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2 years ago

What is the value of angle K to the nearest What is the value of angle K to the nearest tenth?

Mathematics

1 answer:

Nina [5.8K]2 years ago

6 0

Answer:

$Cos K = \frac{adjacent}{opposite} = \frac{5}{6}\\\\K = Cos^{-1}(\frac{5}{6} ) = 33.557\\K= 33.6$

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A machine is used to fill containers with a liquid product. Fill volume can be assumed to be normally distributed. A random samp

motikmotik

Answer:

There is no statistical evidence at 1% level to accept that the mean net contents exceeds 12 oz.

Step-by-step explanation:

Given that a random sample of ten containers is selected, and the net contents (oz) are as follows: 12.03, 12.01, 12.04, 12.02, 12.05, 11.98, 11.96, 12.02, 12.05, and 11.99.

We find mean = 11.015

Sample std deviation = 3.157

a) $H_0: \bar x= 12 oz\\H_a: \bar x >12$

(Right tailed test)

Mean difference /std error = test statistic

$\frac{11.015-12}{\frac{3.157}{\sqrt{10} } } \\=-0.99$

p value =0.174

Since p >0.01, our alpha, fail to reject H0

Conclusion:

There is no statistical evidence at 1% level to accept that the mean net contents exceeds 12 oz.

3 0

3 years ago

Evaluate the definite integral. <br> 1 x4(1 + 2x5)5 dx.

Nata [24]

Answer:

Step-by-step explanation:

Given the definite integral $\int\limits {\dfrac{x^4}{(1-2x^5)^5} } \, dx$ , we to evaluate it. Using integration by substitution method.

Let u = 1-2x⁵ ...1

du/dx = -10x⁴

dx = du/-10x⁴.... 2

Substitute equation 1 and 2 into the integral function and evaluate the resulting integral as shown;

$= \int\limits {\dfrac{x^4}{u^5} } \, \dfrac{du}{-10x^4}$

$= \dfrac{-1}{10} \int\limits {\dfrac{du}{u^5} } \\\\= \dfrac{-1}{10} \int\limits {{u^{-5}du } \\= \dfrac{-1}{10} [{\frac{u^{-5+1}}{-5+1}] \\\\= \dfrac{-1}{10} ({\frac{u^{-4}}{-4})\\\\$

$= \dfrac{u^{-4}}{40} \\\\\\= \dfrac{1}{40u^4} +C$

substitute u = 1-2x⁵ into the result

$= \dfrac{1}{40(1-2x^5)^4} +C$

Hence $\int\limits {\dfrac{x^4}{(1-2x^5)^5} } \, dx$ $= \dfrac{1}{40(1-2x^5)^4} +C$

5 0

3 years ago

(2 tens 1 one)x10 in unit form and standard form

omeli [17]

When the number expression given as (2tens 1 one) x 10 is written in standard form, the standard form is 210 and the unit form is 2 hundred, and 1 ten

<h3>How to write the number in standard form?</h3>

The number expression is given as:

(2tens 1 one) x 10

2 tens is represented as:

2 * 10

1 one is represented as:

1 * 1

So, the number expression can be rewritten as:

(2tens 1 one) x 10 = (2 * 10 + 1 * 1) x 10

Evaluate the product

(2tens 1 one) x 10 = (20 + 1) x 10

Evaluate the sum

(2tens 1 one) x 10 = (21) x 10

Evaluate the product

(2tens 1 one) x 10 = 210

When the number expression given as (2tens 1 one) x 10 is written in standard form, the standard form is 210 and the unit form is 2 hundred, and 1 ten

Using the above steps as a guide, we have:

(5 hundreds 5 tens) * 10 ⇒ 5 thousands and 5 hundreds ⇒ 5500
(2 thousands 7 tens) / 10 ⇒ 2 hundreds and 7 units ⇒ 207
(4 ten thousands 8 hundred) / 10 ⇒ 4 thousands and 8 tens ⇒ 4080