What is the smallest prime number p such that
p^3 + 4p^2 + 4p has exactly 30 positive divisors? [PRMO 2019]

PLEASE GIVE PROPER DETAILED EXPLANATION

A Class A defect is considered very serious and will most likely cause operating failure.

Designed experiments are important tools for optimizing processes, identifying interactions among variables, and reducing variation in processes.

We have,

A Class A defect is typically the most severe type of defect in a manufacturing or quality control context.

It usually means that a product or component has a flaw that is likely to cause it to fail in normal use or operation, posing a significant risk to safety or functionality.

Designed experiments, also known as DOE (Design of Experiments), are a commonly used statistical tool in process optimization and improvement.

They involve careful planning and executing a series of controlled tests or trials to systematically investigate the effects of different process variables or factors on a given output or response variable.

Thus,
A Class A defect is considered very serious and will most likely cause operating failure. Designed experiments are important tools for optimizing processes, identifying interactions among variables, and reducing variation in processes.

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The volume of the right prism include the following: 8,640 in³.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

Next, we would determine the area of the triangle at the base of the right prism as follows:

Base area = 1/2 × ( 36 × 12)

Base area = 1/2 × 432

Base area = 216 in².

Now, we can calculate the the volume of this right prism:

Volume = base area × height

Volume = 216 × 40

Volume = 8,640 in³.

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33ft wire is needed for 6 trees.

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

Each wire is attached to the trunk 3ft. above the ground,

and then anchored to the ground 2.5 ft. from the base of the tree.

So, for each tree total wire = 3+2.5

                                             =5.5 ft.

So, for 6 trees = 5.5*6

                       =33ft

Hence, 33ft wire is needed for 6 trees.

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Answer:

0

Step-by-step explanation:

thanks for the points :)

Answer:

A)  10.8

Step-by-step explanation:

The expression for the power delivered to a resistance in terms of csc^2 2 pi ft is P = I^2_0 R (csc^2 2 pi ft).

According to the given information, the power delivered to a resistance R when an alternating current of frequency f and peak current I_0 passes through it is represented by the equation P = I^2_0 R sin^2 2 pi ft.

To express this equation in terms of csc^2 2 pi ft, we can use the trigonometric identity csc^2 x = 1/sin^2 x. Substituting this identity into the equation, we get P = I^2_0 R (1/sin^2 2 pi ft).

Since csc^2 x is the reciprocal of sin^2 x, we can rewrite the equation as P = I^2_0 R (csc^2 2 pi ft). This expression represents the power delivered to the resistance in terms of csc^2 2 pi ft.

Therefore, the correct expression for the power delivered to the resistance in terms of csc^2 2 pi ft is P = I^2_0 R (csc^2 2 pi ft).

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The best answer regarding the effects of carbon monoxide is option c, CO results in less oxygen loading hemoglobin but unloading is not changed.

Carbon monoxide binds up more tightly to the hemoglobin as compared to the oxygen molecules. This reduces the oxygen-carrying capacity of the blood and results in less oxygen loading onto hemoglobin.

However, once oxygen is already bound to hemoglobin, CO does not significantly affect its release or unloading. Therefore, option c is the most accurate statement among the given choices.

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Answer:

Step-by-step explanation:

how you waiting for help sb help him

2.25 cups of flour he use per patch.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Pablo uses 13.5 cups of flour to make 6 batches of muffins.

For 1 patch amount of flour used

= 13.5 /6

= 2.25 cups

Hence, 2.25 cups of flour he use per patch.

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Answer:

A. t=13 B. K= 23 C. t= 1 3/8

Step-by-step explanation:

A. 2t-30m=20

30 x 1/5= 6

2t-6+6=20+6

2t/2=26/2

t=13

B. 14+m=2k

14+12=2k

14+12=46

46/2=23

k=23

C. 1/8r+t=1

1/8 x (-3)= -3/8

1 - (-3/8)= 1 3/8

t= 1 3/8

Hope it helps!

The solution is:

Maggie will run 5.85 miles next week.

Here, we have,

Given:

Maggie is training to run a 6 mile race.

This week Maggie ran = 4.5 miles

Also Given:

Next week she will run 1.3 times as far as she did this week.

We need to distance she will run next week.

Now we know Next week she will run 1.3 times as far as she did this week.

It means Distance to be run next week will be equal to 1.3 times distance she ran this week.

Framing in equation form we get;

distance she will run next week = 1.3 * 4.5 = 5.85

Hence Maggie will run 5.85 miles next week.

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complete question:

Maggie is training to run a 6 mile race. Her training program has her increase her weekly long run each week. This week she ran a five Maggie is training to run a 6 mile race. Her training program has her increase her weekly long run each week. This week she ran 4.5 miles. Next week she will run 1.3 times as far as she did this week. How far will she run next week?

An object that is in motion as a projectile follows a path or trajectory of a parabola

The function and values are;

Reason:

a) Known parameters are;

Let f(x) = a·x² + b·x + c represent the equation of the parabola modelling the path of the ball, we have;

Points on the path of the parabola = (0, 0), (35, 1.5), 37, 0)

Plugging the values gives;

0 = a·0² + b·0 + c

Therefore, c = 0

1.5 = 35²·a + 35·b

0 = 37²·a + 37·b

Solving gives;

a = -3/140, b = 111/140

The equation of the quadratic function is therefore;

b) The maximum height is given by the vertex of the parabola

The x-coordinate at the vertex is the point \(-\dfrac{b}{2 \cdot a}\)

Which gives;

\(x-coordinate = \dfrac{\frac{111}{140} }{2 \times \dfrac{3}{140} } = 17.5\)

The maximum height is therefore;

\(f(x)_{max} = \dfrac{111}{140} \times 17.5 - \dfrac{3}{140} \cdot 17.5^2 \approx 7.334\)

The maximum height of the ball is approximately 7.334 m

c) The distance the ball has travelled to horizontally is given by half of the range, R as follows;

The range of the motion, R = 37 meters

\(Horizontal \ distance \ to \ maximum \ height = \dfrac{R}{2}\)

Therefore;

\(Horizontal \ distance \ to \ maximum \ height = \dfrac{37}{2} = 18.5\)

The distance the ball has travelled horizontally to reach the maximum height horizontally 18.5 meters

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The likelihood of pulling a spade followed by a face card from a deck is 3/52, or roughly 0.0588. (rounded to four decimal places).

The probability of drawing a spade from a deck of 52 cards is 13/52, or 1/4, since there are 13 spades in the deck.

Once a spade has been drawn and not returned to the deck, there are now 51 cards left in the deck, of which 12 are face cards (the Jack, Queen, and King of each suit). Therefore, the probability of drawing a face card given that a spade has already been drawn is 12/51.

To find the probability of both events happening together (drawing a spade and then a face card), we can multiply the probabilities of each event:

P(drawing a spade, then drawing a face card) = P(drawing a spade) x P(drawing a face card given that a spade has been drawn)

= (1/4) x (12/51)

= 3/52

Therefore, the probability of drawing a spade, then drawing a face card out of a deck is \(3/52\)  , or approximately \(0.0588\) (rounded to four decimal places).

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Answer:

the measure of 7 is 47 degrees, the equation is 2x -5 + 47 = 180 and the value of x is = to 69

Step-by-step explanation:

Answer:

a)  <5 and <7 have congruent angles. That means that both angles are equal, they have the same measure. This means that the measure of <7 is 47°.

<7 = 47°

b) 5 and 6 are adjacent, so this is the equation that we have to do to solve for the value of x.

<5 + <6 = 180°

47° + (2x - 5)° = 180°

c) To solve the linear equation we need to isolate x.

47° + (2x - 5)° = 180°

(2x - 5)° = 180° - 47° = 133°

2x - 5 = 133

2x = 133 + 5 = 138

x = 138/2 = 69

Seema left 6/11 of the book for reading over the weekend.

To calculate the part of the book left for reading during the weekend, we need to subtract the part of the book Seema read during the weekday from the total book.

If Seema reads 5/11 of the book during the weekday, then:

This means 6/11 of the book is left for reading during the weekend. It is important to note that the fraction of the book read during the weekday and the fraction left for reading during the weekend add up to the total book. This means that 11/11 of the book will be read by Seema in total.

This question should be written as:

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Answer:

-1.4f - 24

Step-by-step explanation:

hope this helps <3

Answer:

-1.4f - 24

Step-by-step explanation:

Answer: Not similar

Step-by-step explanation:

They are telling you that you have a Side and a Side that are similar.  The sides of the smaller triangle are multiplied by 2 to get the larger triangle, but you need a 3rd element for it to be similar.  You have SS but you need another side or angle for it to be similar

Not similar

Answer:

Hey mate,here is your answer. Hope it helps you.

Step-by-step explanation:

The answer is c- 8 x 4. As there are 8 groups of 4 the easiest way to calculate is by multiplying them both. Repeated addition is known as multiplication.

When measuring variables, it is often preferable to use a small sample size because the smaller the sample the greater the chance of a spurious result.

Therefore, when measuring variables, it is often preferable to use a small sample size because the smaller the sample the greater the chance of a spurious result.

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Answer:

160

Step-by-step explanation:

Cos 60 = adjacent side /hypotenuse

Cos 60 = 80/x

0.5 = 80/x

Multiply both sides by x or cross multiply

0.5x = 80

Divide both sides by 0.5

X = 160

Answer:

12, 36, 36

Step-by-step explanation:

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Answer:

$12, $36 & $36

Step-by-step explanation:

1 +3+3=7

1/7 ×84 = $12

3/7×84 = $36

3/7×84= $36

When the output is 14 units, the average cost is $128.57. The marginal cost at that output level is $65.71. The output level at which average variable cost equals marginal cost is 9 units.

To find the average cost, we divide the total cost (C) by the output quantity (q). In this case, the cost function is given as \(C = 0.3q^3 - 5q^2 + 85q + 150\). When the output is 14 units, we substitute q = 14 into the cost function and calculate C. Dividing C by 14 gives us the average cost, which is approximately $128.57.

To calculate the marginal cost, we take the derivative of the cost function with respect to q. The derivative represents the rate of change of cost with respect to output. Evaluating the derivative at q = 14 gives us the marginal cost, which is approximately $65.71.

The average variable cost is the variable cost per unit of output. It represents the cost that varies with the level of production. To find the output level where average variable cost equals marginal cost, we need to equate the derivative of the cost function with respect to q to the average variable cost. However, the average variable cost is not given in the question. Without the specific value of the average variable cost, we cannot determine the output level at which it equals marginal cost.

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A sample is taken from the 15th and 50th items from 100 production lines. The sampling method used in this scenario is Systematic sampling.

Systematic sampling is a method in which a sample is taken at regular intervals from a larger population. In this case, the sample is taken from the 15th and 50th items from 100 production lines, meaning that the sample is taken at regular intervals from the larger population of 100 production lines.

This method is different from cluster sampling, which involves dividing the population into groups and then selecting a sample from each group. It is also different from convenient sampling, which involves selecting a sample based on convenience or accessibility.

Finally, it is different from stratified sampling, which involves dividing the population into strata and then selecting a sample from each stratum. Therefore, the correct answer is Systematic sampling.

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Answer:

d

Step-by-step explanation:

The area in the first quadrant between the given circles is 2π.

The given equation of circles are:

x²+y²=16,

x²+y²=16,

x²−4x+y²=0

To evaluate the integral, we'll need to convert the equations into polar coordinates.

The first circle, x² + y² = 16.

In polar coordinates,

x = rcosθ

y = rsinθ.

Substituting these into the equation,

we get r²cos²θ + r²sin²θ = 16.

Simplifying this equation, we have r² = 16,

which simplifies further to r = 4.

The second circle, x² - 4x + y² = 0.

Converting this into polar coordinates, we have

(rcosθ)² - 4(rcosθ) + (rsinθ)² = 0.

Simplifying this equation, we get

r² - 4rcosθ = 0,

Which leads to r = 4cosθ.

To find the area in the first quadrant between these two circles,

Integrate the area element dA over the given region.

The area element in polar coordinates is given by

dA = 1/2 (r² dθ).

Now, set up the integral to evaluate the area:

\(A = \int\limits^{\frac{\pi}{2}}_0 {(\frac{1}{2} r^2)} \, d\theta\\ =\frac{1}{2} \int\limits^{\frac{\pi}{2}}_0 {4cos^2\theta} \, d\theta \\= 8 \int\limits^{\frac{\pi}{2}}_0 {cos^2\theta} \, d\theta\)

Using trigonometric identities,

We can simplify this integral further:

\(= 8 \int\limits^{\frac{\pi}{2}}_0 {(1+cos2\theta)/2} \, d\theta\)                                 [∵ cos2θ = 2cos²θ - 1]

= (1/2) [(8(π/2) + 4sin(2(π/2))) - (8(0) + 4sin(2(0)))]

= (1/2) [(4π + 0) - (0 + 0)]

= 2π

Hence,

The area in the first quadrant between the given circles is 2π.

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Answer: 1/8(2y+3)

Step-by-step explanation: Factor 1/8 out for each term

1/8 is the coefficient of the term because it is the variable that is multiplying something.

To calculate the gain on the sale of the office furniture, we need to determine the asset's book value and compare it to the sale price.

First, let's calculate the accumulated depreciation on the furniture. The furniture was purchased on January 1, 2014, and the straight-line depreciation method is used over 10 years with a salvage value of $80,200.

Depreciation per year = (Cost - Salvage Value) / Useful Life

Depreciation per year = ($746,800 - $80,200) / 10 years

Depreciation per year = $66,160

Next, we need to calculate the accumulated depreciation for the period from January 1, 2014, to May 1, 2021 (the date of the sale). This is approximately 7.33 years.

Accumulated Depreciation = Depreciation per year × Years

Accumulated Depreciation = $66,160 × 7.33 years

Accumulated Depreciation = $484,444.80

Now, we can calculate the book value of the furniture:

Book Value = Cost - Accumulated Depreciation

Book Value = $746,800 - $484,444.80

Book Value = $262,355.20

Finally, we can calculate the gain on the sale:

Gain on Sale = Sale Price - Book Value

Gain on Sale = $300,000 - $262,355.20

Gain on Sale = $37,644.80

Therefore, the gain that should be recognized on the sale of the office furniture is approximately $37,644.80.

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The gain that should be recognized on the sale of the office furniture is $84,080.

The gain is calculated by subtracting the equipment's book value from the sale price. This gain will be reported on the company's income statement. Here is how to calculate the gain:First, find the equipment's book value using the straight-line method of depreciation.

Straight-line depreciation is calculated by taking the difference between the equipment's original cost and its salvage value, and then dividing it by the number of years the equipment is used. The annual depreciation expense is then multiplied by the number of years the equipment is used to find the equipment's book value at the end of its useful life.

For this question, the book value of the equipment at the time of sale is:Cost of equipment: $746,800Salvage value: $80,200Depreciable cost: $746,800 - $80,200 = $666,600Annual depreciation: $666,600 ÷ 10 years = $66,660Book value at the end of 2020: $666,600 - ($66,660 x 7) = $156,420

Next, subtract the equipment's book value from the sale price to find the gain:Sale price: $300,000Book value: $156,420Gain: $143,580Finally, round the gain to the nearest dollar:$143,580 ≈ $143,580.00So the gain that should be recognized on the sale of the office furniture is $84,080.

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Chelsea wants to add one layer of 3 x 3 cubics and Stephen wants to add one layer of 3 x 6 cubics.

From given figure, the dimension of the rectangular prism are:

6 cm × 3 cm × 3 cm

The volume of the rectangular prism would be,

V = l × w × h

V =  6 × 3 × 3

V = 54 cm³

Stephen and Chelsea want to increase the volume of this prism by 72 cubic centimeters.

Chelsea wants to add eight layers.

This means 72 = 8 × 3 × 3 cubics, then one layer in this case consists of 3 x 3 cubics;

Whereas Stephen says they only need to add four layers.

This means 72 = 4 × 3 × 6 cubics, then one layer in this case consists of 3 x 6 cubics.

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Find the complete question below.

Answer:

I think it would take 4 hours! I hope you do Great!

Step-by-step explanation: