- X, what is the value of (f - g)(2)?

Answer:

17C5+11C5

Step-by-step explanation:

Well there are 17 and chooses 5 that's 17C5

there are 11 men abd chooses 5 that's 11C5

so add them up

17C5+11C5

The combination helps us to know the number of ways an object can be selected without a particular manner. The number of ways in which 5 men and 5 women can be selected is 2,858,856.

Permutation helps us to know the number of ways an object can be arranged in a particular manner. A permutation is denoted by 'P'.

The combination helps us to know the number of ways an object can be selected without a particular manner. A combination is denoted by 'C'.

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

where,

n is the number of choices available,

r is the choices to be made.

Given that from a group of 17 women and 11 men, a researcher wants to randomly select 5 women and 5 men for a study.

Now, the number of ways for selection can be written as,

Number of ways in which men can be selected = ¹¹C₅ = 462

Number of ways in which women can be selected = ¹⁷C₅ = 6188

Further, the number of ways for selection can be written as,

Number of ways = Number of ways in which men can be selected × Number of ways in which women can be selected

Number of ways = 462 × 6188

Number of ways = 2,858,856

Hence, the number of ways in which 5 men and 5 women can be selected is 2,858,856.

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Answer:

88 cm

Step-by-step explanation:

Perimeter = 2πr

=2(14)(22/7)

= 88 cm

Answer:

87.97cm

Step-by-step explanation:

This question is asking to solve for the circumference.

The formula for the circumference of a circle is:  [tex]\pi*diameter[/tex]

To work this out you would first need to multiply the radius of 14 by 2, this gives you 28cm. This is because the radius is half of the diameter.

The final step is to multiply pi by the diameter of 28, this gives you 87.97cm (87.9645943). This is because the formula for the circumference of a circle is [tex]\pi * diameter[/tex].

1) Multiply 14 by 2.

[tex]14*2=28[/tex]

2) Multiply pi by the diameter.

[tex]\pi*28^2=87.97 cm[/tex]

Answer:

[tex]\Large \boxed{\mathrm{When \ a \ number \ is \ not \ known}}[/tex]

Step-by-step explanation:

For example, a sum of a number and 6 is 12.

The number is unknown.

Let the number be x.

We can solve for x (unknown number). Subtract 6 from both sides of the equation.

Answer: 1880 pounds

Step-by-step explanation: when you take the average adult weight, around 160 lbs. you multiply that by eight. you get 1280. then you estimate that each of the children weigh around 100 lbs, then you add 600 to 1280 and get 1,880 lbs

Answer:

23

Step-by-step explanation:

Take the amount of money and divide by the hour

46/2 = 23

23 dollars for every hour

The constant of proportionality is 23

verifying, by putting [tex] \theta=60^{\circ}[/tex]

LHS≠RHS

hence the question is FALSE

Answer:

This event is independent this statement is true because we cannot control the motion of a dice.

Step-by-step explanation:

Hope it will help you :)

Answer:I'm pretty sure it's independent

Answer:

Below

Step-by-step explanation:

Notice that x is between 10 and -10 but takes only the values that are integers.

The inequalities:

● we can write an inequality that includes all these values.

● -10 《 x 《 10

This is a possible inequality

Multiply both sides by 2 and you will get a new one:

● -20 《 2x 《 20

You can multiply it by any number to generate a new inequality.

Or you can add or substract any number.

Answer:

Step-by-step explanation:

We first need to find h. Since h is the x coordinate of Q, and Q is on the line 3x + 4y = 6, we will plug in the x value of h and the y value of 3 and solve for h:

3h + 4(3) = 6 and

3h + 12 = 6 and

3h = -6 so

h = -2

The coordinates for Q are (-2, 3). Now we can use that to find the slope of the line QR:

[tex]m=\frac{8-3}{3-(-2)}=\frac{5}{5}=1[/tex]

So the slope of QR is 1. Now we will choose one of the coordinates on line QR as our x and y coordinates to write the equation for the line in point slope form then in standard form:

y - 8 = 1(x - 3) and

y - 8 = x - 3 and

y - x = 5 or

-x + y = 5. If your teacher does not want you to lead with a negative:

x - y = -5 would be your equation in standard form.

Answer:

1. Write both ratios as fractions and reduce them completely. If they are the same fraction, the ratios form a proportion.

2. Write both ratios as fractions. Do the cross products by multiplying the denominator of each fraction by the numerator of the other fraction. If the cross products are equal, the ratios form a proportion.

Answer:

(7, 5)

Step-by-step explanation:

(x+5)/2, ( y-3)/2)=(6,1)

(x+5)/2=6, x= 7

( y-3)/2=1, y=5

Answer:

Step-by-step explanation:

[tex]9^{-4}[/tex]

=[tex]\frac{1}{9^{4} }[/tex]                   ∴     [tex]x^{-n} = \frac{1}{x^{n} }[/tex]

=[tex]\frac{1}{9*9*9*9}[/tex]

=[tex]\frac{1}{6561}[/tex]

Hi there! :)

Answer:

[tex]\huge\boxed{m\leq 2}[/tex]

Equation:

8m - 6 ≤ 10

Add 6 to both sides:

8m ≤ 16

Divide both sides by 8:

8m/8 ≤ 16/8

m ≤ 2

Answer:

8m - 6≤ 10

m≤2

Step-by-step explanation:

8m - 6≤ 10

Add 6 to each side

8m - 6+6≤ 10+6

8m ≤ 16

Divide each side by 8

8m/8 ≤16/8

m≤2

Answer:

see below (I hope this makes sense!)

Step-by-step explanation:

Constants, as the name suggest, stay constant, meaning that their value never changes. For example, 2 will always be 2 and 9.4 will always be 9.4. On the other hand, the values of variables can change. Take, for example, the variable 2x. When x = 1, 2x = 2 and when x  =2, 2x = 4 so the value of 2x can change depending on what x is. You can't combine constants and variables because they are not like terms, basically, one can change and the other can't and you cannot combine terms that are not like each other.

Answer:

Surface area of a cone = 461.58 In²

Step-by-step explanation:

Surface area of a cone = πrl + or

Surface area of a cone = πr(r+l)

Where r = radius

Radius= diameter/2

Radius=14/2

Radius= 7 inch

And l slant height= 14 inch

Surface area of a cone = πr(r+l)

Surface area of a cone = π*7(7+14)

Surface area of a cone = 7π(21)

Surface area of a cone = 147π

Surface area of a cone = 461.58 In²

Answer:

-6xy - 16x -24y -64

Step-by-step explanation:

(2x+8)(-3y-8) =

To find the answer,

First multiply, the first number on both sides,

2x * -3y = -6xy

Then the first number on the left side and the second number on the right side,

2x * -8 = -16x

Then the second number on the left side and the first number on the right side,

8 * -3y = -24y

Then the second number on the left side and the second number on the right side,

8 * -8 = -64

Now add all the answers,

-6xy -16x -24y -64

Answer:

-6xy-16x-24y-64

Step-by-step explanation:

(2x+8)(-3y-8)​

Foil

First 2x*-3y = -6xy

outer -8*2x = -16x

inner -3y *8 = -24y

last -8*8 = -64

Add them together

-6xy-16x-24y-64

Answer:

-10.

Step-by-step explanation:

f(x) = 2x, x = -5.

f(-5) = 2(-5)

= 2 * (-1) * 5

= 10 * (-1)

= -10.

Hope this helps!

Answer:

11.21157846 =x

Step-by-step explanation:

We know log b (a) = c  can be written as b^c =a

log 3 (x) = 2.2

3^2.2 = x

11.21157846 =x

Answer:

[tex]\large \boxed{\sf \bold{A.} \ x=11.21}[/tex]

Step-by-step explanation:

[tex]\large \sf log_3 (x)=2.2[/tex]

Solve this by converting the logarithmic statement into its equivalent exponential form, using the relationship:

[tex]\large \sf log_b(y)=x[/tex]

[tex]\large{\sf y=b^x}[/tex]

Apply the relationship.

[tex]\large \sf log_3 (x)=2.2[/tex]

[tex]\large \sf x=3^{2.2}[/tex]

[tex]\large \sf x=11.21157845...[/tex]

[tex]\large \sf x \approx 11.21[/tex]

For a given initial quantity A, a decrease of x% can be written as:

A - A*(x%/100%) = A*(1 - x%/100%)

With this, we need to construct an exponential decrease equation for the given situation, and we will find that the equation is:

P(t) = 300*(0.77)^t

Now let's see how we found that.

In this case, we know that:

The initial number of animals is 300.

They decrease at an anual rate of 23%.

This means that after the first year, the population will be:

P(1) = 300 - 300*(23%/100$) = 300*( 1 - 0.23) = 300*(0.77)

After another year, the population decreases again, so we get:

P(2) = 300*(0.77) - 300*(0.77)*(23%/100$) = 300*(0.77)^2

Here we already can see the pattern, the population in the year t, we will get:

P(t) = 300*(0.77)^t

Then we can see that the correct option is C.

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Answer:

Area : 14+10+40=64 square unit

Step-by-step explanation:

the area of the top rectangle with sides  2 and 7

A=2*7=14 square unit

the area of the middle rectangle with sides : (7-5)=2 and side (7-2)=5

Area=5*2=10 square unit

the bottom rectangle : sides 10 and 4

Area=10*4=40

add the areas : 14+10+40=64 square unit

Answer: 17.5 miles

Step-by-step explanation:

P=price, L=length

Firm A:

P=2L+10

Firm B:

P=2.40L+3

2.40L+3=2L+10

L=17.5

The fare would be the same for 17.5 miles for both firms.

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here, Firm A charges £20 for a 5 mile journey and £30 for a 10 mile journey . let the fixed component of the fare be k and charge for travelling per mile be x then we have,     20=5x+k. . . (1)

                                                   30=10x+k. . . .(2)

solving these two equations we get x=2 and k = 10

Now let the length of the journey that both firm charge the same is equal to  L and given here that firm B charges a pickup fee of £3 and then £2.40 for each mile travelled. Thus forming the equations we get

2L+10=2.40L+3

0.40L=7

      L=17.5

Hence, The fare would be the same for 17.5 miles for both firms.

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Answer:

Question 2;

A. 25·x²·y²²

Question 3;

f(g(x)) = 4·x, represents the amount Aurora earns per hour

Step-by-step explanation:

Question 2;

(5·x·y⁵)²(y³)⁴ = (25×x²×y¹⁰)×y¹²

(25×x²×y¹⁰)×y¹² = 25×x²×y¹⁰⁺¹² = 25×x²×y²²

Therefore, the correct option is A. 25·x²·y²²

Question 3;

The given functions are;

The function f(x) = 0.5·x is the earnings of Aurora per ticket sold

The function g(x) = 8·x is the number of tickets Aurora sells per hour

Therefore, we have;

f(g(x)) = 0.5 × g(x) = 0.5 × 8·x = 4·x

The value of the function of a function f(g(x)) = 4·x, represents the amount Aurora earns per hour.

Answer:

n³ - 7

Step-by-step explanation:

n³ - 7

The required expression for the 7 subtracted from the cube of a number is x³- 7.

Given that,
A string of statements is given,
Here, we have to transform the statement, 7 is subtracted from the cube of a number into a mathematical inscription.

Arithmetic, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

A mathmetical expression is formulated structure of a statement using variables.

Let the number be x,
Now 7 subtracted from the cube of number x
= x³ - 7

Thus, the required expression for the 7 subtracted from the cube of a number is x³- 7.

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Answer:

--1-- (of set 23456)

2   4

5 3

 6

--2-- (of set 23456)

2   3

5 4

 6

--3-- (of set 23456)

2   5

6 3

 4

--4-- (of set 23456)

2   3

6 5

 4

--5-- (of set 23456)

3   5

4 2

 6

--6-- (of set 23456)

3   2

4 5

 6

--7-- (of set 23456)

3   6

5 2

 4

--8-- (of set 23456)

3   2

5 6

 4

--9-- (of set 23456)

3   5

6 4

 2

--10-- (of set 23456)

3   4

6 5

 2

--11-- (of set 23456)

4   5

3 2

 6

--12-- (of set 23456)

4   2

3 5

 6

--13-- (of set 23456)

4   6

5 3

 2

--14-- (of set 23456)

4   3

5 6

 2

--15-- (of set 23456)

5   4

2 3

 6

--16-- (of set 23456)

5   3

2 4

 6

--17-- (of set 23456)

5   6

3 2

 4

--18-- (of set 23456)

5   2

3 6

 4

--19-- (of set 23456)

5   6

4 3

 2

--20-- (of set 23456)

5   3

4 6

 2

--21-- (of set 23456)

6   5

2 3

 4

--22-- (of set 23456)

6   3

2 5

 4

--23-- (of set 23456)

6   5

3 4

 2

--24-- (of set 23456)

6   4

3 5

 2

--1-- (of set 34567)

3   5

6 4

 7

--2-- (of set 34567)

3   4

6 5

 7

--3-- (of set 34567)

3   6

7 4

 5

--4-- (of set 34567)

3   4

7 6

 5

--5-- (of set 34567)

4   6

5 3

 7

--6-- (of set 34567)

4   3

5 6

 7

--7-- (of set 34567)

4   7

6 3

 5

--8-- (of set 34567)

4   3

6 7

 5

--9-- (of set 34567)

4   6

7 5

 3

--10-- (of set 34567)

4   5

7 6

 3

--11-- (of set 34567)

5   6

4 3

 7

--12-- (of set 34567)

5   3

4 6

 7

--13-- (of set 34567)

5   7

6 4

 3

--14-- (of set 34567)

5   4

6 7

 3

--15-- (of set 34567)

6   5

3 4

 7

--16-- (of set 34567)

6   4

3 5

 7

--17-- (of set 34567)

6   7

4 3

 5

--18-- (of set 34567)

6   3

4 7

 5

--19-- (of set 34567)

6   7

5 4

 3

--20-- (of set 34567)

6   4

5 7

 3

--21-- (of set 34567)

7   6

3 4

 5

--22-- (of set 34567)

7   4

3 6

 5

--23-- (of set 34567)

7   6

4 5

 3

--24-- (of set 34567)

7   5

4 6

 3

Step-by-step explanation:

This javascript code is extremely brute-force, but it does the job:

function checkIfInSet(i, set) {

   return i.toString().split('').sort().join('') === set;

}

function checkIfMagic(s) {

   return (parseInt(s[0]) + parseInt(s[1]) == parseInt(s[3]) + parseInt(s[4]))

}

function printMagic(s) {

   console.log(`${s[0]}   ${s[4]}`);

   console.log(` ${s[1]} ${s[3]}`);

   console.log(`  ${s[2]}\n`);

}

function checkSet(set) {

   let counter = 1;

   for(let i=1; i<99999; i++) {

       if (checkIfInSet(i, set) && checkIfMagic(i.toString())) {

           console.log(`--${counter++}-- (of set ${set})`);

           printMagic(i.toString());

       }

   }

}

checkSet('23456');

checkSet('34567');

Answer:

80 feet

Step-by-step explanation:

1 inch represents 10 feet

Then 8 inches represent = 8 × 10

= 80 feet

Answer:

The answer is

Step-by-step explanation:

The distance between two points can be found by

[tex] \sqrt{ ({x _{1} - x_{2} })^{2} + ({y_{1} } - y_{2} )^{2} } [/tex]

where

( x1 , y1) and ( x2 , y2) are the points

So the distance between (-4,4) and (1,0) is

We have the final answer as

Hope this helps you

Answer:

3rd option is correct

Step-by-step explanation:

If the table represents a function, that means that it is proportional. But the value increases and decreases, showing no proportional relationship.

So, the answer could be 1st or 3rd as they tell that the table doesn't represent a function.

1st answer says the table doesn't represent a function because the 2 (y-values) are similar;

Their x-values are different so, this answer is wrong.

3rd answer says that the table doesn't represent a function x-value increases, while y-value increases and decreases;

The statement is correct because it this table doesn't represent a proportional relationship as its y-values are increasing and decreasing while its x-values are only increasing.

So, the 3rd option is correct.

Answer:

Quaterly

Step-by-step explanation:

Answer:

[tex]3 \sqrt{2} [/tex]

Step-by-step explanation:

[tex] \frac{6}{ \sqrt{2} } = \frac{6}{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } = \frac{6 \sqrt{2} }{2} = 3 \sqrt{2} [/tex]

We can't have a fraction that has a number under square root as it's denominator. So we will have to rationalize it, which means we will multiply the numerator and also the denominator by the number that is under the square root.

Hope this helps ;) ❤❤❤

Answer:

[tex]\boxed{\sf 3\sqrt{2}}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{6}{\sqrt{2} }[/tex]

[tex]\sf Multiply \ both \ numerator \ and \ denominator \ by \ \sqrt{2}[/tex]

[tex]\displaystyle \frac{6 \times \sqrt{2} }{\sqrt{2} \times \sqrt{2} }[/tex]

[tex]\displaystyle \frac{6\sqrt{2} }{2 }[/tex]

[tex]\sf Simplify[/tex]

[tex]3\sqrt{2}[/tex]

Answer:

18

Step-by-step explanation:

3⋅6−2+2​

Use PEMDAS = Parentheses, Exponent, Multiplication, Division, Addition, Subtraction

First we multiply, then add or subtract so,

18 - 2 + 2

Now we subtract,

16 + 2

Now we add,

18