The scale of a map is 1 inch : 12 miles. The distance on the map between zionsville and lafayette is 8 inches. what is the actual distance, in miles, between zionsville and lafayette?

It is proved that x⁻¹/(x⁻¹ + y⁻¹) + x⁻¹/(x⁻¹ - y⁻¹) = 2y²/(y² - x²).

What is an equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions written on the left and right sides. We have LHS = RHS (left-hand side = right-hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it contains no "equal to" symbol. It will be regarded as a phrase.

Given that

x⁻¹/(x⁻¹ + y⁻¹) + x⁻¹/(x⁻¹ - y⁻¹) = 2y²/(y² - x²)

Now solve the left-side expression:

L.H.S =

x⁻¹/(x⁻¹ + y⁻¹) + x⁻¹/(x⁻¹ - y⁻¹)

Now apply the formula a⁻¹ = 1/a:

= (1/x)/(1/x +1/y) + (1/x)/(1/x - 1/y)

= (1/x)/((x+y)/xy) + (1/x)/((y-x)/xy)

Now taking common  (1/x)/(1/xy):

= (1/x)/(1/xy)[1/(x+y) + 1/(y-x)]

= (xy)/(x)[(y - x + x + y)/(x+y) (y-x)]

= y[2y/(x+y) (y-x)]

Applying the algebraic identity (x - y)(x + y) = x² - y²:

= 2y²/(y² - x²)

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Answer:

a8

Step-by-step explanation:

Here you go.

nth term is ar^n-1

The equation of the perpendicular line is 5x - 3y = 15

The complete question is added as an attachment

From the question, we have the following parameters that can be used in our computation:

The points on the line are

(-3, 2) and (2, -1)

So, the slope (m) is

m = (-1 - 2)/(2 + 3)

Evaluate

m = -3/5

The equation of the perpendicular line is then calculated as

y = -1/m(x - x1) + y1

Where

(x1, y1) = (3, 0)

So, we have

y = 5/3(x - 3)

This gives

3y = 5x - 15

Rewrite as

5x - 3y = 15

So, the equation is 5x - 3y = 15

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113.399 grams make up a quarter pound or 0.25 pounds.

The unit of measurement known as a QP, or quarter pound, is frequently used in the sale and distribution of food item measures.

Kilograms equal 2.2046 pounds.

1,000 grams make up one kilogram.

Alternatively, 1,000 grams is 2.2046 pounds.

So, one pound equals x grams.

Divide 1,000 grams by 2.2046 to get 453.597 grams in a pound.

So, one pound is 453.597 grams.

453.597 divided by 0.25 to get 0.25 pounds, or 0.25 pounds, is 113.399 grams.

To achieve precise and consistent outcomes, weight measures are frequently used in cooking and baking. A quarter pound of a culinary item, such as butter or sugar, is also referred to as a QP.

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The required height of domino number 7 is 11.76 cm (rounded to two decimal places).

Arithmetic progression is the series of numbers that have common differences between adjacent values.

Here,
Since each subsequent domino is 13% taller than the one before, we can find the height of each domino by multiplying the height of the previous domino by 1.13.

Starting with the height of the smallest domino, we can calculate the height of each subsequent domino using this rule:

Height of domino n = Height of domino (n-1) × 1.13

Using this formula, we can find the height of each domino:

Height of domino 1 = 5.00 cm × 1.13 = 5.65 cm

Height of domino 2 = 5.65 cm × 1.13 = 6.38 cm

Height of domino 3 = 6.38 cm × 1.13 = 7.21 cm

Height of domino 4 = 7.21 cm × 1.13 = 8.16 cm

Height of domino 5 = 8.16 cm × 1.13 = 9.22 cm

Height of domino 6 = 9.22 cm × 1.13 = 10.41 cm

Height of domino 7 = 10.41 cm × 1.13 = 11.76 cm

Therefore, the height of domino number 7 is 11.76 cm (rounded to two decimal places).

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The length of side x in simplest radical form with a rational denominator is   [tex]\sqrt{3} /2[/tex].

What is the equilateral triangle?

In an equilateral triangle, all sides are equal in length.

That means that all the angles of the triangle will be congruent.

Since a triangle has 3 angles that always add up to 180 degrees, each angle is 60 degrees.

Therefore, the hypotenuse of the equilateral triangle is 1.

So,

[tex]x = 1 * sin60[/tex]°

[tex]x = 1 * \sqrt{3} /2\\x = \sqrt{3} /2[/tex]

Hence, The length of side x in simplest radical form with a rational denominator is   [tex]\sqrt{3} /2[/tex].

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The weight of th baby elephant in the month of March would be 247.5 Kg.

Weight of a body is the force exerted by the earth on the body on the surface of the earth towards its center.

Given is that in January a baby elephant weighs 180kg. By March the weight of the baby elephant had increased by ⅜.

Assume the weight of the baby elephant in March would be {x} Kg. We can write -

{x} = 180 + 3/8 of 180

{x} = 180 + 3/8 x 180

{x} = 180 + 67.5

{x} = 247.5 Kg

Therefore, the weight of th baby elephant in the month of March would be 247.5 Kg.

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The value of the average normal distribution with a 95% degree of confidence is Z 1.96 as 95% of the area under the standard normal distribution curve should fall between -Z and Z, hence Z should be selected to reflect this.

In statistics, the standard normal distribution is a bell-shaped curve with a mean of 0 and a standard deviation of 1. The region beneath the curve between any two values represents the chance of seeing a value inside a given range.

At a 95% confidence level, the value of Z should be chosen so that 95% of the area under the standard normal distribution curve is between -Z and Z. Using a calculator or a generic table of the normal distribution, we may determine Z = 1.96 with a 95% confidence interval. In 95% of the situations, the values of the classic normal distribution lie between +/- 1.96 standard deviations from the mean.

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The equation of the line passing through (9,11) and perpendicular to the line passing through (6,1) and (2,1) is x = 6

Find the slope of the line passing through (6,1) and (2,1):

The slope of a line passing through two points (x1,y1) and (x2,y2) is given by:

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

Substituting the given coordinates, we get:

slope = (1 - 1) / (2 - 6) = 0

Therefore, the slope of the line passing through (6,1) and (2,1) is 0.

Find the slope of the line perpendicular to the line passing through (6,1) and (2,1):

The slope of a line perpendicular to a line with slope m is given by:

perpendicular slope = -1/m

Substituting the slope of the line passing through (6,1) and (2,1), we get:

perpendicular slope = -1/0 (which is undefined)

This means that the line perpendicular to the line passing through (6,1) and (2,1) is a vertical line passing through the point (6,1) and (2,1).

Write the equation of the line passing through (9,11) and perpendicular to the line passing through (6,1) and (2,1):

Since the line passing through (6,1) and (2,1) is a horizontal line with equation y = 1, the line perpendicular to it is a vertical line passing through the point (6,1) and (2,1). The equation of a vertical line passing through a point (a,b) is given by:

x = a

Substituting the value of x = 6 (since the vertical line passes through (6,1) and (2,1)), we get:

x = 6

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The error in the solution is that, In step 2, the Distributive Property was applied incorrectly.

Equations are mathematical expressions consisting of two or more variables and constants on two sides connected by an equal to sign.

Solution of the equation is the value of the variable that the equation holds true.

Given equation is,

8 - [tex]\frac{a}{2}[/tex] = 3 (4 - 5a)

Using the multiplication property of equality, multiplying whole equation by 2,

(2 × 8) - a = 6 (4 - 5a)

16 - a = 6 (4 - 5a)

Distributive property states that, for three numbers or expressions, a, b and c,

a (b + c) = ab + ac

Applying that,

6 (4 - 5a) = (6 × 4) - (6 × 5a) = 24 - 30a

But the student didn't multiply 6 with 5a, and thus he got 24 - 5a in step 2.

Hence the incorrect step is step 2 because of incorrect use of distributive property.

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Your question is a bit confusing. The complete question with an image is given below.

A student provided the steps for solving an equation. Which statement describes the error in the solution?

Equation : 8 - [tex]\frac{a}{2}[/tex] = 3 (4 - 5a)

Answer: look at the image for the answer and explanation

Step-by-step explanation:

The percentage of the increase in the cost of season tickets is 8%.

A ratio or value that may be stated as a fraction of 100 is called a percentage. Moreover, it is indicated by the symbol "%."

Given:

In the last year,

$2450 was the cost of the season ticket.

This year, the cost is $2,646.

Let n be the percentage in increase amount in the season ticket.

So, applying the percentage formula,

2646 - 2450 = (2450 x n/100)

196 = 2450 x n/100

19600 = 2450 x n

Applying cross multiplication,

we get,

n = 19600/2450

n = 8

Therefore, the required value of the percentage is 8%.

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To calculate the value of g we have to multiply the G( universal gravitational constant) and M( mass of body) divide by R square.

Earth's acceleration caused by gravity, or the magnitude of g, is 9.8 m/s2. According to this, an item falling freely on Earth would accelerate by 9.8 metres per second. The gravity of the Earth is to blame for this acceleration.

The acceleration due to gravity formula is given by

[tex]g = \frac{GM}{R^2}[/tex]

Where,

G is the universal gravitational constant, G = 6.674×10-11m3kg-1s-2.

M is the mass of the massive body measured using kg.

R is the radius of the massive body measured using m.

g is the acceleration due to gravity measured using m/s2.

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The total cost for 10 hours of work would be 25 + 50(10) = 525.

Cost is the monitorial associated with the purchase of production of food or service if can include the prices of material of which is over it and other expenses that are related to the production of the code of service cost is a major fraction of when deciding whether to purchase a product something as it is and indicator of the value of the product of sound service.
The marginal cost of producing 5 items can be calculated using the equation C(x)=1300+4x/10. The marginal cost is the cost associated with producing one additional item. To calculate the marginal cost, we can plug in x=5 into the equation.

The equation in slope-intercept form for cost, c, after h hours of service is c = 25 + 50h.

The total cost for 8 hours of work would be 25 + 50(8) = 425.

The total cost for 10 hours of work would be 25 + 50(10) = 525.

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Answer:

Step-by-step explanation:

256. You can make this observation because they pattern has a rule that you multiply by 2 to get the next number.

Answer:

Another observation we can make about this number pattern is that each term is obtained by doubling the previous term. This means that the pattern is an example of exponential growth, where the growth factor is 2.

We can also observe that the sequence is a power of 2, where the first term is 2^2, the second term is 2^3, the third term is 2^4, and so on. In other words, the nth term in the sequence can be represented by the formula 2^(n+1).

Additionally, we can see that the sequence is an increasing sequence, where each term is greater than the previous one. This is because we are multiplying each term by 2, which means that each subsequent term will be twice as large as the previous one.

The expression below are correct:

πr_c^2h_c / 4 = πr_p^2h_p / 5

h_c / h_p = (r_p / r_c)^2 * (5 / 4)

To prove that the equation

πr_c^2h_c / 4 = πr_p^2h_p / 5

and

h_c / h_p = (r_p / r_c)^2 * (5 / 4)

are correct, we can use some algebraic manipulation and the properties of ratios.

Starting with the first equation, we can simplify it as follows:

πr_c^2h_c / 4 = πr_p^2h_p / 5

5πr_c^2h_c = 4πr_p^2h_p (multiply both sides by 20 to get rid of fractions)

5r_c^2h_c = 4r_p^2h_p (cancel out π on both sides)

Next, we can rearrange the second equation to solve for h_c:

h_c / h_p = (r_p / r_c)^2 * (5 / 4)

h_c = h_p * (r_p / r_c)^2 * (5 / 4) (multiply both sides by h_p)

Now we can substitute this expression for h_c into the simplified version of the first equation:

5r_c^2h_c = 4r_p^2h_p

5r_c^2(h_p * (r_p / r_c)^2 * (5 / 4)) = 4r_p^2h_p (substitute h_c)

5r_c^2r_p^2(5/4) = 4r_p^2h_p (simplify)

5r_c^2 = (16/25)h_p (divide both sides by 4r_p^2)

Finally, we can substitute this expression for h_p into the earlier expression we found for h_c:

h_c = h_p * (r_p / r_c)^2 * (5 / 4)

h_c = (5/16)r_c^2 (substitute for h_p)

h_c / r_c^2 = 5/16

This means that the ratio of the height to the radius squared for cylinder c is 5/16, which is a constant value. We can also rearrange the simplified first equation to solve for h_p in terms of r_c and r_p:

5r_c^2h_c = 4r_p^2h_p

h_p = (5/4)h_c(r_c/r_p)^2 (divide both sides by 4r_p^2 and multiply by 5/4)

Substituting this expression for h_p into the second equation, we get:

h_c / h_p = (r_p / r_c)^2 * (5 / 4)

h_c / ((5/4)h_c(r_c/r_p)^2) = (r_p / r_c)^2 * (5 / 4) (substitute for h_p)

1 / ((5/4)(r_c/r_p)^2) = (r_p / r_c)^2 * (5 / 4) (simplify)

Now we can simplify this expression using the fact that (r_p / r_c)^2 = 1 / (r_c / r_p)^2:

1 / ((5/4)(r_c/r_p)^2) = (1 / (r_c/r_p)^2) * (5/4)

1 / (5/4) = (r_c/r_p)^4 * (5/4)

4/5 = (r_c/r_p)^4

(r_c/r_p)^2 = √(2/√5) or -(√2/√(√5))

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Answer:

8x8 > 9x7 (64 > 63)

Step-by-step explanation:

The equation of the line that passes through the point (2, 1) and has a slope of -5/2 is y=(-5/2)*x+6.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=3x+4. Where:

m= the slope.

b= the constant term that represents the y-intercept.

For the given example: m=3 and b=4.

The question gives:

Point : (2,1) , where x=2 and y=1

Slope= -5/2

From the  standard form of the linear equation ( y= mx+b) and the given point and the slope, you can write:

y=mx+b

1=-5/2*(2)+b , thus you can find b.

1=-5+b

-b=-5-1

-b=-6

b=6

If b=6 and m=-5/2, you can write the linear equation:

y=mx+b

y=(-5/2)*x+6

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The equation of line that models this is y = -5/2x + 6

The equation of a line is typically written in slope-intercept form, which is y = mx + b, where m is the slope of the line, and b is the y-intercept.

The slope (m) is a measure of how steep the line is, and it can be calculated using the formula:

y = mx + c

In the given question, the slope is -5/2 and the points are (2, 1)

Substituting the values into the formula of equation of line;

y = mx + c

1 = -5/2(2) + c

1 = -5 + c

c = 1 + 5

c = 6

The equation is y = -5/2 + 6

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Answer:

About 16 years

Step-by-step explanation:

The formula for compound interest is

[tex]P(t)=P_{0}(1+r/n)^n^t[/tex], where P0 is the principal, r is the interest rate, n is the number of compounding periods, and t is the time in years.

For this problem, our n = 12 because there are 12 months in a single year and we must convert our percentage to a decimal (3.60/100 = 0.0360): [tex]7000=4000(1+0.0360/12)^1^2^t\\7000=4000(1.003)^1^2^t\\1.75=1.003^1^2^t\\log(1.75)=log(1.003)^1^2^t\\log(1.75)=12t*log(1.003)\\\frac{log(1.75)}{log(1.003)} =12t\\1/12*\frac{log(1.75)}{log(1.003)}=t\\ 15.56818868=16=t[/tex]

The conversion of the unit centimeters to feet is written as 147 centimeters = 4.82283 feet.

Centimeters and feet are the units that are used for measuring the length of the any given parameter.

Conversion of the unit centimeter into feet is written as :

Value of  one centimeter =  0.0328084 feet.

To convert the given value 147 centimeters substitute in the given relation we have,

⇒ ( 147 × 1 ) centimeters = ( 147 ×  0.0328084 ) feet

⇒ 147 centimeters = ( 4.822835 ) feet

⇒  147 centimeters = ( 4.8228 ) feet ( Round upto four decimals )

Therefore, after conversion the measurements centimeters to feet we have 147 cm is equal to  ( 4.8228 ) feet ( Round upto four decimals ) .

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Answer:

[tex] \sf \: a) \: 2x + 7y - 2 [/tex]

[tex] \sf \: c) \: 7y - 2 + 2x [/tex]

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

The expression is,

→ -2x + 3 + 7y + 4x - 5

Let's simplify the expression,

→ -2x + 3 + 7y + 4x - 5

→ -2x + 4x + 7y + 3 - 5

→ (-2x + 4x) + (7y) + (3 - 5)

→ (2x) + 7y + (-2)

→ 2x + 7y - 2

→ 7y - 2 + 2x

Hence, option (a) & (c) is correct.

Step-by-step explanation:

-2x + 3 + 7y + 4x - 5 = 2x + 7y - 2

as addition is commutative (= can be done in any sequence of terms), the right answers are variations in the sequence of these 3 terms :

A and C are correct.

B and D disqualify themselves right away by including mixed terms of xy. you can never ever create such a mixed term just out of addition or subtraction of single x and y terms. you need multiplication to do that. but there is none.

A for loop in MATLAB allows a user to repeatedly execute a set of instructions for a specific number of times or until a specified condition is met.

In MATLAB, a for loop is a control structure that allows users to repeatedly execute a block of code a specific number of times or until a specific condition is met. The loop variable takes on a sequence of values specified by the user, and the statements within the loop are executed for each value of the loop variable.

For loops are a powerful tool in MATLAB for automating repetitive tasks and iterating over arrays and matrices, among other uses. They can help streamline complex computations and make code more efficient and easier to read.

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Answer:

Step-by-step explanation:

1 yard = 1/2in shadow

Then 8ft = 192 * 1/2in

Then the radio tower is 192 yards (1 yard = 3 feet)

The radio tower = 576 feet

Answer:

Step-by-step explanation:

576

Yes, in solid geometry a square is a rhombus. A rhombus has all four sides equal just like a square for why it is also known as a titled square.

A rhombus can be thought of as a special parallelogram since it is a quadrilateral with two pairs of parallel sides. Similar to a square, a rhombus likewise has equal sides on each of its four sides. As a result, it's frequently referred to as a tilted square.

According to definition, a square is a regular quadrilateral with four equal sides and four equal 90-degree angles.

Rhombus also has four equal sides.

Therefore, a square is a rhombus with all of its angles being right angles.

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The complete question is:

Given. a square proof it’s a rhombus.

Answer: The average rate of change from (-3,5) is 4.

Step-by-step explanation: This question is incomplete there a function is needed

So, suppose f(x) = 2x²-5

Given that, x= -3 to x= -5

let a = -3 and b=5

F(a) = F(-3) = 2(-3)²-5 = 13

F(b) = F(5) = 2(5)² -5 = 45

The gradient of the surface can be described as a vector.

The gradient of a surface, which is a vector, represents the size and direction of the sharpest increase in value at a certain location. The magnitude of this vector, which denotes the direction of the greatest rate of rise of the surface, indicates how steep the rise is. The influence of this gradient is felt along a surface, which is the difference. It stands in for a unit that is level with the ground.

In mathematics, the vector grad f(x,y,z) = (df/dx, df/dy, df/dz) represents the gradient of a three-variable function with scalar values, f(x,y,z). Variables like optimization and electromagnetism employ the gradient of a surface, which is a crucial notion in vector calculus. In particular, the gradient of a surface is frequently used to compute the normal vector to a surface or to identify the direction of the steepest rise or drop in a landscape.

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The instantaneous rate of change calculator is the tool that displays the rate of change

The change in the rate at a certain point is referred to as the instantaneous rate of change in mathematics. It is equivalent to the rate of change in a function's derivative value at a particular location. The obtained graph is identical to the slope of the tangent line if a graph for the instantaneous rate of change at a particular point is drawn.

A free online tool known as the Instantaneous Rate of change calculator shows the rate of change, the first-order differential equation for the specified function. This tool speeds up the calculation and shows the rate of change at a particular position in a split second. With time, the tool is now widely accepted and is often used is variety of calculations.

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the sample data supports the claim that the politician's chance of being elected is less than 70%.

To test whether the politician's claim is valid, we can perform a hypothesis test using the null hypothesis that the true probability of the politician being elected is 0.7 and the alternative hypothesis that the true probability is less than 0.7.

Let p be the true probability of the politician being elected. We have:

Null hypothesis: H 0 : p = 0.7

Alternative hypothesis: H a : p < 0.7 (one-tailed test with alpha = 0.05)

We can use the sample proportion, denoted by p, to estimate the true proportion p. The test statistic for testing the above hypotheses is given by:

z = (p - p) / √(p×(1-p)/n)

where n = 500 is the sample size. Under the null hypothesis, the test statistic follows a standard normal distribution. Using the given sample proportion p = 0.6, we can compute the test statistic as follows:

z = (0.6 - 0.7) / √(0.7×(1-0.7)/500) = -3.05

The corresponding p-value for this test statistic is P(Z < -3.05) = 0.0012 (using a standard normal distribution table or calculator).

Since the p-value (0.0012) is less than the significance level (0.05), we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the true probability of the politician being elected is less than 0.7. In other words, the sample data supports the claim that the politician's chance of being elected is less than 70%.

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The value of x is 24.

If chosen at random, the probability that he plays two games is 7/29

John Venn popularized the Venn diagram in the 1880s, which is a type of diagram that displays the logical relationship between sets. The diagrams are used in probability, logic, statistics, linguistics, and computer science to teach basic set theory and to show basic set relationships.

To find the value of x:

x + (42 - x) + (42 -x ) + (30-x) + 186 -42 + x - x -30 + x

=>150x + x = 174

x= 24.

From the Venn diagram, the number of students that play both games is 42

Hence, the probability is 42/174

Simplified further, it becomes:

7/29

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Answer: The new perimeter is 2334 inches.

Step-by-step explanation:

The way to find perimeter is 2L + 2W. The original length was 799 inches and 23 inches were added. 799 in. + 23 in. = 822 in. The width is 245 in. 2(822) + 2(245) = Perimeter. 1844 in. + 490 in. = 2334 in. is the Perimeter.