Consider H0: μ = 45 versus H1: μ < 45. A random sample of 25 observations produced a sample mean of 41.8. Using α = .025 and the population is known to be normally distributed with σ = 6.

Answer:

13 cm

Step-by-step explanation:

Area of the square is [tex]169 \:\:cm^{2}[/tex]

The square is rotated to form a cylinder. Now, we first need to find the side of the square, the cylinder is formed by rotating along its side.

Now area of square [tex]169 \:\:cm^{2}[/tex]

We know that area of square is [tex]\text{side}\times\text{side}[/tex]

So, [tex]\text{side}\times\text{side}=169[/tex]

[tex]\text{side}\times \text{side}=13\times13[/tex]

[tex]\text{side}=13 \:\text{cm}[/tex]

Now, as the cylinder is formed by rotating along its length, and we know that all the sides of a square is equal.

So, one side becomes the height of the cylinder and the other becomes the circumference.

Hence, the height of the cylinder is 13 cm.

Value of Aurora's benefits as 30percent of her salary is equals to $7500.

" Percentage is defined as the hundredth part of the given whole number."

According to the question,

Salary amount of Aurora = $25,000

Benefit value = 30 percent of ( $25,000)

Therefore,

30 percent of ( $25,000) = 30% of 25,000

                                          =  [tex]\frac{(30) * (25,000)}{100}[/tex]

                                          = $7,500

Hence, value of Aurora's benefits as 30percent of her salary is equals to $7500.

Learn more about percentage here

https://brainly.com/question/13450942

#SPJ2

Laundromat A = 6.35 +1.25 = 7.60 for one load

Laundromat B = 5.95 +0.85 = 6.80 for one load

7.60-6.80 = 0.80

 Laundromat B is has the better price by 0.80 cents

the fraction is 180/365

this can get reduced to 36/73

Final answer:

Multi-step algebra equations involve operations like addition, subtraction, multiplication, or division to solve for an unknown. These equations require simplifying terms, solving for unknowns, and checking the answers. Money examples and practice statements are useful for understanding these concepts.

Explanation:

Multi-step algebra equations are problems that require more than one operation, such as addition, subtraction, multiplication, or division, to solve for the unknown variable. The following steps are typically involved in solving these equations:

An example of this process could be the following scenario: You are given two equations in a word problem involving motion, one equation for velocity and another for time. To find the distance traveled, you would identify the known variables and the unknown variable (in this case, distance), simplify both equations as much as possible, and then combine them to solve for distance.

Money examples are often used for educational purposes because they provide a familiar context for understanding mathematical principles, making them easier to grasp. Additionally, practicing with state-ments, such as covering up a number to solve for it with the remaining information, can help build problem-solving skills.

The values of c such that the function f is continuous are: c = -2.79 and c = 1.79

The function is given as:

[tex]f(x) = \left\{ \begin{array}{lcl} {5} - x^{2}, & & x \le c \\ x, & & x > c \end{array}\right.[/tex]

For the function to be continuous, then the following must be true

[tex]5 - x^2 = x[/tex]

Substitute c for x

[tex]5 - c^2 = c[/tex]

Express as a quadratic function

[tex]c^2 + c - 5 = 0[/tex]

Using a graphing calculator, the values of c are:

c = -2.79 and c = 1.79

Read more about continuous functions at:

https://brainly.com/question/9412728

The value of 6 (3/4) divided by 1 (7/8) is 3 (3/5).

A fraction is a part of the whole represented by a/b, where a and b are any integers

The given numbers are 6 (3/4) and 1 (7/8).

Simplify the mixed fractions:

6(3/4) = 27/4 and 1 (7/8) = 15/8

Now, divide 27/4 by 15/8:

27/4 ÷ 15/8

= 27/4 × 8/15

= 18/5

= 3 (3/5)

Hence, The value of 6 (3/4) divided by 1 (7/8) is 3 (3/5).

Learn more on fractions here:

brainly.com/question/10354322

#SPJ3

To solve the equation l = 14j + 3k for j, subtract 3k from both sides and then divide by 14, giving j = (l - 3k) / 14.

To solve the equation l=14j+3k for j, you need to isolate j on one side of the equation. Here's how it is done step by step:

Therefore, the solution to the equation for j is: j = (l - 3k) / 14.

https://brainly.com/question/18262581

#SPJ2

The data represents a normal distribution where approximately 68 percent of the pages will have a number of occurrences of the letter t within one standard deviation of the mean, 95 percent within two standard deviations, and more than 99 percent within three standard deviations.

The sentence that most closely summarizes the data is: For data having a distribution that is bell-shaped and symmetric, the following are true:

Using this information, we can conclude that approximately 68 percent of the pages in the book will have a number of occurrences of the letter t within one standard deviation of the mean, which is 44. Approximately 95 percent of the pages will have a number of occurrences within two standard deviations, and more than 99 percent will have a number of occurrences within three standard deviations.

https://brainly.com/question/30390016

#SPJ13

The properties that were used to derive the properties of logarithms are the properties of exponent because logarithms are exponents. The properties of exponents are: product of powers, power to a power, quotient of powers, power f a product and power of a quotient.

As an example, the log property log(a^k) = k log (a) can be derived from the exponential property (b^a)^k = b^(ak).

Likewise,

log (ab) = log (a) + log (b) comes from c^(a+b) = c^a*c^b

Proof:

Let x = c^a and y=c^b

Then, 

log (x) = a and log (y) = b (base c)

log (xy) = log (c^a * c^b) = log (c^(a+b)) = a+b = log(x) + log (y)

Answer:

The height of the cylinder shaped can = 8.17 inches

Step-by-step explanation:

Volume of the cylinder shaped can = 1 gallon

1 gallon = 231 cubic inches

So, Volume of the cylinder shaped can = 231 cubic inches

Radius of the can = 3 inches

[tex]\text{Now, Volume of the cylinder = }\pi\times radius^2\times height\\\\\implies 231=3.14\times 3^2\times height\\\\\implies height=\frac{231}{3.14\times 9}\\\\\implies height\approx 8.17\text{ inchjes}[/tex]

Hence, The height of the cylinder shaped can = 8.17 inches

The two consecutive even integers that sum to 138 are 68 and 70. The equation n + (n + 2) = 138 was used to determine these integers.

The problem is asking for two consecutive even integers whose sum is 138. Let's denote the first integer as n (where n is an even number). As the problem says the numbers are consecutive even integers, we know the next number must be n + 2.

We can form an equation based on the information given. The sum of these two integers is equal to 138, so:

If we simplify the equation, it becomes:

Therefore, the two consecutive numbers are 68 and 70 as they add up to 138.

https://brainly.com/question/34290341

#SPJ11

if 1 inch = 30 miles

 thn multiply 30 x 5.6

30 x 5.6 = 168 miles apart

The actual distance between Springfield and Columbia is 168 miles.

Therefore, the correct answer is:

b. 168 mi

To find the actual distance between Springfield and Columbia, we can use the scale provided in the map.

Given that 1 inch on the map represents 30 miles in real life, and the distance on the map from Springfield to Columbia is 5.6 inches, we can use the following calculation to find the actual distance:

[tex]\[ \text{Actual distance} = \text{Map distance} \times \text{Scale factor} \][/tex]

[tex]\[ \text{Actual distance} = 5.6 \, \text{inches} \times 30 \, \text{miles/inch} \][/tex]

[tex]\[ \text{Actual distance} = 168 \, \text{miles} \][/tex]

So, the actual distance between Springfield and Columbia is 168 miles.

Therefore, the correct answer is:

b. 168 mi