Find the domain and range of the function f(x) = square root of sinx

The quality control manager at a light bulb factory needs to estimate the mean life of a batch (population) of light bulbs. We a

Nadusha1986 [10]

Answer:

a)95% confidence intervals for the population mean of light bulbs in this batch

(325.5 ,374.5)

b)

The calculated value Z = 4 > 1.96 at 0.05 level of significance

Null hypothesis is rejected

The manufacturer has not right to take the average life of the light bulbs is 400 hours.

Step-by-step explanation:

Given sample size n = 64

Given mean of the sample x⁻ = 350

Standard deviation of the Population σ = 100 hours

The tabulated value Z₀.₉₅ = 1.96

95% confidence intervals for the population mean of light bulbs in this batch

$(x^{-} - Z_{\frac{\alpha }{2} } \frac{S.D}{\sqrt{n} } , x^{-} + Z_{\frac{\alpha }{2} }\frac{S.D}{\sqrt{n} } )$

$(350 - 1.96\frac{100}{\sqrt{64} } , 350 + 1.96\frac{100}{\sqrt{64} } )$

$(350 -24.5, 350 +24.5)$

(325.5 ,374.5)

b)

Explanation:-

Given mean of the Population μ = 400

Given sample size n = 64

Given mean of the sample x⁻ = 350

Standard deviation of the Population σ = 100 hours

Null hypothesis : H₀:The manufacturer has right to take the average life of the light bulbs is 400 hours.

μ = 400

Alternative Hypothesis: H₁: μ ≠400

The test statistic

$Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }$

$Z = \frac{350 -400}{\frac{100}{\sqrt{64} } }$

|Z| = |-4|

The tabulated value Z₀.₉₅ = 1.96

The calculated value Z = 4 > 1.96 at 0.05 level of significance

Null hypothesis is rejected.

Conclusion:-

The manufacturer has not right to take the average life of the light bulbs is 400 hours.

5 0

2 years ago

Simplify 2p × 3p2 ×4p3

stepladder [879]

Answer: 24p^6

How to: Simplify the expression.

Have a great day ! Sorry if it's wrong :)

6 0

2 years ago

A waiter at a restaurant has diarrhea what should happen?

Vilka [71]

The waiter should go home. It is because it is improper with regards to food safety and pathogenic bacteria such as E.coli can contaminate the food. Though the productivity of the restaurant will decrease, food safety must come first to reduce customer complaints.

8 0

2 years ago

Stanley has a collection of seashells. He found 35% of his collection on Florida beaches. If Stanley has 49 seashells from Flori

m_a_m_a [10]

Answer:

The number of seashells he have in his collection all together is 140.

Step-by-step explanation:

Given:

Stanley has a collection of seashells. He found 35% of his collection on Florida beaches.

Stanley has 49 seashells from Florida.

Now, to find the number of seashells of his collection altogether.

Let the number of seashells all together be $x.$

Percentage of seashells found on Florida beaches = 35%.

Number of seashells found on Florida beaches = 49.

Now, to get the number of seashells altogether we put an equation:

$35\%\ of\ x=49.$

⇒ $\frac{35}{100} \times x=49$

⇒ $0.35\times x=49$

⇒ $0.35x=49$

Dividing both sides by 0.35 we get:

⇒ $x=140.$

Therefore, the number of seashells he have in his collection all together is 140.

4 0

2 years ago

The segments shown below could form a triangle.

olga2289 [7]

By the Triangle Inequality Theorem, the sum of two sides should be greater than the length of the third side, while the difference of these two sides should be less than the length of this third side. Normally you would take the absolute value of the difference of these two side as you wouldn't know which is greater than the other!

The simplest way to prove whether these line segments can form a triangle, is by going against this theory. Let us prove that the line segment don't form a triangle. As you can see, adding 7 and 1 is greater than 1, respectively 7 and 7 is greater than 1. Thus -

Solution = A. True

3 0

1 year ago