Expand the following using the Binomial Theorem and Pascal’s triangle (2x − 3y)^4

Answer:

360th customer

Step-by-step explanation:

To find the customer that will receive both the free popcorn and the free movie rental, we have to list the multiples of 40 and 45 until we get a multiple that is the same for both of them.

Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, 440

Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360

360 is the first multiple that is same for multiples of 40 and 45

So the 360th customer will receive both items.

(Sorry if my explanation is hard to understand. I haven't done this kind of math in a while)

Hope it helps (●'◡'●)

Answer:

4th option

Step-by-step explanation:

If ∠ 1 = ∠ 2 = ∠ 3

Then ∠ 1 = ∠ 3 is true

Answer:

The second one the measure of angle?1 is less then angle 3 is the correct answer.

Answer:

25

Step-by-step explanation:

You need to simplify

.

.

.

.

................... :)

Answer:

D

Step-by-step explanation:

9+24-16+8= 25

Answer:

United States, Canada, Dominican Republic, Cuba, Venezuela, Japan, Panama

Step-by-step explanation:

Taking a look at a list of Major League Baseball most valuable players, the countries are:

United States(most players are US-born).

Canada(Joey Votto in 2010).

Dominican Republic(Albert Pujols and Vlad Guerrero Sr. for example).

Cuba(last Jose Abreu in 2020)

Venezuela(last Jose Altuve in 2017)

Japan(Ichiro in 2001).

Panama(Rod Carew)

Answer:

1. [tex]x=2[/tex]

2. Simplify by combining like terms

3. [tex]x=1[/tex]

4. [tex]k=0.5[/tex]

5. [tex]y=3[/tex]

Step-by-step explanation:

1. [tex]2.5(6x-4)=10+4(1.5+0.5x)[/tex]

Distribute within the parenthesis

[tex]15x-10=10+6+2x[/tex]

Combine like terms

[tex]15x-10=16+2x[/tex]

Isolate the variable expression by using the addition/subtraction properties of equality

[tex]13x=26[/tex]

Isolate the variable by using the division/multiplication properties of equality

[tex]x=2[/tex]

2. Like terms are always combined as soon as possible but never before the distributive property is applied.

3. You can find the solution by comparing the tables.

4. [tex]6k+10.5=3k+12[/tex]

Apply the addition/subtraction properties of equality

[tex]3k=1.5[/tex]

Apply the division/multiplication properties of inequality

[tex]k=0.5[/tex]

5. [tex]y+3=-y+9[/tex]

Addition/subtraction properties

[tex]2y=6[/tex]

Division/Multiplication properties

[tex]y=3[/tex]

This is because the nth term is found by adding the previous two terms

F(n) = nth term

F(n-1) = term just before the nth term

F(n-2) = term before the F(n-1) term

F(n) = F(n-1) + F(n-2)

We can re-index values of n to say this equivalent statement

F(n+2) = F(n+1) + F(n)

Based on either equation mentioned, adding F(51) and F(52) will get us F(53). In other words, the 51st and 52nd terms add to the 53rd term.

Answer:

175 + 30h

Step-by-step explanation:

Hope this helps

Answer:

total cost = 175+30h

Step-by-step explanation:

Total cost = fixed cost + cost per hour * hours

total cost = 175+30h  where h is the number of hours

Answer:

35/40

Step-by-step explanation:

To compare, both denominator should be same.

[tex]\frac{15}{20}=\frac{15*2}{20*2}=\frac{30}{40}\\\\\\\frac{30}{40} \ < \ \frac{35}{40}\\\\\\\frac{15}{20} \ < \ \frac{35}{40}[/tex]

[tex]\sf{\bold{\blue{\underline{\underline{Given}}}}}[/tex]

[tex]\sf{\bold{\red{\underline{\underline{To\:Find}}}}}[/tex]

⠀⠀⠀⠀

[tex]\sf{\bold{\purple{\underline{\underline{Solution}}}}}[/tex]

we have to find the greater number between 15/20 and 35/40

To do this,

we have to compare the denominator same.

According to the question,

we have to find the greatest one

[tex]\sf{\bold{\green{\underline{\underline{Answer}}}}}[/tex]

⠀⠀

[tex]\therefore\mathrm{\dfrac{35}{40} > \dfrac{15}{20} }[/tex]

⠀⠀

Hello,

It is the Fibonacci 's suit.

[tex]u_1=5\\u_2=4\\u_3=u_1+u_2=5+4=9\\u_4=u_2+u_3=4+9=13\\u_5=u_3+u_4=9+13=22\\u_6=13+22=35\\u_7=22+35=57\\u_8=35+57=92\\u_9=57+92=149\\\\\\\boxed{u_{n+2}=u_{n}+u_{n+1}}\\[/tex]

Answer:

B

Step-by-step explanation:

Firstly, we solve for x

-x ≥ 2 * 4

-x ≥ 8

Multiply both sides by -1

x ≤ -8

So we look at the inequality represented by this;

We can see that the correct inequality is option B;

Answer:

(1/3) r2 =(1/3) r +14

1/6 divided by 83 r + 14

97r

i think...

I hope this helps you!

XoXo Mashayla

Step-by-step explanation:

Answer:

(a + 1) (b + 2 ) = 2a + b + ab + 2

Step-by-step explanation:

[tex](a +1 )(b + 2) \\\\= a( b+ 2) + 1 (b +2) \\\\= ab + 2a + b + 2\\\\=2a + b + ab + 2[/tex]

[tex](a + 1)(b + 2) \\ = a(b + 2) + 1(b + 2) \\ = ab + 2a + b + 2[/tex]

Answer ↦ [tex]\boxed{\tt{ab + 2a + b + 2}}[/tex]

↦ Distributive Property.

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

Answer:

[tex]10^2a^2b[/tex]

Step-by-step explanation:

Exponents are a way of shortening multiplication statements. The exponent represents how many times a term is being multiplied by itself. So, when two terms have the same base it can be written with exponents. For example. 10*10 can be written as [tex]10^2[/tex] because 10 is being multiplied 2 times. Therefore, if we do this with every term you get [tex]10^2a^2b[/tex].

Answer:

Step-by-step explanation:

Answer:

143

Step-by-step explanation:

to find the area we multiply half of the sum of the bases with height

(18+8)/2*11 = 143

2^5 = 32

Hope this helps! :)

Answer:

32

Step-by-step explanation:

[tex]2^{5}[/tex]

= 2 × 2 × 2 × 2 × 2

= 4 × 4 × 2

= 16 × 2

= 32

Answer:

4

Step-by-step explanation:

The greatest number of plates Jill can split the 20 cookies and 12 brownies into can be determined by calculating the highest common factor and 20 and 12

Factors of 12 = 1, 2, 3, 4, 6, 12

Factors of 20 = 1, 2,4, 5, 10, 20

Answer: $32

Step-by-step explanation:

Since the boutique was having a 20% storewide sale and Erica bought 2 dresses which originally cost $80 each, therefore the sale for each dress will be:

= $80 - (20% × $80)

= $80 - (0.2 × $80)

= $80 - $16

= $64

Therefore, on each dress Erica saves $16. The amount of savings enjoyed will then be:

= $16 × 2

= $32

Answer:

x=29°

Step-by-step explanation:

as lines are parallel.

external alternate angles are equal.

7x-86=4x+1

7x-4x=1+86

3x=87

x=87/3=29

Explanation:

If the diagonals are congruent, then we'd have a rectangle. Any rectangle is a parallelogram, but not the other way around.

If we had a non-rectangular parallelogram, with none of the angles 90 degrees, then the diagonals will not be the same length.

Choices A, C and D are true for any parallelogram (rectangle or not).

Answer:

Father=41

Son=19

Step-by-step explanation:

Father=f

Son=s

f+s=60

Eight years ago would mean that 16 is subtracted from 60 since there is both of them

3s+s=4s

4s=44

s=11

11+8=19

33+8=41

First graph is the correct one.

when x= 1

y=f(x) = -√1 = -1

when x= 2

y= -√2

Answer:  30 cans (buy them by the six-pack; so you'd buy 5 six-packs)

==============================================================

Explanation:

Let's say you buy six-packs only. Divide the amount of money you have over the cost per six-pack.

15/(2.59) = 5.7915 which rounds down to 5.

If you buy six-packs only, then you can buy a max of 5 of them. That gets you 5*6 = 30 cans of soda.

-------------

Now let's say you buy individual cans only. We'll use the same idea mentioned earlier but this time divide over 0.80

15/(0.80) = 18.75 which rounds down to 18

We round down because we can't buy that 19th can of soda (note how 19*0.80 = 15.2 which is larger than 15).

So if you buy individual cans only, then you can get a max of 18 cans.

We see that it's better to go with the six-pack option (in the first section) since we can get 30 cans compared to 18 cans.

Answer:

18

Step-by-step explanation:

42+12= 63

63/7=9

9*2=18

Answer:

18

Step-by-step explanation:

plato/edmentum

Answer:

Step-by-step explanation:

[tex]\frac{14}{4}*\frac{33}{10}=\frac{7}{2}*\frac{33}{10}\\\\ =\frac{7*33}{2*10}\\\\=\frac{231}{20}\\\\=11\frac{11}{20}[/tex]

Answer:

-64 is the 26th number

it's an arithmetic sequence because the difference between the number is constant : -3

they are all -3 in difference

Step-by-step explanation:

an = a1 + (n-1)d

an = the nᵗʰ term in the sequence

a1=the first term in the sequence

d=the common difference between terms

-64 = 11 + (n - 1)-3

-64=11 -3n+3

-78 = -3n

n = 26

===========================================================

Explanation:

Let's label the friends as A,B,C,D.

Person A has a probability of 7/16 when it comes to ordering a certain color of cotton sweatshirt.

Then 6/15 is the probability for person B. Note how the 7 and 16 drop by 1 for each. This is because no repeats are allowed. If person A goes for a blue sweatshirt, then person B cannot select blue as well.

Person C's probability is 5/14 and person D has a probability of 4/13

-------------------------

So we have these fractions: 7/16, 6/15, 5/14, 4/13

Once again, we have the numerators and denominators counting down by 1 each time.

Multiplying those fractions gets us...

(7/16)*(6/15)*(5/14)*(4/13)

(7*6*5*4)/(16*15*14*13)

840/43680

(1*840)/(52*840)

1/52

So if you did 52 trials of this, then you should expect about 1 of those trials is where each friend orders a different color cotton sweatshirt.

1/52 = 0.0192 = 1.92% approximately

So this happens about 1.92% of the time.

Answer:

The number of ways is 26,400 ways

Step-by-step explanation:

Given;

total number of men, M = 10

total number of women, W = 12

number of committees to be formed = 6

If there must be equal gender, then it must consist of 3 men and 3 women.

[tex]The \ number \ of \ ways = 10C_3 \times 12C_3\\\\The \ number \ of \ ways =\frac{10!}{3!7!} \times \frac{12!}{3!9!} \\\\T he \ number \ of \ ways = 120 \times 220 = 26,400 \ ways[/tex]

Therefore, the number of ways is 26,400 ways

This triangle is an isosceles triangle because it has two congruent sides. Therefore, the two bottom angles are also congruent. And, the sum of the interior angles of a triangle is 180 degrees.

180 = 104 + (9x - 25) + (9x - 25)

180 = 104 + 18x - 50

180 = 54 + 18x

126 = 18x

x = 7

Hope this helps!

Answer:

Step-by-step explanation:

The range is the set of y-values.

The graphed function has its range between 0 and 7, both inclusive.

So the range is: