MATHEMATICS COLLEGE

The mean gross annual incomes of certified welders are normally distributed with the mean of $20,000 and a standard deviation of $2,000. The ship building association wishes to find out whether their welders earn more or less than $20,000 annually. The alternate hypothesis is that the mean is not $20,000. If the level of significance for this two-tailed test is 0.10, what is/are the critical value(s)

Answers

Answer 1
Answer:

Answer:

At the 0.10 level of significance the z table gives critical values of -1.645 and 1.645 for two-tailed test.

Step-by-step explanation:

We are given that the mean gross annual incomes of certified welders are normally distributed with the mean of $20,000 and a standard deviation of $2,000.

The ship building association wishes to find out whether their welders earn more or less than $20,000 annually.

Let \mu = mean gross annual incomes of certified welders

So, Null Hypothesis, H_0 : \mu = $20,000    

Alternate hypothesis, H_A : \mu \neq $20,000

Here, null hypothesis states that the mean income of welders is equal to $20,000.

On the other hand, alternate hypothesis states that the mean income of welders is not $20,000.

Also, the test statistics that would be used here is One-sample z teststatistics as we know about the population standard deviation;

                              T.S. =  (\bar X-\mu)/((\sigma)/(√(n) ) )  ~ N(0,1)

where, \bar X = sample mean income

            \sigma = population standard deviation = $2,000

            n = sample size

Now, at the 0.10 level of significance the z table gives critical values of -1.645 and 1.645 for two-tailed test.

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After an 80% reduction you purchase a new sofa on sale for $108 what was the original price

Answers

Answer:

$540

Step-by-step explanation:

Define x as:

x = the Original Price, in dollars ($)

Then,

x - (80%)x = 108, where we note that (80%)x is the reduction amount, so that

20%x = 108,

0.2x = 108,

x = 108/0.2 = $540

Final answer:

The original price of the sofa was $540.

Explanation:

Question:

After an 80% reduction, you purchase a new sofa on sale for $108. What was the original price?

Detailed Answer:

To find the original price, we need to determine what the 80% reduction represents in terms of the original price. If the sale price is 80% of the original price, then we can set up the equation: sale price = 0.2 * original price. We know the sale price is $108, so we can solve for the original price by dividing both sides of the equation by 0.2: original price = $108 / 0.2 = $540. Therefore, the original price of the sofa was $540.

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The planet Mars has a radius of 3400 km. What is the volume of Mars?Write your answer in scientific notation to three decimal places.

Answers

Answer:

1.646×10¹¹ km³.

Step-by-step explanation:

From the question given, we obtained the following information:

Radius (r) = 3400 km

Volume (V) =.?

The shape of a planet is spherical in nature. Thus, we shall apply the formula for calculating the volume of a sphere to obtain the volume of Planet Mar as illustrated below:

Radius (r) = 3400 km

Pi (π) = 3.14

Volume (V) =.?

Volume of a sphere = 4/3 πr³

V = 4/3 × 3.14 × (3400)³

V = 4/3 × 3.14 × 3.9304×10¹⁰

V = 1.646×10¹¹ km³

From the calculations made above, the volume of Planet Mar is 1.646×10¹¹ km³

Megan buys 3 bracelets and 3 necklaces. Each bracelet costs 5. Megan pays on 40 and gets 4 change. what is the cost of one necklace?

Answers

The necklaces cost $3 each

What is the y-intercept of a line that has a slope of -3 and passes through point (-5, 4)?О-17
О-11
O-7
O-19

Answers

Answer:

0, -11

Step-by-step explanation:

y-4=-3(x-(-5))

y-4=-3x-15

y=-3x-15+4

y=-3x-11   the ordered to the origin is -11

the y-intercept is at the point (0, -11)

Hope this helps

Savannah recorded the average rainfall amount, in inches, for two cities over the course of 6 months.City A: {4, 3.5, 5, 5.5, 4, 2}
City B: {5, 6, 3.5, 5.5, 4, 6}
(a) What is the mean monthly rainfall amount for each city?
(b) What is the mean absolute deviation (MAD) for each city? Round to the nearest tenth.
(c) What is the median for each city?

Answers

Answer:

City A: {2, 3.5, 4, 4, 5, 5.5}

City B: {3.5, 4, 5, 5.5, 6, 6}

Mean is the average.

Average of City A = 4 (2+3.5+4+4+5+5.5 = 24 and 24/6 = 4)

Average of City B = 5 (3.5+4+5+5.5+6+6 = 30 and 30/6 = 5)

Mean Absolute Deviation

Mean Absolute Deviation of City A = 0.8

Mean Absolute Deviation of City B = 0.8

Median is the middle (after putting it in order least to greatest)

Median of City A = 4

Median of City B = 5.25 (5+5.5 = 10.5 and 10.5/2 =5.25)

Step-by-step explanation:

hope this helps!

Compact and oversized tires are produced on two different machines. The table shows the number of each type of tire produced, y, depending on the number of hours, x, the machines work.

Answers

Answer:

OPTION B: 57x - 3

Step-by-step explanation:

Total tires produced is the sum of number of over-sized tires and the number of compact tires.

So, we have when x = 1, tires, y = 23 + 31 = 54

When x = 2, total tires y = 48 + 63  = 111

When x = 3, total tires y = 73 + 95  = 168

When x = 4, total tires y = 98 + 127 = 225

We can substitute the options to check which one will be the correct representation.

Option A: 55x - 1

When x = 1, y = 55(1) - 1    = 54

When x = 2, y = 55(2) - 1  = 109    $ \ne $    111

So, this option is eliminated.

Option B: 57x - 1

When x = 1, y = 57(1) - 3    =   54

When x = 2, y = 57(2) - 3  =   111

When x = 3, y = 57(3) - 3  =   168

When x = 4, y = 57(4) - 3  =   225

These values exactly match with the values from the table. So, Option B is the right answer.

Option C: 110x - 2

When x = 1, y = 110(1) - 2 = 108  $ \ne $  54

Hence, this option is incorrect.

Option D: 114x - 6

When x = 1, y = 114(1) - 6 $ \ne $  54

Hence, this option is also eliminated.

Option B is the required answer.

Answer: D

Step-by-step explanation:

the person above me was on the right track but needed to multiply the sum of the y values by 2. Therefore the answer should be D
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