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Nataly_w [17]
3 years ago
6

Solve for x 9 (x +2) < 3(3-5)

Mathematics
1 answer:
Julli [10]3 years ago
7 0

Step-by-step explanation:

9x+18 < 9-15

1)9-15= -6

9x+18 < -6

9x+18= -5

9x= (-5) - 18

9x= -23

x= 23/9=2 5/9

X=2,55556

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Researchers at the National Cancer Institute released the results of a study that investigated the effect of weed-killing herbic
jolli1 [7]

Answer:

The 95% confidence interval for the difference in the proportion of cancer diagnoses between the two groups is (0.3834, 0.5166).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction between normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

The randomly sampled 400 dogs from homes where an herbicide was used on a regular basis, diagnosing lymphoma in 230 of them.

This means that:

p_h = \frac{230}{400} = 0.575, s_h = \sqrt{\frac{0.575*0.425}{400}} = 0.0247

Of 200 dogs randomly sampled from homes where no herbicides were used, only 25 were found to have lymphoma.

This means that:

p_n = \frac{25}{200} = 0.125, s_n = \sqrt{\frac{0.125*0.875}{200}} = 0.0234

Distribution of the difference:

p = p_h - p_n = 0.575 - 0.125 = 0.45

s = \sqrt{s_h^2+s_n^2} = \sqrt{0.0247^2 + 0.0234^2} = 0.034

Confidence interval:

The confidence interval is:

p \pm zs

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

95% confidence level

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

The lower bound is 0.45 - 1.96(0.034) = 0.3834

The upper bound is 0.45 + 1.96(0.034) = 0.5166

The 95% confidence interval for the difference in the proportion of cancer diagnoses between the two groups is (0.3834, 0.5166).

3 0
3 years ago
The price of a bracelet is $1.29. If the tax rate is 5%, find the total cost of<br> the bracelet
Salsk061 [2.6K]

Answer: $1.35

Step-by-step explanation:

1.29 * 5% = 1.29 * 0.05 = 0.0645

0.0645 rounds down to 0.06

1.29 + 0.06 = 1.35

3 0
3 years ago
Help again because i suck
sukhopar [10]

Answer:

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Step-by-step explanation:

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8 0
3 years ago
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The area of a rectangle is 105 square units. Its width measures 7 units. Find the length of its diagonal. Round to the nearest t
mezya [45]

Answer:

16.6

Step-by-step explanation:

The rectangle has an area of 105. It's width is 7.

1: Find the length

     \frac{area}{width}=length

     \frac{105}{7}= 15

      Length=15

2: Pythagorean theorem

      a^{2} +b^2=c^2

       7^{2}+15^2=c^2

       49+225=c^2

        275=c^2

         \sqrt{275} = \sqrt{c^2\\}

          16.55≈c

           Rounded to nearest tenth

              16.6

6 0
3 years ago
If h(x)=(fog)(x) and h(x) = sqrt x+5, find g(x) if f(x) = sqrtx+2
Katen [24]

Answer: The value of g(x) is x+3.

Step-by-step explanation:

Since we have given that

h(x)=f\circ g(x)

Here,

h(x)=\sqrt{x+5}\\\\and\\\\f(x)=\sqrt{x+2}

We need to find the value of g(x):

f(x)=\sqrt{x+2}\\\\f(g(x))=\sqrt{g(x)+2}\\\\h(x)=\sqrt{g(x)+2}\\\\\sqrt{x+5}=\sqrt{g(x)+2}\\\\x+5=g(x)+2\\\\g(x)=x+5-2=x+3

Hence, the value of g(x) is x+3.

3 0
3 years ago
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