Help with problem in photo pls

a) The profit at a sales level of 14 trees is $180.40.

b) The average change in profit sales is $13.96 per tree [(ΔP/Δx) = 97.75/7].

c) The instantaneous rate of change of profit at a sales level of 14 trees is $19.72 per tree.

d) The equation of the tangent line at (5, f(5)) is y = 6x - 25.

a. To find the profit at a sales level of 14 trees, we need to evaluate the profit function at x = 14:

P(x) = 20x - 0.01x^2 - 100

P(14) = 20(14) - 0.01(14)^2 - 100 = $180.40

Therefore, the profit at a sales level of 14 trees is $180.40.

b. To find the average change in profit sales from 12 to 19 trees, we need to calculate the average rate of change of the profit function over this interval:

Δx = 19 - 12 = 7

ΔP = P(19) - P(12) = (2019 - 0.0119^2 - 100) - (2012 - 0.0112^2 - 100) = $97.75

Therefore, the average change in profit sales is $13.96 per tree [(ΔP/Δx) = 97.75/7].

c. To find the instantaneous rate of change of profit at a sales level of 14 trees, we need to find the derivative of the profit function at x = 14:

P(x) = 20x - 0.01x^2 - 100

P'(x) = 20 - 0.02x

P'(14) = 20 - 0.02(14) = $19.72

Therefore, the instantaneous rate of change of profit at a sales level of 14 trees is $19.72 per tree.

d. To find the equation of the tangent line at (5, f(5)), we need to find the slope of the tangent line and its y-intercept:

f(x) = x^2 - 4x

f'(x) = 2x - 4

f'(5) = 2(5) - 4 = 6

The slope of the tangent line at (5, f(5)) is 6.

To find the y-intercept of the tangent line, we can use the point-slope form of a line:

y - f(5) = m(x - 5)

y - (5^2 - 4*5) = 6(x - 5)

y - 5 = 6x - 30

y = 6x - 25

Therefore, the equation of the tangent line at (5, f(5)) is y = 6x - 25.

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The probability of drawing a shape that is red or a circle is 7/16 from the bag that contains 4 red circles, 3 blue circles, and 9 yellow triangles.

Number of red circles = 4

Number of blue circles = 3

Number of yellow triangles = 9

Total number of all items = 4+3+9 = 16

Thus, the total number of possible outcomes is 16.

The probability of getting a red shape  = 4/16

The probability of getting a circle   = 4/16 + 3/16 = 7/16

To calculate the probability of drawing an item circle or red color,

P(red or circle) = P(red) + P(circle) - P(red and circle)

P(red or circle) = 4/16 + 7/16 - 4/16

P(red or circle) = 7/16

Therefore, we can conclude that the probability of drawing a shape that is red or a circle is 7/16.

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The critical value needed to test for independence between the type of restoration and sensory disorders is 6. 635.

To evaluate the correlation between sensory impairments and restoration type, a chi-square test of independence can be used. To determine the critical value for this statistical test, consult the chi-square distribution table at a 0.01 significance level.

The degrees of freedom for a chi-square test of independence :

Degrees of Freedom ( df ) = ( Number of Rows - 1 ) x ( Number of Columns - 1 )

The number of rows from the table = 2

Number of columns is also = 2

The df is therefore:

df = (2 - 1) x (2 - 1) = 1 x 1 = 1

The critical value for χ² with 1 degree of freedom at a 0. 01 significance level can be founding using the Chi - Square table to be approximately 6.635.

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Full question is:

In recent years, concerns have been expressed about adverse health effects from amalgam dental restorations, which contain mercury. The table shows results from a study in which some patients were treated with amalgam restorations and others were treated with composite restorations that do not contain mercury. Use a 0. 01 significance level to find the critical value needed to test for independence between the type of restoration and sensory disorders.

The quadratic function in standard form that passes through the given points would be f (x ) = 5x ² - 70x + 225

A quadratic function in standard form is given by the equation:

f ( x ) = ax ²  + bx + c

The system of equations would be:

25 a + 5b + c = 0

81 a + 9b + c = 0

49 a + 7b + c = -20

With a series of calculations, we can find the value of b and c :

b = - 14 a = - 14 ( 5 ) = -70

25 ( 5 ) - 70 (5) + c = 0

125 - 350 + c = 0

c = 225

This gives us the quadratic function of :

f ( x ) = 5x ² - 70x + 225

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Answer:is 230

Step-by-step explanation:

230 i hoped i helped

When the value of x is 7 the value of p will be equal to 8.

It is given that P varies inversely with x, so we can write that

p=k/x

where k is the proportionality constant.

here we can find the value of k by substituting the value of p and x with 7 and 8 in the relation that is given above, we get:

7=k/8

k=7*8

k=56

we the value of k to be 56 after putting the values in the relation.

Now if x is changed to 7, and k is equal to 56 we can get the value of p by putting the known values in the same relation.

p=k/x

p=56/7

p=8.

Therefore, when the value of x is 7 the value for p will be equal to 8.

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Once we apply one of these tests and determine whether the series converges or diverges, we can then further analyze the series to find its sum, if it exists.

To test the convergence of a series, we typically use one of several tests, depending on the nature of the series. Some of the commonly used tests are:

Divergence test: If the terms of a series do not approach zero, the series must diverge. The test states that if lim(n->inf) an != 0, then the series diverges.

Comparison test: If the terms of a series are positive and can be compared with a known convergent or divergent series, we can determine the convergence or divergence of the given series. If an <= bn for all n and the series sum of bn converges, then the series sum of an also converges. If an >= bn for all n and the series sum of bn diverges, then the series sum of an also diverges.

Limit comparison test: If the terms of a series are positive, we can compare the given series with a known convergent series, using the limit comparison test. If lim(n->inf) (an/bn) = L, where L is a positive finite number, then both series either converge or diverge.

Ratio test: If the terms of a series approach zero and the ratio of consecutive terms approaches a limit L, then the series converges if L < 1 and diverges if L > 1. If L = 1, the test is inconclusive.

Root test: If the terms of a series approach zero and the nth root of the absolute value of the nth term approaches a limit L, then the series converges if L < 1 and diverges if L > 1. If L = 1, the test is inconclusive.

Alternating series test: If the terms of a series alternate in sign and decrease in magnitude, then the series converges.

There are also other tests, such as integral test, p-series test, and Dirichlet test, among others, which can be used to test the convergence of certain types of series.

Once we apply one of these tests and determine whether the series converges or diverges, we can then further analyze the series to find its sum, if it exists.

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The interest he had received in total after eight years is 1396.59 kroner

From the question, we have the following parameters that can be used in our computation:

Principal, P = 7000

Rate, r = 2.3%

Time, t = 8

The interest he had received in total after eight years is calculated as

I = P(1 + r)^t - P

Substitute the known values in the above equation, so, we have the following representation

I = 7000(1 + 2.3%)^8 - 7000

Evaluate

I = 1396.59

Hence, the total interest is 1396.59 kroner

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The volume of a cone with a slant height of 13 cm and radius of 5 cm is A. 100 pi cm³.

To obtain the volume of the cone we would use the formula:

V = (1/3)πr²h

where V is the volume of the cone, r is the radius of the base of the cone, and h is the height of the cone.

Since we are given the slant height (s) of the cone, not its height (h), we would use the Pythagorean theorem to find the height of the cone:

s² = r² + h²

where s is the slant height, r is the radius of the base, and h is the height.

We are given that the slant height (s) is 13 cm, and the radius (r) is 5 cm. So, we can solve for the height (h) this way:

13² = 5² + h²

169 = 25 + h²

h² = 144

h = 12 cm

Now that we know the height of the cone, we can substitute the values into the formula for the volume:

V = (1/3)πr²h

V = (1/3)π(5²)(12)

V = (1/3)π(25)(12)

V = (1/3)π(300)

V = 100π cm³

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If the terminal side of angle λ intersects the unit circle at point (-0. 358, 0. 934), the approximate decimal value of cot(λ) is -0.383.

To find the approximate decimal value of cot(λ), we first need to determine the values of x and y on the unit circle. Since the given point (-0.358, 0.934) lies on the unit circle, we can use the Pythagorean theorem to find the missing side:

x² + y² = 1
(-0.358)² + (0.934)² = 1
0.128 + 0.872 = 1
1 = 1

Therefore, we have x = -0.358 and y = 0.934. Since cot(λ) = cos(λ)/sin(λ), we can use the values of x and y to calculate the cosine and sine of λ:

cos(λ) = x = -0.358
sin(λ) = y = 0.934

Substituting these values into the formula for cot(λ), we get:

cot(λ) = cos(λ)/sin(λ) = -0.358/0.934 ≈ -0.383

Therefore, the approximate decimal value of cot(λ) is -0.383.

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The value of x and y in the right triangle are 11.31 units and 8 units respectively.

The tangential ratio of ∠P and ∠Q are 16 / 12 and 12 / 16 respectively.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The side of a right angle triangle can be found using trigonometric ratios as follows:

tan 45 = opposite / adjacent

tan 45 = 8 / y

cross multiply

y = 8 / tan 45

y = 8  /1

y = 8 units

Therefore,

sin 45 = opposite / hypotenuse

sin 45 = 8 / x

cross multiply

x = 8 / sin 45

x = 11.313816999

x = 11.31 units

Let's find the tangent ratio of ∠p and ∠q.

Hence,

tan ∠P = 16 / 12

tan ∠Q = 12 / 16

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The factory can make 500 batches of candle wax with 25 grams of red coloring powder.

For the given question the easiest and the simplest approach will be by using the unit conversion method to solve the problem.

We need to convert the unit from grams to milligrams.

So, 25 grams of red coloring powder will be equal to:

25 grams * 1000mg/grams = 25000mg.

Now it is given that it takes 50 mg to make a single batch of candle wax. So, the number of batches that can be made using 25,000 mg of red coloring powder is equal to:

25000mg/50mg per batch = 500 batches.

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---------------------------

|           | Popcorn | No Popcorn |

---------------------------

| Drink     |    74   |     15     |

---------------------------

| No Drink  |    10   |     6      |

---------------------------

The completed two-way table is as shown above.

We construct a two-way table summarizing the results. Let's use the information provided:

1. 105 people entered the theatre
2. 84 people had popcorn
3. 10 out of 84 people with popcorn did not have a drink
4. 6 people walked in without popcorn or a drink

Now let's construct the two-way table:

---------------------------
|           | Popcorn | No Popcorn |
---------------------------
| Drink     |    A    |     B      |
---------------------------
| No Drink  |    C    |     D      |
---------------------------

We need to fill in the values for A, B, C, and D:

1. A = People with popcorn and a drink = Total with popcorn - those without a drink = 84 - 10 = 74
2. C = People with popcorn but no drink = 10 (given in the question)
3. D = People with neither popcorn nor a drink = 6 (given in the question)
4. To find B, we need to find the total number of people with a drink. We know 105 people entered, and 6 had neither popcorn nor a drink, so there were 105 - 6 = 99 people with either popcorn or a drink. Since 84 people had popcorn, this means there were 99 - 84 = 15 people with only a drink.
5. B = People with a drink but no popcorn = 15

Now let's fill in the table:

---------------------------
|           | Popcorn | No Popcorn |
---------------------------
| Drink     |    74   |     15     |
---------------------------
| No Drink  |    10   |     6      |
---------------------------

So, the completed two-way table is as shown above.

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Answer:

D.5

Step-by-step explanation:

8x – 6 > 12 + 2x

= 8x−2x>12+6= 6x>18

= x>38x−2x>12+6

= 6x>18

= x>3

From the given options the only value which is greater than 3 is Option (D) 5

The given circle has a radius of 11.2,

Given radius of the circle (r) = 11.2

The diameter of the given circle = 2*r = 2*11.2 = 22.4

The circumference of the given circle = 2πr = 2*3.14*11.2 = 70.336

The area of the given circle =  πr² = 3.14*(11.2)² = 393.88

From the above analysis, we can conclude that the diameter of the circle is 22.4 and the circumference of the circle is 70.336 and the area of the circle is 383.88.

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Walmart's decision to use its own fleet of trucks to pick up products directly from manufacturers and deliver them to its stores is a strategic move that has the potential to benefit both Walmart and manufacturers.

By using its own fleet, Walmart will be able to cut down on transportation costs and gain more control over the supply chain, which can lead to better efficiency and cost savings. This is especially important given Walmart's massive scale, with over 4,000 stores in the US alone.

For manufacturers, this move by Walmart could be a relief as they can focus on their core competency of making products rather than managing logistics. With Walmart taking over the transportation aspect, manufacturers can rest assured that their products will be delivered on time and in the right condition.

The fact that Walmart already has a large fleet of trucks and trailers means that it has the capacity to implement this new program without too much additional investment. However, it remains to be seen how manufacturers will respond to this proposal, as they may have existing contracts with other carriers or may be hesitant to rely too heavily on Walmart for their transportation needs.

Overall, Walmart's move towards using its own fleet of trucks is a smart one that has the potential to benefit both the retailer and its suppliers.

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Thus, we can label the points B and C' in the coordinate plane as follows

     |

     |

 C'  |

     |

------B(2, -3)

     |

     |

     |

To reflect a point across the y-axis, we keep the x-coordinate the same but change the sign of the y-coordinate.

Point B is located at (2, -3), so it looks like

     |

     |

     |

     |

------B(2, -3)

     |

     |

     |

     |

To reflect point C across the y-axis, we change the sign of the y-coordinate, but keep the x-coordinate the same. If point C is located at (x, y), then its reflected image, C', would be located at (-x, y).

Since we don't have the coordinates for point C, we cannot plot it accurately. However, we know that its reflected image would be located at (-x, y), so we can label it as C' for now.

So, the reflected image of point C across the y-axis, C', would be located at (-x, y). Thus, we can label the points B and C' in the coordinate plane as follows

     |

     |

 C'  |

     |

------B(2, -3)

     |

     |

     |

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The critical number A is 2

To find the critical number A for the function f(x) = 7(x-2)^(2/3):

We need to first find the derivative of the function and then set it equal to zero or identify where it is undefined.

Step 1: Find the derivative of f(x).
f'(x) = d/dx[7(x-2)^(2/3)]
Using the chain rule, we get:
f'(x) = (2/3) * 7(x-2)^(-1/3) * (1)

= (14/3)(x-2)^(-1/3)

Step 2: Set the derivative equal to zero or identify where it is undefined.
The derivative will never be zero since (14/3) is a constant and (x-2)^(-1/3) will never equal zero.

However, the derivative is undefined when the exponent -1/3 leads to a division by zero in the denominator.

This occurs when (x-2) = 0.

Solving for x, we get:
x-2 = 0
x = 2

Therefore, the critical number A is 2. The two important intervals for the function f(x) = 7(x-2)^(2/3) are (-∞, 2) and (2, ∞).

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There are no other combinations to consider.

To determine the possible combinations, since Chris wants to list the thirteen states in chronological order as they continued to join the union, there is only one combination possible.

This is because the order is based on the dates the states joined, which is a fixed sequence. Here are the steps for listing the states:

1. Begin with Delaware, as it was the first state to join the union on December 17, 1787.
2. Follow with Pennsylvania, which joined on December 12.
3. Add New Jersey, which joined on December 18.
4. Continue listing the remaining ten states in the order they joined.

As the order is determined by the joining dates, there are no other combinations to consider.

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The calculated number of times you would expect to roll a three or a six is 32 times

From the question, we have the following parameters that can be used in our computation:

Cube = 96

In a cube, we have the following probability equation

P(3 or 6) = 1/6 + 1/6

When the sum is evaluated, we have

P(3 or 6) = 2/6

So, when the die is rolled 96 times, we have

Expected value = 2/6 * 96

Evaluate the products

Expected value = 32

Hence, the expected number of times is 32

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The unit rate in teaspoons per cup is 2 teaspoons per cup

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Unit rate = teaspoons/Recipe

Substitute the known values in the above equation, so, we have the following representation

Unit rate = (4/3)/(2/3)

Evaluate

Unit rate = 2

Hence, the unit rate is 2

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The value of x in the data set is 101.

The mean of a data set is the sum of all the data divided by the count n.

Therefore, let's find the mean of the data set as follows:

The mean is  the sum of the data divided by the total number of data.

Hence, let's find the value of x using the mean

108  = 102 + 120 + 103 + 112 + 110 + x  / 6

108 = 547 + x / 6

Cross multiply

108 × 6 = 547 + x

648 = 547 + x

x = 648 - 547

x = 101

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The mathematical model that pattern using an equation to represents  the height is h, the leaf scar is l is given by x = c × l × √n × cos(n × φ) , and y = c × l × √n × sin(n × φ) + h.

The pattern of leaf scars on a tree trunk is often modeled using a mathematical function called a phyllotaxis spiral.

This spiral can be represented by the polar equation,

r = c × √n

where r is the radius of the spiral,

n is the index of the leaf scar,

c is a constant that determines the tightness of the spiral,

and the angle of rotation is equal to,

θ = n × φ

where φ is the golden angle, which is approximately 137.5°.

To incorporate the height h and leaf scar size l into the model,

Make the following modifications,

Add a vertical displacement factor h to the polar equation, which shifts the spiral upward by h units.

Multiply the radius by a factor that is proportional to the size of the leaf scar l.

The modified polar equation for the phyllotaxis spiral would be,

r = c × l × √n

θ = n × φ

where r is the radius of the spiral,

n is the index of the leaf scar,

c is a constant that determines the tightness of the spiral,

l is the size of the leaf scar,

and φ is the golden angle.

To convert this polar equation to a Cartesian equation that relates x and y coordinates,

x = r × cos(θ)

y = r × sin(θ) + h

Substituting the expressions for r and θ from above, we get,

x = c × l × √n × cos(n × φ)

y = c × l × √n × sin(n × φ) + h

Therefore, mathematical equation that models the phyllotaxis spiral of leaf scars on a tree trunk, taking into account the height h and the size of the leaf scar l is

x = c × l × √n × cos(n × φ)

y = c × l × √n × sin(n × φ) + h

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The AA Similarity Theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. We can complete the figure by drawing a line segment of length 10.5 from point A to point H.

Using this theorem, we can write the following if-then statement to describe the given illustration:

If angle RH is congruent to angle A and angle NH is congruent to angle E, then triangle PHN is similar to triangle AHE.

This means that the corresponding sides of these triangles are proportional to each other. We can use this information to complete the figure by finding the length of side AH.

Since triangle PHN is similar to triangle AHE, we can set up the following proportion:

PH/AH = HN/HE

We know that PH = 6 and HN = 8, and we want to find AH. Let x represent the length of AH.

6/x = 8/14

Cross-multiplying gives us:

6 * 14 = 8 * x

Simplifying:

84 = 8x

Dividing both sides by 8:

x = 10.5

Therefore, we can complete the figure by drawing a line segment of length 10.5 from point A to point H.

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To solve the inequality -1/4a > 3a, we need to first multiply both sides by -4 to get rid of the fraction:
-1a > 12a
Next, we can subtract 12a from both sides to get:
-13a > 0
Dividing both sides by -13 gives us:
a < 0

To solve the inequality b – 12 > -3, we can add 12 to both sides:
b > 9

Now we need to find values of a and b that satisfy both inequalities. Since a < 0, we can try any negative value of a. Let's try a = -1:

-1/4(-1) > 3(-1)
1/4 > -3

This inequality is true, so we can move on to the next inequality. Let's plug in a = -1 and see if it satisfies b > 9:

b – 12 > -3
b > 9

Since -1 satisfies both inequalities, the values that make both inequalities true are: a = -1 and any value of b greater than 9.

The statement "La tangente de 60° es igual al triple de la tangente de 20°" is not true.

To solve the problem "La tangente de 60° es igual al triple de la tangente de 20°," follow these steps:

Step 1: Write down the equation based on the problem statement:
tan(60°) = 3 * tan(20°)

Step 2: Find the tangent values for the given angles:
tan(60°) = √3
tan(20°) = 0.36397 (approximate value)

Step 3: Plug the tangent values into the equation and check if the statement is true:
√3 = 3 * 0.36397

Step 4: Calculate the right side of the equation:
3 * 0.36397 = 1.09191 (approximate value)

Step 5: Compare the two values:
√3 ≈ 1.73205 (approximate value)

Since 1.73205 ≠ 1.09191, the statement "La tangente de 60° es igual al triple de la tangente de 20°" is not true.

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The length of the fabric piece is 5 cm.

We are given the width and area of the fabric piece and need to find its length. Here are the steps:

1. The terms involved in this problem are width, length, and area.
2. The formula to calculate the area of a rectangle is Area = Width × Length.
3. We are given the width (6 cm) and area (30 cm²) of the fabric piece.
4. To find the length, we'll rearrange the formula: Length = Area ÷ Width.
5. Plug in the given values: Length = (30 cm²) ÷ (6 cm).
6. Perform the calculation: Length = 5 cm.

So, the length of the fabric piece is 5 cm.

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Answer:

b

Step-by-step explanation:

point B has coordinates (0, 0 ) which is the origin

The zeros for this quadratic equation is [-1, 0].

In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;

y = ax² + bx + c

Where:

Next, we would solve the quadratic function by using the factorization method as follows;

y = x² + 2x + 1

x² + 2x + 1 = 0

x² + x + x + 1 = 0

x(x + 1) + 1(x + 1) = 0

(x + 1)(x + 1) = 0

x = -1.

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