What number when multiplied by itself is 23 greater than the preceding number when it is multiplied by itself?

The length of time a full length movie runs from opening to credits is normally distributed with a mean of 1.9 hours and standar

Llana [10]

Answer:

a) The probability that a random movie is between 1.8 and 2.0 hours = 0.2586.

b) The probability that a random movie is longer than 2.3 hours is 0.0918.

c) The length of movie that is shorter than 94% of the movies is 1.4 hours

Step-by-step explanation:

In the above question, we would solve it using z score formula

z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation

a) A random movie is between 1.8 and 2.0 hours

z = (x-μ)/σ,

x1 = 1.8,

x2 = 2.0

μ is the population mean = 1.9

σ is the population standard deviation = 0.3

z1 = (1.8 - 1.9)/0.3

z1 = -1/0.3

z1 = -0.33333

Using the z score table

P(z1 = -0.33) = 0.3707

z2 = (2.0 - 1.9)/0.3

z1 = 1/0.3

z1 = 0.33333

p(z2 = 0.33) = 0.6293

= P(- 0.33 ≤ z ≤ 0.33)

= 0.6293 - 0.3707

= 0.2586

The probability that a random movie is between 1.8 and 2.0 hours = 0.2586

b) A movie is longer than 2.3 hours

z = (x-μ)/σ,

x1 = 2.3

μ is the population mean = 1.9

σ is the population standard deviation = 0.3

z = (2.3 - 1.9)/0.3

z = 4/0.3

z = 1.33333

P(z = 1.33) = 0.90824

P(x>2.3) = = 1 - 0.90824

= 0.091759

≈ 0.0918

The probability that a random movie is longer than 2.3 hours is 0.0918.

3) The length of movie that is shorter than 94% of the movies.

z = (x-μ)/σ

Probability (z ) = 94% = 0.94

Movie that is shorter than 0.94

= P(1 - 0.94) = P(0.06)

Finding the P (x< 0.06) = -1.555

≈ -1.56

μ is the population mean = 1.9

σ is the population standard deviation = 0.3

-1.56 = (x - 1.9)/ 0.3

Cross multiply

-1.56 × 0.3 = x - 1.9

- 0.468 + 1.9 = x

= 1.432 hours

≈ 1.4 hours

Therefore, the length of movie that is shorter than 94% of the movies is 1.4 hours

5 0

2 years ago

A pizza lover wants to compare the average delivery times for four local pizza restaurants. Over the course of a few weeks, he o

xenn [34]

Answer:

At least two of the restaurant have different mean delivery time.

Step-by-step explanation:

The ANOVA known as Analysis of variance involves the hypothesis testing of means on the basis of variances. The null hypothesis in ANOVA is taken as the equality mean i.e. H0: All means are equal. Whereas alternative hypothesis consists of at least two means are not equal.

The problem states that a pizza lover is comparing average delivery time. The null and alternative hypothesis in this case would be

H0: All restaurant have equal mean delivery time.

H1: At least two restaurant have different mean delivery time.

8 0

2 years ago

Triangle $ABC$ has altitudes $\overline{AD},$ $\overline{BE},$ and $\overline{CF}.$ If $AD = 12,$ $BE = 14,$ and $CF$ is a posit

Shalnov [3]

Answer:

CF = 7

Step-by-step explanation:

Given: Δ ABC

Altitudes ⇒ AD = 12 , BE = 14 and CF = ?

The area of the triangle = 0.5 AD * BC ⇒ (1)

OR area = 0.5 BE * AC ⇒ (2)

OR area = 0.5 CF * AB ⇒ (3)

By equating (1) and (3)

∴ 0.5 CF * AB = 0.5 AD * BC

∴ $CF = \frac{AD*BC}{AB} =\frac{12BC}{AB}$ ⇒ (4)

By equating (1) and (2)

0.5 BE * AC = 0.5 AD * BC

∴ $\frac{AC}{BC} = \frac{AD}{BE} =\frac{12}{14} =\frac{6}{7}$ (5)

We should know that about the relation between the sides of the triangle:

The sum of two sides will be greater than the third side

So, AB < BC + AC ⇒ divide both sides by BC

∴ $\frac{AB}{BC} < 1+\frac{AC}{BC}$

By substitution from (5) with AC/BC

∴ $\frac{AB}{BC}$

∴ $\frac{BC}{AB} > \frac{7}{13}$ ⇒ (6)

By substitution from (6) at (4)

∴ CF > 12 * 7/13

CF > 6.46

But CF is a positive integer

∴ CF = 7

4 0

2 years ago

The temperature in degrees Kelvin is 273 degrees less than the temperature in degrees Celsius. Use the formula LaTeX: C=\frac{5}

katrin2010 [14]

Answer:

°F = 9/5 (°K - 273) + 32

Step-by-step explanation:

°C = °K - 273

°F = 9/5 °C + 32

Put the 1st formula in the 2nd

°F = 9/5 (°K - 273) + 32

5 0

2 years ago

Read 2 more answers

In each represent the common form of each argument using letters to stand for component sentences, and fill in the blanks so tha

arlik [135]

Answer:

a

$a \to b$

$\neg b$

$\neg a$

b

If all prime numbers are odd, then 2 is odd.

2 is not odd.

Therefore, it is not the case that all prime numbers are odd.

Step-by-step explanation:

Considering part A

The first sentence is

If all computer programs contain errors, then this program contains an error.

The second sentence is

This program does not contain an error.

The third sentence is

Therefore, it is not the case that all computer programs contain errors.

Now we will use a and b as the letter to denote the component sentences and $\neg a$ and $\neg b$ when the component sentences is not the case

So a = If all computer programs contain errors

and

b = this program contains an error.

Generally then is represented as $\to$

Hence the first sentence is denoted as

$a \to b$

The second sentence is represented as

$\neg b$

The third sentence is represented as

$\neg a$

So part a can be represented as

$a \to b$

$\neg b$

$\neg a$

Considering part B

Here the objective is to fill in the blank spaces so that the logic of the sentence in part b is as that in part a

Now comparing the second statement a and b

"This program does not contain an error" = "2 is not odd" = $\neg b$

Hence "this program contains an error." = "2 is odd" = b

Now comparing the third statement a and b

Therefore, it is not the case that all computer programs contain errors.

=

Therefore, it is not the case that all prime numbers are odd

=

$\neg a$

Hence

If all computer programs contain errors, = if all prime numbers are odd.= a

3 0

2 years ago