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3 years ago

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

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

So, 96% confidence interval for the population mean, $\mu$ is ;

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

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

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

= [54.30 , 55.70]

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

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3 years ago

A tiger ate food that weighed 15% of its body weight. If it ate 75lb., how much does the tiger weigh?

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11.25 lbs, if I calculated this correctly.

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3 years ago

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