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2 years ago

Solve 5/3x + 1/3x = 13 1/3 + 8/3x then identify x.

Mathematics

1 answer:

belka [17]2 years ago

3 0

After solving $\frac{5}{3}x+\frac{1}{3}x=13\frac{1}{3}+\frac{8}{3}x$ we get value of x = -20

Step-by-step explanation:

We need to solve the fractions and find value of x.

The given fraction is:

$\frac{5}{3}x+\frac{1}{3}x=13\frac{1}{3}+\frac{8}{3}x$

Solving:

$\frac{5}{3}x+\frac{1}{3}x=13\frac{1}{3}+\frac{8}{3}x\\\frac{5}{3}x+\frac{1}{3}x=\frac{40}{3}+\frac{8}{3}x\\ Subtract\,\,\frac{8}{3}x\,\,on\,\,both\,\,sides:\\ \frac{5}{3}x+\frac{1}{3}x-\frac{8}{3}x=\frac{40}{3}+\frac{8}{3}x-\frac{8}{3}x\\Simplifying:\\ \frac{5x+1x-8x}{3}=\frac{40}{3}\\ \frac{-2x}{3}=\frac{40}{3}\\Multiply\,\,both\,\,sides\,\,by\,\,3\\-2x=40\\x=\frac{40}{-2}\\x=-20$

So, After solving $\frac{5}{3}x+\frac{1}{3}x=13\frac{1}{3}+\frac{8}{3}x$ we get value of x = -20

Keywords: Solving fractions

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A liquid dietary product implies in its advertising that use of the product for one month results in an average weight loss of a

BigorU [14]

Answer:

Following are the responses to the given question:

Step-by-step explanation:

Please find the table in the attached file.

mean and standard deviation difference: $\bar{d}=\frac{\Sigma d}{n} =\frac{-4-6-.......-4-4}{8}=-4.125 \\\\S_d=\sqrt{\frac{\Sigma (d-\bar{d})^2 }{n-1}}=\sqrt{\frac{(-4 + 4.125)^2 +.......+(-4 +4.125)^2 }{8-1}}= 1.246$

For point a:

hypotheses are:

$H_0 : \mu_d \geq -3\\\\H_a : \mu_d < -3\\\\$

degree of freedom:

$df=n-1=8-1=7$

From t table, at $\alpha = 0.05$ , reject null hypothesis if $t$ .

test statistic:

$t=\frac{\bar{d}-\mu_d }{\frac{s_d}{\sqrt{d}}}=\frac{ -4.125- (-3)}{\frac{1.246}{ \sqrt{8}}} =-2.55$

because the $t=-2.553$ , removing the null assumption. Data promotes a food product manufacturer's assertion with a likelihood of Type 1 error of 0.05.

For point b:

From t table, at $\alpha =0.01$ , removing the null hypothesis if $t$ .

because $t=-2.553 >-2.908$ , fail to removing the null hypothesis.

The data do not help the foodstuff producer's point with the likelihood of a .01-type mistake.

For point c:

Hypotheses are:

$H_0: \mu_d \geq -5\\\\H_a: \mu_d < -5$

Degree of freedom:

$df=n-1=8-1=7$

From t table, at $\alpha =0.05$ , removing the null hypothesis if $t$ .

test statistic: $t=\frac{\bar{d}-\mu_d}{\frac{s_d}{\sqrt{n}}} =\frac{-4.125-(-5)}{\frac{1.246}{\sqrt{8}}}=1.986$

Since $t-1.986 >-1.895$ , The null hypothesis fails to reject. The results do not support the packaged food producer's claim with a Type 1 error probability of 0,05.

From t table, at $\alpha= 0.01$ , reject null hypothesis if $t$ .

Since $t=1.986>-2.998$ , fail to reject null hypothesis.

Data do not support the claim of the producer of the dietary product with the probability of Type 1 error of .01.

5 0

2 years ago

Kelvin and Lewie each design surveys in order to determine the average number of people who buy food at the mall. Kelvin surveys

Lisa [10]

Answer:

Lewie Survey produces less valid result.

Step-by-step explanation:

Given:

1. Kelvin surveys every other person leaving the food area.

2. Lewie surveys every fifth person leaving the mall's main entrance.

Therefore,

Kelvin will able to produce valid result as he is surveying every person who is leaving food court.

Means,

There are high chances that would have bought food from the court.

Whereas,

Lewie is surveying every fifth person leaving the the mall's entrance.

Therefore,

Here probability to produce valid result is less as they may have not buy food or they may visited other shops.

So, Lewie survey will produce less valid result.

8 0

1 year ago

Read 2 more answers

A. The average yearly salary of a lawyer is $24 thousand less than twice that of an architect.

erastovalidia [21]

Answer:

The average yearly salary of the architect is $62,000 and the lawyer is $100,000.

Step-by-step explanation:

Given:

The average yearly salary of a lawyer is $24 thousand less than twice that of an architect.

Combined, an architect and a lawyer earn $ 210 thousand.

Now, to find the average yearly salary of an architect and a lawyer.

Let the average yearly salary of an architect be $x.$

So, the average yearly salary of the lawyer = $2x-24,000.$

Combined, architect and lawyer earn = $\$210,000.$

Now, to get the average salary of the architect and lawyer:

$x+(2x-24000)=210000$

$x+2x-24000=210000\\\\3x-24000=210000$

Adding both sides 24000 we get:

$3x=186,000\\\\Dividing\ both\ sides\ by\ 3\ we\ get:\\\\x=62000.$

The average salary of architect = $62,000.

Now, to get the average salary of lawyer by substituting the value of $x$ :

$2x-24000\\\\=2(62000)-24000\\\\=124000-24000\\\\=\$100,000.$

The average salary of lawyer = $100,000.

Therefore, the average yearly salary of the architect is $62,000 and the lawyer is $100,000.

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2 years ago

An element with mass 730 grams decays by 28.8% per minute. How much of the element is remaining after 10 minutes, to the nearest

trasher [3.6K]

$\bf \qquad \textit{Amount for Exponential Decay}\\\\
A=P(1 - r)^t\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{initial amount}\to &730\\
r=rate\to 28.8\%\to \frac{28.8}{100}\to &0.288\\
t=\textit{elapsed time}\to &10\\
\end{cases}
\\\\\\
A=730(1-0.288)^{10}\implies A=730(0.712)^{10}$

6 0

2 years ago

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Lulu used these steps to solve the equation 8x−2=2(4x−2)8x-2=2(4x-2). Which choice describes the meaning of her result, -2=-4-2=

monitta

I would choose B. because first of all negative -2 can't be equal to -4 (but that's just my opinion)

6 0

2 years ago

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