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3 years ago

Solve the equation for x. 2/3x- 1/9x+ 5 = 20

Mathematics

2 answers:

lina2011 [118]3 years ago

8 0

Answer:

x = 27

Step-by-step explanation:

2/3 x - 1/9 x + 5 = 20 Subtract 5 from both sides

2/3 x - 1/9 x = 15 Change 2/3 to x/9

3*2/3*3 - 1/9 x = 15

6/9 x - 1/9 x = 15

5/9 x = 15 Multiply both sides by 9

5x / 9 * 9 = 15 * 9

5x = 135 Divide by 5

x = 27

saw5 [17]3 years ago

7 0

Answer:

27 if variable is near the fraction,

-1/129 if variable is in the denominator and not numerator

Step-by-step explanation:

make 2/3 have the same denominator as -1/9

2/3*3/3=6/9

6/9x-1/9x=5/9

5/9x+5 = 20

20-5 = 15

5/9x = 15

15/(5/9x) -> x= -1/129

if you mean the whole equation has the variable x and no the denominator then it is equal to 27

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The space provided.

gtnhenbr [62]

The answer is 488 sq cm.

rectangle:

A=lw
A=(22)(17)
A=374

triangle:
A=(1/2)bh
A=(1/2)(19)(22-10)
A=(1/2)(19)(12)
A=(1/2)228
A=114

rectangle + triangle:
374 + 114 = 488

5 0

3 years ago

The personnel department of a large corporation wants to estimate the family dental expenses of its employees to determine the f

Verizon [17]

Answer:

CI(95%): [205,5;400.8]dolars

Step-by-step explanation:

Hello!

So you need to construct a confidence interval for the average family dental expenses (μ) using the sample given in the problem. To estimate it you need to first choose a statistic. For this small sample, considering that the variable has a normal distribution (I made a quick Shapiro Wilks test, with p-value 0.3234, you can assume normality) the best statistic to use is the Student's t-test.

t= [x(bar)-μ]/S/√n ≈ t₍ₙ₋₁₎

The formula for the confidence interval to estimate the mean is

x(bar)± $t_{n-1; 1-\alpha/2}$ * (S/√n)

The critical value is from a t-distribution with 11 degrees of freedom

± $t_{n-1; 1-\alpha/2} = t_{11; 0.975} = 2.201$

>remember since it's two-tailed, to get the right critical value you have to divide α by 2. So in the text, you received a confidence level of 1-α=0.95 so α=0.05 then α/2=0.025 and 1-α/2=0.975

To construct the interval, you need to first calculate the sample mean and the standard derivation.

Sample

115; 370; 250; 593; 540; 225; 117; 425; 318; 182; 275; 228

n= 12

∑xi = 3638 ∑xi² = 1362670

Sample mean

x(bar): (∑xi)/n = 3638/12 = 303.17 dolars

Standard derivation

S²= 1/n-1*[∑xi²- (∑xi)²/n] = 1/11 * [1362670-((3638)²/12)] = 23614.47 dolars²

S= 153.67 dolars

Confidence interval (95%)

303.17± 2.201* (153.67/√12)