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Final answer:

The two consecutive positive odd integers that satisfy the given condition, where the square of the smaller plus three times the median equals 24, are 3 and 5.

Explanation:

The question asks to find two consecutive positive odd integers such that the square of the smallest integer, added to 3 times the median integer, is 24. Let's denote the smallest of these integers as n. Since they are consecutive odd integers, the next integer would be n+2. The equation based on the given condition would be n² + 3(n + 2) = 24.

Expanding and solving the equation gives:

n² + 3n + 6 = 24

n² + 3n - 18 = 0

(n+6)(n-3) = 0

Solving for n, we find n = 3 (since we are looking for positive integers and n+6=0 leads to a negative value).

Thus, the two consecutive positive odd integers are 3 and 5, meeting the given conditions.

For a better understanding of the solution provided here please go through the diagram in the attached file.

In the diagram, F is the foot of the tree.

T is the top of the tree. Then TF will be the height of the tree.

P is the point on the ground 47 feet from the foot of a tree. Therefore, PF=47.

Now, we know that the tree grows vertical from the ground and thus [tex] \angle F=90^{\circ} [/tex]

Thus, the triangle [tex] \Delta PFT [/tex] is a right triangle.

Now, we can apply the trigonometric ratio, tan in this triangle as:

[tex] tan(\angle P)=\frac{Perpendicular}{Base} =\frac{TP}{PF} [/tex]

[tex] \therefore tan(35^{\circ})=\frac{TF}{47} [/tex]

[tex] TF=47\times tan(35^{\circ})\approx32.91\approx33 [/tex]

Thus, the the height of the tree to the nearest foot is 33 feet.

The height of the tree is 32.90 feet.

P is the point on the ground, T is the top of the tree, and h is the height of the tree. We are given that PT = 47 feet and the angle of elevation from P to T is 35 degrees.

We want to find the height of the tree, which is represented by h in the diagram. We can use the tangent function to solve for h.

The tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right triangle.

In this case, the opposite side is h and the adjacent side is PT = 47 feet. Therefore, we have

tan(35°) = h/47

Solving for h, we get:

h = 47 * tan(35°) ≈ 32.90 feet

Rounding to the nearest foot, we find that the height of the tree is 33 feet.

Answer:13

Step-by-step explanation:

Final answer:

The age of the mammal hide can be determined by using carbon-14 dating. By comparing the remaining amount of carbon-14 to the initial amount and knowing the half-life of carbon-14, the age of the hide can be calculated. In this case, the hide is approximately 778 years old.

Explanation:

The age of the mammal hide can be determined using carbon-14 dating. Carbon-14 (or C-14) is an isotope that is present in all living organisms. When an organism dies, the amount of C-14 in its remains begins to decay.

Based on the information provided, the mammal hide contains 54% of its original amount of C-14. Knowing that the half-life of C-14 is 5,730 years, we can calculate the age of the hide.

To do this, we can set up the following equation: Remaining amount of C-14 = Initial amount of C-14 × (0.5)^(number of half-lives)

Since the hide contains 54% of its original amount of C-14, the remaining amount is 0.54 times the initial amount.

By substituting the known values into the equation, we can solve for the number of half-lives:

0.54 × Initial amount of C-14 = Initial amount of C-14 × (0.5)^(number of half-lives)

Dividing both sides of the equation by the initial amount of C-14 and taking the logarithm of both sides, we can find the number of half-lives:

ln(0.54) = number of half-lives × ln(0.5)

Using a logarithmic calculator, we find that the number of half-lives is approximately 0.136.

Since each half-life spans 5,730 years, we can calculate the age of the hide:

Age of hide = Number of half-lives × Half-life duration

Age of hide = 0.136 × 5,730 years

Therefore, the age of the mammal hide is approximately 778 years.

Answer: 5621

Step-by-step explanation:

i did it

-6, 4 is the answer

Answer:

56

Step-by-step explanation:

Answer:

(0,-24)  

hope this helps you!

(p.s please mark me as brainlyest)

Step-by-step explanation:

I just took the test and got 100%

The answer would be D, because 4 8/6 is equal to 5 2/6.

Hope this helps ;}

Final answer:

The mixed number 5 2/6 simplified is 5 1/3 and when represented as an improper fraction it is 16/3. Upon reviewing the given options, only D) 4 8/6 is equivalent to 5 2/6 or 5 1/3.

Explanation:

To represent the mixed number 5 2/6 in another form, first simplify it by reducing the fraction to its lowest terms. The fraction 2/6 can be simplified to 1/3 because the numerator and denominator share a common factor of 2. So the number becomes 5 1/3. Now, to find an equivalent representation from the given options, you can convert it to an improper fraction: (5 × 3) + 1 = 15 + 1 = 16, so the equivalent improper fraction is 16/3. Looking at the choices provided, none match 5 1/3 exactly, but we can look at them to determine if any are equivalent:

Therefore, the correct answer is D) 4 8/6 as it is another way to represent 5 2/6.

A house is an example of a composite figure that can be decomposed into rectangles and triangles to find the area, which aids in calculating material requirements.

An example of a composite figure in a home or community could be a house, which often consists of several rectangles and triangles. To find the area of a house, you would decompose it into its simpler shapes, calculate the area of each shape, and then sum those areas. Aside from finding the area, decomposition is useful for estimating materials needed for construction or renovations, such as flooring, paint, or roofing. For instance, knowing the areas of separate walls can help determine how much paint is needed for each.

Answer:

We know that the rainwater outflow pipe must drop 1 inch per 25 horizontal inches, this ratio would be:

[tex]\frac{y}{x}=\frac{1}{25}=0.04[/tex]

So, if the drainage pipe has this ratio, then it will function properly. Let's find out:

[tex]\frac{y}{x}=\frac{25}{540}[/tex]

Because, 45 feet is equivalent to 540 inches.

So, the ratio would be:

[tex]\frac{25}{540} \approx 0.046[/tex]