1. Suppose tanφ=32​ and that the angle is in Quadrant 3 . a) Use only fundamental identities to find the exact value of cosφ. b) Use the methods of Section 1.3 (quadrant, reference triangle) to find the exact value of cosφ. c) If you use the inverse tangent, will you be able to find the approximate value of the angle based only on the inverse tangent? In other words, if you hit the inverse tangent button for 2/3 on your calculator, will it give you the angle we are looking for? Briefly explain. d) Find the approximate value of the angle, rounded to the nearest whole degree. e) Write an expression for all coterminal angles to your answer to part d, in radians.

A graph of each inequality is shown in the grid below.

A shape which the solution region represent is a rectangle.

In order to to graph the solution to the given system of inequalities on a coordinate plane, we would use an online graphing calculator to plot the given system of inequalities and then take note of the point of intersection;

0.4r ≤ 120     .....equation 1.

r ≥ 4(360/5)    .....equation 2.

By evaluating the given system of inequalities, we have;

r ≤ 120/0.4

r ≤ 300

r ≥ 4(360/5)

r ≥ 4(72)

r ≥ 288

By combining the system of inequalities, we have:

288 ≤ r ≤ 300

Based on the graph (see attachment), we can logically deduce that the solution to the given system of inequalities is the shaded region between the solid line, and the point of intersection of the lines on the graph representing each.

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The equation of the line that is perpendicular to the equation is y = -1/5x

The given line has a slope of 5, which means that any line perpendicular to it will have a slope that is the negative reciprocal of 5. The negative reciprocal of 5 is -1/5.

Let m be the slope of the line perpendicular to y = 5x - 2. Then, the equation of this line can be written in point-slope form as:

y - y1 = m(x - x1)

where (x1, y1) is the point where the line passes through, which is the origin in this case. So, we have:

y - 0 = (-1/5)(x - 0)

Simplifying this equation, we get:

y = (-1/5)x

Therefore, the line perpendicular to y = 5x - 2 and passing through the origin has a slope of -1/5 and a y-intercept of 0. Its equation is y = (-1/5)x.

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Answer:

5

Step-by-step explanation:

3^2+4^2

9+16=25

sqrt25

It will take 55 days to finish the renovation with 25 men.

If 34 men can finish the renovation in 40 days, we can say that the number of men is inversely proportional to the number of days needed to finish the work. Therefore, we can write:

Number of men × Number of days = Constant

We can find the value of the constant by using the given information:

34 men × 40 days = 1360

This means that the constant is equal to 1360.

If 9 men withdraw before the work started, then the number of men who will work on the renovation is 34 - 9 = 25.

We can now use the constant to find the number of days needed to finish the renovation with 25 men:

25 men × Number of days = 1360

Number of days = 1360 ÷ 25

Number of days = 54.4

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The approximate volume of the basketball is 0.00486 cubic meters.

We have,

The formula for the volume of a sphere is:

V = (4/3)πr³

where V is the volume and r is the radius of the sphere.

Converting the radius of the basketball from inches to meters

4.7 inches = 0.11938 meters

Now we can substitute this value for r in the volume formula:

V = (4/3)π(0.11938)³

Using a value of π = 3.14159 and evaluating the expression in the parentheses, we get:

V ≈ 0.00486 cubic meters

Therefore,

The approximate volume of the basketball is 0.00486 cubic meters.

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The area will rise by a factor of four if we double the base and height of a trapezoid.

A quadrilateral with a single set of parallel sides is referred to as a trapezoid. The parallel and non-parallel sides are referred to as bases and legs, respectively. The distance between the bases of a trapezoid measured perpendicularly is its height.

The formula for a trapezoid's area is:

Area is equal to (base1+base2)*height / 2.

Considering that the height is 6 millimeters, the first base is 5 millimeters, and the secondary base is 7 millimeters, we may determine the trapezoid's initial area as follows:

Area = 1/2 *(5 + 7)* 6 = 36 sq. mm

Doubling the height and both bases:

New base 1 = 2 * 5 = 10 mm

New base 2 = 2 * 7 = 14 mm

New height = 2 * 6 = 12 mm

The new area of such trapezoid can be calculated using the same formula:

New Area = 1/2* (10 + 14) * 12 = 144 sq. mm

When we compare the new area to the old area, we are able to see that the new area has been four times bigger.

So, if the base and height of just a trapezoid are both doubled, the area will grow by a factor four.

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Answer: 2 hours

Step-by-step explanation: (10 min) / (25 square feet)   =  (X minutes) / (300 square feet)

Cross-multiply to solve, as we always do with proportions:

10 * 300  = 25 * x

3000       = 25X

3000/25  = 25X /25

    120     = X

120 minutes * (1 hour / 60 minutes) = 2 hours

The multiplicative rate of change of a function is calculated by taking the ratio of the change in the output to the change in the input, which in this case would be 2.

The multiplicative rate of change of a function is the rate at which the output of the function changes in relation to the input. It is calculated by taking the ratio of the change in the output to the change in the input. The formula for this is:

Multiplicative Rate of Change = (Change in Output)/(Change in Input)

For example, if a function f(x) has an input of 3 and an output of 9, then the multiplicative rate of change of the function would be 2. This can be calculated by taking the difference between the output and the input, which is 9 - 3 = 6, and dividing it by the difference between the input and the output, which is 3 - 0 = 3. Thus, the multiplicative rate of change of the function is 6/3 = 2.

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complete question:

What is the multiplicative rate of change of the function f(x) = 3x?

The value of tan α is  [tex]\frac{3}{4}[/tex] . This value has been obtained by using the concept of trigonometry.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the study of right-angle triangles, which even includes their sides, angles, and relationships.

We know that the value of tan α is the ratio of a triangle's base to the triangle's perpendicular.

In the question, we are given that the base is 15 and the perpendicular is 20.

So, from the above information, we get the value as

⇒tan α = [tex]\frac{15}{20}[/tex]

⇒tan α = [tex]\frac{3}{4}[/tex]

Hence, the value of tan α is  [tex]\frac{3}{4}[/tex] .

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The actual outcome of his investment could still be positive or negative, depending on the actual performance of the individual stock.

Since each stock has a 50% chance of being successful and a 50% chance of failing, the expected value of each stock is:

(0.5 * 500) + (0.5 * (-500)) = 0

That is, the expected value of each stock is zero, because the potential gain of $500 is balanced by the potential loss of $500.

Now, since the stocks are independent, the expected value of Ajay's entire investment is simply the sum of the expected values of each individual stock:

Expected value of Ajay's investment = 222 * 0 = 0

So the expected value of Ajay's investment is also zero dollars. This means that, on average, Ajay should not expect to make a profit or a loss from his investment in these 222 stocks. However, the actual outcome of his investment could still be positive or negative, depending on the actual performance of the individual stocks.

Ajay is going to invest his money into 222 different stocks. Both stocks are independent, and each stock has a 50\%50%50, percent chance of being successful and a 50\%50%50, percent chance of failing. Each stock will make Ajay \$500$500dollar sign, 500 if it succeeds or lose him \$500$500dollar sign, 500 if it fails

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About 16 people among the 1,000 insured people can file a claim for a surgical procedure.

Profit is the financial gain earned by a business or an individual after deducting all the expenses and costs associated with generating that revenue. It represents the difference between the total revenue earned and the total expenses incurred.

The total amount collected in premiums over 3 years for Bracken is:

$100 x 1,000 x 3 = $300,000

Assuming x people among the 1,000 insured people file a claim for a surgical procedure, the total amount paid out in claims by Bracken would be:

$25,000 x x = $25,000x

The total deductible paid by the claimants would be:

$3,500 x x = $3,500x

So, the total amount paid out by Bracken would be:

$25,000x + $3,500x = $28,500x

For Bracken to break even, the total amount collected in premiums should be equal to the total amount paid out in claims plus the deductible for 3 years.

$300,000 = $28,500x + $3,500(1,000 - x)

Simplifying and solving for x, we get:

x = 16

Therefore, about 16 people among the 1,000 insured people can file a claim for a surgical procedure for Bracken to break even over the passage of 3 years.

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The complete question is:

Atrap and Bracken are two rival insurance companies. Atrap and Bracken have premiums of $150 and $100 and deductibles of $2,500 and $3,500 respectively. The average expense of surgery is $25,000. For Bracken to break even (suffer no loss and earn no profit) over the passage of 3 years, about how many people among the 1,000 insured people can file a claim for a surgical procedure?

a -10

b- 14

c- 16

d- 17

e- 20

The value of  tan(A - B)  will be 15/8.

As mentioned,  cscA= -17/15 and A is in Quadrant III and sinB=12/13 where B is in Quadrant I To find tan(A - B), we need to have the values of sin (A - B) and cos (A - B).We know that, sin(A - B) = sinAcosB - cosAsinB and cos(A - B) = cosAcosB + sinAsinB.Since we have the values of sinA, cosA, and sinB, let's find the values of cosA and cosB.First, let's find cosA. We know that cscA = 1/sinA. Therefore, sinA = -15/17.Since A is in Quadrant III, sinA < 0, cosA < 0, and tanA > 0.

By using the Pythagorean identity sin^2A + cos^2A = 1, we get cosA = -8/17.Next, let's find cosB. We know that sin^2B + cos^2B = 1.

Therefore, cosB = sqrt(1 - sin^2B) = 5/13.

Since B is in Quadrant I, sinB > 0, cosB > 0, and tanB > 0.

Now, we have sinA, cosA, sinB, and cosB.

Using the values of sinA, cosA, sinB, and cosB, let's find sin(A - B) and cos(A - B).

sin(A - B) = sinAcosB - cosAsinB= (-15/17)(12/13) - (-8/17)(5/13)= -180/221

cos(A - B) = cosAcosB + sinAsinB= (-8/17)(12/13) + (-15/17)(5/13)= -96/221

Finally, tan(A - B) = sin(A - B) / cos(A - B)= (-180/221) / (-96/221)= 15/8. Therefore, tan(A - B) = 15/8.

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Answer:

5 days .......

Step-by-step explanation:

Stefan has 4½ cups of oat

He uses 3¼ to make granola

What he has left 4½-3¼ = 1¼

If he feeds ¼of a cup to parrots a day, then he has 5 days feed from 1¼

Calculation 1¼ ÷ ¼

Change to improper fraction

5/4 ÷ 1/4 = 5/4 x 4/1

Ans 20/4 = 5days

Step-by-step explanation:

The square root of 22 is an irrational number, which means it cannot be expressed exactly as a finite decimal or a fraction. However, we can approximate it by finding the whole number that is closest to it.

To do this, we can use a calculator or estimation. For example, we can guess that the square root of 22 is between 4 and 5, since 4 squared is 16 and 5 squared is 25. Then we can try averaging these two numbers:

(4 + 5) / 2 = 4.5

This means that 4.5 is an approximate value of the square root of 22. The nearest whole number to 4.5 is 5, so we can say that the whole number nearest to the square root of 22 is 5.

Answer:

-4+3n     (if first value corresponds to n=0)

or

-7+3n     (if first value corresponds to n=1)

Step-by-step explanation:

Notice form each term you just need to add 3
For example, the first term is -4, then the second is -4+3=-1

then the third is -4+3+3=2

So you can start from -4 and 3 for each value.

If n=0 is the start value the sequence will be -4+3n

if the first term is n=1  the sequence will be  -4+3(n-1)=-7+3n

So depends if your sequence starts from n=1 or n=0 (which is usually just a convention)

Answer:

Q1: no idea

Q2: 2 kids get 2 pieces of taffy and 1 piece of licorice and the other three get 2 pieces of licorice and 1 piece of taffy.

Step-by-step explanation:

question 2 is quite obvious but no one can get the same amount of everything so the answer that i gave makes the most sense.

The side opposite to angle B is AC. The side adjacent to angle B is BC. The hypotenuse is segment AB.

A pair of sides are referred to as neighboring if they have a shared angle. The term "hypotenuse" refers to a right-angled triangle's longest side as compared to the base and perpendicular lengths. The right angle, the largest angle of the three angles in a right triangle, lies opposite the hypotenuse side. In essence, only the right triangle possesses the hypotenuse feature, not any other triangles.

From the figure we observe that the side opposite to angle B is AC.

The angle adjacent to angle B is BC.

The hypotenuse is segment AB.

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A triangular bandana has an area of 86 square inches. The height of the triangle is 5 3/8 inches. An equation to find the length of the base of the triangle is 86 = 1/2 * b * 43/8

The length of the triangle's base is 32 inches.

We know that the formula for calculating the area of a triangle is:

1/2 * base * height = area

We also know that the triangle's height is 5 3/8 inches, which may be expressed as a mixed number:

Height = 5 + 3/8 inch = 43/8 inch

Let b be the base of the triangle.

Substituting these numbers into the area formula yields:

86 = 1/2 * b * 43/8

To find b, multiply both sides of the equation by 2/43:

86 * 2/43 = 2/43 * 1/2 * b * 43/8

4 = b/8

b = 32

As a result, the length of the triangle's base is 32 inches.

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Answer:

The dimensions of the rectangle are 5 by 24.

Step-by-step explanation:

Sometimes it's easy to finish solving the system and think that the x and y coordinates are your answer. Remember what the question is asking for - the dimensions of the rectangle.

Hence, 75 is the result of adding the six consecutive integers starting at 10.

Numbers that follow one another sequentially are known as consecutive numbers. Every time there are two numbers, there is a 1 difference.

We can find the sum of these numbers by adding them up if there are six consecutive numbers and 10 is the smallest one.

The six numbers in order are x, x+1, x+2, x+3, x+4, and x+5. We are aware that x equals 10 because 10 is the smallest number.

The six numbers are therefore 10, 11, 12, 13, 14, and 15.

We simply put them together to determine their sum:

10 + 11 + 12 + 13 + 14 + 15 = 75

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There will be 23 highway signs on the road trip, including one at the end of the road trip.

The total length of the road trip is 13.8 hours. To solve for the number of highway signs on the road trip, we need to use the formula for finding out how many times a certain number can fit into another number. This formula is N = A/B, where N is the number of times B can fit into A. In this case, B is the time between highway signs (0.6 hours) and A is the total length of the road trip (13.8 hours). Plugging these values into the formula, we get N = 13.8/0.6 = 23. So, there will be 23 highway signs on the road trip, including one at the end of the road trip.

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The expression that represents the cost after the 11% discount is 0.89c. This means that Boubacar will pay 89% of the original cost after the discount has been applied.

To calculate the discount, you need to determine the discount rate, which is usually a percentage of the original price. Multiply the discount rate by the original price to find the amount of the discount.

Finally, subtract the discount amount from the original price to get the discounted price.

The discount that Boubacar gets on his purchase is 11% of the total cost before tax and discount. To calculate the discount, we multiply the total cost (c) by 11% or 0.11, which gives us:

Discount = 0.11c

To find the cost after the discount, we subtract the discount from the total cost. This gives us:

Cost after discount = c - Discount

Cost after discount = c - 0.11c

Cost after discount = 0.89c

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if it has a diameter of 10, that means its radius is half that or 5.

[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=5\\ h=18 \end{cases}\implies V=\pi (5)^2(18)\implies V\approx 1413.72~in^3[/tex]

The distance of the run is about 7.33 miles.

Let's anticipate that the distance of the run is "d" miles.

We realize that time = distance ÷ velocity.

For the first jogger who averages 8 mph, the time taken to finish the run may be represented as:

t = d ÷ 8

For the second jogger who averages 4 mph, the time taken to complete the same run may be represented as:

t + 35/60 = d ÷ 4

We can simplify this equation by substituting the value of "t" from the first equation:

d ÷ 8 + 35/60 = d ÷ 4

.

Multiplying each aspects through 24 (LCM of 8 and 4), we get:

3D + 7 = 6d

Simplifying this, we get:

d = 7.33 miles (rounded to two decimal locations)

Therefore, the distance of the run is about 7.33 miles.

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The polynomial f(x) = (5 − x)(x + 4)(7x + 3)2 has a degree of 2, a leading coefficient of 49, and a constant coefficient of 60.

The polynomial f(x) = (5 − x)(x + 4)(7x + 3)2 has the following degree, leading coefficient, and constant coefficient:

Degree: The degree of a polynomial is the maximum degree of any term in it.

Here, the term of highest degree is (7x + 3)2 which has a degree of 2.

Therefore, the degree of the polynomial is 2. Leading coefficient: The leading coefficient of a polynomial is the coefficient of the term of highest degree.

Here, the term of highest degree is (7x + 3)2 and it has a coefficient of 49.

Therefore, the leading coefficient of the polynomial is 49. Constant coefficient: The constant coefficient of a polynomial is the coefficient of the term of degree 0.

Here, there is only one such term, which is the constant term 60 (obtained by multiplying the constant terms of each factor: 5 × 4 × 9).

Therefore, the constant coefficient of the polynomial is 60.

Therefore, the polynomial f(x) = (5 − x)(x + 4)(7x + 3)2 has a degree of 2, a leading coefficient of 49, and a constant coefficient of 60.

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Therefore , the solution of the given problem of volume comes out to be the cylinder's height is roughly 5.353 inches, which is the nearest to 119/22 inches.

The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Cubic measurements are denoted by the characters cm3 and in3. To determine an item's size, you could use its bulk, though. The object's weight is typically transformed into mass units like grammes and kilos.

Here,

The formula for a cylinder's capacity can be used to calculate the height:

=> V = πr^2h

where the volume is V, the radius is r, and the height is h.

Inputting the numbers provided yields:

=> 1 1/16 = π(1/4)^2h

Simplifying:

=> 1.0625 = π(1/16)h

=> 1.0625 = (π/16)h

Adding 16/ to both sides:

=> h = (16/π) x 1.0625

=> h = 16.8125/π

=> h ≈ 5.3529

=> H = 5.353 inches is the result of rounding to the closest thousandth.

As a result, the cylinder's height is roughly 5.353 inches, which is the nearest to 119/22 inches.

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The solutions of x1 = 7 and x2 = -3 with x1 through solving the quadratic  equation x²−4x−21=0 by factoring

The equation :x² - 4x - 21 = 0, solve it by factoring it.The first step is to find two numbers that will multiply to give us -21 and add up to -4. These numbers are -7 and 3.So, we rewrite the equation using -7 and 3 instead of  -4x:x² - 7x + 3x - 21 = 0.

Group the first two terms and the last two terms: x(x - 7) + 3(x - 7) = 0.

Factor out the common factor of (x - 7): (x - 7)(x + 3) = 0.

Now, we have two factors that when multiplied, give us zero. This means that either (x - 7) = 0 or (x + 3) = 0.

Solving for x, we get: x = 7 or x = -3.

The solutions are x1 = 7 and x2 = -3.The equation x² - 4x - 21 = 0 can be solved by factoring it. To factor this equation, we first find two numbers that will multiply to give us -21 and add up to -4. These numbers are -7 and 3. Then we rewrite the equation using -7 and 3 instead of -4x.

The resulting equation is x² - 7x + 3x - 21 = 0.

Next, we group the first two terms and the last two terms to get x(x - 7) + 3(x - 7) = 0.

We factor out the common factor of (x - 7) to get (x - 7)(x + 3) = 0.

We then solve for x to get x = 7 or x = -3. Therefore, the solutions are x1 = 7 and x2 = -3.

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Answer:

To ensure that you have grabbed 250 balls of one color, you need to use the Pigeonhole Principle. The worst-case scenario is that you grab 249 balls of each color, totaling 996 balls. Therefore, the smallest amount of balls you need to grab is 997, which guarantees that you have grabbed 250 balls of one color.

To explain further, let's consider the worst-case scenario where you grab 249 red balls, 249 green balls, 249 blue balls, and 249 yellow balls. This totals to 996 balls. However, if you grab just one more ball, you will have a total of 997 balls, and since there are only four colors, at least one color will have 250 balls or more. Therefore, by grabbing 997 balls, you can be sure that you have grabbed at least 250 balls of one color.

Answer:

997

Step-by-step explanation:

I multiplied 249 by 4 first. This is because I wanted to find how many balls the person could grab in total without having 250 of the same color.

249*4= 996

However, the question wants to guarantee that one color has 250.

So I did 996+1=997. (which means there could be: 249 red, 249 yellow, 249 green, and 250 blue)

This means that every other color could be at 249, but one would guarantee to be at 250 with 997 pulls