1. Given the function f(x)=x^2+1, copy and complete the following table

Using sine and cosine rule, the length of fence is 19.84 feet and the number of packets to cover the garden is approximately 48

To find the value of of the length of the fence, we can either use sine rule or cosine rule.

Since we have two sides and an angle, we sine rule first

a/sin A = b / sin B

[tex]\frac{33}{sin 104} = \frac{22}{sin B} \\sin B = 0.6469\\B = 40.31^0[/tex]

Using this, we can find the value of angle C

A + B + C = 180 degrees

Reason: Sum of angles in a triangle is equal to 180 degrees

104 + 40.31 + C = 180

C = 35.69 degrees

We can proceed to use cosine rule to find the length of the fence.

[tex]c^2 = a^2 + b^2 -2(a)(b)cosC\\c^2 = 33^2 + 22^2 - 2(33)(22)cos35.69\\c^2 = 393.71\\c = 19.84 ft[/tex]

Part B

Since one packet will cover 9ft², we need to know the total area of the field to determine the number of packets required.

Using heron's formula;

[tex]s = \frac{a + b + c}{2} \\s = \frac{33 + 22 + 29.84}{2} \\s = 42.42\\[/tex]

The area of the field is

[tex]A = \sqrt{s(s-a)(s-b)(s-c)}\\A = \sqrt{42.42(42.42-33)(42.42-22)(42.42-19.84}\\A = 429.24ft^{2}[/tex]

The number of packets will be

x = 429.24 / 9

x = 47.69≅48 packets

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Answer:  f(x) is -74(x+1/7)^(-1/2)

Step-by-step explanation:

 To find the derivative of f(x), we can use the power rule and the chain rule.

First, let's rewrite f(x) as:

f(x) = -148(x+1/7)^(1/2)

Now, we can apply the power rule:

f'(x) = -148 * (1/2) * (x+1/7)^(-1/2)

Finally, we can use the chain rule:

f'(x) = -148 * (1/2) * (x+1/7)^(-1/2) * 1

f'(x) = -74(x+1/7)^(-1/2)

Therefore, the derivative of f(x) is -74(x+1/7)^(-1/2).

Answer:

Step-by-step explanation:

first graph

y = 5x + 2

2 = y-intercept

5 = slope

the first graph is y = 5x+2 because the y-intercept is 2 and it rises 5 and goes over 1

second graph:

y = 2x + 3

third graph:

y = 3x + 3

The population will reach 12000 bacteria after 56.4 minutes and other solutions are listed below

We can use the formula for exponential growth, which is given by:

N = N0 * e^(kt)

where N is the final population, N0 is the initial population, k is the growth rate constant, and t is time.

To find the initial size of the culture, we can use the values given at 15 minutes and 40 minutes:

100 = N0 * e^(15k)

1800 = N0 * e^(40k)

Dividing the second equation by the first, we get:

18 = e^(25k)

Taking the natural logarithm of both sides, we get:

k = ln(18)/25

Solving for k, we get:

k = 0.1156

Substituting this value of k into the first equation, we can solve for N0:

100 = N0 * e^(15 * 0.1156)

N0 = 17.65

Therefore, the initial size of the culture was 17.65 bacteria.

To find the doubling period, we use the fact that the population doubles when t increases by a certain amount, which we'll call T. That is:

N0 * e^(kT) = 2N0

Dividing by N0 and taking the natural logarithm of both sides, we get:

T = ln(2)/k

Solving for T, we get:

T = ln(2)/k ≈ 6.00 minutes

Therefore, the doubling period is approximately 6 minutes.

To find the population after 115 minutes, we can use the formula with the values of N0, k, and t:

N = N0 * e^(kt) = 17.65 * e^(0.1156 * 115) ≈ 10477448.92

Therefore, the population after 115 minutes is approximately 10477448.92 bacteria.

To find when the population reaches 12000, we set N equal to 12000 and solve for t:

12000 = 17.65 * e^(0.1156t)

Dividing by 17.65 and taking the natural logarithm of both sides, we get:

ln(12000/17.65 ) = 0.1156t

Solving for t, we get:

t ≈ 56.42 minutes

Therefore, the population will reach 12000 bacteria after approximately 56.4 minutes.

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Answer:

3x100-4

Step-by-step explanation:

3x100=300

(3x100)-4

300-4

The average rate of change of P between t = 3 and t = 5 is -18 people/hour.

A possible value of people in line at t = 6, given the average rate of change would be 50.

To find the average rate of change of P between t = 3 and t = 5, we can use the formula:

Average rate of change = (P(5) - P(3)) / (5 - 3)

From the table, we know P(3) = 85 and P(5) = 49.

Average rate of change = (49 - 85) / (5 - 3) = (-36) / 2 = -18 people/hour

To find the possible number of people at t = 6, Let P(6) = x. First, we will find the average rate of change between t = 3 and t = 6:

(P(6) - P(3)) / (6 - 3) = (x - 85) / 3

This value must be negative. Now, we will find the average rate of change between t = 5 and t = 6:

(P(6) - P(5)) / (6 - 5) = (x - 49) / 1

This value must be positive. Since (x - 49) is positive, we know that x > 49. Now we need to find a value for x that also satisfies the condition that the average rate of change between t = 3 and t = 6 is negative. Since (x - 85) / 3 is negative, we know that x < 85.

So, a possible value for P(6) is between 49 and 85. For example, we could choose P(6) = 50, which satisfies both conditions.

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Answer: 36 inches

Step-by-step explanation:

The formula for the circumference of a circle is 2πr where r is the radius of the circle Therefore 2πr=72π so r=72/2 = 36 inches.

Rieko can make 60 bird houses if each bird house requires 1/4 pounds of nails and she has 15 pounds of nails.

If each bird house requires 1/4 pounds of nails and Rieko has 15 pounds of nails, we can use the following equation to determine the number of bird houses she can make:

number of bird houses = amount of nails / amount of nails per bird house

Plugging in the given values, we get:

number of bird houses = 15 / (1/4)

Simplifying the right-hand side by dividing 15 by 1/4, we get:

number of bird houses = 60

Therefore, Rieko can make 60 bird houses if each bird house requires 1/4 pounds of nails and she has 15 pounds of nails.

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The net profit before appropriation is (d). $1,889,000.

To calculate net profit before appropriation to R&R biscuit company by adding all the appropriation expense to share of profit after appropriation and deducting appropriation income.

In this case, interest on capital, drawings and partner's salary are appropriation expense while interest on drawings is appropriation income.

Now,

Net profit before appropriation

= ($650,000+$200,000+$100,000+$30,000-$20,000) + ($650,000+$150,000+$130,000+$25,000-$26,000)

= $960,000 + $929,000

= $1,889,000

So, the correct answer is (d). $1,889,000.

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The polynomial expression that represents the area of the given square is: 4x² + 28x + 49

The formula for the area of a square is expressed as:

Area = side * side

Now, we are given the dimensions of the square and we have:

Side length = x + 7 + x = 2x + 7

Thus:

Area of square = (2x + 7) * (2x + 7)

= 4x² + 14x + 14x + 49

= 4x² + 28x + 49

Thus, we conclude that expression represents the area of the square.

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Answer:

the values of x are 13 and 1.

Step-by-step explanation:

x - 7 = +√36 or x - 7 = -√36

Therefore,

x - 7 = +6 or x - 7 = -6

=> x = 7 + 6 or x = 7 - 6

=> x = 13 or x = 1

Therefore, the values of x are 13 and 1.

Answer: x = 25

Step-by-step explanation:

(x – 7)2 = 36 (Given)

2(x -- 7) = 36 (Associative Property)

2x - 14 = 36 (Distributive Property)

2x - 14 + 14 = 36 + 14 (Addition Property of Equality)

2x = 50 (Simplification)

2x/2 = 50/2 (Division Property of Equality)

x = 25 (Simplification)

Answer:

2

Step-by-step explanation:

no explanation needed.

1. The angle between the hypotenuse and the base is approximately 90 - 23.6 = 66.4 degrees. 2. the angle between the hypotenuse and the perpendicular is approximately 90 - 62.3 = 27.7 degrees.

In trigonometry, cosine (cos) is a trigonometric function that relates the adjacent side and the hypotenuse of a right triangle. It is defined as the ratio of the adjacent side to the hypotenuse. The cosine function is periodic with a period of 360 degrees or 2π radians, and it has a range of values between -1 and 1.

In other words, if we have a right triangle with an angle x, then the cosine of x is equal to the length of the adjacent side of the triangle divided by the length of the hypotenuse.

1.In a right-angled triangle, the cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse. Therefore, cos(x) = adjacent/hypotenuse = 37/39.

Using inverse cosine function on a calculator, we get x ≈ 23.6 degrees.

Therefore, the angle between the hypotenuse and the base is approximately 90 - 23.6 = 66.4 degrees.

2. Again, using the definition of cosine, we have cos(x) = adjacent/hypotenuse = 8/17.

Using inverse cosine function on a calculator, we get x ≈ 62.3 degrees.

Therefore, the angle between the hypotenuse and the perpendicular is approximately 90 - 62.3 = 27.7 degrees.

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We can estimate that the weight οf a child will increase by apprοximately 1.93 kg when they grοw frοm a height οf 1 m tο 1.1 m.

A differential equatiοn is an equatiοn that includes an unknοwn functiοn and its derivative. A differential equatiοn describes a relatiοnship between a functiοn and changes in the functiοn.

The given equatiοn relating weight (W) and height (h) fοr children between 5 and 13 years οld is:

ln(W) = ln(2.4) + 1.84h

We want tο estimate the change in weight when a child grοws frοm a height οf 1 m tο 1.1 m.

First, we need tο calculate the weight at h = 1 m and h = 1.1 m.

At h = 1 m, we have:

ln(W1) = ln(2.4) + 1.84(1)

ln(W1) = ln(2.4) + 1.84

ln(W1) ≈ 2.684

Sο the weight at h = 1 m is apprοximately W1 ≈ e².684 ≈ 14.66 kg.

Similarly, at h = 1.1 m, we have:

ln(W2) = ln(2.4) + 1.84(1.1)

ln(W2) = ln(2.4) + 2.024

ln(W2) ≈ 2.807

Sο the weight at h = 1.1 m is apprοximately W2 ≈ e².807 ≈ 16.59 kg.

Tο estimate the change in weight when the height increases frοm 1 m tο 1.1 m, we can use the differential οf the equatiοn:

dln(W) = 1.84dh

Using differentials, we can apprοximate the change in weight as:

dW ≈ W2 - W1

dW ≈ e².807 - e².684

dW ≈ 1.93 kg

Therefοre, we can estimate that the weight οf a child will increase by apprοximately 1.93 kg when they grοw frοm a height οf 1 m tο 1.1 m.

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Answer:

Step-by-step explanation:

Cone height  h = 8

Cone base  r = sqrt( 24/pi) = 2.764

AB = h - 3 = 5

BC = 5 / tan(β) = 1.727

FB = FC - BC = 1.036482449           ( FB is the radius of cross-section circle)

Area of a cross-section is:  (FB)2 * pi = 3.375 in2

As a result, Mrs. Walker contributed a portion of the overall cost of the supper, which is: 400/61 - (16B + 25L) / (61C) (61C)

A fraction is a number that in mathematics represents a portion of a whole. It consists of a horizontal line between the numerator and denominator of two numbers. The denominator is the total number of equally sized components that make up the whole, whereas the numerator is the number of parts that are being taken into account. As an illustration, the fraction 3/4 denotes three of the four equal pieces. The denominator, 4, indicates that the entire is divided into four equal parts, while the numerator, 3, indicates that three parts are being taken into consideration.

given

Payment to Mr. Lim:

1/5(B + W) = (B + W)/5

Payment to Mr. Bell:

1/4(L + W) = (L + W)/4

These equations can be combined to find the value of W, or the amount Mrs. Walker paid:

(L + W)/4 + W + (B + W)/5 = C

To get rid of the fractions, multiply both sides by 20, which is the least common multiple of 5 and 4. This gives us:

20W + 4(B + W) + 5(L + W) = 20C

By enlarging and condensing, we obtain:

20C = 4B + 4W + 5L + 5W + 20W

9W + 4B + 5L = 20C

Now, we may change the expressions for the payments made to Mr. Lim and Mr. Bell to:

9W plus 4 (1/5 B + W) plus 5 (1/4 L + W) equals 20C.

If we simplify, we get:

9W + 4B + 4W + 4W + 4W + 5L + 5W = 20C.

When we multiply both sides by 20 to once more get rid of the fractions, we get:

400C = 180W + 16B + 16W + 25L + 25W

20C = 4B + 4W + 5L + 5W + 20W

9W + 4B + 5L = 20C

Now, we may change the expressions for the payments made to Mr. Lim

If we simplify, we get:

61W + 16B + 25L = 400C

We may now determine W:

W = (400C - 16B - 25L) / 61

We can divide W by the overall cost C to determine the portion of the cost of the lunch that Mrs. Walker covered:

W/C = (400C - 16B - 25L) / (61C)

W/C = 400/61 - (16B + 25L) / (simplified) (61C)

As a result, Mrs. Walker contributed a portion of the overall cost of the supper, which is: 400/61 - (16B + 25L) / (61C) (61C) .

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Answer: 10 pigs and 3 chickens

Step-by-step explanation:

So the farmer has seen 40 legs

Pigs have 4 legs & Chickens have 2

Pigs: 40/4= 10 pigs

Chickens: 40/2= 20 chickens

So with us know which answer is correct we choose 10 pigs

Then if we have 10 pigs we have 3 chickens

13-10= 3 chickens

In conclusion we have the 10 pigs & 3 chickens

Answer:

4.5 cm.

Step-by-step explanation:

Divide the length by the width to get the perimeter: 360 / 80 = 4.5 cm.

HOPE IT HELP YOU

Solving the quadratic equation, we get the maximum profit is 2451 thousand dollars.

A second-degree algebraic equation in x is known as a quadratic equation. The quadratic equation is written as Ax2 + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.

For an equation to be categorised as a quadratic equation, the coefficient of x2 must be a non-zero term (a 0).

The function is given as

P(q) = -0.01q2 +5q-39

We have

P(q) = -0.01q2 +5q-39

Differentiate

So, we have

P'(q) = -0.01q + 5

Set to 0

So, we have

-0.01q + 5

This gives:

-0.01q = -5

Evaluate

q = 500

Hence, 500 thousand pairs of sunglasses should be sold to maximize profits.

What is the maximum profit?

In (a), we have

q = 500

This gives:

P (500) = (-0.01)500×2 +5×500-39

Evaluating:

P (500) = -10 + 2500 -39

= 2451

Hence, the maximum profit is 2451 thousand dollars.

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When we solve the quadratic equation, we discover that the utmost profit is $2451 thousand dollars.

A quadratic equation is an x-dependent second-degree algebraic problem. [tex]ax^{2} +bx+c=0[/tex], where x is the variable, a and b are the coefficients, and c is the constant element, is how the quadratic equation is expressed.

The coefficient of [tex]x^{2}[/tex] must not be negative for an equation to be categorized as a quadratic equation (a, 0).

The function is given as

P(q) = [tex]-0.01q^2[/tex] +5q-39

We have

P(q) = [tex]-0.01q^2[/tex] +5q-39

Differentiate

So, we have

P'(q) = -0.01q + 5

Set to 0

So, we have

-0.01q + 5

This gives:

-0.01q = -5

Evaluate

q = 500

So, in order to make the most money 500 000 sets of sunglasses should be sold.

In (a), we have

q = 500

This gives:

P (500) = (-0.01)500×2 +5×500-39

Evaluating:

P (500) = -10 + 2500 -39

= 2451

Therefore, the highest profit is $2451 thousand dollars.

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Step-by-step explanation:

First = x

second = x + 2

third = x + 4

3 * x   =  2 ( x+4)

3x = 2x+ 8

x = 8              8   10  and 12

the coordinates of M"A"T"H" are M"(1,8), A"(6,2), T"(5,4), and H"(3,4).

How to find?

The composition r x-axis ° T(7,5) first reflects the quadrilateral MATH about the x-axis and then translates it 7 units to the right and 5 units up.

To find the image of M(-6,-3) after reflection about the x-axis, we flip the sign of the y-coordinate to get M'(-6,3). Then, we translate M' 7 units to the right and 5 units up to get the coordinates of M":

M" = T(7,5) ∘ M' = (7 + (-6), 5 + 3) = (1, 8)

Similarly, we can find the coordinates of A", T", and H":

A' = (-1, 3) → A" = T(7,5) ∘ R(x-axis) ∘ A' = (7 + (-1), 5 - 3) = (6, 2)

T' = (-2, 1) → T" = T(7,5) ∘ R(x-axis) ∘ T' = (7 + (-2), 5 - 1) = (5, 4)

H' = (-4, 1) → H" = T(7,5) ∘ R(x-axis) ∘ H' = (7 + (-4), 5 - 1) = (3, 4)

Therefore, the coordinates of M"A"T"H" are M"(1,8), A"(6,2), T"(5,4), and H"(3,4).

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The inequality x - 19 ≤ 81 is not satisfied when x = 110.

What is inequalities?

In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal. It is a statement that compares two values, usually using one of the following symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).

The given inequality is X – 19 ≤ 81, and we are asked to evaluate it when X = 110. To do so, we substitute X with 110 and simplify the expression. In this case, we get 110 - 19 ≤ 81, which simplifies to 91 ≤ 81. Since this statement is false, we conclude that the inequality X – 19 ≤ 81 is not satisfied when X = 110.

we can substitute x = 110 and simplify:x - 19 ≤ 81

110 - 19 ≤ 81

91 ≤ 81

This statement is false, since 91 is not less than or equal to 81.

Therefore, the inequality x - 19 ≤ 81 is not satisfied when x = 110.

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The expected value of the gas grill is 6.50 million dollars if a development cost of $4 million is invested.

The expected value is the sum of all possible outcomes multiplied by their associated probabilities.

The expected value of the gas grill can be calculated as follows:

Expected value = (0.10 × 3) + (0.50 × 6) + (0.40 × 8)

= 0.30 + 3.00 + 3.20

= 6.50 million dollars

Therefore, the expected value of the gas grill is 6.50 million dollar.

This calculation allows investors to decide whether or not to invest in a specific project, as the expected return must be greater than the development cost.

In this case, the expected value of 6.50 million dollars is greater than the development cost of 4 million dollars, making the investment a viable option.

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The sum of these 40 sampled numbers follows option D: normal distribution, if X follows Poisson distribution.

The likelihood that a certain number of events will occur in a specific period of time or space, provided that they do so with a known constant mean rate and the Poisson distribution describes the distribution of events, regardless of the time since the previous event. When the mean is high, the sum of the Poisson distribution resembles a normal distribution.

The "normal distribution," a continuous probability distribution that is symmetrical at the mean and has a bell-shaped curve. It is also known as the bell curve or the Gaussian distribution. Several natural phenomena, including height, weight, blood pressure, and others, have a normal distribution.

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Short Answers:

a)N*tan(Θ)

b)arctan(h/N)

c)N*tan(A)

Let * stand for multiplication

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The range of resting heart rates is 70 beats per minute. Subtracting the lowest value from the highest value will give us the range.

It is a set of data which is the difference between the highest and lowest values.

The range of resting heart rates, in beats per minute, is calculated by subtracting the minimum value of the data set from the maximum value. In this case, the minimum value = 35

and the maximum value = 105,

so the range of resting heart rates = 105 - 35

= 70 beats per minute

The other answers cannot be the range of the resting heart rates because they are not calculated correctly.

The answer 16 beats per minute (105 - 89 = 16) is the difference between the maximum and the 90th percentile, and the answer 31 beats per minute (85 - 54 = 31) is the difference between the 85th percentile and the median.

The answer 62 beats per minute (95 - 33 = 62) is the difference between the 95th percentile and the minimum.

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Question: