Tyrone is having an 80-foot tree removed from his front yard. One of the tree surgeons ties a rope to the top of the tree and stands 60 feet from the base of the tree while his partner saws through the tree. The rope will help them control the direction in which the tree falls. In the diagram below, side X represents the length of rope needed

Given:

The word is "CALCULATOR."​

To find:

The number of distinct permutations.

Solution:

In the word "CALCULATOR",

The number of letters = 10

In which, we have 2 C, A, L and 1 U, T, O, R.

We know that,

[tex]^nC_r=\dfrac{n!}{(n-r)!}[/tex]

[tex]^nC_n=\dfrac{n!}{(n-n)!}=n![/tex]

To find the number of distinct permutations of the given word need to divide permutation of all letter by the permutations of repeated letters.

[tex]\text{Total ways}=\dfrac{^{10}C_{10}}{^2C_2\ ^2C_2\ ^2C_2\ ^1C_1\ ^1C_1\ ^1C_1\ ^1C_1}[/tex]

[tex]\text{Total ways}=\dfrac{10!}{2!2!2!1!1!1!1!}[/tex]

[tex]\text{Total ways}=\dfrac{10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{2\times 2\times 2\times 1\times 1\times 1\times 1}[/tex]

[tex]\text{Total ways}=453600[/tex]

Therefore, the number of distinct permutations of the word "CALCULATOR" is 453600.

Number of distinct permutation of the word "CALCULATOR." is 453600

How to solve this problem?

Total number of words in "CALCULATOR" is 10

we find out the words that are repeating

A is repeating twice (2)

C is repeating twice (2)

L is repeating twice (2)

Number of permutations = number of letters !/ repeating letters!

Number of distinct permutation =

[tex]\frac{10!}{2!2!2!} \\\frac{10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{2\cdot2\cdot2} \\453600[/tex]

Number of distinct permutation of the word "CALCULATOR." is 453600

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Answer:

5.2 cubic ft

Step-by-step explanation:

took the test

The volume of given cone is 5.23 cubic feet.

Volume is the measure of the capacity that an object holds.

[tex]v = \frac{1}{3} \pi r^{2} h[/tex]

where,

v is the volume of cone

r is the radius of cone

h is the height of cone

According to the question we have

Diameter of cone is 2ft

⇒ radius of the cone = [tex]\frac{2}{2} = 1 feet[/tex]

Height of the cone is 5ft.

Therefore,

The volume of the cone  = [tex]\frac{1}{3}(1)\pi( 1)^{2} (5)[/tex]

Volume of cone = [tex]\frac{1}{3} (3.14)(1)(5) = 5.23 cubic feet[/tex]

Hence, hence the volume of given cone is 5.23 cubic feet.

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Answer: Is A

Step-by-step explanation:

I don't know if I am completely correct

Answer:

s=-4

Step-by-step explanation:

Answer:

110 grams

Step-by-step explanation:

CO2 molecule is made up of Carbon (atomic mass =12) and oxygen (atomic mass=16).

So first finding the mass of 1 molecule of CO2 which is equals to

= mass of 1 carbon atom + masses of 2 oxygen atom, we get

= 12+(16*2)= 12+32= 44 a.m.u.

Now 1 molecule of CO2 has mass 44 amu so mass of 1 mole CO2 will be 44 grams.( 1 a.m.u.=1.6729*10^-33 grams. 1 mole = 6.022*10^23, so 44 a.m.u.=73.6076*10^-33 grams approx. For one mole CO2, 73.6076*10^-33*6.022*10^23 which is approximately equals to 44 grams. )

1 mole CO2= 44grams, so 2.5 moles = 44*2.5= 110 grams

So our answer is 110 grams.

lowkey hope this helped you, good luck whatever you need it for Imaooo

Answer:

A

Step-by-step explanation:

(f*g)(x)=(2)*(x)=2x

A

Answer:

Its non-linear and decreasing

Step-by-step explanation:

Answer:

( -∞,2)

Step-by-step explanation:

The function is decreasing from the left up until the vertex

Answer:

2 t

2 t

2 t

2 t

0.0825 9350 5000 1

2

9350 5000(1.04125)

1.87 1.04125

log(1.87) log(1.04125 )

log1.87 (2t)(log1.04125)

log1.87 2t

log1.04125

15.48512579 2t

t 7.7

Step-by-step explanation:

the answer is 7.7

there will be $9350 in the account after 7 years and 9 months.

The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. A = P(1 + r/n)^nt, where P is the principal balance, r is the interest rate, n is the number of times interest is compounded annually, and t is the number of years, is the formula for compound interest.

Given, If you deposit $5000 into an account paying 8.25% annual interest compounded semiannually.

To calculate time until there is $9350 in the account.

So,

From the general formula of Compound interest:

A = P(1 + r/n)^nt,

where P is the principal balance,

r is the interest rate,

n is the number of times interest is compounded annually,

and t is the number of years,

In our case,

A = 9350

p = 5000

r = 8.25

n = 2

Thus,

9350 = 5000(1 + 8.25/2%)^2*t

(1 + 8.25/2%)^2*t = 9350/5000

t = 7 years 9 months

Therefore, there will be $9350 in the account after 7 years and 9 months.

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Answer:

42.42641

Step-by-step explanation:

Answer:

There are 3 W's in the M's

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer:

well the answer for the first one is -15

Answer:below hopes it helps the link should help aswell

Step-by-step explanation:

https://mathsolver.microsoft.com/en/solve-problem/%60frac%7B%2010%20%7B%20q%20%20%7D%5E%7B%205%20%20%7D%20%20%20%7B%20w%20%20%7D%5E%7B%207%20%20%7D%20%20%20%20%7D%7B%202%20%7B%20w%20%20%7D%5E%7B%203%20%20%7D%20%20%20%20%7D%20%20%20%60frac%7B%204%20%7B%20%60left(%20%7B%20q%20%20%7D%5E%7B%206%20%20%7D%20%20%20%60right)%20%7D%5E%7B%202%20%20%7D%20%20%20%20%7D%7B%20%20%7B%20w%20%20%7D%5E%7B%20-5%20%20%7D%20%20%20%20%7D

y=e^x+3.

The given graph of the function y = e^x

he transformation occur when we add c to the parent function y = e^x giving us a vertical shift c unit in the same direction as the sign.

The y axis of a coordinate plane is the vertical axis. When a function shifts vertically, the value of y changes.

The given parent function: y = e^x,

we can now graph the vertical shift alongside i.e, c=3

Then, the upward shift function is, y = e^x + c

Substitute the value of c=3,

then, the transformed equation becomes, y = e^x + 3

as it goes through (0,4).

∴The equation y = e^x + 3 represents the transformed function.

Answer:

y=e^x+3.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

= 8 * 76 =

10% * $1,913 = 191.3

Total = $608 + $191.3

= $799.3 approximately $799

Answer:

A

Step-by-step explanation:

Answer:

The answer to this problem is 6.

Step-by-step explanation:

Answer: Area=113.1 ft²

Step-by-step explanation:

Area equation= πr2

1/4*π*d^2

1/4*π*12^2≈113.09734ft²

113.1 ft²

Answer:

y = 8

x = 8√5

z = 4√5

Step-by-step explanation:

Using the formula (which is a geometric mean):

a        y

---- = -----

x        a

Where a is the altitude (y), x is a projection (16), and y is the other projection (4):

y        4

---- = -----

16       y

Cross multiply:

y² = 16 (4)

y² = 64

√y² = √64

y = 8

To find x and z, use the Pythagorean Theorem:

16² + y² = x²

256 + 8² = x²

256 + 64 = x²

320 = x²

√320 = √x²

√64√5 = √x²

8√5 = x

x = 8√5

4² + y² = z²

16 + 64 = z²

80 = z²

√80 = √z²

√16√5 = √z²

4√5 = z

z = 4√5

Answer:

7

Step-by-step explanation: 14 - 7 7

Answer:

8 hours

Step-by-step explanation:

t = time for Bob and Nina to make 60 leashes

Bob = 7 in 2 hr  = 3.5 in 1 hr

Nina = 4 in 1 hr

3.5 + 4 = 7.5 leashes per hour

t = 60/7.5 = 8 hours

Answer:

-0.76

Step-by-step explanation:

Answer:

-0.76

Step-by-step explanation:

this is pretty simple subtraction but you just take 14.36 and subtract it by 15.12 and you know it will be a negative number because 15.12 is bigger than 14.36 and so your answer is -0.76

Answer:

x = 150

Step-by-step explanation:

x + x - 15 + 107 + x + 7 + 125 + 122 + 131 = 630

3x + 180 = 630

3x = 450

x = 150

The value of x is 150

A polygon is a closed figure made up of three or more line segments connected end to end.

We are given that seven sided polygon with angle measures x, x minus 15, 107, x plus 7, 125, 122, and 131 degree

Therefore, the sum of all the angles are;

x + x - 15 + 107 + x + 7 + 125 + 122 + 131 = 630

3x + 180 = 630

3x = 450

x = 150

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Answer:

it means there are five books left, and the 36 boxes are filled

hope it's helpful ❤❤❤❤❤❤

THANK YOU.