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4 years ago

2(3x+3)=3(2x+2) can someone please help meee !

Mathematics

1 answer:

Mademuasel [1]4 years ago

6 0

2(3x+3)=3(2x+2)

multiply the first bracket by 2

(2)(3x)=6x

(2)(3)=6

multiply the second bracket by 3

(3)(2x)=6x

(3)(2)=6

6x+6=6x+6

move 6x to the left side

sign changes from +6x to -6x

6x-6x+6=6x-6x+6

0+6=0+6

6=6

Answer:

all real numbers

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Write the interval {x|1 < x < 3} as an i inequality<br> and using interval notation.

MA_775_DIABLO [31]

Answer:

1 < x < 3

(1 , 3)

Step-by-step explanation:

We have been provided with a set that is

{x|1 < x < 3}

We have to write it in both as an inequality and also in the form of interval notation.

The inequality can be found easily by just looking at the given set. It states that the set contains x, such that x is greater than 1 and x is smaller than 3, so the inequality can be written as:

1 < x < 3

To write in interval notation, we use brackets, As both 1 and 3 are not included, we'll use round brackets to show the interval.

(1 , 3)

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4 years ago

A researcher is interested in looking at a new type of insulin that can treat diabetics with high fasting glucose levels. Suppos

Makovka662 [10]

Answer:

The sample size should be at least 79.

Step-by-step explanation:

Let Y be be the resting glocose level of a member of the population chosen randomly, then Y is a random variable with unkown mean λ and Standard deviation σ = 27.

Let X be the sample mean of a sample of lenght n. X has the same mean as Y and the standard deviation is $\sigma = \frac{27}{\sqrt{n}} .$

If n is reasonable high, the Central Limit Theorem states that X has distribution approximately Normal, with mean λ and Standard deviation $sigma = \frac{27}{\sqrt{n}} .$

If we standarize X, we get a random variable W

$W = \frac{X-\lambda}{\frac{27}{\sqrt{n}}} \simeq N(0,1)$

The values of W are tabulated and can be found on the attached file. We want a 95% confidence interval, so we want Z such that

P(-Z < w < Z) = 0.95

Using the symmetry of the normal density function, we get that

P(W < Z) = 0.975

If we look at the table, we will find that Z = 1.96, therefore we have

$P(-1.64 < \frac{X-\lambda}{\frac{27}{\sqrt{n}}} < 1.64) = 0.95$

Equivalently,

$0.95 = P(-1.64*\frac{27}{\sqrt{n}} < X- \lambda < 1.64*\frac{27}{\sqrt{n}})$

Taking out the X and the sign, after reverting the inequalities, we obtain

$P(X -1.64*\frac{27}{\sqrt{n}} < \lambda < X +1.64*\frac{27}{\sqrt{n}}) = 0.95$

Thus, a confidence interval with 95% confidence is

$CI = [ X-1.64*\frac{27}{\sqrt{n}}, X+1.64*\frac{27}{\sqrt{n}}]$

The (absolute) margin of error of this interval is $1.64*\frac{27}{\sqrt{n}} ,$ we want that number to be at most 5, so we take n such that

$1.64*\frac{27}{\sqrt{n}} = 5 \, \rightarrow \frac{1}{\sqrt{n}} = \frac{5}{1.64*27} \, \rightarrow \sqrt{n} = 8.85 \, \rightarrow n = 78.42$

We take n = 79. I hope that works for you!

Download pdf

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3 years ago

Lara’s photo album will hold 5 pictures on each page. She wants to fill all 43 pages with vacation photos. How many photos will

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Answer:

The answer is that Lara would need 9 pages to store all her photos.

Step-by-step explanation:

You would need to first divided 43 divided by 5 to get 8.6.

However, you can't have a tenth of a page so you would have to round to 9 so the answer is that Lara would need 9 pages to store all her photos.

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3 years ago

A store buys a jackets for $20.00 and sells it for 80% more than that what is the selling price of the jacket

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Answer:

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Step-by-step explanation:

in the beginning $20 is %100 so divide 20 by 100 .
you'll get .2 but to make this simple you'll want %10 so multiply .2 times 10 and you get 2 .
now that 2 is %10 and you want %80 you multiply 2 8 times (or add it 8 times) because %10 times 8 = %80 so 2 times 8 = 16 .
now that you have the %80 you want to add it to the %100 because they sold it for %80 then the price they bought if for (you get %180) .
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Answer:

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