A playground is in the shape of a right triangle with an area of 294 yd^2. The shortest side of the playground (one of the legs) is 21 yds. The city council would like to add a path along the longest side of the playground (the hypotenuse). How long would the path be?

Show your work.
Don't forget to label the answer.

The radius of the cone in terms of x is: r = √(x² + 14x + 49). This can be solved by using volume of cone formula.

Volume of cone (V) = 1/3πr²h, where r is the radius and h is the height of the cone.

Given:

h = 9 in.

V = 3πx² + 42πx + 147π

r = ?

Substitute

3πx² + 42πx + 147π = 1/3(π)(r²)(9)

3π(x² + 14x + 49) = (π)(r²)(3)

Divide both sides by 3π

x² + 14x + 49 = r²

Square on both sides

√(x² + 14x + 49) = r

r = √(x² + 14x + 49)

Therefore, the radius of the cone in terms of x is: r = √(x² + 14x + 49).

To learn more about volume of cone on:

brainly.com/question/13677400

#SPJ1

Answer:

2

Step-by-step explanation:

The seventh root of a number is the number that would have to be multiplied by itself 7 times to get the original number so if you multiply 2 by itself 7 times you'd get 128

The initial value of the investment is denoted by 480 in the function.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

V(t) = 480 [tex](1.065)^t[/tex]

V is the total value after t years.

Now,

480 is constant and it indicates the initial value of the investment.

1.065 indicates that there is an increase of 6.5% each year.

Thus,

480 in the function denotes the initial value of the investment.

Learn more about functions here:

https://brainly.com/question/28533782

#SPJ1

Answer:

Inscribed angle

Step-by-step explanation:

Central angles have the vertex as the center of the circle, and chords are not angles

The value of 350 milliliters to ounce after conversion the unit is equal to  11.8349 ounce.

Formula used to convert milliliters to ounce is written as:

One milliliter is equal to 0.033814 fluid ounce .

Now substitute the value 350 milliliters to convert into ounce we get,

⇒ 350 milliliters = ( 350 ) × (  0.033814 ) fluid ounce

⇒ 350 milliliters = ( 11.8349 ) fluid ounce

Therefore, the converted value of the milliliters to ounce for 350 milliliters is equal to  ( 11.8349 ) fluid ounce.

Learn more about milliliters here

brainly.com/question/22405802

#SPJ4

Usually there are 52 Sundays in a year approximately.

There are a total of 52 weeks in a year if we take a rough estimate.

Every week has one sunday in it. So, going by this logic, each year will have about 52 sundays in it.

Now, one thing that we should notice here is that is not certain that there will be definitely 52 sundays. This number of 52 can increase also by a number of one or two because it is possible that the year might not starting from sunday. Because when we do 365/7 we get 52.14 so, this decimal place might include one or two Sundays in it.

To know more about days in year, visit,

https://brainly.com/question/152631

#SPJ4

The limit definition of the derivative is written as [tex]f '(x) &= \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}[/tex]. Here, h is defined as (x₂ – x₁) or ∆x or the change in x.

The limit definition of the derivative is also known as the difference quotient or increment definition of the derivative.  This is a product of the input value difference, (x + h) - x, and the function value difference, f(x + h) - f(x). This can be calculated using the difference quotient formula as follows,

[tex]\begin{aligned}f '(x) &= \lim_{h \to 0}\;\text{(difference quotient)}\\f '(x) &= \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}\end{aligned}[/tex].

Here, f(x) represents (y₁), f(x+h) represents (y₂), x represents x₁, x+h represents x₂, h represents (x₂ – x₁) or ∆x or the change in x, Lim represents the slope M as h→0, and f (x+h) – f (x) – represents (y₂ – y₁).

This provides a measurement of the function's average rate of change over an interval. In other words, this provides the current rate of change.

To know more about the limit definition of derivative:

https://brainly.com/question/29144258

#SPJ4

Option D. Nominal measurement is used primarily to name or categorical data.

Nominal measurement is one of the four levels of measurement used in statistics, along with ordinal, interval, and ratio measurement. Nominal data are qualitative or categorical data that can be assigned to discrete categories based on some characteristic or attribute, such as color, gender, or species. Nominal data do not have a natural ordering, so they cannot be ranked or ordered based on magnitude or size.

Nominal measurement is a type of measurement in which data are named or categorized based on some characteristic or attribute. Nominal data are typically qualitative or categorical in nature, meaning that they are not numerical in value. Examples of nominal data include gender, race, religion, color, or type of animal.

To learn more about Nominal measurement please click on below link.

https://brainly.com/question/27593777

#SPJ4

Answer:2/8 + 2/8

Step-by-step explanation:

so, you start at 2/8

then, you add the extra 2/8

then, you add them together ( don’t forget: when the bottom numbers of the fraction are the same the stay at the same number ex: 3/8 + 3/8 = 6/8)

then after adding them up you get 4/8 which could also mean 1/2

The integral for the mass of a thin wire in the shape of a parabola density is [tex]\int[-1,1]\int[0,x^2] x^2 y^2 dy dx[/tex]

To find the mass of the thin wire in the shape of a parabola with density function ρ(x, y) = [tex]x^2 y^2[/tex],

we can set up a double integral over the region that describes the parabola. The mass M is given by the following integral:

M = ∬ρ(x,y) dA

where dA represents the area element in the xy-plane. To set up this integral, we need to first determine the limits of integration for x and y.

The parabola can be described by the equation y =[tex]x^2[/tex], where x ranges from -1 to 1. Therefore, the limits of integration for x are -1 to 1.

For each value of x, the y-values range from the parabola to the x-axis, which is the region between y = 0 and y = [tex]x^2[/tex]. Therefore, the limits of integration for y are 0 to[tex]x^2[/tex].

Using these limits of integration, the integral for the mass of the thin wire is:

M = ∫∫ρ(x,y) dA

=[tex]\int[-1,1]\int[0,x^2] x^2 y^2 dy dx[/tex]

This integral can be evaluated using standard integration techniques.

To learn more about  Parabola density :

https://brainly.com/question/15089285

#SPJ4

The original price of the article without the discount is %60.

Discount is the state of having a bond's price lower than its face value. The difference between the purchase price and the item's par value is the discount.

Discounts are different types of price reductions or deductions from a product's cost. It is frequently employed in consumer transactions when consumers receive discounts on a range of goods.

Let us suppose original price = x.

Given that, after a discount, the marked price of an article is 48$ and the discount is 20%.

Thus,

48 = x(1 - 20/100)

48 = x(80/100)

x = 60

Hence, the original price of the article without the discount is %60.

Learn more about percentage here:

https://brainly.com/question/14695543

#SPJ1

Answer:

Ms. Perry needs to make an additional 1/24 kg of fudge.

Step-by-step explanation:

Ms. Perry has a total of 8/8 + 1/6 = 13/6 kg of fudge. She needs 1 1/8 kg of fudge for the brownies, which is equivalent to 9/8 kg. To find how much more fudge she needs to make, we can subtract the amount of fudge she already has from the amount she needs:

9/8 - 13/6 = 27/24 - 26/24 = 1/24

Therefore, Ms. Perry needs to make an additional 1/24 kg of fudge.

Answer:

0.06

Step-by-step explanation:

Identify the probability to the nearest hundredth that a point chosen randomly inside the rectangle either is in the hexagon or in the circle

Area of rectangle = 26.2 * 13 =  340.6 sq inch

Area of Hexagon  = 3√3(side)²/2 = 3√3 (1.8)²/2 = 8.42 sq inch

Area of circle = π(radius)² = 3.14 * (2)² = 12.56 sq inch

Area of hexagon + area of circle = 12.56 + 8.42 = 20.98 sq inch

Probability of selecting point inside the hexagon or in the circle  = 20.98/340.6

= 0.06

The conversion of 64kg in pounds  is equivalent to approximately 141.09568 pounds.

The kilogram (kg) is the SI unit of mass. It is equal to the mass of the international prototype of the kilogram. This prototype is a platinum-iridium international prototype kept at the International Bureau of Weights and Measures. One kg is approximately equal to 2.20462262184878 pounds.One pound, the international avoirdupois pound, is legally defined as exactly 0.45359237 kilograms.

To convert 64 kilograms to pounds, you can use the conversion factor of 1 kilogram = 2.20462 pounds.

Therefore,64 kilograms = 64 x 2.20462 pounds

= 141.09568 pounds (rounded to 5 decimal places)

So, 64 kilograms is equivalent to approximately 141.09568 pounds.

For such questions on conversion,

https://brainly.com/question/30775068

#SPJ4.

20 centimeter is approximately equal to 7.8740 inches ( rounded to four decimal places )

To convert 20 cm to inches, we can use the following formula:

1 cm = 0.393701 inches

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

Therefore,

The length in inches = conversion factor × The length in centimeter

Substitute the values in the equation

20 cm = 20 x 0.393701

Multiply the numbers

= 7.8740 inches ( rounded to four decimal places )

Therefore, 20 centimeter is 7.8740 inches

Learn more about conversion factor here

brainly.com/question/5056146

#SPJ4

A continuous variable is a variable that can take on any value within a certain range, and often takes the form of real numbers but a discrete variable is a variable that can only take on specific values within a certain range, and often takes the form of integers

Continuous and discrete variables are two types of quantitative variables in statistics.

A continuous variable is a variable that can take on any value within a certain range, and often takes the form of real numbers. Examples of continuous variables include height, weight, time, temperature, and distance. These variables can be measured using instruments with varying degrees of precision, but they can theoretically take on an infinite number of values.

On the other hand, a discrete variable is a variable that can only take on specific values within a certain range, and often takes the form of integers. Examples of discrete variables include the number of siblings a person has, the number of cars in a parking lot, and the number of points a basketball team scores in a game. These variables can only take on a limited number of values, and often represent counts or whole numbers.

The main difference between continuous and discrete variables is the way they can be measured and the number of possible values they can take. Continuous variables can take on an infinite number of values and can be measured with varying degrees of precision, while discrete variables can only take on specific values and are often measured with exact precision.

Learn more about discrete variable here

brainly.com/question/13339063

#SPJ4

If the  fruit seller threw some rotten apples away and the ratio of apples to oranges became 1 : 4. The fruit seller threw away 630 rotten apples.

To find the number of rotten apples that the fruit seller threw away, we will need to use the given information and set up equations to solve for the unknown variable.

Let's start by using the given information that there were 2/3 as many apples as oranges. We can set up an equation to represent this relationship:

2/3 O = A

Where O is the number of oranges and A is the number of apples.

We are also given that the fruit seller had 2520 apples and oranges in total. We can set up another equation to represent this relationship:

O + A = 2520

Now, we can use the first equation to solve for one of the variables in terms of the other. Let's solve for A in terms of O:

A = (2/3)O

Now we can substitute this expression for A into the second equation:

O + (2/3)O = 2520

Simplifying this equation gives us:

(5/3)O = 2520

Now we can solve for O:

O = (3/5)(2520) = 1512

Now that we know the number of oranges, we can use the first equation to solve for the number of apples:

A = (2/3)(1512) = 1008

So the fruit seller originally had 1008 apples and 1512 oranges.

We are also given that after throwing away some rotten apples, the ratio of apples to oranges became 1:4. We can set up an equation to represent this relationship:

(A - X)/O = 1/4

Where X is the number of rotten apples that were thrown away.

Substituting the values we found for A and O into this equation gives us:

(1008 - X)/1512 = 1/4

Cross-multiplying and simplifying gives us:

4(1008 - X) = 1512

4032 - 4X = 1512

4X = 2520

X = 630


Therefore, the answer to the question is 630.

Learn more about ratio here:

https://brainly.com/question/26460724

#SPJ11

Answer:

[tex]a = \frac{5 \sqrt{2} }{2} [/tex]

[tex]c = \frac{3 \sqrt{3} }{2} [/tex]

Step-by-step explanation:

The first triangle is an isoceles right triangle, so the length of the hypotenuse is √2 times the length of each leg. So we have:

[tex]a \sqrt{2} = 5[/tex]

[tex]a = \frac{5}{ \sqrt{2} } = \frac{5 \sqrt{2} }{2} [/tex]

The second right triangle is a 30°-60°-90° triangle, so the length of the shorter leg is one-half the length of the hypotenuse, and the length of the longer leg is √3 times the length of the shorter leg. Here, the length of the shorter leg is 3/2, or 1.5, and so we have:

[tex] {( \frac{3}{2}) }^{2} + {c}^{2} = {3}^{2} [/tex]

[tex] {c}^{2} = \frac{27}{4} [/tex]

[tex]c = \frac{3 \sqrt{3} }{2} [/tex]

Answer:

Step-by-step explanation:

Decimals are out of 100.

7/10 = 70/100

Which equals to 0.70 or 0.7

So your answer is 0.70 (0.7)

Answer:

The exact decimal equivalent of 7/10 is 0.7

Step-by-step explanation:

The reason for this is because when you divide something by ten you move the decimal place one place to the left.

So then 7.0 becomes 0.7 because the decimal place is moved once divided by ten.

The solution is found by slope of the graph and the solution is 2,200.

Let x the amount of money per hour and y the total amount of money.

Studio A:-

Rents for 100 dollars plus 50 dollars per hour.

[tex]y= 100 + 50x[/tex]

So the slope is 50 and the y intercept is 100.

Studio B:-

rents for 50 dollars plus 75 dollars per hour.

[tex]y= 50 + 75x[/tex]

So the slope is 75 and the y intercept is 50.

ThrTh solution is 2200 , see the gragraphph.

To know more about Slope of graph go through:-

https://brainly.com/question/3493733

#SPJ4

Complete question:- You and your friends decide to rent some studio time to make a CD. Big Notes Studio rents for $100 plus $50 per hour. Great Sounds Studio rents for $50 plus $75 per hour. Solve the system by graphic method.

The required, measure of QK is approximately 10.82.

In a right-angled triangle, its sides, such as hypotenuse, perpendicular, and the base is Pythagorean triplets.

First, we can use the Pythagorean theorem to find the length of side XZ:

[tex]XZ^2 = XY^2 - YZ^2[/tex]

[tex]YZ = \sqrt{(XY^2 - XZ^2) }[/tex]
[tex]= \sqrt(24^2 - 22^2) = 10[/tex]

The length of the perpendicular bisector of XY is half the distance between points A and the midpoint of XY. The midpoint of XY can be found by dividing the length of XY by 2:

midpoint of XY = (X + Y)/2

Since we are given the length of XY, we can find the coordinates of its endpoints X and Y. Let X be the origin (0,0) and let Y have coordinates (24,0) (since XY = 24). Then the midpoint of XY is the midpoint of XY
= (X + Y)/2
= (0 + 24)/2
= (12,0)

Now we can use the distance formula to find the distance between A and the midpoint of XY distance between A and the midpoint of XY
= [tex]= \sqrt((12 - 0)^2 + (0 - 15)^2)[/tex]
= [tex]\sqrt(12^2 + 15^2)[/tex]
=[tex]3 \sqrt(29)[/tex]

This is the length of the perpendicular bisector of XY, which passes through the center of the circumscribed circle. So the distance from Q to the center of the circle is the distance from Q to center = 15 - 9 = 6

Finally, we can use the Pythagorean theorem to find QK:

[tex]QK^2 = QJ^2 + JK^2 = QJ^2 + (distance \ from \ Q \ to\ center)^2[/tex]

[tex]QK^2 = 9^2 + 6^2 = 81 + 36 = 117[/tex]

[tex]QK = \sqrt(117)\\ = 10.82[/tex]

Therefore, QK is approximately 10.82.

Learn  more about Pythagorean triplets here:

brainly.com/question/22160915

#SPJ1

The mean of the data is 16.5 and the standard deviation is 7.28

The given data set is a small sample of 12 observations.

To determine the type of distribution, we can first create a histogram or a boxplot of the data.

A histogram of the data shows that the distribution is unimodal and slightly right-skewed.

Alternatively, we can calculate the skewness of the data. If the skewness is close to zero, then the data is approximately symmetric. If the skewness is positive, then the data is right-skewed. If the skewness is negative, then the data is left-skewed.

Calculating the skewness of the data set, we get:

skewness = (n / ((n - 1) * (n - 2))) * Sum[(xi - x-bar)^3 / s^3]

where n is the sample size, x-bar is the sample mean, s is the sample standard deviation, and Sum is the sum of the values in the data set.

Using this formula, we get a skewness of approximately 0.456, which indicates that the distribution is slightly right-skewed.

Based on these findings, we can conclude that the distribution of the data set is approximately normal, but slightly right-skewed.

To find the best measure of center and spread, we can calculate the sample mean and sample standard deviation, respectively.

Sample mean:

mean = (1 + 7 + 11 + 14 + 17 + 17 + 17 + 21 + 21 + 23 + 23 + 26) / 12 = 16.5

Sample standard deviation:

s = sqrt((1/11) * [(1 - 16.5)^2 + (7 - 16.5)^2 + ... + (26 - 16.5)^2]) = 7.28

Therefore, the best measure of center for this data set is the sample mean of 16.5, and the best measure of spread is the sample standard deviation of 7.28.

Learn more on mean here;

https://brainly.com/question/14532771

#SPJ1

a) 30 minutes are taken to have the same amount of water.

b) Both pools have an amount of 1372.5 liters when 30 minutes have passed.

A linear function is one that produces a straight line when plotted. Generally, it is a polynomial function with a maximum degree of 1 or 0. 

Now in the given question ,

a) Physically speaking, the capacity (Q) of each pool, in liters, is equal to the product of flow rate , in liters per minute, and time (t), in minutes. Hence, we derive the following functions :

First pool,

[tex]Q_1=915+15.25t\\[/tex]           ...... (1)

Second pool,

[tex]Q_2=45.75t[/tex]                   ....... (2)

The following expression can be used to calculate how long it will take to find two pools with the same amount of water:

[tex]Q_1=Q_2[/tex]                       ........ (3)

By putting value of (1) and (2) in (3),

915 + 15.25 t = 45.75 t

30.5 t = 915

t = 915 ÷ 30.5

t = 30 minutes

30 minutes are taken to have the same amount of water.

b) By (2) and knowing that t = 30 , then we have the corresponding amount:

[tex]Q_2=45.75t\\\\Q_2=45.75*30\\\\Q_2=1372.5L[/tex]

Both pools have an amount of 1372.5 liters when 30 minutes have passed.

To learn more on linear functions, visit:

brainly.com/question/14165558

#SPJ1

Answer:

1 Microliter = 0.001 Milliliter

Step-by-step explanation:

A unit can be used for measurement, and is commonly found in mathematics to describe length, size, etc.

Converting these units:

Therefore, for every 1 microliter it is equivalent to 0.001 Milliliter.

Answer:

110

Step-by-step explanation:

The volume of the rectangular prism in the image is 480 cubic units.

What is volume ?

Volume is a measurement of the amount of space occupied by a three-dimensional object. It is a physical quantity that is measured in cubic units such as cubic meters (m³), cubic centimeters (cm³), or cubic feet (ft³).

The image shows a rectangular prism with a length of 12 units, a width of 8 units, and a height of 5 units.

To find the volume of a rectangular prism, you need to multiply its length, width, and height.

So, the volume of the rectangular prism in the image is:

Volume = length x width x height

Volume = 12 units x 8 units x 5 units

Volume = 480 cubic units

Therefore, the volume of the rectangular prism in the image is 480 cubic units.

To learn more about Volume from given link.

https://brainly.com/question/1578538

#SPJ1

Answer:

[tex](u \circ \; w)(2) = \boxed{7}[/tex]

[tex](w \circ \;u)(2) = \boxed{3}[/tex]

Step-by-step explanation:

We have the two functions as

[tex]u(x) = x^2 + 3\\\\w(x) = \sqrt{x + 2}[/tex]

[tex](u \circ w)(x)[/tex] also written as [tex]u(w(x))[/tex]  is the composite function;  it means that
[tex]x = w(x)[/tex] should be substituted in [tex]u(x)[/tex]

To determine [tex](u \circ w)(x)[/tex], simply substitute the expression for [tex]w(x)[/tex] wherever there is an x in [tex]u(x)[/tex]

For a specific value of x, in this case x = 2,

Part 1
[tex](u \circ w)(2):\\\\w(2) = \sqrt{2 + 2} = 4(u \circ w)(2) = 2^2 + 3 = 4 + 3 = 7[/tex]

For [tex](w \circ u)(x),[/tex] we substitute the expression for [tex]u(x)[/tex] into [tex]w(x)[/tex] wherever an [tex]x[/tex] appears in [tex]w(x)[/tex]

For a specific value of x, say 2, find the value of u(2) and substitute it into [tex]w(x)[/tex]

[tex]u(2) = 2^2 + 3 = 7[/tex]

[tex](w \circ u)(2), = \sqrt{7 + 2} = \sqrt{9} = 3\\[/tex]

Answer:

$129,870.13 AUD

Step-by-step explanation:

To find out what we need to solve, we can use these exchange rates:

Now, we need to divide 100,000 by 0.77.

We do this because we need to figure out how many times 0.77 must be multiplied to get 100,000. Then, we take that amount, and multiply that by however many AUD's you have.

Therefore, for every $100,000 USD, there is $129,870.13 AUD.

The distance between two cities are 7000 miles apart.

What is distance ?

Distance is the amount of space between two points or objects. In the context of the question you asked earlier, "distance between two cities" refers to the actual physical distance between the two cities in terms of miles.

Given by the question:
On the map, 500 miles is represented by each 0.5 inches. Therefore, 1 inch represents 1000 miles.

So, the distance between the two cities on the map is 7 inches. This corresponds to a real-world distance of:

distance on map / scale on map = actual distance

7 inches * 1000 miles/inch = 7000 miles

Therefore, the two cities are 7000 miles apart.

To know more about Distance visit:
https://brainly.com/question/15256256
#SPJ1