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3 years ago

Chen's report will take 8 1/3 hours to complete. He has worked 3/5 of that time doing research. How long has he worked?

Mathematics

2 answers:

Katarina [22]3 years ago

7 0

He has worked only 5 hours on his report

Sergeu [11.5K]3 years ago

4 0

He has worked for 5 hours. 8 and 1/3 is equal to 24/3. Multiply that by 3/5 to get 75/15 which simplifies to 5.

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In Citi A the temperature rises 9° from 8 AM to 9 AM then the temperature drops 8° from 9 AM to 10 AM and Citi b the temperature

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Step-by-step explanation:

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Two alloys A and B are being used to manufacture a certain steel product. An experiment needs to be designed to compare the two

sveta [45]

Answer:

Step-by-step explanation:

From the given information, we can compute the table showing the summarized statistics of the two alloys A & B:

Alloy A Alloy B

Sample mean $\bar {x} _A = 49.5$ $\bar {x} _B = 45.5$

Equal standard deviation $\sigma_A = 5$ $\sigma_B= 5$

Sample size $n_A = 30$ $n_{B}= 30$

Mean of the sampling distribution is :

$\mu_{\bar{X_1}-\bar{X_2}}= 49.5-45.5 \\ \\ = 4.0$

Standard deviation of sampling distribution:

$\sigma_{\bar{x_1}-\bar{x_2} }= \sqrt{\sigma^2_{\bar{x_1}-\bar{x_2} }} \\ \\ = \sqrt{\dfrac{\sigma_1^2}{n_1} + \dfrac{\sigma^2_2}{n_2} } \\ \\ =\sqrt{\dfrac{25}{30}+\dfrac{25}{30}} \\\\=\sqrt{1.667} \\ \\ =1.2909$

Hypothesis testing.

Null hypothesis: $H_o: \mu_A -\mu_B = 0$

Alternative hypothesis: $H_A:\mu_A -\mu_B > 4$

The required probability is:

$P(\overline X_A - \overline X_B>4|\mu_A - \mu_B) = P\Big (\dfrac{(\overline X_A - \overline X_B)-\mu_{X_A-X_B}}{\sigma_{\overline x_A -\overline x_B}} > \dfrac{4 - \mu_{X_A-\overline X_B}}{\sigma _{\overline x_A - \overline X_B}} \Big) \\ \\ = P \Big( z > \dfrac{4-0}{1.2909}\Big) \\ \\ = P(z \ge 3.10)\\ \\ = 1 - P(z < 3.10) \\ \\ \text{Using EXCEL Function:} \\ \\ = 1 - [NORMDIST(3.10)] \\ \\ = 1- 0.999032 \\ \\ 0.000968 \\ \\ \simeq 0.0010$

This implies that a minimal chance of probability shows that the difference of 4 is not likely, provided that the two population means are the same.

Since the P-value is very small which is lower than any level of significance.

Then, we reject $H_o$ and conclude that there is enough evidence to fully support alloy A.

3 0

3 years ago

A cleaning company uses 10 lbs each of chemicals A, B and C for each house it cleans. After some quality complaints, the company

umka21 [38]

Answer:

25%

Step-by-step explanation:

Let us first derive an equation for the productivity.

Given

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Amount of Chemicals = 30 (10 x A, B, C)

Now the formula for productivity is as follow

Productivity % (P) = (Output/Input) * 100

Assuming the current productivity is 100%. We get the value for required output but using the value of 30 (Amount of Chemicals) as Input

$100 = \frac{x}{30}*100\\ x = 30$

Since we now know the value for desired output. We replace the value of input by 40, since 10 lbs of Chemicals have been increased per house.

$Productivity(P) = \frac{30}{40}*100\\ Productivity(P) = 75$

The new Productivity is 75%

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4 years ago

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netineya [11]

Answer:

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Arc length of a parametric curve is:

L = ∫ₐᵇ √((dx/dt)² + (dy/dt)²) dt

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L = ∫₀²ᵖⁱ √((1 − sin t)² + (1 − cos t)²) dt

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L = ∫₀²ᵖⁱ √(1 − 2 sin t + sin²t + 1 − 2 cos t + cos²t) dt

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