Answer:
X=20
Step-by-step explanation:
The answer is C
Using Pascal’s Theorem, expand the expression 〖(2x-y)〗^3
Answer:
(2x - y)³ = 8x³ - 12x²y + 6xy² - y³
Step-by-step explanation:
Pascal's Theorem uses a set of already known and easily obtainable numbers in the expansion of expressions. The numbers serve as the coefficients of the terms in the expanded expression.
For the expansion of
(a + b)ⁿ
As long as n is positive real integer, we can obtain the coefficients of the terms of the expansion using the Pascal's triangle.
The coefficient of terms are obtained starting from 1 for n = 0.
- For the next coefficients of terms are 1, 1 for n = 1.
- For n = 2, it is 1, 2, 1
- For n = 3, it is 1, 3, 3, 1
The next terms are obtained from the previous one by writing 1 and summing the terms one by one and ending with 1.
So, for n = 4, we have 1, 1+3, 3+3, 3+1, 1 = 1, 4, 6, 4, 1.
The Pascal's triangle is
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1
The terms can also be obtained from using the binomial theorem and writing the terms from ⁿC₀ all through to ⁿCₙ
So, for n = 3, the coefficients are 1, 3, 3, 1
Then the terms are written such that the sum of the powers of the terms is 3 with one of the terms having the powers reducing from n all through to 0, and the other having its powers go from 0 all through to n
So,
(2x - y)³ = [(1)(2x)³(-y)⁰] + [(3)(2x)²(-y)¹] + [(3)(2x)¹(-y)²] + [(1)(2x)⁰(-y)³]
= (1×8x³×1) + (3×4x²×-y) + (3×2x×y²) + (1×1×-y³)
= 8x³ - 12x²y + 6xy² - y³
Hope this Helps!!!
27) Jake tells a joke to 3 people and each of those people tells the joke to 3 more people,
and so on. How many people will hear the joke in the 4th round of jokes told? How
many people will hear the joke in total after the fourth round?
Answer:
15
Step-by-step explanation:
Answer:
12 people heard the joke?
Step-by-step explanation:
Find the perimeter of an equilateral triangle where area is 72cm.
Answer:
38.68 cm
Step-by-step explanation:
Perimeter of an equilateral triangle : P = 3a
Area of an equilateral triangle : A = [tex]\frac{\sqrt{3} }{4}a^2[/tex]
a = side length
The area is given, solve for a.
[tex]72= \frac{\sqrt{3} }{4}a^2[/tex]
[tex]a = 12.894839[/tex]
The side length is 12.894839 centimeters.
Find the perimeter.
P = 3a
P = 3(12.894839)
P = 38.684517 ≈ 38.68
The perimeter is 38.68 centimeters.
HELP ASAP ILL GIVE BRAINLIEST !!! The social studies teacher wants to know whether students in the entire school but for a model of the United Nations activity or student government activity the teacher just a random sample from the following groups all teachers in the school I’ll boys in each grade or students in each grade I’ll send some social studies club which group best represents the population he should take a random sample from to get the best results for his survey
Answer:
Hello There. ☆~---_●₩●__---☆~ The students in each grade, that way it wont focus just on one group like the club, the teachers, or the boys.
Hope It Helps!~ ♡
ItsNobody~ ☆
hi if anyone is good with extraneous solutions pleaseeeeeee help meeee tessa solves the equation below by first squaring both sides of the equation√x^2-3x-6=x-1 what extraneous solution does tessa obtain x=
Answer:
x = -7/5
Step-by-step explanation:
If we square both sides of the equation, we get:
[tex]\sqrt{x^2-3x-6}=x-1\\ (\sqrt{x^2-3x-6})^2=(x-1)^2\\x^2-3x-6=x^2-2x+1\\[/tex]
Then, solving for x, we get:
[tex]x^2-3x-6=x^2-2x+1\\-3x-6=2x+1\\-6-1=2x+3x\\-7=5x\\\frac{-7}{5}=x[/tex]
So, x is equal to -7/5
Answer:
its -7
Step-by-step explanation:
gots it right!
Find the total surface area of the cone in the figure. ( use rr=3.14.)
Answer:
Answer D
Step-by-step explanation:
The formula is [tex]A = pi r(r+\sqrt{h^2+r^2})[/tex]. We have our r (radius) and h (height), so plugging it all in would give us A = (3.14)(5 + sqrt(12^2)+(5^2). After computing this, you would get answer D, 282.6.
what’s the opposite of negative two
Answer: The answer is two
Step-by-step explanation: If you look for opposites of a number its either negative or positive. So when the answer is negative, the opposite is positive and if the answer is positive, the opposite is negative.
Answer:
[tex]\boxed{2}[/tex]
Step-by-step explanation:
The opposite of a number is the number that is the same distance from 0 on the number line.
-2 opposite is 2.
One variable in a study measures how many serious motor vehicle accidents a subject has had in the past year. Explain why the mean would likely be more useful than the median for summarizing the responses of the 60 subjects.
Answer:
The mean is more useful in this case because it would give an average value of the accidents for example 3 accidents per year but the median would give the middle value which may be 5 or greater or much lesser than the average. It would not give an approximate value of occurrences.
Step-by-step explanation:
Mean is the averaage of all the values.
Median is the value of the data which gives an estimate of the middle value. Middle values can be different than the average values.
The mean is
1) rigorously defined by a mathematical formula.
2) based on all the observations of the data
3) affected by extreme values
The meadian is
1) computed for open end classes like income etc.
2) not rigorously defined
3) is located when the values are not capable of quantitative measurment.
4) is not affected by extreme values.
The mean is more useful in this case because it would give an average value of the accidents for example 3 accidents per year but the median would give the middle value which may be 5 or greater or much lesser than the average. It would not give an approximate value of occurrences.
21.65 to 1 decimal place
Answer:
21.7
Step-by-step explanation:
When anything is 5 or above in a decimal place you round up to the next number for example
2.35 this would round up to be 2.4
21.65
Place value of 1 = ones place
Face value of 1 = 1
Note : The face value of a number will not change at all
Hope it helps you..If it's wrong plz say and I'll try to recorrect it :)
An accountant receives a salary of $262,000 per year. During the year, he plans to spend $99,000 on his mortgage, $54,000 on food, $32,000 on clothing, $41,000 on household expenses, and $28,000 on other expenses. With the money that is left, he expects to buy as many shares of stock at $250 per share as possible. Using the equation below, determine how many shares will he be able to buy? What was the sum of the accountant's expenses?
Answer:
Number of shares = 32 shares
Accountant total expenses= $254000
Step by step explanation:
The accountant salary is $262000
He spends $99000 on mortage
Spends $54000 on foods
Spends $32000 on clothing
Spends $41000 on household
Spends $28000 on others
Total expenses= 99000+54000+32000+41000+28000
Total expenses =$254000
Remaining money = 262000-254000
Remaining money= $8000
If shares = $250 for one
To know the amount he buys with the remaining money
We divide remaining money by shares cost
= $8000/$250
= 32 shares
Which statement describes the order of rotational symmetry for an isosceles triangle?
Answer: it should be b, 1. :)
Step-by-step explanation:
help I don't understand
Answer:
x = 9.9 in.
2 of the same type of triangle = 1 square
To find x, you have to remember that a square is made from two right triangles combined. In this photo, we can see that the length and width of the triangle have the same value (the two sides that point up and to the right), so that means if we multiply the area by two, then we get the area of a square or two of the same triangle's area.
Step 1:
To find the area of the square/two triangles, multiply the area by two.
[tex]49*2=98[/tex]
98 is the area of the square.
Step 2:
Now we have to find the square of 98 (find two numbers that are the same that multiply to 98).
[tex]\sqrt{98}[/tex]
When we solve this square, we find out that it is not a perfect number. So:
[tex]\sqrt{98} =\\9.89949[/tex]
That is just an estimate of x, so when we round to the nearest tenth, we get 9.9.
To check our answer, multiply 9.9 by 9.9 and we get 98.01, but since we rounded our answer, 98.01 is correct. If we round that to 98 and divide by 2, we get our original area of one triangle, 49.
x = 9.9
Answer:
9.9
Step-by-step explanation:
Well let's work backwards.
If the area is 49 then we do 49*2 because after doing b*h you divide by 2.
So 49*2 = 98.
If the b and h is the same then we find the square root of 98,
which is 9.899494937.
Thus,
the answer is 9.9 rounded to the nearest tenth.
Hope this helps :)
100 POINTS!!!! Answer to the picture below.
Answer:
A 23 of people who prefer plan 1 are from the 35-45 age group and 42% of people from the 46-55 age group prefer plan 2.
Step-by-step explanation:
add everyone who prefers plan 1 = 60
age 36-45 / total of plan 1 = 14/60 = .23 or 23%
add everyone in age group 46-55 = 50
in age group 46-55 and prefers plan 2 = 21 / 50 = 0.42 or 42%
Answer:
[tex]\boxed{\mathrm{Option \ B}}[/tex]
Step-by-step explanation:
Total people in 36 - 45 age group = 50
Who prefer plan I = 14
%age of people preferring plan 1 among 36-45 age group:
=> [tex]\frac{14}{50} * 100[/tex]
=> 0.28 * 100%
=> 28%
Now,
Total People in 46-55 age group = 50
Those who prefer plan II = 21
%age of people preferring plan II among 46-55 age group:
=> [tex]\frac{21}{50} * 100[/tex]
=> 0.42 * 100%
=> 42%
Improving the quality of high-value decision making by an executive will save an organization far more money than improving the quality of lesser-value decisions made at a lower level.
A. True
B. False
Answer:
A. True
Step-by-step explanation:
Since it is lesser, it will also bring in lesser profit :)
6.52
65.2
0.652
order it least to greatest which comes first?
Answer:
Hey! The answer will be below!! :)
Step-by-step explanation:
In least to greatest the answer will be....
0.652, 6.52, 65.2
0.652 comes first because since the decimal point is between the 0 and 6
It’s also because 0 is less than 6 and 65.
Here is a easy way to do this, when you have this kind of question.
First look where the decimal is.
Pretend it’s a whole number like, 0.652 becomes 0
And 6.52 becomes 6, also 65.2 becomes 65
You have to use the decimal to find out least to greatest, also you will have to round the number.
So remember, when ever you have this kind of question...after the decimal point like 65.2 you take away the .2 and just have 65....this will help you do least to greatest faster! :)
Hope this helps!
Answer:
0.652, 6.52, 65.2
Step-by-step explanation:
You have to round to find the answer in a easy way.
Least to greatest would be 0.652, 6.52, 65.2
Hop it will help u
Find the length L of the curve
[tex]y = \sqrt{x} [/tex]
from the point P(0,0) to the point Q(4,2)
Answer:
4.647 to the nearest thousandth.
Step-by-step explanation:
The formula for the length of an arc between x = a and x = b is
a
∫ √( 1 + (f'(x))^2) dx
b
Here f(x) = √x so
we have ∫ (√( 1 + (1/2 x^-1/2))^2 ) between x = 0 and x = 4.
= ∫ ( √( 1 + 1/(4x)) dx between x = 0 and x = 4.
This is not easy to integrate but some software I have gives me the following
length = √17 + 1/8 log(33 + 1/8 √17)
= 4.647.
Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the convergence or divergence of the series using other methods.
[infinity] n = 1 n2/5n n = 1
lim n→[infinity] an + 1/an =
a. converges
b. diverges
Answer:
A. The series CONVERGESStep-by-step explanation:
If [tex]\sum a_n[/tex] is a series, for the series to converge/diverge according to ratio test, the following conditions must be met.
[tex]\lim_{n \to \infty} |\frac{a_n_+_1}{a_n}| = \rho[/tex]
If [tex]\rho[/tex] < 1, the series converges absolutely
If [tex]\rho > 1[/tex], the series diverges
If [tex]\rho = 1[/tex], the test fails.
Given the series [tex]\sum\left\ {\infty} \atop {1} \right \frac{n^2}{5^n}[/tex]
To test for convergence or divergence using ratio test, we will use the condition above.
[tex]a_n = \frac{n^2}{5^n} \\a_n_+_1 = \frac{(n+1)^2}{5^{n+1}}[/tex]
[tex]\frac{a_n_+_1}{a_n} = \frac{{\frac{(n+1)^2}{5^{n+1}}}}{\frac{n^2}{5^n} }\\\\ \frac{a_n_+_1}{a_n} = {{\frac{(n+1)^2}{5^{n+1}} * \frac{5^n}{n^2}\[/tex]
[tex]\frac{a_n_+_1}{a_n} = {{\frac{(n^2+2n+1)}{5^n*5^1}} * \frac{5^n}{n^2}\\[/tex]
aₙ₊₁/aₙ =
[tex]\lim_{n \to \infty} |\frac{ n^2+2n+1}{5n^2}| \\\\Dividing\ through\ by \ n^2\\\\\lim_{n \to \infty} |\frac{ n^2/n^2+2n/n^2+1/n^2}{5n^2/n^2}|\\\\\lim_{n \to \infty} |\frac{1+2/n+1/n^2}{5}|\\\\[/tex]
note that any constant dividing infinity is equal to zero
[tex]|\frac{1+2/\infty+1/\infty^2}{5}|\\\\[/tex]
[tex]\frac{1+0+0}{5}\\ = 1/5[/tex]
[tex]\rho = 1/5[/tex]
Since The limit of the sequence given is less than 1, hence the series converges.
An epidemiologist is observing the decay pattern of a pathogenic bacteria after applying a vaccine. He starts with 2,000 bacteria that decay at a rate of 4.5% per hour. He will check on the bacteria in 36 hours. How many bacteria will he find? Round your answer to the nearest whole number.
Answer:
396
Step-by-step explanation:
Farmer Hanson is putting together fruit baskets. He has 240 apples and 150 pears. What is the largest number of baskets he can put together so that he can have the same number of apples and same number of pears in each basket considering no fruit is left out?HELP NOWWWWW
Answer: The largest number of baskets he can put together so that he can have the same number of apples and the same number of pears in each basket considering no fruit is left out is 30.
Step-by-step explanation:
Given, Farmer has 240 apples and 150 pears.
The largest number of baskets he can put together so that he can have the same number of apples and the same number of pears in each basket considering no fruit is left out = GCF(240,150)
Prime factorization of 240 and 150 :
[tex]240=2\times2\times2\times2\times3\times5\\150=2\times3\times5\times5[/tex]
Greatest common factor of 240 and 150 = [tex]2\times3\times5=30[/tex]
Hence, the largest number of baskets he can put together so that he can have the same number of apples and the same number of pears in each basket considering no fruit is left out is 30.
Find the distance between (-3,5) and (-9,5).
Answer:
6 units
Step-by-step explanation:
Distance between 2 points
[tex] = \sqrt{(x1 - x2)^{2} + (y1 - y2)^{2} } [/tex]
Thus, distance between (-3, 5) and (-9, 5)
[tex] = \sqrt{( - 3 - ( - 9))^{2} + (5 - 5)^{2} } \\ = \sqrt{( - 3 + 9)^{2} } \\ = \sqrt{6 ^{2} } \\ = 6[/tex]
Alternatively, notice that this line is a horizontal line as both points have the same y-coordinate of 5.
Thus, distance between the 2 points
= -3 -(-9)
= -3 +9
= 6 units
Which of the following is the standard deviation of the random variable x
Answer: B. 1.414
Step-by-step explanation:
let x be the random variable denotes the number of die.
Numbers on 5-faced die = 1,2,3,4,5
Probability of getting any number = [tex]\dfrac{1}{5}[/tex]
Mean = [tex]\bar {x}=\sum p_ix_i[/tex]
[tex]\\\\\Rightarrow\bar{x}=\dfrac{1}{5}(1)+\dfrac{1}{5}(2)+\dfrac{1}{5}(3)+\dfrac{1}{5}(4)+\dfrac{1}{5}(5)\\\\=\dfrac{1}{5}(1+2+3+4+5)\\\\=\dfrac{1}{5}(15)=3[/tex]
Standard deviation: [tex]\sigma=\sum \sqrt{\dfrac{(x_i-\bar{x})^2}{N}}[/tex]
[tex]=\sqrt{\dfrac{(1-3)^2+(2-3)^2+(3-3)^2+(4-3)^2+(5-3)^2}{5}}\\\\=\sqrt{\dfrac{4+1+0+1+4}{5}}\\\\=\sqrt{\dfrac{10}{5}}\\\\=\sqrt{2}\approx1.414[/tex]
Hence, the standard deviation of the random variable x is 1.414.
Thus, the correct option is B.
Translate the phrase into a variable expression. Use the letter sto name the
variable. If necessary, use the asterisk (*) for multiplication and the slash
(1) for division.
the product of 60 and the number of seconds...
Answer:
The statement
the product of 60 and the number of seconds is written as
60 * s
Hope this helps you
What are the vertical asymptote(s) of y= (x-6)/(x+8) (x-7)
Answer:
x = -8 and x= 7
Step-by-step explanation:
recall that for a rational expression, the vertical asymptotes occur at x-values that causes the expression to become undefined. These occur when the denominator becomes zero.
Hence the asymptototes will occur in x-locations where the denominator , i.e
(x+8)(x-7) = 0
solving this, we get
(x+8) = 0 ----> x = -8
or
(x-7) = 0 ------> x = 7
hence the asymptotes occur x = -8 and x= 7
Answer:
x = -8 and x = 7.
Step-by-step explanation:
The vertical asymptotes are lines that the function will never touch.
Since no number can be divided by 0, the function will not touch points where the denominator of the function is equal to 0.
[tex]\frac{x - 6}{(x + 8)(x - 7)}[/tex], so the vertical asymptotes will be where (x + 8) = 0 and (x - 7) = 0.
x + 8 = 0
x = -8
x - 7 = 0
x = 7
The vertical asymptotes are at x = -8 and x = 7.
Hope this helps!
It takes 52 minutes for 5people to paint 5 walls. How many minutes does it take 20 people to paint 20 walls?
Answer:
52 minutes
Step-by-step explanation:
This should be a proportional statement, because if each individual person painted there own wall it should still take 52 minutes.
Tunde and Martha are married and share their income. Tunde earns $1,500 per year less than Martha. If their annual income is $47,500, how much does each earn?
Answer:
p=2m
p+m=51
take the 2m and plug that in for p -> 2m+m=51
3m=51
m=51/3
m=17 then plu the value of m into Paula's points
p=2(17)
p=34
Use Lagrange multipliers to solve the given optimization problem.
Find the maximum value of f(x, y)-xy subject to x + 2y 52.
fmax=______
Also find the corresponding point
(x, y)=__________.
Answer:
fmax = xy = 26 × 13 = 338
(x,y) = (26,13)
Step-by-step explanation:
Given that:
f(x, y) = xy
subject to x + 2y = 52
So;
x = 52 - 2y
and;
f(x, y) = xy
f(x, y) = (52- 2y) y
f(x, y) = 52y - 2y²
In order to maximize this function;
52y - 2y² = 0
26 y - y² = 0
26 - 2y = 0
-2y = -26
y = -26/-2
y = 13
Again:
x = 52 - 2y
x = 52 - 2(13)
x = 52 - 26
x = 26
fmax = xy = 26 × 13 = 338
(x,y) = (26,13)
what is the area of the shaded region between the two z-scores indicated in the diagram? z=-1.24 and z= 0.84
Answer:
0.6921 (69.21%)
Step-by-step explanation:
The area of the shaded region between the two z-scores refer to the probability between the two z-scores value( The total area under a standard normal distribution curve is 1)
So the area we want to determine in this case is as follows;
P(-1.24<z<0.84) = P(z<0.84) - P(z<-1.24)
What we use to calculate this finally is the standard normal distribution table
We use this to get these values so we can calculate the probability.
Using the standard normal distribution table;
P(-1.24<z<0.84) = 0.69206 which is approximately 0.6921
Which of the following points is collinear with (2, 1) and (3, 3)?
O (0,0)
O (1,-1)
O (4,4)
O(-1,-2)
HELP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!??????????!!!!!!!!!
Answer:
O (1,-1) is collinear with (2, 1) and (3, 3).
Step-by-step explanation:
equation of line in point slope form is
y-y1/x-x1 = m
where m is the slope of line
slope of line is given by
m = (y2-y1)/(x2-x1)
where(x1,x2) and (y1,y2) are points on the given line
_______________________________________
Given point
(2, 1) and (3, 3)?
m = 3-1/3-2 = 2
Equation of line
y-1/x-2 = 2
=> y-1 = 2(x-2)
=> y-1 = 2x-4
=> y= 2x-4+1
=> y = 2x-3
col-linear points are one which lie on the same line
To solve the problem we will check which of the given points satisfy the equation of line derived above.
y = 2x-3
(0,0)
if we put value of x = 0 the above equation we should get y =0
y = 2*0 -3 = -3
since -3 is not equal to 0, hence (0,0) is not collinear with (2, 1) and (3, 3).
1,-1
y = 2*1 -3 = -1
since -1 is equal to -1, hence (1,-1) is collinear with (2, 1) and (3, 3).
(4,4)
y = 2*4-3 = 5
since 5 is not equal to 4 , hence (4,4) is not collinear with (2, 1) and (3, 3).
(-1,2)
y = 2*-1 -3 = -5
since -5 is not equal to 2, hence (-1,2) is not collinear with (2, 1) and (3, 3).
Hence answer is O (1,-1) s collinear with (2, 1) and (3, 3).
If A=p+prt, than t equalls?
Answer:
[tex]\boxed{t=\frac{A-p}{pr}}[/tex]
Step-by-step explanation:
[tex]A=p+prt[/tex]
Subtract p on both sides.
[tex]A-p=p+prt-p[/tex]
[tex]A-p=prt[/tex]
Divide both sides by pr.
[tex]\displaystyle \frac{A-p}{pr} =\frac{prt}{pr}[/tex]
[tex]\displaystyle{\frac{A-p}{pr} =t}[/tex]
Answer:
A=p+prt
=>A/R=2pt
=>A/RT=2p
=>A/RTP=2
=>A/2RP=T
Not Logical.....LollllllFollow meehhhh ⚡❤♥️✨♥️❤❤❤There are 450 people and each pays 5 dollars how much do you get? Please show me the work
Answer:
The total amount is $2250.
Step-by-step explanation:
Given that each person pays $5 and there is 450 people so you have to multiply :
$5 × 450 = $2250