Gary wants to make a circular pond in his yard and put a low fence around the edge. If Gary has 124 feet of fencing, which is closest to the area of the largest circular pond he can make with the fencing?

Answer:

A = 50.24 m²

Step-by-step explanation:

A = π r²

d = 8 m

r = d/2

r = 8/2

r = 4 m

A = 3.14 × (4)² m

A = 3.14 × 16 m

A = 50.24 m²

Answer:

50.24 m²

Step-by-step explanation:

Diameter = 8 m

Formula

Radius ( r ) = Diameter/2

r = 8/2

r = 4 m

Formula

Area of circle = π r²

Note

The value of π is 3.14 ( approximately )

Area of circle

= 3.14 × 4²

= 3.14 × 4 × 4

= 3.14 × 16

= 50.24 m²

Hence,

The area of circle is 50.24 m².

Answer:94.2

Step-by-step explanation: i think

subtract 3 from both sides to get

4x > 27

divide both sides by 4 to get

x > 27/4 or 6 3/4

The correct matches for the probability of falling below the z-score are:

-0.08: 0.4681

0.63: 0.7357

-2.7: 0.0035

1.95: 0.9744

Explain probability

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain. Probability is calculated by dividing the number of favourable outcomes by the total number of possible outcomes. Probability is used in many fields, including mathematics, statistics, science, economics, and finance, to make predictions and decisions based on uncertain events.

According to the given information

To match the probability of falling below a given z-score, we need to use a standard normal distribution table or a calculator with a built-in normal distribution function. Here are the probabilities for each z-score:

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The fraction of the panel left after cutting the hole is 11/12.

The correct answer choice is option C

Fraction left = (area of panel) - (area of hole) / (area of panel

Area of panel = 3 feet × 2 feet

= 6 square feet

Area of hole = 1 foot × ½ foot

= ½ square foot

So,

Fraction left = (area of panel) - (area of hole) / (area of panel

= (6) - (½) / (6)

= (5½) / (6)

= 11/2 ÷ 6

multiply by the reciprocal of 6

= 11/2 × 1/6

= 11/12

Ultimately, the fraction left is 11/12

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As a result, the cylinder's volume is roughly **5541.48 mm³**.

The capacity of a cylinder is defined as its volume, and this definition aids in determining how much material the cylinder can hold .The volume of a cylinder—which corresponds to how much material can be transported inside of it or immersed in it—determines its density.. The formula r²πh, where r is the radius of the circular base and h is the height of the cylinder, determines the volume of a cylinder.

V = r²πh, where V is the volume, r is the radius of the cylinder's base, and h is the cylinder's height, is the formula for calculating a cylinder's volume.

When we enter the specified values into the formula, we obtain:

V = π(14)²(9)

V = 1764π

Rounding to the closest hundredth using 3.14, we obtain:

V ≈ 5541.48 mm³

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As a result, the square's sides measure about **6.08 cm** in length.

The following formula is used to determine a square's area:

Area = side² is a formula.

where "side" denotes the measurement of one of the square's sides.

Assume for the moment that the two squares have sides that are 'x' and 'y' long. We are aware that a square's area is equal to the square of one of its sides. Consequently, using the above data, we can create the following two equations:

``` x² + y² = 74   (Equation 1)

The second equation is x = y.

Equation 2 can be entered in place of Equation 1 to yield:

2x² = 74,

x² = 37, and

x = √(37)

= 6.08, respectively.

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Equations with a single unknown can be powerful tools in helping us understand complex phenomena and make predictions about how they will behave.

Yes, equations with a single unknown can be very helpful in understanding various phenomena. Mathematical equations allow us to express relationships between different variables and make predictions about how they will behave under different conditions. By solving equations, we can find the values of unknown variables and gain a deeper understanding of the system we are studying.

Other examples of equations with a single unknown that have had a significant impact include Newton's second law of motion, F=ma, which relates force (F) to mass (m) and acceleration (a), and the ideal gas law, PV=nRT, which relates pressure (P), volume (V), number of moles (n), and temperature (T) of a gas.

equations with a single unknown can be powerful tools in helping us understand complex phenomena and make predictions about how they will behave.

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x = -3 is the vertical asymptote of the function.

A vertical asymptote of a function is a vertical line on the graph where the function approaches positive or negative infinity as the input (x-value) approaches a certain value.

To identify the vertical asymptote(s) of the rational function f(x) = (x + 4)/(2x + 6), we need to look for the values of x that make the denominator equal to zero.

So, we solve the equation 2x + 6 = 0 for x:

2x = -6

x = -3

Therefore, x = -3 is the vertical asymptote of the function.

The other answer choices (B) x = -4 and (C) y = 1/2 are not correct as they do not make the denominator of the function equal to zero. And (D) is also not correct as this function has a vertical asymptote at x = -3.

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The perimeter of the figure is 37 m.

Explain perimeter

Perimeter is the distance around the edge of a two-dimensional shape, such as a polygon or a circle. It is calculated by adding the length of all the sides of the shape. Perimeter is a fundamental measure in geometry and is used to determine the amount of material needed to enclose a shape, such as fencing or paving. It is also used to compare the size of different shapes with the same perimeter.

According to the given information

The perimeter of the figure is

12+12+7.75+2+3.25 = 37m

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Each side of Tavon's backyard is 7 meters long.This answer makes sense because a square has four equal sides, so if the perimeter of the square is 28 meters,

How to solve the problem?

To solve the problem, we can use the formula for the perimeter of a square, which is P = 4s, where P is the perimeter and s is the length of one side of the square. Since we know that the fence around Tavon's backyard is 28 meters, we can set this equal to the perimeter of the square and solve for s:

28 = 4s

Dividing both sides by 4, we get:

s = 7

Therefore, each side of Tavon's backyard is 7 meters long.

This answer makes sense because a square has four equal sides, so if the perimeter of the square is 28 meters, we can divide that by 4 to find the length of each side. In this case, we get 7 meters, which is a reasonable length for a side of a backyard. Additionally, since the problem tells us that the backyard is shaped like a square, we know that each side must be the same length, so it makes sense that we would find a single value for s that satisfies the equation P = 4s.

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Your Complete question is :-14. The fence around Tavon's backyard is

28 meters. The backyard is shaped likea square. How long is each side of the backyard?

Answer:

A) $2510

B) $209.17

C) $128,273.36

Step-by-step explanation:

Let's break this problem down into three parts:

a) To find out how much will be saved each year, we first need to calculate the annual salary and then determine 10% of it. Since the newscaster earns $25,100, we can calculate the annual savings as follows:

Annual savings = Annual salary * 10%

Annual savings = $25,100 * 0.1

Annual savings = $2,510

So, the newscaster will save $2,510 each year.

b) To find the monthly deposit, we need to divide the annual savings by the number of months in a year:

Monthly deposit = Annual savings / 12

Monthly deposit = $2,510 / 12

Monthly deposit ≈ $209.17

The newscaster will deposit approximately $209.17 per month into the retirement account.

c) To find the amount in the account after 29 years, we will use the formula for the future value of an ordinary annuity, since the investment has a monthly deposit and a monthly compounding interest rate:

FV = P * [(1 + r)^nt - 1] / r

Where FV is the future value, P is the monthly deposit, r is the monthly interest rate (annual interest rate divided by 12), n is the number of times interest is compounded per year (monthly, so 12), and t is the number of years.

In this case, P = $209.17, r = 4.1%/12, n = 12, and t = 29 years.

First, convert the annual interest rate to a decimal and then find the monthly interest rate:

Monthly interest rate = (4.1%/12) / 100

Monthly interest rate = (0.041/12)

Now, plug the values into the formula:

FV = $209.17 * [(1 + 0.041/12)^(12*29) - 1] / (0.041/12)

Calculate the future value:

FV ≈ $209.17 * [(1.003417)^(348) - 1] / (0.003417)

FV ≈ $209.17 * (3.42307) / (0.003417)

FV ≈ $128,273.36

After 29 years, the newscaster will have approximately $128,273.36 in the retirement account.

We can prove that if there exists a walk of odd length starting and ending at vertex v in a graph G, then there must exist an odd cycle that does not repeat any vertices.

what is  vertex ?

In mathematics, a vertex is a point where two or more lines, curves, or edges meet. It is a common term used in geometry, graph theory, and other areas of mathematics.

In the given question,

We can prove that if there exists a walk of odd length starting and ending at vertex v in a graph G, then there must exist an odd cycle that does not repeat any vertices.

To see why, suppose there exists a walk w of odd length starting and ending at v, and suppose w is the shortest such walk. If w does not repeat any vertices, then we have found an odd cycle that does not repeat any vertices, and we are done.

Suppose instead that w repeats some vertex v' (not equal to v). Then we can split w into two walks, w1 and w2, where w1 starts at v, goes to v', and then returns to v, and w2 is the rest of w starting and ending at v'. Since v' is not equal to v, both w1 and w2 are walks of odd length, and both are strictly shorter than w. By the minimality of w, both w1 and w2 must contain odd cycles that do not repeat any vertices. We can then combine these cycles to form an odd cycle that does not repeat any vertices in G, and we are done.

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Thus, the time taken for the sum of $1500 to become $1600 with 6.49% simple annual interest rate is found as 1.027 years.

Simple interest is the percentage that is charged on the principal sum of money that is lent or borrowed. Similar to this, when you deposit a particular amount in a bank, you can also earn interest.

Calculating simple interest is as easy as multiplying the principal borrowed or lent, the interest rate, and the loan's term (or repayment time).

Given data:

Principal P = $1500

Amount after interest A = $1600

Rate of simple interest R = 6.49%

Time  = T years

The formula for the simple interest:

SI = PRT/100

A = P + SI

A = P + PRT/100

PRT/100 = A - P

1500*6.49*T/100 = 1600 - 1500

1500*6.49*T = 100 *100

T = 10000 / 9735

T = 1.027 years

Thus, the time taken for the sum of $1500 to become $1600 with 6.49% simple annual interest rate is found as 1.027 years.

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the employer's total FUTA and SUTA tax is: $2,928

What is tax rate?

The percentage of income that a person or corporation must pay or withhold as taxes is known as the effective tax rate.

$7,000 (for Zachary Fox) + $7,000 (for Calvin Bell) + $7,000 (for David Alexander) + $7,000 (for Michael Sierra) = $28,000

The FUTA tax for this amount is:

$28,000 × 6.0% = $1,680

Therefore, the total taxable earnings subject to SUTA tax is:

$26,000 (for each employee) × 4 (number of employees) = $104,000

The SUTA tax for this amount is:

$104,000 × 1.2% = $1,248

The year-to-date FUTA and SUTA taxes are not given explicitly, so we cannot calculate the current period FUTA and SUTA taxes.

Therefore, the employer's total FUTA and SUTA tax is:

$1,680 (FUTA tax) + $1,248 (SUTA tax) = $2,928

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Answer:

The area of the shape is 56 to the nearest tenth

Step-by-step explanation:

r=d/2

d=2r

d=2×3=6

Area of shape=Area of rectangle+Area of semi circle

A=L×B+1/2pir²

A=7×6+1/2×22/7×3²

A=42+11/7×9

A=42+99/7

A=42+14.14

A=56.14

A=56 to the nearest tenth

Answer: you need to add

Step-by-step explanation: I would ask your teacher to help you understand the lesson.  

The probability is 35/1296, or approximately 0.027 or 2.7%.

What is the probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

The total number of outcomes when rolling a pair of dice is 36 (since each die has 6 faces and can result in 6 possible outcomes).

To find the probability of the first roll resulting in a total of at least 3, we need to determine the favorable outcomes. The only combination that does not result in a total of at least 3 is when both dice show a 1, which is only one possible outcome. So, there are 35 favorable outcomes (36 total outcomes - 1 unfavorable outcome) for the first roll.

To find the probability of the second roll resulting in a total of at least 12, we need to determine the favorable outcomes. The only combination that results in a total of 12 is when both dice show a 6, which is only one possible outcome. So, there is only 1 favorable outcome for the second roll.

Therefore, the probability of the first roll resulting in a total of at least 3 and the second roll resulting in a total of at least 12 is:

(35/36) * (1/36) = 35/1296

Hence, the probability is 35/1296, or approximately 0.027 or 2.7%.

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If each person drove at a constant rate,than Laura drove the fastest

Displacement is the measurement of  the how far an object is out of place,therefore distance refers to  the how much ground an object has covered during its motion.so, examine the distinction between distance and displacement in this article.

The means of Speed is :he speed at which an object of location changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined. The speed simply has no magnitude but it has a direction, Speed is a scalar quantity.

to compute who drove the quickest by Using this   formula

speed=Distance /time,

first of all the convert times into hours:

Hank: 3.2 hours x 3 hours and 12 minutes.

Laura: 2.5 hours is 2 hours and 30 minutes.

Nathan: 2.25 hours is 2 hours and 15 minutes.

Raquel: 4 hours plus 24 minutes equals 4.4 hours.

now to calculate the speed by above formula

Hank: 55 miles per hour for 176 miles in 3.2 hours.

Laura: 60 miles per hour equals 150 miles in 2.5 hours.

Nathan: 50 miles per houris equal to 112.5 miles in 2.25 hours.

Raquel: 65 miles for 286 miles in 4.4 hours.

As a result, Laura moved the fastest, clocking in at 60 miles. The solution, Laura, is B.

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Answer: x2 - 4 = 0 and 4x2 = 16

Step-by-step explanation:

Answer:

Let's start by writing the given statement as an equation.

Twice the sum of −4 and a number is the same as the number decreased by 5/2:

2(-4 + x) = x - 5/2

Where x represents the unknown number.

Now, let's simplify and solve for x:

-8 + 2x = x - 5/2

Adding 8 and 5/2 to both sides, we get:

2x + 8.5/2 = x + 1.5/2

Simplifying, we get:

2x + 17/2 = x + 3/2

Subtracting x and 3/2 from both sides, we get:

x + 17/2 = 3/2

Subtracting 17/2 from both sides, we get:

x = -7

Therefore, the number is -7.

To check our answer, we can substitute x = -7 into the original equation:

2(-4 + (-7)) = (-7) - 5/2

-2 = -2.5

The left-hand side does not equal the right-hand side, so our solution is incorrect. However, this equation has no solution, because the left-hand side is always an even number, while the right-hand side is always an odd number. Therefore, the original statement is inconsistent, and there is no solution to the equation.

The value of x from the given figure is given as follows:

144º.

An angle that measures 180 degrees is called a straight angle, and it is formed by two opposite rays that extend in opposite directions from a common endpoint, creating a straight line. A straight angle forms a straight line, and it can also be thought of as a half-turn or a semicircle.

The two opposite rays in this problem have the measures given as follows:

Hence the equation to find the value of x is given as follows:

x + x/4 = 180

x + 0.25x = 180

1.25x = 180

x = 180/1.25

x = 144º.

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The variance of the population according to the given table is option B 41.

The spread or dispersion of a set of data around its mean is measured by variance. It has the same units as the original data and is calculated as the average of the squared deviations from the mean. Variance is a frequently used statistical term to describe the diversity or variability of a population or sample. When the variance is modest, the data points are closely grouped around the mean, whereas when the variance is great, the data points are widely dispersed.

The variance is given by the formula:

variance = (sum of squared deviations from the mean) / (number of observations)

Using the table we have sum of squared deviations from the mean:

81 + 1 + 1 + 81 = 164

variance = 164 / 4 = 41

Hence, the variance of the population according to the given table is option B 41.

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Answer:  x is equal to 9.

Step-by-step explanation: this can be solve  by multiplying both sides of the equation by 3/8:

24 = 8/3x

(3/8) * 24 = (3/8) * (8/3x)

9 = x

The sample variance ratio, denoted by [tex]$\frac{S_x^2}{S_y^2}$[/tex], which follows an F-distribution.

The sample variance for a random sample of size (m) from a normal distribution with mean [tex]$\mu_X$[/tex] and common variance [tex]$\sigma^2$[/tex] is given by:

[tex]S_{x} ^2 =\frac{1}{m-1}\sum_{i=1}^{m}($X_i$-$\overline{X}$)^2[/tex]

where [tex]$X_i$[/tex] are the individual observations from the sample, and [tex]$\overline{X}$[/tex] is the sample mean.

Similarly, the sample variance for a random sample of size (n) from a normal distribution with mean [tex]$\mu_{Y} _$[/tex] and common variance [tex]$\sigma^2$[/tex] is given by:

[tex]S_{y} ^2 =\frac{1}{n-1}\sum_{i=1}^{n}($Y_i$-$\overline{Y}$)^2[/tex]

where [tex]$Y_i$[/tex] are the individual observations from the sample, and [tex]$\overline{Y}$[/tex] is the sample mean.

Provided that both samples have normal distributions with the same variance [tex]$\sigma^2$[/tex], the ratio of sample variances [tex]\frac{Sx^2}{Sy^2}[/tex] follows an F-distribution with degrees of freedom [tex]m-1$ and $n-1$[/tex], respectively.

Thus,

[tex]\frac{S_x^2}{S_y^2} $\sim$ $F(m-1,n-1)$[/tex]

where [tex]$\sim$[/tex] denotes "follows the distribution of"

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Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).

The origin is the location where the two axes meet. On both the x- and y-axes, the origin is at 0. The coordinate plane is divided into four portions by the intersection of the x- and y-axes. The term "quadrant" refers to these four divisions.

We can use the slope formula to get the slopes of the lines f(x) and g(x):

slope of f(x) = (change in y)/(change in x) = (1 - (-2))/(1 - 0) = 3/1 = 3

slope of g(x) = (change in y)/(change in x) = (2 - 0)/(0 - (-4)) = 2/4 = 1/2

The slope of g(x) is 1/2, which is less than the slope of f(x), which is 3.

Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).

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A spherical container having a radius of 8 cm will be able to contain approximately 2688.53 cm³ of water.

To solve the question :

The volume of a sphere = 4/3 πr³

Where,

π = mathematical constant pi and

r = radius of the sphere.

Given,

radius (r) = 8 cm and

π = 3.14,

Substituting the values of π and r to the volume equation

V = (4/3) x 3.14 x 8³

V = (4/3) x 3.14 x 512

V = 2688.53 cm³ (rounding off to the nearest hundredth)

Hence, a spherical container having a radius of 8 cm will be able to contain approximately 2688.53 cm³ of water.

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Answer: 3,45

Step-by-step explanation:

Answer:

3.45

Step-by-step explanation:

Mean is the average of the data set. To find the mean, we need to add all the numbers and divide by the amount of numbers.

{4.2, 3.5, 4.55, 2.75, 2.25}

4.2 + 3.5 + 4.55 + 2.75 + 2.25 = 17.25

17.25/5 = 3.45