A group decides to go white rafting on the river map of the river has a scale in which 1.5 inches represents 5 miles on the map distance between the starting point in the ending point of their trip is 12 inches. What is the actual distance from the starting point to the ending point.

The distance from the bottom of the building to the point where the ladder is touching the building for triangle 2, obtained using trigonometric ratio of tangent is 12 feet. The correct option is therefore;

12 feet

The trigonometric ratios are the value relationship between an interior angle of a right triangle and two of the sides of the triangle.

The right triangles are similar, therefore, the tangent of the angle the ladder makes with the ground are the same, which indicates;

tan(θ) = (Length of the side facing the angle θ) ÷ (Length of the side adjacent to the angle θ)

The side facing the angle is the distance from the bottom to the point where the ladder touches the building.

The adjacent to the angle is the horizontal distance from the bottom to the ladder to the building.

Therefore; tan(θ) = 18/12 = x/8

Where x = The distance from the bottom of the building to the point the ladder touches the building for triangle 2

18/12 = x/8

x = 18/12 × 8 = 12

The distance, x = 12 feet

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Answer:

12?

Step-by-step explanation:

I'm not too sure! I am in the middle of taking the test right now.

180.6 is not a reasonable value for the true mean weight of the residents of the town.

Given that the mean weight to be 189 pounds with a margin of error of 8 pounds.

So, the range of the mean weight is =

(189 + 8, 189 - 8)

(197, 181)

Therefore the range will lie between 197 and 181.

Hence 180.6 is not a reasonable value for the true mean weight of the residents of the town.

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The dimensions of the rectangular horse pen are 40 feet (width) and 42 feet (length).

The area of a rectangle is expressed as:

Area = length × width

Given that,  the length of the pen will be 2 feet longer than the width, so the width is x feet and the length can be expressed as (x + 2) feet.

Using area of rectangle:

Area = length × width

1680 = (x + 2) × x

Simplify

1680 = x² + 2x

x² + 2x - 1680 = 0

Solve for x:

Using factoring

(x + 42)(x - 40) = 0

Hence:

x + 42 = 0 or x - 40 = 0

x = -42 or x = 40

Since we are dealing with dimensions, we use the positive value:

The valid solution is x = 40.

This represents the width of the horse pen.

The length can be found by adding 2 to the width:

Length = x + 2

Plug in x = 40

= 40 + 2

= 42

Therefore, the length is 42 feets.

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The probability P(x < 4) will be 0.273. The correct option is A.

Probability is a branch of mathematics that deals with the measurement and analysis of uncertainty. In other words, probability is the measure of the likelihood or chance that a particular event will occur.

Since X is a continuous uniform distribution between 1 and 12, the probability density function (PDF) is given by:

f(x) = 1/11 for 1 ≤ x ≤ 12

= 0 otherwise

The probability P(X < 4) can be calculated as follows:

P(X < 4) = ∫[from 1 to 4] f(x) dx

= ∫[from 1 to 4] 1/11 dx

= [1/11 * x] (from 1 to 4)

= (4/11) - (1/11)

= 3/11

Rounding this to three decimal places, we get:

P(X < 4) ≈ 0.273

Therefore, the answer is 0.273.

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Factor of x ^2+7x−18 is (x−2)(x+9).

We have,

In mathematics, factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.

We are given a polynomial expression in terms of variable x as:

x² - 7x + 18

so, we have,

x ^2+7x−18

=x ^2−2x+9x−18

=x(x−2)+9(x−2)

=(x−2)(x+9)

∴ x ^2+7x−18=(x−2)(x+9)

Hence, Factor of x ^2+7x−18 is (x−2)(x+9)

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complete question:

Factor completely x² - 7x + 18.

Prime

(x-9)(x-2)

(x-9)(x+2)

(x + 9)(x+2)

The perimeter of the square that is given in the diagram above would be = 96cm

To calculate the perimeter of a square, the formula for the perimeter of a square should be used and this is given below.

That is ;

perimeter = 4a

where ;

a = side length = 24cm

Perimeter = 4× 24 = 96cm

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A) The total amount of the repair that is covered by the insurance is $2970.

B) He would need to pay $2000.

C) The insurance company will have to pay $2750.

A) To calculate the total amount of the repair that is covered, we need to consider the deductible and the 8% tax.

The repair cost before tax is $4750. Since the insurance adjuster approves any repairs, the deductible of $2000 needs to be subtracted from the repair cost.

Repair cost after deductible = $4750 - $2000 = $2750.

Now, we need to add the 8% tax to the repair cost after deductible.

Tax amount = 8% of $2750 = $2750 * 0.08 = $220.

Total amount of the repair that is covered = Repair cost after deductible + Tax amount

Total amount of the repair that is covered = $2750 + $220 = $2970.

Therefore, the total amount of the repair that is covered by the insurance is $2970.

B) If John has had no previous claims in the past year, he would be responsible for paying the deductible amount. In this case, John's deductible is $2000. So, he would need to pay $2000.

C) The insurance company will be responsible for paying the remaining amount after the deductible has been paid. In this case, the remaining amount is the total repair cost minus the deductible.

Amount insurance company has to pay = Total repair cost - Deductible

Amount insurance company has to pay = $4750 - $2000 = $2750.

Therefore, the insurance company will have to pay $2750.

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The ratios associated to the line segment QR are QP : PR = 1 : 4 and QP : QR = 1 : 5.

In this problem we find a line segment defined by points Q(x, y) = (1, 7) and R(x, y) = (- 9, - 8) and whose partition point is P(x, y) = (- 1, 4), whose ratios must be found. First, find the lengths of line segments QP and PR by Pythagorean theorem:

QP = √[(- 1 - 1)² + (4 - 7)²]

QP = √[(- 2)² + (- 3)²]

QP = √13

PR = √[[- 9 - (- 1)]² + (- 8 - 4)²]

PR = √[(- 8)² + (- 12)²]

PR = 4√13

QR = 5√13

Second, determine the ratios:

QP : PR = √13 : 4√13

QP : PR = 1 : 4

QP : QR = √13 : 5√13

QP : QR = 1 : 5

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Given two points (7,-2) and (-3,-10), we can determine the slope of the line passing through them as follows:

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

slope = (-10 - (-2)) / (-3 - 7)

slope = -8 / -10

slope = 4 / 5

Since we want a line perpendicular to this line, we need to find its negative reciprocal. The negative reciprocal of 4/5 is -5/4.

Now that we have the slope of the perpendicular line, we can use the point-slope form of a line to find its equation. The point-slope form is:

y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is a point on the line.

Using the point (-8,-12), we can substitute the values into the equation:

y - (-12) = -5/4(x - (-8))

y + 12 = -5/4(x + 8)

Simplifying, we get:

y + 12 = -5/4x - 10

y = -5/4x - 22

Therefore, the equation of the perpendicular line passing through the point (-8,-12) is y = -5/4x - 22 in point-slope form.

The missing measurements on the triangle are given as follows:

m < H = 65º, y = 32.2, c = 35.5.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

The sum of the internal angle measures of a triangle is of 180º, hence the measure of angle H is given as follows:

m < H + 25 + 90 = 180

m < H = 65º.

Regarding the angle of 25º, we have that 15 is the opposite side, while y is the adjacent side, hence the measure of y is given as follows:

tan(25º) = 15/y

y = 15/tangent of 25 degrees

y = 32.2.

Applying the Pythagorean Theorem, the value of c is obtained as follows:

c² = 15² + (32.2)²

[tex]c = \sqrt{15^2 + 32.2^2}[/tex]

c = 35.5.

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Part A: The total value of the loan with semi-annual compounding is $36,351.74.

Part B: The total value of the loan with quarterly compounding is $36,645.80.

Part C: The difference between the total interest accrued on each loan is $294.06, with the loan that compounds quarterly accruing more interest due to the more frequent compounding periods, which results in a higher effective interest rate over the same time period.

Part A:

To find the total value of the loan with semi-annually compounded interest, we can use the formula for compound interest:

[tex]A = P(1 + r/n)^{ (nt) }[/tex]

Where:

A = the total amount paid

P = the principal amount borrowed

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, P = $20,000, r = 0.06 (6%), n = 2 (semi-annually compounded), and t = 10 years.

[tex]A = 20000(1 + 0.06/2)^{(2*10) } = $36,109.13[/tex]

Therefore, the total value of the loan with semi-annually compounded interest is $36,109.13.

Part B:

To find the total value of the loan with quarterly compounded interest, we use the same formula but with n = 4 (quarterly compounded):

[tex]A = 20000(1 + 0.06/4)^{(4*10)} = $36,533.71[/tex]

Therefore, the total value of the loan with quarterly compounded interest is $36,533.71.

Part C:

The difference between the total interest accrued on each loan is the difference between the total amount paid for each loan minus the principal borrowed:

For the semi-annually compounded loan:

Total interest = $36,109.13 - $20,000 = $16,109.13

For the quarterly compounded loan:

Total interest = $36,533.71 - $20,000 = $16,533.71

The difference in total interest accrued between the two loans is:

$16,533.71 - $16,109.13 = $424.58

The loan with quarterly compounded interest accrues more interest due to the higher compounding frequency.

The difference in total interest accrued between the two loans is relatively small, but over time it can add up.

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The compound interest is solved and answer to part b) is not double the answer to part a) because the interest is compounded monthly, not annually.

Given data ,

To calculate how much was in Tristan's account at the end of one year, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the amount at the end of the time period, P is the principal (the initial deposit), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.

In this case, P = $750, r = 0.0325, n = 12 (since the interest is compounded monthly), and t = 1. Plugging in these values, we get:

A = $750(1 + 0.0325/12)⁽¹²ˣ¹⁾ = $8,086.43

Therefore, there was $8,086.43 in Tristan's account at the end of one year.

b)

To calculate how much was in Tristan's account at the end of two years,

t = 2,

A = $750(1 + 0.0325/12)⁽¹²ˣ²⁾ = $16,575.29

Hence , there was $16,575.29 in Tristan's account at the end of two years

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Pick the first option.

f(x) is dependent on x.

the 2nd option is wrong; the dependent variable is the output, the independent variable is the input.

3rd option is wrong, dependent determines the range.

4th is wrong, x is independent variable.

Answer:

1,000 - 50x > 600

-50x > -400

$0.00 < x < $8.00

Answer:

90Y + 36

Step-by-step explanation:

just multiply the length by the width.

9 X (8y + 4 + 2y)

= 9 X (10y + 4)

= 90Y + 36

1. In the short run, the firms in the competitive industry will earn positive profits because the market price is higher than the minimum of the average cost curve. The Option A.

2. If the market price is P4, the individual firm in a competitive industry will earn zero profit. The Option B

3. Firm would be encouraged to enter this market for all price that exceeds P4. The Option D,

When the market price is between P4 and P6, firms in a competitive industry are able to earn positive profits in the short run because the price is above their average variable cost (AVC) but below their average total cost (ATC).

This means that firms are covering their variable costs and also making a contribution towards their fixed costs. As a result, they are earning positive profits. But, in the long run the firms will enter the industry and increase supply causing market price to decrease towards P4 where firms earn zero economic profits in the long run.

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The value and the slope of the curve at point (x, y) = (7, 2) are 2 and 1 / 7, respectively.

In this problem we find the case of a line tangent to a curve at point (x, y) = (7, 2) and that passes through the point (x, y) = (0, 1). The equation of the line is described by following formula:

y = m · x + b

Where:

And the slope of the line is found by secant line formula:

m = Δy / Δx

First, determine the slope of the secant line:

m = (2 - 1) / (7 - 0)

m = 1 / 7

f'(7) = 1 / 7

Second, find the value of the curve:

f(7) = 2

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The lower quartile of the given data set is 63.

To find the lower quartile (Q1), we need to determine the value that divides the data set into the lower 25% of the values.

First, we need to sort the data set in ascending order: 61, 61, 62, 64, 66, 69, 69, 70, 72, 73, 74, 78.

Next, we calculate the position of the lower quartile using the formula: (n+1)/4, where n is the number of data points. In this case, we have 12 data points, so (12+1)/4 = 13/4 = 3.25.

Since 3.25 is not a whole number, we can find the lower quartile by taking the average of the data points at positions 3 and 4.

The data point at position 3 is 62, and the data point at position 4 is 64.

Therefore, the lower quartile (Q1) is the average of 62 and 64:

(Q1) = (62 + 64)/2 = 126/2 = 63.

Hence, the lower quartile of the given data set is 63.

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The height of the square pyramid is approximately 91.92 inches.

In a square pyramid, the slant height (s) is the hypotenuse of a right triangle formed by the height (h), half the length of the base (b/2), and the slant height (s). We can express this relationship as:

[tex]s^2 = (b/2)^2 + h^2[/tex]

Given that the length of one side of the base (b) is 25.2 in and the slant height (s) is 93.7 in, we can substitute these values into the equation:

[tex]93.7^2 = (25.2/2)^2 + h^2[/tex]

Simplifying:

[tex]8761.69 = 316.8 + h^2[/tex]

Subtracting 316.8 from both sides:

[tex]h^2 = 8444.89[/tex]

Taking the square root of both sides:

h ≈ 91.92 in

Therefore, the height of the square pyramid is approximately 91.92 inches.

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The measure of the angle BCA is 50 degrees.

The angles at the circumference subtended by the same arc are equal.

The angles at the circumference on the same segment theorem states that angles in the same segment of the circle are equal.

Therefore, let's use the theorem to find the angle ∠BCA in the circle.

Hence,

∠BCA = ∠BOA

Finally,

∠BCA =  50 degrees.

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Answer:

The number of ways to construct a string of 4 digits without repetition can be found using the permutation formula.

The formula for finding the number of permutations of n objects taken r at a time without repetition is:

P(n, r) = n! / (n - r)!

Where n is the total number of objects and r is the number of objects being chosen.

In this case, we have 10 digits (0-9) to choose from, and we need to choose 4 digits without repetition. Therefore, the number of ways to construct a string of 4 digits without repetition is:

P(10, 4) = 10! / (10 - 4)!

P(10, 4) = 10! / 6!

P(10, 4) = (10 × 9 × 8 × 7) / (4 × 3 × 2 × 1)

P(10, 4) = 10,080

Therefore, there are 10,080 ways to construct a string of 4 digits without repetition using the digits 0-9.

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The earthquake registered 3.6 on the Richter scale.

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The function for this problem is given as follows:

R = log(A/0.0001)

The amplitude of the earthquake was of 0.3954, hence the magnitude of the earthquake is obtained as follows:

R = log(0.3954/0.0001)

R = 3.6.

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The trend line that best fits the data in this problem is given by the following option:

Option D.

For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, that is:

Residual = Observed - Predicted.

Hence the graph of the line of best fit should have the smallest possible residual values, meaning that the points on the scatter plot are the closest possible to the line.

As option D has the points the closest to the line, it is the correct option in the context of this problem.

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Answer:

3/4

Step-by-step explanation:

(75 divided by 25 / 100 divided by 25) = 3/4

a. Probability of landing on A = 2/6 = 1/3. b. Probability of landing on C, D, or E = 3/6 = 1/2. c. The probabilities are not equal, the spinner is not fair.

a. Since there are 6 equal-sized sections on the spinner and only 2 sections labeled A, the probability of the pointer landing on A is given by:

Probability of landing on A = Number of favorable outcomes / Total number of possible outcomes

Number of favorable outcomes = 2 (since there are 2 sections labeled A)

Total number of possible outcomes = 6 (since there are 6 equal-sized sections on the spinner)

Probability of landing on A = 2/6 = 1/3

b. To find the probability of the pointer landing on C, D, or E, we need to determine the number of favorable outcomes (sections labeled C, D, or E) and the total number of possible outcomes.

Number of favorable outcomes = 3 (since there are 3 sections labeled C, D, or E)

Total number of possible outcomes = 6 (since there are 6 equal-sized sections on the spinner)

Probability of landing on C, D, or E = Number of favorable outcomes / Total number of possible outcomes

Probability of landing on C, D, or E = 3/6 = 1/2

c. To determine if the spinner is fair, we need to check if the probabilities of landing on each letter are equal. From the previous calculations, we found that the probability of landing on A is 1/3 and the probability of landing on C, D, or E is 1/2.

Since the probabilities are not equal, the spinner is not fair.

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