what is the prime factorization for 37

The rate of change of the area of the circle when the radius is 39 centimeters is 1976π cm²/min. This uses the concept of related rates in calculus and the area formula A = πr².

The problem deals with the concept of related rates in calculus. In this problem, we're looking at how the rate of change of the radius of a circle impacts the rate of change of the area of the circle. The formula for the area of a circle is A = πr².

Differentiating both sides with respect to time(t) gives dA/dt = 2πr(dr/dt). In this case, dr/dt (the rate of change of the radius) is given as 8 cm/min. To find dA/dt (the rate of change of the area) when r = 39 cm, we substitute these values into the differentiated equation: dA/dt = 2π(39cm)(8 cm/min) = 1976π cm²/min

So, the rate of change of the area when r = 39 centimeters is 1976π cm²/min. As the radius increases, the area of the circle increases at a rate directly proportional to the radius.

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To evaluate the expression 4x-3 for x = -3, we substitute -3 into the expression and follow the order of operations, resulting in a value of -15.

To evaluate the expression 4x-3 when x is -3, we simply substitute -3 in place of x and calculate the result as follows:

Therefore, evaluating 4x-3 when x is -3 gives us -15.

Answer:

Your answer is B=4

Step-by-step explanation:

hope it helps once again

The expected number of bad apples is [tex]\( \frac{2}{10} \times 3 = 0.6 \) bad apples.[/tex]

The expected number of bad apples when grabbing 3 apples from a pool of 10, of which 2 are bad, can be calculated using probability.

To calculate this, follow these steps:

1. Calculate the probability of picking a bad apple:

  The probability of picking a bad apple is the ratio of the number of bad apples to the total number of apples. In this case, it's [tex]\( \frac{2}{10} = 0.2 \) or 20%.[/tex]

2. Multiply the probability by the number of apples picked:  

  Multiply the probability of picking a bad apple by the number of apples you're picking.  

 [tex]\( 0.2 \times 3 = 0.6 \)[/tex]

When you pick 3 apples randomly from a pool of 10, you're essentially conducting a sampling experiment. The probability of picking a bad apple on any given pick is[tex]\( \frac{2}{10} \),[/tex]  which simplifies to 0.2 or 20%.

Since you're picking 3 apples, you multiply the probability of picking a bad apple by 3 to find the expected number of bad apples. This is because in expectation, you would expect that proportion of bad apples in your sample. So, [tex]\( 0.2 \times 3 = 0.6 \)[/tex], which means you would expect to pick approximately 0.6 bad apples when picking 3 from the pool of 10, assuming the picking is random.

So, the final answer is that you would expect about 0.6 bad apples when picking 3 apples from a pool of 10, of which 2 are bad.

complete question

There are 10 apples in the fridge and 2 of them are bad. if you grab 3 apples, what is the expected number of bad apples

There are 6 sides of the die, let us say that side 1 is S1, side 2 is S2 and so on.

Assigning a value of 3 to S1, so the probabilities are:

                                          Probability

S1 = 3                                    3/8

S2 = 1                                    1/8

S3 = 1                                    1/8

S4 = 1                                    1/8

S5 = 1                                    1/8

S6 = 1                                    1/8

total = 8                               

The combinations that the sum of the two rolls will be 4 are:

S1 and S3

S3 and S1

S2 and S2

So the total probability is:

P = (3/8) * (1/8) + (1/8) * (3/8) + (1/8) * (1/8)

P = 0.1094 = 10.94%

So there is about 0.1094 or 10.94% probability that the sum will be 4.

Answer: [tex]\frac{1}{4}[/tex]

Step-by-step explanation: If this is from a quiz from Buzz (Acceleration Education) Then this is the answer.

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Lucy will be paid $1260 in interest in the first 6 years.

To calculate the interest Lucy will be paid in the first 6 years, we will use the simple interest formula:

Interest = Principal x Rate x Time

Given:

Plugging in the values, we get:

Interest = $7000 x 0.03 x 6 = $1260

Therefore, Lucy will be paid $1260 in interest over the first 6 years.

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The explicit formula for the given sequence is a_n = 3 + 4(n-1).

The given sequence is (3, 7, 11, 15, 19, 23, 27, ...).

To find the explicit formula for this sequence, we can observe that each term is obtained by adding 4 to the previous term. So, the formula can be written as:

an = 3 + 4(n-1)

where n represents the position of the term in the sequence.

The correct strategy is (4x275) - 100. So option (3) is correct.

To find 4 multiplied by 275 using the given strategies, let's go through each one:

1. (4x300) + (4x25):

First, calculate (4x300) = 1200. Then, calculate (4x25) = 100. Finally, add these results together: 1200 + 100 = 1300.

2. (4x300) - (4x25):

Calculate (4x300) = 1200. Then, calculate (4x25) = 100. Now, subtract the second result from the first: 1200 - 100 = 1100.

3. (4x275) - 100:

Simply multiply 4 by 275 to get 1100. Then, subtract 100: 1100 - 100 = 1000.

4. (4x200) + 75:

Calculate (4x200) = 800. Then, add 75: 800 + 75 = 875.

The correct strategy is the third one: (4x275) - 100.

Detailed Calculation:

1. [tex]\(4 \times 275 = 1100\)[/tex]

2. [tex]\(1100 - 100 = 1000\)[/tex]

So, using the strategy of (4x275) - 100, the result is 1000.

x = square feet

total cost = 500 + 600x

see picture for the graph

equation: y = 1.50x

Answer:

Step-by-step explanation:

took the test (k12) and its halfway to 50 if you see in the picture

a) [tex]\[ \theta = 67.9^\circ, 112.1^\circ \][/tex], b) [tex]\[ \theta = 133.7^\circ, 226.3^\circ \][/tex], c) [tex]\[ \theta = 122.7^\circ, 302.7^\circ \][/tex], d) [tex]\[ \theta = 35.8^\circ, 215.8^\circ \][/tex], e) [tex]\[ \theta = 45.5^\circ, 314.5^\circ \][/tex] and f) [tex]\[ \theta = 154.4^\circ, 334.4^\circ[/tex].

Let's solve each part:

(a) [tex]\(\sin \theta = 0.9263\)[/tex]

1. Find the reference angle using [tex]\(\theta = \sin^{-1}(0.9263)\)[/tex]:

[tex]\[ \theta \approx 67.9^\circ \][/tex]

2. Since [tex]\(\sin \theta\)[/tex] is positive, the angles are in the first and second quadrants:

[tex]\[ \theta_1 \approx 67.9^\circ \][/tex]

[tex]\[ \theta_2 \approx 180^\circ - 67.9^\circ = 112.1^\circ \][/tex]

So, the solutions are:

[tex]\[ \theta = 67.9^\circ, 112.1^\circ \][/tex]

(b) [tex]\(\cos \theta = -0.6909\)[/tex]

1. Find the reference angle using [tex]\(\theta = \cos^{-1}(-0.6909)\)[/tex]:

[tex]\[ \theta \approx 133.7^\circ \][/tex]

2. Since [tex]\(\cos \theta\)[/tex] is negative, the angles are in the second and third quadrants:

[tex]\[ \theta_1 \approx 133.7^\circ \][/tex]

[tex]\[ \theta_2 \approx 360^\circ - 133.7^\circ = 226.3^\circ \][/tex]

So, the solutions are:

[tex]\[ \theta = 133.7^\circ, 226.3^\circ \][/tex]

(c) [tex]\(\tan \theta = -1.5416\)[/tex]

1. Find the reference angle using [tex]\(\theta = \tan^{-1}(-1.5416)\)[/tex]:

[tex]\[ \theta \approx -57.3^\circ \][/tex]

2. Adjust the reference angle to fall within the interval [tex]\([0^\circ, 360^\circ)\)[/tex]:

[tex]\[ \theta_1 = 360^\circ - 57.3^\circ = 302.7^\circ \][/tex]

3. Since [tex]\(\tan \theta\)[/tex] is negative, the angles are in the second and fourth quadrants:

[tex]\[ \theta_2 = 180^\circ + (-57.3^\circ) = 122.7^\circ \][/tex]

So, the solutions are:

[tex]\[ \theta = 122.7^\circ, 302.7^\circ \][/tex]

(d) [tex]\(\cot \theta = 1.3952\)[/tex]

1. Find the reference angle using [tex]\(\theta = \cot^{-1}(1.3952)\)[/tex]:

[tex]\[ \theta \approx 35.8^\circ \][/tex]

2. Since [tex]\(\cot \theta\)[/tex] is positive, the angles are in the first and third quadrants:

[tex]\[ \theta_1 \approx 35.8^\circ \][/tex]

[tex]\[ \theta_2 \approx 180^\circ + 35.8^\circ = 215.8^\circ \][/tex]

So, the solutions are:

[tex]\[ \theta = 35.8^\circ, 215.8^\circ \][/tex]

(e) [tex]\(\sec \theta = 1.4293\)[/tex]

1. Convert to [tex]\(\cos \theta\)[/tex]:

[tex]\[ \cos \theta = \frac{1}{1.4293} \approx 0.6996 \][/tex]

2. Find the reference angle using [tex]\(\theta = \cos^{-1}(0.6996)\)[/tex]:

[tex]\[ \theta \approx 45.5^\circ \][/tex]

3. Since [tex]\(\cos \theta\)[/tex] is positive, the angles are in the first and fourth quadrants:

[tex]\[ \theta_1 \approx 45.5^\circ \][/tex]

[tex]\[ \theta_2 \approx 360^\circ - 45.5^\circ = 314.5^\circ \][/tex]

So, the solutions are:

[tex]\[ \theta = 45.5^\circ, 314.5^\circ \][/tex]

(f) [tex]\(\csc \theta = -2.3174\)[/tex]

1. Convert to [tex]\(\sin \theta\)[/tex]:

[tex]\[ \sin \theta = \frac{1}{-2.3174} \approx -0.4316 \][/tex]

2. Find the reference angle using [tex]\(\theta = \sin^{-1}(-0.4316)\)[/tex]:

[tex]\[ \theta \approx -25.6^\circ \][/tex]

3. Adjust the reference angle to fall within the interval [tex]\([0^\circ, 360^\circ)\)[/tex]:

[tex]\[ \theta_1 = 360^\circ - 25.6^\circ = 334.4^\circ \][/tex]

4. Since [tex]\(\sin \theta\)[/tex] is negative, the angles are in the third and fourth quadrants:

[tex]\[ \theta_2 = 180^\circ + (-25.6^\circ) = 154.4^\circ \][/tex]

So, the solutions are:

[tex]\[ \theta = 154.4^\circ, 334.4^\circ[/tex]

The complete question is:

Approximate, to the nearest 0.1°, all angles θ in the interval [0°, 360°) that satisfy the equation. (Enter your answers as a comma-separated list.)

(a) sin θ = 0.9263

θ = °

(b) cos θ = −0.6909

θ = °

(c) tan θ = −1.5416

θ = °

(d) cot θ = 1.3952

θ = °

(e) sec θ = 1.4293

θ = °

(f) csc θ = −2.3174

θ = °

Final answer:

The radius of a circle with a circumference of 201 centimeters is approximately 32 centimeters, found by dividing the circumference by 2 times pi (π), using 3.14 as the value of pi. The correct answer is A) 32 centimeters.

Explanation:

The question asks us to find the radius of a circle when its circumference is given to be 201 centimeters. We use the circumference formula of a circle, which is C = 2πr, where C stands for circumference, π (pi) is a constant approximately equal to 3.14, and r represents the radius of the circle.

To find the radius, we rearrange this formula to solve for r:

Divide both sides of the equation by 2π to isolate r.

Plug in the given circumference value, C = 201 cm, and the approximate value of pi, π = 3.14, into the rearranged formula.

So the calculation would be r = C / (2π) = 201 / (2 * 3.14) = 201 / 6.28. When we compute this, we get r ≈ 32 centimeters to the nearest whole number.

Therefore, the correct answer is A) 32 centimeters.

On average during their trip, their speed was 3184.8 miles/hr.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

We know Distance = Speed×Time.

∴ Speed = Distance/Time.

Given, The distance from Earth to the moon is exactly 238,855 miles and it took astronauts 75 hours.

So, the average speed is (238855/75) miles/hr.

= 3184.8 miles/hr.

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To find the number of quarters and nickels, we can set up a system of equations using the total number of coins and the total value of the coins. Solving this system of equations, we find that Kevin and Randy have 27 quarters and 14 nickels.

To solve this problem, we can set up a system of equations. Let's use the variables q (number of quarters) and n (number of nickels). We know that there are a total of 41 coins, so we can write the equation q + n = 41. We also know that the total value of the coins is $7.45, so we can write the equation 0.25q + 0.05n = 7.45.

Now we can solve this system of equations using substitution:

Therefore, Kevin and Randy have 27 quarters and 14 nickels in their jar.