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4 years ago

Express the confidence interval 0.866 (plusminus) 0.037 in open interval form (ie, (0.155,0.855)).

Mathematics

1 answer:

RSB [31]4 years ago

5 0

Answer: (0.829, 0.903)

Step-by-step explanation:

The given confidence interval : 0.866 (plusminus) 0.037

i.e. 0.866 ± 0.037

Identity we use here:

$a\pm b=(a-b,\ a+b)$ (*)

Now, the given confidence interval can be written as :

$0.866 \pm 0.037 \\\\=(0.866-0.037,\ 0.866+0.037)\ \ \text{[By using (*)]}\\\\=(0.829,\ 0.903)$

Hence, the required confidence interval in open interval form would be (0.829, 0.903) .

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A convex hexagon has interior angles with measures x^0, (5x - 103); (2x + 60), (7x - 31), (6x -6), and (9x - 100), what is the v

cestrela7 [59]

Answer:

x = 30.66°

Step-by-step explanation:

The sum of the interior angles of a hexagon is 720°

Each angles are x^0, (5x - 103); (2x + 60), (7x - 31), (6x -6), and (9x - 100),

we add all these angles together

x^0 + (5x - 103) + (2x + 60) + (7x - 31) + (6x -6) + (9x - 100) = 720

x^0 = 1

1 + (5x - 103) + (2x + 60) + (7x - 31) + (6x -6) + (9x - 100)

1 + 5x - 103 +2x + 60 + 7x -31 + 6x - 6 + 9x - 100 = 720

1 - 103 + 60 - 31 - 6 - 100 + 5x + 2x + 7x + 6x + 9x = 720

1 - 180 + 29x = 720

-179 + 29x = 720

29x = 720 + 179 = 889

x = 889/29 = 30.655 ≅ 30.66°

3 0

3 years ago

Calculate the area under the graph of f(x) = 1/xlnx from x = e to x = e^e

Gnom [1K]

Using integration, it is found that the area under the graph of f(x) in the desired interval is of 1 unit squared.

<h3>How is the area under a graph found?</h3>

The area under the graph of a curve f(x) between x = a and x = b is given by the following integral:

$A = \int_{a}^{b} f(x) dx$

In this problem, the function and the limits of integration are given by:

$f(x) = \frac{1}{x\ln{x}}$

$a = e, b = e^e$

Hence:

$A = \int_{e}^{e^e} \frac{1}{x\ln{x}} dx$

Using substitution:

$u = \ln{x}$

$du = \frac{1}{x} dx$

$dx = x du$

Hence:

$\int \frac{1}{x\ln{x}} dx = \int \frac{1}{u} du = \ln{u} = \ln{\ln{x}}$

Applying the Fundamental Theorem of Calculus:

$A = \ln{\ln{e^e}} - \ln{\ln{e}} = \ln{e\ln{e}} = \ln{\ln{e}} = \ln{e} - \ln{1} = 1$

Hence, the area under the graph of f(x) in the desired interval is of 1 unit squared.

To learn more about integration, you can take a look at brainly.com/question/20733870

7 0

3 years ago

What happens to the volume of a sphere when its diameter is tripled?

spin [16.1K]

V = 4/3 pi r^3

r is directly proportional to the diameter

and v is proportional to r^3

so

v is proportional to d^3

for d tripled

v is (3)^3 = 27 times original

8 0

3 years ago

Four milliliters of ink A is added to 10 milliliters of ink B, forming a mixture of inks. Ink A contains 10% blue pigment. Ink B

DochEvi [55]

The question involves what is referred to as a mass balance and can be solved as follows:
Ink A is:
total = 4ml
blue = 4 x 0.1 = 0.4ml
remaining = 3.6ml
Ink B is:
total = 10ml
blue = x
Remaining = 10 - x
Now, upon combination:
total = 4ml + 10ml = 14ml
Blue = 14ml * 0.35 = 4.9ml
Blue in total = blue in A + blue in B
4.9 = 0.4 + x
x = 4.5ml
Percentage of blue ink in B = 4.5/10 x 100
= 45%
The answer is A

5 0

4 years ago

Read 2 more answers

Only evens

VARVARA [1.3K]

Answer:

2. for the first equation, it works, for the second it doesnt so the answer is no

i cant graph for you, but its easy, just use y=mx+b m being the slope which is rise over run

8. x=6, y=-1

10. x=-5 y=5

this is all i could do in such a short notice, but i hope it helped you!

Step-by-step explanation:

for 8, $2x-x+5=11\\x+5=11\\x=6$

for 10,

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4 years ago

Express the confidence interval 0.866 (plusminus) 0.037 in open interval form (ie, (0.155,0.855)).​

Express the confidence interval 0.866 (plusminus) 0.037 in open interval form (ie, (0.155,0.855)).