To find the number of dust particles in a 1200 cubic meter bedroom with 3.4 x 10⁹ particles per cubic meter, multiply the volume by the number of particles per volume, resulting in approximately 4.08 trillion dust particles.
To calculate the number of dust particles in the bedroom, we need to multiply the volume of the bedroom by the number of dust particles per cubic meter. Given that the bedroom is 1200 cubic meters and that there are 3.4 x 10⁹ particles of dust per cubic meter, we can use the following calculation:
Number of particles = Volume of the bedroom x Number of particles per cubic meter
Number of particles = 1200 m³ x 3.4 x 10⁹ particles/m3
Number of particles = 4.08 x 10¹² particles
Therefore, there are approximately 4.08 trillion dust particles in the bedroom of the house.
Which expression can be used to convert 80 US dollars (USD) to Australian dollars (AUD)?
1 USD = 1.0343 AUD
1 AUD = 0.9668 USD
Factor completely: x4 + 8x2 + 16
Final answer:
The expression x⁴ + 8x² + 16 is a perfect square trinomial and it can be factored completely as (x² + 4)².
Explanation:
To factor completely the expression x⁴ + 8x² + 16, we should first recognize that this is a perfect square trinomial. A perfect square trinomial takes the form a² + 2ab + b², and can be factored into (a + b)².
Comparing our given expression to the perfect square trinomial, we see that x⁴ is the square of x² and 16 is the square of 4. Moreover, 8x² is twice the product of x² and 4, suggesting that the expression is indeed, a perfect square. Thus, we can factor it as:
(x² + 4)²
In conclusion, the expression x⁴ + 8x² + 16 can be factored completely as (x² + 4)².
Final answer:
To factor the expression [tex]x^4 + 8x^2 + 16[/tex] t is a perfect square trinomial.
Explanation:
To factor the expression [tex]x^4 + 8x^2 + 16[/tex] t is a perfect square trinomial of the form [tex]a^2 + 2ab + b^2[/tex]. The square root of the first term is [tex]x^2[/tex] the square root of the last term is 4, and twice the product of these square roots is [tex]8x^2[/tex], which matches the middle term of the given expression. Therefore, we can rewrite the expression as [tex](x^2 + 4)^2[/tex]. This is the completely factored form of the expression.[tex]a^2 + 2ab + b^2[/tex]
A square has an area of 49 units what is the length of each side
Evaluate the summation of 2 n plus 5, from n equals 1 to 12..
A. 29
B. 36
C. 216
D. 432
Option: C is the correct answer.
C. 216
Step-by-step explanation:We are asked to evaluate the sum of the following summation:
[tex]\sum_{n=1}^{12} (2n+5)[/tex]
Now, this summation could also be written as:
[tex]\sum_{n=1}^{12} (2n+5)=\sum_{n=1}^{12} 2n+\sum_{n=1}^{12} 5[/tex]
i.e.
[tex]\sum_{n=1}^{12} (2n+5)=2\sum_{n=1}^{12} n+\sum_{n=1}^{12} 5[/tex]
Now, we know that:
[tex]\sum_{n=1}^{12} n=1+2+3+4+....+12\\\\i.e.\\\\\sum_{n=1}^{12} n=\dfrac{12(12+1)}{2}[/tex]
Since,
[tex]\sum_{i=1}^{n} i=\dfrac{n(n+1)}{2}[/tex]
i.e.
[tex]\sum_{n=1}^{12} n=78[/tex]
and
[tex]\sum_{n=1}^{12} 5=5+5+....+5\ (\text{twelve\ times})\\\\i.e.\\\\\sum_{n=1}^{12} 12=12\times 5\\\\i.e.\\\\\sum_{n=1}^{12} n=60[/tex]
Hence, we have:
[tex]\sum_{n=1}^{12} (2n+5)=2\times 78+60[/tex]
i.e.
[tex]\sum_{n=1}^{12} (2n+5)=156+60[/tex]
i.e.
[tex]\sum_{n=1}^{12} (2n+5)=216[/tex]
Solve for the roots in the equation below...
x^3 - 27 = 0
If an outcome measure is normally distributed, this means that
A normally distributed result means that when the data is plotted on a graph, we can actually see a bell shaped curve. That highest frequency or peak is centered on the average value. Because it is shaped like this, we can say that:
most scores are around the average with some scores being lower or higher
Antoine is graphing the total number of prizes needed, P, based on the number of entries in a contest, E. He knows that for every 10 entries, he will need 1 prize, and he would like for his graph to show the total number of prizes needed for 100 and 150 entries. Select from the drop-down menus to correctly complete each statement.
To best show this information, the scale for the P-axis of his graph should go from 0 to at least ___ , and the E-axis of his graph should go from 0 to at least ___.
Is f(x)=13.7e^0.04t an example of exponential growth or decay
Please Help!
Economists recommend that the GDP (gross domestic product) growth rate of a nation be between 7.1 and 7.9 percent inclusively. Identify the compound inequality that show these GDP rates.
7.1 ≤ g ≤ 7.9
7.1 ≤ g <7.9
7.1 < g <7.9
7.1 < g ≤ 7.9
The compound inequality which represents the recommendation of economists for a GDP growth rate to be between 7.1 and 7.9 percent (inclusive) is given by '7.1 ≤ g ≤ 7.9'. This mathematical expression indicates that the acceptable rates are all the values including and between 7.1 & 7.9.
Explanation:In the context of mathematics, specifically the subject of inequalities, the student's question is asking to represent the given GDP rates as a compound inequality. A compound inequality is a statement with two inequalities joined by the word 'and' or 'or'.
Here, economists recommend the GDP growth rate to be between 7.1 and 7.9 percent (inclusive). So, the GDP growth rate (let's denote it as 'g') is more than or equal to 7.1 percent and, at the same time, less than or equal to 7.9 percent. So, the compound inequality which represents this situation is 7.1 ≤ g ≤ 7.9. So the correct option from the provided ones is the first one: '7.1 ≤ g ≤ 7.9'.
This inequality tells us that the growth rates 'g' are all the values including and between 7.1 & 7.9. This is crucial information for economists when monitoring the health and progress of a nation's economy. The percentage rate of GDP growth is a measure of economic success and can impact many aspects like standard of living, employment rates, and business growth.
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A rate for internet acess is $5 per month plus $0.25 per hour of use. write a function rule to show how the monthly bill depends on the number of hours used. if you spend one hundred and twenty-two horus in a month, how much will the monthly bill come to
Answer:
Its A o.22
Step-by-step explanation:
BRAINLIEST ASAPPPP!!!
Which of the following questions is a statistical question?
How many sticks of gum can you chew at one time?
Where can gum be purchased?
How many types of gum are there?
How many sticks of gum come in a standard pack?
Answer:
The answer is How many sticks of gum can you chew at one time? (I got it right on my test)
Step-by-step explanation:
Option A is the correct answer.
We need to find from the given options which is the statistical question.
What is the statistical question?A statistical question is one that can be answered by collecting data and where there will be variability in that data. This is different from a question that anticipates a deterministic answer.
Now from the given options, we can say that,
The best and most correct answer among the choices provided by your question is the first choice which states that "How many sticks of gum can you chew at one time? "
Therefore, option A is the correct answer.
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What is 840 divde by 10 to the third power
Write an equation of the line that passes through (2, 7) and (0, −5)
y=
Yuki has a ribbon that is 11 1/4 feet long. She divides it into pieces that are each 1 7/8 feet long. She uses three piece to make a bow. How many bows can she make in all?
Which function is a horizontal compression of its parent function f(x)=x^7 by a factor of 4?
q(x)=(1/4x)^7
r(x)=(4x)^7
s(x)=4x^7
t(x)=1/4x^7
thank you!
The answer is r(x) = (4x)^7
Which expression is equivalent to 3x+10−x+12?
A: 4x + 22
B: 2x + 22
C: 24x
D: 26x
What is the slope of a line that is parallel to the line represented by the equation 3x + 4y = 12?
Answer:
- 3/4
Step-by-step explanation:
this answer is correct
What correctly describes the relationship between the Russian Orthodox Church and the princes of kiev
Answer: the church was dependent on the princes power
Step-by-step explanation:
Your garden is in the shape of a trapezoid. The width is 2 feet. The parallel bases are 4 feet and 6 feet. What is the area of your garden?
Answer:
10 square feet
Step-by-step explanation:
The explanation is in the picture below.
Your welcome :)
Which ratio is not equivalent to the other three 2/3 12/15 6/9 1827,
Anyone know how to do the fireworks display portfolio?
Final answer:
To create a fireworks display portfolio, you can use physical methods such as printing photos or employ digital tools like a word processor, presentation software, or Web 2.0 tools. Ensure you use your own photos, review them to demonstrate key concepts learned, and include them in your final project.
Explanation:
To create a fireworks display portfolio, you have several options. One method involves printing your photos and physically attaching them to paper or poster board, then writing reflections beside them. For a more modern touch, you might opt to create your portfolio digitally using a word processor. In this format, it's important to only use your own photos rather than those with Creative Commons licenses or other sourced images.
Alternatively, you can employ presentation software or various Web 2.0 tools like Glogster (EDU) or VoiceThread for a dynamic and interactive portfolio. When creating your fireworks display portfolio, it is crucial to consider the visual and descriptive elements that highlight what you've learned. Make sure to review your flash photos, choose the sets that best demonstrate the three distance settings or the three settings in the assignment prompt, and be ready to discuss their relevance to the concepts learned in class, such as conservation of momentum and center of mass regarding fireworks.
Lastly, ensure that you download your photos to a computer to include them in the end-of-course final project portfolio. This portfolio will serve as a cohesive collection of your work and understanding of the subject matter.
Substitute the values of x and y into the expression -3x 2 + 2y 2 + 5xy - 2y + 5x 2 - 3y 2. Match that value to one of the numbers.
1. x = 2, y = -1
9.17
2. x = 0, y = 2.5
1.665
3. x = -1, y = -3
-11.25
4. x = 0.5, y =
14
5. x = , y =
-1
6. x = √2, y = √2
0.44
Between which weeks was the change in money earned the greatest?
What is the value of x?
A. 110 degrees
B. 35 degrees
C. 145 degrees
D. 60 degrees
Decide which of the two points lies on the graph of the line
2x-5y=-14
A. 2,-2
B. -2,2
Nitrogen gas accounts for what percentage of the atmosphere? select one:
a. approximately 50%
b. 1%
c. 99%
d. 78%
e. 0.03%
Nitrogen gas makes up approximately 78% of the atmosphere, not 50%, 1%, 99%, or 0.03%.
The correct answer is: d. 78%
Nitrogen gas (N2) makes up a significant portion of the Earth's atmosphere.
To determine the correct percentage, we need to consider the composition of the atmosphere:
The Earth's atmosphere is primarily composed of several gases, with the most abundant being nitrogen (N2) and oxygen (O2).
Other gases such as argon, carbon dioxide, neon, helium, and trace amounts of other gases are also present.
The correct answer is: d. 78%
Nitrogen gas (N2) constitutes approximately 78% of the Earth's atmosphere, making it the most abundant gas.
Oxygen (O2) is the second most abundant gas, accounting for about 21% of the atmosphere.
The remaining 1% consists of trace gases like argon, carbon dioxide, and others.
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The holding tanks are congruent. Each is in the shape of a cylinder that has been cut in half vertically. The bottom of each tank is a curved surface and the top of the pool is a flat surface. What is the volume of both tanks if the radius of tank #1 is 30 feet and the height of tank #2 is 110 feet? You must explain your answer using words, and you must show all work and calculations to receive credit.
The figure in the picture is made up of 5 congruent squares. If the perimeter of the entire figure is 21.6 cm, find its area.
a. Name one line segment that is parallel to AB
b. Name one line segment that is skew to AB
c. Name a pair of parallel planes.
Answer:
A) CD
B) AB
C) Plane ABCD is parallel to EFGH.
Plane BDFH is parallel to ACGE.
Plane ABFE is parallel to CDHG.
Step-by-step explanation:
We are given the following in the question:
A cuboid ABCDEFGH is given.
A) line segment that is parallel to AB
A line segment that is parallel to AB is CD.
B) line segment that is skew to AB
Skew lines are the line that never lie in the same plane and never intersect each other.
Thus line segment FH is skew to line segment AB.
C) pair of parallel planes.
Plane ABCD is parallel to EFGH.
Plane BDFH is parallel to ACGE.
Plane ABFE is parallel to CDHG.
For △ABC, which side is opposite angle B?
side AC
side AB
side BC
Angle D in △EDF is a right angle.
What is the value of tan F ?
4/3
3/4
3/5
4/5
What is the trigonometric ratio for sin Z ?
Enter your answer, as a simplified fraction, in the boxes.
What is the trigonometric ratio for cosD ?
Enter your answer, as a simplified fraction, in the boxes.
Tessa has leaned a ladder against the side of her house. The ladder forms a 63˚ angle with the ground and rests against the house at a spot that is 8 meters high.
Which length is the best approximation for the distance along the ground from the bottom of the ladder to the wall?
2 m
3 m
4 m
5 m
The relationships between the sides and angles of the right triangles in
the question are given by trigonometric ratios.
Correct responses;1. Side AC[tex]\displaystyle 2. \hspace{0.3 cm}\frac{4}{3}[/tex][tex]\displaystyle 3. \hspace{0.3 cm}\frac{3}{5}[/tex][tex]\displaystyle 4. \hspace{0.3 cm}\frac{7}{25}[/tex]5. 4 m.Methods used to arrive at the above responses;1. The given triangle is ΔABC
The side opposite angle B is the side not bearing the letter B which is the side AC
2. The tangent of the angle, F, is given by the following formula;
[tex]\displaystyle tan(F) = \mathbf{\frac{Opposite \ side \ to \ angle \ F}{Adjacent \ side \ to \ angle \ F}}[/tex]
Therefore;
[tex]\displaystyle \underline{ tan(F) = \frac{4}{3}}[/tex]3. The sine of the angle Z is given by the following formula;
[tex]\displaystyle sin (Z) = \mathbf{ \frac{Opposite \ side \ to \ angle \ Z}{Hypotenuse \ side \ of \ right \ triangle}}[/tex]
Therefore;
[tex]\displaystyle sin(Z) = \mathbf{\frac{XY}{40}}[/tex]
XY = √(40² - 32²) = 24
Which gives;
[tex]\displaystyle \underline{sin(Z) = \frac{24}{40} = \frac{3}{5}}[/tex]4. The trigonometric ratio for cos(D) is given as follows;
[tex]\displaystyle cos(D) = \mathbf{ \frac{Adjacent \ side \ to \ angle \ \angle D}{Hypotenuse \ side \ of \ right \ triangle}}[/tex]
Therefore;
[tex]\displaystyle cos(D) = \frac{21}{75} = \frac{7}{25}[/tex]
[tex]\displaystyle \underline{ cos(D) = \frac{7}{25} }[/tex]5. The tangent of the angle 63° is expressed as follows;
[tex]\displaystyle tan(63^{\circ}) = \mathbf{\frac{8 \, m}{Distance \ AB \ (ground \ distance \ from \ wall)}}[/tex]
Therefore;
[tex]\displaystyle Distance \ AB = \frac{8 \, m}{tan(63^{\circ})} \approx \mathbf{4.076 \, m}[/tex]
The approximate distance from the bottom of the ladder o the wall is 4 mLearn more about trigonometric ratios here:
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