Can someone please help me on number 8. Explain how you got the answer please .

Final answer:

To determine the total area of the mural, we calculate the area of one student's square, which is 100 square inches, and multiply by the total number of squares in the mural, resulting in 2500 square inches for the total area.

Explanation:

Mrs. Deaton's 6th grade class is working on a mural where each student contributes a square with a side length of 10 inches. The mural will be arranged in a larger square with five student squares along each side. To determine the total area of the mural, we will calculate the area of one student's square and then multiply by the total number of squares.

First, the area of one student's square is found by squaring the side length:

Area of one square = side length × side length = 10 inches × 10 inches = 100 square inches.

Since the mural is a square consisting of 5 student squares on each side:

Total number of student squares = 5 × 5 = 25 squares.

Finally, to find the total area of the mural, we multiply the area of one square by the total number of squares:

Total area of mural = area of one square × total number of squares = 100 square inches × 25 = 2500 square inches.

The total area of the mural is 2500 square inches.

Answer:

The area of triangle DEF is 9 square units.

Step-by-step explanation:

It is given that triangle ABC and DEF are similar and the ratio of the side lengths in triangle ABC to triangle DEF is 1:3.

Let the length of their sides be x and x respectively.

If two triangles are similar then the ratio of their areas is equal to the square of the ratio of their sides.

Since triangle ABC and DEF are similar, therefore

[tex]\frac{Area(ABC)}{Area(DE F)}=\frac{(x)^2}{(3x)^2}[/tex]

[tex]\frac{1}{Area(DE F)}=\frac{(x)^2}{9(x)^2}[/tex]

Cancel out the common factors.

[tex]\frac{1}{Area(DE F)}=\frac{1}{9}[/tex]

On cross multiplication, we get

[tex]1\times 9=1\times Area(DE F)}[/tex]

[tex]9=Area(DE F)}[/tex]

Therefore the area of triangle DEF is 9 square units.

Part A: The average rate of change of section A is 12 and that of B is 300.

Part B: The average rate of change of Section B is 25 times greater than that of Section A due to the exponential nature of the function h(x).

Explaining the average rate of change for two sections and comparing their values in an exponential function context,

One rate of change is greater than the other because of the exponential growth nature of the function. The function h(x) = 3 [tex](5)^x[/tex] is an exponential function, and the rate of change increases rapidly as x increases, leading to a much greater average rate of change for Section B than Section A.

The question is:

Given the function h(x) = 3 [tex](5)^x[/tex], Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3.

Part A: Find the average rate of change of each section.

Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other.

The first term of the geometric sequence is 3 and the common ratio is 2.

To identify the first term and the common ratio of a geometric sequence, we can use the formula:  an = a1 * r^(n-1), where an is the nth term, a1 is the first term, r is the common ratio, and n is the position of the term.

Given a5 = 48 and a11 = 3,072, we can substitute the values into the formula:

48 = a1 * r^(5-1)

3,072 = a1 * r^(11-1)

By dividing the second equation by the first equation, we can eliminate a1:

64 = r^6

Taking the sixth root of both sides gives:

r = 2

Substituting this value back into the first equation, we can solve for a1:

48 = a1 * 2^4

a1 = 3

So, the first term (a1) is 3 and the common ratio (r) is 2.

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Answer:

Its 3.6

Step-by-step explanation:

You turn {5, 12, 1, 6, 11} into {2, 5, 6, 1, 4} add them into 18 then divide by 5 into 3.6

Zöe's error is in mixing units of seconds and minutes in her measurements. Her total time of 12 minutes should be converted into seconds (720 seconds) to match the 30 and 60 second ad times. The correct equations for her problem are x + 2y = 720 and y = 2x.

The given question relates to system of linear equations and misunderstandings in time measurements. The discrepancy in Zöe's equations relates to the units she used for the ad times and the total time. She was dealing with 30 second and 60 second ads (measuring them in seconds), but she attempted to balance this against a total time of 12 minutes (measured in minutes).

The correct approach would be to ensure that all the times are using the same units. Since there are 60 seconds in a minute, Zöe's total time should be expressed as 720 seconds. Additionally, she sold twice as many 60 second ads as 30 second ads. Therefore, her equations should be: x + 2y = 720 and y = 2x.

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The question relates to formulating equations based on given constraints. Zöe's error is in not taking into account that the sum of the times for the 30 and 60-second ads should be 12 minutes. Moreover, the relation between the quantities of the 30 and 60-second ads should be such that the latter is double the former.

The question presents a situation where Zöe has to schedule ads for a radio station with a fixed time frame. The constraints are that she has 12 minutes every hour to fill with either 30 second ads or 60 second ads, and that she sold twice as many 60 second ads as she did 30 second ads. Here, x represents the number of 30 second ads and y represents the number of 60 second ads.

Given these criteria, Zöe should set up two equations. The first equation will express the total time consumed by ads: (0.5x + y) minutes = 12 minutes. The second equation represents the relationship of the number of ads: y = 2x.

The error in the way the problem is stated seems to revolve around Zöe's representation of the constraints. She should consider the fact that the total time occupied by the 30 and 60-second ads must equal 12 minutes. Furthermore, the relationship between the number of 30 and 60-second ads should be factored into the equations, with the 60-second ads being twice the number of 30-second ads.

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The probability of not drawing an E is 5/8. Expressed as a decimal, it is 0.625, and as a percentage, it is 62.5%.

To determine the probability that the letter E is not selected by Mary, we first look at the total number of E's in the mix and the total number of letters. There are three E's and a total of eight letters. To calculate the probability of not drawing an E, we need to find the number of outcomes that are not E, which is 8 total letters minus 3 E's, leaving us with 5 non-E letters.

The probability of not drawing an E can be calculated as the number of non-E letters over the total number of letters: P(not E) = 5/8. To express this as a decimal, we divide 5 by 8 to get 0.625. To express it as a percentage, we simply multiply the decimal by 100, resulting in 62.5%.

Therefore, the probability that E will NOT be the letter Mary selects is 5/8 as a fraction, 0.625 as a decimal, and 62.5% as a percentage.

The population growth function represented by an initial value A that increases 22% per year with x representing time in years is y=A(1.22)^x.

The function which represents an initial population that increases 22% per year, where A is the initial value and x is time in years, is given by y=A(1.22)^x. This formula calculates the future value (y) based on the premise of exponential growth, which embodies a continual increase year after year. The rate of growth is 22%, therefore we add this to 100% to get 122% (1.22). This entire value is raised to the power of x, representing the number of time periods (years).

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B the second one. It shows all the steps correctly

Final answer:

The equation to find the cost of 3.5 pounds of grapes, with one pound costing $1.55, is represented by the proportion 1 pound / 3.5 pounds = $1.55 / x. By solving this equation, we find that x, the total cost for 3.5 pounds of grapes, is $1.55 multiplied by 3.5 = $5.425

Explanation:

The student is asking about the cost of 3.5 pounds of grapes, given that one pound costs $1.55. To find the equivalent ratio that can be used to calculate the cost of 3.5 pounds, we can set up a proportion where the cost of 1 pound is to 3.5 pounds as $1.55 is to the unknown cost (let's call it x). The equation representing the pair of equivalent ratios is:

1 pound / 3.5 pounds = $1.55 / x.

To solve for x, we multiply both sides of the equation by 3.5 pounds, which gives us:

1 pound * ($1.55 / 1 pound) * 3.5 = x

And this simplifies to:

x = $1.55 * 3.5 = $5.425

Therefore, by calculating $1.55 * 3.5, we can find the cost of 3.5 pounds of grapes.

Answer:

Prove that KL is equal to c by Pythagorean Theorem.

Step-by-step explanation:

In the two triangles triangle KLM is a right triangle with sides a and b as the two legs of the right triangle .We can apply Pythagorean Theorem to find KL.

In triangle KGF two sides are a and b .If we prove KL=EF then Pythagorean Theorem will be true for triangle KGF and hence we can prove triangle KGF to be a right triangle.

The correct option to prove triangle KGF to be a right triangle is to Prove that KL is equal to c by Pythagorean Theorem.

Let us suppose we have a triangle ABC as shown in the attached image.

Now, let us we draw a  perpendicular line from the vertex A to the base BC. Let the line meets the base BC at D.

Then, this perpendicular line AD will separate the triangle  ABC into two right angle triangle ADB and triangle ADC.

Answer:

4to5 and 3to7

Step-by-step explanation:

:)hope this helped