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siniylev [52]
3 years ago
12

What is the solution to 3/4(x+8)>1/2(2x+10)

Mathematics
1 answer:
Kryger [21]3 years ago
4 0

Answer:

3/4(x+8)=1/2(2x+10)  

One solution was found :

x = 4

Rearrange:

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

3/4*(x+8)-(1/2*(2*x+10))=0  

Step by step solution:

Step  1  :

           1

Simplify   —

           2

Equation at the end of step  1  :

  3                1

 (— • (x + 8)) -  (— • (2x + 10))  = 0  

  4                2

Step  2  :

Step  3  :

Pulling out like terms :

3.1     Pull out like factors :

  2x + 10  =   2 • (x + 5)  

Equation at the end of step  3  :

  3                

 (— • (x + 8)) -  (x + 5)  = 0  

  4                

Step  4  :

           3

Simplify   —

           4

Equation at the end of step  4  :

  3                

 (— • (x + 8)) -  (x + 5)  = 0  

  4                

Step  5  :

Equation at the end of step  5  :

 3 • (x + 8)    

 ——————————— -  (x + 5)  = 0  

      4          

Step  6  :

Rewriting the whole as an Equivalent Fraction :

6.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  4  as the denominator :

            x + 5     (x + 5) • 4

   x + 5 =  —————  =  ———————————

              1            4      

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 fractions that have a common denominator :

6.2       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:

3 • (x+8) - ((x+5) • 4)     4 - x

———————————————————————  =  —————

           4                  4  

Equation at the end of step  6  :

 4 - x

 —————  = 0  

   4  

Step  7  :

When a fraction equals zero :

7.1    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:

 4-x

 ——— • 4 = 0 • 4

  4  

Now, on the left hand side, the  4  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  4-x  = 0

Solving a Single Variable Equation :

7.2      Solve  :    -x+4 = 0  

Subtract  4  from both sides of the equation :  

                     -x = -4

Multiply both sides of the equation by (-1) :  x = 4

One solution was found :

                  x = 4

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A particular variety of watermelon weighs on average 20.4 pounds with a standard deviation of 1.23 pounds. Consider the sample m
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d) This value is c = 20.6153.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation \frac{\sigma}{\sqrt{n}}.

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

A particular variety of watermelon weighs on average 20.4 pounds with a standard deviation of 1.23 pounds. This means that \mu = 20.4, \sigma = 1.23

Consider the sample mean weight of 100 watermelons of this variety. This means that n = 100.

a. What is the expected value of the sample mean weight? Give an exact answer.

By the Central Limit Theorem, it is the same as the mean of the population. So the expected value of the sample mean weight is 20.4 pounds.

b. What is the standard deviation of the sample mean weight? Give your answer to four decimal places.

By the Central Limit Theorem, that is:

s = \frac{\sigma}{\sqrt{n}} = \frac{1.23}{\sqrt{100}} = 0.123

The standard deviation of the sample mean weight is 0.123.

c. What is the approximate probability the sample mean weight will be less than 20.27?

This is the pvalue of Z when X = 20.27.

Since we are working with the sample mean, we use s instead of \sigma in the Z score formula

Z = \frac{X - \mu}{s}

Z = \frac{20.27 - 20.4}{0.123}

Z = -1.06

Z = -1.06 has a pvalue of 0.1446.

This means that there is a 14.46% probability the sample mean weight will be less than 20.27.

d. What is the value c such that the approximate probability the sample mean will be less than c is 0.96?

This is the value of X = c that is in the 96th percentile, that is, it's Z score has a pvalue 0.96.

So we use Z = 1.75

Z = \frac{X - \mu}{s}

1.75 = \frac{c - 20.4}{0.123}

c - 20.4 = 0.123*1.75

c = 20.6153

This value is c = 20.6153.

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