Two-third of Leon's tropical fish in his tank is equal to one-fourth of harry's tropical fish in his tank Find the ratio of the no. Of Leon's tropical fish to the no. Of harry's tropical fish What fraction of the number of harry's tropical fish is the number of Leon's tropical fish

Area = side squared

625 = side squared

side = sqrt 625

side = 25 m

perimeter = 4 x side

perimeter = 100 m

Answer:

100 meters

Step-by-step explanation:

In order to calculate the perimeter, we must have the side length.

The area of a square can be found using the following formula.

\(a=s^2\)

We know the area is 625 square meters. We can substitute 625 m² in for a.

\(625 m^2=s^2\)

We want to find the side length, s. Therefore, we must isolate s. s is being squared. The inverse of a square is a square root. Take the square root of both sides of the equation.

\(\sqrt{625m^2}=\sqrt{s^2}\)

\(\sqrt{625m^2}=s\)

\(25 m=s\)

The perimeter of the square can be found using the following formula.

\(p=4s\)

We know the side length is 25 meters. We can substitute 25 m in for s.

\(p =4*25m\)

Multiply.

\(p=100m\)

The perimeter of the field is 100 meters.

Answer:

3/4

Step-by-step explanation:

Thus, the explicit formula for the simple interest sequence A(n) = P + (n-1)(i.P) is: A(n) = P * (1 + i * (n-1)).

Simple interest is a method of calculating interest on a loan or investment where interest is charged only on the initial principal amount. In simple interest, the interest rate is applied to the original principal amount, and the interest earned remains the same throughout the entire term of the loan or investment.

by the question.

The formula for a simple interest sequence A(n) = P + (n-1) (i.P) represents the value of an investment that earns simple interest over n periods, where:

A(n) is the value of the investment after n periods.

P is the principal or initial investment

i is the interest rate per period as a decimal fraction (e.g. 0.05 for 5%)

n is the number of periods

To derive the explicit formula for A(n), we can use the formula for simple interest:

I = P * i * n

where I am the total interest earned over n periods. We can then express A(n) as:

A(n) = P + I

Substituting the expression for I, we get:

A(n) = P + P * i * (n-1)

Simplifying, we can factor out P to get:

A(n) = P * (1 + i * (n-1))

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Answer:

it is 80°

cause it is coming from the same cord AB

O and C will be same

Answer:

x = 40

Step-by-step explanation:

x = 80÷2 = 40

Central angle theorem

Part a: margin of error = 1.93.

Part b: confidence interval is (19.59, 23.45)

Part a: margin of error,

The sample size is 64 customers, the population standard deviation is 6, and the confidence level is 99%.

Mean sample = 21.52

Sample size = 64

Confidence level = 99%

Standard deviation = 6

Standard error of mean= 0.75

Z-value= -2.5758 (Taken from Z table)

Interval half width = 1.9319

The output has a margin of error of 1.93 at 99% confidence.

Part b: mean amount spent for lunch.

Interval upper limit= 19.59

Interval lower limit= 23.45

99% confidence interval is (19.59, 23.45) from the output.

Mean amount = 23.45 + 19.59 / 2

Mean amount = 1.93

Thus, the mean amount spent on lunch is 1.93.

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The compete question is-

Data were collected on the amount spent by 64 customers for lunch at a major Houston restaurant. These data are contained in the file named Houston. Based upon past studies the population standard deviation is known with = $6.

Click on the datafile logo to reference the data.

Round your answers to two decimal places.

a. At 99% confidence, what is the margin of error?

b. Develop a 99% confidence interval estimate of the mean amount spent for lunch.

Answer:

Slope-intercept

y = 3/4(x) - 7

Point slope

y -5= 3/4(x - 16)

Step-by-step explanation:

In slope-intercept

We have the general slope intercept as;

y = mx + b

where m is the slope and b is the y-intercept

in this case, m = 3/4 and b = -7

So we have;

y = 3/4(x) - 7

In point-slope

we have the general form as;

y-y1 = m(x-x1)

So what we have is as follows;

y -5= 3/4(x - 16)

Where we have (x1,y1) = (16,5)

Answer:

p = -2

Step-by-step explanation:

Start by dividing both sides by 81 to get the power by itself.

\(3^p \cdot 81 = 9\\\\3^p=\frac{9}{81}=\frac{1}{9}\)

Write the fraction using a power of 3.

\(3^p=\frac{1}{3^2}\\\\3^p=3^{-2}\\\\p=-2\)

This assumes you know about negative exponents:  \(a^{-n}=\frac{1}{a^n}\)

Here, the outer sum is over the variable $i$ and it ranges from $1$ to $n$. For each value of $i$, the inner sum is over the variable $j$ and it ranges from $1$ to $3$.

The expression $j^2$ is the summand, which is added for each value of $j$.

The given sigma notation is:

n

___

\    j^2

/___

j=1

Expanding this sigma notation, we have:

= 1^2 + 2^2 + 3^2 + ... + (n-1)^2 + n^2

= (1 + 4 + 9 + ... + (n-1)^2) + n^2

The sum of squares up to n-1 can be expressed using the formula:

1^2 + 2^2 + 3^2 + ... + (n-1)^2 = n(n-1)(2n-1)/6

Substituting this in the above expression, we get:

= n(n-1)(2n-1)/6 + n^2

= (2n^3 - 3n^2 + n)/6

Therefore, the expanded form of the given sigma notation is (2n^3 - 3n^2 + n)/6.

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Answer:

26.88 mm

Step-by-step explanation:

4.2 x 12.8 = 53.76/2 = 26.88

Answer:

28.3 i think

Step-by-step explanation:

Answer:

-117

Step-by-step explanation:

2x1+48-5x48+96-23=-117

First multiplication

2×1=2

5×48=240 ->

2+48-240+96-23

2+48=50

50-240=-190

-190+96=-94

-94-23=-117

Hope that helped! Let me know if you have any further questions.

Without the dimensions of the NW ¼, it is not possible to determine the exact area in acres of the described tract.

To calculate the area in acres contained in the described tract, we need some additional information. Specifically, we need to know the dimensions of the quarter section (NW ¼) in question. The quarter section is typically a unit of land measurement used in legal descriptions in the United States, and its size can vary depending on the specific area and context.

Once we have the dimensions of the quarter section (NW ¼), we can use that information to calculate the area of the described tract. However, without the size of the NW ¼, it is not possible to determine the exact area in acres contained in the described tract.

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Answer:

x = -4

Step-by-step explanation:

The intervals must be length ∈ (20,40) and width ∈(0,20)

The formula for area is equal to the product of the length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides.

Given here, let the length be x an width be y then we have

2(x+y)=80

x+y     = 40

x=y-40

again we have 400<xy<600

                        400<40y-y²<600

  Thus y²-40y+400<0

                 y<20 and therefore x>20

Hence, The intervals must be length ∈ (20,40) and width ∈(0,20)

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Answer:

Step-by-step explanation:

Given the system of equations:

Multiply the first equation by 4 and the second one by 3 and add up:

Find y:

Eq(1)×5 and (2)×2

Subtracting

On putting in eq(1)

(6,-3) is the soln

The area of the square is 25ft² and the perimeter is 20ft.

It's important to note that the area of a square is calculated as:

= Side ²

The perimeter is calculated as:

= 4 × Side

From the information given, the side is 5ft. The area will be:.

= 5 × 5

= 25ft²

The perimeter will be:

= 4 × Sode

= 4 × 5ft.

= 20 feet

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The completely factored form of the provided polynomial is  (p -2) (p+ 2) (p² +4). The option 4 is the correct option.

Polynomial equations is the expression in which the highest power of the unknown variable is n (n is a real number).

The polynomial equation given in the problem is,

\(p^4 - 16\)

Let the factor form of the polynomial is f(p). Thus,

\(f(p)=p^4 - 16\\f(p)=p^4 - 2^4\\f(p)=(p^2)^2- (2^2)^2\)

Using the formula of difference of squares, we get,

\(f(p)=(p^2-4)(p^2+4)\\f(p)=(p^2-2^2)(p^2+4)\\f(p)=(p-2)(p+2)(p^2+4)\)

Thus, the completely factored form of the provided polynomial is  (p -2) (p+ 2) (p² +4). The option 4 is the correct option.

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Answer:

D Edge 2022

Step-by-step explanation:

The radius of the circle inscribed in the right triangle ABC, where AC = 8, is 4 units.

In a right triangle ABC inscribed in a circle with center O and radius r, we can use the property that the hypotenuse of a right triangle is the diameter of the circle.

Given that AC is the hypotenuse of the right triangle, we have AC = 8. Since AC is the diameter of the circle, we can write 2r = AC. Therefore, we have 2r = 8, which simplifies to r = 4.

So the radius of the circle is 4 units.

To understand why this is true, let's consider the properties of a circle inscribed in a right triangle.

In a right triangle, the hypotenuse is the longest side and is opposite the right angle. When a circle is inscribed in a right triangle, the center of the circle lies at the midpoint of the hypotenuse.

Since AC is the hypotenuse of the right triangle ABC, the center of the circle O lies at the midpoint of AC. Therefore, AO and CO are radii of the circle, and they are equal in length.

In our case, AC = 8, so the radius of the circle is half of AC, which is 4.

This result holds true for any right triangle inscribed in a circle. The radius of the circle is always half the length of the hypotenuse.

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a) P(t) = 19600 * ( 1 + 0.05 ) ^ t

b)  The estimated value of the population in the year 2008 is 25,958.

Given: The population has a continuous growth rate (r) = 5% per year.

The population in the year 2000 was 19600.

Let we consider a function P(t), where t is time or number of years at which we have to find the value of the function P(t).

Consider 2000 be the initial year of the region. so at t = 0, the population was 19600.

We know that the time value increase equation can be written as.

P(t) = Initial value * ( 1 + rate / 100) ^ t

According to the question ,

rate(r) = 5%

Initial value = 19600

The required equation is:

P(t) = 19600 * ( 1 + 0.05 ) ^ t

Now, we have to estimate the population in the year 2008.

So the time span from 2000 to 2008 is (difference from the initial year to the target year)

t = 2008 - 2000 = 8

t = 8

Therefore the estimated population in the year 2008 is:

P(8) = 19600 ( 1 + 0.05 ) ^ 8

      = 28,958.12669

Now population cannot be a decimal number so the answer is 28,958(rounded to the closest integer value).

Hence, the estimated value of the population in the year 2008 is 25,958.

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Disclaimer: The question is incomplete. The complete question is mentioned below:

The fox population in a certain region has a continuous growth rate of 5 percent per year. It is estimated that the population in the year 2000 was 19600.

(a) Find a function that models the population t years after 2000 (t=0 for 2000).

(b) Use the function from part (a) to estimate the fox population in the year 2008.

Answer:

the answer is below

Step-by-step explanation:

Demand seems to be based on price.

Therefore we must consider two things:

that "x" is equal to the price and that "y" is equal to the average attendance.

Thus:

the two points would be:

(x1, y1) = (10,27000)

(x2, y2) = (6.39000)

The slope of a straight line is given by:

m = (y2-y1) / (x2-x1)

we replace:

m = (39000 - 27000) / (6 - 10) = 12000 / -4 = -3000

The equation of a straight line can be expressed like this

y = m * x + b.

where

m is the slope and b is the y-intercept.

we replace

y = -3000 * x + b.

To solve for b, replace x and y with the value of one of the points on the line.

We choose (6.39000). and we replace:

39000 = -3000 * 6 + b

39000 = -18000 + b

39000 + 18000 = b

b = 57000.

if we replace we have:

the equation becomes y = -3000 * x + 57000

since it is the demand and * x is the price.

t = d (x), therefore the equation becomes

d (x) = -3000 * x + 57000.

d (x) = 57000 - 3000 * x.

when x = 0, the price is 0 and the demand will be 57000, which will be more than the stadium can contain because the stadium can only contain 50,000.

So:

when x = 6, the price is 6 and the demand is 57000 - 18000 = 39000.

when x = 10, the price is 10 and the demand is 57000 - 30000 = 27000.

Answer:

\( \boxed {( 4, - 10)}\)

Step-by-step explanation:

\(y = {x}^{2} - 8x + 6\)

Here are some formulas that you might need.

\(h = - \frac{b}{2a} \\ k = \frac{4ac - {b}^{2} }{4a} \)

The vertex of graph is at (h, k) from the vertex form.

\(x = h \\ y = k\)

Substitute in the formula.

\(h = - \frac{( - 8)}{2(1)} \\ h = \frac{8}{2} \\ h = 4\)

Next we find the value of k.

\(k = \frac{4(1)(6) - {( - 8)}^{2} }{4(1)} \\ k = \frac{24 - 64}{4} \\ k = \frac{ - 40}{4} \\ k = - 10\)

Therefore the vertex is (4,-10).

The estimate of the maximum error in S is 0.042 square feet.

The maximum error in the calculated surface area is given by:

dS = 0.143 * (0.7 * dw * w ** 0.3 + 0.648 * dh * h ** 0.352)

where dw and dh are the errors in the measurements of w and h, respectively.

If the errors in measurements of w and h are at most 1%, then dw = 0.01w and dh = 0.01h.

Substituting these values into the equation for dS, we get:

dS = 0.143 * (0.7 * 0.01w * w ** 0.3 + 0.648 * 0.01h * h ** 0.352)

= 0.0143 * (0.7w ** 0.3 + 0.648h ** 0.352)

= 0.0143 * (0.21w + 0.482h)

The maximum error in the calculated surface area is 0.0143 * (0.21w + 0.482h), which is approximately 0.042 square feet.

Therefore, the estimate of the maximum error in S is 0.042 square feet.

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Answer:

54.36

Step-by-step explanation:

Cos\(Cos59 = \frac{28}{x} \\x=\frac{28}{cos59} =54.36\)