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Korolek [52]
3 years ago
5

6x-2(-3x-5)=154 What the answer

Mathematics
1 answer:
Fofino [41]3 years ago
7 0

Answer:

x = 12

Step-by-step explanation:

Simplifying

6x + -2(-3x + -5) = 154

Reorder the terms:

6x + -2(-5 + -3x) = 154

6x + (-5 * -2 + -3x * -2) = 154

6x + (10 + 6x) = 154

Reorder the terms:

10 + 6x + 6x = 154

Combine like terms: 6x + 6x = 12x

10 + 12x = 154

Solving

10 + 12x = 154

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-10' to each side of the equation.

10 + -10 + 12x = 154 + -10

Combine like terms: 10 + -10 = 0

0 + 12x = 154 + -10

12x = 154 + -10

Combine like terms: 154 + -10 = 144

12x = 144

Divide each side by '12'.

x = 12

Simplifying

x = 12

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A survey was conducted to determine the average age at which college seniors hope to retire in a simple random sample of 101 sen
tatyana61 [14]

Answer:

96% confidence interval for desired retirement age of all college students is [54.30 , 55.70].

Step-by-step explanation:

We are given that a survey was conducted to determine the average age at which college seniors hope to retire in a simple random sample of 101 seniors, 55 was the  average desired retirement age, with a standard deviation of 3.4 years.

Firstly, the Pivotal quantity for 96% confidence interval for the population mean is given by;

                         P.Q. =  \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }  ~ t_n_-_1

where, \bar X = sample average desired retirement age = 55 years

            \sigma = sample standard deviation = 3.4 years

            n = sample of seniors = 101

            \mu = true mean retirement age of all college students

<em>Here for constructing 96% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.</em>

<u>So, 96% confidence interval for the population mean, </u>\mu<u> is ;</u>

P(-2.114 < t_1_0_0 < 2.114) = 0.96  {As the critical value of t at 100 degree

                                               of freedom are -2.114 & 2.114 with P = 2%}  

P(-2.114 < \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } } < 2.114) = 0.96

P( -2.114 \times {\frac{s}{\sqrt{n} } } < {\bar X-\mu} < 2.114 \times {\frac{s}{\sqrt{n} } } ) = 0.96

P( \bar X-2.114 \times {\frac{s}{\sqrt{n} } } < \mu < \bar X+2.114 \times {\frac{s}{\sqrt{n} } } ) = 0.96

<u>96% confidence interval for</u> \mu = [ \bar X-2.114 \times {\frac{s}{\sqrt{n} } } , \bar X+2.114 \times {\frac{s}{\sqrt{n} } } ]

                                           = [ 55-2.114 \times {\frac{3.4}{\sqrt{101} } } , 55+2.114 \times {\frac{3.4}{\sqrt{101} } } ]

                                           = [54.30 , 55.70]

Therefore, 96% confidence interval for desired retirement age of all college students is [54.30 , 55.70].

7 0
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The given details are illustrations of addition and subtractions of fractions.  The scuba driver is at an elevation of -5\frac{1}{15} ft below the sea  level.

Given that:

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From the question, we understand that the diver starts at the sea level.

This is represented with 0ft.

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