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marta [7]
3 years ago
10

If the measures of the angles of a triangle are represented by 2x,3x -15 and 7x +15 the triangle is

Mathematics
1 answer:
SIZIF [17.4K]3 years ago
7 0
To get the type of triangle mentioned we need to find the value of x first.
Sum of angles in a triangle add up to 180°, thus
2x+(3x-15)+(7x+15)=180
2x+3x-15+7x+15=180
12x=180
x=15°
thus the respective sizes will be:
2x=30°
3x-15=30°
7x+15=120°
Since the triangle has two congruent angles we conclude that the triangle is called Isosceles triangle
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Answer:

The confidence interval estimate of the population mean is :

(0.61 ppm, 0.90 ppm)

The correct option is (A).

Step-by-step explanation:

The amounts of mercury​ (ppm) found in tuna sushi sampled at different stores in a major city are:

S = {0.58, 0.82, 0.10, 0.98, 1.27, 0.56, 0.96}

A (100-\alpha )\% confidence interval for the population mean (μ) is an interval estimate of the true value of the mean. This interval has a (100-\alpha )\% probability of consisting the true value of mean.

⇒ Since the population standard deviation is not provided we will use the <em>t</em>-distribution to construct the 99% confidence interval for mean.

⇒ The formula for confidence interval for the population mean is:

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Here,

\bar x = sample mean

<em>s </em>= sample standard deviation

<em>n</em> = sample size

t_{\alpha/2,(n-1)} = critical value.

The degrees of freedom for the critical value is, (<em>n</em> - 1) = 7 - 1 = 6.

The significance level is: \alpha =1-Confidence\ level=1-0.99=0.01

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**Use the <em>t</em>-table for the critical value.

Compute the sample mean and sample standard deviation as follows:

\bar x=\frac{1}{7}(0.58+ 0.82+ 0.10+ 0.98+ 1.27+ 0.56+ 0.96) =0.753

\int\limits^a_b {x} \, dx s=\sqrt{\frac{\sum (x{i}-\bar x)^{2}}{n-1} } =\sqrt{\frac{1}{6} \times 0.859743} =0.379

The 99% confidence interval for μ is:

x^{2} CI=0.753\pm 3.143\times\frac{0.379}{\sqrt{7}} \\=0.753\pm0.143\\=(0.61, 0.896)\\\approx(0.61, 0.90)

The confidence interval estimate of the population mean is:

(0.61 ppm, 0.90 ppm)

The upper and lower limit of the 99% confidence interval indicates that the true mean value is less than 1 ppm. This implies that there is not too much mercury in tuna sushi

Because it is possible that the mean is not greater than 1 ppm. Also, at least one of the sample values is less than 1 ppm, so at least some of the fish are safe.

Thus, the correct option is (A).

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