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boyakko [2]
3 years ago
12

Solve the equation 6x + 12 = 4x - 18

Mathematics
2 answers:
Nataly [62]3 years ago
5 0

Answer:

x = 15

Step-by-step explanation:

collect like terms

6x+4x= -18-12

2x= -30

divide through by 2

2x/2= -30/2

x = -15

therefore

x = -15

kenny6666 [7]3 years ago
4 0

Answer:

X = -15

Step-by-step explanation:

6X +12 = 4X -18

Subtract 4X from both sides

2X +12 = -18

Subtract 12 from both sides

2X = -30

Divide both sides by 2

X = -15

So basically just have the unknown on one side and normal numbers on the other. Make sure you do the same thing on both sides.

Mark me as brainliest if this helps!

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⦁ Find the sum of the series . 15 sigma n=1, (2n-1) Show your work
sergejj [24]

Answer:

225

Step-by-step explanation:

The sum of this series is given by the formula:

S_n=\frac{n}{2}[2a+(n-1)d]

Where

S_n is the sum

a is the first term (we get this by plugging in n = 1 into "2n-1", we have 2(1) - 1 = 1)

n is the number of terms (the sum is defined for n = 1 to n = 15, so 15 terms)

d is the common different (the difference is successive terms. Here, 2nd term would be 2(2) - 1 = 3, and first term was 1, so d = 3 -1 = 2)

<em>plugging in the info, we will get the sum:</em>

<em>S_n=\frac{n}{2}[2a+(n-1)d]\\S_{15}=\frac{15}{2}[2(1)+(15-1)(2)]\\=225</em>

<em>The sum is 225</em>

4 0
3 years ago
The ratio of potatoes to turnips is 1:1 if there are 473 potatoes how many turnips are there
navik [9.2K]

Answer:

There would be 473 turnips.

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
On Friday Merinda uses 1/4 of the box of pancake mix to make pancakes. On Saturday she uses 1 1/2 times as much pancake mix as F
Mashutka [201]

Answer:

3/8 of the box

Step-by-step explanation:

On Friday Merinda uses 1/4 of the box of pancake mix to make pancakes.

On Saturday she uses 1 1/2 times as much pancake mix as Friday.

On Friday = 1/4 of the box

On Saturday = 1 1/2 × pancake mix as Friday

\dfrac{3}{2}\times \dfrac{1}{4}\\\\=\dfrac{3}{8}

Hence, 3/8 of the box of pancake mix does Merinda use on Saturday.

4 0
3 years ago
(2(n+1)-1)^2-(2n-1)^2 simplified
Westkost [7]

Answer: 8n

Let's simplify step-by-step.

(2(n+1)−1)2−(2n−1)2

Distribute:

=4n2+4n+1+−4n2+4n+−1

Combine Like Terms:

=4n2+4n+1+−4n2+4n+−1

=(4n2+−4n2)+(4n+4n)+(1+−1)

=8n

7 0
2 years ago
According to a study done by Nick Wilson of Otago University Wellington, the probability a randomly selected individual will not
Lorico [155]

Answer and Step-by-step explanation:

From the question statement we get know that it is Binomial distribution because there are only two possible outcomes so we need to use Binomial Probability Distribution for this question.

Formula for the Binomial Probability Distribution:

P(X)=   p^x q^(n-x)

Where,

  • C_x^n=n!/(n-x)!x!   (i.e. combination)
  • x= total number of successes
  • p=probability of success (p=1-q)  
  • q=probability of failure (q=1-p)
  • n=number of trials
  • P(X)= probability of total number of successes

Answer and explanation for each part of the question are as follow:

a.What is the probability that among 10 randomly observed individuals exactly 4 do not cover their mouth when sneezing?

Solution:

Given that

n=10  

p=0.267 (because p is the probability of success which is “number of individuals not covering their mouths when sneezing” in the question)

q=1-0.267=0.733  

x=4 (number of successes i.e. individuals not covering their mouths)

C_x^n=n!/(n-x)!x!=10!/(10-4)!4!=210

P(X)=C_x^n   p^x q^(n-x)=210×〖(0.267)〗^4×〖0.733〗^(10-4)

P(X)=210×0.00508×0.155  

P(X)=0.165465  

b. What is the probability that among 10 randomly observed individuals fewer than 3 do not cover their mouth when sneezing?

Solution:

Given that

n=10  

p=0.267 (because p is the probability of success which is “number of individuals not covering their mouths when sneezing” in the question)

q=1-0.267=0.733  

x=3 (number of successes i.e. individuals not covering their mouths)

C_x^n=n!/(n-x)!x!=10!/(10-3)!3!=120

P(X)=C_x^n   p^x q^(n-x)=120×(0.267)^3×〖0.733〗^(10-3)

P(X)=120×0.01903×0.1136  

P(X)=0.25962  

c. Would you be surprised if, after observing 18 individuals, fewer than half covered their mouth when sneezing? why?

Solution:

Given that

n=18  

p=0.267 (because p is the probability of success which is “number of individuals not covering their mouths when sneezing” in the question)

q=1-0.267=0.733  

x=9 (x is the number of successes “number of individuals not covering their mouths when sneezing”, if less than half cover their mouth then more than half will not cover), so let x=9

C_x^n=n!/(n-x)!x!=18!/(18-9)!9!=48620

P(X)=48620×(0.267)^9×〖0.733〗^(18-9)  

P(X)=48620×0.00000689×0.0610  

P(X)=0.020  

Yes, I am surprised that probability of less than 9 individuals covering their mouth when sneezing is 0.020. Which is extremely is small.

3 0
3 years ago
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