On average, how many times must a 6-sided die be rolled until a 6 turns up twice in a row?

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]

Answer:

10 square feet

Step-by-step explanation:

The explanation is in the picture below.

Your welcome :)

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

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.

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.

https://brainly.com/question/31904612

#SPJ11

Option: C is the correct answer.

                          C.  216

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]

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.

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.

The relationships between the sides and angles of the right triangles in

the question are given by trigonometric ratios.

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;

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;

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]

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]

Learn more about trigonometric ratios here:

https://brainly.com/question/8517005

The answer is r(x) = (4x)^7

Answer:

Its A o.22

Step-by-step explanation:

Answer:

- 3/4

Step-by-step explanation:

this answer is correct

Final answer:

The sequence of substitutions of the coins on the table results in a final arrangement of coins with a total value of 121 cents or $1.21. This problem combines sequence patterns with coin values to find the total.

Explanation:

We have a problem involving a series of substitutions of coins, and we need to calculate the total value of the coins on the table after these substitutions. We start with 12 pennies, which are initially worth 1 cent each.

Step 1: Every other coin is replaced with a nickel, so we replace every 2nd penny with a 5-cent coin (nickel). The sequence starts with a penny (P), so the even positions will now be nickels (N). The sequence now looks like P, N, P, N, P, N, P, N, P, N, P, N.

Step 2: Every third coin is replaced with a dime, which is worth 10 cents. This means the 3rd, 6th, 9th, and 12th positions will now be dimes (D). The sequence becomes P, N, D, N, P, D, P, N, D, N, P, D.

Step 3: Every fourth coin is replaced with a quarter, which is worth 25 cents. Positions 4, 8, and 12 are affected. The sequence is now P, N, D, Q, P, D, P, Q, D, N, P, Q.

Let’s calculate the total value of the coins:

6 Pennies (P): 6 * 1 cent = 6 cents

2 Nickels (N): 2 * 5 cents = 10 cents

3 Dimes (D): 3 * 10 cents = 30 cents

3 Quarters (Q): 3 * 25 cents = 75 cents

Adding all these values together: 6 cents + 10 cents + 30 cents + 75 cents = 121 cents or $1.21.

This problem requires understanding of sequence patterns and knowledge of United States coin values to determine the total value of the coins.

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.

For similar question on abundant gas.

https://brainly.com/question/11735363

#SPJ6

Answer: the church was dependent on the princes power

Step-by-step explanation:

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.

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.

To learn more about the statistical question visit:

https://brainly.com/question/11253919.

#SPJ2