Pls help due today xxx

Pls Help Due Today Xxx

Answers

Answer 1

By using exponents, we can write the expressions  (6⁵)¹⁰ as  6⁵⁰.

What is an exponent?

The exponent of a number says how many times to use the number in a multiplication.

Also, exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.

If  an expression is given as (6⁵)¹⁰ , using exponents, we can write the  expressions in the form of \(6^k\) as shown below;

The expression "k" is an integer {0, 1, 2, 3, etc}

By applying rule of exponent for the multiplication of powers, (6⁵)¹⁰ is simplified as;

(6⁵)¹⁰ = 6⁵⁰

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Related Questions

Please help! Will give BRAINLIEST!!!!!

Please help! Will give BRAINLIEST!!!!!

Answers

Answer:

looks like 1 from the graph.

please answer soon! :/

please answer soon! :/

Answers

Answer:

D

Step-by-step explanation:

The decrease in losses is 3 and 3/5 is 60%

Answer:

D

Step-by-step explanation:

If you multiply 5 by 2, you get 10, I automatically view that as 100%, multiply 2 by 20(simplified for the 100 stance) you have 3 games won this season, multiply that by 20 and you have 60, give us a 60% decrease. Sorry if you don't understand, but hope this helps!

ALMOST DONE!


*IF YOU PUT SOMETHING RUDE, RANDOM, OR ANYTHING OF THAT TO BE RUDE OR TO STEAL POINTS I WILL REPORT*

ALMOST DONE!*IF YOU PUT SOMETHING RUDE, RANDOM, OR ANYTHING OF THAT TO BE RUDE OR TO STEAL POINTS I WILL

Answers

Answer:

Oh I learned this in 6th grade but im in 7th right now its 2-4=-2

Step-by-step explanation:

I need help plz and thank you

I need help plz and thank you

Answers

Answer:

x is 75 degree and y is 140 degree

A probability is a numerical value that indicates the chance, or likelihood, of a specific event occurring.
Select one:
True
False

Answers

This statement is true

A probability is a numerical value that indicates the chance, or likelihood, of a specific event occurring. Probability is the measure of the likelihood of a random event happening, and it is expressed as a number between 0 and 1, with 0 implying that the event would never occur and 1 implying that it is certain to happen.

The probability of an event happening is referred to as its likelihood. Probability can be expressed as a fraction, percentage, or decimal, and it is a vital tool in statistics. It is frequently utilized in mathematics to estimate real-world situations that involve random variables such as coin flips, weather patterns, stock market trends, and even sporting events.

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When you fill your coffee at a gas station, you're supposed to get 8 ounces of coffee with a standard deviation of .7 ounces. A random sample of 50 "8 ounce" coffees is collected and measured and the mean was found to be 7.8 ounces.

Answers

Answer:

The answer is below

Step-by-step explanation:

When you fill your coffee at a gas station, you're supposed to get 8 ounces of coffee with a standard deviation of .7 ounces. A random sample of 50 "8 ounce" coffees is collected and measured and the mean was found to be 7.8 ounces. a) Find a 90% confidence interval. b) Interpret the confidence interval in the context.

Solution:

The confidence = 90% = 0.9, mean (μ) = 7.8 ounces, standard deviation (σ) = 0.7 ounces, sample size (n) = 50

α = 1 - C = 1 - 0.9 = 0.1

α/2 = 0.1 / 2 = 0.05

The z score of α/2 is the same as the z score of 0.45 (0.5 - 0.05) which is equal to 1.65

The margin of error (E) is given by:

\(E = z_\frac{\alpha}{2} *\frac{\sigma}{\sqrt{n} } \\\\E=1.65*\frac{0.7}{\sqrt{50} } =0.16\)

The confidence interval = μ ± E = 7.8 ± 0.16 = (7.64, 7.96)

b) This means that we are 90% confident that any selected coffee has a weight between 7.64 ounce to 7,96 ounce



Find the inverse of each matrix, if it exists.

[0 -5 9 6]

Answers

To find the inverse of a matrix, we need to determine if it is invertible, or non-singular. A matrix is invertible if and only if its determinant is non-zero.

Let's calculate the determinant of the given matrix:

[0  -5  9  6]

To calculate the determinant, we can use the formula for a 4x4 matrix:

det(A) = aei - afh - bdi + bfg + cdh - ceg

Substituting the values from the given matrix:

det(A) = 0(-5)0 - 0(9)6 - (-5)(0)6 + (-5)(9)0 + 9(0)6 - 9(-5)0

= 0 + 0 - 0 + 0 + 0 + 0

= 0

The determinant of the matrix is zero, which means it is not invertible. Therefore, the inverse of the matrix does not exist.

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out of total student 3/5 are girls .On a particular day one third boys and 2/5 girls were absent. If total absentees was 280 find total number of students​

Answers

Answer:

Step-by-step explanation:

Calculate fraction of boys

If girls =3/5, then boys = 1 - 3/5 = 2/5.

Calculate fraction of students absent

Girls - 2/5 of 3/5 = 6/25

Boys - 1/3 of 2/5 = 2/15

6/25+2/15=28/75

Calculate total number of students

If 28/75 = 280

280/28=10

10x75=750

Total number of students = 750

find the axis of symmetry and vertex of y=-2x^3+8​

Answers

Answer:

Vertex:(0,8)     Axis of Symmetry: x=0

Step-by-step explanation:

Unit 11 homework 11 volume and surface area of similar solids

Answers

Answer:

Step-by-step explanation:

1. No

2. Yes

3. Scale factor: 5:7

what type of rank 8 spell is granted to death students at level 58?

Answers

The Death students in Wizard101 are granted with the Scarecrow spell as their rank 8 spell at level 58.What is Scarecrow? Scarecrow is a rank 8 spell that is only granted to Death wizards. This spell deals 530-610 damage to all enemies and gives the player half of that damage back as health.

It also costs 7 pips to cast, making it a powerful spell that can help the wizard defeat multiple enemies at once. Scarecrow's damage output, as well as its healing effects, make it an excellent choice for Death wizards who are soloing the game or facing multiple enemies in a battle. Its main weakness is its high pip cost, which can make it difficult to cast in the early stages of a battle when the wizard may not have accumulated enough pips yet to cast it. Nonetheless, Scarecrow is a powerful and useful spell that can help Death wizards survive tough battles.The Scarecrow spell is not only exclusive to Death students but also a prized possession of some of the toughest bosses and enemies in the game. For example, Malistaire the Undying, one of the most difficult bosses in the game, uses Scarecrow as one of his main spells, making it an even more coveted and powerful spell for Death wizards to have in their arsenal.

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find the axis of symmetry for this parabola y=-2x^2-4x-11
write your answer as an equation

Answers

Answer:

x = - 1

Step-by-step explanation:

Given a parabola in standard form

y = ax² + bx + c ( a ≠ 0 ) , then the equation of the axis of symmetry is

x = - \(\frac{b}{2a}\)

y = - 2x² - 4x - 11 ← is in standard form

with a = - 2 and b = - 4 , thus

x = - \(\frac{-4}{-4}\) = - 1

x = - 1 is the equation of the axis of symmetry

Amani earns 41 dollars per week working part-time at a book store. She makes one dollar more for each book that she sells. The amount, A (in dollars), that
Amani earns in a week if she sells b books is given by the following.
A=41+b
How much does Amani earn in a week if she sells 18 books?

Answers

Amani earns 59 dollars in a week if she sells 18 books.

Amani earns a base amount of $41 per week for working part-time at the bookstore. In addition to that, she earns an extra dollar for each book she sells. The equation A = 41 + b represents her total earnings, where A represents the amount she earns and b represents the number of books she sells.

To find out how much Amani earns in a week if she sells 18 books, we substitute the value of b (18) into the equation:

A = 41 + 18

This simplifies to:

A = 59

Therefore, if Amani sells 18 books in a week, she will earn $59.

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A tree 18 meter high is broken off 3 meter from the ground . how far from the foot of the tree will the top strike the ground ?​

Answers

Answer:

Therefore, the top of the tree will strike the ground about 17.75 meters away from the foot of the tree.

Step-by-step explanation:

We can solve this problem using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the tree trunk and the ground form one leg of the triangle, and the broken off portion of the tree forms the other leg, while the distance the top of the tree falls is the hypotenuse.

Let's call the distance we want to find "x". Then, we can set up the following equation:

x^2 = 18^2 - 3^2

where 18 is the height of the tree, and 3 is the distance from the ground where the tree is broken.

Simplifying the right-hand side of the equation, we get:

x^2 = 315

Taking the square root of both sides, we get:

x = sqrt(315) ≈ 17.75

He science club has 4 members. The club bought b bumper stickers to split among its members. Write an expression that shows how many bumper stickers each member will get

Answers

Answer:

b / 4

Step-by-step explanation:

If you are splitting b bumper stickers between 4 members, you must divide the number of bumper stickers by the number of members, which is 4! Dividing is just like if you were to divvy something up between people, but it is a mathematical term! This will give you  b / 4.

Find the area of the shaded regions. Give your answer as a completely simplified
exact value in terms of л (no approximations).
72°
D
72°
0 10 in.
R
C

Find the area of the shaded regions. Give your answer as a completely simplifiedexact value in terms

Answers

The area of the shaded regions is,

A  = 40π

Since The formula for the area of a sector is:

Area = 1/2 r²(R)

Where, “r” represents the radius while “R” represents the radian measure of a sector.

Here, The radius is in the image above as 10 inches.

However, we still need the radian measure of the two sectors.

To find this measure, we can use the following conversion:

1 degree =  π / 180 radians

Because the two sectors have a given measure of 72 degrees, we need to multiply both sides of the above conversion by 72:

72 degrees = 72π / 180 radians

Reduce the fraction on the right side of the equation:

72 degrees = 2π / 5

We now have the radian measure of both sectors. Now simply insert this and any other known values into the “area of a sector” formula above:

Area = 1/2 × 10² × 2π/5

Area = 20π

We have the area of one sector is equal to, 20 pi.

Hence, For the area of the shaded regions simply multiply the proven area by 2 to get a total area of ,

= 2 x 20π

= 40π

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The region between the line y=1 and the graph of y= x+1, 0≤x≤4 is revolved about the x-axis. Find the volume of the generated solid.

Answers

The volume of the generated solid is 80π/3, given the region between the line y=1 and the graph of y= x+1, 0≤x≤4 revolved about the x-axis.

To solve the problem, the region between the line y

=1 and the graph of y

= x+1, 0≤x≤4

must be revolved about the x-axis to generate a solid. The volume of the generated solid will be calculated.Using the formula for finding the volume of a solid of revolution, which is given by:V

= π∫[f(x)]^2dx

The area of the generated solid will be obtained.

π ∫ (x+1 - 1)^2 dx

= π ∫ (x^2 + 2x) dx

Solve for the integral using the power rule,

π ∫ (x^2 + 2x) dx

= π[(x^3/3) + x^2]_0^4

= π[[(4)^3/3] + (4)^2 - [0^3/3] - 0^2]

= π[64/3 + 16]

= 80π/3.

The volume of the generated solid is 80π/3, given the region between the line y

=1 and the graph of y

= x+1, 0≤x≤4

revolved about the x-axis.

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For problems 1 - 4, write a two-column proof.

Answers

Answer:

Solution given:

1:

<5=<6

<5+<4=180°[co interior angle]

Substituting value of<5

<6+<4=180°[it shows a property of co interior angle]

So

l || m

2:

<1=90°[ l is perpendicular to t]

<2=90°[m is perpendicular to t]

since

<1=<2[shows property of corresponding angle]

:.

l || m.

3:

<1=<2

<1=<3

substituting value of<1 in second one

<2=<3[which shows property of alternate Angel]

So

Segment ST || segment UV.

4:

<RSP=<PQR......[I]

<QRS+<PQR=180°.....[ii]

from equation I and ii we get

<RSP+<QRS=180°[which shows property of co interior angle ]

So

Segment PS || segment QR

For problems 1 - 4, write a two-column proof.

These pictures are the questions given in the pdf, let's get the solutions.

1) Solution

It is given that,

→ <5 = <6

Then the co interior angles,

→ <5+ <4 = 180°

Now substituting value of <5,

→ <6+ <4 = 180°

This shows property of co interior angle.

Therefore, L II m.

2) Solution

Take it as,

→ <1= 90°

In above eq. L is perpendicular to t.

→ <2 = 90°

In above eq. m is perpendicular to t.

Then it will be,

→ <1 = <2

It shows property of corresponding angle.

Therefore, L II m.

3) Solution

It is given that,

→ <1 = <2 and <1 = <3

Now substitute,

The value of <1 in second one,

→ <2 = <3

This shows property of alternate angle.

Therefore, ST II UV.

4) Solution

It is given that,

→ <RSP = <PQR --- (1)

→ <QRS + <PQR = 180° --- (2)

Now from the equation (1) and (2),

→ <RSP + <QRS = 180°

It shows property of co interior angle.

Therefore, PS II QR.

For problems 1 - 4, write a two-column proof.
For problems 1 - 4, write a two-column proof.

Write an addition, subtraction, multiplication, and division problem that all equal -3.

Answers

Answer:

-5+2

3-6

3 x -1

-6 divided by 2

Select the correct answer.There are 6 adult chaperones, 21 female students, and 23 male students on a bus for a field trip.What is the probability that a randomly chosen person on the bus is an adult chaperone or a male student? A- 1/2 B- 29/50C- 2/3D- 1/29a whole explanation and answer will get marked brainiest

Select the correct answer.There are 6 adult chaperones, 21 female students, and 23 male students on a

Answers

Let A be the event that we choose an adult chaperone and let B be the event that we pick a male student. Then, we want to calculate the following probability.

\(P(A\cup B)\)

where the symbol between A and B means the union of events, which could be understood as "or". Using the properties of probability, we have

\(P(A\cup B)=P(A)+P(B)-P(A\cap B)\)

where the symbol on the right, between A and B, is the intersection, which can be understood as "and". Since we are going to pick only one person, it is impossible that we pick an adult chaperona and a male student. So,

\(P(A\cap B)=0\)

So we have

\(P(A\cup B)=P(A)+P(B)\)

Now, we want to calculate P(A) and P(B).

To calculate the probability of each event, we first count the number of possibilities that the event is true.

Note that since we have 6 adult chaperones, we have 6 possibilites such that the event A is true. Now, to calculate the probability of A, we simply divide this number by the total number of people on the bus (which is 50). So we get

\(P(A)=\frac{6}{50}\)

In the same manner, for event B, we have a total of 23 possibilities such that the event B is true. Then

\(P(B)=\frac{23}{50}\)

Finally, by replacing this values in the original expression, we have

\(P(A\cup B)=P(A)+(B)=\frac{6}{50}+\frac{23}{50}=\frac{29}{50}\)

Praveena Limited makes a single product, T, using a single raw material R. Standard cost relating to T have been calculated as follows. Standard cost schedule Per Unit (Rs) Direct material, R, 10kg at Rs. 20 per kg 200 Direct labour, 5 hours at Rs.6 per hour 30 Variable production overhead, 5 hours at Rs.1 per hour 5 Fixed production overhead, 5 hours at Rs.10 per hour 50 Standard cost 285 Standard profit 95 Standard selling price 380 The company expects to produce 900 units in month of April 2021. During April 2021 the actual results are as follows. 800 units of product T were produced and sold at Rs. 312,000. 7800 kgs costing Rs. 159,900 were bought and used. 4200 hours were worked during the month and total wages were Rs. 24,150. The variable production overhead for the month was Rs. 4,900. The fixed production overhead for the month was Rs. 47,000. 1. Calculate the following variances for the month of April 2021. a. Direct material cost variance and direct material usage variance b. Direct labor rate variance and direct labor efficiency variance c. Variable overhead expenditure variance and variable overhead efficiency variance d. Fixed overhead expenditure variance, fixed overhead efficiency variance and fixed overhead capacity variance e. Sales price variance and sales volume variance 8 1. Prepare a summary of total cost variances and total sales variances. 2. Identify possible causes for the variances and recommend corrective actions for adverse variances.

Answers

To calculate the variances, we need to compare the actual results with the standard costs. Let's calculate each variance:

a. Direct material cost variance:
Actual cost of material = Rs. 159,900
Standard cost of material = 800 units × (10 kg × Rs. 20/kg) = Rs. 160,000
Direct material cost variance = Actual cost - Standard cost
Direct material cost variance = Rs. 159,900 - Rs. 160,000 = Rs. -100 (Adverse)

Direct material usage variance:
Actual quantity used = 7800 kg
Standard quantity allowed = 800 units × 10 kg = 8000 kg
Standard price per kg = Rs. 20/kg
Direct material usage variance = (Actual quantity used - Standard quantity allowed) × Standard price per kg
Direct material usage variance = (7800 kg - 8000 kg) × Rs. 20/kg = Rs. -40,000 (Adverse)

b. Direct labor rate variance:
Actual rate per hour = Rs. 24,150 / 4200 hours = Rs. 5.75/hr
Standard rate per hour = Rs. 6/hr
Direct labor rate variance = (Actual rate per hour - Standard rate per hour) × Actual hours worked
Direct labor rate variance = (Rs. 5.75/hr - Rs. 6/hr) × 4200 hours = Rs. -525 (Adverse)

Direct labor efficiency variance:
Actual hours worked = 4200 hours
Standard hours allowed = 800 units × 5 hours = 4000 hours
Standard rate per hour = Rs. 6/hr
Direct labor efficiency variance = (Actual hours worked - Standard hours allowed) × Standard rate per hour
Direct labor efficiency variance = (4200 hours - 4000 hours) × Rs. 6/hr = Rs. 1200 (Favorable)

c. Variable overhead expenditure variance:
Actual variable overhead = Rs. 4,900
Standard variable overhead = 800 units × (5 hours × Rs. 1/hr) = Rs. 4000
Variable overhead expenditure variance = Actual variable overhead - Standard variable overhead
Variable overhead expenditure variance = Rs. 4,900 - Rs. 4000 = Rs. 900 (Adverse)

Variable overhead efficiency variance:
Actual hours worked = 4200 hours
Standard hours allowed = 800 units × 5 hours = 4000 hours
Standard variable overhead rate per hour = Rs. 1/hr
Variable overhead efficiency variance = (Actual hours worked - Standard hours allowed) × Standard variable overhead rate per hour
Variable overhead efficiency variance = (4200 hours - 4000 hours) × Rs. 1/hr = Rs. 200 (Favorable)

d. Fixed overhead expenditure variance:
Actual fixed overhead = Rs. 47,000
Standard fixed overhead = 800 units × (5 hours × Rs. 10/hr) = Rs. 40,000
Fixed overhead expenditure variance = Actual fixed overhead - Standard fixed overhead
Fixed overhead expenditure variance = Rs. 47,000 - Rs. 40,000 = Rs. 7,000 (Adverse)

Fixed overhead efficiency variance:
Actual hours worked = 4200 hours
Standard hours allowed = 800 units × 5 hours = 4000 hours
Standard fixed overhead rate per hour = Rs. 10/hr
Fixed overhead efficiency variance = (Actual hours worked - Standard hours allowed) × Standard fixed overhead rate per hour
Fixed overhead efficiency variance = (4200 hours - 4000 hours) × Rs. 10/hr = Rs. 2000 (Favorable)

Fixed overhead capacity variance:
Standard hours allowed =

The equation of the line that goes through the point (8, 7) and is parallel to the line 4x + 4y = 2 can be written in the form y = mx + b, where m = b =

Answers

The equation of the line parallel to 4x + 4y = 2 and passing through (8, 7) can be written as y = -x + 15.

To find the slope of the line 4x + 4y = 2, we need to rewrite the equation in slope-intercept form, y = mx + b. We can start by isolating y in the given equation:

4y = -4x + 2

Dividing both sides by 4, we get:

y = -x + 0.5

Comparing this equation with the form y = mx + b, we see that the slope of the line is -1.

Since we are looking for a line parallel to the given line, it will have the same slope of -1. Now, we can use the point (8, 7) to determine the y-intercept. Substituting the values of x and y into the equation y = mx + b, we get:

7 = -1(8) + b

7 = -8 + b

b = 15

Therefore, the equation of the line parallel to 4x + 4y = 2 and passing through (8, 7) can be written as y = -x + 15.

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x⁴+8x³+34x²+72x+81 factories it.​

Answers

Answer:

The expression x⁴ + 8x³ + 34x² + 72x + 81 cannot be factored further using simple integer coefficients. It does not have any rational roots or easy factorizations. Therefore, it remains as an irreducible polynomial.

a theater sells adult and child tickets to its plays. 2 adult tickets and 3 child tickets cost $30.75. 3 adult tickets and 2 child tickets cost $33.00. let represent the cost of 1 adult ticket, and represent the cost of 1 child ticket. which system of equations can be used to determine the cost of each type of ticket? a. b. c. d.

Answers

The system of equations that can be used to represent the cost of each type of ticket is  2a + 3c = 30.75   and 3a + 2c = 33   .

In the question ,

it is given that ,

a theater sells adult and child tickets for its play .

the cost for 2 adult ticket and 3 child ticket is = $30.75

and the cost for 3 adult tickets and 2 child tickets = $33.00

let the cost of 1 adult ticket = "a"   and

let the cost of 1 child ticket = "c"

So, According to the question ,

the equation to represent both the situation is

2a + 3c = 30.75   and

3a + 2c = 33

Therefore , The system of equations that can be used to represent the cost of each type of ticket is  2a + 3c = 30.75   and 3a + 2c = 33   .

The given question is incomplete , the complete question is

A theater sells adult and child tickets to its plays. 2 adult tickets and 3 child tickets cost $30.75. 3 adult tickets and 2 child tickets cost $33.00. let "a' represent the cost of 1 adult ticket, and "c" represent the cost of 1 child ticket . Write a system of equations can be used to determine the cost of each type of ticket ?

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If 1 litre = 1000ml, then 4/5 of a litre = _____​

Answers

Answer:

800ml.

Step-by-step explanation:

If 1 litre = 1000 ml, then

\(\small\sf{\quad\dfrac{4}{5} \: of \: a \: litre}\)

\( : \implies\small\sf{\dfrac{4}{5} \: of \: 1000}\)

\( : \implies\small\sf{\dfrac{4}{5} \times 1000}\)

\( : \implies\small\sf{\dfrac{4 \times 1000}{2}}\)

\( : \implies\small\sf{\cancel{\dfrac{4000}{5}}}\)

\( : \implies\small{\sf{800 \: ml}}\)

∴ The answer is 800 ml.

Please solve quickly.

Please solve quickly.

Answers

The statements that are true or false about both figures are as follows:

The bases are the same and the height of the triangle is twice the height of the rectangle: False

The heights are the same and the base of the rectangle is half the base of the triangle: True

The base and height if the rectangle are both twice the base and height of the triangle: False

The base and height of both figures are the same: False

How to find the area of a rectangle and triangle?

The formula for the area of a rectangle is:

Area = Length * Width

The formula for the area of a triangle is:

Area = ¹/₂ * base * height

The area of rectangle according to Darnell is 30 and as such:

Length * Width = 30

Area of rectangle according to Valerie is 30 and as such:
¹/₂ * base * height = 30

Thus:

¹/₂ * base * height = Length * Width

Thus:

base * height = 2(Length * Width)

We can say that:

The heights are the same and the base of the rectangle is half the base of the triangle

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if the radius of the wheel is 21 cm what is the distance traveled by the wheel in 3 revolution​

Answers

Answer:

  396 cm

Step-by-step explanation:

You want the distance traveled by a wheel of radius 21 cm in 3 revolutions.

Circumference

The circumference of the wheel is ...

  C = 2πr

  C = 2π(21 cm) = 42π cm

Revolutions

In 3 revolutions of the wheel, it travels 3 times that distance, or ...

  3(42π cm) = 126π cm ≈ 396 cm

The distance traveled is about 396 cm.

__

Additional comment

The value shown is rounded to the nearest centimeter. The attachment shows the value to higher precision, for the usual approximations of pi.

<95141404393>

if the radius of the wheel is 21 cm what is the distance traveled by the wheel in 3 revolution

The mean for the distribution of sample means is always equal to the mean for the population from which the samples are obtained. A) True B) False

Answers

The statement "The mean for the distribution of sample means is always equal to the mean for the population from which the samples are obtained" is A) True.

The mean for the distribution of sample means is always equal to the mean for the population from which the samples are obtained. This is a fundamental principle in statistics and is known as the central limit theorem.

The distribution of sample means is a probability distribution that shows the average values of a variable for all possible samples of a certain size taken from a population. The mean of this distribution is equal to the mean of the population.

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What is the maximum value of this function on the interval [-2,0]

What is the maximum value of this function on the interval [-2,0]

Answers

Answer:

2,0?

Step-by-step explanation:

To do this, find your first derivative and then find where it is equal to zero. Because we are only concerned about the interval from -5 to 0, we only need to test points on that interval. (i really don't know hot to explain)

In how many different ways can we sit n people around a round table? The sits are indistinguishable but the relative position of people is not. 3. A license plate can have four one-digit numbers or two one-digit numbers and two letters. How many different license plates are there?

Answers

There are 686,000 different license plates.

To solve this problem, we can fix one person's position and arrange the remaining (n-1) people around the table.

Since the seats are indistinguishable, we divide the total number of arrangements by n to avoid counting duplicate arrangements.

The number of different ways to sit n people around a round table is (n-1)!.

A license plate can have four one-digit numbers or two one-digit numbers and two letters.

For the first case, where the license plate has four one-digit numbers, there are 10 choices for each digit (0-9).

Therefore, there are 10 choices for the first digit, 10 choices for the second digit, 10 choices for the third digit, and 10 choices for the fourth digit. In total, there are 10^4 = 10,000 different license plates.

For the second case, where the license plate has two one-digit numbers and two letters, there are 10 choices for each digit and 26 choices for each letter (assuming only uppercase letters).

Therefore, there are 10 choices for the first digit, 10 choices for the second digit, 26 choices for the first letter, and 26 choices for the second letter. In total, there are 10^2 * 26^2 = 676,000 different license plates.

Different license plate = 10,000 + 676,000

                                     = 686,000

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