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2 years ago

What value of x is in the solution set of 2(3x - 1) = 4x - 6? EO -10

Mathematics

2 answers:

lakkis [162]2 years ago

8 0

Answer:

x = - 1

Step-by-step explanation:

Given

2(3x - 1) ≥ 4x - 6 ← distribute parenthesis on left side

6x - 2 ≥ 4x - 6 ( subtract 4x from both sides )

2x - 2 ≥ - 6 ( add 2 to both sides )

2x ≥ - 4 ( divide both sides by 2 )

x ≥ - 2

The only value in the list greater than - 2 is - 1

x = - 1 is in the solution set

tensa zangetsu [6.8K]2 years ago

5 0

Answer:

D) -1

Step-by-step explanation:

6x-2≥4x-6

6x-4x≥-6+2

2x≥-4

x≥-4÷2

x≥-2

Only -1 is greater than -2 in the list.

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2 years ago

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Gina sold 5/8 of a mushroom pizza and 3/4 of an onion pizza to the same family.How much pizza in all did the family buy?

Murrr4er [49]

Answer:

1 and 3/8 of pizza

Step-by-step explanation:

5/8 + 3/4

3/4 x 2 to get the same denominator as 5/8

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2 years ago

Pedro cut a sheet of poster board into 10 equal parts. His brother used some of the poster board and now 8/10 is left. Pedro wan

yawa3891 [41]

Answer: 8

Step-by-step explanation:

Given: Pedro cut a sheet of poster board into 10 equal parts.

let x be the total sheet.

then, one part of sheet= $\frac{1}{10}$ of the sheet

Now, His brother used some of the poster board and now 8/10 is left.

Therefore, if Pedro wants to make a sign from each remaining part of the poster board.

then, The number of signs he can make= $\frac{8}{10}\div \frac{1}{10}=\frac{8}{10}\times\frac{10}{1}=8$

Hence, Pedro can make 8 signs.

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2 years ago

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A random sample from a normal population is obtained, and the data are given below. Find a 90% confidence interval for . 114 157

melamori03 [73]

Answer:

$103.160 \leq \sigma \leq 187.476$

And the upper bound rounded to the nearest integer would be 187.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

Data given: 114 157 203 257 284 299 305 344 378 410 421 450 478 480 512 533 545

The confidence interval for the population variance $\sigma^2$ is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

On this case we need to find the sample standard deviation with the following formula:

$s=sqrt{\frac{\sum_{i=1}^{17} (x_i -\bar x)^2}{n-1}}$

And in order to find the sample mean we just need to use this formula:

$\bar x =\frac{\sum_{i=1}^n x_i}{n}$

The sample mean obtained on this case is $\bar x= 362.941$ and the deviation s=132.250

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=17-1=16$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a tabel to find the critical values.