Recal the binomial theorem:
[tex]\displaystyle (a+b)^n = \sum_{k=0}^n \binom nk a^{n-k} b^k[/tex]
Then
[tex]\displaystyle (2q+p)^{21} = \sum_{k=0}^{21} \binom{21}k (2q)^{21-k} p^k = \sum_{k=0}^{21} \binom{21}k 2^{21-k} q^{21-k} p^k[/tex]
We get the q⁴p¹⁷ term when k = 17, and its coefficient would be
[tex]\dbinom{21}{17} 2^{21-17} = \dfrac{21!}{17!(21-17)!} 2^4 = \dfrac{21\cdot20\cdot19\cdot18}{4\cdot3\cdot2\cdot1}\cdot2^4 = \boxed{95,760}[/tex]
A restaurant keeps eggs in a rack that has 5 layers each layer has 5 row with 5 eggs in each row
What is 2 hundredths in standard form in fifth grade
0.02
0._ is tenths and
0.0_ is hundredths
Answer:
Step-by-step explanation:
5th Grade Math 1.2, Place Value of Whole Numbers, Standard Form ... this is the name of the video. I hope it helps.
Order from greatest to least: 3.008,3.825,3.09,3.18
Answer:
G: 3.825
3.18
3.09
L: 3.008
Step-by-step explanation:
G is greatest, L is least.
Hope this helps!
Find the surface area! Please I need it quick
Step-by-step explanation:
We first find the area of a trapezium and rectangular faceFourmula to find the are of a trapezium is:Area=1/2*(B+b)*h =1/2*3.7*1.9 =3.515m²Since every rectangular face is different we gotta find each of themArea1=4.8*2.1 =10.08 m²Area2=4.8*1.4=6.72m²Area3=4.8*2.3=11.05m²Area4=4.8*1.9=9.12m²Now we find the area of the whole prismArea=3.515*2+10.08+6.72+11.05+9.12Area=44m²Sorry my wireless went down!!!Hope this helps and you already know what I would like to gethow to solve this.im stuck in this question for 20 mins. Plzz answer
Answer:
Find the minimum or maximum value of the function g (I) = -3x^2 - 6x + 5. Describe the domain and range of the function, and where the function is increasing and decreasing. > -1 all real numbers The function The maximum value is I < 0 The domain is and the range is right of I left -1 is increasing to the of I= and decreasing to the 0 12 :: yo y0 :: 8 :: IS-1 :: -1 :: 0 :: I> 0 :: 1 :: 8 :: < 0 :: left :: all real numbers :: y -8 :: y < 8 :: y8
Step-by-step explanation:
Lin is baking cakes. Each cake needs 34 cup of brown sugar, and Lin uses 412 cups of brown sugar for the entire batch of cakes. How many cakes does Lin bake?
Answer:
12
Step-by-step explanation:
412 ÷ 34 = 12.1176...
Round down to 12 cakes
If Each cake needs 34 cup of brown sugar, and Lin uses 412 cups of brown sugar for the entire batch of cakes then Lin can bae 12 cakes.
What is Division?A division is a process of splitting a specific amount into equal parts.
Given that Lin is baking cakes. Each cake needs 34 cup of brown suga
Lin uses 412 cups of brown sugar for the entire batch of cakes
We need to find the number of cakes Lin bake with 412 cups of brown sugar.
To find this we have to divide 412 by 34 cup.
412/34
Four hundred twelve by thirty four
12.111
Hence, if Each cake needs 34 cup of brown sugar, and Lin uses 412 cups of brown sugar for the entire batch of cakes then Lin can bae 12 cakes.
To learn more on Division click:
https://brainly.com/question/21416852
#SPJ2
PLS HELP WILL MARK BRAINLIEST!
Answer:
10 adultsStep-by-step explanation:
Convert 50 kg into pounds:
50*2.2 = 110 lbsNumber of adults the elevator can take:
1200 / 110 = 10 (rounded down)Answer:
The Elevator can hold 10 adults
Step-by-step explanation:
Step 1- Convert kg to lbs to get 110lbs
Step 2- Divide 1200 (the elevators max compacity) by 110 to get 10
Step 3- The elevator can hold 10 adults
-Rocketgamer360
Daniel is a piano teacher. He charges the same amount, s, for every teaching session. After 19 sessions, he has earned $1,235. How much does Daniel charge for 1 teaching session? Write a division equation.
Answer:
£65
Step-by-step explanation:
1235 / 19 = 65
(Meeting character limit)
giving Brainliest to whoever answer both
Justine and Kate are training for a race.
At every training session Justine runs x miles and Kate runs 3 more miles than Justine.
In one week, Justine and Kate both train every day.
In the 7 days they run 63 miles in total between them.
How many miles do Justine and Kate each run per day?
Answer:
Justine runs 3 miles a day and Kate runs 6 miles a day.
Step-by-step explanation:
x = number of miles ran in a day
x(7) + (x+3)(7) = 63
7x + 7x + 21 = 63
14x + 21 = 63
14x = 42
x = 3
3 + 3 = 6
Justine runs 3 miles a day and Kate runs 6 miles a day.
Please help me! :D <3
Answer:
Well 5 times 1 is 2.5 which can't be and integer
so I looked it up an this is what I got How do you write 2.5 as an integer?
If this is the question, then Integer-Part[2.5] = 2, and the Fractional-Part[2.5] = . 5.
I would put 3 it because 2.5 as a hole number is 3
Step-by-step explanation:
YALL I RLLY DONT KNOW HOW I HAVE 13 OVERDUE ASSIGNMENTS BUT PLEASE HELPING ME JUST ON MATH would make my day....
Answer:
Should be second option: (-6.5,-3.5)
The actual coordinates are (-6.4,-3.6) but the points are rounded.
Step-by-step explanation:
Since these two lines are both in slope-intercept form, all you have to do is graph them, and what ever point they cross each other at, is the solution to this system of equations. (Hint: you can also go online and search desmos graphing calculator, to see how it's graphed, for additional help).
(I've graphed and labeled them for you above btw⤴⤴⤴)
Hope this helps you :)
HELPPP!!!! Both questions are incredibly confusing to me !!!!!
Answer:
Step-by-step explanation:
I'm going to start with problem 3. You need to become familar with the kind of tricks teachers play on you.
Problem 3 depends on getting RS = RW.
RT = RT Reflexive property
<STR = <WTR A straight line having 1 rt angle actually has 2
ST = TU They are marked as equal
Triangle STR=Triangle WTR SAS
RS = RW Corresponding parts of = triangles are =
8x = 6x + 5 Subtract 6x from both sides
8x -6x = 6x - 6x + 5 Combine
2x = 5 Divide by 2
2x/2 = 5/2
x = 2.5
RU = 6*2.5 + 5
RU = 15 + 5
RU = 20
Now we can play with Question 4.
This question depends on the method used in three, although not entirely.
What you need to know is that W is on RT when you take a ruler and make RT longer. You can put W anywhere as long as it is on RT when it is made longer.
Directions
Make RT longer. Draw down and to your right.
Put a point anywhere on the length starting at T. Label this new point as W. There's your W. It goes anywhere on the part of RT made longer.
Draw UW.
Label UW as 8
Now draw another line from S to W. Guess what? By the methods used in question 3, it's also 8. So SW = 8
TW = TW Reflexive
<UTW = STW Same reason as in 3. UtW is a right angle
UT = ST Given (the marking tells you so.
ΔUTW = ΔSTW SAS
UW = SW Corresponding parts of = triangles are =
SW = 8
Please help me with this question. I don't think I understand it. Quadratic functions graphing #15-19.
Will pick brainliest answer, thank you :)
Answer:
15) (1, 1) and (-1, 1)
16) (1, 2) and (-1, 2)
17 (1,1/2) and (-1, 1/2)
18) (1,1/4) and (-1, 1/4)
19) 16 is vertical stretch, 17 and 18 is vertical compressed
Step-by-step explanation:
for qs 15-18 since x is 1 or -1 if you sq 1 or -1 you will always get 1
so y is the "a" value in the equation y=ax²
for qs 19
y=ax²
so if a>1 -- then vertical stretch
when 0<a<1 -- then vertical compressed
someone please help meeeee! I don't know what the solution is!
Answer:
(2,4)
Step-by-step explanation:
Answer:
(2,4)
Step-by-step explanation:
Solve for the first variable in one of the equations, then substitute the result into the other equation
Noah earns $9.65 per hour. How much will he
earn next week if he works 18 hours?
Answer:
$1215.90
Step-by-step explanation
You take Noah's pay per hour of $9.65 then multiply it by how many hours he works 18. You then take that and multiply it by 7 for the days of the week.
Janelle came to bat 464 times in 131 games. At this rate, how many times should she expect to have at bat in a full season of 162 games?
The rate at which she bats is an illustration of ratio and proportions
She's expected to bat 574 times in 162 games
In 131 games, she bat 464 times
Represent this as a ratio
[tex]\mathbf{Ratio = 131 : 464}[/tex]
Let the number of times she bat in 162 games be represented with x.
So, the ratio is represented as:
[tex]\mathbf{Ratio = 162 : x}[/tex]
Equate both ratios
[tex]\mathbf{162 : x = 131 : 464}[/tex]
Express as fractions
[tex]\mathbf{\frac{x}{162 }= \frac{464}{131 }}[/tex]
Multiply both sides by 162
[tex]\mathbf{x= \frac{464}{131 } \times 162}[/tex]
Multiply
[tex]\mathbf{x= \frac{75168}{131 } }[/tex]
Divide
[tex]\mathbf{x= 574}[/tex]
Hence, she's expected to bat 574 times in 162 games
Read more about ratios and proportions at:
https://brainly.com/question/7810782
Find the value of h and k.
Answer:
h = 6, k = 6.5
Step-by-step explanation:
The segment marked h is half the length of the one marked 3h-6.
2h = 3h -6
6 = h . . . . . . . add 6-2h
__
The segment marked k is half the length of the one marked 2h+1.
2k = 2(6) +1
k = 13/2 = 6.5 . . . . divide by 2
The values of h and k are 6 and 6.5, respectively.
if g(x)=x^2+2x, find g(-6)
Answer:
-6/2+2×(-6)
-3+(-12)
-3-12
-15
find the lowest common multiple of: 10 ,15 and 18
Answer:
90
Step-by-step explanation:
a drink in japan costs 374 yen. The exchange rate is £1 = 189 yen. What is the cost in pounds
Answer:
Roughly £2
Step-by-step explanation:
multiply the echange rate by 2 , its 378Yen
find meh x pls 10 points Uwu
−5/6=−1/4−7/10x
answer is 5/6
Step-by-step explanation:
multiplying by 60, we get,
50=15+42x
we can simplify it, 42x= 35,or x=5/6
What is the slope of the line?
y-4=-7(x-6)
Answer: −7
Step-by-step explanation:
use a point on the number line to represent a number ot whose absulute vaue is?
Answer:
A
Step-by-step explanation:
Please anyone I’m desperate
Answer:
the answer is B) 12a+6b
Step-by-step explanation:
3+9=12 so 3a+9a=12a,
7-1=6 so 7b-(1)b=6b
Step-by-step explanation:
calm down ! just breathe.
these are totally simple additions and one also very simple subtraction to make.
you know that you can combine terms based on the same variable, right ?
3a + 9a = 12a
7b - b = 6b
the result is then
12a + 6b, so B is the right answer.
this bases already on the same principle of actual numbers.
2×3 + 5×3 = 7×3 because this is also
(2 + 5) × 3
or
6×5 + 6×3 = 6×8 because this is also
6 × (5 + 3)
or
7×8 - 4×8 = 3×8 because this is also
(7 - 4) × 8
and so on.
Given a circle with radius 5cm and using π=3.14 calculate it's circumference (I will make you Brainliest)
Answer:
Circumference = 31.4 feet
Area= 78.5 sq. feet.
Step-by-step explanation:
brainliest please?????
what is the answer ?????
Difference = 60 - 48 = 12
Percentage = [tex] \frac{12}{60} \times 100 = \frac{12}{3} \times 5 = 4 \times 5 = 20\% \\ [/tex]
Calculate the frequency of a wave with a speed of 250m/s and a wavelength of 50m.
HELPPPPPPPPPPPPPPPPPPPPPPPP PLS
Answer:
formulasfrequency=speed/wavelength
f=250/50
f=50hz
what is 400x800 do any one knows
Answer:
Step-by-step explanation:
320000 is your answer
A piano teacher gives lessons that are each Three-fourths hour long. How many piano lessons can the teacher fit into a 12-hour work day? Assume no breaks are taken in the 12 hour period.
6
9
11
16
Answer:
26.6666666667
Step-by-step explanation:
3/4 of a hour is 45 minutes 12 ÷ by 0.45 would equal 26.6666666667