The following examples illustrate the inverse property of multiplication. Study the examples, then choose the statement that best describes the property.

1
5
• 5 = 1

√2 (
1
√2
) = 1

Inverse property of multiplication: For all real numbers except , a • = 1.

There are 56 different combinations of 5 friends that can be selected from the group of 8 friends (option C)

To determine the number of different combinations of 5 friends that can be selected from a group of 8 friends, we use the concept of combinations in combinatorial mathematics.

The number of ways to choose [tex]\( k \)[/tex] elements from a set of [tex]\( n \)[/tex] elements is given by the binomial coefficient [tex]\(\binom{n}{k}\)[/tex], which is calculated as:

[tex]\[\binom{n}{k} = \frac{n!}{k!(n-k)!}\][/tex]

In this scenario:

[tex]\( n = 8 \)[/tex] (total number of friends)

[tex]\( k = 5 \)[/tex] (number of tickets available, hence number of friends to be chosen)

We need to calculate [tex]\(\binom{8}{5}\)[/tex]:

[tex]\[\binom{8}{5} = \frac{8!}{5!(8-5)!} = \frac{8!}{5! \cdot 3!}\][/tex]

First, we calculate the factorials involved:

[tex]\( 8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 40320 \)[/tex]

[tex]\( 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \)[/tex]

[tex]\( 3! = 3 \times 2 \times 1 = 6 \)[/tex]

Now, substitute these values into the binomial coefficient formula:

[tex]\[\binom{8}{5} = \frac{40320}{120 \times 6} = \frac{40320}{720} = 56\][/tex]

Therefore, there are [tex]\( 56 \)[/tex] different combinations of 5 friends that can be selected from the group of 8 friends.

Set the two sets of parentheses in the denominator equal to zero and solve for the x’s. These would be the vertical asymptotes

(X+2) = 0

X = -2

(X-1)=0

X =1

The vertical asymptotes are -2 and 1

To simplify the expression 54, divide it by 2 and 3 to get the simplified result of 9.

To simplify the expression 54, you need to consider the properties of the number 54. First, note that 54 is divisible by 2. Next, check if it is also divisible by 3. If it is, continue dividing by 3 until you can no longer do so. In this case, 54 is divisible by both 2 and 3, so you can simplify it as follows:

Therefore, the simplified expression 54 is equal to 9. So, the correct answer is A. 20.

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Volume of the cylinder is 3696 m²

Step-by-step explanation:

⇒ V = 22/7 × 14² × 6 = 3696 m²

Answer:

Step-by-step explanation:

y−intercept=  

−7

1

​  

=−0.14286

Answer:

y=2/15x-3

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-5-(-3))/(-15-0)

m=(-5+3)/-15

m=-2/-15

m=2/15

y-y1=m(x-x1)

y-(-3)=2/15(x-0)

y+3=2/15(x)

y+3=2/15x

y=2/15x-3

Step-by-step explanation:

[tex] (\frac{3}{2} ) \frac{9}{7} = \frac{3}{2} \times \frac{9}{7} = \frac{27}{14} \\ [/tex]

Answer:

it means 3/2 of 9/7

Step-by-step explanation:

those are fractions

Answer:

A and B

Step-by-step explanation:

A.

The points are (1,2) and (4,8)

(4,8)=4(1,2)

(4,8)∝(1,2)

B.

The points are(1,6)and (3,4)

We don't established any relation between them.

So , there is no relation between them.

C.

The points are (1,6) and (3,4)

We don't established any relation between them.

So , there is no relation between them.

D.

The points are (2,1) and (4,2)

(4,2) = 2(2,1)

(4,2)∝(2,1)

Answer:

No, the expressions are NOT equivalent.

Step-by-step explanation:

Solve each:

11t - 4t

(11 × 2) - (4 × 2)

22 - 8

= 14

4t - 11t

(4 × 2) - (11 × 2)

8 - 22

= -14

14 is NOT equivalent to -14

Answer:

=50x+116

Step-by-step explanation:

5+5x(10)−88+200−1

=5+50x+−88+200+−1

Combine Like Terms:

=5+50x+−88+200+−1

=(50x)+(5+−88+200+−1)

=50x+116

Answer:

166

Step-by-step explanation:

remember order of operations

PEMDAS

parentheses ( )

exponents x^2

multiply or divide (from left to right) * /

add or subtract (from left to right) + -

first step multiply 5*10=50

5+50-88+200-1

next 5+50=55

55-88+200-1

next 55-88= -33

-33+200-1

next -33+200= 167

167-1= 166

Answer:

996 in²

Step-by-step explanation:

The figure is composed of a square and a triangle.

Using Pythagoras' identity on one of the right triangles within the triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides

let the base of the right triangle be x, then

x² + 35² = 37², that is

x² + 1225 = 1369 ( subtract 1225 from both sides )

x² = 144 ( take the square root of both sides )

x = [tex]\sqrt{144}[/tex] = 12

Thus the base of the upper triangle = 2x = 2 × 12 = 24

Area of upper triangle = 0.5 bh ( b is the base and h the height )

Area = 0.5 × 24 × 35 = 12 × 35 = 420 in²

The length of the side of the square is therefore 24 in

Area = 24 × 24 = 576

Total area = 576 + 420 = 996 in²

The value of [tex]\sec\theta =\pm\sqrt{\frac{11}{8}}[/tex].

Solution:

Given data:

[tex]$\tan^2\theta=\frac{3}{8}[/tex]

To find the value of [tex]\sec\theta:[/tex]

Using trigonometric identity,

[tex]\sec^2\theta=1+\tan^2\theta[/tex]

Substitute [tex]\tan^2\theta=\frac{3}{8}[/tex] in the identity, we get

[tex]$\Rightarrow \sec^2\theta=1+\frac{3}{8}[/tex]

1 can be written as [tex]\frac{1}{1}[/tex].

             [tex]$ =\frac{1}{1} +\frac{3}{8}[/tex]

Do cross multiplication.

            [tex]$ =\frac{8}{8} +\frac{3}{8}[/tex]

Denominators are same, so you can add the fractions.

            [tex]$ =\frac{8+3}{8}[/tex]

[tex]$\Rightarrow \sec^2\theta =\frac{11}{8}[/tex]

Taking square root on both sides, we get

[tex]$\Rightarrow \sec\theta =\pm\sqrt{\frac{11}{8}}[/tex]

Option B is the correct answer.

Hence the value of [tex]\sec\theta =\pm\sqrt{\frac{11}{8}}[/tex].

Answer:

Step-by-step explanation:

let x represent the leg length

if we use the Pythagorean theorem we get:

x² + x² = 12²

then

2x² = 12²

Then

x² = 144/2 = 72

then

x = √(72)

 =8,485281374239

Answer:

its A :)

Step-by-step explanation:

Answer:

23/100

Step-by-step explanation:

Any percent is out of 100, so you can just say 23/100. This works for any percentage but you can still simplify it. 23/100 is already in its simplest form so you can not simplify it any more. 23% in decimal form is 0.23.

The correct answer is y=3/2x+4

Answer:

128 yards

Step-by-step explanation:

Final answer:

By applying the Pythagorean theorem to the right-angled triangle sail, with the longest edge being the hypotenuse (16 yards) and the bottom edge as one side (8 yards), the height of the sail is calculated to be approximately 13.856 yards.

Explanation:

To determine how tall the sail is, we can use the Pythagorean theorem if we assume that the sail is a right-angled triangle, which is common in sailboat sails. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. If we let the longest edge (16 yards) be the hypotenuse (c) and the bottom edge (8 yards) be one of the other sides (a), we can find the height (b) of the sail using the equation:

c² = a² + b²

So,

16² = 8² + b²

256 = 64 + b²

b² = 256 - 64

b² = 192

b = √192

b ≈ 13.856 yards (rounding to three decimal places)

Therefore, the sail is approximately 13.856 yards tall.

Answer:

Always write it except if distributing 1. This does NOT apply for -1!

Step-by-step explanation:

Answer:

1.29 minutes

Step-by-step explanation:

The scientist has a record of the amount of rainfall during the afternoon as around 0.43 minutes in each hours.

Now, we have to calculate the total amount of rainfall in three hours.

As the each hour rainfall is of 0.43 minutes, so the total rainfall in three hours will be (0.43 × 3) = 1.29 minutes. (Answer)

Answer:

Step-by-step explanation:

programs can be written in multiply languages. for this solution I'll be writing in C++.

#include<iostream> // this is called the preprocessor definition

using namespace std;

int main()                      //the main function

{

   int num, product;      //declaration of the variables

    cout << "enter the whole number";  

    cin >> num;

    product = num * 12;

     cout << product; // displaying the final results

     return 0;

}

Answer:

5.175

Step-by-step explanation:

Answer:

5.175

Step-by-step explanation:

80

The question implies that you're counting by tens & the number comes after 70 and before 90. This is the only number that fits this description.

Using logical concept, the value of the number in question will be 80.

Let the number be n ;

Hence, we have ;

70, n, 90

n - 70 = 10 - - (1)

90 - n = 10 - - - (2)

Using either of the two expressions, we can obtain the value of n :

n - 70 = 10

n = 10 + 70

n = 80

Hence, the number is 80

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Answer:

5

Step-by-step explanation:

The median is 5. Cross off the dots on both sides one by one until you reach the center.

Answer:

study more that should help you out

Step-by-step explanation:

study more

Answer:

try to study

Step-by-step explanation:

Answer:

i think its 11,700

Step-by-step explanation:

Answer:

11,700

Step-by-step explanation:

When trying to find the new area, you take you 2 numbers, 52 and 15, square the 15,  then multiply them

52 x 15^2 = 11,700

Answer:

          [tex]\large\boxed{\large\boxed{5ft}}[/tex]

Explanation:

A ramp is modeled by a right triangle with hypotenuse equal to the length of the ramp, horizontal leg equal to the ground length(horizontal run), and vertical leg equal to the rise.

Hence, you can use Pythagora's theorem:

            [tex](13ft)^2=(12ft)^2+y^2[/tex]

Solve of the y, which represents the rise:

              [tex]y^2=(13ft)^2-(12ft)^2=169ft^2-144ft^2=25ft^2\\\\y=5ft[/tex]

Final answer:

Using the Pythagorean theorem with the length of the ramp as the hypotenuse (13 feet) and the horizontal distance covered (12 feet), it is determined that the ramp rises 5 feet high.

Explanation:

To determine how high the ramp rises, we can use the Pythagorean theorem, which states that in a right-angled triangle the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (adjacent and opposite).

Let's denote:

Using the Pythagorean theorem:

a² + b² = c²

Substituting the known values:

12² + b² = 13²

144 + b² = 169

To find b, we subtract 144 from both sides of the equation:

b² = 169 - 144

b² = 25

Taking the square root of both sides gives us the height:

b = √25 = 5 feet

Therefore, the ramp rises 5 feet high.

Answer:

Step-by-step explanation:

Let g = amount of general admission tickets

Let s = amount of student tickets

Since seventy people attended the concert, this includes the people who bought general admission tickets and the people who bought the student tickets. As a result, g + s = 70. A student ticket is $3.25, so it would be 3.25s and a general admission ticket is $4.75, so it would be 4.75g. Since there was $272.50 collected in all, the second equation would be 3.25s + 4.75g = 272. 50.

g + s = 70

4.75g + 3.25s = 272.50

Multiply the first equation by 3.25 (or 4.75) so that you can use elimination to get rid of one variable.

3.25g + 3.25s = 227.50

4.75g + 3.25s = 272.50

Now, you subtract so that you can eliminate s.

-1.50g = -45

g = 30

This means that there are 30 general admission tickets. Now, you substitute 30 in for g to find s.

30 + s = 75

Subtract 30 from both sides.

s = 45

This means that there are 30 general admission tickets and 45 student tickets.

Answer: 135cm

Step-by-step explanation

Volume of a cylinder = πr²h

Volume of a cone. = 1/3πr²h

The two shapes are both solid shapes.

Since the have same volume, we can then equate the two together and solve for the height of the cone.

Now make H the height and R the radius of the cylinder and h the height and r the radius of the cylinder.

Now equating the two

πR²H = 1/3πr²h

Now substitute for the values now

Multiply through by 3

3πR²H = πr²h

But π is common so it could be obliterated from the equation

3R²H = r²h

3 x 12² x 20 = 8² x h

3 x 144 x 20 = 64 x h

60 x 144 = 64h

8640. = 64h

Therefore

h = 8640/64

= 135cm

Answer: 35 F

Step-by-step explanation:

night time

let's say the original number is "a".

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{5\% of "a"}}{\left( \cfrac{5}{100} \right)a}\implies \cfrac{5a}{100} \\\\\\ \stackrel{\textit{"a" increased by 5\%}}{a + \cfrac{5a}{100}\implies \cfrac{105a}{100}}~\hfill \stackrel{\textit{5\% of }\frac{105a}{100}}{\left( \cfrac{5}{100} \right)\cfrac{105a}{100}}\implies \cfrac{525a}{10000}\implies \cfrac{21a}{400}[/tex]

[tex]\bf \stackrel{\frac{105a}{100}\textit{ increased by 5\%}}{\cfrac{105a}{100}+\cfrac{21a}{400}}\implies \cfrac{21a}{20}+\cfrac{21a}{400}\implies \cfrac{420a+21a}{400}\implies \cfrac{441a}{400} \\\\\\ 1.1025a\implies 1a+0.1025a\implies \stackrel{\textit{original}}{a} + \stackrel{\textit{10.25\% added}}{\cfrac{10.25}{100}a}[/tex]