Answer:
Please check the explanation!
Step-by-step explanation:
Given the polynomial
[tex]\left(x+y\right)^5[/tex]
[tex]\mathrm{Apply\:binomial\:theorem}:\quad \left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i[/tex]
[tex]a=x,\:\:b=y[/tex]
[tex]=\sum _{i=0}^5\binom{5}{i}x^{\left(5-i\right)}y^i[/tex]
so expanding summation
[tex]=\frac{5!}{0!\left(5-0\right)!}x^5y^0+\frac{5!}{1!\left(5-1\right)!}x^4y^1+\frac{5!}{2!\left(5-2\right)!}x^3y^2+\frac{5!}{3!\left(5-3\right)!}x^2y^3+\frac{5!}{4!\left(5-4\right)!}x^1y^4+\frac{5!}{5!\left(5-5\right)!}x^0y^5[/tex]
solving
[tex]\frac{5!}{0!\left(5-0\right)!}x^5y^0[/tex]
[tex]=1\cdot \frac{5!}{0!\left(5-0\right)!}x^5[/tex]
[tex]=1\cdot \:1\cdot \:x^5[/tex]
[tex]=x^5[/tex]
also solving
[tex]=\frac{5!}{1!\left(5-1\right)!}x^4y[/tex]
[tex]=\frac{5}{1!}x^4y[/tex]
[tex]=\frac{5}{1!}x^4y[/tex]
[tex]=\frac{5x^4y}{1}[/tex]
[tex]=\frac{5x^4y}{1}[/tex]
[tex]=5x^4y[/tex]
similarly, the result of the remaining terms can be solved such as
[tex]\frac{5!}{2!\left(5-2\right)!}x^3y^2=10x^3y^2[/tex]
[tex]\frac{5!}{3!\left(5-3\right)!}x^2y^3=10x^2y^3[/tex]
[tex]\frac{5!}{4!\left(5-4\right)!}x^1y^4=5xy^4[/tex]
[tex]\frac{5!}{5!\left(5-5\right)!}x^0y^5=y^5[/tex]
so substituting all the solved results in the expression
[tex]=\frac{5!}{0!\left(5-0\right)!}x^5y^0+\frac{5!}{1!\left(5-1\right)!}x^4y^1+\frac{5!}{2!\left(5-2\right)!}x^3y^2+\frac{5!}{3!\left(5-3\right)!}x^2y^3+\frac{5!}{4!\left(5-4\right)!}x^1y^4+\frac{5!}{5!\left(5-5\right)!}x^0y^5[/tex]
[tex]=x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5[/tex]
Therefore,
[tex]\left(x\:+y\right)^5=x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5[/tex]
A basketball player scored 26 points in one game. In basketball, some baskets are worth 3 points, some are worth 2 points, and free-throws are worth 1 point. He scored four more 2-point baskets than he did 3-point baskets. The number of free-throws equaled the sum of the number of 2-point and 3-point shots made. How many free-throws, 2-point shots, and 3-point shots did he make?
Answer:
3 points = 2
2 points = 6
1 point = 8
Step-by-step explanation:
Given that:
Total point scored = 26
Let number of 3 point basket = x
Number of 2 point basket = x + 4
Number of free throws = x + x + 4 = 2x + 4
Hence,
Total 3 points = 3x
Total 2 points 2(x + 4)
Total free throw points = 2x + 4
3x + 2(x + 4) + 2x + 4 = 26
3x + 2x + 8 + 2x + 4 = 26
7x + 12 = 26
7x = 26 - 12
7x = 14
x = 2
Number of 3 points = x = 2
2 points = (x+4) = 2+4 = 6
1 point = (2x+ 4) = 2(2) + 4 = 8
The number of free-throws, 2-point shots, and 3-point sho ts he made are;
free-throws = 8
2 points = 6
3 points = 2
Let the number of 3 points basket be x
He scored four more 2-point baskets than he did 3-point baskets. Thus;
y = x + 4
number of free-throws equaled the sum of the number of 2-point and 3-point sho ts made. Thus;
z = x + x + 4
z = 2x + 4
Thus;
Total 3 points = 3x
Total 2 points = 2(x + 4)
Total fr ee points = 2x + 4
Since he scored a total of 26 points, then;
Which property is not used to simplify the following expression?
Answer:
The last one of commutative property of addition since there is no swapping of numbers related with addition.
Help please: Select all statements that are true about the linear equation. y = 1/2x - 2
A taxi company had 12 taxis originally. After expanding the company now has 18 taxis. Is this an increase or decrease? What was the percent change?
Answer:
This is an increase by 50%.
Step-by-step explanation:
The taxi company has 12 taxis originally, and then got 6 more to get 18. They added, so that is an increase.
18 / 12 = 1.5, so it is a 50% increase.
Please mark as brainliest!
1-2/3+9/2 Plz help!! Best answer with explanation will get Brainiest!!!
Answer: 4.83333333333
Can be the answer probably
Step-by-step explanation:
A hotel has a budget of $16,000 to buy 84 new mattresses. Each mattress costs $209. The hotel manager says, “Since 80 × $200 = $16,000, I can stay within the budget.”Use the drop-down box to tell whether the manager’s reasoning is logical.
The hotel manager’s reasoning
Choose... is or is not
logical.
Answer:
No, it isn't logical.
Step-by-step explanation:
The manager is rounding the numbers down, so that will make the estimate go down.
Answer:
The hotel manager's reasoning is not logical.
Step-by-step explanation:
The hotel manager's reasoning is not logical because the total price is extremely overbudget. It would have been more realistic to round it up 210 and do 85 mattresses. They are exactly 1,556 dollars overbudget.
I WILL MARK BRAINIEST
Answer:
x=65
Step-by-step explanation:
x+65=2x
-x -x
----------------
65=x
Brainliest pleaseneed mad help bro, this is so confusing
3) 4 hours worked for $12; 7 hours worked for $28 *
o yes
Answer:
no
Step-by-step explanation:
12 ÷4= 3
7 x3=21
7 hours = $21
Answer:
Not Equivalent.
Step-by-step explanation:
Find the slope plz!!
Answer:
1/4 should be the answer bc it goes up one and over 4. which goes back to the rise over run thing.
Answer:
slope is 1/4
Step-by-step explanation:
[tex]\frac{4-3}{6-2} =\frac{1}{4}[/tex]
A hotel has a budget of $16,000 to buy 84 new mattresses. Each mattress costs $209. The hotel manager says, “Since 80 × $200 = $16,000, I can stay within the budget.”
Answer:
The hotel manager under-estimated. Without estimation, the exact price would be $17,556.
Step-by-step explanation:
He should've over-estimated the money to $210, and the mattresses to 90. So 210 × 90 is $18,900. So even if he did underestimate or overestimate, he still would not have been able to afford the mattresses.
Answer:
hotel has a budget of $16,000 to buy 84 new mattresses. Each mattress costs $209. The hotel manager says, “Since 80 × $200 = $16,000, I can stay within the budget.”
Step-by-step explanation:
100
How many degrees is StartFraction 15 Over 16 EndFraction pi radians? 84.375° 93.75° 168.75° 337.5°
Answer:
x = 168.75°
Step-by-step explanation:
Angle Measurement Units
To convert from different units for angle measurements, we have to recall that:
180 degrees = π radians
If we are given the angle in degrees, multiply by π/180 to convert it to radians.
If the angle is given in radians, multiply by 180/π to convert to degrees.
We are given the angle:
[tex]\displaystyle x=\frac{15}{16}\pi[/tex]
Multiplying by 180/π:
[tex]\displaystyle x=\frac{15}{16}\pi\cdot \frac{180}{\pi}[/tex]
Simplifying:
[tex]\displaystyle x=\frac{15*180}{16}[/tex]
x = 168.75°
Answer:
C. 168.75 degrees
Step-by-step explanation:
Simlplify the expression. 2.3h(6-k)
Answer:
13.8h-2.3hk
Step-by-step explanation:
A 48 ft rope is cut into 5 pieces according to the
ratio 2:2:3:4:5. What is the length. In feet, of the
longest piece?
A. 3
B. 6
C. 9
D. 15
please Answer ASAP
Answer:I think it d
Step-by-step explanation:
The length of the longest piece will be 15 ft.
We have a 48 ft rope is cut into 5 pieces according to the ratio →
2 : 2 : 3 : 4 : 5.
We have to determine the length in feet of the longest piece.
A rope of length 'y' ft is cut in the ratio 2:5. What is the length of smallest piece?Now -
2x + 5x = y
x = [tex]$\frac{y}{7}[/tex]
Smallest piece is of length → 2x → [tex]$\frac{2y}{7}[/tex]
According to the question, we have -
Length of rope = 48 ft
Ratio in which they are cut = 2 : 2 : 3 : 4 : 5.
Therefore -
2x + 2x + 3x + 4x + 5x = 48
16x = 48
x = 3
Length of the longest piece = 5x = 5 x 3 = 15ft
Hence, the length of the longest piece will be 15 ft.
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In which step did Moses first make a mistake in his work?
Which equation has a slope of and goes through the point (-3.4)?
Answer:
Find the Equation of a Line Given That You Know a Point on the Line And Its Slope. The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept.
A system of equations is graphed on the grid.
Which system of equations does the graph represent?
Answer:
y = x + 4
y = -2x - 4
Step-by-step explanation:
Since equation of the line having slope 'm' and y-intercept 'b' is given by,
y = mx + b
Slope of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope of line passing through (1, 5) and (-1, 3),
m = [tex]\frac{5-3}{1+1}[/tex] = 1
y-intercept 'b' = 4
Therefore, equation of the line is,
y = 1.x + 4
y = x + 4
Now slope of another line passing through (-4, 4) and (-1, -2) will be,
m = [tex]\frac{4+2}{-4+1}[/tex]
m = -2
y-intercept 'b' of this line = -4
Equation of the other line,
y = (-2)x - 4
y = -2x - 4
Therefore, system of equations is,
y = x + 4
y = -2x - 4
The system of equations is given by: y = x + 4 and y = -2x - 4
A linear equation is given by:
y = mx + b;
where y, x are variables, m is the rate of change and b is the y intercept.
The first line passes through point (-1, 3) and (1, 5) hence:
[tex]y- y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-3=\frac{5-3}{1-(-1)} (x-(-1))\\\\y=x+4[/tex]
The second line passes through point (-4, 4) and (-1, -2) hence:
[tex]y- y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-4=\frac{-2-4}{-1-(-4)} (x-(-4))\\\\y=-2x-4[/tex]
The system of equations is given by: y = x + 4 and y = -2x - 4
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Another one bites the dust.
Answer:
C
Step-by-step explanation:
PLS GIVE BRAINLIEST
Re write the quadratic function in standard form
y=6(x-3)^2+4
Answer:
y= 6[tex]x^{2}[/tex] - 36x + 58
Step-by-step explanation:
6 ( [tex]x^{2}[/tex] - 6x +9) + 4
6[tex]x^{2}[/tex] - 36x + 54 + 4
6[tex]x^{2}[/tex] - 36x + 58
Find the value of n in the diagram.
Answer:
the answer should be 20
A recipe for macaroni and cheese
calls for 2 cups of cheese; this makes
7 servings. How many cups will you
need for 28 servings?
Answer:
4 cups
Step-by-step explanation:
No explanation
Each factory at a candy company has 199 workers. There are 13 factories.
How many workers are employed at the candy company? pls help me on this
Answer:
2587
Step-by-step explanation:
so 199 workers per factory with 13 factories it is 199 times 13 which equals 2587
Unendo wishes to maximize the weekly profit of producing and selling the game. Find the price, p, per game that generates maximum profit.
Answer:
Following are the solution to this question:
Step-by-step explanation:
Please find the complete question in the attached file.
The highest benefit is where the unit benefit equals the marginal income
Marginal price = 17q
Score of income=-0.05q
MC = MR
MC=17
MR =DERIVATIVE OF ([tex]80q-0.05 q^2[/tex])
[tex]=80-2 \times 0.05q\\\\=80-0.1q[/tex]
[tex]\to MR=MC \\\\[/tex]
[tex]80-0.1q=17\\\\80-17= 0.1q\\\\0.1q=63\\\\q= \frac{63}{0.1}\\\\q=630[/tex]
Retail prices calculation
[tex]\to P=80-630 \times 0.05[/tex]
[tex]=80 -31.5\\\\= 48.5[/tex]
Find the Unit Rate: If 12 50.7 FI. Oz. bottles cost $84 how much does one bottle cost? Find the init Rate.
Your statement is a little ambiguous due to type mistake, so I am assuming you meant to say:
'if 12 fl. oz. bottles cost $84 how much does one bottle cost? Find the Unit Rate.
so I am solving based on '12 fl. oz.' bottles costing $84.
Answer:
unit rate = 7 $ per fl. oz.
Therefore, the 7 $ per fl. oz is the unit rate.
Step-by-step explanation:
We know that a unit rate is basically a fraction (also called ratio) between two different units with a denominator of 1.
For example, kilometers per hour, and heartbeats per minute, etc.
Here, I assume, by 'unit rate' means you mean to say 'cost per fl. oz.'
Given
The cost of 12 fl. oz. bottlers = cost $84
The cost of 1 bottle cost = $84 ÷ 12 oz = 7 $ per fl. oz.
Hence,
unit rate = 7 $ per fl. oz.
Therefore, the 7 $ per fl. oz is the unit rate.
Overall, divorce rates have declined in the last 20 years, but among middle-aged couples, the rates are rising. Do an internet search to find what current statistics are available for different groups of individuals, then describe three factors that contribute to contemporary rises in middle-aged divorce rates.
Answer:
The current divorce rate is about 7% based on the survey.
Step-by-step explanation:
The divorces occur when two person fails to accept each other as a life partner. In the country the divorce rate is about 7% of which mostly couples are at the age of 20 - 25. The people of age 30 plus are less likely to get divorced as they have matured mind sets which accepts each other differences and tries to adjust the situation.
Divorce describes a form of marital separation which is usually undertaken by a court. It occurs when one or both partners decide to quit being married.
The middle age divorce rate continues to rise, as it is being reported in various channels. Currently the middle age divorce rate stands at about 17% per 1000 married person.The causes of rising divorce rates among middle - aged may include :
Rising cases of infidelity as spouses continue to find it difficult to be committed in marrige. Sacrifices which helps foster lasting partnership can no longer be undertaken.
Also, the need to be independent as taken over at this time, as partners begin to see marriage as a bond age which prevents or curtails them from what they would love to indulge in.
Lastly, some now see divorce as norm due to the social influence it has transmitted across to various individuals. Now, so many choose to divorce at any minor challenge marriage brings.
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Is 1/3 greater than 0.4
Answer:
No because 1/3 in decimal form is 0.333333 which is less than 0.4
Step-by-step explanation:
Raju and Ann saved a total of $1560. After Raju gave Ann $50, Raju had 5 times as much money as Ann. How much did Raju have at first?
Step-by-step explanation:
let amt of money Raju has be r and Ann be a.
a + r = 1560
a = 1560 - r --(1)
r - 50 = 5(a + 50)
r = 5a + 300 --(2)
sub (1) into (2):
r = 5(1560 - r) + 300
r = 8100 - 5r
6r = 8100
r = 1350
therefore he has $1350 at first.
Topic: simultaneous eqn + algebraic equations
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An expression is a sentence with a minimum of two numbers or variables and at least one math operation such as addition, subtraction, multiplication, or division.
The amount of money Ann has at first is $1350.
What is an expression?An expression is a sentence with a minimum of two numbers or variables and at least one math operation such as addition, subtraction, multiplication, or division.
We have,
Let the amount of money Raju = R
Let the amount of money Ann = A
Now,
Raju and Ann saved a total of $1560.
This statement can be written as:
R + A = 1560 ____(1)
After Raju gave Ann $50, Raju had 5 times as much money as Ann.
This statement can be written as:
R - 50 = 5 ( A + 50 )
R - 50 = 5A + 250
R - 5A = 250 + 50
R - 5A = 300 _____(2)
From (1)
R = 1560 - A _____(3)
Putting (3) in (2),
1560 - A - 5A = 300
1560 - 6A = 300
1560 - 300 = 6A
1360 = 6A
A = 1260 / 6
A = 210
Putting A = 210 in (3) we get,
R = 1560 - A
R = 1560 - 210
R = 1350
Thus the amount of money Ann has at first is $1350.
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You are rolling one die. Let event A = rolling a six and let event B = rolling a number less than
four. What is the probability of A or B?
Answer:
2/3
Step-by-step explanation:
A = rolling a six
B = rolling a number less than 4
Probability of A or B
P(A) or P(B) = P(A) + P(B) - P(AnB)
Probability = (number of required outcome / Total possible outcomes)
P(A) = 1 / 6
P(B) :
Required outcomes = (3, 2, 1) = 3
P(B) = 3/6 = 1/2
P(AnB) = A={6} ; B = {1,2,3} ; AnB = {}
P(AnB) = 0
Hence,
P(A) or P(B) = 1/6 + 1/2 - 0
= (1 + 3) / 6
= 4/ 6
= 2/3
2. Simplify ((–3)2)3
Answer:
-18
Step-by-step explanation:
((-3)2)3
First, you multiply -3 and 2 which equals -6
-3·2=-6
Then, you multiply -6 and 3 which equals -18
-6·3=-18
Which of the following best describes the graph above?
A. Function only
B. Relation only
C. Both relation and function
D. Neither relation nor a function
Answer: C
Step-by-step explanation:
We know that a relation is any set of ordered pairs, but a function is when there is only one y value for x value.
So, basically, if a graph is a function, it is a relation as well.
Let’s check if this is a function.
We can use the vertical line test- if we draw a vertical line through any point on the graph and it only intersects one point, it is a function
In our case, it passes the vertical line test.
Therefore, it is both a function and a relation, which corresponds to letter C.
Hope this helps! :)