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lara31 [8.8K]
3 years ago
8

Find the area and perimeter

Mathematics
1 answer:
Andrei [34K]3 years ago
4 0
I think the answer is 22
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1. A food safety guideline is that the mercury in fish should be below 1 part per million​ (ppm). Listed below are the amounts o
Sauron [17]

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:

                                          \bar x\pm t_{\alpha/2,(n-1)}\times \frac{s}{\sqrt{n}}

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

The critical value is:

t_{\alpha/2,(n-1)}=t_{0.01/2, 7}=t_{0.05,7}=3.143

**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).

6 0
3 years ago
What is 5 times 3773377373
Gwar [14]
5x377337737=1.886688687
8 0
3 years ago
The reciprocal of a fraction must be found to solve the problem. What is the reciprocal fraction that is required?
kolezko [41]
6/31 is the answer for your question.
3 0
2 years ago
Read 2 more answers
Give a geometric description of the following system of equations.a. 2x−4y=12 −3x+6y=−15.b. 2x−4y=12 −5x+3y=10.a. 2x−4y=12 −3x+6
Reptile [31]

Answer:

a. No solution, parallel lines.

b. One solution.

Step-by-step explanation:

Given the system of equations:

a. 2x-4y=12

-3x+6y=-15

b. 2x-4y=12

-5x+3y=10

To give a geometric description of the given system of equations.

The geometric description of a system of equations in 2 variables mean the system of equations will represent the number of lines equal to the number of equations in the system given.

i.e.

Number of planes = Number of variables

Number of lines = Number of equations in the system.

Here, we are given 2 variables and 2 equation in each system.

So, they can be represented in the xy-coordinates plane.

And the number of solutions to the system depends on the following condition.

Let the system of equations be:

A_1x+B_1y+C_1=0\\A_2x+B_2y+C_2=0

1. One solution:

There will be one solution to the system of equations,  If we have:

\dfrac{A_1}{A_2}\neq\dfrac{B_1}{B_2}

2. Infinitely Many Solutions: (Identical lines in the system)

\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}= \dfrac{C_1}{C_2}

3. No Solution:(Parallel lines)

\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}\neq\dfrac{C_1}{C_2}

Now, let us discuss the system of equations one by one:

a. 2x-4y=12 OR 2x-4y-12=0

-3x+6y=-15 OR -3x+6y+15=0

A_1 = 2, B_1 = -4, C_1 = -12\\A_2 = -3, B_2 = 6, C_2= 15

Here, the ratio:

\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2} = -\dfrac{2}{3}\\\dfrac{C_1}{C_2} = -\dfrac{4}{5}

\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}\neq\dfrac{C_1}{C_2}

Therefore, no solution i.e. parallel lines.

b. 2x-4y=12 OR 2x-4y-12=0

-5x+3y=10 OR -5x+3y-10=0

A_1 = 2, B_1 = -4, C_1 = -12\\A_2 = -5, B_2 = 3, C_2 = -10

\dfrac{A_1}{A_2}= -\dfrac{2}{5}\\\dfrac{B_1}{B_2} = -\dfrac{4}{3}\\\dfrac{C_1}{C_2} = -\dfrac{6}{5}

\dfrac{A_1}{A_2}\neq\dfrac{B_1}{B_2}

So, one solution.

Kindly refer to the images attached for the graphical representation of the given system of equations.

6 0
2 years ago
.45, .75, .5, .625 in greatest to least
GREYUIT [131]

Answer:

0.75, 0.625, 0.5, 0.45

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
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