Nathan drove 234 miles in 6 hours. On average how fast did he drive in miles per hour?

The reference angle for A = -300° is given by R = 60°

Every angle is measured from the positive part of the x-axis to its terminal line (the line that determines the end of the angle) traveling counterclockwise. For angles in the first quadrant, i.e., angles less than or equal to 90 degrees, the reference angle is equal to the original angle.

The reference angle is always positive

0° to 90°: reference angle = angle

90° to 180°: reference angle = 180° - angle

180° to 270°: reference angle = angle - 180°

270° to 360°: reference angle = 360° - angle

Given data ,

Let the reference angle be represented as R

Now , let the given angle be A

A = -300°

And , for 270° to 360°: reference angle = 360° - angle

when the angle is negative and less than -270°

The reference angle is given by adding 360° to it and the angle lies in the first quadrant

So , the reference angle R = A + 360°

R = -300 + 360

R = 60°

Hence , the reference angle is 60°

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The exponential model for the data is y=0.646(1.087)ˣ.

Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).

From the table we have, (8, 1.26), (10, 1.49)

We know that, the general form of exponential model is y=abˣ.

Here, substitute (8, 1.26) in y=abˣ, we get

1.26=ab⁸ -------(i)

a=1.26/b⁸

Here, substitute (10, 1.49) in y=abˣ, we get

1.49=ab¹⁰ -------(ii)

a=1.49/b¹⁰

1.26/b⁸ = 1.49/b¹⁰

1.26=1.49/b²

b²=1.49/1.26

b=1.087

Substitute b=1.087 in equation (i), we get

1.26=a(1.087)⁸

1.26=a(1.95)

a=1.26/1.95

a=0.646

So, the equation is y=0.646(1.087)ˣ

Therefore, the exponential model for the data is y=0.646(1.087)ˣ.

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Answer:

Find the value of b using the formula for the equation of a line.

y = mx+b

Replace the known value of m in the slope y-intercept form of the equation.

y=(1)x+b

Replace the known value of b in the slope y-intercept form of the equation.

y=(1)x+4

Simplify the slope y-intercept form of the equation.

Remove parentheses.

y=(1)x+4

Multiply 1 by x

y=1x+4

Remove parentheses.

y=(1)x+4

Multiply x by 1

this is the answer : y=x+4

i hope this helps.

Answer: To determine the total dollar amount of Finished Goods Inventory at the end of March, we need to calculate the total cost of the jobs that have been completed during March and have been transferred to the Finished Goods Inventory.

From the information given, we know that the company has no beginning Work in Process or Finished Goods inventories, so all the costs incurred during March are related to the jobs started during the month.

Let's start by calculating the total cost of Job 2, which is finished but not sold by the end of March. We will then use this cost to calculate the total cost of the jobs that have been completed during March and transferred to the Finished Goods Inventory.

Job 2:

Direct materials: Rs. 10,000

Direct labor: Rs. 8,000

Overhead applied: 60% x Rs. 10,000 = Rs. 6,000

Total cost of Job 2: Rs. 24,000

Now, let's calculate the total cost of the jobs that have been completed during March:

Job 1:

Direct materials: Rs. 6,000

Direct labor: Rs. 4,000

Overhead applied: 60% x Rs. 6,000 = Rs. 3,600

Total cost of Job 1: Rs. 13,600

Job 3:

Direct materials: Rs. 8,000

Direct labor: Rs. 5,000

Overhead applied: 60% x Rs. 8,000 = Rs. 4,800

Total cost of Job 3: Rs. 17,800

Total cost of jobs completed during March: Rs. 13,600 + Rs. 17,800 = Rs. 31,400

Since the company has no beginning Finished Goods Inventory, the total cost of the jobs completed during March and transferred to the Finished Goods Inventory is equal to the total cost of the Finished Goods Inventory at the end of March.

Therefore, the total dollar amount of Finished Goods Inventory at the end of March is Rs. 31,400.

Step-by-step explanation:

1) The volume of the first rectangular prism is 175 ft³

2) The volume of the second rectangular prism is 60ft³

3) The volume of the third rectangular prism 140ft³

4) The volume of the Fourth rectangular prism 216ft³

Note that in order to find the volume of area of a complex figure, you must deconstruct it into manageable proportions.

Shape 1 above, we deconstructed the rectangular prism into two 3 dimensional shapes with the following metrics:

a)

Length = 7ft

Height = 2ft

widht = 2ft

Volume = Volume = 7ft x 2ft x 2ft
Volume = 28  ft³

b)

Length = 7ft

Height = 3ft

width = 7ft
Volume = 147 ft³

Total Volume = 28  ft³ + 147 ft³

Volume for Shape 1 = 175 ft³

Shape 2 above, we deconstructed the rectangular prism into two 3-dimensional shapes with the following metrics:

a) Length = 3ft

Height = 2ft

width = 1ft

Volume = 6 ft³

b) Length = 6ft

Height = 3ft

width = 3ft

Volume = 54 ft³

Thus, total volume for shape 2 is:

Volume = 6 + 54

Volume = 40 ft³

Shape 3, above, we deconstructed the rectangular prism into two 3-dimensional shapes with the following metrics:

a) Length = 7ft

Height = 1ft

width = 2ft
Volume = 14ft³

b)
Length = 7ft

Height = 3ft

width = 6ft
Volume = 126ft³

Thus, the total volume fior shape 3, =

Volume = 14ft³ + 126ft³

Volume = 140ft³


Shape 4, above, we deconstructed the rectangular prism into two 3-dimensional shapes with the following metrics:

a) Length = 4ft

Height = 3ft

width = 2ft
Volume = 24 ft³


b) Length = 4ft

Height = 12ft

width = 4ft
Volume = 192 ft³

Thus, the total volume for Shape 4:

Volume =  24 ft³+ 192 ft³
Volume = 216ft³

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Answer:

21 miles per gallon

Step-by-step explanation:

find the gradient of the line:

change in y = 105 - 21 = 84

change in x = 5 - 1 = 4

gradient is change in y/ change in x

= 84/4 = 21

The expression for the given Venn Diagrams are:

A Venn diagram employs circles or other shapes that overlap to show the logical connections between two or more groups of objects.

They frequently serve to visually group objects while highlighting how they differ and how they are similar.

The union of two sets A and B is a new set that contains all the elements that are in A or in B or in both. It is denoted by A ∪ B.

Example: Let A = {1, 2, 3} and B = {3, 4, 5}, then A ∪ B = {1, 2, 3, 4, 5}.

The intersection of two sets A and B is a new set that contains all the elements that are in both A and B. It is denoted by A ∩ B.

Example: Let A = {1, 2, 3} and B = {3, 4, 5}, then A ∩ B = {3}.

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The largest portion of the yard they can fence in with 90 feet of fencing has an area of 2025/π  feet².

Explain area of circular portion?

The area of a circular portion is the amount of space within the boundary of the circular shape. It is given by the formula A = πr², where r is the radius of the circle.

Now,

To determine the area of the largest portion of the yard, we need to find the radius of the circular portion.

The circumference of a circle is 2πr. Since they have 90 feet of fencing, we can write:

90 = 2πr

Solving for r, we get:

r = 45/π

The area of the circular portion is given by the formula A = πr². Substituting r, we get:

A = π(45/π)² = 2025/π  feet²

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With the infοrmatiοn prοvided, the sοlutiοn is 2x + y = 9.

A mathematical equatiοn, including such 6 x 4 = 12 x 2, states that twο numbers οr values are equivalent. a meaningful nοun. An equatiοn is used when twο οr even mοre factοrs must be cοnsidered jοintly in οrder tο understand οr explain the whοle situatiοn.

Given:

Slοpe οr gradient οf line = -2

The lοcatiοn where the line passes = (1,7)

Equatiοn οf a line thrοugh (h,k) with a slοpe οf m:

(y - k) = (x -h) m

Equatiοn οf a line thrοugh (1,7) with a slοpe οf (-2): -

⇒ (y - 7) = (x - 1)(-2)

⇒ y - 7 = - 2x + 2

⇒ y = -2x + 2 + 7

⇒ y = -2x + 9

οr

⇒2x + y = 9

Verificatiοn οf respοnse:

We may check οur respοnse by substituting (1,7) in the fοrmula 2x+y=9.

⟹ LHS = (2×1)+7

⟹ LHS = 2+7

⟹ LHS = 9

Therefοre , LHS = RHS.

Alsο, yοu can use the equatiοn tο determine the gradient οr slοpe and cοnfirm yοur sοlutiοn.

⟹ Slοpe is equal tο -(cοefficient οf x)/ (cοefficient οf y)

⟹ Slοpe = - 2 /1

⟹ slοpe = -2

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The response to the given question would be that Because it has a interest higher interest rate and a longer term than option 3, option 1 would generate the greatest interest.

By dividing the principal by the interest rate, the passage of time, and other factors, simple interest is determined. Simple return equals principle plus interest plus hours is the formula used in marketing. The easiest way to compute interest is by using this method. The most typical method for calculating interest is as a portion of the principle amount. For example, if he borrows $100 from a buddy and agrees to pay back the loan at 5% interest, he will only pay his share of the 100% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and you must charge interest when you lend it. Typically, interest is determined as an annual percentage of the loan total. The interest rate of the loan is defined as this ratio.

The following would be the order of 2000 simple interest generated on an investment, from least to most:

2000 invested for 20 years at 3% simple interest

2000 invested for three years at 10% simple interest

2000 invested at 10% simple interest for nine years

Because of its longer length and lower interest rate than the other two alternatives, Option 2 would yield the least amount of interest.

Due to its higher interest rate and longer period, option 3 would generate more interest than option 2.

Because it has a higher interest rate and a longer term than option 3, option 1 would generate the greatest interest.

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The equation can be converted as: 2 (S - 1/2 u t) / t.

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

Let's start by simplifying the equation using the distributive property of multiplication:

S = 1/2 u t + 1/2 v t

Next, we can isolate the variable v by subtracting 1/2 u t from both sides of the equation:

S - 1/2 u t = 1/2 v t

Now we can multiply both sides of the equation by 2 to eliminate the fraction:

2 (S - 1/2 u t) = v t

Finally, we can solve for v by dividing both sides of the equation by t:

v = 2 (S - 1/2 u t) / t

Therefore, the solution for v is v = 2 (S - 1/2 u t) / t.

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Answer:

B) 15 days

Step-by-step explanation:

Total Work = (Number of men) x (Hours worked per day) x (Number of days)

Using this formula, we can find the total amount of work to be done in the scenario given in the question:

Total Work = (20 men) x (6 hours per day) x (10 days) = 1200 hours

(a) To find out how many hours a day the remaining 16 men should work to finish the work in 10 days, we need to subtract the work that was not done due to the absence of the 4 men:

Remaining Work = Total Work - Work not done by 4 men

Remaining Work = 1200 - (4 men) x (6 hours per day) x (10 days)

Remaining Work = 840 hours

To finish the remaining work in 10 days, the 16 men would need to work:

Hours per day = Remaining Work / (Number of men) x (Number of days)

Hours per day = 840 / (16 men) x (10 days)

Hours per day = 5.25 hours

Therefore, the 16 men would need to work 5.25 hours per day to finish the work in 10 days.

(b) To find out how many hours a day the remaining 16 men should work to finish the work in 15 days, we need to calculate the total amount of work that needs to be done each day:

Daily Work = Total Work / Number of days

Daily Work = 1200 / 15

Daily Work = 80 hours

To finish the daily work of 80 hours, the 16 men would need to work:

Hours per day = Daily Work / Number of men

Hours per day = 80 / 16

Hours per day = 5 hours

Therefore, the 16 men would need to work 5 hours per day to finish the work in 15 days.

Step-by-step explanation:

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The altitude of the plane to the nearest meter is 9210 meters and if the plane descends at a rate of 750 meters per minute, the pilot will have 12.28 minutes.

What is right angled triangle ?

A right-angled triangle is a triangle that has one angle that measures 90 degrees (a right angle). This means that the other two angles must add up to 90 degrees as well. The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs. The Pythagorean theorem, which states that the sum of the squares of the legs of a right-angled triangle is equal to the square of the hypotenuse, is a fundamental concept in mathematics and has many practical applications. Right-angled triangles are used in fields such as engineering, architecture, and physics to calculate distances, heights, and angles.

a) Let's use the Pythagorean theorem to find the altitude of the plane. We have a right triangle with the slant range as the hypotenuse, the ground range as one leg, and the altitude as the other leg. So, we can use:

altitude² + ground range² = slant range²

altitude² + 10.15² = 14.5²

altitude² = 14.5² - 10.15²

altitude² = 84.9025

altitude ≈ 9.21 km or 9210 meters (rounded to the nearest meter)

b) If the plane descends at a rate of 750 meters per minute, the pilot will have:

time = altitude / descent rate

time = 9210 / 750

time ≈ 12.28 minutes (rounded to two decimal places).

Therefore, the altitude of the plane to the nearest meter is 9210 meters and if the plane descends at a rate of 750 meters per minute, the pilot will have 12.28 minutes.

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The probability that the next person will purchase no costume is 80%.

What is the difference between a probability and an odds?

The possibility of an event occurring can be expressed using odds and probability, but they are computed and understood in different ways.

Probability, which is stated as a number between 0 and 1 (or between 0% and 100%), is the possibility that an event will occur. By dividing the number of positive possibilities by the total number of potential outcomes, the probability of an event happening is determined.

The possibility of an event happening is expressed differently by odds, which are expressed as a ratio of the number of favourable events to the number of negative outcomes. It is possible to state odds as "odds for" or "odds against."

Now,

The total number of visitors who purchased costumes is:

71 (exactly one) + 12 (more than one) = 83

The total number of visitors who did not purchase a costume is: 349

The probability that the next person will purchase no costume is:

349 / (349 + 83) = 349 / 432 ≈ 0.8079

Hence, the probability that the next person will purchase no costume is 80%.

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The answers to all limits are:

(a) lim x → a [ f(x) + 2g(x)] =  -6,

(b) lim x → a [h(x) − 3g(x) + 1] = 13

(c) lim x → a [ f(x)g(x)] = -8

(d) lim x → a [g (x)]² = 16

(e) lim x → a 3√6 + f(x) / 2g(x)

The central limit theorem states that if you take sufficiently large samples from a population, the samples' means will be normally distributed, even if the population isn't normally distributed.

(a) lim x → a [ f(x) + 2g(x)]

= lim x → a f(x) + 2 lim x → a g(x) (using algebraic limit theorem)

= 2 + 2(-4)

= -6

(b) lim x → a [h(x) − 3g(x) + 1]

= lim x → a h(x) - 3 lim x → a g(x) + lim x → a 1 (using algebraic limit theorem)

= 0 - 3(-4) + 1

= 13

(c) lim x → a [ f(x)g(x)]

= lim x → a f(x) * lim x → a g(x) (using algebraic limit theorem)

= 2 * (-4)

= -8

(d) lim x → a [g(x)]²

= [lim x → a g(x)]^2 (using algebraic limit theorem)

= (-4)^2

= 16

(e) lim x → a 3√6 + f(x) / 2g(x)

= [3√6 + lim x → a f(x)] / [2 lim x → a g(x)] (using algebraic limit theorem)

= [3√6 + 2] / [2(-4)]

= (-3√6 - 2) / 8

Therefore, the answers to all limits are:

(a) lim x → a [ f(x) + 2g(x)] =  -6,

(b) lim x → a [h(x) − 3g(x) + 1] = 13

(c) lim x → a [ f(x)g(x)] = -8

(d) lim x → a [g (x)]² = 16

(e) lim x → a 3√6 + f(x) / 2g(x)

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The difference is 7.76 × 10³ in scientific notation.

What is scientific notation?

Scientific notation is a way of expressing a number as a number between 1 and to multiplied by a power of 10.

We can perform the subtraction in the usual way, using the fact that the numbers are already in scientific notation:

(8.4 × 10³) − (6.4 × 10²) = 8.4 × 1000 − 6.4 × 100

= 8400 − 640

= 7760

To write this in scientific notation, we can express the result as a number between 1 and 10 multiplied by an appropriate power of 10. In this case, we can write:

7760 = 7.76 × 10³

Therefore, the difference is 7.76 × 10³ in scientific notation.

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The formula used to find any term of the geometric sequence is found as: an = 2(2)ⁿ⁻¹.

The geometric sequence equations has the general form an=a1rⁿ⁻¹, where r denotes the common ratio, a1 denotes the first term, and n denotes the term's position in the sequence.

sequence: 2, 4, 8, 16, 32, …

a1 = 2

r = 4/2 = 2

So,

an = 2(2)ⁿ⁻¹

Thus, the formula used to find any term of the geometric sequence is found as: an = 2(2)ⁿ⁻¹.

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The inequality which represents the least number of days that Kelli needs to run to reach her goal is

2 1/4 + 1/3d ≥ 4.

The least number of days after Monday that Kelli needs to run to reach her goal is 5.25 days

Monday= 2 1/4 miles

Other days of the week = 1/3 miles

Her goal =™4 miles

Number of days = d

2 1/4 + 1/3d ≥ 4

subtract 2 1/4 from both sides

1/3d = 4 - 2 1/4

1/3d = 4 - 9/4

1/3d = 16-9 /4

1/3d = 7/4

divide both sides by 1/3

d = 7/4 ÷ 1/3

d = 7/4 × 3/1

= 21/4

d = 5.25 days

Hence, Kelli will reach her goal in at least 5.25 days.

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Answer: 20 inches

Step-by-step explanation: Let's quickly create some equations to represent what's going on. We can say i are inches and m are miles. Then, 5i=3m because 5 inches represents 3 miles.

5i=3m

5/3i=1m One mile represents 5/3 of an inch/

12(5/3i)=12m We multiply by 12 since we want to know what 12 miles are

60/3i=12m=20i      12 miles is equal to 20 inches

Hope this helps! For practice, if 10 inches represented half a mile on a map, how many feet are represented by 36 miles?

The function g(x) = 3/(x-2) + 5 is a transformation of the parent function f(x) = 1/x with a horizontal shift of 2 units to the right, a vertical stretch by a factor of 3, and a vertical shift of 5 units up.

The function g(x) = 3/(x-2) + 5 is a transformation of the parent function f(x) = 1/x.

Here are the transformations that were applied to f(x) to obtain g(x):

1. Horizontal shift: The denominator of f(x) is x, which means that the vertical asymptote is at x = 0. By subtracting 2 from x in the denominator of g(x), we are shifting the vertical asymptote to x = 2. This is a horizontal shift of 2 units to the right.

2. Vertical stretch: The coefficient 3 in front of the fraction means that the function is stretched vertically by a factor of 3 compared to f(x). This means that the distance between the horizontal asymptotes (which are at y = 0 for f(x) and y = 5 for g(x)) is three times larger for g(x) than for f(x).

3. Vertical shift: The constant 5 added to the fraction means that the entire function is shifted vertically by 5 units compared to f(x). This means that the horizontal asymptote of g(x) is at y = 5 instead of y = 0.

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The heaviest fish caught weighed more than 12 pounds.

What is mean in statistics?

In statistics, the mean is a measure of central tendency, which represents the average value of a set of numbers. It is calculated by adding up all the values in the data set and dividing the sum by the number of values. The mean is also called the arithmetic mean or the average. It is commonly used to describe the typical value of a group of numbers.

To determine which statement is supported by the data, we need to analyze the weights of the fish that Terri and her father caught. Here are some possible statements that could be supported by the data:

A. The average weight of the fish caught was less than 7 pounds.

B. The heaviest fish caught weighed more than 12 pounds.

C. The total weight of the fish caught was more than 60 pounds.

D. The range of weights of the fish caught was between 4 and 12 pounds.

To determine which statement is supported, we can calculate some basic statistics:

Mean (average) weight: (5.6 + 11.0 + 4.0 + 12.2 + 7.0 + 10.0 + 4.2) / 7 = 7.8 pounds

Maximum weight: 12.2 pounds

Minimum weight: 4.0 pounds

Range of weights: 12.2 - 4.0 = 8.2 pounds

Total weight: 5.6 + 11.0 + 4.0 + 12.2 + 7.0 + 10.0 + 4.2 = 54 pounds

Based on this analysis, we can see that statement C ("The total weight of the fish caught was more than 60 pounds") is not supported by the data, as the total weight was only 54 pounds.

Statement A ("The average weight of the fish caught was less than 7 pounds") is also not supported, as the average weight was 7.8 pounds.

Statement B ("The heaviest fish caught weighed more than 12 pounds") is supported, as the heaviest fish weighed 12.2 pounds.

Finally, statement D ("The range of weights of the fish caught was between 4 and 12 pounds") is also supported, as the weights ranged from 4.0 to 12.2 pounds.

Therefore, the correct answer is either B or D, depending on the context of the question.

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Answer: From part b, we know that the number of sides in my envelope is t + q = 10 + 6 = 16, and the number of sides in my partner's envelope is 2t - q = 20 - 6 = 14.

To determine the number of sides in both envelopes combined, we add these values: 16 + 14 = 30.

Therefore, the combined number of sides in both envelopes is 30.

Step-by-step explanation:

Answer:

Tahlia was correct in remembering that you can find the slope of a line using the slope formula.

She was also correct that the slope is 0.5.

However, if you use the slope-intercept formula y = mx + b, you still have to find b (the y-intercept) by plugging in one of the two points and the slope.

So, if we plug in the first point and the slope into the line, we can find b and thus the full equation of the line:

[tex]-7.5=0.5(-3)+b\\-7.5=-1.5+b\\b=-6\\\\y=0.5x-6[/tex]

If Shaun eats popping candy while drinking a can of soda, soda streams out of Shaun's nose and he gets embarrassed. It isn't the case that soda streams out of Shaun's nose and he gets embarrassed. So, it isn't the case that Shaun eats popping candy while drinking a can of soda. The logical form of this argument is denying the antecedent. The Option B is correct.

If we represent the argument in logical symbols, it would look like this:

The argument can be summarized as follows:

If P, then Q.

Not P.

Therefore, not Q.

This is the form of denying the antecedent, where the argument asserts that if P is true, then Q must also be true. However, the argument then proceeds to deny the antecedent by claiming that P is not true, and therefore, Q must not be true either.

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We may calculate the distance from Carlos and the tree as [tex]D = 781.23[/tex] ft using trigonometric relationships.

Many functions in trigonometry offer excellent illustrations of how calculus may be used in practical situations. By the way, basic trigonometry primarily deals with the algebraic features of circular functions, therefore basic calculus is not always simpler than basic trigonometry. On the other hand, calculus is fundamentally non-algebraic in nature.

The mnemonic SOHCAHTOA makes it simple for us to recall the three primary trigonometric ratios.

Then one of the cathetus of the triangle is equal to:

[tex]275ft - 6ft = 269ft[/tex]

That cathetus is the opposite cathetus to the angle of 19° (the elevation angle). And the adjacent cathetus is the distance between Carlos and the tree.

Then we can use the relation:

Where:

[tex]a=19^{0}[/tex]

opposite cathetus [tex]=269ft[/tex]

adjacent cathetus [tex]=D[/tex]

Replacing that, we get

[tex]tan(19^{0} ) = 269ft/D[/tex]

Solving for D, we get:

[tex]D = 269ft/tan(19^{0} ) = 781.2ft[/tex]

So we conclude that Carlos is at [tex]781.23[/tex] ft of the tree.

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For the new height requirements, this branch of the military requires women's heights to be at least 2.52 in and at most 6.96in.

If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.

If we have

[tex]X \sim N(\mu, \sigma)[/tex]

(X is following normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex]  )

then it can be converted to standard normal distribution as

[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]

(Know the fact that in continuous distribution, probability of a single point is 0, so we can write

[tex]P(Z \leq z) = P(Z < z) )[/tex]

Also, know that if we look for Z = z in z tables, the p value we get is

[tex]P(Z \leq z) = \rm p \: value[/tex]

We are given that;

Mean= 63.8 in

Standard deviation= 2.3 in

Requirement of women height= 58in - 80in.

Now,

To find the minimum and maximum height requirements for this branch of the military, we need to use the standard normal distribution formula, which converts any normal distribution to a standard normal distribution with a mean of 0 and a standard deviation of 1.

We can find the z-scores for the minimum and maximum heights as follows:

For the minimum height requirement:

z = (58 - 63.8) / 2.3 = -2.52

For the maximum height requirement:

z = (80 - 63.8) / 2.3 = 6.96

Using a standard normal distribution table or calculator, we can find the corresponding probabilities for these z-scores:

For a z-score of -2.52, the probability is 0.0059 or 0.59%

For a z-score of 6.96, the probability is very close to 1, or 100%

Therefore, the new height requirements for this branch of the military are:

At least 58 inches, which corresponds to a z-score of -2.52

At most 80 inches, which corresponds to a z-score of 6.96

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Answer:

The given expression simplifies to zero.

Step-by-step explanation:

Tangent Trigonometric Identity:

[tex]\boxed{\tan \theta=\dfrac{\sin \theta}{\cos \theta}}[/tex]

Given expression:

[tex]\tan^2 \theta \cos^2 \theta - \sin^2 \theta[/tex]

To simplify the given expression, rewrite tan²θ using the tan trigonometric identity:

[tex]\implies \dfrac{\sin^2 \theta}{\cos^2 \theta} \cdot \cos^2 \theta - \sin^2 \theta[/tex]

[tex]\implies \dfrac{\sin^2 \theta \cos^2 \theta}{\cos^2 \theta} - \sin^2 \theta[/tex]

Cancel the common factor cos²θ:

[tex]\implies \sin^2 \theta - \sin^2 \theta[/tex]

Add similar elements:

[tex]\implies \sin^2 \theta - \sin^2 \theta=0[/tex]

Therefore, the given expression simplifies to zero.

Check the picture below.

The greatest common factor of 4x³y² and 12x²y is: 4x²y.

The GCF is a term used to refer to the largest common factor between any two or more numbers (Greatest Common Factor). The GCF of two natural integers, x and y, is the largest possible number that equally and completely divides both x and y. GCF is typically calculated using the following three techniques: division, multiplication, and prime factorization.

Now in the given question,

4x³y² can be written as = 2×2×x×x×x×y×y

12x²y can be written as = 2×2×3×x×x×y

The common factors among them are:

2×2×x×x×y = 4x²y.

Therefore, the greatest common factor of 4x³y² and 12x²y is: 4x²y.

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The tax owed by a person in 2021 who had a single filling status with a taxable income of $ 62, 000 is $ 9, 388. 50.

In 2021, the Internal Revenue Service issued rates such that a person with a single filling status and earning $ 62, 000 per year would be subject to tax of ;

= 4, 664 + 22 % of the amount over $ 40, 525

This means that the tax owed by this taxpayer with a $ 62, 000 gross income is :

= 4, 664 + ( 22 % x ( 62, 000 - 40, 525 ) )

= 4, 664 + ( 22 % x 21, 475 )

= 4, 664 + 4, 724. 50

= $ 9, 388. 50

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