You have been really sick, so you went to the doctor. The culture taken shows you have 400,000 bacteria. Your doctor prescribes a strong antibiotic which makes the bacteria decrease by a half every 4 hours. How many bacteria will be left after a day?

Option (D) No, it is not possible to take a cross section of a tetrahedron and get an octagon because the number of sides on the resulting shape cannot exceed the number of faces on the solid. A tetrahedron, having only four faces, cannot have a cross section with eight sides like an octagon.

The question asks if it is possible to take a cross section of a tetrahedron and get an octagon. A tetrahedron is composed of four triangular faces, six edges, and four vertices. It is the simplest of all the ordinary convex polyhedra and the only one with fewer than 5 faces. The provided options suggest various reasons why an octagon could or could not result from a cross section of a tetrahedron. The correct answer is D: No, because the number of sides on the resulting shape cannot exceed the number of faces on the solid.

A cross section that intersects a solid will typically not have more sides than the number of faces of the solid itself. Since a tetrahedron has only four faces, any cross-section made through it cannot naturally have more than four sides, thus it cannot result in an octagon, which has eight sides. The concept of symmetry or the fact that an octagon has twice as many sides as a tetrahedron does not relate to the possibility of such a cross section.

Answer

you work it out the same way the first guy did, except instead of

2 (180-x) - 6 = 124, it's

2(90-x) -6 = 124.

the first guy divided by the supplement instead of the complement.

Step-by-step explanation:

To find the measure of the angle, you can use the equation 2(90 - x) - 6 = 124, where x represents the angle. By solving for x, you can determine that the measure of the angle is 25 degrees.

To find the measure of the angle, we can use the information provided in the question. Let's let the measure of the angle be x degrees. The complement of the angle can be found by subtracting the measure of the angle from 90 degrees, since the sum of an angle and its complement is always 90 degrees. Therefore, the complement of the angle is 90 - x degrees.

According to the given equation, twice the measure of the angle's complement less 6 is equal to 124. We can write this as 2(90 - x) - 6 = 124. Now we can solve for x:

2(90 - x) - 6 = 124

180 - 2x - 6 = 124

-2x + 174 = 124

-2x = -50

x = 25

Therefore, the measure of the angle is 25 degrees.

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By subtracting the eliminated participants in each round from the original number, it is determined that 25 participants were still competing at the beginning of the fourth round.

To find out how many participants were still competing at the beginning of the fourth round of the spelling bee, we need to perform some calculations based on the given percentages of participants eliminated in each round.

Therefore, 25 participants were still competing at the beginning of the fourth round.

Answer: D

Step-by-step explanation:

Final answer:

To calculate the percent of increase from 4.5 inches to 13.5 inches, subtract the original value from the new value, divide by the original value, and then multiply by 100, resulting in a 200% increase.

Explanation:

To find the percent of increase from one number to another, you can use the formula: (New Value - Original Value) / Original Value × 100%. Applying this to the question, the original value is 4.5 inches, and the new value is 13.5 inches.

Therefore, the percent of increase from 4.5 inches to 13.5 inches is 200%.

Answer:

The length of segment DE is 3.2  (A)

Step-by-step explanation:

Answer:

36° is correct.

Step-by-step explanation:

The degree of rotational symmetry is equal to 360° divided by the number of sides of a regular polygon

360° ÷ 10 = 36°

Answer:

A regular decagon is mapped onto itself every time it is rotated by 36°

Step-by-step explanation:

A regular decagon means a polygon with 10 sides and all sides are equal.

Refer the given figure, if we rotate by 36° we will get same decagon.

So a regular decagon is mapped onto itself every time it is rotated by 36°

Answer:

Option C - All real numbers                                      

Step-by-step explanation:

Given : Function [tex]y=\cos \theta[/tex]

To find : The domain of given function ?

Solution :

Domain is defined as the set of values for which function is defined.

We have given the function,

[tex]y=\cos \theta[/tex]

We know, for any value of [tex]\theta[/tex] the function  [tex]y=\cos \theta[/tex] is defined.

Which means the set of all real numbers defined the given function i.e. [tex]x\in(-\infty,\infty)[/tex]

Therefore, Option C is correct.

The domain of  [tex]y=\cos \theta[/tex] is all real numbers.

The geometric mean of the pair of numbers 36 and 4 is calculated by getting the square root of the product of the two numbers, which gives us the geometric mean as 12.

To find the geometric mean of the pair of numbers 36 and 4, we use the formula for the geometric mean of two positive numbers, which is the square root of the product of the two numbers.

When we multiply 36 and 4 we get 144. So, the geometric mean of 36 and 4 is the square root of 144, which equals 12.

Therefore, the geometric mean of the numbers 36 and 4 is 12.

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r = 0.9 (a strong linear association in which y increases as x increases)

r = -1.0 (a perfect linear association in which y decreases as x increases)

r = -0.6 (a moderate linear association in which y decreases as x increases)

r = 0.1 (no linear association or a very weak association)

Approximately 85.323 feet of fence is needed to enclose the garden.

To find the length of the fence needed to enclose Maria's triangular garden, we can use the Law of Sines since we know one side length and its opposite angle.

The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant:

[tex]\[ \frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)} \][/tex]

Where:

- a, b, c are the side lengths of the triangle.

- A, B, C are the angles of the triangle.

Given that one side length is 29 feet and its opposite angle is 65°, let's denote the other two angles as B  and C . Since the sum of angles in a triangle is 180°, we can find angle C as 180° - 65° - 44° = 71°.

Now, we can use the Law of Sines to find the lengths of the other two sides:

[tex]\[ \frac{29}{\sin(65°)} = \frac{b}{\sin(44°)} \][/tex]

Solving for b:

[tex]\[ b = 29 \times \frac{\sin(44°)}{\sin(65°)} \][/tex]

b ≈ [tex]24.438 \text{ feet} \][/tex]

Similarly, we can find the length of side c  using the same formula:

[tex]\[ \frac{29}{\sin(65°)} = \frac{c}{\sin(71°)} \][/tex]

[tex]\[ c = 29 \times \frac{\sin(71°)}{\sin(65°)} \][/tex]

c ≈ [tex]31.885 \text{ feet} \][/tex]

Finally, to find the total length of the fence needed, we sum up the lengths of all three sides:

[tex]\[ \text{Total fence length} = 29 + 24.438 + 31.885 \][/tex]

[tex]\[ \text{Total fence length}[/tex] ≈ [tex]85.323 \text{ feet} \][/tex]

So, approximately 85.323 feet of fence is needed to enclose the garden.