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vampirchik [111]
2 years ago
12

4.16×10^−5 divided by 8.0×10^−4 in scientific notation

Mathematics
1 answer:
Fynjy0 [20]2 years ago
6 0

Answer: 13/250 or 0.052

Step-by-step explanation:

4.16 (1/100000)/ 8 (10^-4)

Then keep doing order of operations and dividing down.

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(3x + 5y = 7<br> { 4x - y = 5
dalvyx [7]

Answer:

Step-by-step explanation:

Solution by substitution method

3x+5y=7

and 4x-y=5

Suppose,

3x+5y=7→(1)

and 4x-y=5→(2)

Taking equation (2), we have

4x-y=5

⇒y=4x-5→(3)

Putting y=4x-5 in equation (1), we get

3x+5y=7

⇒3x+5(4x-5)=7

⇒3x+20x-25=7

⇒23x-25=7

⇒23x=7+25

⇒23x=32

⇒x=32/23

→(4)

Now, Putting x=32/23

in equation (3), we get

y=4x-5

⇒y=4(32/23)-5

⇒y=(128-115)/23

⇒y=13/23

∴y=13/23   and x=32/23

5 0
1 year ago
Triangle ABC is shown on the grid below. Which value best represents the length of AB
ankoles [38]

Answer:

Lenght us 6

Step-by-step explanation:

7 0
2 years ago
|3k-2|=2|k+2| solve please
djyliett [7]
3k-2=2k+4
-2k. -2k
k-2=4
+2. +2
k =6
4 0
3 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
Write the equation of a parabola having the vertex (1, −2) and containing the point (3, 6) in vertex form. Then, rewrite the equ
In-s [12.5K]
PART A

The equation of the parabola in vertex form is given by the formula,

y - k = a {(x - h)}^{2}

where

(h,k)=(1,-2)

is the vertex of the parabola.

We substitute these values to obtain,


y  + 2 = a {(x - 1)}^{2}

The point, (3,6) lies on the parabola.

It must therefore satisfy its equation.


6  + 2 = a {(3 - 1)}^{2}


8= a {(2)}^{2}


8=4a


a = 2
Hence the equation of the parabola in vertex form is


y  + 2 = 2 {(x - 1)}^{2}


PART B

To obtain the equation of the parabola in standard form, we expand the vertex form of the equation.

y  + 2 = 2{(x - 1)}^{2}

This implies that

y + 2 = 2(x - 1)(x - 1)


We expand to obtain,


y + 2 = 2( {x}^{2}  - 2x + 1)


This will give us,


y + 2 = 2 {x}^{2}  - 4x + 2


y =  {x}^{2}  - 4x

This equation is now in the form,

y = a {x}^{2}  + bx + c
where

a=1,b=-4,c=0

This is the standard form
7 0
3 years ago
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