The domain of the function [tex]\(f(x, y, z) = 4 - x^2 - y^2 - z^2\)[/tex] is the set of all real numbers for [tex]\(x\)[/tex], [tex]\(y\),[/tex] and [tex]\(z\)[/tex].
To find and sketch the domain of the function [tex]\(f(x, y, z) = 4 - x^2 - y^2 - z^2\)[/tex], we need to determine the set of values for [tex]\(x\)[/tex], [tex]\(y\)[/tex], and [tex]\(z\)[/tex] for which the function is defined, i.e., the values that do not lead to any mathematical inconsistencies.
In this case, the function involves three variables, and it is defined for all real values of [tex]\(x\)[/tex], [tex]\(y\)[/tex], and [tex]\(z\)[/tex]. There are no restrictions on the domain because the square of a real number is always non-negative. Thus, [tex]\(x^2\)[/tex], [tex]\(y^2\)[/tex], and [tex]\(z^2\)[/tex] are non-negative for any real \(x\), \(y\), and \(z\).
In interval notation, we can express this as:
[tex]\[\text{Domain} = (-\infty, \infty) \times (-\infty, \infty) \times (-\infty, \infty)\][/tex]
This domain represents the entire three-dimensional space, and the function is defined for all points within this space. As such, sketching the domain involves visualizing the entire 3D space, which is an unbounded region without any specific shape or boundary.
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The surface area of an open-top box with length L, width W, and height H can be found using the formula: A= 2LH + 2WH + LW Find the surface area of an open-top box with length of 7 cm, width 6 cm, and height 3 cm.
Final answer:
The surface area of an open-top box with a length of 7 cm, width of 6 cm, and height of 3 cm is calculated using the formula and comes out to be 120 cm².
Explanation:
To find the surface area of an open-top box with given dimensions, we use the formula: A= 2LH + 2WH + LW. Substituting in the provided lengths for length (L), width (W), and height (H):
A = 2(7 cm)(3 cm) + 2(6 cm)(3 cm) + (7 cm)(6 cm)
A = 2(21 cm²) + 2(18 cm²) + 42 cm²
A = 42 cm² + 36 cm² + 42 cm²
A = 120 cm²
This gives us the total surface area of the open-top box which is 120 cm².
The number of bacteria (b) in a batch of refrigerated food is given by the function b(t) = 20t2 − 70t + 300, where t is the temperature of the food in degrees Fahrenheit. The function t(h) = 2h + 3 gives the temperature of the food h hours after it is removed from refrigeration. Which expression correctly represents the number of bacteria (b) in the food as a function of the number of hours (h) the food is unrefrigerated?
An airline, believing that 4% of passengers fail to show for flights, overbooks (sells more tickets than there are seats). suppose that for a particular flight involving a jumbo-jet with 267 seats, the airline sells 276 tickets.
a. what is the expected number of ticket holders that will fail to show for the flight?
The expected number of ticket holders that will fail to show for the flight is 11.
Given that,
There is a fail percentage of 4%.There are 267 seats.And, the 276 airline tickets are sold.Based on the above information,
= 276%
= 2.76
Now the number of ticket holders who fail for presenting the flight should be
[tex]= 2.76\times 4[/tex]
= 11
Therefore we can conclude that the expected number of ticket holders that will fail to show for the flight is 11.
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How l can write a brief summary about measurement for 3rd grade
what percent of 176 is 17.6
69.5 is What precent of 85?
you earn $70 per week mowing lawns one week you work 10 hours during the week and spend $20 on gasoline for your mower how much do you earn each hour
20. What percent of 392 is 98? 22. 33% of what number is 145? 24, 17 is 40% of what number?
What is the smallest natural number that has three distinct prime factors in its factorization?
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If (7^2)x = 1, what is the value of x? Explain your answer.
If (7^0)x = 1, what are the possible values of x? Explain your answer.
(7^2)x = 1
7^2 = 49
49x = 1
x = 1/49
(7^0)x=1
7^0 = 1 (anything raised to 0 = 1)
1x = 1
x = 1
The sum of two integers is greater than 12. One integer is 10 less than the other. What are the values of the integers?
Which second-degree polynomial function has a leading coefficient of 3 and roots –4 and 6?
how do you factor 30n^2b-87nb+30b?
After a discount of 10%, the price of a pair of jeans, including tax, was $69.62. The following equation can be used to find x, the price of the pair of jeans without the discount:
x - 0.1x + 0.07(x - 0.1x) = 69.62
What is the price of the pair of jeans without the discount?
A-$70.58
b-$72.29
c-$74.86
d-
a girl is the same age if she takes 3/4 of her age +9 or 1/4 +21. what is her age?
Given that the restaurant is located in a city with a population over 500,000, what is the probability that it is in the northeast?
The probability is 0.187 or 18.7% that the restaurant chosen at random is in the north east and is located in a city with a population over 500,000.
To find the likelihood that a haphazardly picked eatery from the 588 outlets situated in a city with a populace more than 500,000 is in the north east, we really want to know the quantity of cafés that meet these two rules and are situated in the north east.
Let's look for this information using the table:
Northeast Midwest South West More than 500,000 Over 500,000 110 95 178 66 Less than 500,000 53 39 38 9 The table indicates that 110 restaurants are located in the north east of the United States in cities with more than 500,000 residents. In this manner, the likelihood that a haphazardly picked eatery from the 588 outlets situated in a city with a populace more than 500,000 is in the north east is:
P(Northeast and North of 500,000) = 110/588 = 0.187
Thus, the likelihood is 0.187 or 18.7% that the café picked aimlessly is in the north east and is situated in a city with a populace more than 500,000.
Q equal 1/2 p plus 15 solve for p
what is an angle between a side of a polygon and the extension of its adjacent side
The angle between a side of a polygon and the extension of its adjacent side is the exterior angle at that vertex, forming a linear pair with the adjacent interior angle.
Angle between a side of a polygon and the extension of its adjacent side: When considering a polygon, the angle between a side and the extension of its adjacent side is equal to the exterior angle of the polygon at that vertex. This angle forms a linear pair with the adjacent interior angle of the polygon.
there are 182 seats in a theater. The seats are evenly divided into 13 rows. How many seats are in each row
In an eye color study, 25 out of 50 people in the sample had brown eyes. in this situation, what does the number .50 represent?
The number .50 in the context of this question represents the proportion (or probability) of people in the sample who have brown eyes. It's calculated by dividing the count of individuals with brown eyes by the total number of individuals in the sample.
Explanation:In this context, the number .50 represents the proportion or probability of people with brown eyes in the sample. This number is obtained by dividing the number of people with brown eyes (25) by the total number of people in the sample (50).
Hence, .50 means there is a 50% chance that a randomly selected person from the sample will have brown eyes. This is often used in the field of statistics where proportions are utilized to represent probabilities of outcomes.
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What is 2r+7+r=? I'm not sure
Help with #30 Please!
The sum of three consecutive integers is 90. Find the integers
The sum of three consecutive integers is 90. So you know that 3 numbers that are next to each other in numerical order equals 90.
First step: Make an equation:
Let's take x as the smallest of the three numbers.
[tex]x +(x+1)+(x+2)=90[/tex]
2nd step: Open the brackets:
[tex]x+x+1+x+2=90[/tex]
3rd step: Simplify:
[tex]3x+3=90[/tex]
4th step: Keep similar integers on one side of the equation
[tex]3x+3-3=90-3[/tex]
5th step: Solve for x:
[tex]3x=87[/tex]
[tex]\frac{3x}{3} =\frac{87}{3}[/tex]
[tex]x=29[/tex]
So if the numbers are consecutive, they have to be next to each other.
Answer: 29, 30, 31
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There are 9 red and 6 green marbles in a bag. A child reaches in the bag and randomly takes one marble. What is the probability pf that child getting a green marble
Answer: The required probability that the child took a green marble is 40%.
Step-by-step explanation: Given that there are 9 red and 6 green marbles in a bag and a child reaches in the bag and randomly takes one marble.
We are to find the probability that the child took a green marble.
Let S denote the sample space of choosing a marble from the bag and A be the event of choosing a green marble.
Then,
n(S) = 9 + 6 = 15 and n(A) = 6.
Therefore, the probability of event A will be
[tex]P(A)=\dfrac{n(A)}{n(S)}=\dfrac{6}{15}=\dfrac{2}{5}\times 100\%=40\%.[/tex]
Thus, the required probability that the child took a green marble is 40%.
Kareem runs 6 miles in 55 minutes. At the same rate, how many miles would he run in 44 minutes?
Sara bought two pounds of strawberries for $5.12. What is price in dollars per ounce of strawberries 1 pound =16 ounces
Hello, I am taking Quantitative methods for business, which has a lot of excel based mathematics and I was wondering if anyone could help. Here is the question:
Refer to the table that illustrates customer’s complaints about a manufacturing company.
A. What is the probability a customer complained during the guarantee period?
B. What is the probability that a customer complained about an electrical problem or a mechanical problem?
Table is included in attachment. Also Thank you!!!
Justin is exchanging dollars for rolls of quarters and rolls of dimes at a bank. Each roll of quarters has a value of $10 and each roll of dimes has a value of $5. He exchanges $90 and receives 11 rolls of coins. How many of each type of roll of coins did he receive?
6 rolls of dimes = $30.
6 rolls of quarters = $60.
Answer:
7 roll of quarter and 4 roll of dimes.
Step-by-step explanation:
Let x be the number of rolls of quarters and y be the number of rolls of dimes,
Given,
Total rolls = 11
⇒ x + y = 11 ------(1),
Also, the total value of $ 90 in which Each roll of quarters has a value of $10 and each roll of dimes has a value of $5.
⇒ 10x + 5y = 90 ------(2),
Equation (2) - 5 × Equation (1),
We get,
5x = 90 - 55
⇒ 5x = 35 ⇒ x = 7
From equation (1),
7 + y = 11 ⇒ y = 4
Hence, the number of roll of quarters = 7,
And, the number of roll of dimes = 4
Write the point-slope form of the equation of the line passing through the points (-5, 6) and (0, 1).
A) y + 6 = -1(x – 5)
B) y – 6 = -1(x + 5)
C) y + 6 = 1(x – 5)
D) y – 6 = 1(x + 5)
The point-slope form of the equation of the line passing through the points (-5, 6) and (0, 1) is [tex]\( \boxed{A) y + 6 = -1(x - 5)} \)[/tex].
To find the point-slope form of the equation of the line passing through the points (-5, 6) and (0, 1), we first need to calculate the slope (m) using the formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Given points:
[tex]\((-5, 6)\) and \((0, 1)\)[/tex]
Calculate the slope m:
[tex]\[ m = \frac{1 - 6}{0 - (-5)} = \frac{-5}{5} = -1 \][/tex]
Now that we have the slope m = -1, we can use the point-slope form of the equation of a line, which is:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Choose one of the points, let's use [tex]\((-5, 6)\) as \((x_1, y_1)\)[/tex]:
[tex]\[ y - 6 = -1(x + 5) \][/tex]
Now, simplify and compare with the given options:
[tex]\[ y - 6 = -1(x + 5) \][/tex]
So, the point-slope form of the equation of the line passing through the points (-5, 6) and (0, 1) is [tex]\( \boxed{A) y + 6 = -1(x - 5)} \)[/tex].
What is factor out the coefficient of the variable of 4h-3