Domain and rang of these

Given:

Cost of gift = $20.48

Mark pays for [tex]\dfrac{2}{3}[/tex] of the gift and John pays for the remaining [tex]\dfrac{1}{3}[/tex].

To find:

The amount paid by each boy.

Solution:

We have,

Cost of gift = $20.48

Mark pays for [tex]\dfrac{2}{3}[/tex] of the gift. So, the amount paid by Mark is:

[tex]20.48\times \dfrac{2}{3}\approx 13.653[/tex]

John pays for the remaining [tex]\dfrac{1}{3}[/tex]. So, the amount paid by John is:

[tex]20.48\times \dfrac{1}{3}\approx 6.827[/tex]

Therefore, the amount paid by Mark and John are $13.653 and $6.827 respectively.

Given:

The batting order for nine players on a team with 11 people.

To find:

The number of possibilities for the given scenario.

Solution:

First, we need to select 9 players from 11 people, it involves combination, i.e. [tex]^{11}C_9[/tex].

Second, we need to arrange the order of 9 selected players, it involves permutation, i.e., [tex]^9P_9[/tex].

The number of possibilities for the given scenario is:

[tex]\text{Possibilities}=^{11}C_9\times ^9P_9[/tex]

[tex]\text{Possibilities}=\dfrac{11!}{(11-9)!9!}\times \dfrac{9!}{(9-9)!}[/tex]

[tex]\text{Possibilities}=\dfrac{11\times 10\times 9!}{2!9!}\times \dfrac{9!}{0!}[/tex]

[tex]\text{Possibilities}=\dfrac{110}{2\times 1}\times \dfrac{9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{1}[/tex]

[tex]\text{Possibilities}=55\times 362880[/tex]

[tex]\text{Possibilities}=19958400[/tex]

Therefore, the following scenario involves both permutation and combination, and the number of possibilities is 19958400.

Answer:

h

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

An exponential function is a function where the number is raised to a constant power

exponential function is usually in the form : f(x) = [tex]a^{x}[/tex]

a is positive and not equal to 1

x is a real number

to determine which option is an exponential function, determine which of the options have a common ratio

Option A :

28/7 = 4

49 / 28 = 1.75

option C

12 / 4 = 3

36 /12 = 3

the correct answer is C

Step-by-step explanation:

So here is my attempt. And i guess its correct

which one.

................................

Step-by-step explanation:

................

Answer:

x = 15

Step-by-step explanation:

If A parallel to B then ∠ 2 and ∠ 4 are same- side interior angles and sum to 180° , then

2x + 10 + 4x + 80 = 180 , that is

6x + 90 = 180 ( subtract 90 from both sides )

6x = 90 ( divide both sides by 6 )

x = 15

B. 63

some simple googling would've been able to help you with this. but 0 isn't prime or composite, not sure about 1, 19 is prime, 63 is a definite composite

Answer:

It will take approximately 25 months

Step-by-step explanation:

The amount owed on the credit card statement, P = $2,000

The interest rate of the credit on the credit card, r = 18.9%

The minimum monthly payment made, M = $100

The equal monthly installment formula is given as follows;

[tex]M = \dfrac{P \cdot \left(\dfrac{r}{12} \right) \cdot \left(1+\dfrac{r}{12} \right)^n }{\left(1+\dfrac{r}{12} \right)^n - 1}[/tex]

Therefore, we get;

[tex]100 = \dfrac{2,000 \cdot \left(\dfrac{0.189}{12} \right) \cdot \left(1+\dfrac{0.189}{12} \right)^n }{\left(1+\dfrac{0.189}{12} \right)^n - 1} = \dfrac{2,000 \times\left(0.01575 \right) \cdot \left(1.01575 \right)^n }{\left(1.01575\right)^n - 1}[/tex]

100×1.01575ⁿ - 100 = 31.50×1.01575ⁿ

100×1.01575ⁿ - 31.50×1.01575ⁿ = 100

68.5×1.01575ⁿ = 100

1.01575ⁿ = 100/68.5

n = ln(100/68.5)/ln(1.01575) ≈ 24.21 (which is approximately 25 months, by rounding up to the nearest whole number)

Therefore, it will take approximately 25 months to pay off the credit card debt

Given:

For en exponential function f(a):

[tex]f(-3)=18[/tex]

[tex]f(1)=59[/tex]

To find:

The value of f(0).

Solution:

The general form of an exponential function is:

[tex]f(x)=ab^x[/tex]          ...(i)

Where, a is the initial value and b is the growth/ decay factor.

We have, [tex]f(-3)=18[/tex]. Substitute [tex]x=-3,f(x)=18[/tex] in (i).

[tex]18=ab^{-3}[/tex]            ...(ii)

We have, [tex]f(1)=59[/tex]. Substitute [tex]x=1,f(x)=59[/tex] in (i).

[tex]59=ab^{1}[/tex]            ...(iii)

On dividing (iii) by (ii), we get

[tex]\dfrac{59}{18}=\dfrac{ab^{1}}{ab^{-3}}[/tex]

[tex]3.278=b^{1-(-3)}[/tex]

[tex]3.278=b^{4}[/tex]

[tex](3.278)^{\frac{1}{4}}=b[/tex]

[tex]1.346=b[/tex]

Substituting the value of b in (iii).

[tex]59=a(1.346)^1[/tex]

[tex]\dfrac{59}{1.346}=a[/tex]

[tex]43.83358=a[/tex]

[tex]a\approx 43.83[/tex]

The initial value of the function is 43.83. It means, [tex]f(0)=43.83[/tex].

Therefore, the value of f(0) is 43.83.

Answer:

38

Step-by-step explanation:

To find the value of f(6), we substitute the value 6 where x is into the function. You would get:

7(6) - 4

42 - 4

f(6) = 38

Answer:

See my writting here have answer

Answer:

$5084745.76271

Step-by-step explanation:

Given data

Final amount= $6000000

Rate=6%

Time= 3 years

Now let us find the initial amount which is the principal

using the simple interest formula we have

6000000 = P(1+0.06*3)

6000000 =P(1+0.18)

6000000 =P*1.18

P= 6000000 /1.18

P=$5084745.76271

Hence the initial deposite is $5084745.76271

Answer:

B

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y - 6 = 5(x - 2) ← is in point- slope form

with slope m = 5 → B

Answer:

x² + 2² =(√15)²

x²+ 4. =15

x² =15-4

x² =11

x. =√11 mi

so the answer is 4th option

Answer:

Step-by-step explanation:

MM oute le iloa

Answer:

_____________________________

2 x 5 = 10

2 x 4 = 8

10 + 8 = 18

______________________________

5 + 4 = 9

_______________________________

_ 9 = 18

18 : 9 = 2

Given:

Total number of gym members = 685

257 said they use the treadmill, 157 said they use the elliptical, and 85 said they use both.

To find:

a. The venn diagram.

b. The probability that a member uses the treadmill only?

Solution:

(a)

We have,

Total number of gym members = 685

Treadmill user = 257

Elliptical user = 157

Who use both = 85

Only treadmill user is:

[tex]257-85=172[/tex]

Only Elliptical used

[tex]157-85=72[/tex]

Therefore, the venn diagram for the given situation is shown below.

(b)

The member who use treadmill only = 172

Total user = 685

The probability that a member uses the treadmill only is:

[tex]P(\text{Only treadmill})=\dfrac{\text{Only treadmill users}}{\text{Total users}}[/tex]

[tex]P(\text{Only treadmill})=\dfrac{172}{685}[/tex]

Therefore, the probability that a member uses the treadmill only is [tex]\dfrac{172}{685}[/tex].

Answer:

C. x ≥ -4

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Step-by-step explanation:

Step 1: Define

Identify

-10x ≤ 40

Step 2: Solve for x

Answer:

C. x ≥ -4

Step-by-step explanation:

To solve this inequality isolate the variable. Do this by using the properties of equality, specifically the division property. So, divide both sides by -10. This equals, x ≤ -4. However, whenever an inequality is divided or multiplied by a negative number the sign must be flipped. Therefore, the final answer is x ≥ -4.

Answer:

did i got it correct if yes follow plz

used a graphing tool to, well, graph it

see the solution in the screenshot, it's the point where the two lines intersect

Answer:

P=2.5

Step-by-step explanation:

12p = 25+5

12p = 30

P =30/12

Simplification:

P= 15/6

= 5/2 = 2.5

Answer:

[tex] \rm Numbers = 4 \ and \ -3.[/tex]

Step-by-step explanation:

Given :-

The sum of two numbers is 1 .

The product of the nos . is 12 .

And we need to find out the numbers. So let us take ,

First number be x

Second number be 1-x .

According to first condition :-

[tex]\rm\implies 1st \ number * 2nd \ number= -12\\\\\rm\implies x(1-x)=-12\\\\\rm\implies x - x^2=-12\\\\\rm\implies x^2-x-12=0\\\\\rm\implies x^2-4x+3x-12=0\\\\\rm\implies x(x-4)+3(x-4)=0\\\\\rm\implies (x-4)(x+3)=0\\\\\rm\implies\boxed{\red{\rm x = 4 , -3 }}[/tex]

Hence the numbers are 4 and -3

Step-by-step explanation:

[tex]numbers \: = x \: and \: y \\ x \times y = - 12......(1) \\ x + y = 1..... ..(2) \\y = 1 - x \\ put \: this \: in \: (1) \\ x(1 - x) = - 12 \\ x - {x}^{2} = - 12 \\ - x + {x}^{2} - 12 = 0 \\ factorise \\ {x}^{2} - 4x + 3x - 12 = 0 \\ x(x - 4) + 3(x - 4) = 0 \\ (x - 4)(x + 3) = 0 \\ x = + 4 \: or \: - 3 \\ thank \: you[/tex]

Answer:

[tex]h = 6 + 11 - 22 \\ h = 17 - 22 \\ h = - 5[/tex]

Answer:

-5

Step-by-step explanation:

6+11 = 17↓

17-22 = -5

or

11-22 = -11↓

-11+6 = -5

Answer:

The length of tape to wrap = 5 cm

Step-by-step explanation:

Let the length of tape used to wrap 1 present be = x

Tape length            Number of presents

   15 cm                            3

      x                                 1

     [tex]\frac{15}{x} = \frac{3}{1} \\\\x \times 3 = 1 \times 15\\\\x = \frac{15}{3} = 5 \ cm[/tex]

( f ∘ g ) ( x ) is equivalent to f ( g ( x ) ) . We solve this problem just as we solve f ( x ) . But since it asks us to find out f ( g ( x ) ) , in f ( x ) , each time we encounter x, we replace it with g ( x ) . In the above problem, f ( x ) = x + 3 . Therefore, f ( g ( x ) ) = g ( x ) + 3 . ⇒ ( f ∘ g ) ( x ) = 2 x − 7 + 3 ⇒ ( f ∘ g ) ( x ) = 2 x − 4 Basically, write the g ( x ) equation where you see the x in the f ( x ) equation. f ∘ g ( x ) = ( g ( x ) ) + 3 Replace g ( x ) with the equation f ∘ g ( x ) = ( 2 x − 7 ) + 3 f ∘ g ( x ) = 2 x − 7 + 3 we just took away the parentheses f ∘ g ( x ) = 2 x − 4 Because the − 7 + 3 = 4 This is it g ∘ f ( x ) would be the other way around g ∘ f ( x ) = 2 ( x + 3 ) − 7 now you have to multiply what is inside parentheses by 2 because thats whats directly in front of them. g ∘ f ( x ) = 2 x + 6 − 7 Next, + 6 − 7 = − 1 g ∘ f ( x ) = 2 x − 1

Hello,

[tex]f(x)=7x-3\\g(x)=x^2\\\\(fog)(x)=g(f(x))=g(7x-3)=(7x-3)^2=49x^2-42x+9\\\\(gof)(x)=f(g(x))=f(x^2)=7x^2-3\\\\(fog)(0)=g(f(0))=49*0^2-42*0+9=9\\\\(gof)(0)=f(g(0))=7*0^2-3=-3\\[/tex]

Since i don't know what is (g°O(1)  and you haven't correct your question ,

i has put the 2 possibles answsers.

Answer:

d)

Step-by-step explanation:

>The domain are all the values of x , so you can graph on the calculator that on the x-axis the graph starts at 9 and keeps going to the right so the domain is x≥9 or [9,∞)

or

>Solve for x in the given equation when f(x) =y = 0 to find the roots

√(x-9) = 0 , square both sides

x-9 = 0 , add 9 to both sides

x= 9

from this root the graph moves to the right to ∞

the domain is [9, ∞)

Answer:

[tex]a)\ 5.06 * 10\³[/tex]

[tex]b)\ 6.079 * 10^6[/tex]

[tex]c)\ 3\ crore = 30\ million[/tex]

[tex]d)\ 999999[/tex]

[tex]e)\ 10478[/tex]

[tex]f)\ 78[/tex]

[tex]g)\ 2730[/tex]

Step-by-step explanation:

Solving (a): 5060 as a power of 10

We simply move the decimal between 5 and 6. The number of zeros to move backward is 4.

So,

[tex]5 0 6 0 = 5.06 * 10^3[/tex]

Solving (b): 6079000 as a power of 10

We simply move the decimal between 6 and 0. The number of zeros to move backward is 4.

So,

[tex]6079000 = 6.079 * 10^6[/tex]

Solving (c): 3 crore to millions

[tex]1\ crore = 10\ million[/tex]

Multiply by 3

[tex]3\ crore = 30\ million[/tex]

Solving (d): The greatest 6 digits

The greatest unit digit is 9. So, we simply write out 9 in 6 places

[tex]Greatest= 99999[/tex]

Solving (e): The least 5-digit formed from 4,1,8,0,7

To do this, we start the number from the smallest non-zero digit.

The remaining 4 digits will then be in an increasing order

So, we have:

[tex]Least = 10478[/tex]

Solving (f):

[tex]18 - 7 + 9 * \frac{48}{6} - 5[/tex]

Using BODMAS

Evaluate the division, first

[tex]18 - 7 + 9 * 8 - 5[/tex]

Then multiplication

[tex]18 - 7 + 72 - 5[/tex]

Add up the remaining digits

[tex]78[/tex]

Solving (g): This question is not clear.

I will assume the expression is:

[tex]\frac{72}{ 12}* [ \frac{180}{4}*{10 +(15 - \frac{45}{9}*2)}][/tex]

Evaluate all divisions

[tex]6* [ 45*{10 +(15 - 5*2)}][/tex]

Solve the multiplication in brackets

[tex]6* [ 45*{10 +(15 - 10)}][/tex]

Remove the inner bracket

[tex]6* [ 45*{10 +5}][/tex]

Evaluate 45 * 10

[tex]6* [ 450 +5}][/tex]

Remove the bracket

[tex]6* 455[/tex]

Multiply

[tex]2730[/tex]

That's impossible. There are no solutions.

Answer:

[tex] a_n = 2n^2 + n + 1 [/tex]

Step-by-step explanation:

4, 11, 22, 37, 56

11 - 4 = 7

22 - 11 = 11

37 - 22 = 15

56 - 37 = 19

After the first difference, 11 - 4 = 7, each difference is 4 more than the previous difference.

Difference of differences:

11 - 7 = 4

15 - 11 = 4

19 - 15 = 4

Since we need the difference of differences to find a constant, this must be a second degree function.

[tex] a_1 = 4 = 2^2 + 1(0)[/tex]

[tex] a_2 = 11 = 3^2 + 2 = 3^2 + 2(1) [/tex]

[tex] a_3 = 22 = 4^2 + 6 = 4^2 + 3(2) [/tex]

[tex] a_4 = 37 = 5^2 + 12 = 5^2 + 4(3) [/tex]

[tex]a_5 = 56 = 6^2 + 20 = 6^2 + 5(4)[/tex]

[tex] a_n = (n + 1)^2 + (n)(n - 1) [/tex]

[tex] a_n = (n + 1)^2 + (n)(n - 1) [/tex]

[tex] a_n = n^2 + 2n + 1 + n^2 - n [/tex]

[tex] a_n = 2n^2 + n + 1 [/tex]

[tex] \huge\boxed{\mathfrak{Answer}}[/tex]

[tex]3(x + 4) = 123 \\ 3x + 12 = 123 \\ 3x = 123 - 12 \\ 3x = 111 \\ x = \frac{111}{3} \\ x = 37[/tex]

=> The answer is 37.

Answer:

X=37

Step-by-step explanation:

3(x+4)=123

3x+12=123

3x=123-12

3x=111

3x/3 =111/3

x=37