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Ira Lisetskai [31]
2 years ago
10

What is the volume, in cubic inches, of a rectangular prism with a height of 19 inches, a width of 11 inches, and a length of 4

inches?
Mathematics
1 answer:
jolli1 [7]2 years ago
7 0

Answer:

836

Step-by-step explanation:

4 times 19 times 11

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The mean weight of an adult is 69 kilograms with a variance of 121. If 31 adults are randomly selected, what is the probability
amid [387]

Answer:

0.2236 = 22.36% probability that the sample mean would be greater than 70.5 kilograms.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Also, important to remember that the standard deviation is the square root of the variance.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, the sample means with size n of at least 30 can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 69, \sigma = \sqrt{121} = 11, n = 31, s = \frac{11}{\sqrt{31}} = 1.97565

What is the probability that the sample mean would be greater than 70.5 kilograms?

This is 1 subtracted by the pvalue of Z when X = 70.5. So

Z = \frac{X - \mu}{\sigma}

By the Central limit theorem

Z = \frac{X - \mu}{s}

Z = \frac{70.5 - 69}{1.97565}

Z = 0.76

Z = 0.76 has a pvalue of 0.7764

1 - 0.7764 = 0.2236

0.2236 = 22.36% probability that the sample mean would be greater than 70.5 kilograms.

8 0
3 years ago
Square root of -1? PLEASE HELP
kolezko [41]

My understanding it would be letter ( i )  because it is imaginary.  

7 0
2 years ago
5. The scale of a map says that 8 cm represents 5 km.
sleet_krkn [62]

Answer:

a. 12.8 cm    b. 3.125

Step-by-step explanation:

To find any scale drawing use a proportion with one unit of values on the top and the other on the bottom. For example 8cm/5km = x/8km. So you would multiply 8 cm and 8 km and then divide by 5 to get 12.8 cm. For the second question plug in 5m in the numerator and solve for its denominator.

3 0
2 years ago
Read 2 more answers
What is 25% of 80?<br><br> ( show how u did it cause I have to write it down
Wewaii [24]

Answer:

20

Step-by-step explanation:

Write 25% as 25/100 · Since, finding the fraction of a number is same as multiplying the fraction with the number, we have 25/100 of 80 =         25/100 × 80

4 0
2 years ago
A long solenoid with radius r = 7 cm and n = 3,170 turns/m carries a current i = 6. 7 a. What is the magnitude of the magnetic f
kondaur [170]

The magnitude of the magnetic field in the central area inside the solenoid, in T is 0.0267 T

<h3>Magnetic field inside solenoid</h3>

The magnetic field inside the central area of the solenoid is given by B = μ₀ni where

  • μ₀ = permeability of free space = 4π × 10⁻⁷ Tm/A,
  • n = number of turns per unit length = 3,170 turns/m and
  • i = current in solenoid = 6.7 A

Since B = μ₀ni

Substituting the values of the variables into the equation, we have

B = μ₀ni

B = 4π × 10⁻⁷ Tm/A × 3,170 turns/m × 6.7 A

B = 4π × 10⁻⁷ Tm/A × 21239 A-turns/m

B = 84956π × 10⁻⁷ T

B = 266897.15 × 10⁻⁷ T

B = 0.026689715 T

B ≅ 0.0267 T

So, the magnitude of the magnetic field in the central area inside the solenoid, in T is 0.0267 T

Learn more about magnetic field inside a solenoid here:

brainly.com/question/25562052

6 0
2 years ago
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