The cylinder shown here has a height of 7 centimeters and a radius of 4 centimeters. What is the area of the base of the cylinder? Express your answer in terms of 1. Do not include units (cm2) in your answer. Use pi to represent the n symbol. For example: 321 would be typed as 32pi​

Answer:

x = 6\(\sqrt{2}\)

Step-by-step explanation:

Using the cosine ratio in the right triangle and the exact value

cos45° = \(\frac{1}{\sqrt{2} }\) , then

cos45° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{6}{x}\) = \(\frac{1}{\sqrt{2} }\) ( cross- multiply )

x = 6\(\sqrt{2}\)

The enzyme that has a very similar reaction mechanism to 6-phosphogluconate dehydrogenase in glucose oxidation by the citric acid cycle is isocitrate dehydrogenase.

Isocitrate dehydrogenase is a key enzyme in the citric acid cycle, also known as the Krebs cycle  or TCA cycle. It catalyzes the conversion of isocitrate to alpha-ketoglutarate, while producing NADH and CO2 as byproducts. This reaction is an important step in the oxidation of glucose and the production of energy in the form of ATP. The reaction mechanism of isocitrate dehydrogenase involves the removal of a carboxyl group from isocitrate, resulting in the formation of an intermediate molecule called oxalosuccinate. This intermediate is then decarboxylated to produce alpha-ketoglutarate. The overall reaction is coupled with the reduction of NAD+ to NADH. 6-phosphogluconate dehydrogenase, on the other hand, is involved in the pentose phosphate pathway and plays a role in glucose metabolism. Although it operates in a different pathway, the reaction mechanism of 6-phosphogluconate dehydrogenase shares similarities with isocitrate dehydrogenase, particularly in the decarboxylation step and the involvement of NAD(P)+ as a cofactor.

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The length of the third side of the right triangle is approximately 16.49 units.

Pythagoras' theorem is a fundamental principle in mathematics that relates to the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs).

In the given question,

In a right triangle, the height is the perpendicular line segment that connects the base to the opposite vertex (the point where the two legs of the triangle meet).

We can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

So, in this case, we have:

Base = 13

Hypotenuse = 21

Let the height be h.

Using the Pythagorean theorem, we have:

21² = 13² + h²

441 = 169 + h²

Subtracting 169 from both sides, we get:

272 = h²

Taking the square root of both sides, we get:

h = √(272)

Simplifying, we get:

h = 16.49 (rounded to two decimal places)

Therefore, the length of the height of the right triangle is approximately 16.49 units.

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Answer:

8050 m²

Step-by-step explanation:

We can divide the diagram up into two components: a rectangle with a width of 60 m and a height of 80 m, and a triangle with a base of 130 m (190 - 60) and a height of 50 m (80 - 30).

The area of the rectangle:

A = lw

A = 60 m (80 m)

A = 4800 m²

The area of the triangle:

A = 1/2 b*h

A = 1/2 (130 m) (50 m)

A = 1/2 (6500 m²)

A = 3250 m²

Now, we can add the areas of the two separate components:

A = 4800 m² + 3250 m²

A = 8050 m²

Answer:

T ≥ 8x

50 ≥ 8x .......1

x ≤ 6

Liam can buy lunch for 6 people.

Step-by-step explanation:

Let x represent the number of people Liam can buy lunch for.

Given;

Lunch cost per person r = $8 per person

The total amount he has T = $50

The cost of buying lunch for c people is;

C = $8 × x

C = 8x

Therefore, to be able to buy lunch for them, the total cost C must be less than the total amount he has.

T ≥ C

Substituting C, we have;

T ≥ 8x

50 ≥ 8x ,.......1

Solving the inequalities;

8x ≤ 50

x ≤ 50/8

x ≤ 6.25

To the nearest whole number;

x ≤ 6

Liam can buy lunch for 6 people.

Answer:

1:12

Step-by-step explanation:

To simplify 3 yards :

3 yd.* 36 in. = 108 inches

9:108 simplified :

9/9 = 1

108/9 = 12

So, the ratio for the scale factor is 1:12 :)

Answer:

9

Step-by-step explanation:

7x = 4x +27

3x=27

divide by 3

x=9

(you can also use symbolab)

The equation that can be used to find t, the number of minutes that Luis rode his bike last week, is t = 875/3, which represents the total time in minutes for his 25-mile ride based on the average time it took him to ride 3 miles.

We can use proportions to find the number of minutes Luis rode his bike last week. Since Luis took 35 minutes to ride 3 miles, we can set up a proportion to relate the time and distance for his entire ride: 35 minutes / 3 miles = t minutes / 25 miles

To solve for t, we cross-multiply and simplify: 35 * 25 = 3 * t, 875 = 3t, t = 875 / 3, t ≈ 291.67 minutes

Therefore, the equation that can be used to find t, the number of minutes that Luis rode his bike last week, is t = 875/3, which represents the total time in minutes for his 25-mile ride based on the average time it took him to ride 3 miles.

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Answer:

not sure what type you mean but here are options

Step-by-step explanation:

30+4=34

thirty-four

The first step to be performed when computing Σ(X + 2)2 is Square each value. The correct answer is a

When computing Σ(X + 2)2, we need to square each value before performing any further calculations. The expression (X + 2)2 represents squaring each value of X and adding 2 to the result.

This step ensures that each value is squared before any additional operations are performed. The squared values are then used in subsequent calculations, such as summing the squared values or applying other mathematical operations. Therefore, the first step is to square each value, as mentioned in option a.

The expression Σ(X + 2)2 represents the sum of the squared values of (X + 2). To compute this sum, we need to follow these steps:

Your question is incomplete but most probably your question was

What is the first step to be performed when computing

Σ(X + 2)2?

a. Square each value

b. Add 2 points to each score

C. Sum the squared values

D. Sum the (X +2) values

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Given:

The lengths of legs of a right triangle are \(12a^5\) and \(9a^5\).

To find:

The perimeter of a right triangle.

Solution:

In a right angle triangle,

\(Hypotenuse=\sqrt{Leg_1^2+Leg_2^2}\)

\(Hypotenuse=\sqrt{(12a^5)^2+(9a^5)^2}\)

\(Hypotenuse=\sqrt{144a^{10}+81a^{10}}\)

\(Hypotenuse=\sqrt{225a^{10}}\)

On further simplification, we get

\(Hypotenuse=\sqrt{(15a^{5})^2}\)

\(Hypotenuse=15a^5\)

Now, the perimeter of the triangle is the sum of all of its sides.

\(Perimeter=Leg_1+Leg_2+Hypotenuse\)

\(Perimeter=12a^5+9a^5+15a^5\)

\(Perimeter=36a^5\)

Therefore, the perimeter of the right triangle is \(36a^5\).

36 motorcycles were repaired during the month.

To solve this problem, we can use the formula for the total number of wheels of a vehicle, which is equal to the number of vehicles multiplied by the number of wheels per vehicle. In this case, the number of wheels per vehicle is 4 since both autos and motorcycles have 4 wheels each. This formula can be expressed as: Wheels = Vehicles × Wheels per Vehicle.

We can substitute the given values of the total number of wheels (336) and the number of wheels per vehicle (4) into the formula, and solve for the number of vehicles (V): Wheels = Vehicles × Wheels per Vehicle → 336 = Vehicles × 4 → Vehicles = 336 ÷ 4 → Vehicles = 84.

Since we know that both autos and motorcycles were repaired, and the total number of vehicles was 84, we can use the information that 120 vehicles were repaired to solve for the number of motorcycles (M) that were repaired.

If the total number of vehicles was 84, and 120 vehicles were repaired, then the number of motorcycles that were repaired must be equal to the difference between the total number of vehicles and the total number of autos, which is 120 - 84 = 36.

Therefore, 36 motorcycles were repaired during the month.

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the exact formula for X(n) is given by the sum of i from 1 to 4n + 1. The closed-form formula for X(n) is (4n + 1)(4n + 2)/2, expressed as a polynomial function. The asymptotic value of X(n) is approximately 4n^2, representing the growth rate as n approaches infinity.

(i) The exact formula for X(n) can be determined by analyzing the procedure PrintXs(n) and counting the number of times the letter "X" is printed. In this case, the outer loop runs for 4n + 1 iterations, and for each iteration, the inner loop runs i times. Thus, the total number of "X" letters printed is given by the sum of i from 1 to 4n + 1.

(ii) To express X(n) as a closed-form polynomial function, we can simplify the sum mentioned above. By using the formula for the sum of an arithmetic series, the closed-form formula for X(n) can be written as X(n) = (4n + 1)(4n + 2)/2.

(iii) The asymptotic value of X(n) can be expressed using the e-notation, which represents an estimate of the growth rate. In this case, as n approaches infinity, the dominant term in the expression (4n + 1)(4n + 2)/2 is 4n^2. Therefore, we can express the asymptotic value of X(n) as X(n) ~ 4n^2.

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The decimal value of the 2 in the hexadecimal number F42AC16 is 131,072.

To determine the decimal value of the 2 in the hexadecimal number F42AC16, we need to understand the positional value system of hexadecimal numbers. In hexadecimal, each digit represents a power of 16. The rightmost digit has a positional value of 16^0, the next digit to the left has a positional value of 16^1, the next digit has a positional value of 16^2, and so on.

In the given hexadecimal number F42AC16, the 2 is the fifth digit from the right. Its positional value is 16^4. Calculating the decimal value: 2 * 16^4 = 2 * 65536 = 131,072. Therefore, the decimal value of the 2 in the hexadecimal number F42AC16 is 131,072.  None of the provided options (a) 409610, b) 51210, c) 25610, d) 210) matches the correct decimal value of 131,072.

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Answer:

1/5 miles

Step-by-step explanation:

2/5 divided by 2 = 1/5

Automated External Defibrillator(AEDs) administer an electrical shock. So it is dangerous to use n a victim who is lying on a conductive surface.

In the given question we have to explain what is a danger that would stop us from using an AED.

AEDs can be hazardous to use in damp settings, endangering the patient or the person supplying care. When treating the cardiac arrest sufferer, you must be especially careful because AEDs administer an electrical shock. When submerged in water, never use an AED.

Do not use an AED on a victim who is laying on conductive material. If other people are close to conductive items like metal bleachers or sheet metal, they could also get shocked.

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The measure of x, AB, BC, and AC are 8, 69, 69 and 138 respectively

The point where two lines meet is known as an angle:

Given the following expressions

AB = 3(3x -1)

AC = 5(2x+2)

If B lies in the middle of AC then;

Hence;

AB + AB = AC

2AB = AC

2(9x-3) = 5(2x+2)

18x - 6 = 10x + 10

18x - 10x = 10 + 6

2x = 16

x = 16/2

x = 8

Get AB

AB = 9x - 3

AB = 9(8) - 3

AB = 72 - 3

AB = 69

Since AB = BC, hence the measure of BC os 69

Get the measure of AC:

AC = AB + BC

AC = 69 + 69

AC = 138

hence the measure of x, AB, BC, and AC are 8, 69, 69 and 138 respectively

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Answer:

Please check the graph attached.

Step-by-step explanation:

Given the function

f(x)= 6x-5

and

g(x)=f(x) +9

g(x)=f(x) +9 means 9 is added into the output of the parent function f(x).

It means the function g(x) would be shifted 9 units up.

Please check the attached diagram.

The red graph represents the graph f(x)= 6x-5.

It is clear that the y-intercept of the graph f(x)= 6x-5 is (0, -5)

The blue graph represents the graph g(x)=f(x) +9

It is clear that the y-intercept of the graph g(x)=f(x) +9 is (0, 4)

Conclusion:

It is clear that g(x)=f(x) +9 has been shifted up by 9 units from the  f(x)= 6x-5.

x rounded to 1 decimal place is approximately 3.4 cm.

To work out the value of x, we can use the trigonometric function cosine (cos).

The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.

In this case, the length of the adjacent side is

x, and the length of the hypotenuse is 6 cm.

The given angle θ is 55°.

Using the cosine function, we have:

\(cos(\theta ) =\frac{adjacent }{hypotenuse}\)

\(cos(55^{\circ}) =\frac{x}{6}\)

To solve for x, we can rearrange the equation:

\(x = 6 \times cos(55^{\circ})\)

Now we can calculate x using the given values:

\(x \approx 6 \times cos(55^{\circ})\)

\(x \approx 6 \times 0.5736\)

\(x \approx 3.4416\)

Therefore, x rounded to 1 decimal place is approximately 3.4 cm.

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Answer: 2021

Step-by-step explanation:

The bounds for a 95% confidence interval could be option (B) 72 and 79

We know that the 98% confidence interval has bounds of 73 and 80. This means that if we were to repeat the same experiment many times, we would expect that 98% of the time, the true population mean would fall within this range.

To find the bounds for a 95% confidence interval, we can use the fact that a higher confidence level corresponds to a wider interval, and a lower confidence level corresponds to a narrower interval.

Since we want a narrower interval for a 95% confidence level, we can expect the bounds to be closer to the sample mean. We can calculate the sample mean as the midpoint of the 98% confidence interval

(sample mean) = (lower bound + upper bound) / 2 = (73 + 80) / 2 = 76.5

Next, we can use the formula for a confidence interval:

(sample mean) ± (z-score) × (standard error)

where the z-score depends on the desired confidence level, and the standard error depends on the sample size and sample standard deviation. Since we don't have this information, we can assume that the sample size is large enough (i.e., greater than 30) for the central limit theorem to apply, and we can use the formula

standard error = (width of 98% CI) / (2 × z-score)

For a 98% confidence interval, the z-score is 2.33 (found using a standard normal distribution table or calculator). Plugging in the values, we get

standard error = (80 - 73) / (2 × 2.33) = 1.70

Now, we can use this standard error to calculate the bounds for a 95% confidence interval

(sample mean) ± (z-score) × (standard error) = 76.5 ± 1.96 × 1.70

Simplifying, we get

(lower bound) = 76.5 - 3.33 = 73.17

(upper bound) = 76.5 + 3.33 = 79.83

Therefore, the correct option is (B) 72 and 79

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The correct graph of the piece-wise function in this problem is given by the following option:

Graph C.

A piece-wise function is a function that has different definitions, depending on the intervals of the input x of the function.

For this problem the function has three definitions, given as follows:

This means that the function is not defined at x = 2, that is, it has an open circle at x = 2, meaning that Graph A is incorrect.

Graph C is then the correct graph, as:

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Answer:

13

Step-by-step explanation:

this is because you have to look for the most common number

Question:

Yan is climbing down a ladder. Each time he descends 4 rungs on the ladder, he stopped to see how much farther he has to go. If Yan made eight stops with no extra steps, which expression best shows another way to write the product of the number of ladder rungs that Yan and climbed?

4+4+4+4

8+8+8+8

(-1)(4+4+4+4)

(-8) + (-8) + (-8) + (-8)

Answer:

\(Total = (-8) +(-8) +(-8) +(-8)\)

Step-by-step explanation:

Given

\(Rungs = -4\) --- It is negative because he is climbing down

\(Steps = 8\)

Required

An expression for the number of rungs climbed

To do this, we simply multiply the number of rungs by the steps taken.

\(Total = Rungs * Steps\)

\(Total = -4 * 8\)

This can be rewritten as:

\(Total = -8 * 4\)

The product, when written as sum is:

\(Total = (-8) +(-8) +(-8) +(-8)\)

Answer:

x=12

Step-by-step explanation:

x/3 - x/6 =2

2x -x = 12

No idea if this makes sense but this is what I came up with.

Given three sequences. Sequence A is 30, 40, 50, 60, 70,... Sequence B is 0, 5, 15, 30, 50,..

Sequence C is 1, 2, 4, 8, 16,...

The formula describing the term of sequence A is given below:

The formula describing the term of sequence B is given below:

The formula describing the term of sequences C is given below: