find the length of ac

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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Short Answers:

a)N*tan(Θ)

b)arctan(h/N)

c)N*tan(A)

Let * stand for multiplication

Hope this is helpful to someone:)

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:

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)

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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If yοu invest $150 a mοnth fοr 8 years, then leave the mοney in the accοunt, withοut making additiοnal payments, fοr anοther 12 years.

a) Yοu will have  yοu will have apprοximately $59,073.95 at the end οf 20 years.$59,073.95 at the end οf 20 years.

b) Earned apprοximately $26,673.95 in interest οver the 20-year periοd.

The wοrth οf a series οf recurrent payments at a specific future date, assuming a specific rate οf return, οr discοunt rate, is the future value οf annuity.

Let's first calculate the tοtal number οf mοnths in 20 years:

20 years x 12 mοnths/year = 240 mοnths

a. we can use the fοrmula fοr the future value οf an annuity:

[tex]FV = PMT x (((1 + r/n)^(n*t) - 1) / (r/n))[/tex]

where:

PMT = the mοnthly payment ($150)

r = the annual interest rate (2.4% οr 0.024)

n = the number οf times the interest is cοmpοunded per year (12)

t = the tοtal number οf years (20)

FV = 150 x (((1 + 0.024/12)^(12*20) - 1) / (0.024/12))

FV ≈ $59,073.95

Therefοre, yοu will have apprοximately $59,073.95 at the end οf 20 years.

b. Tο calculate the amοunt οf interest yοu earned, we can subtract the tοtal amοunt οf mοney yοu invested frοm the future value:

Interest = FV - Tοtal amοunt invested

Interest = $59,073.95 - ($150 x 12 x 8 x 12)

Interest ≈ $26,673.95

Therefοre, yοu earned apprοximately $26,673.95 in interest οver the 20-year periοd.

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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:

2

Step-by-step explanation:

no explanation needed.

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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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

he is literally hitting the gritty

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

Answer:

1)$15000

2)0.55%

3)0.55

4)3

5)24.75

Step-by-step explanation:

5)1500×0.55×3/100

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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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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Answer:

3x100-4

Step-by-step explanation:

3x100=300

(3x100)-4

300-4

Answer:

Spinning Swings

10 more riders

Step-by-step explanation:

To find which ride will have more riders each hour, we need to first convert an hour into minutes.

[tex]\text{1 hour = 60 minutes}[/tex]

Now we let's first find how many riders there will be in the race cars.

So there are 25 riders every 30 minutes.

in 60 minutes there will be:

[tex]25 \times 2 = 50 \ \text{Riders}[/tex]

Now for the spinning swings there are 20 riders every 20 minutes.

In 60 minutes there will be:

[tex]20 \times 3 = 60 \ \text{Riders}[/tex]

Therefore, the spinning swings will have more riders as [tex]60 > 50[/tex].

Now to find how many more riders there will be in the spinning swings.

We simply subtract the total number of riders of each ride from each other.

[tex]\text{Race Cars = 50}[/tex]

[tex]\text{Spinning Swings = 60}[/tex]

[tex]60 - 50 = 10[/tex]

There will be 10 more riders in the spinning cups than the race cars.

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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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).

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

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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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.

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:

The correct answers are: To determine the consumer's eligibility for credit and  To set pricing for credit lines.

what is pricing?

"Pricing" refers to the process of determining the value or cost of a product or service and setting a specific price for it. Pricing decisions involve taking into account various factors such as production costs, market demand, competition, and profit margins, among others. Pricing can also involve setting

In the given question,

Based on section 1.3.2, Credit scores, on page 22 of the report, the two purposes for which credit card issuers use credit scores are:

To determine the consumer's eligibility for credit.

To set pricing for credit lines.

Therefore, the correct answers are:

To determine the consumer's eligibility for credit

To set pricing for credit lines

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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 sum of the digits of the product p×q is 8

A positive integer bigger than one that can be divided only by itself and by one is referred to as a prime number.

Given that: p³ - pq² = 42024

p (p² - q²) = 42024

Since factors, 42024 = 2³ x 3 x 17 x 103, and p and q are prime numbers, we can see that p must be 3, 17 or 103, We can try each case:

If p = 3 then we have:

3 (9 - q²) = 42024

q² = -13,999

This equation has no real solutions for q, so p cannot be 3.

If p = 17, then we have:

17 (289 - q²) = 42024

q² = -2183

This equation also has no real solutions for q, so p cannot be 17 either.

If p = 103, then we have:

103 (10609 - q²) = 42024

10609 - q² = 408

q² = 10201

q = 101

This equation also has a solution for q = 101, so p = 103

Product of pq = 103×101 = 10403

So, the sum of the digits of the product pq = 1+0+4+0+3 = 8

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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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