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4 years ago

I NEED HELP!!!!!!!!!!!!!!!!!!!4/7X+ 5/14X= 39 The solution is _____

Mathematics

2 answers:

den301095 [7]4 years ago

4 0

Answer:

x=42

Your welcome!

weeeeeb [17]4 years ago

3 0

Answer:

x=42

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

4/7*x+5/14*x-(39)=0

Simplify 5/14

((4/7• x) + (5/14 • x)) - 39 = 0

Simplify 4/7

4 5x

((— • x) + ——) - 39 = 0

7 14

Find the Least Common Multiple

The left denominator is : 7

The right denominator is : 14

Number of times each prime factor

appears in the factorization of:

Prime

Factor Left

Denominator Right

Denominator L.C.M = Max

{Left,Right}

7 1 1 1

2 0 1 1

Product of all

Prime Factors 7 14 14

Least Common Multiple:

Calculate multipliers for the two fractions

Denote the Least Common Multiple by L.C.M

Denote the Left Multiplier by Left_M

Denote the Right Multiplier by Right_M

Denote the Left Deniminator by L_Deno

Denote the Right Multiplier by R_Deno

Left_M = L.C.M / L_Deno = 2

Right_M = L.C.M / R_Deno = 1

Calculate multipliers for the two fractions

Denote the Least Common Multiple by L.C.M

Denote the Left Multiplier by Left_M

Denote the Right Multiplier by Right_M

Denote the Left Deniminator by L_Deno

Denote the Right Multiplier by R_Deno

Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

L. Mult. • L. Num. 4x • 2

—————————————————— = ——————

L.C.M 14

R. Mult. • R. Num. 5x

—————————————————— = ——

L.C.M 14

Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

4x • 2 + 5x 13x

——————————— = ———

14 14

13x

——— - 39 = 0

Subtracting a whole from a fraction

Rewrite the whole as a fraction using 14 as the denominator :

39 39 • 14

39 = —— = ———————

1 14

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding up the two equivalent fractions

13x - (39 • 14) 13x - 546

——————————————— = —————————

14 14

Pull out like factors :

13x - 546 = 13 • (x - 42)

13 • (x - 42)

————————————— = 0

When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

13•(x-42)

————————— • 14 = 0 • 14

Now, on the left hand side, the 14 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

13 • (x-42) = 0

Solve : 13 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Solve : x-42 = 0

Add 42 to both sides of the equation :

x = 42

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3 years ago

We learned in Exercise 4.18 that about 90% of American adults had chickenpox before adulthood. We now consider a random sample o

liraira [26]

Answer:

a) 108 people with a standard deviation of 3.286335

b) No

c) 0.218163 or around 21.82%

d) See explanation below.

Step-by-step explanation:

This situation can be modeled with the Binomial Distribution which gives the probability of an event that occurs exactly k times out of n, and is given by

$\large P(k;n)=\binom{n}{k}p^kq^{n-k}$

where

$\large \binom{n}{k}$ = combination of n elements taken k at a time.

p = probability that the event (“success”) occurs once

q = 1-p

In this case, the event “success” is finding an American adult who had chickenpox before adulthood with probability p=0.9

and n=120 American adults in the sample.

The standard deviation for this binomial distribution is

$\large s=\sqrt{npq}$

where n is the sample size 120

We consider a random sample of 120 American adults. How many people in this sample would you expect to have had chickenpox in their childhood?

If about 90% of American adults had chickenpox before adulthood, we expect to find 90% of 120 = 0.9*120=108 people in the sample who had chickenpox in their childhood.

The standard deviation would be

$\large s=\sqrt{120*0.9*0.1=3.286335}$

Would you be surprised if there were 105 people who have had chickenpox in their childhood?

No, because 105 and 108 are in the interval [mean - s, mean +s]

What is the probability that 105 or fewer people in this sample have had chickenpox in their childhood?

The probability that 105 or fewer people in this sample have had chickenpox in their childhood is

$\large \sum_{k=0}^{105}\binom{120}{k}0.9^k0.1^{120-k}$

We compute this value easily with a spreadsheet and we get

$\large \sum_{k=0}^{105}\binom{120}{k}0.9^k0.1^{120-k}=0.218163\approx 21.82\%$

How does this probability relate to your answer to part (b)?

A binomial distribution with np>5 and nq>5 with n the sample size as is the case here, behaves pretty much like a Normal distribution with mean np and standard deviation $\large \sqrt{npq}$ , so around 60% of the data are in the interval [mean -s, mean +s] and 40% outside, so roughly 20% of the data should be in [0, mean-s]