if you have 20 meters of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose?

From the given information provided, the 12th term of the geometric sequence 7, -35, 175 is -341,796,875.

To find the 12th term of the geometric sequence 7, -35, 175, we can use the formula for the nth term of a geometric sequence:

an = a₁ × r⁽ⁿ⁻¹⁾

where aₙ is the nth term, a₁ is the first term, r is the common ratio, and n is the term number we want to find.

First, we need to find the common ratio (r) between any two consecutive terms. We can do this by dividing any term by its preceding term:

r = (-35) / 7 = -5

Now, we can use the formula to find the 12th term:

a₁₂ = 7 × (-5)⁽¹²⁻¹⁾

a₁₂ = 7 × (-5)¹¹

a₁₂ = 7 × (-48828125)

a₁₂ = -341,796,875

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Answer: The area of a triangle is 1036.8 square units.

To find the area of a triangle, we can use the formula

Area = (1/2) * base * height

In this case, we are given that the first base is 32 and the second base is twice the first base, or 2*32 = 64. The height is given as 21.6. Therefore, we can plug these values into the formula and solve for the area:

Area = (1/2) * (32 + 64) * 21.6

Area = (1/2) * 96 * 21.6

Area = 1036.8

Therefore, the area of the triangle is 1036.8 square units.

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We can conclude that it is unlikely to obtain a random sample of size 9 from this population with a mean of 24 and a standard deviation of 4.1 because the sample mean of 24 is different from the population mean of 20.

To answer this question, we can use a t-test to determine if the sample mean of 24 is significantly different from the population mean of 20.

The t-test formula is:

t = (x' - μ) / (s / √(n))

Where x' is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.

Plugging in the values given in the question, we get:

t = (24 - 20) / (4.1 / √(9)) = 2.93

To determine if this t-value is significant, we need to compare it to the critical t-value for a two-tailed test with 8 degrees of freedom (n-1). Using a t-table or calculator, we find the critical t-value to be approximately 2.31 at a 5% significance level.

Since our calculated t-value of 2.93 is greater than the critical t-value of 2.31, we can reject the null hypothesis that the sample mean is equal to the population mean.

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Scale Factor is equal to [tex]\frac{2}{3}[/tex]. Length of EH is equal to 16 units and length of AB is equal to 9.

4. A scale factor is the ratio of the scales of an original object and a new object.

Scale factor = Ordinated dimension / original dimension

Scale factor = [tex]\frac{10}{15}[/tex]

Scale factor = [tex]\frac{2}{3}[/tex]  (or) 0.67

5. Length of EH

Scale factor = [tex]\frac{EH}{AD}[/tex]

[tex]\frac{EH}{AD}[/tex] = [tex]\frac{2}{3}[/tex]

[tex]\frac{EH}{24} = \frac{2}{3}[/tex]

EH = 2 * 8

EH = 16 units

6. Length of AB

Scale factor = [tex]\frac{EF}{AB}[/tex]

[tex]\frac{EF}{AB}[/tex] = [tex]\frac{2}{3}[/tex]

[tex]\frac{6}{AB} = \frac{2}{3}[/tex]

AB = 3 * 3

AB = 9 units.

Therefore, Scale Factor is equal to [tex]\frac{2}{3}[/tex]. Length of EH is equal to 16 units and length of AB is equal to 9.

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the range of the function is at least $400 plus $50 for each month after the purchase. The average monthly cost of owning the cell phone can be represented as:

C(t) = 400 + 50t

Where t is the number of months after the purchase.

Since C(t) is a linear function, its range is all real numbers greater than or equal to 400, since the initial cost of the phone is 400 and the monthly cost is a positive constant. Therefore, the range of C(t) is:

Range of C(t) = {C(t) | C(t) ≥ 400} or [400, ∞)

In other words, the range of the function is all possible average monthly costs of owning the phone, which is at least $400 plus $50 for each month after the purchase.

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By function, The fact that this number is 1/2 indicates the half-life of the substance is 1 year.

How would you define a function in plain English?

A function is described as a relationship between a set of inputs and one output for every one of them. Simply described, a function is an association of inputs where each input is coupled to a single, distinct output.

                             Every function has an associated domain, codomain, or range. A mathematical function is a rule that, given the values of one or more independent variables and the dependent variable, determines the value of the dependent variable.

300 represents the initial amount of the substance, the amount present at t=0.

0.5 is the fraction of substance remaining at the end of each year. The fact that this number is 1/2 indicates the half-life of the substance is 1 year.

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Answer:

The slope of the line passing through the points (-6,-5) and (-1,1) can be found using the formula:

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

where (x1, y1) = (-6,-5) and (x2, y2) = (-1,1)

slope = (1 - (-5)) / (-1 - (-6)) = 6/5

Now, using point-slope form of the equation of a line, we get:

y - y1 = m(x - x1)

where m = 6/5 and (x1, y1) = (-6,-5)

y + 5 = 6/5(x + 6)

y + 5 = 6/5x + 6.72

y = 6/5x + 6.72 - 5

y = 6/5x + 1.72

Therefore, the equation of the line passing through the points (-6,-5) and (-1,1) is:

y = 6/5x + 1.72

Option (c) y=6/5x is not the correct equation of the line. The correct answer is (d) y=6/5x + 11/6.

Answer:

20- gon

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

given the sum of the interior angles is  3240° , then

180° (n - 2) = 3240 ( divide both sides by 180° )

n - 2 = 18 ( add 2 to both sides )

n = 20

then the polygon is a 20- gon

Answer: C - 105

Step-by-step explanation:

75+75=150

360-150=210

210/2=105

The surface area of the cylinder with radius 5 inches and rectangle with height 4 inches is equal to 282.6 square inches.

Radius of the base = 5 inches

Height of the rectangle = 4 inches

Surface area of a cylinder

= area of the top and bottom circular faces + the area of the curved surface.

Here,

Rectangle represents the curved surface of the cylinder, with a height of 4 inches and a length equal to the circumference of the base.

Circumference of the base is equal to,

Circumference

= 2πr

= 2 x 3.14 x 5

= 31.4 inches (approx.)

Area of the curved surface of the cylinder is ,

Curved surface area

= Length x Height

= 31.4 inches x 4 inches

= 125.6 square inches

Area of each circular face of the cylinder is ,

Circular face area

= πr²

= 3.14 x 5²

= 78.5 square inches

Substitute the value to get total surface area of the cylinder we have,

Total surface area of the cylinder

= 2 x Circular face area + Curved surface area

= 2 x 78.5 square inches + 125.6 square inches

= 282.6 square inches (approx.)

Therefore, the surface area of the cylinder is approximately equal to 282.6 square inches.

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The dimensions that will produce the maximum enclosed area for two adjacent rectangular safe play areas of equal size with 200 feet of fencing is 100 feet by 100 feet.

To solve this problem, use the area of a rectangle formula A = lw, where l is the length and w is the width.

Since the two play areas must be of equal size, let's call the length and width l and w, respectively.

We know that the total length of fencing is 200 feet, so l + w = 200 feet.

We can then solve for l by rearranging the equation as l = 200 - w.

We then substitute this into the area equation to get A = (200 - w)w.

To maximize the area, differentiate this equation to get A' = w - 200.

Set this to 0 and solve for w to get w = 100. Since l + w = 200, l = 100 as well.

Therefore, the maximum enclosed area is produced by dimensions of l = 100 feet and w = 100 feet.

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The two solutions to e² = 6x using Newton's method are x_left = 1.23151 and x_right = 2.157545.

To find the solutions of e² = 6x using Newton's Method, we will follow these steps:

Let f(x) = e² - 6x. Then we want to find the roots of f(x) = 0, which are the solutions to e² = 6x.

We need to choose a starting point x₀. A good choice is x₀ = 1, since it's a reasonable approximation to the solutions.

Apply Newton's Method to find the next approximation x₁:

x₁ = x₀ - f(x₀)/f'(x₀),

where;

Plugging in the values, we get:

x₁ = x₀ - (e² - 6x₀)/(-6) = x₀ + (e²/6 - x₀)

Use x₁ as the new starting point and repeat the process until we achieve the desired level of accuracy.

In this case, we want to find the solutions to six significant figures, so we will repeat the process until the difference between xₙ and xₙ₋₁ is less than 0.000005 (the sixth decimal place).

Using a calculator, we can apply Newton's Method iteratively to find the two solutions:

Iteration 1:

x₁ = x₀ - f(x₀) / f'(x₀)

x₁ = 1 - (e² - 6)/(-6) = 1.231509

Iteration 2:

x₂ = 1.231509 - (e² - 6)/(-6) = 1.463018

Iteration 3:

x₃ = 1.463018 - (e² - 6)/(-6) = 1.694527

Iteration 4:

x₄ = 1.694527 - (e² - 6)/(-6) = 1.926036

Iteration 5:

x₅ = 1.926036 - (e² - 6)/(-6) = 2.157545

The second solution to six significant figures is x_right = 2.157545

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The probability of selecting a ball that has an even number from a bag containing 13 balls numbered 1 through 13 is 6/13 or approximately 0.4615. This is because out of the 13 balls, 6 of them have even numbers.

To calculate the probability, we use the formula:

Probability = Number of Favorable Outcomes / Total Number of Outcomes

In this case, the favorable outcomes would be the number of even numbers, which is 6. The total number of outcomes would be 13 (the total number of balls in the bag). Therefore, the probability of selecting a ball that has an even number is 6/13.

Another way to look at this is to think of the probability as the ratio of favorable outcomes to total possible outcomes. In this case, the ratio is 6:13, which can be simplified to 3:6 or 1:2. Since one out of every two outcomes is favorable, the probability is 0.5, which is the same as 6/13.

To further understand the concept of probability, consider the example of a fair coin. If a fair coin is flipped, the probability of getting either heads or tails is 50%. This is because the ratio of favorable outcomes (one head and one tail) to total possible outcomes (two heads and two tails) is 1:2.

In conclusion, the probability of selecting a ball that has an even number from a bag containing 13 balls numbered 1 through 13 is 6/13 or approximately 0.4615.

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The need for capital by the Sport Bat Corporation will spread through the financial system as it interacts with banks, investors, and the broader financial markets.

When the Sport Bat Corporation needs to borrow $2 million to upgrade their equipment, they will likely seek a loan from a financial institution, such as a bank. The bank will evaluate the creditworthiness of the company and may require collateral or a personal guarantee before approving the loan.

Once the loan is approved, the bank will add the Sport Bat Corporation's loan to their portfolio of assets. The bank may choose to sell the loan to other investors, such as insurance companies or pension funds, to diversify their portfolio and manage risk.

These investors will then receive the interest payments on the loan as a source of income. The loan may be bundled together with other loans and sold as a package, called a securitization, to other investors in the financial markets, thus representing the spread of the loan throughout the financial system.

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Answer:

x-14=52|+14

x=52+14

x=66 candies

Step-by-step explanation: If Anna gives 14 candies to her sister, she remains with 52. How many candies does Anna have ?

If wendy can build a fort in 12 hours, al can build the same fort in 8 hours, the time taken by Wendy and Al working together to build the fort is 24/5 hours

To solve this problem, we need to use the concept of work and time. Let's assume that the fort is the unit of work that needs to be completed, and the time required to complete this unit of work is the time taken by Wendy and Al working together.

Let's denote the time taken by Wendy to build the fort as TW and the time taken by Al to build the fort as TA. From the problem, we know that TW = 12 hours and TA = 8 hours.

Let's also denote the time taken by Wendy and Al working together to build the fort as T. We can use the formula:

Work = Rate x Time

where the rate is the amount of work done per unit time.

Let's assume that Wendy's rate of work is RW, and Al's rate of work is RA. Then the rate of work of both of them working together is the sum of their individual rates of work:

RW + RA = 1/T

We can also express their individual rates of work as the inverse of the time taken by them to complete the work:

RW = 1/TW

RA = 1/TA

Substituting these values in the above equation, we get:

1/TW + 1/TA = 1/T

Substituting the given values of TW and TA, we get:

1/12 + 1/8 = 1/T

Simplifying this equation, we get:

5/24 = 1/T

T = 24/5 hours

In other words, it would take them 4 and 4/5 hours to complete the work if they worked together.

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Answer:

x = 80

y = 160

Step-by-step explanation:

The sum of all arc measures that make up a circle is 360°. Therefore:

[tex]\implies 200^{\circ} + y^{\circ} = 360^{\circ}[/tex]

[tex]\implies 200^{\circ} + y^{\circ} - 200^{\circ} = 360^{\circ} - 200^{\circ}[/tex]

[tex]\implies y^{\circ} = 160^{\circ}[/tex]

[tex]\implies y=160[/tex]

If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one-half the measure of its intercepted arc.

Therefore, according to the Tangent and Intersected Chord Theorem, the measure of angle x is equal to half of the measure of arc y:

[tex]\implies x^{\circ}=\dfrac{1}{2} y^{\circ}[/tex]

[tex]\implies x^{\circ}=\dfrac{1}{2} \cdot 160^{\circ}[/tex]

[tex]\implies x^{\circ}=80^{\circ}[/tex]

[tex]\implies x=80[/tex]

[tex]\hrulefill[/tex]

Harold therefore walks an average distance of 10 metres when moving from one location to another.

All the points in a plane that are equally spaced from a fixed point known as the centre make up a circle, which is a geometric form. The radius of a circle is the separation between any two points on the circle and its centre. A circle's diameter is defined as a line segment whose endpoints are on the circle and which goes through the centre of the circle. Circles are helpful in many areas of mathematics and science due to a number of significant characteristics.

given

A circle with a dimension of 100 metres has a circumference of d, where d is the diameter. As a result, this circle's diameter is:

C = d = (100) = 100 m

Harold will walk from one spot to the next after completing 1/6

of the circle's circumference because the circle's circumference has six points that are all equally spaced apart. As a result, Harold travels the following distance between each location:

Distance equals 1/6 * C * 1/6 * 100 * (50/3) metres.

b) The average of the distances between each location, which we just discovered to be (50/3) metres, represents the average distance that Harold covers when moving from one place to another. The circle has six evenly distributed points, so the average distance travelled by Harold is:

(Total distance travelled) / Mean distance (Number of segments)

Total distance travelled equals the distance between two adjacent locations on the circle, which is C/2, or (1/2) 100 metres, or 50 metres.

Segment count equals number of marks - 1 (i.e., 6 - 1 = 5).

The average distance Harold travels while strolling is as follows:

Typical distance is calculated as (Total distance travelled) / (Number of segments), which equals (50) / 5 = 10 metres.

Harold therefore walks an average distance of 10 metres when moving from one location to another.

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Check the picture below.

so the ball hits the ground when g(x) = 0

[tex]\stackrel{g(x)}{0}=-16t^2+30t\implies 0=-2t(8t-15) \\\\[-0.35em] ~\dotfill\\\\ 0=-2t\implies \boxed{0=t} \\\\[-0.35em] ~\dotfill\\\\ 0=8t-15\implies 15=8t\implies \cfrac{15}{8}=t\implies \stackrel{ seconds }{\boxed{1.9\approx t}}\qquad \textit{falls to the ground}[/tex]

we get two values for "t", once at 0, because that's when the ball was at rest before being kicked.

The winner of the election got 26320 votes.

Let's first find the total number of votes cast in the election. We know that 2/3 fraction of the electors voted for the first candidate and 1/4 of the electors voted for the second candidate. Therefore, the remaining 1/12 of the electors voted for the third candidate. So, we have:

2/3 + 1/4 + 1/12 = 8/12 + 3/12 + 1/12 = 12/12 = 1

This means that all the electors voted, and the total number of votes cast is equal to the total number of electors.

Now, let's find the number of votes the third candidate got, which is 1/12 of the total number of votes. We know that this is equal to 3290. So, we have

1/12 x Total Number of Votes = 3290

Multiplying both sides by 12, we get:

Total Number of Votes = 3290 x 12 = 39480

Now, we can find the number of votes the first candidate got, which is 2/3 of the total number of votes. We have:

2/3 x Total Number of Votes = 2/3 x 39480 = 26320 votes

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As per the given statement, the quadratic equation is to be used to find the exact solutions to this equation, and the quadratic equation is given by [tex]ax² + bx + c = 0[/tex].

To solve the quadratic equation, we can use the quadratic formula given by[tex]x = (-b ± sqrt(b² - 4ac)) / 2a[/tex] Where x is the variable, a, b, and c are coefficients with a ≠ 0, and sqrt is the square root symbol.To find the exact solutions to this equation, we can use the quadratic formula with a = 2, b = 6, and c = 12.

Substituting these values in the quadratic formula, we get

[tex]x = (-6 ± sqrt(6² - 4 × 2 × 12)) / 2 × 2= (-6 ± sqrt(36 - 96)) / 4= (-6 ± sqrt(-60)) / 4= (-6 ± i√60) / 4= (-3 ± i√15) / 2[/tex]

Hence, the exact solutions to the given equation are [tex](-3 + i√15) / 2 and (-3 - i√15) / 2.[/tex]

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Answer:

1/4x - 3 = 12

Step-by-step explanation:

You know you have 1/4x and need to take three from it to equal 12

Around noon, when the forecast temperature is about 4 degrees Celsius higher than the measured temperature, the difference is at its greatest.

The strength and direction of the linear connection between two variables are measured by the correlation coefficient. Its value goes from -1 to 1, and it is represented by the symbol "r". A perfect negative correlation, or r = -1, implies that as one variable rises, the other variable falls in an exact predictable manner. There is no linear relationship between the two variables if r = 0, which implies there is no correlation between the two variables. When r = 1, there is a perfect positive correlation, meaning that when one measure rises, the other rises in an exact predictable manner.

given

The maximum temperature for a specific day is shown in the provided image alongside the predicted maximum temperature.

The blue line depicts the expected maximum temperature, while the red line depicts the actual maximum temperature.

We can see that throughout the day, the forecast temperature is typically greater than the actual temperature.

Around noon, when the forecast temperature is about 4 degrees Celsius higher than the measured temperature, the difference is at its greatest.

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The aquarium tank that holds 190 liters of water equals to 50.15 gallons. Therefore, the answer to the given problem is 50.15 gallons.

Conversion factors are the ratios that describe the numerical relationship between two units of measurement.

The conversion factor of liters to gallons is 1 gallon is 3.8 liters.

Therefore, by multiplying the given value of liters by the conversion factor of liters to gallons, we can convert liters to gallons.

190 liters x 1 gallon/3.8 liters = 50.15 gallons

Thus, the aquarium tank that holds 190 liters of water equals to 50.15 gallons.

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The approximate price per square inch of the cookie cake is $0.50

The area of a circle is given through the formulation:

A = πr^2

In which r is the radius of the circle.

for the reason that diameter of the cookie cake is 6 inches, the radius is half of of that, or three inches.

Substituting this into the formulation, we've:

A = π(3^2) = 28.26 square inches (approximate)

The value per square inch is the overall value of the cookie cake divided with the aid of its area:

value per square inch = $14.13 / 28.26 sq.in = $0.50 (approximate)

Therefore, the approximate price per square inch of the cookie cake is $0.50

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If the square of Ethan's age is added to Jordan's age, the result is [tex]56[/tex], which equals Ethan's age. The answer is that Ethan is [tex]6[/tex] years old.

A person's birth date is compared to the day on which their age has to be computed as part of the age calculation process. The age of the individual is calculated by subtracting the person's age from the given date. Provided Date - Birthdate is used to compute age.

A person's age is merely a measurement of how long they have been living. These metrics don't adequately describe who you are or what you have accomplished. At any age, either old or young, one may do anything.

The solution states that [tex]56[/tex] is equal to [tex]4[/tex] times Jordan's age multiplied by the square of Ethan's age. This may be expressed as an equation:

[tex]x^2 + 4(x-1) = 56[/tex]

Simplifying the equation:

[tex]x^2 + 4x - 4 = 56[/tex]

[tex]x^2 + 4x - 60 = 0[/tex]

We can solve this quadratic equation by factoring:

(x+10)(x-6) = 0

Therefore, [tex]x = -10[/tex] or [tex]x = 6[/tex]. We can discard the negative value since age cannot be negative, so Ethan's age is [tex]6[/tex].

To check, we can substitute x=6 into the original equation:

[tex]6^2 + 4(6-1) = 36 + 20 = 56[/tex]

So the solution is Ethan is [tex]6[/tex] years old.

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Answer:

Looks like J is right.

Step-by-step explanation:

Because the others are not right, and J was what my calculator said the numbers belonged to as in groups.

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Answer: i believe its 15.12

Step-by-step explanation:

Answer:

x = 13°

Step-by-step explanation:

-> all angles of triangle add up to 180°

-> right angle = 90°

-> GIVEN: 90° and 23°

90° + 23° + (6x-11) = 180°

6x-11 = 67°

6x = 78°

[tex]\frac{6x}{6} =\frac{78}{6}[/tex]

x = 13°

Yes, the value of 0.75 to 0.83 for a 95% confidence interval is plausible.

A confidence interval is a range of values that has a 95% chance of containing the true population parameter, which in this case is the population proportion (p).

A 95% confidence interval has a margin of error of 5%. Thus, a range of 0.75 to 0.83 has a 95% chance of containing the true population proportion p.

The 95% confidence interval is an estimated range of values which is calculated from sample data, with a 95% chance of containing the true population parameter, p. To calculate the confidence interval, the confidence level and the margin of error must be known.

The confidence level is the probability that the confidence interval will contain the true population parameter, and the margin of error is the amount that the sample statistic can differ from the true population parameter.

A 95% confidence level has a margin of error of 5%, meaning that the sample statistic can be up to 5% away from the true population parameter.

In this case, the 95% confidence interval for the population proportion is 0.75 to 0.83. This means that the range of 0.75 to 0.83 has a 95% chance of containing the true population proportion p, and is thus a plausible value for the population proportion.

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