)) + 9 = -2(-(x - 9)) + 9

Simplifying this expression, we distribute the negative sign:

f(g(x)) = -2(-x + 9) + 9

Multiplying -2 by each term inside the parentheses gives:

f(g(x)) = 2x - 18 + 9

Combining like terms, we get:

f(g(x)) = 2x - 9

(b) Similarly, to find g(f(x)), we substitute f(x) into the function g(x). We have f(x) = -2x + 9, so:

g(f(x)) = -(f(x) - 9) = -(-(2x - 9) - 9)

Again, we distribute the negative sign:

g(f(x)) = -(2x - 9 + 9) = -(2x - 18)

Simplifying, we get:

g(f(x)) = -2x + 18

(c) To determine whether the functions f and g are inverses of each other, we need to check if f(g(x)) = x and g(f(x)) = x.

From part (a), we found that f(g(x)) = 2x - 9. To check if f(g(x)) = x, we set 2x - 9 equal to x and solve for x:

2x - 9 = x

x = 9

Therefore, f(g(x)) = x for x = 9.

From part (b), we found that g(f(x)) = -2x + 18. To check if g(f(x)) = x, we set -2x + 18 equal to x and solve for x:

-2x + 18 = x

3x = 18

x = 6

Therefore, g(f(x)) = x for x = 6.

Since f(g(x)) = x and g(f(x)) = x for specific values of x, we can conclude that the functions f and g are inverses of each other.

Learn more about inverse functions

brainly.com/question/29141206

#SPJ11

Answer:

E

Step-by-step explanation:

Perimeter =5s+5s+2s+2s+0.75+0.75

2 off each implies part E

Answer:

8000 feet i think so yeah

Digby Corporation's retained earnings for the midyear on July 31st were $15.959 million.

The retained earnings refer to the portion of the company's accumulated profits that have not been distributed to common stockholders.

We can compute the retained earnings are the difference between the total assets and total liabilities and common stock since common stock plus retained earnings are equal to stockholders' equity.

Digby Corporation

Midyear ended July 31st

Cash of $2.010 million

Total Assets = $43.091 million

Total Liabilities of $25.862 million

Total Common Stock of $1.270 million

Total liabilities and common stock = $27.132 million ($25.862 + $1.270)

Total Assets = $43.091 million

Less total liabilities and common stock $27.132 million

Retained earnings = $15.959 million ($43.091 - $27.132)

Learn more about the retained earnings at https://brainly.com/question/25631040.

#SPJ1

Matrix multiplication involves multiplying the corresponding elements of the rows in one matrix with the corresponding elements of the columns in another matrix and summing them up. In the given case, the product of the matrices [2 6 1 0] and [-1 5 3 1] results in 31.

Matrix multiplication is an important operation in linear algebra and is used in various applications, including solving systems of linear equations, transformations, and finding areas and volumes.

To find the product of two matrices, we need to perform matrix multiplication. The given matrices are:

Matrix A: [2 6 1 0]

Matrix B: [-1 5 3 1]

To perform matrix multiplication, we need to multiply the corresponding elements of the rows in Matrix A with the corresponding elements of the columns in Matrix B and sum them up.

The first element of the resulting matrix will be the sum of the products of the first row of Matrix A with the first column of Matrix B:

(2 * -1) + (6 * 5) + (1 * 3) + (0 * 1) = -2 + 30 + 3 + 0 = 31

Hence, the product of the given matrices [2 6 1 0] and [-1 5 3 1] is 31.

To know more about Matrix multiplication, visit

https://brainly.com/question/28869656

#SPJ11

1. To determine the number of tubs John must sell per show to break even, we need to consider the fixed costs and the contribution margin per tub. The contribution margin is the difference between the selling price and the variable cost per tub.

In this case, the variable cost is the wholesale cost of $30 per tub. The contribution margin per tub is $80 - $30 = $50.  To calculate the break-even point, we divide the fixed costs by the contribution margin per tub:

Break-even point = Fixed costs / Contribution margin per tub

Break-even point = $900 / $50 = 18 tubs

Therefore, John must sell at least 18 tubs per show to break even.

2a. To earn a profit of $1,100 per show, we need to determine the sales volume in units necessary. The desired profit is considered an additional fixed cost in this case. We add the desired profit to the fixed costs and divide by the contribution margin per tub:

Sales volume for desired profit = (Fixed costs + Desired profit) / Contribution margin per tub

Sales volume for desired profit = ($900 + $1,100) / $50 = 40 tubs

Therefore, John needs to sell 40 tubs per show to earn a profit of $1,100.

2b. To determine the sales volume in dollars necessary to earn the desired profit, we multiply the sales volume in units (40 tubs) by the selling price per tub ($80):

Sales volume in dollars for desired profit = Sales volume for desired profit * Selling price per tub

Sales volume in dollars for desired profit = 40 tubs * $80 = $3,200

Therefore, John needs to achieve sales of $3,200 to earn a profit of $1,100 per show.

c. Income Statement (condensed version):

Sales Revene: 40 tubs * $80 = $3,200

Variable Costs: 40 tubs * $30 = $1,200

Contribution Margin: Sales Revenue - Variable Costs = $3,200 - $1,200 = $2,000

Fixed Costs: $900

Operating Income: Contribution Margin - Fixed Costs = $2,000 - $900 = $1,100

The condensed income statement confirms the answers from parts a and b, showing that the desired profit of $1,100 is achieved by selling 40 tubs and generating sales of $3,200.

3. The margin of safety represents the difference between the actual sales volume and the breakeven sales volume.

Margin of safety in sales dollars = Actual Sales - Breakeven Sales = $3,200 - ($50 * 18) = $2,300

Margin of safety in units = Actual Sales Volume - Breakeven Sales Volume = 40 tubs - 18 tubs = 22 tubs

Margin of safety as a percentage = (Margin of Safety in Sales Dollars / Actual Sales) * 100

Margin of safety as a percentage = ($2,300 / $3,200) * 100 ≈ 71.88%

Therefore, the margin of safety is $2,300 in sales dollars, 22 tubs in units, and approximately 71.88% as a percentage.

Learn more about income statement here: brainly.com/question/32948100

#SPJ11

Answer:63.75 :)

Step-by-step explanation:

Answer:

$63.75

Step-by-step explanation:

85 x 75/100

85/1 x 3/4

255/4 - > $63.75

- You should already know how to do this yourself as this is very easy and basic question.

The measure of angle b is which is a supplement of angle a is 162 degrees.

If angles a and b are supplementary, that means they add up to 180 degrees.

Given that;

Since angle a and angle b are supplementary, So, we can set up the equation:

a + b = 180

We know that angle a measures 18 degrees, so we can substitute this value into the equation:

18 + b = 180

Solving for b, we can subtract 18 from both sides:

b = 180 - 18

b = 162 degrees

Therefore, angle b measure 162 degrees.

Learn more about supplementary angles here: https://brainly.com/question/13045673

#SPJ1

We can ensure trigonometric functions compute values appropriately by validating the results against known values. In order to ensure that the argument is in a short interval surrounding a place where an approximation is highly accurate, one performs a range reduction prior to computing things like a cos or sin.

By comparing the results to established values, we can make sure trigonometric functions compute values correctly. As an example, if we wanted to validate the cosine of 45 degrees, we could compare the result to the known value of 0.707. If the computed value is within a small margin of error of the known value, then we can assume the trigonometric function is computing values appropriately.

In order to calculate functions like cos or sin, one must first perform a range reduction to make sure the input is inside a narrow range surrounding a point where an approximation is highly accurate. It is typically close to zero.

To learn more about trigonometric functions link is here

brainly.com/question/6904750

#SPJ4

A 24U rack is approximately 44.5 inches (113.03 cm) tall.

What is Expression in math ?

An expression is made up of one or more integers or variables, as well as one or more operations.

The "U" unit in a rack height refers to unit of measurement for the height of equipment in a standard 19-inch server rack.

1U is equal to 1.75 inches (4.45 cm)

so, 24U is equal to 24 * 1.75 inches = 42 inches (106.68 cm).

However, in practice, the height of a 24U rack is typically slightly taller to account for the height of the mounting brackets and other hardware.

Hence, A 24U rack is approximately 44.5 inches (113.03 cm) tall.

To know more about Expressions visit,

https://brainly.com/question/1859113

#SPJ4

Answer:

4.091miles

Step-By-Step:

If Babe Ruth hit 60 home runs and the distance between each base is 90ft and there are 4 bases we find out how much ft 1 home run would be so...

90×4= 360ft

so 1 home run is 360ft...since we need to find 60 we multiply it by 60

360ft×60= 21,600ft

but we need to give our answer In Miles therefore we convert 21,600ft to miles which is

4.091

Babe Ruth run 4.091 miles from his home runs in 1927.

Hope this helped you- have a good day bro cya)

The t-coordinate of the solution to this system represents C. the time at which the ball and the dog's mouth are at the same height.

A coordinate time scale is a time standard designed for use as the time coordinate in the calculation.

When Laurie throws a tennis ball toward her dog from a height, the t-coordinate of the solution to this system represents the time at which the ball and the dog's mouth are at the same height

The complete question is:

Laurie throws a tennis ball toward her dog from a height of 4.5 ft. The initial vertical velocity of the ball is 18 ft/s. At the same time as Laurie throws the ball, her dog jumps with an initial vertical velocity of 21 ft/s. When the dog jumps, its mouth is 1.5 ft above the ground. What does the t-coordinate of the solution to this system represent?

Learn more about coordinates on:

https://brainly.com/question/17206319

#SPJ1

Answer:

C

Step-by-step explanation:

I got it right

Here is the full question.

In order for a vaccine to be effective, it should reduce a person's chance of acquiring a disease. Consider a hypothetical vaccine for malaria‚- a tropical disease that kills between 1.5 and 2.7 million people every year.1 Suppose the vaccine is tested with 700 volunteers in a village who are malaria-free at the beginning of the trial. Three hundred of the volunteers will get the experimental vaccine and the rest will not be vaccinated. Suppose that the chance of contracting malaria is 10% for those who are not vaccinated.

Construct a two-way table to show the results of the experiments if:

(a) The vaccine has no effect

(b) The vaccine cuts the risk of contracting malaria in half

Answer:

Step-by-step explanation:

From the given information above:

Suppose, there is no effect from the vaccine, the risk of having malaria for vaccine & no vaccine is equal to 0.1

Now, the Probability of not having malaria if vaccinated or no vaccinated = 1 - 0.1 = 0.9

Therefore: the table is shown below as follows:

                             Malaria              No Malaria                Total

Vaccinated          300 × 0.1 = 30     300 × 0.9 = 270    300

No Vaccine          400 × 0.1 = 40    400 × 0.9 = 360      700-300 = 400

Total                     40 + 30 = 70      270 + 360 = 630       700

(b)

The risk of malaria for vaccinated if the vaccine cuts the risk of contracting malaria in half are equal to 0.1/2 = 0.05

Thus; the probability of not getting malaria if vaccinated = 1 - 0.05 = 0.95

The table can then be computed as follows:

                             Malaria                No Malaria                 Total

Vaccinated       300 × 0.05 = 15     300 × 0.95 = 285       300

No Vaccine      400 × 0.1 = 40         400 × 0.9 = 360         700-300 = 400

Total                 40 + 15 = 55             285 + 360 = 645       700

An angular resolution of 0.56 arcseconds is required to see the Sun and Jupiter as separate objects. This is an extremely small angle and would necessitate the use of a large telescope.

Angular resolution is defined as the minimum angle between two objects that enables a viewer to see them as distinct objects rather than as a single one. A better angular resolution corresponds to a smaller minimum angle. The angular resolution formula is θ = 1.22 λ / D, where λ is the wavelength of light and D is the diameter of the telescope. Thus, the angular resolution formula can be expressed as the smallest angle between two objects that allows a viewer to distinguish between them. In arcseconds, the answer should be given to two significant figures.

To see the Sun and Jupiter as distinct points of light, we need to have a good angular resolution. The angular resolution is calculated as follows:

θ = 1.22 λ / D, where θ is the angular resolution, λ is the wavelength of the light, and D is the diameter of the telescope.

Using this formula, we can find the minimum angular resolution required to see the Sun and Jupiter as separate objects. The Sun and Jupiter are at an average distance of 5.2 astronomical units (AU) from each other. An AU is the distance from the Earth to the Sun, which is about 150 million kilometers. This means that the distance between Jupiter and the Sun is 780 million kilometers.

To determine the angular resolution, we need to know the wavelength of the light and the diameter of the telescope. Let's use visible light (λ = 550 nm) and assume that we are using a telescope with a diameter of 2.5 meters.

θ = 1.22 λ / D = 1.22 × 550 × 10^-9 / 2.5 = 2.7 × 10^-6 rad

To convert radians to arcseconds, multiply by 206,265.θ = 2.7 × 10^-6 × 206,265 = 0.56 arcseconds

The angular resolution required to see the Sun and Jupiter as distinct points of light is 0.56 arcseconds.

This is very small and would require a large telescope to achieve.

In conclusion, we require an angular resolution of 0.56 arcseconds to see the Sun and Jupiter as separate objects. This is an extremely small angle and would necessitate the use of a large telescope.

To know more about angular resolution visit:

brainly.com/question/31858807

#SPJ11

If the sample has the same mix of people, in the same proportions, as the population being studied then sociologists know if the sample they are using is representative. So the option c is correct.

No subject is off-limits when sociologists use the sociological lens and start asking questions. Every facet of human behaviour has the potential to be studied. Sociologists cast doubt on the society that people have built and inhabit. They observe behavioral patterns as individuals navigate that world.

Sociologists have uncovered workplace patterns that have revolutionized industries, family patterns that have educated parents, and educational patterns that have supported structural changes in classrooms by using sociological methodologies, methodical research, and a scholarly interpretive approach.

To learn more about Sociology link is here

brainly.com/question/25099331

#SPJ4

The complete question is;

How do sociologists know if the sample they are using is representative?

a. If the people in the sample freely volunteered to serve as representatives

b. If the sample has an even number, decided by the researcher, of people from several different categories or backgrounds

c. If the sample has the same mix of people, in the same proportions, as the population being studied

d. If the participants have been interviewed to reveal possible bias.

The boundary lines are y > -3x + 4: dotted line and  y <= 8x + 1: solid line

From the question, we have the following parameters that can be used in our computation:

y > -3x + 4

y <= 8x + 1

The boundary line for the inequality "<" is a dotted line, which means that the endpoint is not included in the solution set.

The boundary line for the inequality ">=" is a solid line, which means that the endpoint is included in the solution set.

Read more about inequality at

https://brainly.com/question/25275758

#SPJ1

Answer:

(5x+4)(x-3)

Step-by-step explanation:

Answer:

(x - 3)(5x + 4)

Step-by-step explanation:

5x² - 11x - 12

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 5 × - 12 = - 60 and sum = - 11

the factors are - 15 and + 4

use these factors to split the x- term

5x² - 15x + 4x - 12 ( factor first/second and third/fourth terms )

= 5x(x - 3) + 4(x - 3) ← factor out (x - 3) from each term

= (x - 3)(5x + 4)

Probability that the arrow will stop on the same letter twice = 1/3 (c).

What is probability?

The area of arithmetic called likelihood deals with numerical representations of the chance that a happening can occur or that an announcement is true.

Main body:

Given : Maria will spin the arrow on the spinner 2 times.

To find : What is the probability that the arrow will stop on the same letter twice.

Solution : We have given a spinner that spin twice and stop on the same letter.

Formula for probability = no. of favourable outcome/ total outcomes

Here, total part of spinner = 3 and it spin two times

So, total possible outcome = 6.  Arrow stay on same letter twice( favorable outcome) =2.

Plugging the values in formula :

Probability =  2/6

Probability =  1/3

Therefore,  probability that the arrow will stop on the same letter twice =  (c).

To know more about probability click on the link below

https://brainly.com/question/24756209

#SPJ4

Given:

Circumference of a circle = C

Diameter of a circle = d

To find:

The relationship between the circumference, c, and diameter, d, of any circle.

Solution:

We know that, circumference of a circle is

\(C=2\pi r\)

It can be written as

\(C=(2r)\pi \)

\(C=d\pi \)         \([\because d=2r]\)

On dividing both sides by d, we get

\(\dfrac{C}{d}=\pi \)

Therefore, the correct option is (F).

To interpret this line plot with fraction addition and subtraction, we need to understand how to read the plot and how to perform the necessary calculations with fractions.

Looking at the line plot above, we can see that each horizontal line represents one pound, and each vertical line represents one baby's weight. The numbers on the vertical axis show the weights of the babies in pounds. For example, there are two babies that weigh 6 pounds, three babies that weigh 7 pounds, two babies that weigh 8 pounds, and so on. To find the difference in weight between the two heaviest babies, we need to first determine which babies are the heaviest. From the line plot, we can see that the two heaviest babies are the ones at the top of the plot, which both weigh 9 pounds. Converting the weight of the heaviest baby to a fraction with a denominator of 72 gives us 9/1 x 72/72 = 648/72. Converting the weight of the second heaviest baby to a fraction with a denominator of 72 gives us 8/1 x 72/72 = 576/72. Now that both weights are expressed as fractions with a common denominator, we can subtract them to find the difference: 648/72 - 576/72 = 72/72 = 1

Therefore, the difference in weight between the two heaviest babies is 1 pound, or 1/72 of a hundredweight (since there are 100 pounds in a hundredweight). The answer we were asked to provide is a proper fraction, so we can express this as 1/72. In summary, to interpret a line plot with fraction addition and subtraction, we need to understand how to read the plot to determine the weights of the babies, how to perform the necessary calculations with fractions, and how to express our answer as a proper fraction if required.

To know more about subtraction visit:-

https://brainly.com/question/1927340

#SPJ11

Answer:

12.25 an hour

Step-by-step explanation:

there are 24 hours in a day, 24*5 (days) = 120

24/8 (the number of hours he uses each day) is 3

divide 120 by 3 and you get the amount of hours he works a week, 40

$490 (the amount he makes in a week) divided by 40 (the amount of hours he works a week) and you get your answer of $12.25 an hour

Putting it all together, we get:

A:

[-3 0 0]

[ 0 1 0]

[ 0 0 -1]

which is an orthogonal matrix with the first row being a multiple of (3, 3, 0).

An orthogonal matrix is a square matrix whose columns and rows are orthonormal vectors, i.e., each column and row has unit length and is orthogonal to the other columns and rows.

Let's start by finding a vector that is orthogonal to (3, 3, 0). We can take the cross product of (3, 3, 0) and (0, 0, 1) to get such a vector:

(3, 3, 0) x (0, 0, 1) = (3*(-1), 3*(0), 3*(0)) = (-3, 0, 0)

Note that this vector has length 3, so we can divide it by 3 to get a unit vector:

(-3/3, 0/3, 0/3) = (-1, 0, 0)

So, the first row of the orthogonal matrix A can be (-3, 0, 0) or a multiple of it. For simplicity, we'll take it to be (-3, 0, 0).

To find the remaining two rows, we need to find two more orthonormal vectors that are orthogonal to each other and to (-3, 0, 0). One way to do this is to use the Gram-Schmidt process.

Let's start with the vector (0, 1, 0). We subtract its projection onto (-3, 0, 0) to get a vector that is orthogonal to (-3, 0, 0):

v1 = (0, 1, 0) - ((0, 1, 0) dot (-3, 0, 0)) / ||(-3, 0, 0)||^2 * (-3, 0, 0)

= (0, 1, 0) - 0 / 9 * (-3, 0, 0)

= (0, 1, 0)

We can then normalize this vector to get a unit vector:

v1' = (0, 1, 0) / ||(0, 1, 0)|| = (0, 1, 0)

So, the second row of the orthogonal matrix A is (0, 1, 0).

To find the third row, we take the cross product of (-3, 0, 0) and (0, 1, 0) to get a vector that is orthogonal to both:

(-3, 0, 0) x (0, 1, 0) = (0, 0, -3)

We normalize this vector to get a unit vector:

v2' = (0, 0, -3) / ||(0, 0, -3)|| = (0, 0, -1)

So, the third row of the orthogonal matrix A is (0, 0, -1).

Putting it all together, we get:

A:

[-3 0 0]

[ 0 1 0]

[ 0 0 -1]

To know more about orthogonal matrix,

https://brainly.com/question/31629623

#SPJ11

The x value of the solutions to the system is 4

From the question, we have the following parameters that can be used in our computation:

The graph

This point of intersection of the lines of the graph represent the solution to the system graphed

From the graph, we have the intersection point to be

(x, y) = (4, -2)

This means that

x = 4

Hence, the x value of the solutions to the system is 4

Read more about equations at

https://brainly.com/question/148035

#SPJ1

Step-by-step explanation:

v = u + at

v-u = at

a = (v -u)/t

When t = 4, u=10, v=50

a = (50-10)/4

a= 40/4

a = 10

Carson Kelly is expected to hit approximately 31 home runs in 2024.

To find how many home runs Carson Kelly is expected to hit in 2024, we can use the formula for compound interest, where the initial amount is the number of home runs he hit in 2019, and the interest rate is the expected growth rate of his home run hitting ability, which is 12 percent or 0.12 as a decimal.

Let H be the number of home runs hit in 2019, and H(n) be the number of home runs hit in year n, then we can write:

H(n) = H * (1 + r)^n

Where r is the growth rate, and n is the number of years into the future.

If we plug in the given values, we can find the number of home runs Carson Kelly is expected to hit in 2024, which is 5 years after 2019.

H = 18 (number of home runs in 2019)

r = 0.12 (growth rate)

n = 5 (number of years into the future)

H(5) = 18 * (1 + 0.12)^5

H(5) = 18 * 1.7623

H(5) = 31.9214

It's important to note that this is simply an estimate based on the given growth rate, and the actual number of home runs he hits in 2024 may vary based on many factors, including injuries, team support, and the skill of opposing pitchers, among others.

For such more questions on home runs

https://brainly.com/question/11923973

#SPJ8

The proof of OP=1/2MN will get us 2

MNO is a right-angled triangle with right-angle MON, and P is the midpoint of MN. To demonstrate: OP=1/2MN Because midpoints will be involved, names for M and N should be multiples of 2.

Let M and N have receptive coordinates of (0,2m) and (2n,0).

Midpoint = \(\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2} }{2}\)

The coordinates of P are

midpoint = \(\frac{2n+0}{2} , \frac{2m+0}{2}\)

midpoint =(n,m)

The coordinates of P are (n,m).

Distance formula:

d=√(\(x^{2}-x_{1} ^2 +(y_{2} -y_{1} )^2\\\)

Using distance formula, the distance between O(0,0) and P(n,m) is

OP=√(n-0)^2+(m-0)^2 =√n^2+m^2

Using distance formula, the distance between M(0,2m) and N(2n,0) is

MN=√(2n-0)^2+ (0-2m)^2

MN=2√(4n^2+4m^2

On further simplification we get

MN=√4(n^2+m^2)

MN=2√(n^2+m^2)

MN=2(OP)

Divide both sides by 2.

1/2MN=OP

Interchange the sides.

OP=1/2MN

Hence proved

Learn more about right angles here:https://brainly.com/question/1248322

#SPJ4

Answer:

$4.85

Step-by-step explanation:

Add the numbers:

2.95

1.05

0.85

4.85

The given region's graph is as follows. \(\text{x} = \text{y}^2\) is a parabola that opens rightward and passes through the horizontal line that intersects the parabola at \(\text{(0, 2)}\) and \(\text{(4, 2)}\).

The region is a parabolic segment that is shaded in the diagram. The volume of the region obtained by rotating the region bounded by \(\text{x} = \text{y}^2\), \(\text{x} = 0\), and \(\text{y} = 2\) around the \(\text{x}\)-axis can be calculated using the shell method.

The shell method states that the volume of a solid of revolution is calculated by integrating the surface area of a representative cylindrical shell with thickness \(\text{Δx}\) and radius r.

To know more about horizontal visit:

https://brainly.com/question/29019854

Step-by-step explanation:

75° and (3x + 15)° are supplementary (add up to 180°).

Therefore 75 + 3x + 15 = 180, 3x = 90 and x = 30.

Answer:

x = 30

Step-by-step explanation:

3x + 15 and 75 are adjacent angles and are supplementary, then

3x + 15 + 75 = 180

3x + 90 = 180 ( subtract 90 from both sides )

3x = 90 ( divide both sides by 3 )

x = 30