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navik [9.2K]
2 years ago
9

Ethan bought 4 packages of pencils. After he gave 8 pencils to his friends, he had 40 pencils left over. How many pencils were i

n each package? Use the drop-down menus to solve the problem arithmetically and algebraically
Mathematics
1 answer:
swat322 years ago
8 0

Answer:

12 pencils in each package.

Step-by-step explanation:

Given:

Ethan bought 4 packages of pencils.

No of Packages = 4

No of pencils given to friend = 8 pencils

No of pencils left over =40 pencils

∴Total Number of Pencils = No of pencils given to friend + No of pencils left over =40+8 =48

Total Number of pencils in each package = \frac{\textrm{Total Number of Pencils}}{\textrm{No Of Packages}}= \frac{48}{4}= 12 \ pencils

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Which of the following is the expansion of (3c + d2)6?
vovangra [49]

Answer: Option A) 729c^6 + 1,458c^5d^2 + 1,215c^4d^4 + 540c^3d^6 + 135c^2d^8 + 18cd^{10} + d^{12} is the correct expansion.

Explanation:

on applying binomial theorem,  (a+b)^n=\sum_{r=0}^{n} \frac{n!}{r!(n-r)!} a^{n-r} b^r

Here a=3c, b=d^2 and n=6,

Thus, (3c+d^2)^6=\sum_{r=0}^{6} \frac{6!}{r!(6-r)!} (3c)^{n-r} (d^2)^r

⇒ (3c+d^2)^6= \frac{6!}{(6-0)!0!} (3c)^{6-0}.(d^2)^0+\frac{6!}{(6-1)!1!} (3c)^{6-1}.(d^2)^1+\frac{6!}{(6-2)!2!} (3c)^{6-2}.(d^2)^2+\frac{6!}{(6-3)!3!} (3c)^{6-3}.(d^2)^3+\frac{6!}{(6-4)!4!} (3c)^{6-4}.(d^2)^4+\frac{6!}{(6-5)!5!} (3c)^{6-5}.(d^2)^5+\frac{6!}{(6-6)!6!} (3c)^{6-6}.(d^2)^6

⇒(3c+d^2)^6= \frac{6!}{(6-)!0!} (3c)^6.d^0+\frac{6!}{(5)!1!} (3c)^5.d^2+\frac{6!}{(4)!2!} (3c)^4.d^4+\frac{6!}{(6-3)!3!} (3c)^3.d^6+\frac{6!}{(2)!4!} (3c)^2.d^8+\frac{6!}{(1)!5!} (3c).d^{10}+\frac{6!}{(0)!6!} (3c)^0.d^{12}

⇒(3c+d^2)^6=(3c)^6.d^0+\frac{720}{120} (3c)^5.d^2+\frac{720}{48} (3c)^4.d^4+\frac{720}{36} (3c)^3.d^6+\frac{720}{48} (3c)^2.d^8+\frac{720}{120} (3c).d^{10}+.d^{12}

⇒(3c+d^2)^6=729c^6 + 1,458c^5d^2 + 1,215c^4d^4 + 540c^3d^6 + 135c^2d^8 + 18cd^{10} + d^{12}

3 0
2 years ago
Read 2 more answers
Adam, imran and shakeel we're playing a card game. Adam scored × points Imran scored 3 points fewer than Adam Shakeel scored twi
Alex_Xolod [135]

Answer:

Step-by-step explanation:

During the card game, the number of points that Adam scored is x. Imran scored 3 points fewer than Adam. It means that the number of points that Imran scored is

(x - 3) points

I)Shakeel scored twice as many points as imran. It means that the expression for the number of points that Shakeel scored is

2(x - 3) points

Ii) Together they scored 39 points. Therefore, the equation which may be used to find the value of × would be

x + x - 3 + 2(x - 3) = 39

x + x - 3 + 2x - 6 = 39

x + x + 2x - 3 - 6 = 39

4x - 9 = 39

3 0
2 years ago
A new technology for the production of integrated circuits is being mastered. The technology will be rejected if the percentage
max2010maxim [7]

Answer:

5901

Step-by-step explanation:

The margin of error is the critical value times the standard error.

ME = CV × SE

For α = 0.05, the critical value is z = 1.96.

The standard error of a proportion is √(pq/n).  Given p = 0.04, then q = 1−p = 0.96.

The margin of error is 0.5% or 0.005.

Plugging in:

0.005 = 1.96 √(0.04 × 0.96 / n)

n ≈ 5901

8 0
1 year ago
Solve for $a$: $3a-7(3-a)=5$. Express your answer as a common fraction in simplest form.
SashulF [63]

Answer:

2.6

Step-by-step explanation:

just put one part of the equation in y1 and the other in y2 and hit 2nd trace 5 an hit enter 4 times

then it will bring a graph hit enter 3 time again and it will show u the answer at the bottom left

3 0
2 years ago
Question 1(Multiple Choice Worth 2 points)
earnstyle [38]
These are 3 questions and 3 answers.

1) Find


\lim_{x \to \ 2^+} f(x)

Answer: 4.

Explanation:

The expression means the limit as the function f(x) approaches 2 from the right.

Then, you have to use the function (the line) that comes from the right of 2 and gets as close as you want to x = 2.

That is the line that has the open circle around y = 4, and that is the limit searched.

2) Use the graph to determine the limit if it exists.

Answer:

\lim_{x \to \ 2^-} f(x) = 3

\lim_{x \to \ 2^+} f(x)=-3

To determine each limit you use the function from the side the value of x is being approached.

Note, that since the two limits are different it is said that the limit of the function as it approaches 2 does not exist.

3) 
Answer: - 1


\lim_{x \to \ 3^-} f(x) = -1

To find the limit when the function is approached to 3 from the left you follow the line that ends with the open circle at (3, -1).

Therefore, the limit is - 1.
5 0
2 years ago
Read 2 more answers
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