Mathematics College

In how many different ways can the curator of a museum arrange five of eight paintings horizontally on the wall?

Answers

Answer 1
8C5=8!/(3!5!)=56
There are 56 ways a curator can arrange the paintings.
Answer 2

The requried number of ways that 5 paintings to be chosen is 56 ways.

What are permutation and combination?

In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.

Here,
Total number of paintings = 8
Total number of paintings to be arranged = 5
Number of ways = 8C5
                         = 8!/[8-5]!5!     [nCr = n!/[n-r]!r!]

                         = 56 ways

Thus, the requried number of ways that 5 paintings to be chosen is 56 ways.

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Related Questions

Simplify the expression 3 1/3/3 1/3. Explain how the expression and its simplified form show that the set of irrational numbers is not closed under division

Answers

The expression given is ambiguous according to the standard rules of math (PEMDAS) due to the lack of appropriate parentheses and probably the exponentiation symbol ^.

From the context, I assume it to mean
(3^(1/3)) / (3^(1/3)) = 1

Since 3^(1/3) is the cube-root of 3, and is thus irrational.
However, the quotient is exactly 1, which is a rational number.

The example is therefore a counter-example for the statement that "set of irrational numbers is closed under division", or stated differently,
"the set of irrational numbers is not closed under division"

What is the value of x?


6 + 8x
-------------- = 5x
2

A) -2
B) -1
C) 1/3
D) 3

Answers

The ans is choice D. since there nothing under 5x, imagine there is a 1 under. After that, you can simply cross multiply, so it would be 1(6+8x)= 2(5x). 6+8x= 10x now combine like terms so subtract 8x from both sides and divide 6 by 2 and you will get 3 
I just took the test the answer is D.3

Solve For L: A = L ⋅ W ⋅ H

L=aw/h

L=wh/a

L=a/wh

L=w/ha

Answers

Ok so what you're trying to do is get L by itself so to do this you move everything to the other side:
A=L*WH
[tex] \frac{A}{WH} [/tex]=L
So you answer would be: C
your answer would be the third one C

There are six different sixth roots of 64. That is, there are six complex numbers that solve x^6=64

Please help

Answers

There are two possible solutions:

1)
When we know that:

[tex]\sqrt[n]{z}=\sqrt[n]{|z|}\Big(\cos\frac{\phi+2k\pi}{n}+i\sin\frac{\phi+2k\pi}{n}\Big)\qquad\text{for}\quad k=0,1,\ldots,n-1[/tex]

when [tex]z=|z|(\cos\phi+i\sin\phi)[/tex]

then:

[tex]x^6=64\quad|\sqrt[6]{(\ldots)}\\\\x=\sqrt[6]{64}[/tex]

For [tex]x=64[/tex] we have:

[tex]64=|64|(\cos0+i\sin0)\quad\Rightarrow\quad \phi=0[/tex]

and:

[tex]\sqrt[6]{64}=\sqrt[6]{64}\Big(\cos\frac{0+2k\pi}{6}+i\sin\frac{0+2k\pi}{6}\Big)\qquad\text{for}\quad k=0,1,\ldots,5\\\\\\ \sqrt[6]{64}=2\Big(\cos\frac{k\pi}{3}+i\sin\frac{k\pi}{3}\Big)\qquad\text{for}\quad k=0,1,\ldots,5 [/tex]

k = 0

[tex]2\Big(\cos\frac{0}{3}+i\sin\frac{0}{3}\Big)=2(1+0i)=2\cdot1=\boxed{2}[/tex]

k = 1

[tex]2\Big(\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\Big)=2\Big(\frac{1}{2}+i\frac{\sqrt{3}}{2}\Big)=\boxed{1+i\sqrt{3}}[/tex]

k = 2

[tex]2\Big(\cos\frac{2\pi}{3}+i\sin\frac{2\pi}{3}\Big)=2\Big(-\frac{1}{2}+i\frac{\sqrt{3}}{2}\Big)=\boxed{-1+i\sqrt{3}}[/tex]

k = 3

[tex]2\Big(\cos\frac{3\pi}{3}+i\sin\frac{3\pi}{3}\Big)=2\Big(\cos\pi+i\sin\pi\Big)=2(-1+0i)=\boxed{-2}[/tex]

k = 4

[tex]2\Big(\cos\frac{4\pi}{3}+i\sin\frac{4\pi}{3}\Big)=2\Big(-\frac{1}{2}-i\frac{\sqrt{3}}{2}\Big)=\boxed{-1-i\sqrt{3}}[/tex]

k = 5

[tex]2\Big(\cos\frac{5\pi}{3}+i\sin\frac{5\pi}{3}\Big)=2\Big(\frac{1}{2}-i\frac{\sqrt{3}}{2}\Big)=\boxed{1-i\sqrt{3}}[/tex]

So the answer is:

[tex]x=\{2,\,1+i\sqrt{3},\,-1+i\sqrt{3},\,-2,\,-1-i\sqrt{3},\,1-i\sqrt{3}\}[/tex]

2)
We don't know method (1). If so, we could use following identities:

[tex](1)\quad a^2-b^2=(a+b)(a-b)\\\\(2)\quad a^3-b^3=(a-b)(a^2+ab+b^2)\\\\(3)\quad a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]

There will be:

[tex]x^6=64\\\\x^6-64=0\\\\(x^3)^2-8^2=0 \qquad\text{from (1)}\\\\(x^3+8)(x^3-8)=0\\\\(x^3+2^3)(x^3-2^3)=0\qquad\text{from (2) and (3)}\\\\ (x+2)(x^2-2x+4)(x-2)(x^2+2x+4)=0\qquad(\star)[/tex]

Now, we complete the square for:

[tex]x^2-2x+4=x^2-2x+1+3=(x^2-2x+1)+3=(x-1)^2+3=\\\\=(x-1)^2+(\sqrt{3})^2=(x-1)^2-(-1)(\sqrt{3})^2=(x-1)^2-i^2(\sqrt{3})^2=\\\\=(x-1)^2-(i\sqrt{3})^2=\text{from (1)}=\boxed{(x-1-i\sqrt{3})(x-1+i\sqrt{3})}[/tex]

and for:

[tex]x^2+2x+4=x^2-2x+1+3=(x^2+2x+1)+3=(x+1)^2+3=\\\\=(x+1)^2+(\sqrt{3})^2=(x+1)^2-(-1)(\sqrt{3})^2=(x+1)^2-i^2(\sqrt{3})^2=\\\\=(x+1)^2-(i\sqrt{3})^2=\text{from (1)}=\boxed{(x+1-i\sqrt{3})(x+1+i\sqrt{3})}[/tex]

When we return to [tex](\star)[/tex]:

[tex](x+2)(x^2-2x+4)(x-2)(x^2+2x+4)=0\\\\(x+2)(x-1-i\sqrt{3})(x-1+i\sqrt{3})(x-2)(x+1-i\sqrt{3})(x+1+i\sqrt{3})=\\=0[/tex]

And we have answer:

[tex]x=\{-2,\,1+i\sqrt{3},\,1-i\sqrt{3},\,2,\,-1+i\sqrt{3},\,-1-i\sqrt{3}\} [/tex]

To find the six sixth roots of 64, you can use polar form and De Moivre's Theorem to calculate the complex numbers. The roots are 2, 1+i√3, -1+i√3, -2, -1-i√3, and 1-i√3.

[tex]X^6 = 64[/tex]

The sixth roots of 64 are complex numbers and can be found by writing 64 in polar form and applying De Moivre's Theorem. Let's find the six roots:

First root: 2(cos(0) + i sin(0)) = 2

Second root: 2(cos(π/3) + i sin(π/3)) = 2(1/2 + i√3/2) = 1 + i√3

Third root: 2(cos(2π/3) + i sin(2π/3)) = 2(-1/2 + i√3/2) = -1 + i√3

Fourth root: -2

Fifth root: -2(cos(-π/3) + i sin(-π/3)) = -2(1/2 - i√3/2) = -1 - i√3

Sixth root: -2(cos(-2π/3) + i sin(-2π/3)) = -2(-1/2 - i√3/2) = 1 - i√3

What is 8.038×108 in standard form?

80,308,000

80,380,000

83,800,000

803,800,000

Answers

Okay. I think what you mean by this is 8.038 * 10^8. 10^8 = 100,000,000. When you multiply that by 8.038, you get 803,800,000. The answer is D.

Answer:

803,800,000

Step-by-step explanation:

8.038×10^8 in standard form

To get standard form we multiply the decimal number by 10^8

10^8 is 100000000

Now we multiply

8.038×100000000

Move the decimal number 3 places to the right and add 5 more zeros

803800000

So the standard form of the given expression is

803,800,000

The following formula relates three quantities force mass and acccelerations
F=ma

Answers

True.  Dissect "F=ma" and you'll get "Force," "mass" and "acceleration."

Bess practices trumpet 1/2 hr on Monday and 1 3/5 hr on Wednesday.



How many hours does Bess practice trumpet?

Answers

She practice for 2.1 or 2 1/10
She practiced for 2.1 hours total

Tyquan uses the greatest common factor and the distributive property to rewrite this sum: 75 + 60 What expression does Tyquan write? 3(25 + 20) 5(15 + 12) 25(3 + 60) 15(5 + 4)

Answers

the GCF of 75 and 60 is 15

75/15 = 5
60/15 = 4

so ur expression is : 15(5 + 4) <==
The answer is 15(5+4)

what is (9x^4-x^2y^2-5y^4)-(3x^4+2x^2y^2-7y^4)

Answers

(9x⁴ - x²y² - 5y⁴) - (3x⁴ + 2x²y² - 7y⁴)
9x⁴ - x²y² - 5y⁴ - 3x⁴ - 2x²y² + 7y⁴
6x⁴ - 3x²y² + 2y⁴

domain of the function

Answers

hello : 
 y exist : x+6 ≥ 0
x ≥ -6

McDonald's is the king of the burger world, as it has more hamburger joints than any other restaurant chain. In 2013, McDonald's had 1427 locations in Canada. If the population of Canada was approximately 35.16 million citizens in 2013, what was the number of McDonald's restaurants per capita in Canada in 2013? Express your answer in scientific notation rounded correctly to three decimal places.

Answers

Sent you a picture of the solution.

In 2013, there were approximately 4.509 McDonald's restaurants per 100,000 people in the US.

To calculate the number of McDonald's restaurants per capita in the US in 2013, we divide the total number of McDonald's locations (14267) by the population of the US (316,500,000).

[tex]\[ \text{McDonald's per capita} = \frac{14267}{316500000} \][/tex]

Performing the division, we get [tex]\( 4.509 \times 10^{-5} \)[/tex].

This means there were approximately 4.509 McDonald's restaurants per 100,000 people in the US in 2013.

So, the number of McDonald's restaurants per capita in the US in 2013 is [tex]\( 4.509 \times 10^{-5} \) or \( 4.509 \times 10^{-5} \)[/tex] McDonald's per person.

A right triangle has one angle that measure 23o. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm. What is the approximate area of the triangle? Round to the nearest tenth. Area of a triangle = bh

Answers

Answer:

162.8 cm²

Step-by-step explanation:

The formula for the area of a triangle is

A = 1/2bh, where b is the base and h is the height.

The base can be represented as the given leg, 27.6 cm.  We do not know the height.  We must use the Pythagorean theorem to find this:

a²+b² = c²

27.6²+b² = 30²

761.76+b² = 900

Subtract 761.76 from each side:

761.76+b²-761.76 = 900-761.76

b² = 138.24

Take the square root of each side:

√(b²) = √(138.24)

b = 11.8

Now we use the area formula:

A = 1/2(11.8)(27.6) = 162.84 ≈ 162.8

The area of a given right triangle is 162.8 cm².

What is area?

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

Given that, the base can be represented as the given leg, 27.6 cm.  We do not know the height.  

Using Pythagorean theorem,

a²+b² = c²

27.6²+b² = 30²

761.76+b² = 900

761.76+b²-761.76 = 900-761.76

b² = 138.24

b = √(138.24)

b = 11.8

The formula for the area of a triangle is

A = 1/2bh, where b is the base and h is the height

A = 1/2(11.8)(27.6) = 162.84 ≈ 162.8

Therefore, the area of a given right triangle is 162.8 cm².

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Distributive property of 68/4

Answers

Start with 68/4.  Rewrite 68 as (4)(17)/4.  Cancel the 4s.  Result:  17.

The trick here is to rewrite 68 as 4(17).

Store A advertises a sale for 3 loaves of bread for $5.94. Explain how to use an equivalent rate to find the unit price of the bread at Store A.

Answers

Answer: I wrote the rate, with $5.95 in the numerator and 3 loaves in the denominator. I needed to find an equivalent rate expressed as a fraction with the denominator of 1. I noticed 3 loaves divided by 3 gave a denominator of 1, so I divided $5.94 by 3 to find that each loaf costs $1.98.

Just did it on Edge 2021

Btw Can you mark me brainlest pls

The equivalent rate of the bread is $1.98.

Since the store advertises a sale for 3 loaves of bread for $5.94, in order to find the equivalent rate, the person has to divide $5.94 by 3. This will be:

= $5.94/3

= $1.98

Therefore, the equivalent rate of the loaves of bread will be $1.98

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What is the value of x? 58 92 121 63

Answers

(184-58)/2 = x
126/2 = x
63 = x

Answer:

Angle x =  63 °.

Step-by-step explanation:

Given  : A circle larger arc angle 184° and smaller arc angle 58°.

To find: What is the value of x.

Solution : We have given that  larger arc angle 184°

Smaller arc angle 58°.

Angle formed by tangent and chord = x

m∠x = [tex]\frac{1}{2}( 184 - 58 )[/tex].

m∠x =   [tex]\frac{1}{2}( 126)[/tex].

m∠x =  63 °.

Therefore, Angle x =  63 °.

The tensile strength of paper is modeled by a normal distribution with a mean of 35 pounds per square inch and a standard deviation of 2 pounds per square inch. what is the probability that the strength of a sample is less than 38 lb/in2? round your answer to 4 decimal places.

Answers

Given
mean=35 psi
std dev=2 psi
distribution normal

For probability that X<38, 
calculate
Z score = (X-mean)/std dev
=(38-35)/2=1.5
P(X<38)
=P(Z<1.5)
=0.9331928  from tables.

So probability that the strength of a random sample <38 pis = 0.9332

Express each repeating decimal as a fraction.

1.
1.8[4]

2.
2.1[26]

Answers

Hello,

1.8444444....=1.8+1/10*0.44444....
=1.8+1/10*4/9
=1.8+4/90
=162/90+4/90
=166/90
=83/45

2.126262626...=2.1+1/10*0.262626...
=2.1+1/10*26/99
=2.1+26/990
=2079/990+26/990
=2105/990
=421/198


Answer:

1.8444444....=1.8+1/10*0.44444....

=1.8+1/10*4/9

=1.8+4/90

=162/90+4/90

=166/90

=83/45

2.126262626...=2.1+1/10*0.262626...

=2.1+1/10*26/99

=2.1+26/990

=2079/990+26/990

=2105/990

=421/198

Jacks has 18 marbles,he loses 6 of them.

What fraction of the marbles does he lose?

Answers

6/18
1/3

Hope this helps!

In the numer 6,666.666 how does the 6 in the hundredths place compare to 6 in the place to its left

Answers

the six to the left is worth more than the six in the hundredths

hope

i helped

0.06 vs 0.6
the 6 in the hundreths place is 1/10 the value of the 6 in the place to the left

A coin is tossed 10 timesWhat is the probability of getting all heads?

Answers

The probability of getting all heads is 1/2

there is two sides, one head an one tail, or 1/2 chance of getting heads

Tossed 10 times, it still has 1/2

hope this helps

There are 60 minutes in 1 hour. What fraction of an hour is 4 minutes? Write your answer in lowest terms.

Answers

4 minutes/60 minutes

Divide the numerator and denominator by 4
1/15

Final answer: 1/15

The fraction of an hour is 4 minutes in lowest terms is 1/15.

What fraction of an hour is 4 minutes in lowest terms?

To find the fraction of an hour that 4 minutes represents, we need to compare the number of minutes to the total number of minutes in an hour, which is 60.

We can set up a fraction where the numerator represents the number of minutes we want to find the fraction for (4 minutes) and the denominator represents the total number of minutes in an hour (60 minutes).

So, the fraction can be written as 4/60.

To simplify the fraction to its lowest terms, we can divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 60 is 4.

Dividing both the numerator and denominator by 4, we get:

4/60 = (4 ÷ 4) / (60 ÷ 4) = 1/15.

Therefore, 4 minutes in lowest terms is equal to 1/15th of an hour.

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Find the range of the graphed function?

Answers

for finding range pay attention to y axis max of function is 5 and its min is -9
B is true

B is the correct answer                                            

Besides the 90° angle measure, what are the other two angle measures of a right triangle with side lengths 5, 12, and 13? Round to the nearest degree.

Answers

In the right triangle, the longest side is the hypotenuse.
Let α be the angle opposite to the side with a length of 12 units, then according to the Law of sines:

[tex] \frac{13}{sin90^o}= \frac{12}{sin \alpha } \ \ \to \ \ sin \alpha = \frac{12 \cdot sin90^o}{13}= \frac{12*1}{13} \approx 0.923 \ \ \to \ m\angle \alpha \approx 67^o[/tex]

In a triangle, the three interior angles always add to 180° ⇒

third angle = 180 - 90 - 67 = 23°

Answer:
67° and 23°  (to the nearest degree).

The other two angles are 23 degrees and 67 degrees.

What is Trigonometry?

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given,

Given a right angled triangle with one angle 90 degrees.

We need to find the other two angle measures of a right triangle with side lengths 5, 12, and 13

The relations in a right triangle are given as follows:

The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.

The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.

The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.

In this problem, the hypotenuse is the largest size of 13.

The angle opposite to the side of length 5 is found as follows:

sinθ=5/13

θ=sin⁻¹5/13

θ=23

By angle sum of 3 angles is of 180º, the other angle is of 67º.

Hence, the other two angles are 23 degrees and 67 degrees.

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How many pairs of whole numbers have a sum of 99

Answers

does anyone know lol
44 pairs. I believe that's the right answer.

You want to replace the countertops in a kitchen. One counter measures 24 inches by 6 feet. The other is 30 inches by 4 feet. If the new countertop costs $42.00 per square foot, what will be the cost of the new top?

Answers

First, multiply to find the total square footage of the counter.

2 ft x 6 ft=12 square feet
2.5 ft x 4 ft=10 square feet
Total square feet of the counter is 22 square feet.

To find the total cost, just multiply the area by the cost per square foot.
$42 x 22=$924

Answer:

The cost of the new top $924.

Step-by-step explanation:

You want to replace the counter-tops in a kitchen.

The dimensions of the first counter is 24 inches by 6 feet.

i.e [tex]24 \text{ inch} \times 6 \text{ feet}[/tex]

or [tex]2\text{ feet} \times 6 \text{ feet}[/tex]

As 1 feet =12 inches

Hence the area of the counter is [tex]2\times 6=12\text{ feet}^2[/tex]

The dimensions of the second counter is 30 inches by 4 feet.

i.e [tex]30 \text{ inch} \times 4 \text{ feet}[/tex]

or [tex]2.5\text{ feet} \times 4 \text{ feet}[/tex]

Hence the area of the counter is [tex]2.5\times 4=10\text{ feet}^2[/tex]

Hence, the total area will be [tex]12+10=22 \text{ feet}^2[/tex]

The unit cost of the counter-top is [tex]\$42.00\text{ feet}^2[/tex]

So the net cost will be,

[tex]=42\times 22=\$924[/tex]

The sample variance is 18.7. what is the sample standard deviation? answer to two decimal places.

Answers

I think that the sample standard might be 18.5 and 19, but, I might be very wrong. 

I have 5 digits. My 4s are worth 4 [10,000s] and 4 * 10. One of my 3s is worth 3,000. The other is worth 1/10 as much. My other digit is a 2. What number am I?

Answers

The given information are actually the digits and their place values in multiples of 10. To know the identity of the number, simply multiply the digit with its place value. The solution is as follows:

4(10,000) + 4(10) + 3,000 + 3,000(1/10) + 2 = 43,342

Thus, the 5-digit number is 43,342.

one positive integer is 5 less than another. the product of the two integers is 36. what are the integers?

Answers

 let the numbers be x and (x-5)

x(x-5)=36

x^2-5x-36=0

solving the equation we get

x=9 and x= -4
 
now find out the integers

1st number = x

2nd number = x-5

x*(x-5) = 36

x^2-5x =36

x^2 -5x-36 = 0

factor the polynomial:

(x-9) (x+4)

9-9 = 0, -4 +4 = 0

 so x = 9 or -4

 the question states a positive number

 so x = 9

 the 2 numbers are 9 and 4

 

Use the function below to find f(4).

Answers

f(x) = 1/3 * 4^x.......f(4)....so we sub in 4 for x
f(4) = 1/3 * 4^4
f(4) = 1/3 * 256
f(4) = 256/3 <===

Answer:  The correct option is (C) [tex]\dfrac{256}{3}.[/tex]

Step-by-step explanation:  The given function is

[tex]f(x)=\dfrac{1}{3}\times 4^x.[/tex]

We are to find the value of f(4).

To find the value of f(4), we need to substitute the value of x as 4 in the given definition of function f(x).

Substituting x = 4 in f(x), we have

[tex]f(4)=\dfrac{1}{3}\times 4^4=\dfrac{1}{3}\times 256=\dfrac{256}{3}.[/tex]

Therefore, the value of f(4) is [tex]\dfrac{256}{3}.[/tex]

Option (C) is correct.

Which of the following is a true equation?

1) 10 + 3 + 1 = 13 + 6
2) 4 - 3 = 7
3) 4 + 3 - 3 = 7 - 3
4) 4 + 3 = 7 + 3

Answers

4 + 3 - 3 = 7 - 3
           4 = 4

answer

3) 4 + 3 - 3 = 7 - 3
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