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5. An archway has vertical sides 10 feet high. The top of an archway can



be modeled by the quadratic function f(x) = -0. 5x2 + 10 where x is the



horizontal distance, in feet, along the archway. How far apart are the



walls of the archway? Round your answer to the nearest tenth of a foot.



Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.



293

The venue breaks even when 1,250 people buy tickets, and the total value of tickets sold at that point is $100,000.

To find the break-even point for the venue, we need to set the musician's charges (C(x) = 64x + 20,000) equal to the venue's earnings from ticket sales ($80 per ticket).  Hence,

1. Set the musician's charges equal to the venue's earnings:

64x + 20,000 = 80x

2. Subtract 64x from both sides:

20,000 = 16x

3. Divide both sides by 16:

x = 1,250

At the break-even point, 1,250 people need to buy tickets. To find the value of the total tickets sold at this point:

1. Multiply the number of attendees (x) by the ticket price:

Total ticket sales = x * ticket price

2. Substitute the values:

Total ticket sales = 1,250 * $80

3. Calculate the total ticket sales:

Total ticket sales = $100,000

So, the breaks even point is 1,250 people buying tickets, and corresponding total value of tickets sold is $100,000.

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Answer:

Step-by-step explanation:

Solution: -4

The graph gets closer and closer to the line x=-4 but never touches it.

If George's bicycle has a mass of 15 grams, then it is highly unlikely that he has stated the correct mass, as 15 grams is an extremely low mass for a bicycle.

A typical bicycle weighs anywhere from 7 to 15 kilograms. It is highly unlikely that a bicycle would weigh only 15 grams, as this is much lighter than the lightest bicycle ever made.

Therefore, it is reasonable to assume that George made a mistake and meant to say 15 kilograms instead of grams.

Assuming the mass of the bicycle is 15 kilograms, removing the front wheel will decrease the mass slightly, but not by a significant amount.

The front wheel typically accounts for around 1-2 kilograms of the total mass of the bicycle, so removing it would leave a mass of approximately 14 kilograms.

However, assuming he made a mistake and meant to say 15 kilograms, then the mass of the bicycle without the front wheel would be approximately 14 kilograms.

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lim (1 - a^(1-a)) / (ln(a)) as x -> a This is the value of the given limit.

To find the value of the given limit, which can be represented as lim (a^x - x^a) / (x^x - a^a) as x approaches 'a', you can apply L'Hôpital's Rule, which states that if the limit of the ratio of the derivatives of two functions exists, then the limit of the original functions is equal to that limit.

First, differentiate the numerator and denominator with respect to x:

Numerator: d(a^x - x^a) / dx = a^x * ln(a) - a * x^(a-1)
Denominator: d(x^x - a^a) / dx = x^x * ln(x)

Now, we can find the limit of the ratio of the derivatives as x approaches 'a':

lim (a^x * ln(a) - a * x^(a-1)) / (x^x * ln(x)) as x -> a

After substituting 'a' for 'x' in the limit:

lim (a^a * ln(a) - a * a^(a-1)) / (a^a * ln(a)) as x -> a

Now, cancel out the common term a^a * ln(a):

lim (1 - a^(1-a)) / (ln(a)) as x -> a

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Answer: less than

Step-by-step explanation:

Answer:

To convert the equation 3x - 15y = 11 into slope-intercept form, we need to solve for y.

First, we'll subtract 3x from both sides:

-15y = -3x + 11

Next, we'll divide both sides by -15:

y = (3/15)x - (11/15)

Simplifying the fraction:

y = (1/5)x - (11/15)

This is the slope-intercept form, where the slope is 1/5 and the y-intercept is -11/15.

Saturn is approximately 9.52 times further from the sun than Earth.

To find out how many times further from the sun Saturn is compared to Earth, we need to divide Saturn's distance from the sun by Earth's distance from the sun.

First, let's correct the distances given:
- Earth's distance from the sun: 1.496 x 10^8 km
- Saturn's distance from the sun: 1.4246 x 10^9 km (I assume you missed the exponent)

Now, let's calculate the ratio:

Ratio = (Saturn's distance) / (Earth's distance)
Ratio = (1.4246 x 10^9 km) / (1.496 x 10^8 km)

To make the calculation easier, let's factor out the common exponent (10^8):

Ratio = (1.4246 x 10) / (1.496)
Ratio ≈ 9.52

So, Saturn is approximately 9.52 times further from the sun than Earth.

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The number of bacteria contained in the human body is 40 times as great as the number of genes contained in the human body.

To find out how many times greater the number of bacteria in the human body is than the number of genes, we need to divide the number of bacteria by the number of genes:

4 × 10^13 (number of bacteria) ÷ 1 × 10^12 (number of genes)

= 40

Therefore, the number of bacteria contained in the human body is 40 times as great as the number of genes contained in the human body.

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The truck would have lost 36% of its initial value.

The value in dollars, v(x), of a certain truck after x years can be represented by a mathematical function or equation. In the absence of a specific equation, it is difficult to provide an answer.

However, I can provide an example of a possible equation that represents the depreciation of a truck's value over time.

Let's assume that the truck loses 20% of its value every year. If the initial value of the truck is V0 dollars, then the value of the truck after x years, Vx, can be represented by the following equation:

Vx = [tex]V0(0.8)^x[/tex]

In this equation, the term [tex](0.8)^x[/tex] represents the percentage of the truck's value that remains after x years of depreciation. For example, after one year, the truck's value would be V1 = [tex]V0(0.8)^1[/tex] = 0.8V0,

which means that the truck would have lost 20% of its initial value. After two years, the truck's value would be V2 = V0[tex](0.8)^2[/tex]= 0.64V0,

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Answer:

The answer to your problem is:

The radius of circle F is 28.

Circle F and circle D are similar.

Step-by-step explanation:

How to find the radius:

A = π × [tex]r^{2}[/tex]

But the radius of a circle from diameter. If you can recall the diameter d, the radius is r = d / 2.

By looking at our facts we can actually see ( if we use the comparing method ) that the circles, F & D are very much similar.

Thus the answer to your problem is:

The radius of circle F is 28.

Circle F and circle D are similar.

The height of the outside is given as 17.44 meters

The equation of hyperbola is :

[tex]y^2 - x^2 = 38[/tex]

=>[tex]y^2/38 - x^2/38 = 1[/tex]

(of the form [tex]y^2/a^2 - x^2/b^2 = 1[/tex] and transverse axis is y-axis.)

Here, [tex]a^2 = b^2 = 38[/tex]

[tex]c^2 = a^2 + b^2 = 38+38 = 76[/tex]

( a is the distance of vertices from the center and c is the distance of foci from the center.)

Distance between walls = 2 a = [tex]2*\sqrt(38) = 12.33[/tex] meters at the center

and = [tex]2c = 2*\sqrt(76) = 17.44[/tex] meters at the end when the line joining

end points of the wall on one side is through the foci point.

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Answer:

11. x = 16

12. x = 26

Step-by-step explanation:

11. ∠1 + ∠2 = 90°

   ∠1 = 42°

   ∠2 = 90° - 42° = 48°

   3x = 48

   x = 16

12. ∠C + ∠D = 180°

∠C = 128°

∠D = 180° - 128° = 52°

2x = 52

x = 26

The degree of the monomial expression -3xy²z(-2x²yz) is derived to be equal to 8.

A monomial is a type of algebraic expression that consists of only one term. It is an expression in which the variables and their exponents are multiplied together, with no addition or subtraction involved. The degree of a monomial is the sum of the exponents of its variables.

Given the monomial:

-3xy²z(-2x²yz)

We can simplify it by multiplying the coefficients and adding the exponents of the variables:

-3(-2)x^(2+1) y^(2+1) z^(1+1)

= 6x³y³ z²

Therefore, the degree of the given monomial expression is: 3 + 3 + 2 = 8.

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Answer:

1/221.

Step-by-step explanation:

Probability(first card is a King) = 4/52 = 1/13 (as there are 4 kings in the pack).

Now there are 51 cards left in the pack, 3 of which are Kings, so:

Probability(second card is a King) = 3/51 = 1/17.

These 2 events are independent so we multiply the probabilities:

Required probability =

1/13 * 1/17

= 1/221.

As per the probability, the expected demand for bananas per week is 182.5 pounds.

To model this problem, we can use decision analysis, which involves identifying the possible outcomes, assigning probabilities to each outcome, and calculating the expected value of each decision.

In this case, the possible outcomes are the demand for bananas, which can be 100, 150, 200, or 250 pounds per week. The probabilities of each demand level are given as 0.20, 0.25, 0.35, and 0.20, respectively.

Let X denote the demand for bananas in pounds. Then, the expected demand for bananas, denoted as E(X), can be calculated as follows:

E(X) = 100(0.20) + 150(0.25) + 200(0.35) + 250(0.20) = 182.5

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In the expression πr² + πrℓ, the part of the expression that is π is a constant.

A constant is a value that does not change in an expression, and in this case π represents a fixed value of approximately 3.14159. It is not a coefficient, which is a numerical factor that multiplies a variable, nor a variable or term, which represent varying quantities in an expression.

Hello, I am Alyssa Ann Verrett.

Put the numbers in order:

City A: {2, 3.5, 4, 4, 5, 5.5}

City B: {3.5, 4, 5, 5.5, 6, 6}

a)

The mean monthly rainfall amount for city A: 4 in;

The mean monthly rainfall amount for city B: 5 in;

b)

The MAD monthly rainfall amount for city A: 0.8 in;

The MAD monthly rainfall amount for city B: 0.8 in;

c)

The median monthly rainfall amount for city A: 4 in;

The median monthly rainfall amount for city A: 5.25 in;

Step-by-step explanation:

a) The general definition of mean of a set X is:

mean = (x₁ + x₂ + x₃ + ... xₙ)/n

For City a:

mean = (4+3.5+5+5.5+4+2)/6 = 4

For City b:

mean = (5+6+3.5+5.5+4+6)/6 = 5

b) The general definition of mean absolute deviation of a set X is:

MAD = (|x₁-mean| + |x₂-mean| + |x₃-mean| + ... + |xₙ-mean|)/n

For City a:

MAD = ( |4-4| + |3.5-4| + |5-4| + |5.5-4| + |4-4| + |2-4| )/6 = (0 + 0.5 + 1 + 1.5 + 0 + 2)/6 = 5/6 =0.8

For City b:

MAD = ( |5-5| + |6-5| + |3.5-5| + |5.5-5| + |4-5| + |6-5| )/6 = (0 + 1 + 1.5 + 0.5 + 1 + 1)/6 = 5/6 = 0.8

c) The general definition of median depends on the quantity of elements in the set X and it represents the middlemost value of the set:

When the quantity is odd:

median= x₍ₙ₊₁₎/₂

When the quantity is even:

median= (xₙ/₂ + x ₙ₊₂/₂) /2

For City A:

median = 2, 3.5, 4, 4, 5, 5.5 = (4 + 4) / 2 = 4

For City B:

median = 3.5, 4, 5, 5.5, 6, 6 = (5 + 5.5) / 2 = 5.25

Answer:

y = 5x + 5

Step-by-step explanation:

If x is the number of boxes sold and y is the cost

The first box costs $10

Each additional box costs $5.

If the total number of boxes sold is x, then after selling the first box for $10, there will be x - 1 boxes left to be sold

The cost of x -1 boxes at $5 per box = 5(x - 1) = 5x - 5

Therefore for a total of x boxes sold the total cost, y in dollars is
y = 10 (for the first box)  +  5x - 5 (for the remaining x - 1 boxes)

= 10 + 5x - 5

= 5 + 5x

which in standard form is written as
y = 5x + 5

We can verify our equation using specific numbers for x
For x = 1
y = 5 + 5(1) = 10   ; since only one box has been sold, the cost is fixed at $10

For x = 2 y = 5 + 5(2) = 5 + 10 = $15
This works out to since first box is sold at $10 and the second box at $5

Leave it to you to work out for other numbers

12+13 = 25, therefor the answer is correct

Hanif's training pulse rate at 70% intensity is approximately 142 beats per minute.

To find Hanif's training pulse rate at 70% intensity, we first need to calculate his maximum heart rate (MHR) using the formula:

MHR = 220 - age

Substituting Hanif's age, we get:

MHR = 220 - 14 = 206

Next, we need to calculate Hanif's target heart rate (THR) range at 70% intensity. This range is between 70% and 85% of his MHR. To calculate the lower end of the range, we multiply his MHR by 0.7:

THR lower = 0.7 × MHR = 0.7 × 206 = 144.2 (rounded to one decimal place)

To calculate the upper end of the range, we multiply his MHR by 0.85:

THR upper = 0.85 × MHR = 0.85 × 206 = 175.1 (rounded to one decimal place)

So Hanif's target heart rate range at 70% intensity is between 144.2 and 175.1 beats per minute.

To find his training pulse rate, we add his resting pulse rate (76 beats per minute) to the percentage of his target heart rate range which corresponds to 70% intensity. This is given by:

Training pulse rate = resting pulse rate + (0.7 × (THR upper - resting pulse rate))

Substituting the values we calculated, we get:

Training pulse rate = 76 + (0.7 × (175.1 - 76)) ≈ 142

Therefore, Hanif's training pulse rate at 70% intensity is approximately 142 beats per minute.

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Since the derivative of a constant is always 0, we can drop the last term:
f’(x) = -21/x^4 + 4/x^3 + 1/x^2

Using the rules of differentiation, we can find the derivative of f(x) by taking the derivative of each term separately. The power rule and the constant multiple rule will come in handy here.

f(x) = 7/x^3 – 2/x^2 – 1/x + 140

f’(x) = d/dx(7/x^3) – d/dx(2/x^2) – d/dx(1/x) + d/dx(140)

To find the derivative of 7/x^3, we can use the power rule, which states that the derivative of x^n is nx^(n-1).

f’(x) = -21/x^4 – (-4/x^3) – (-1/x^2) + 0

To find the derivative of -2/x^2, we can again use the power rule:

f’(x) = -21/x^4 + 4/x^3 – (-1/x^2) + 0

To find the derivative of -1/x, we use the power rule once more:

f’(x) = -21/x^4 + 4/x^3 + 1/x^2 + 0

And since the derivative of a constant is always 0, we can drop the last term:

f’(x) = -21/x^4 + 4/x^3 + 1/x^2

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Rectangles are relatable to factors because of their areas and perimeter equations

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

Explaining why rectangles are relatable to factors

Rectangles are relatable to factors because of the following reasons

Perimeter = 2 * (Length + width)

Area = Length * width

This means that in calculating the areas and the perimeters of a rectangles, we make use of arithmetic expressions

These arithmetic expressions, when expanded form terms and factors of  expression

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The critical value for this hypothesis test is 1.676.

To test the claim that manufacturing workers in Racine and Kenosha had the same salary as workers across the state, we can conduct a hypothesis test with the following null and alternative hypotheses:

We can use a t-test for the sample mean to test this hypothesis. At a 90% confidence level, we have a significance level of alpha = 0.10. Since this is a two-tailed test (we are testing for a difference in either direction), we will split the significance level evenly between the two tails, so alpha/2 = 0.05.

We need to calculate the critical value of the t-distribution with n-1 degrees of freedom, where n is the sample size. In this case, n = 54, so the degrees of freedom is 53. We can use a t-distribution table or a calculator to find the critical value. For a two-tailed test with alpha/2 = 0.05 and 53 degrees of freedom, the critical value is approximately 1.676.

Therefore, the critical value for this hypothesis test is 1.676.

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The length of segment BC is given as follows:

BC = 47.2 km.

The Law of Cosines is a trigonometric formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is also known as the Cosine Rule.

The Law of Cosines states that for any triangle with sides a, b, and c and angle C opposite to side c, the following equation holds true:

c² = a² + b² - 2ab cos(C)

The parameters for this problem are given as follows:

a = 27.8, b = 24.7, C = 129.1

Hence the length of segment BC is given as follows:

(BC)² = 27.8² + 24.7² - 2 x 27.8 x 24.7 x cosine of 129.1 degrees

(BC)² = 2249.0497

[tex]BC = \sqrt{2249.0497}[/tex]

BC = 47.2 km.

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The bearing of U from T in the image is 32 degrees South by West of T

In mathematics, bearings refer to the direction of an object or location in relation to two points. It is determined by the angle between the line joining them and that of the north.

Measured typically in degrees, it follows a cardinal system where 0° or 360° signifies North; East stands for 90°, South denotes at 180° while West represents 270°.

Thus, it can be seen that the bearing of U from T in the image is 32 degrees South by West of T

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Answer:

u = 2

Step-by-step explanation:

To evaluate the integral ∫(3/(√(x² + 8514))) dx, we can use the substitution u = x² + 8514 and du/dx = 2x, which gives us:

∫(3/(√(x² + 8514))) dx = (3/2)∫(1/√u) du
= (3/2) * 2√u + C
= 3√(x² + 8514) + C

Note that we absorbed the arbitrary constant into C as much as possible.
It seems that your question contains some typos and unclear expressions. However, I can help you evaluate a definite integral that includes fractions and an arbitrary constant.

Consider the integral:

∫(3√(x² + 8514) dx)

To solve this integral, let's perform a substitution:

u = x² + 8514
du = 2x dx

Now, we can rewrite the integral as:

(3/2) ∫(√u du)

Now, we can integrate:

(3/2) ∫(u^(1/2) du) = (3/2) * (2/3) * u^(3/2) + C

Now, substitute u back with the original expression:

(3/2) * (2/3) * (x² + 8514)^(3/2) + C = (x² + 8514)^(3/2) + C

So, the evaluated integral is:

(x^2 + 8514)^(3/2) + C

Where C is the arbitrary constant.

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Answer:

a = 16

b = 8z

Step-by-step explanation:

Expanding the given expression, we get:

(4y + z)^2 = (4y + z) × (4y + z)

= 16y^2 + 8yz + z^2

Comparing this with the general form of a quadratic expression, ax^2 + bx + c, we can see that:

a = 16

b = 8z

Therefore, the value of a is 16 and the value of b is 8z.

The value of the trigonometric expression sin c - cos c is: s - r

The three most common trigonometric ratios are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

We are given that:

sinb = r and cos b = s

Thus, from the diagram attached, we can see that:

sin B = rh/h = r

cos B = sh/h = s

Thus, using trigonometric ratios, we can equally say that:

cos C = rh/h = r

sin C = sh/h = s

Thus:

sin c - cos c = s - r

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