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]
The distance, d, that an object foto is directly proportional to the square of the time, t, it has been in free fall. An object that has been in free fall for 8 seconds has fallen 1024 feet. Determine the distance the object has fallen if it has been falling for 2 seconds
Answer:
d = 64 feet
Step-by-step explanation:
Given that d is directly proportional to t² then the equation relating them is
d = kt² ← k is the constant of proportion
To find k use the condition t = 8 , d = 1024 , then
1024 = k × 8² = 64k ( divide both sides by 64 )
16 = k
d = 16t² ← equation of proportion
When t = 2 , then
d = 16 × 2² = 16 × 4 = 64 feet
Reindeers eat 62 apples an hour, there is 24 hours in a day, how many do they eat
Does anyone one have the vocabulary words and definitions for this iready lesson? (Pls help this is graded)
Answer:
absolute value
coefficient
constant
counterexample
equation
expression
evaluate
inequality
I hope that helps maybe give brainliest if it does!
Love,
-Banana
What is the area of this triangle NO LINks OR I WILL REPORT
Answer:
18 square inches
Step-by-step explanation:
Area of triangle = bxh/2
b=3, h=12
Area = 3x12/2
Area = 36/2
Area = 18 square inches
Simplify 80−−√
4 5√
5 16−−√
5 4√
16 5√
Answer:
The answer is the 3rd choice
Step-by-step explanation:
dwfegrhtytg pls helpp
Answer:
The answer to Y/X is 4/1
Dave spent 21 minutes completing a race. He walked 9 minutes and jogged the rest. What
is the ratio of time he jogged to time he walked?
Marco is making rice but wants to decrease the recipe to make less.
Which fraction could he multiply his ingredient amounts by in order to produce less rice?
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
3^x X 9^4 = 3^n
Find n in terms of x
Answer:
n = x + 8
Step-by-step explanation:
Using the rules of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]
Then
[tex]3^{x}[/tex] × [tex]9^{4}[/tex] = [tex]3^{n}[/tex]
[tex]3^{x}[/tex] ×[tex](3^2)^{4}[/tex] = [tex]3^{n}[/tex]
[tex]3^{x}[/tex] × [tex]3^{8}[/tex] = [tex]3^{n}[/tex]
[tex]3^{x+8}[/tex] = [tex]3^{n}[/tex]
Since bases on both sides are equal, both 3, then equate exponents
n = x + 8
What is the estimated total of 674, 692, 724, and 739?
Answer:
2800 is a good estimate
Step-by-step explanation:
Rounding to the nearest hundred
674 = 700
692 = 700
724 = 700
739 = 700
700+700+700+700 = 2800
A salesman sells a car for 960,000.If he receives a commission of 15%,how much will be his commission?
Answer:
144 000
Step-by-step explanation:
960 000 × 0.15
= 144 000
Answer:
144,000
Step-by-step explanation:
[tex] \frac{15}{100} \times 960000 \\ 15 \times 9600 \\ 144000[/tex]
find the sum of the following APs. a 2 + 4 + 6+ ... + 98 + 100
Answer:
S=2+4+6+…+100
S=100+98+96+…+2
Adding the two yields
2S=102+102+102+…+102 = 50(102)
Thus S=50(51)=2550
If a bag contains 10 blue marbles, 5 green Marbles, and 3 red marbles, What is the ratio of red marbles to all Marbles? be sure to simplify/ an equivalent ratio
Answer:
1 red marble to 6 total marbles
Step-by-step explanation:
There are 3 red marbles, and (10 + 5 + 3) total marbles.
There are 3 red marbles to 18 total marbles
therefore the ratio is 3 to 18 which can be simplified by dividing both sides of the ratio by 3
the ratio is 3/3 : 18/3 which is 1:6
Find the slope given two points: (-9, -2) and (-5,0)
Answer:
1/7
Step-by-step explanation:
Consider the line passing through these two points. The increase in x (run) from the first to the second is 14; the increase in y (rise) is 2.
Thus the slope of this line is m = rise/run = 2/14, or m = 1/7
Answer:
[tex]m = \frac{1}{2}[/tex]
Step-by-step explanation:
To find the slope using two given sets of coordinates, the following function can be used:
[tex]m = \frac{y2-y1}{x2 - x1}[/tex]
Where x1,y1 are one set of coordinates and x2,y2 are the other set:
[tex]m = \frac{0 - (-2)}{-5 - (-9)}\\[/tex]
[tex]m = \frac{0 + 2}{-5 + 9}[/tex]
[tex]m = \frac{2}{4}[/tex]
This can be simplified down to:
[tex]m = \frac{1}{2}[/tex]
Hope this helps!
2^-5 =
Can someone please help
Answer:
[tex]\frac{1}{32}[/tex]
Step-by-step explanation:
Using the rule of exponents
[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex] , then
[tex]2^{-5}[/tex] = [tex]\frac{1}{2^{5} }[/tex] = [tex]\frac{1}{32}[/tex]
hiroshi borrowed 3 nonfiction books from the library. This was 25% of the books he checked out. how many books did Hiroshi take out?
Answer:
12 books
Step-by-step explanation:
25% is the same as 1/4
3=25%=1/4
if you multiply 3 by 4 you get 100% or 12
You can also do this by adding 9, aka 3*3, to 3 to get 3*4=12.
The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of 3 cm/s. When the length is 11 cm and the width is 5 cm, how fast is the area of the rectangle increasing?
Answer: 89 cm^2/minute
Step-by-step explanation:
Initial Area: 11 x 5 = 55 cm^2
Area after 1 minute: 18 x 8 = 144 cm^2
The area of the triangle is increasing by
please help me i’ll love you so much if you help
Answer:
1. yes
2. no
3.no
Step-by-step explanation:
You can just distribute to see if it matches up with the other expression.
7/9 - 2/8 x 49 in simplest form
Answer:
7/9 - 2/8 x 49
First, according to BODMAS we will solve multiplication7/9 - 2/8 x 49 = 7/9 - 49/4= -61/12Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
Use 3.14
Jerry is building a model car. The picture shows one of the wheels for the car. The wheel has a diameter of 30 millimeters.
30 mm
Which is closest to the distance around the outside edge of the wheel?
We want to find the distance around the outside wheel of the car given that we know its diameter. We will see that this distance is 94.2mm
So the distance around the outside edge of the wheel will be equal to its circumference.
We do know that for a circle of diameter D the circumference is defined as:
C = pi*D
Where pi = 3.14
Here we do know that the diameter is 30 mm, then the circumference of the wheel will be:
C = 3.14*30mm = 94.2 mm
This is the distance around the outside edge of the wheel.
If you want to learn more about circumferences you can read:
https://brainly.com/question/17009561
Answer the question in the picture below
Answer:
16.25, 20, 13.75, 12.5, 7.5
Step-by-step explanation:
1cm= 2.5m
6.5x2.5= 16.25
8x2.5= 20
5.5x2.5= 13.75
5x2.5= 12.5
3x2.5= 7.5
f (x)=x^2 what is g (x)
Answer:
Answer is X =0
Step-by-step explanation:
I Found This on a app
please help asap…………
100 POINTS WHEN ANSWERED AND BRAINLIEST GIVEN TO FIRST CORRECT ANSWER WHENEVER IT LETS ME
Hello there, below here is an attached file of the particular question I have. Thank you so much for coming here to answer! I appreciate you, and I hope have a good day or night!
Answer:
a: 0
b: 1,3
c: 2
Step-by-step explanation:
a: 4 is the y intercept meaning 0 is the number of seconds when the ball is 4 feet in the air
b: to easily find this, we can graph.
1st screenshot is for B.
We see that y=52 intersects twice with the graph, meaning the ball was at 52 feet twice. the times are 1 second and 3 seconds
a: we graph again, but with y=68 we see that it only intersects once. at x=2.
Write a formula for the volume V of a prism where B is the area of the base and h is height
Answer:
a pyramidal prism is 1/3 the volume of a similar rectangular prism of same base and height
so V=(1/3)bh
V=36
H=6
find area of base
36=(1/3)b6
36=2b
divide both sides by 2
18=b
the area of the base is 18 square units
Step-by-step explanation:
the answer is : V= B.h
The coordinates of a point change as follows during a dilation:
(-6, 3) ----> (-2, 1)
What is the scale factor?
Answer:
The answer is D. (6,9)
Step-by-step explanation:
Glad to help
There were 6 teams in a baseball tournament. Each team played against every other team exactly once during the tournament. A team earned 2 points for a win, 1 point for a tie, and 0 points for a loss. What was the total number of points earned by all 6 teams in the tournament?
Since there were 6 teams in a baseball tournament, and each team played against every other team exactly once during the tournament, and a team earned 2 points for a win, 1 point for a tie, and 0 points for a loss, to determine what was the total number of points earned by all 6 teams in the tournament, since a series of results have not been raised, the following table should be made:
Possible outcomes: 5 wins = 5 x 2 = 10 4 wins and 1 a draw = 4 x 2 + 1 = 9 4 wins and 1 loss = 4 x 2 = 8 3 wins and 2 draws = 3 x 2 + 2 x 1 = 8 3 wins, 1 draw and 1 loss = 3 x 2 + 1 = 7 3 wins and 2 losses = 3 x 2 = 6 2 wins and 3 draws = 2 x 2 + 3 x 1 = 7 2 wins, 2 draws and 1 loss = 2 x 2 + 2 x 1 = 6 2 wins, 1 draw and 2 losses = 2 x 2 + 1 = 5 2 wins and 3 losses = 2 x 2 = 4 1 win and 4 draws = 2 x 1 + 4 x 1 = 6 1 win, 3 draws and 1 loss = 2 x 1 + 3 x 1 = 5 1 win, 2 draws and 2 losses = 2 x 1 + 2 x 1 = 4 1 win, 1 draw and 3 losses = 2 x 1 + 1 x 1 = 3 1 win and 4 losses = 2 x 1 = 2 5 draws = 5 x 1 = 5 4 draws and 1 loss = 4 x 1 = 4 3 draws and 2 losses = 3 x 1 = 3 2 draws and 3 losses = 2 x 1 = 2 1 draw and 4 loss = 4 x 1 = 1 5 losses = 0
Learn more in https://brainly.com/question/6283215
HELP HELP HELPP PLEASEDEEEE
what is 16% x 19
SHOW WORK PLEASEEEEEEE PLS PLS PLSSSSSSSS
Answer:
3.04
Step-by-step explanation:
16% is 0.16. Multiply 0.16 * 19 to get 3.04
Answer:
this last answer will come 304
Sam has 3 more than twice the number of baseball cards that Catherine has. Together Sam and Catherine have 51 baseball cards. How many cards do Sam and Catherine each have?
Answer:
catherine has 16 card and sam also has 16 card
What was the primary goal of mine workers’ strikes? A. to stop poor pay and dangerous working conditions B. to open new land to mining operations C. to reduce regulations on mining practices D. to advocate for more settlement of the territory Please select the best answer from the choices provided A B C D Mark this and return
Answer:
The Answer is A, to stop poor pay and dangerous working conditions