if 17sin=8 find the value of 2tantheta/1+tan²theta​

The value of the experimental probability of tossing heads is,

⇒ 1 / 3

We have to given that;

Coin Toss Results: T, H, T, H, T, H, T, T, T, T, H, T, H, T, T

Where, H stands for heads and T stands for Tails.

Hence, Total outcomes = 15

And, Head outcomes = 5

Thus, The value of the experimental probability of tossing heads is,

⇒ 5 / 15

⇒ 1 / 3

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The initial value for the function f(x) = 3 (5/4)ˣ is 3.

The base for this function is 5/4.

The domain for this function is all real numbers.

The range for this function is all positive real numbers greater than 0.

The exponential function is given as follows:

f(x) = 3 (5/4)ˣ

To find the initial value of an exponential function, we need to evaluate the function at x=0. In this case, we have:

f(0) = 3 (5/4)⁰

f(0) = 3

Therefore, the initial value of the function is 3.

The base of an exponential function is the constant factor that is raised to the power of x. In this case, the base is 5/4.

The domain of an exponential function is all real numbers since the function is defined for all values of x.

The range of an exponential function is all positive real numbers greater than 0 since the function is always positive and can approach 0 but never reach it.

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The complete question is as follows:

Consider the exponential function: f(x) = 3 (5/4)ˣ

The initial value for this function is ____.

The base for this function is ____.

The domain for this function is ____.

The range for this function is ____.

The region that satisfy the requirements in this situation is added as an attachment

Here, we have,

Identifying the region that satisfy the requirements in this situation

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

Type A

5 pounds of oats and 7 pounds of corn per bag.

Type B

6 pounds of oats and 4 pounds of corn per bag

This means that

Oats = 5x + 6y

Corn = 7x + 4y

Using the resulting mixtures, we have

5x + 6y ≥ 150

7x + 4y ≥ 140

For the bags available, we have

0 ≤ x ≤ 20 and 0 ≤ y ≤ 25

See attachment

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Answer:

2 hours and 28 minutes

Step-by-step explanation:

English = 1 1/6 hrs = 1hr 10min (1/6×60 to obtain the minutes part)

Maths = 1 3/10hrs = 1hr 18min (3/10×60)

Total time = 2hrs 28 mins

The equation which have same value as 3/5 (30x - 15) = 72 are 18x- 9 = 72 and 3(6x- 3) = 72

We have,

3/5 (30x - 15) = 72

Now, simplifying the equation we get

3/5 (30x) - 3/5(15) = 72

18x - 9 = 72

Now, add both side 9 we get

18x- 9 +9 = 72 + 9

18x = 81

Now, divide both side by 18 we get

18x/ 18 = 81

x = 4.5

So, the equation which have same value as 3/5 (30x - 15) = 72 are 18x- 9 = 72 and 3(6x- 3) = 72

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During both the Great Recession and the COVID-19 recession, the Fed implemented policies to purchase long-term bonds and mortgage-backed securities, as well as cutting the federal funds rate to near zero.

The Fed implemented some policy actions during both the Great Recession and the COVID-19 recession, while others were implemented only during the latter. Let's take a closer look:

A. Purchase long-term corporate bonds: Both

During both recessions, the Fed implemented a policy of purchasing long-term corporate bonds. This is a form of quantitative easing, where the central bank buys bonds to increase the money supply and lower long-term interest rates. By lowering borrowing costs for businesses, the Fed aims to encourage investment and boost economic growth.

B. Purchase long-term Treasuries: Both

Similar to the purchase of long-term corporate bonds, the Fed also implemented a policy of purchasing long-term Treasuries during both recessions. This has the same goal of increasing the money supply and lowering long-term interest rates, making it cheaper for the government to borrow money and for individuals and businesses to finance investments.

C. Eliminate the requirement that banks hold reserves: COVID-19

During the COVID-19 recession, the Fed eliminated the requirement that banks hold reserves. This meant that banks could lend more money to individuals and businesses, which could help stimulate the economy.

D. Purchase mortgage-backed securities: Both

During both recessions, the Fed implemented a policy of purchasing mortgage-backed securities. This was done to support the housing market and make it easier for people to obtain mortgages and refinance their homes.

E. Support lending to smaller nonfinancial firms: COVID-19

During the COVID-19 recession, the Fed implemented a policy of supporting lending to smaller nonfinancial firms. This was done to help small businesses, which are often hit hardest during economic downturns, access credit and stay afloat.

F. Cut the federal funds rate to near zero: Both

During both recessions, the Fed cut the federal funds rate to near zero. This is the interest rate that banks charge each other for overnight loans, and it affects other interest rates throughout the economy. By cutting the federal funds rate, the Fed aims to make borrowing cheaper and stimulate economic activity.

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Effective:

Thirty children suffered broken bones last year because of outdated playground equipment.

Studies show that safe playground equipment helps promote children's development.  

Tax money spent on our children's safety is tax money well spent.

New playground equipment can be used to enhance our children's education.

Ineffective:

Other schools in the area have new playground equipment.

The nurse's office is conveniently located next to the playground.

Here, we have,

The education is a discipline that is concerned with methods of teaching and learning in schools or school-like environments as opposed to various non-formal and informal means of socialization (e.g., rural development projects and education through parent-child relationships).

Education can be thought of as the transmission of the values and accumulated knowledge of a society. In this sense, it is equivalent to what social scientists term socialization or enculturation.

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complete question:

In a speech about the importance of installing new and safer school playground equipment, which reasons most effectively express the speaker's viewpoint?

label as

Effective or Ineffective

Thirty children suffered broken bones last year because of outdated playground equipment.

Studies show that safe playground equipment helps promote children's development.

New playground equipment can be used to enhance our children's education.

Other schools in the area have new playground equipment.

Tax money spent on our children's safety is tax money well spent.

The nurse's office is conveniently located next to the playground.

By using the Unitary Method we get the number of children who went on an excursion was 63. Thus, the total number of children at school is 90.

We are given that,

No. of children who stayed at school is 27,

Also, 70% of the children went on an excursion.

Suppose, the total number of children in percentage is 100%

Out of which 70% went on an excursion

Thus, the children who stayed at school is 100% - 70% = 30%

By using the Unitary method, we can find out the number of 70% of children.

If 30% of the children are 27

Then 70% of the children are = 27 × 100

                                                        30

                                                 = 63

∴ the total no. of children in the school = 27 + 63

                                                                 = 90

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Answer:

A) Vertical angles are congruent.

The diagram below shows a square based pyramid. Point O is directly above the center of the base.

a) The length of AC = 26.87 cm

b) The perpendicular height = 66.961 cm

Considering ΔOAD,

cos 82° = [tex]\frac{19/2}{OC}[/tex]

OC = [tex]\frac{9.5}{cos \ 82}[/tex] = [tex]\frac{9.5}{0.1391}[/tex] = 68.296

Considering the base ABCD, the length of the diagonal AC,

It is given as [tex](AC)^2 = 19^2 + 19^2[/tex] = 361 + 361 = 722

AC = 26.87 cm

MC = [tex]\frac{1}{2}[/tex] (AC) = [tex]\frac{1}{2} (26.87)[/tex] = 13.435

Considering ΔOMC,

[tex](OM)^2 = (OC)^2 - (MC)^2 = (68.296)^2 + (13.435)^2[/tex]

= 4664.343 - 180.499 = 4483.844

OM = 66.961

Therefore, the length AC = 26.87 cm and the perpendicular height = OM = 66.961 cm.

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Answer:

5/21  or  24% probability

Step-by-step explanation:

There is 5 points on line DF and 21 points on line AK

Therefor it is 5/21  or .239095=approx. 24%

Answer:

28m^2

Step-by-step explanation:

According to the information we can infer that the area of the triangle is 14.25 square centimeters.

To find the area of a triangle, we can use Heron's formula. Heron's formula states that the area of a triangle with side lengths a, b, and c is given by:

where s is the semi-perimeter of the triangle, calculated by:

In this case, the side lengths of the triangle are given as 5.7 cm, 7 cm, and 5 cm. Let's calculate the area using Heron's formula:

Now, we can substitute the values of s, a, b, and c into the formula:

Calculating the expression inside the square root:

Rounding to two decimal places, the area of the triangle is approximately 8.02 square centimeters.

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Answer:

x + 1.4x = 180

2.4x = 180

x = 75, so 1.4(75) = 105

Answer:

P = 165/360 = 11/24 = about .46

= about 45.83%

R₁-->43(R₁)+9(R₂) is the row operation we apply to make 1 in the 1st row and a column.

The given matrix is [tex]\left[\begin{array}{ccc}9&4&-9\\-43&-19&44\end{array}\right][/tex]

We have to make 1 in row 1 and column 1

We have to apply a row operation to make 1 in the row 1 and column 1

R₁-->43(R₁)+9(R₂)

[tex]\left[\begin{array}{ccc}0&1&9\\-43&-19&44\end{array}\right][/tex]

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Answer:

A

Step-by-step explanation:

I'm assuming it is A since it said the 51,000 were originally issued and then adding on the 4,100, you get 55,100.

The polynomial equation passing through the point ( -2 , -18 ) is given by the function f(x) = x³ - 2x² - 7x + 8

Given data ,

A function with a graph that bounces off the x-axis at (-1,0), crosses it at (4,0), and goes through the point (-2,-18)

Now , the value of the function is

If a graph of a polynomial equation bounces off the x-axis at (-1,0), crosses it at (4,0), and goes through the point (-2,-18), it means that the function has a zero of multiplicity 2 at x=-1, a zero at x=4, and passes through the point (-2,-18)

To write a polynomial equation for this function, we can use the zero product property and write the factors that correspond to each of the zeros:

f ( x ) = (x + 1)² (x - 4)

On simplifying , we get

f ( x ) = x³ - 2x² - 7x + 8

Hence , the function is f ( x ) = x³ - 2x² - 7x + 8

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Using permutation, there 240 ways we can make an order.

A permutation is an arrangement of objects in a definite order. The members or elements of sets are arranged here in a sequence or linear order.

The formula of permutation is given as;

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

In the given question, we can choose one type of cone in 8 ways, 1 type of flavor in 5 ways and 1 type of topping in 6 ways, the total number of ways will be;

Number of ways = 8 * 5 * 6 = 240 ways

The total number of ways in which we can choose 8 type of cone, 5 flavors and 6 toppings in one order is 240 ways.

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Answer:

46°

Step-by-step explanation:

If you want to crack this problem, you have to remember one thing: triangles are awesome. They always add up to 180°. Let me show you how:

First, let's look at angle BOC. It's the third angle of triangle BOC, so we can find it by subtracting the other two angles from 180°:

Next, let's use a cool trick: angle AOD is an exterior angle of triangle AOB, which means it's equal to the sum of the two angles inside the triangle that are not touching it. Those are angles AOB and BOC. We can write this as an equation:

m∠AOD = m∠AOB + m∠BOC (2x + 12)° = (28)° + (190° - 10x) Now we can solve for x by doing some math magic:

Finally, we can plug in x into the expression for angle AOD and simplify:

m∠AOD = (2x + 12)° m∠AOD = (2 x 17.17 + 12)° m∠AOD = (34.34 + 12)° m∠AOD = 46.34°

And there you have it: angle AOD is 46.34°, which is pretty close to option 46°

footnotes for in-depth understanding:

I realized that angle AOB is part of a quadrilateral with the points A, O, B, and C. This shape has four angles that add up to 360°. Here's what I did:

I looked at the other three angles of the shape: angle AOC, angle BOC, and angle COA. I used the information they gave me to find their values. Angle AOC is double angle AOD, and angle COA is double angle DOC. So I wrote:

I also used the answer I got for angle BOC in the last question:

Then I used the fact that the four angles of the shape add up to 360° to make an equation and solve for angle AOB:

To find m∠AOB, I simplified and rearranged the equation:

So, the value of angle AOB is 154° - 6x. When x is equal to 17.17, as we found before, angle AOB is equal to 154° - (6 x 17.17), which is about 27°. That's how I found angle AOB.

Answer:

Step-by-step explanation:

its 4:1 because 16 divided by 4 is 4.

The ratio of the radius of cone A to cone B is 4:1.

We are given that;

The ratio = 16:1

Now,

If we divide the surface area of cone A by the surface area of cone B, we get:

[tex]SA_A / SA_B = (πr_A(r_A + l_A)) / (πr_B(r_B + l_B)) SA_A / SA_B = (r_A(r_A + l_A)) / (r_B(r_B + l_B))[/tex]

Simplify this equation by using the fact that[tex]r_A / r_B = l_A / l_B = k,[/tex]where k is a constant. We get:

[tex]SA_A / SA_B = (r_A(r_A + k r_A)) / (r_B(r_B + k r_B)) SA_A / SA_B = (r_A^2(1 + k)) / (r_B^2(1 + k)) SA_A / SA_B = (r_A^2) / (r_B^2)[/tex]

Take the square root of both sides to get:

[tex]sqrt(SA_A / SA_B) = r_A / r_B[/tex]

Substitute the given ratio of 16:1 for SA_A / SA_B and simplify to get:

[tex]sqrt(16/1) = r_A / r_B 4/1 = r_A / r_B 4:1 = r_A : r_B[/tex]

Therefore, by the ratio the answer will be 4:1.

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Answer:

2.4 Hope it helped! It was so easy!

After considering the given set of options we conclude that the number of options that do justify the given question are  s+2.3=6.8, s-2.3-6.8 then Options D and E apply.

Here we have to apply the principle of subtraction

Dean ran 2.3 fewer kilometers than Sam. So, we can say that Sam ran 2.3 km more than Dean. We can represent the distance Dean ran as d and the distance Sam ran as s.

So, we can place the equation as s-2.3=6.8 because Dean ran 6.8 km and we know that he ran 2.3 km less than Sam.

To evaluate out how far Sam ran, we need to solve for s. We can do this by adding 2.3 to both sides of the equation:

s-2.3+2.3=6.8+2.3

s=9.1

So Sam ran 9.1 km

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The complete question is

Dean ran 2.3 fewer kilometers than Sam. If Dean ran 6.8 km, how far did Sam run?

Select all that apply.

A) You know the difference in the distances the boys ran , so this is a subtraction problem.

B) You are finding the total distance the boys ran, so this is an addition problem.

C) Dean ran part of the distance Sam ran, so this is a multiplication problem.

D) The correct equation is: s+2.3=6.8.

E) The correct equation is s-2.3-6.8.

F) The correct equation is 2.3-6.8.

The probability of event A occurring first is 1/5.

To find the probability of event A occurring first, we need to calculate the probability of A and B not occurring simultaneously. We can express this probability using the formula:

P(A and not B) = P(A) - P(A and B)

Here, P(A and not B) denotes the probability of A occurring but not B, and P(A and B) denotes the probability of both A and B occurring simultaneously.

We are given that A U B = 6, which means that the number of outcomes in either A or B or both is 6. We can express this as:

P(A or B) = 6/20

Since P(A or B) = P(A) + P(B) - P(A and B), we can rearrange this equation to get:

P(A) = P(A or B) + P(A and B) - P(B)

We know that P(A or B) = 6/20, P(B') = 20, A' = 6, and U = 20. From B', we can find P(B) as:

P(B) = B'/U = 20/20 = 1

We can now substitute these values into the equation to get:

P(A) = 6/20 + P(A and B) - 1

Simplifying this, we get:

P(A and not B) = P(A) - P(A and B) = 5/20 - P(A and B)

We know that A' = 6, which means that the number of outcomes that are not in A is 6. Using this, we can express P(A and B) as:

P(A and B) = U - A' - B' = 20 - 6 - 20 = -6

Since A and B are mutually exclusive, we can simplify the equation P(A or B) = P(A) + P(B) to:

P(A or B) = P(A) + P(B)

Substituting the values we know, we get:

6/20 = P(A) + 1

Simplifying this equation, we get:

P(A) = 1/5

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The cosine of the angle is equal to √2/2.

The Pythagorean Identity states that in a right triangle with hypotenuse c and legs a and b, the following relationship holds:

a² + b² = c²

Where c is the longest side of the right triangle, called the hypotenuse, and a and b are the two shorter sides.

Using this identity, we can relate the sine and cosine of an angle as follows:

sin²θ + cos²θ = 1

where θ is the angle in question.

In this question, we are given that sinθ = (√2)/2 and that the angle θ terminates in Quadrant I.

Using the given value of sinθ, we can substitute it into the Pythagorean Identity as follows:

(sinθ)² + (cosθ)² = 1

(√2/2)² + (cosθ)² = 1

2/4 + (cosθ)² = 1

1/2 + (cosθ)² = 1

(cosθ)² = 1 - 1/2

(cosθ)² = 1/2

Taking the square root of both sides, we get:

cosθ = ± √(1/2)

Since we are in Quadrant I, we know that the cosine of the angle must be positive, so we can take the positive square root:

cosθ = √(1/2)

Simplifying the square root, we get:

cosθ = √2/2

Therefore, the cosine of the angle θ is √2/2, as required.

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The calculated value of x in the unit circle is 81

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

The circle

The sum of angles on a circumference of a circle is 360 degrees

using the above as a guide, we have the following:

x + 69 +  x + 49 + 80 = 360

When the like terms are evaluated, we have

2x = 360 - 80 - 49 - 69

Evaluate

2x = 162

So, we have

x = 81

Hence, the value of x is 81

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Answer:

$3.50

Step-by-step explanation:

There are six equally likely outcomes when rolling a fair die, with each outcome having a probability of 1/6. Let X be the random variable representing the amount Jim wins, then:

X = 1, 2, 3, 4, 5, or 6, each with probability 1/6.

The mathematical expectation (or expected value) of X, denoted E(X), is the sum of each outcome multiplied by its probability:

E(X) = (1)(1/6) + (2)(1/6) + (3)(1/6) + (4)(1/6) + (5)(1/6) + (6)(1/6)

= 21/6

= 3.5

Therefore, Jim's mathematical expectation is $3.50 per roll, which means on average he can expect to win $3.50 per roll in the long run.

Answer:

Step-by-step explanation:

Begin with monthly his take-home pay (after taxes and other withholdings): $2,000

Subtract all necessary monthly expenses.

$2,000 monthly take-home pay

- $700 rent & utilities

- $400 food

- $400 student loan payment

- $200 personal expenses

- $200 auto insurance & repairs

= $100, which is the maximum amount that Jacob can commit to monthly expenses for his vehicle.

After totaling his monthly necessary expenses ($1,900), it is evident that Jacob could allocate up to $100 per month towards a vehicle payment without having a safety margin, given his monthly take-home pay of $2000.

To calculate the maximum amount Jacob can commit for a monthly vehicle payment, we need to subtract all his necessary monthly expenses from his monthly take-home pay. Jacob's current expenses include:

Adding these expenses together, Jacob spends $1,900 on necessary expenses each month. Therefore, if we subtract this from his monthly take-home pay of $2,000, we find that Jacob could theoretically allocate as much as $100 per month ($2000 - $1900) towards a vehicle payment with no safety margin.

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Answer:

1. Maths has huge effect on daily basis.

2. I feel much more confident with math skills.

Step-by-step explanation:

1. Numerous ways in which maths influences our lives on a daily basis. When budgeting our expenses, measuring ingredients when cooking, calculating the amount of money we must pay for goods or services, and calculating the amount of time it will take to travel between two points, we all use maths. We also utilise maths to determine the best value for our money by comparing the costs of several options, computing savings or discounts, and so on. A lot of occupations, like engineering, science, finance, and technology, depend heavily on maths.

2. I am proficient and accurate at completing simple mathematical operations like addition, subtraction, multiplication, and division as well as calculating sales tax and interest. These abilities are crucial for daily living and, with practise, they emerge naturally. While many people have no trouble with these math concepts, others might. Recognising our mathematical strengths and shortcomings is crucial so that we may focus on enhancing our abilities and navigating daily life more comfortably and confidently.

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Answer:

B) 1 - (-6) / -2 -4

Step-by-step explanation:

The slope formula is:

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

where (x1, y1) and (x2, y2) are two points on the line.

For the points (4, -6) and (-2, 1), we can choose (4, -6) as (x1, y1) and (-2, 1) as (x2, y2), or vice versa. It doesn't matter which point we choose as (x1, y1) and which one we choose as (x2, y2), as long as we're consistent in our choice.

Let's choose (4, -6) as (x1, y1) and (-2, 1) as (x2, y2). Then we can write:

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

m = (1 - (-6)) / (-2 - 4)

Simplifying this expression, we get:

m = 7 / (-6)

So the correct way to set up the slope formula for the line that passes through the points (4, -6) and (-2, 1) is:

B) 1 - (-6) / -2 -4

m = (1 - (-6)) / (-2 - 4) = 7 / (-6)