MATHEMATICS COLLEGE

A four pack of batteries cost 5.16 at this price what is the cost of

Answers

Answer 1

Answer:

Answer:

1.29 for 1 pack

Step-by-step explanation:

5.16/4=1.29

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A trapezoid has an area of 60 square inches. The height of the trapezoid is 5 inches. What is the length of the longer base if the longer base is three times the length of the shorter base?

An article suggested that yield strength (ksi) for A36 grade steel is normally distributed with μ = 44 and σ = 5.0. (a) What is the probability that yield strength is at most 40? Greater than 62? (Round your answers to four decimal places.) at most 40 greater than 62 (b) What yield strength value separates the strongest 75% from the others? (Round your answer to three decimal places.)

Answers

Answer:

Step-by-step explanation:

Using normal distribution,

z = (x - μ)/σ

μ= mean = 44 and

σ = standard deviation= 5.0

a) The probability that yield strength is at most 40=

P( x lesser than or equal to 40)

z = (40-44)/5= -0.8

Looking at the normal distribution table,

P( x lesser than or equal to 40) =0.2119

b) P(x greater than 62) = 1 - P(x lesser than or equal to 62)

z = (62-44)/5= 3.6

Looking at the normal distribution table,

P(x greater than 62) = 1 -0.99984

= 0.00016

c)P( 42 lesser than or equal to x lesser than or equal to 62)

= P(x lesser than or equal to 62) - P( x lesser than or equal to 40)

= 0.99987-0.2119= 0.78797

d) What yield strength value separates the strongest 75% from the others.

To get x for strongest 75, we get the z value corresponding to 0.75 from the table

z = 0.675= (x-44)/5

x = 3.375+44 = 47.375

The rest is 25% = 0.25

we get the z value corresponding to 0.25 from the table)

z = -0.67 = (x-44)/5

-3.35= x -44

x = -44+3.35= 40.65

yield strength value that separates the strongest 75% from the others

=47.375-40.65= 6.725

Final answer:

The probability that the yield strength is at most 40 is approximately 0.2119 and the probability that it is greater than 62 is approximately 0.0001. The yield strength value that separates the strongest 75% from the others is approximately 40.628 ksi.

Explanation:

This question is about calculating probabilities and percentiles using the properties of the normal distribution. The yield strength for the A36 grade steel is normally distributed with a mean (μ) of 44 and a standard deviation (σ) of 5.0.

(a) To find the probability that the yield strength is at most 40, we will need to calculate the Z-score value for the yield strength of 40. The Z-score can be calculated using the following formula: Z = (X - μ) / σ , where X is the observed value, μ is the mean, and σ is the standard deviation. For X = 40, μ = 44, and σ = 5.0, the Z-score is -0.8. Looking up the Z-score in the standard normal distribution table, the probability that the yield strength is at most 40 is approximately 0.2119. Using a similar process, we find that the probability that the yield strength is greater than 62 is less than 0.0001, very close to zero.

(b) To determine the yield strength value that separates the strongest 75% from the others, we find the Z-score that corresponds to a cumulative probability of 0.25 in the standard normal distribution table (because the strongest 75% corresponds to the weakest 25%). That Z-score is approximately -0.6745. Using the formula Z = (X - μ) / σ to solve for X gives us X = σZ + μ = 5.0 * -0.6745 + 44 = 40.6275, which rounded to three decimal places is 40.628.

Learn more about Normal Distribution here:

brainly.com/question/34741155

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Eric has attended summer camp for 5 weeks every summer for 6 years. How many days has he attended camp in 6 years?

Answers

Answer:

210 days

Step-by-step explanation:

There are 7 days in a week and since he goes for 5 weeks every summer, he goes for 35 days every year. Since he has attended for 6 years, multiply 35 by 6 to get 210, the number of days he has attended camp for.

Answer:

210 days

Step-by-step explanation:

Eric has attended 5 weeks summer camp for a year.

They are asking for 6 years

∴6*5 = 30 weeks Eric had totally in 6 years.

But they want the answer in days:

1 week = 7 days

30 weeks = 30*7 = 210 days

(If this helps you I am happy, if there is a mistake let me know.)

Your welcome

One table at a bake sale has 75 oatmeal cookies. Another table has 60 lemon cupcakes. Which table allows for more rectangular arrangements when all the cookies and cupcakes are displayed?

Answers

75 = 3·5², so has 6 divisors. 6 rectangles are possible if you make the distinction between 1×75 and 75×1.

60 = 2²·3·5, so has 12 divisors. 12 rectangles are possible under the same conditions.

The cupcake table can be arranged more ways.

_____

When 1 is added to each exponent of the prime factors, the product of those sums is the number of divisors. For 75: (1+1)(1+2) = 6; for 60: (1+2)(1+1)(1+1) = 12.

Arrangement is simply the order, which items are displayed or presented.

The table of 60 lemon cupcakes allow more rectangular arrangements

The given parameters are:

$\mathbf{Oatmeal = 75}$

$\mathbf{Lemon = 60}$

The rectangular arrangement (R) is calculated as follows:

$\mathbf{R = (Area)/(n)}$

Where n represents the number of items, and Area represents the area of the rectangular table

For the oatmeal, we have:

$\mathbf{R_1 = (Area)/(75)}$

$\mathbf{R_1 = 0.0133Area}$

For the lemon, we have:

$\mathbf{R_2 = (Area)/(60)}$

$\mathbf{R_2 = 0.0167Area}$

By comparison, 0.0167Area is greater than 0.0133Area

Hence, the table of 60 lemon cupcakes allow more rectangular arrangement

Answers

Answer:

The 93% confidence interval for the true proportion of masks of this type whose lenses would pop out at 325 degrees is (0.3154, 0.5574). This means that we are 93% sure that the true proportion of masks of this type whose lenses would pop out at 325 degrees is (0.3154, 0.5574).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{(\pi(1-\pi))/(n)}$

In which

z is the zscore that has a pvalue of $1 - (\alpha)/(2)$ .

For this problem, we have that:

$n = 55, \pi = (24)/(55) = 0.4364$

93% confidence level

So $\alpha = 0.07$ , z is the value of Z that has a pvalue of $1 - (0.07)/(2) = 0.965$ , so $Z = 1.81$ .

The lower limit of this interval is:

$\pi - z\sqrt{(\pi(1-\pi))/(n)} = 0.4364 - 1.81\sqrt{(0.4364*0.5636)/(55)} = 0.3154$

The upper limit of this interval is:

$\pi + z\sqrt{(\pi(1-\pi))/(n)} = 0.4364 + 1.81\sqrt{(0.4364*0.5636)/(55)} = 0.5574$

Which shows one way to determine the factors of x3 + 5x2 – 6x – 30 by grouping?x(x2 – 5) + 6(x2 – 5)
x(x2 + 5) – 6(x2 + 5)
x2(x – 5) + 6(x – 5)
x2(x + 5) – 6(x + 5)