a teacher wants to arrange 3 copies of introduction to geometry and 4 copies of introduction to number theory on a bookshelf. in how many ways can he do that? (all the copies of each book are identical.)

Answers

Answer 1

The total number of ways to arrange 3 copies of introduction to geometry and 4 copies of introduction to number theory on a bookshelf is 35.

A permutation of a set of objects is an ordering of those objects. When some of those objects are identical, the situation is transformed into a problem about permutations with repetition. Problems of this form are quite common in practice; for instance, it may be desirable to find orderings of boys and girls, students of different grades, or cars of certain colors, without a need to distinguish between students of the same grade (or cars of the same color, or people of the same gender).

Total number of copies = 3 +4 = 7

Number of ways to arrange 7 copies together = 7!

However, there are 3 copies of introduction to geometry and 4 copies of introduction to number theory. Thus, all copies of each book are identical.

Now, the total number of ways to arrange 7 copies together

= $\frac{7!}{3!* 4!}$

=35

Thus, the total number of ways to arrange 3 copies of introduction to geometry and 4 copies of introduction to number theory on a bookshelf is 35.

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Related Questions

a 'scooped' pyramid has a cross-sectional area of x 4 at a distance x from the tip. what is its volume if the distance from tip to base is 5?

Answers

The volume of the 'scooped' pyramid is approximately 26.6667 cubic units.

To find the volume of the 'scooped' pyramid, we first need to determine the area of its base. Since the cross-sectional area of the pyramid is x 4 at a distance x from the tip, we can assume that the area at the tip is zero. This means that the area of the base is 4 times the area at a distance of 5 from the tip (since the distance from tip to base is 5).

Therefore, the area of the base is 4x4 = 16 square units. To find the volume, we can use the formula for the volume of a pyramid, which is:

Volume = (1/3) x Base Area x Height

In this case, the height of the pyramid is 5 units. So, we can substitute the values we have:

Volume = (1/3) x 16 x 5

Volume = 26.6667 cubic units

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For the curve (x^2+y^2)^3−8x^2y^2=0 find an equation of the tangent line at (1,−1)

Answers

Answer:

x - y = 2

Step-by-step explanation:

You want an equation for the tangent to (x^2+y^2)^3−8x^2y^2=0 at the point (x, y) = (1, -1).

Inspection

A graph of the curve shows it has a slope of +1 at (x, y) = (1, -1).

In point-slope form the equation of the line is ...

y -k = m(x -h) . . . . . . . . line with slope m through point (h, k)

y -(-1) = 1(x -1) . . . . . . substituting known values

x - y = 2 . . . . . . . . rearranging to standard form

Additional comment

Differentiating implicitly, you get ...

3(x^2 +y^2)^2(2x·dx +2y·dy) -16xy^2·dx -16x^2y·dy = 0

at (1, -1), this is ...

3(1 +1)^2(2·dx -2·dy) -16·dx +16·dy = 0

8dx -8dy = 0 . . . . simplified

dy/dx = 1

Then we can proceed with the point-slope equation as above.

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For the curve (x^2+y^2)^38x^2y^2=0 find an equation of the tangent line at (1,1)

5 (3 - x) < -23 + 6

Answers

Answer:

x > 32/5

Step-by-step explanation:

A wholesaler carries 6,600 different items in their store. In a normal week, demand occurs for 4,800 of these items. Of those 4,800 items, 250 are not available for the entire week and another 270 items are available for only part of the week What is the wholesaler's in-stock probability during a normal week? Note: Round your answer as a percentage rounded to 1 decimal place.

Answers

Rounded to 1 decimal place, the wholesaler's in-stock probability during a normal week is approximately 89.2%.

To calculate the wholesaler's in-stock probability during a normal week, we need to consider the number of items that are available for the entire week and divide it by the total demand.

Total demand = 4,800 items

Items not available for the entire week = 250 items

Items available for only part of the week = 270 items

Therefore, the number of items available for the entire week can be calculated as follows:

Items available for the entire week = Total demand - Items not available for the entire week - Items available for only part of the week

= 4,800 - 250 - 270

= 4,280 items

The in-stock probability can be calculated by dividing the number of items available for the entire week by the total demand and then multiplying by 100 to convert it to a percentage:

In-stock probability = (Items available for the entire week / Total demand) * 100

= (4,280 / 4,800) * 100

= 89.1666...

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For some transformation kinetics that obey the Avrami equation, the parameter n is known to have a value of 1.1
- if it takes 185 seconds for the transformation to go to 90% completion. determine the parameter K. Also determine the rate of transformation r.

Answers

For an Avrami equation with n=1.1, when the transformation takes 185 seconds for 90% completion, the parameter K is approximately 0.0386. The rate of transformation ® is approximately 0.1216 per second.

The Avrami equation is given by the formula t = K(1 – exp(-r^n)), where t is the time, K is the rate constant, r is the rate of transformation, and n is the Avrami exponent. Given that n = 1.1, and it takes 185 seconds for 90% completion, we can substitute these values into the equation.
0.9 = 1 – exp(-r^1.1)
Rearranging the equation, we get:
Exp(-r^1.1) = 0.1
Taking the natural logarithm of both sides:
-r^1.1 = ln(0.1)
Solving for r:
R = (-ln(0.1))^0.9091 ≈ 0.1216 per second
Now, we can substitute the obtained value of r into the Avrami equation:
185 = K(1 – exp(-0.1216^1.1))
Solving for K:
K = 185 / (1 – exp(-0.1216^1.1)) ≈ 0.0386
Therefore, the parameter K is approximately 0.0386, and the rate of transformation is approximately 0.1216 per second.

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3 to the power of 2 * 3 to the power of 4

Answers

Answer: 729

Step-by-step explanation: what we are seeing here is known as exponents, how exponents work is that you have to multiply a number a certain times, depending on the power of #.

3^2 = 9 because simplified, its 3 * 3

3^4 = 81 because simplified, its 3 * 3 * 3 * 3

now the solution would be 9 * 81, which equals 729

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hope this helps

Solve the equation. First estimate using the perfect square closest to 54. Then use a calculator.d2=54Estimate.

Answers

Estimates are used to get the approximated value of an expression.

The estimate of $d^2 = 54$ is 7The actual value is: 7.34846923

The equation is given as:

$d^2 = 54$

The perfect closest to 54 is: 49

So, the equation becomes

$d^2 \approx 49$

Take square of both sides

$d \approx \sqrt{49$

$d \approx 7$

The actual value is calculated as follows:

$d^2 = 54$

Take square roots

$d = \sqrt{54$

$d = 7.34846923$

Hence, the estimate is less than the actual value

Answers

Answer : 1+1 = 11

22+22 = 2222

what is 10 to the 100th power

Answers

Answer:

EZ!!! 1e+100

Step-by-step explanation:

Given parallelogram ABCD, diagonals AC and BD intersect at point E. AE=11x−3 and CE=12−4x. Find x

Answers

Answer:

x = 1

Step-by-step explanation:

The diagonals of a parallelogram bisect each other, thus

AE = CE , substitute values

11x - 3 = 12 - 4x ( add 4x to both sides )

15x - 3 = 12 ( add 3 to both sides )

15x = 15 ( divide both sides by 15 )

x = 1

Hazel and Tom travel the same 18 km route.

Hazel starts at 9. 00 am and walks at a constant speed of 4. 8 km/h

Tom starts at 9. 39 am and runs at a constant speed.

Tom overtakes Hazel at 10. 15 am

At what time does Tom finish the route?

Answers

Answer:

11:27 am.

Step-by-step explanation:

The time which has passed when Tom overtakes Hazel is after Hazel has walked 1 hr 15 minutes and in that time Hazel has walked

1.25 * 4.8

= 6 km.

So, Tom runs 6 km in 10:15 - 9.39 = 36 minutes

= 0.6 hrs.

So, Tom's speed is 6/0.6 = 10 km/hr.

and Tom will take 18/10 = 1.8 hours to finish the route,

= 1 hr 48 minutes

So he finishes the route at

9:39 + 1:48

= 11:27 am.

Solve——6^2x+2•6^3x=1

Answers

Answer:

-2/5 this is the answer to 6^2x+2•6^3x=1

helpppppppppp plsssssss

Answers

Answer: I think it might be the one u chose but im not sure but if i got it wrong then im sorry and feel free to correct me

Step-by-step explanation:

Answer:

parallal

neither

perpendicular

Step-by-step explanation:

Hopes this helps! : D

And I am so sorry if I get you the wrong answers.

I NEED HELPPP pleaseeeeeee !!!!!!

Answers

Reflection across the x axis

help me please it's due at 2:30

Answers

Answer:

i have the same doubt

Step-by-step explanation:

if the cafteria has 80 custmores on tusday which predicton for tuesday is not supported by the data table.

Answers

The number of bottles of apple juice sold will be 6 times the number of bottles of cranberry juice sold is not supported. Then the correct option is B.

What are ratio and proportion?

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

The table is given below.

Kind of juice Number of bottles sold

Monday Tuesday

Apple 11 22

Cranberry 7 14

Orange 18 36

Pineapple 4 8

Total 40 80

The number of bottles of apple juice sold will be 6 times the number of bottles of cranberry juice sold is not supported. Then the correct option is B.

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The complete question is given below.

A) The number of bottles of cranberry juice sold will be 6 more than the number of bottles of pineapple juice sold.

B) The number of bottles of apple juice sold will be 6 times the number of bottles of cranberry juice sold.

C) There will be a total of 50 bottles of orange and cranberry juice sold.

Eliminate

D) The difference between the number of bottles of apple juice sold and the number of bottles of pineapple juice sold will be 14.

if the cafteria has 80 custmores on tusday which predicton for tuesday is not supported by the data table.

IS THIS RIGHTT???????

Answers

Answer:

No the correct answer would be square root of 19

Step-by-step explanation:

i got you

No, I don’t think so, the answer is about 4.36, you have use square root.

Graph each quadratic equation using a table of values. Identify all key characteristics.
1. y = x2 + 10x + 26
.
J
Axis of Symmetry:
4
T
Vertex:
Domain:
Range:
..

Answers

Answer:

See graph below

Step-by-step explanation:

The domain is (-∞,∞) and the range is [1,∞)

Graph each quadratic equation using a table of values. Identify all key characteristics.1. y = x2 + 10x

Pleaseeeeee helpppppppp i will mark brainlest

Answers

Answer:

Step-by-step explanation:

Answer:

B=40°

Step-by-step explanation:

Sum of angles in a triangle =180°

90°+50°+x°=180°

140°+×°=180°

Collect like terms

x°=180°-140°

x°=40°

Circle the points that are on the line given by the equation y = -2x.
A) (-2,4)
B) (1, 3)
C) (2,4)
D) (3, -6)

Answers

Answer:

Only points (A) and (D) are on the line.

an environmental protection agency study of 12 automobiles revealed a correlation of 0.47 between engine size and emissions. at the .01 significance level, they want to test whether or not the population correlation is positive. what is the computed value of the test statistic? 0.47 0.22 2.94 1.68

Answers

The computed value of the test statistic is 2.94.

What is Statistics?

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

We have a sample size of n = 12, engine size (x) and emissions (y) are the two variables being correlated, and the sample correlation coefficient is r = 0.47.

The null hypothesis is that the population correlation is zero (H0: ρ = 0) and the alternative hypothesis is that the population correlation is positive (Ha: ρ > 0).

To compute the test statistic, we need to first calculate the degrees of freedom (df), which is (n-2) = 10 in this case.

We can then use the formula for the test statistic, which is:

t = (r√(df)) / √1 - r²

Substituting the values we have, we get:

t = (0.47 √10) / √(1 - 0.47²)

t = 2.94

Therefore, the computed value of the test statistic is 2.94.

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to estimate the height of a building, two students find the angle of elevation from a point at ground level down the street from the building to the top of the building is 30 degrees. from a point that is 300 feet closer to the building, the angle of elevation at ground level to the top of the building is 50 degrees. If we assume that the street is level, use this information to estimate the heigh of the building

Answers

The calculated height of the building is 335.95 feet

How to estimate the height of the building

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

Angles = 30 degrees and 50 degrees

Distance from the base = 300 feet

Represent the height of the building and the closer distance with x

So, we have

tan(30) = y/x

tan(50) = y/(x - 300)

Make x the subject

So, we have

x = y/tan(30)

x = y/tan(50) + 300

Subtract the equations

y/tan(30) = y/tan(50) + 300

So, we have

y/tan(30) - y/tan(50) = 300

Evaluate

y(0.893) = 300

Divide both sides by 0.893

y = 335.95

Hence, the height of the building is 335.95 feet

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Can somebody help me please

Answers

The area of figure is 272.52 square units.

The given figure consist:

A parallelogram of,

length = 12

width = 18

Since we know that,

Area of parallelogram = length x width

= 12 x 18

= 216 square units

And it consist of a semicircle of,

radius = 12/2

= 6

Since we know that,

Area of semicircle is = πr²/2

= 3.14 x 6 x 6/2

= 56.52 square units

Thus,

The area of figure is sum of both areas,

⇒ 216 + 56.52

Hence, area is

⇒ 272.52 square units

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can anyone help me this is very confusing?

Answers

Answer:

answer is 2

Step-by-step explanation:

Answer:

Nick it's me Julie I have 18 accounts now

Step-by-step explanation:

Rabbits can exhibit a number of colors in their coats: black, white, tan, brown, red, and grey. A disease randomly kills off most of the population and leaves only black and grey rabbits. Future generations are only black or grey. What is the term used to describe this phenomenon

Answers

Answer:

Genetic drift

Step-by-step explanation:

I took da test

The term used to describe this phenomenon of future generation fluctuations would be Genetic drift.

What is Genetic drift?

Genetic drift refers to the random fluctuations in the number of offspring in a population.

Rabbits can exhibit several colors in their coats: black, white, tan, brown, red, and grey.

A disease randomly kills off most of the population and leaves only black and grey rabbits.

Future generations are only black or grey. We can see that the future rabbits have some common colors that are given by their parents.

So, this must be Genetic drift.

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Two step inequalities:

The seventh grade class is putting on a variety show to raise money. It cost $700 to rent the banquet hall that they are going to use. If they charge $15 for each ticket, how many tickets do they need to sell in order to raise at least $1000?

Answers

Answer:

67 tickets (with $5 extra)

Step-by-step explanation:

1000÷15= Number of tickets

Please help its due 12:00 Am

Answers

Answer:

440h is the expression. When 3 1/4 is evaluated you get 1,430 calories burned.

Step-by-step explanation:

440 represents the number of calories she burns per hour. To represent the hour, we place a variable which is h. After we write the expression, we substitute 3 1/4 for h. When I did this, I turned 3 1/4 into an improper fraction, which was 13/4, and then divided 13 by 4 to get 3.25

Multiple 3.25 by 440 to get an answer of 1,430 calories burned.

Hope this helps :)

7. Write 0.7 as a fraction/ the 7 is repeating decimal btw

Answers

Answer:

7/10

Step-by-step explanation:

Considering that the lower intersection is a translation of the upper intersection what does this mean about the measures of the corresponding angles

Answers

This mean about the measures of the corresponding angles the lower intersection is a translation of the upper intersection. This means that corresponding angles overlap each other on translation. So, the corresponding angles are congruent This is further explained below.

What is angles?

Generally, angles is simply defined as the angle formed when two lines or surfaces meet, or the distance between them (typically measured in degrees).

In conclusion, What does this imply about the sizes of the associated angles Simply said, the bottom intersection is a literal translation of the higher one. What this indicates is that, when translated, the relevant angles overlap. As a result, the two angles are equal.

Answers

Answer:

A=2(wl+hl+hw)

Step-by-step explanation:

(9x9+17x9+17x9)

=387

=2x387=774

A=774

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