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mars1129 [50]
3 years ago
6

Solve for x: four over five x + four over three = 2x

Mathematics
1 answer:
makkiz [27]3 years ago
8 0
The answer is...: x = 10/9
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The values of 60, 62, and 84 were common to both samples. The three values are identified as outliers with respect to the age-gr
postnew [5]

Answer:

Only 60 is an identified outlier

Step-by-step explanation:

Given

<u>Age group: 40 to 50</u>

Min = 60           Q_1 = 70           Median= 73

Q_3 = 76              Max = 85

<u>Conditions for outlier</u>

Value > Q_3 + 1.5 * IQR

Value < Q_1 - 1.5 * IQR

<em>See attachment for complete question</em>

<u>Required</u>

Which of 60, 62 and 84 is an outlier of age grout 40 to 50 years

First, calculate the IQR of group 40 to 50.

This is calculated as:

IQR = Q_3 - Q_1

Where:

Q_3 = 76 and Q_1 = 70

So:

IQR = 76 - 70

IQR = 6

<em>Next, is to test the outlier conditions on each value (i.e. 60, 62 and 84)</em>

<u></u>

<u>Testing 60</u>

<u>Condition 1</u>

Value > Q_3 + 1.5 * IQR

60 > 76 + 1.5 * 6

60 > 76 + 9

60 > 85 --- False

<u>Condition 2</u>

Value < Q_1 - 1.5 * IQR

60 < 70 - 1.5 * 6

60 < 70 - 9

60 < 61 --- True

<em>Because one of the conditions is true, then 60 is an outlier of group 40 - 50 years</em>

<em></em>

<u>Testing 62</u>

<u>Condition 1</u>

Value > Q_3 + 1.5 * IQR

62> 76 + 1.5 * 6

62 > 76 + 9

62 > 85 --- False

<u>Condition 2</u>

Value < Q_1 - 1.5 * IQR

62 < 70 - 1.5 * 6

62 < 70 - 9

62 < 61 --- False

<em>Because both conditions are false, then 62 is  not an outlier of group 40 - 50 years</em>

<em></em>

<u>Testing 84</u>

<u>Condition 1</u>

Value > Q_3 + 1.5 * IQR

84> 76 + 1.5 * 6

84 > 76 + 9

84 > 85 --- False

<u>Condition 2</u>

Value < Q_1 - 1.5 * IQR

84 < 70 - 1.5 * 6

84 < 70 - 9

84 < 61 --- False

<em>Because both conditions are false, then 84 is  not an outlier of group 40 - 50 years</em>

5 0
3 years ago
What is the sum of the complex number 2+3i and 4+8i, where i=√-1?
ser-zykov [4K]
2+3i+4+8i
2+4+3i+8i
6+11i
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3 years ago
Please help me on this it’s due please help me
GuDViN [60]
9 1/2 * 15.15 = $143.925 dollar
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2 years ago
The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y - 4 =1/4(x-8). What is the slop
Gelneren [198K]

Answer:1/4

Step-by-step explanation:

5 0
3 years ago
PLEASE HELP QUICKLY 15 POINTS, WILL MARK BRAINLIEST
zhuklara [117]

Answer:

Binomial expansion also known as binomial theorem is a quick and easy way of expanding by multiplying binomial expression that has been raised to large power.

Step-by-step explanation:

A binomial is a polynomial with two terms. From the above definition given, if for instance an expression of (5x-4)²² was given, it wouldn't be that easy to multiply out by hand which is why the binomial theorem formula was created.

Another example to buttress this point is if we have (a³+2ab+b2)(a+b) expanding this will give a³+3a2b+b³ = a³+3a2b) +3ab²+b³)a+b = a⁴+ 4a³b+ 6a²b²+4ab³+b4..

This calculation could go on and on because it gets longer as we go but to make it easier and simpler, the best method to use here is the binomial theorem or expansion and the formula states thus:

n. n

(x+y)ⁿ = € {n}xⁿ-k*y^k

k=0 {k} = € {n} x^k*y^n-k

k=0 {k}

{n}

{k}. = binomial coefficient of each term

It should from the example given that we have index power(power raised)called exponent such that when an exponent is 0, we get 1 , i.e anything raised to power 0 =1

e.g (x+y)^0 = 1

And also when an exponent is 1, then the answer remain unchanged such that (x+y)¹= x+y. An exponent of 2 means to multiply given term by itself in two times and so on.

So to expantiate an expression like

a³+3a²b+3ab²+b³.. This expression has its index power(exponent) start with 3 such that .

The a goes down in the form.. 3,2,1,0 while the exponents of b go upwards in the form 0,1,2,3coeffiThe terms 0-n goes thus

k=0 k=1 k=2 k=3

a³ a² a 1

1 b. b² b³

which equals an-kbk.. This is confusing right. This is how it works

k=0 k=1 k=2 k= 3

an-kb^k. an-kb^k an-kb^k an-k^bk

a³-0b^0. a3-1b¹ a3-2b2 a3-3b3

a³ a²b. ab² b³

So when we put all this together we have: a³+a²b+ ab²+ b³. Actually this answer is correct but what we are missing here is the coefficient of n because we needs to include it.

So this becomes a³+3a²b +3ab²+b³ , the coefficient of n here is 3.

Now if we are to look at the result we got before from(a+b)^0 up to (a+b)³

And here that we have 3 as coefficient but where it is not shown we put 1 which is.

1

1a+ 1b

1a+2ab+ 1b²

1a³ +3a²b+3ab²+1b³... We solve this using pascal triangle.

1 This is solved by adding

1 1 each two numbers above

1 2 1 together to get the one

1 3 3 1 below.

1 4 6 4 1

This pascal pattern can be used for any exponents..1,2,3,5....60...120....n

Binomial theorem is basically the essence of this Pascal triangle pattern.

As stated earlier that the formula of binomial theorem is

n

€{n}a^n-kb^k

n-1 where €= summation

n= numbers given

k=coefficient of n

Now, let's to put into practical by solving this expression.

(x+y)ⁿ=€ⁿ {n}a^n-k* b^k

k=0 {k}

But before we solve this, its important we know the basis of Pascal triangle by using factorial to solve it with the formula n!/k!(n-k)! Such that

Factorial is n multiplied in descending order(i.e multiplying Numbers between 1-n)

K- coefficient of n

N- product of all the numbers between 1&n. For instance we are given this 4!/3!(4-3)! = 4!/3!*1!

= 4*3*2*1/3*2*1 *1 = 24/6 = 4

Now let's go back to the previous example of (x+y)ⁿ where n=4

(x+y)⁴= €⁴ {4} x^4-k*y^k

k=0 {k}

(x+y)⁴= €{4} (x^4-0)y^0 + {4} (x^4-1) *y¹

{0} {1}

+{4} (x^4-2)*y² + {4} (x^4-3)*y³

{2} {3}

+ {4} (x^4-4) * (y⁴)

{4}

= 1*x⁴y^0 + 4*x³y¹ + 6*x²y² +4*x¹y³ +1*x^0y⁴=

x⁴+4x³y +6x²y² + 4xy³ +y⁴(Final answer)

Please note that:

When solving binomial theorem expression, the easiest way to do this is by remembering the patterns below:

* first term's exponent start at n and go down

* second term's exponent start at 0 and goes up

* coefficient are solved with pascal triangle using n!/k!(n-k)!

5 0
3 years ago
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