A landscape architect is designing a pool that has this top view. How much water will be needed to fill this pool 4 feet deep?​

The radius of this circle with center (8, 2) is equal to 6.71 units.

In Mathematics and Geometry, the distance between two (2) points that are on a coordinate plane can be calculated by using the following mathematical equation:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

By substituting the given points into the distance formula, the radius of this circle can be calculated as follows;

Distance = √[(14 - 8)² + (-1 - 2)²]

Distance = √[(6)² + (-3)²]

Distance = √[36 + 9]

Distance = √45

Distance = 6.71 units.

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Complete Question:

What is the radius of the circle with Center: (8, 2), Point on Circle: (14,-1)? 2 decimal places

Answer:

The product of -6 is not a well-formed question. A product refers to the result of multiplying two or more numbers together, but there is no other number specified in the question. If you provide more information or context, I would be happy to assist you.

Step-by-step explanation:

The amount of fudge the student gives to her sister, which is (1/2) of her remaining fudge, calculated using fractions is 16 ounces

A fraction is a representation of a part of a whole, by setting the quantity representing the part as the numerator and the quantity representing the whole as the denominator with both quantities separated by the fraction bar.

Part of the question obtained from a similar question posted online can be presented as follows;

The amount of fudge the student has = 3 pounds

The amount of fudge the student eats = 1 pound of the fudge

Required; The amount of fudge the student has left

The amount of fudge the student has left = 3 - 1 = 2 pounds

The fraction of the remaining fudge the student gives to her sister = (1/2)

Therefore;

The amount of fudge the student gives her sister = (1/2) × 2 pounds = 1 pound

1 pound = 16 ounces

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a)Traveled 0.3 miles in 1 hour.

b) The fraction representation is 3/10 miles per hour.

a) To find out how many miles the person traveled in 1 hour, we need to divide the distance traveled by the time taken.

Distance traveled = 1/5 miles

Time taken = 3/2 hours

To make it easier to divide, we can convert the time taken to a fraction with a common denominator of 10:

3/2 = 15/10

Now we can divide the distance by the time:

1/5 ÷ 15/10 = 1/5 x 10/15 = 2/15

This tells us that the person traveled 2/15 miles in one-tenth of an hour (i.e., 6 minutes).

To find out how many miles per hour they traveled, we can convert the fraction to a rate by multiplying it by the reciprocal of the time fraction (i.e., 10/3):

2/15 x 10/3 = 2/9

Therefore, the person traveled 2/9 miles per hour.

b) To write this as a model fraction representation, we can express it as a single fraction:

2/9 = 3/10 (rounded to the nearest tenth)

So the person traveled at a rate of 3/10 miles per hour.

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The proportion of eligible voters who would support the businesswoman is less than or equal to 0.6, and the proportion of eligible voters who would support the businesswoman is greater than 0.6.

In statistics, a hypothesis is a statement or assumption about a population parameter that is being tested for its truthfulness based on sample data. It is a tentative explanation for an observation or phenomenon and is used to make predictions about the outcome of an experiment or study. Hypotheses can be either null hypotheses, which state that there is no significant difference or relationship between variables, or alternative hypotheses, which propose that there is a significant difference or relationship.

(a) The hypotheses that the businesswoman should test are:

H0: The proportion of eligible voters who would support the businesswoman is less than or equal to 0.6.

Ha: The proportion of eligible voters who would support the businesswoman is greater than 0.6.

(b) The p-value is greater than the significance level of 0.05, which suggests that the results are not statistically significant. Therefore, the businesswoman should not run for office. There is not enough evidence she has enough supporters.

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We number of bags is 10 bags of fertilizer to complete the job.

Algebra is a branch of mathematics that deals with the study of mathematical symbols and their manipulation. It involves the use of letters, symbols, and equations to represent and solve mathematical problems.

In algebra, we use letters and symbols to represent unknown quantities and then use mathematical operations such as addition, subtraction, multiplication, division, and exponentiation to manipulate those quantities and solve equations. We can use algebra to model and solve real-world problems in various fields such as science, engineering, economics, and finance.

The total area of the football field is:

360 feet × 160 feet = 57,600 square feet

To find out how many bags of fertilizer are needed, we need to calculate how many 1000-square-foot areas there are on the field:

57,600 square feet ÷ 1000 square feet/area = 57.6 areas

So there are 57.6 areas on the football field.

We need 8 pounds of fertilizer per 1000 square feet, so to find out how many pounds we need for the whole field, we can multiply by the number of areas:

8 pounds/1000 square feet × 57.6 areas = 460.8 pounds

Therefore, we need 460.8 pounds of fertilizer to cover the football field.

Since the fertilizer comes in 50-pound bags, we can divide the total amount of fertilizer needed by 50 to find out how many bags we need:

460.8 pounds ÷ 50 pounds/bag ≈ 9.22 bags

We can't buy a fraction of a bag, so we need to round up to the nearest whole bag. Therefore, we need 10 bags of fertilizer to complete the job.

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The complete question is:

You are applying fertilizer to a football field. The field is 360 feet long and 160 feet wide. You use 8 pounds of fertilizer per 1000 square feet. The fertilizer comes in 50- pound bags. How many bags of fertilizer will you need to complete this job?

Answer: Area=3.125 square feet

Step-by-step explanation:

2.5x2.5=6.25

6.25/2= 3.125

Answer:

A = 50 ft²

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

given that 1 inch equals 4 feet , then

b = 2.5 in = 2.5 × 4 feet = 10 feet

h = 2.5 in = 2.5 × 4 feet = 10 feet

then

A = [tex]\frac{1}{2}[/tex] × 10 × 10 = 5 × 10 = 50 ft²

Answer: ∠EGF and/or ∠CGB

Step-by-step explanation:

Starting Angle: ∠CGE

Possible Supplements: ∠EGF and ∠CGB

the greatest common factor of 72 and 96 is 24

The company would incur a loss of $14,800,000 if it spends an additional $200,000 on advertising to achieve sales of 35,000 units.

Sales generally refer to the total amount of goods or services that a business sells during a given period of time, typically measured in monetary terms. Sales can also refer to the process of selling products or services, including activities such as prospecting, lead generation, sales presentations, and closing deals.

To calculate the operating profit with sales of 35,000 units and an additional selling expense of $200,000, we need to first calculate the total revenue and the total cost, and then subtract the total cost from the total revenue.

From the table provided, we can see that the selling price per unit is $900 and the variable cost per unit is $600. Therefore, the contribution margin per unit is:

Contribution margin per unit = Selling price per unit - Variable cost per unit

= $900 - $600

= $300

Since the sales target is 35,000 units, the total contribution margin is:

Total contribution margin = Contribution margin per unit x Number of units sold

= $300 x 35,000

= $10,500,000

The total cost can be calculated as follows:

Total cost = Fixed cost + Variable cost

= $3,500,000 + ($600 x 35,000)

= $25,100,000

Adding the additional selling expense of $200,000, the new total cost becomes:

New total cost = $25,100,000 + $200,000

= $25,300,000

Therefore, the operating profit with sales of 35,000 units and an additional selling expense of $200,000 is:

Operating profit = Total revenue - Total cost

= ($900 x 35,000) - $25,300,000

= $10,500,000 - $25,300,000

= -$14,800,000

This indicates that the company would incur a loss of $14,800,000 if it spends an additional $200,000 on advertising to achieve sales of 35,000 units.

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Doppler Effect happens when there is shift in frequency during a realtive motion between a source and the observer of that source.

It can be calculated as:

[tex]f_o=f_s\huge \text(\dfrac{c+v_o}{c+v_s}\huge \text )[/tex]

where:

c is the speed of light (c = 332m/s)

all the subscripted s is related to the Source (frequency, velocity);

all the subscripted o is related to the Observer (frequency, velocity);

As the source is moving towards the observer and the observer is moving towards the source, the velocities of each are opposite related to direction.

So, the frequency perceived by the observer:

[tex]f_o=460\huge \text(\dfrac{332+32}{332-40}\huge \text)[/tex]

[tex]f_o=460\huge \text(\dfrac{364}{292}\huge \text)[/tex]

[tex]f_o=460(1.247)[/tex]

[tex]f_o= 573.6 \ \text{Hz}[/tex]

At this condition, the observer hears the train's horn in a perceived frequency of 573.6 Hz

Answer:

The perceived frequency of sound is the amount of sound wave that pass a point in a given amount of time

The perceived frequency you hear is

370.9 Hertz

The function is given as:

[tex]f_{o}=\frac{c+V_{o} }{c-V_{o} }[/tex] x  [tex]f_{s}[/tex]

From the question

[tex]c=332[/tex] --- speed of the sound

[tex]V_{o} =32[/tex] ---current speed of the train

[tex]V_{s} = 40[/tex] --- speed of the opposite train

[tex]f_{s} =460[/tex] --- frequency of the sound wave

This gives:

[tex]f_{o}= \frac{332-32}{332+40}[/tex]  ×[tex]460[/tex]

[tex]f_{o}= \frac{300}{372} x460[/tex]

Rewrite as:

[tex]f_{o}= \frac{300x460}{372}[/tex]

[tex]f_{o}= 370.9[/tex]

Answer:

hope this might help you!!

Answer:

a

Step-by-step explanation:

Answer:

Step-by-step explanation:

y=2 and x=0 making it (0,2)

As a result, the item's final price is $53.50 and the sales tax is $3.50.

The government levies a consumption tax known as sales tax on the purchase of goods and services. The seller often calculates it as a percentage of the purchase price and collects it. After then, the vendor transfers it to the government .. The funding of government services and programmers comes from sales tax

We can multiply the item's price by the applicable sales tax rate to determine the sales tax:

Price of Item  x   Sales Tax Rate equals Sales Tax

Sales Tax: $50.00 x 7% = $3.50

We can multiply the item's price by the applicable sales tax to determine the entire cost of the purchase, including tax:

Price of Item + Sales Tax = Total Cost

$50.00 plus $3.50 equals $53.50 as a total

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1.

f'(x) = 8 · x^(8-1) = 8·x^7

2.

g'(x) = -4· 4·x^(4-1) = -16·x^3

3.

h(x) = 1/x^5 = x^(-5), so

h'(x) = -5·x^(-5-1) = -5·x^(-6) or -5 / x^6

The surface area of this cylinder is 942 millimeter square

The formula for the surface area of a cylinder is expressed as;

SA = 2πr h + 2πr²

Given that the parameters are identified as;

From the information given, we have that;

Surface area = 2 × 3.14 × 10 × 5  + 2× 3.14 × 10²

Find the square values

Surface area = 2 × 3.14 × 10 × 5  + 2× 3.14 × 100

Multiply the values

Surface area = 314 + 628

Now, add the values

Surface area = 942 mm²

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Step-by-step explanation:

This function has two pieces, each of which is the absolute value of a linear expression. We need to consider the function separately for different ranges of x.

When -5 < x < 0, then x + 5 is negative and x - 5 is also negative. Therefore, we have:

y = -(x - 5) - (x + 5) = -2x

When 0 ≤ x < 5, then x + 5 is positive and x - 5 is negative. Therefore, we have:

y = (x - 5) + (x + 5) = 2x

So the function y = |x - 5| + |x + 5| can be written as:

y =

-2x if -5 < x < 0

2x if 0 ≤ x < 5

Notice that the function is not defined for x ≤ -5 or x ≥ 5.

Answer:

Step-by-step explanation:

Given a graph of muffins versus cups of flour, you want to know the constant of proportionality and the equation relating muffins (m) and cups (c).

The slope of the line on the graph is easily found by looking at the "muffins" (y) value for "cups" (x) equal to 1. That point is (c, m) = (1, 4).

The line goes through the origin (0, 0), so the slope is the ratio of y to x.

  m = y/x = 4/1 = 4

This is the constant of proportionality.

The constant of proportionality is 4, choice A.

The equation of a proportional relationship is ...

  y = kx . . . . . . where k is the constant of proportionality

Here, the independent variable (horizontal axis) is "cups", represented by 'c'. The dependent variable is "muffins", represented by 'm'. Using the above constant of proportionality, the equation is ...

  m = 4c . . . . . choice D

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The values of x are the two expressions equal to All real numbers except 2.

We are given that rational expression has been simplified below.

(x+4)(x-2)x+4

9(x-2)

WE know that X=4/9 is simplified, but we can simplify the other side by canceling out the (x-2) in the numerator and denominator.

The expression should be;

(x + 4)(x - 2)/9(x - 2)= (x + 4)/9.

After simplification by (x - 2) , the remainder will be;

(x + 4)/9.

When x = -4,  both sides equal to zero.

When x = 0 , both sides equal to 4/9

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Measure of ∠ADB  is 240 degrees,  the area of the shaded region is 42.67π m² and arc length ADB  is 10.67π m

Given that the circle has a center O.

The radius of the circle is 8 m.

The measure of ∠AOB is 120°

We need to determine the area of the shaded region and the length of the arc ADB.

The measure of ∠ADB is given by

∠ADB = 360 - ∠AOB

= 360 - 120

=240 degrees

The area of the shaded region can be determined using the formula,

A = (θ/360) πr²

A = (θ/360) ×3.14× 8²

A = 42.67 m²

Thus, the area of the shaded region is 42.67π m²

The length of arc ADB can be determined using the formula,

Arc length =  (θ/360) 2πr

=10.67π m

Hence,  measure of ∠ADB  is 240 degrees,  the area of the shaded region is 42.67π m² and  length of arc ADB  is 10.67π m

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The estimated number of quarts of blood the individual with the given weight will have would be = 2.7 quarts.

The body weight of the first individual = 200 pounds

The volume of blood = 6 quarts.

Therefore a person of 90 pounds = X quarts.

That is;

200 pounds = 6 quarts

90 pounds = X quarts

make X quarts the subject of formula;

X = 90×6/200

= 540/200

= 2.7 quarts

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When 14,277s is converted to hr, min and hr, it gives 3 hours, 57 minutes, 7 seconds.

Conversion is the process of changing the value of one form to another. It is also the conversion between different units of measurement for the same quantity.

How to determine this

When 60 seconds makes 1 minute

60 minutes makes 1 hour

14,277 seconds to minutes

When 60 seconds = 1 minute

14,277 seconds = x

x = 14,277/60 minutes

x = 237 minutes 7 seconds

By converting 237 minutes to hour

When 60 minutes = 1 hour

237 minutes = x

x = 237/60 hours

x = 3 hours 57 minutes.

Therefore, the conversion is 3 hours 57 minutes 7 seconds

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Okay, here are the steps to solve this:

* The recipe calls for 1 teaspoon of cinnamon for every 4 cups of granola mix.

* We are making 12 cups of granola.

* So to make 12 cups, we need 12 / 4 = 3 times as much cinnamon.

* Since each 4 cups uses 1 teaspoon, 12 cups will need 3 teaspoons.

Therefore, for 12 cups of granola mix, the recipe will call for 3 teaspoons of cinnamon.

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Step-by-step explanation:

We have the triple integral:

∫∫∫E x^2 + y^2 + z^2 dV

where E is the ball x^2 + y^2 + z^2 ≤ 81.

In spherical coordinates, the volume element is given by:

dV = ρ^2 sin φ dρ dθ dφ

where ρ is the radial distance, φ is the polar angle (measured from the positive z-axis), and θ is the azimuthal angle (measured from the positive x-axis).

Substituting into the integral, we get:

∫φ=0 to φ=π ∫θ=0 to θ=2π ∫ρ=0 to ρ=9 ρ^2 sin φ (ρ^2) dρ dθ dφ

= ∫φ=0 to φ=π ∫θ=0 to θ=2π ∫ρ=0 to ρ=9 ρ^4 sin φ dρ dθ dφ

= ∫φ=0 to φ=π ∫θ=0 to θ=2π (1/5)(9^5) sin φ dθ dφ

= (2π/5)(9^5)(-cos φ)|φ=0 to φ=π

= (2π/5)(9^5)(-(-1 - 1))

= (4π/5)(9^5)

≈ 114413.73

Therefore, the value of the triple integral is approximately 114413.73.

Okay, let's evaluate each modeling equation candidate based on the r^2 value:

a. y=16.5839•1.0185^x

No r^2 value given, so cannot determine if this is the best fit.

b. y=0.985515x-2.81333

No r^2 value given for this linear model, so cannot determine if it is the best fit.

c. y=-0.0000758936x^3+0.0143444x^2+0.207549x+7.70667

This is a 3rd order polynomial model, but no r^2 is given, so cannot determine if it is the best fit.

d. y=0.00182197x^2+0.785098x+1.195

If this model has the highest r^2 value, it would be the best fit.

Based on the information provided, the only option that could potentially be the best fit is choice d, the quadratic model y=0.00182197x^2+0.785098x+1.195, if it has the highest r^2 value. But without the actual r^2 values for each model, a definitive determination cannot be made.

Does this help explain the approach? Let me know if you have any other questions!

A​ T-shirt is launched with an initial upward velocity of 78 feet per second, the T-shirt will reach its maximum height in approximately 2.44 seconds.

The height of the T-shirt is given by the function h(t) = -16t^2 + 78t + 5, where h is the height in feet and t is the time in seconds.

To find the time it takes for the T-shirt to reach its maximum height, we need to find the vertex of the parabolic function.

The vertex occurs at the time t = -b/2a, where a = -16 and b = 78 are the coefficients of the quadratic function.

t = -b/2a = -78/(2*(-16)) = 2.4375

Therefore, the T-shirt will reach its maximum height in approximately 2.44 seconds.

To find the maximum height, we substitute this value of t into the equation for h:

h(2.4375) = -16(2.4375)^2 + 78(2.4375) + 5 ≈ 97.19 feet

Therefore, the maximum height of the T-shirt is approximately 97.19 feet.

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