A 25,000-mile steel band is placed around the earth, snugly fit at the equator. The band is cut, and 36 inches of string is spliced into the steel band. This new, larger circular band is placed around the earth, so its center coincides with the center of the earth, and a gap is created. How wide is this gap?

When you have finished, post your work showing the formula used for calculating the gap (g), show all calculations solving for g (gap), and a statement interpreting the results of your work.

So, the answer is $285,671.10 (Option b) that must be deposited earning 6.2% compounded yearly in order to make the annuity payment of $25,312 for 20 years.

The formula to determine the future value of an annuity is given by

FV = PV(1+r)^n + PMT( (1+r)^n - 1) / r

Where:

FV is the future value of the annuity

PV is the present value of the annuity

PMT is the payment made at the end of each period

r is the interest rate per period

n is the number of periods

We know that the payment made at the end of each period (PMT) is $25,312, the interest rate (r) is 6.2% and the number of periods (n) is 20.

We are looking for the present value of the annuity (PV)

So we can substitute the known values into the formula and solve for PV:

PV = PMT( (1+r)^n - 1) / (r (1+r)^n)

PV = $25,312 * ( (1+0.062)^20 - 1) / (0.062 (1+0.062)^20)

PV = $25,312 * (1.062^20 - 1) / (0.062 * 1.062^20)

PV = $25,312 * (1.062^20 - 1) / (0.062 * 1.062^20)

PV = $25,312 * (2.547 - 1) / (0.062 * 2.547)

PV = $25,312 * 1.547 / 0.157

PV = $285,671.10

Therefore, the answer is $285,671.10 (Option b) that must be deposited earning 6.2% compounded yearly in order to make the annuity payment of $25,312 for 20 years.

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This is an example of Stratified Random Sampling.

Stratified random sampling is a method of sampling where the population is divided into subgroups or strata based on certain characteristics and then a random sample is selected from each subgroup.

In this case, the population of grocery shoppers in major cities in the United States is divided into subgroups based on the five metro areas where Kroger has seen the biggest growth: Phoenix, Detroit, Los Angeles, Atlanta, and Dallas-Fort Worth.

Then, every person 23 years of age or older in those cities are selected to participate in the survey, ensuring that the sample is representative of the population in those specific areas.

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Transforming the quantity of the third root of x to the fourth power, to the fifth power into an expression with a rational exponent is; x^(20/3)

We are given an algebraic quantity as:

third root of x to the fourth power, to the fifth power

We want to transform that into an expression with a rational exponent.

Converting the given algebraic quantity is;

(∛x⁴)⁵

This expression could also be written as:

[x^(4/3)]⁵

By the power rule of exponents, we can expand it to get;

x^(4/3 * 5)

= x^(20/3)

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The equation to represent the total cost as a function of the number of packages delivered is C(p) = 12.50 + 0.25p.

The revenue as a function of the number of packages delivered. is R(p) = 4.25p

a. i. The equation to represent the total cost, C, as a function of the number, p, of packages delivered is C(p) = 12.50 + 0.25p

ii. The revenue, R, as a function of the number, p, of packages delivered. is R(p) = 4.25p

b. The algebraic model for the profit function P(p) = R(p) - C(p) = 4.25p - (12.50 + 0.25p) = 4.00p - 12.50

c. i. C(p) has domain of all non-negative integers (p ≥ 0) and range of all real numbers greater than or equal to $12.50 (C(p) ≥ $12.50)

ii. R(p) has domain of all non-negative integers (p ≥ 0) and range of all real numbers greater than or equal to $0 (R(p) ≥ $0)

iii. P(p) has domain of all non-negative integers (p ≥ 0) and range of all real numbers (P(p) can be any real number)

Note: The domain of p is limited to 27 in this case as the maximum packages that can be delivered is 27.

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240 square feet is the area of a square mural. The approximate length of one side of the mural is between 15 and 16 feet.

The area of a square is described as the number of square units needed to fill a square. In general, the area is described as the territory occupied inside the boundary of a flat object or 2d figure. The calculation of area is done in square units, with the standard unit being square metres (m²).

The area of the square = (side)²

240 = (side)²

side = √240

side = 4√15

side = 15.49 feet

Hence, The approximate length of one side of the mural is between 15 and 16 feet.

Therefore, the correct option is (4).

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The final statement is: 1)50:40 2) 600:480

The quantitative relation between two amounts shows the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"

Given here: The ratio of distance travelled between a cheetah and an impala as 5:4

Part 1) If the cheetah travels 50 feet then impala would travel 40 feet.

Part 2) If the impala travels 480 feet then the cheetah must travel 600 feet.

Hence, The required final ratios of distance travelled are 1) 50:40 and 2) 600:480

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Answer: if the boat costs 12,500 and raises by 7 percent a year.

Step-by-step explanation:

7 percent of 12,500 is 875 and if it kept raising for 18 years we would multiply 875 X 18 which equals 15750 and then we would add the original which would give us 28250$

so the answer is 28250$

3 minutes is not a measure of distance, it is a measure of time.

Time is a measure of duration, not of distance. Distance is measured in kilometers and is the physical length between two points. Time is measured in seconds, minutes, hours, days, and so on. It is the measure of the amount of time that passes between two events. For example, 3 minutes is the amount of time that passes between two events, but it does not represent a measure of distance. Distance is best measured in terms of kilometers, meters, or other such units. Time is best measured in terms of seconds, minutes, hours, days, or other such units. Therefore, 3 minutes is not a measure of distance; rather, it is a measure of time

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The required scale factor between the building and toy model is given as 900.

The scale factor is defined as the ratio of the modified change in length to the original length.

Here,
The area of the front side of the toy building is 1 square foot.
The real building's front side has an area of 900 square feet.
The real buildings as a dilation of the toy,
Scale factor = 900 /1
Scale factor = 900

Thus, the required scale factor between the building and the toy model is given as 900.

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4. [tex]WX=WY, WV=WZ[/tex]

6. Substitution property of equality

9. SAS similarity

Answer: I think 3 1/2

Step-by-step explanation: mere guess, sorry

The slope-intercept form of 3x 5y 10 0 is y = (3/5)x - (10/5).

This is a linear equation of the form y = mx + b, where m is the slope, and b is the y-intercept. In this equation, the slope m is equal to 3/5, and the y-intercept b is equal to -10/5. To calculate the slope (m), we need to divide the coefficient of x (3) by the coefficient of y (5). The answer is 3/5. To calculate the y-intercept (b), we need to divide the constant (10) by the coefficient of y (5). The answer is -10/5. Therefore, 3x 5y 10 0 written in slope-intercept form is y = (3/5)x - (10/5).The slope-intercept form of 3x 5y 10 0 is y = (3/5)x - (10/5).

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Complete question: What is the equation of the line represented by 3x + 5y = 10 in slope-intercept form?

The equation of the vertical line passing through (-5,-2) is x = -5.

In the given question, we have to find the equation of the vertical line through (−5, −2).

The given point is (−5, −2).

Vertical Line is a line that runs perpendicular to the Y-axis. It runs in a straight line from top to bottom and vice versa.

We are aware that the y-axis' slope is unknown.

Therefore, any vertical line is perpendicular to the y-axis and has an arbitrary slope.

The vertical line equation is given as x = k, where k can take on any value along the x-axis.

We must enter x = -5 because the line passes through the point (-5, -2).

So, x = k = -5

Hence, the equation of the vertical line passing through (-5,-2) is x = -5.

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The complete question is:

What is the equation of the vertical line through (−5, −2)?

Answer: -1

Step-by-step explanation:h(x) = -x - 3

so

h(-2) = - (-2) - 3 = 2 - 3 = -1

Answer:

h(-2) = -1

Step-by-step explanation:

subsitute x = -2 into h(x) = -x -3

h(-2) = -(-2)-3

h(-2) = -1

I hope this helps you :)

The exponent of a number is the number of times it is multiplied by itself. Product of Powers and Power to a Power are examples of exponent characteristics.

In algebra, the seven exponent properties are as follows:

1. A byproduct of power.

2. The power quotient is in charge.

3. The power's reign.

4. The product power rule.

5. The efficacy of a quotient rule.

6. The zero-power rule.

7. The negative exponent rule.

For example, 2 to the third (written as 2³) is equivalent to 2 x 2 x 2 = 8. 2 × 3 = 6 is not equivalent to 2³. Remember that a number multiplied by one equals itself.

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Height (h) is the dependent variable and minutes (m) is the independent variable in the equation h=60-4m.

In algebra, a symbol (usually a letter) used to indicate an unknown numerical value in an equation or algebraic statement. A variable is a quantity that is changeable rather than fixed. In mathematics, a variable is an alphabet or phrase that represents an unknown amount, unknown value, or unknown number. Variables are very useful in algebraic expressions or algebra. As an example, the variables x and 9 are constants in the linear equation x+9=4.

Here,

m- minutes is the independent variable

h- height is the dependent variable

The dependent variable is height h and independent variable is minutes m as the equation is h=60–4m.

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The average rate of f(x) is -2.1 and The average rate of g(x) is -5.8

What is function ?

Function can be defined in which it relates an input to output.

Given ,

functions are ,

f(x) =  - 0.3 x²

g(x) = - 0.6 x²

and interval 2 <=  x  <= 5

So, the average rate  =  f ( 5 ) - f(2 )  /  5 - 2

= -0.3 * 5 * 5  +  0.3* 2 * 2 / 3

= -7.5 + 1.2 / 3

= -6.3 / 3

= - 2.1

So, the average rate of g(x)  =  f ( 5 ) - f(2 )  /  5 - 2

= -0.6 * 5 * 5  +  0.6* 2 * 2 / 3

= -15 + 2.4 / 3

= -17.4 / 3

= - 5.8

Therefore, The average rate of f(x) is -2.1 and The average rate of g(x) is -5.8

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Become familiar with the distance formula, a Pythagorean theorem application that can be used to determine the separation between two places.Height after three seconds is 144 feet

Become familiar with the distance formula, a Pythagorean theorem application that can be used to determine the separation between two places. To compute the separation between any two points, the Pythagorean theorem can be rewritten as d=((x 2-x 1)2+(y 2-y 1)2). Summary.The following literal equation relates the variables of distance, rate, and time:

distance=rate×timed=rt

You will have traveled 180 miles if, for instance, your speed is 60 mph and you drive for three hours.

Height after three seconds is 144 feet

H(t) =16 t²

Given

The phrase 16t power 2

Fixing (a)

As an algebraic expression, write.

Let H stand in for the height at time t.

We thus have:

H(t) =16 t²

The height after three seconds, for solving (b)

This suggests that:

t= 3

H(t) = 16 t2

H((3) = 16*32

H((3) = 16*9 H((3) = 144

by substituting 3 for t.

hence the height is 144 feet.

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Answer: (x - 10)^2 is the equation

The length of c in the right angle triangle is 8.6 mm.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

The sides of a right angle triangle c an be found using Pythagoras's theorem as follows:

Hence,

c² = a² + b²

Hence,

Therefore,

c² = 5² + 7²

c² = 25 + 49

c² = 74

square root both sides

c = √74

c = 8.60232526704

Therefore,

c = 8.6 mm

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The exression is 1/2p - 20 and Irene scored 90 points.

Let's assume that Irene scored p points.

Then, Edwin's score would be 20 points less than half of Irene's score: (1/2)*p - 20.

b) If Edwin scored 25 points,

We can substitute this into the expression from part a to find the value of p: (1/2)*p - 20 = 25.

Solving for p, we have p = 90.

So, Irene scored 90 points.

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Answer:

$321.60

Step-by-step explanation:

area = 4 * 5 = 20

20 * 16.08 = 321.60

Answer:

$321.60

Step-by-step explanation:

Answr:

1.the y intercept is 4 as the base fee is $4

2.£28

3. 2(rate per mile driven)

Step-by-step explanation:

2.

2x7=14

14+4=28

The length s of the circular arc is; 27π/4

The formula for length of arc is;

L = (θ/ 360) * (2πr)

where;

θ is central angle

r is radius

From the diagram, we see that;

θ = 3π/4

r = 9

Now, 360 degrees in radians is 2π. Thus;

L = (3π/4)/(2π) * 2π(9)

L = (3π/4) * 9

L = 27π/4

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The value of the angle m∠ KJL  in the triangle is 68 degrees.

The angle m∠ KJL can be found using triangle exterior angle theorem. The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

Therefore, the angle can be found as follows:

∠JLM = 141 degrees

∠JKL = 73 degrees

Hence,

∠JLM = ∠ KJL + ∠JKL

∠ KJL = 141 - 73

∠ KJL = 68 degrees

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The system of equations models this if Batman completed obstacles and Superman completed obstacles are b + s = 24 and 4s = 20.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, Batman completed 4 more than three times the number of obstacles that Superman completed.

let, The number of obstacles completed by superman is 's'.

Therefore, b = 3s + 4, and b + s = 24.

b + s = 24.

3s + 4 + s = 24.

4s = 20.

So, The expression models this if Batman completed obstacles and Superman completed obstacles are,

b + s = 24 and 4s = 20.

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Answer: The complementary angle of 35° is 55°. true

Step-by-step explanation:

We can find the complementary angle of 35° using subtraction. We do this by subtracting 35° from 90°.

Answer:

A- TRUE

Step-by-step explanation:

subtract 35° from 90° to find complementary angle which is 55°.

The substitution method is one of the algebraic approaches to solving simultaneous linear equations. It applies to substitute the value of any one of the variables from one equation into the other equation.

The substitution method is a simple method to solve a system of linear equations algebraically and find the solutions of the variables. As the name implies, it applies to finding the value of the x-variable in terms of the y-variable from the first equation and then substituting the value of the x-variable in the second equation.

In this method, we can find the value of the y-variable by solving the equation. And then, we can substitute the value of y in any of the given equations to find the value of x. 

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Answer: 41

Step-by-step explanation:

Discriminant = b^2 - 4ac

= 3^2 - 4 * -8 * 1

= 9 - (-32)

= 41