Estimate the area under the curve and above the x-axis with 4 Subintervals.

F(t) = t(20-t)

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.

Learn more about triangles in: https://brainly.com/question/2773823
#SPJ2

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:

x + 1.4x = 180

2.4x = 180

x = 75, so 1.4(75) = 105

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.

To know more about Pythagorean Identity here

https://brainly.com/question/343682

#SPJ1

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

To know more about probability here

https://brainly.com/question/11234923

#SPJ1

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:

1 over 16 or 1/16

Step-by-step explanation:

All thanks to the multiplication of probability rule, if you have the probability of 2 events and you want to know what the probability of them both happening is you simply multiply the two probabilities.

So the probability is 1/4 x 1/4=1/16

the probability is 1/16.

I hope my answer helps solve your problem, and teaches you some things.

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

Learn more about the probability visit:

https://brainly.com/question/13604758

#SPJ1

Answer:

3) tanθ = -√3

4) tanθ = undefined

Step-by-step explanation:

For your third problem, we are given:

[tex]\displaystyle{\cos \theta = -\dfrac{1}{2}}[/tex]

And [tex]\displaystyle{\theta}[/tex] lies in quadrant 2 which is [tex]\displaystyle{90^{\circ} < \theta < 180^{\circ}}[/tex]. Since tangent is the division of sine over cosine, and cosine is in negative while sine is positive according to unit circle in quadrant 2. Therefore, the value of tangent is negative.

We lack sinθ to find tanθ. Therefore, we have to find sinθ first. We can use the identity:

[tex]\displaystyle{\sin^2 \theta + \cos^2 \theta = 1}[/tex]

To solve for sinθ, subtract cos²θ both sides:

[tex]\displaystyle{\sin^2 \theta + \cos^2 \theta - \cos^2 \theta= 1-\cos^2 \theta}\\\\\displaystyle{\sin^2 \theta= 1-\cos^2 \theta}[/tex]

Substitute cosθ = -1/3. Therefore:

[tex]\displaystyle{\sin^2 \theta= 1-\left(-\dfrac{1}{2}\right)^2}\\\\\displaystyle{\sin^2 \theta= 1-\dfrac{1}{4}}\\\\\displaystyle{\sin^2 \theta=\dfrac{4}{4}-\dfrac{1}{4}}\\\\\displaystyle{\sin^2 \theta = \dfrac{3}{4}}[/tex]

Since the value of sinθ is positive in quadrant 2. Hence:

[tex]\displaystyle{\sin \theta = \sqrt{\dfrac{3}{4}}}\\\\\displaystyle{\sin \theta = \dfrac{\sqrt{3}}{2}}}[/tex]

Now find the value of tanθ by sinθ/cosθ. Therefore:

[tex]\displaystyle{\tan \theta = \dfrac{\dfrac{\sqrt{3}}{2}}{-\dfrac{1}{2}}}\\\\\displaystyle{\tan \theta = -\sqrt{3}}[/tex]

Therefore, tanθ = -√3.

Next, to your fourth problem. To find tanθ again but given that sinθ = -1 in range of 0 ≤ θ < 2π.

Again, we have to apply the identity like the third problem. In this case, we solve for cosθ so we have the formula of:

[tex]\displaystyle{\cos^2 \theta = 1-\sin^2 \theta}[/tex]

Substitute in sinθ:

[tex]\displaystyle{\cos^2 \theta = 1-(-1)^2}\\\\\displaystyle{\cos^2 \theta = 1-1}\\\\\displaystyle{\cos^2 \theta = 0}[/tex]

Therefore:

[tex]\displaystyle{\cos \theta = 0}[/tex]

Since tanθ is sinθ/cosθ. We have -1/0 which is undefined. Therefore there are no tanθ values.

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)

Answer:

A) Vertical angles are congruent.

Answer:

2.4 Hope it helped! It was so easy!

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.

To know more about recession here

https://brainly.com/question/18075358

#SPJ1

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.

To know more about Mathematics in daily life,

https://brainly.com/question/11923394

Answer:

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

= about 45.83%

Value of cosθ will be cosθ = (√2)/2 after using Pythagorean Identity.

The Pythagorean Identity states that sin²θ + cos²θ = 1. We can use this identity to find cosθ given that sinθ = (√2)/2 and θ terminates in Quadrant I.

Since sinθ = (√2)/2 and θ terminates in Quadrant I, we can draw a right triangle with angle θ in Quadrant I, opposite side equal to √2, adjacent side equal to 1, and hypotenuse equal to √3.

Using the Pythagorean Theorem, we can find the length of the hypotenuse as:

h² = a² + b²

√3² = 1² + (√2)²

3 = 1 + 2

3 = 3

So, the length of the hypotenuse is √3.

Now, we can use the Pythagorean Identity to find cosθ:

sin²θ + cos²θ = 1

Substituting sinθ = (√2)/2:

(√2/2)² + cos²θ = 1

Simplifying:

2/4 + cos²θ = 1

1/2 + cos²θ = 1

cos²θ = 1 - 1/2

cos²θ = 1/2

Since θ terminates in Quadrant I and sinθ is positive, we know that cosθ is also positive. Therefore, taking the positive square root of both sides, we get:

cosθ = √(1/2) = (√2)/2

So, cosθ = (√2)/2.

Learn more about Pythagorean Identity at

brainly.com/question/10285501

#SPJ1

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.

Learn more about education here:

brainly.com/question/29775571

#SPJ1

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.

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.

Learn more on permutation here;

https://brainly.com/question/12468032

#SPJ1

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]

To learn more on Matrices click:

https://brainly.com/question/28180105

#SPJ1

The rocket will hit the ground approximately 2.57 seconds after launch.

The equation given is:

y = -16x² + 177x + 98

where y represents the height of the rocket in feet, and x represents the time elapsed since launch in seconds. This is a quadratic equation in standard form, where the coefficient of x² is negative, indicating that the graph of the equation is a downward-opening parabola.

To find the time when the rocket hits the ground, we need to find the value of x when y = 0, since the rocket's height is zero when it hits the ground. We can substitute y = 0 into the equation and solve for x:

0 = -16x² + 177x + 98

We can then use the quadratic formula to solve for x:

x = (-b ± √(b² - 4ac)) / 2a

where a = -16, b = 177, and c = 98.

Plugging in the values, we get:

x = (-177 ± √(177² - 4(-16)(98))) / 2(-16)

x = (-177 ± √(62721)) / (-32)

Simplifying further, we get:

x = (-177 ± 251) / (-32)

We can discard the negative value since time cannot be negative, and round the positive value to the nearest 100th of a second:

x ≈ 2.57 seconds

To know more about equation here

https://brainly.com/question/10413253

#SPJ1

Gabriella would have in fraction 2/85 of the bricks left to use after tomorrow

Given that,

total number of bricks she bought = 85

The ratio of bricks she use yesterday = 53/85

The ratio of bricks she use today = 20/85

Following tomorrow, the fraction of the bricks still have,

1 -  (53/85 + 20/85)

= 1 - 83/85

= 2/85 of the bricks

Hence,

2/85 of bricks left.

To learn more about fractions visit:

https://brainly.com/question/10354322

#SPJ1

Answer: 13086.45

Step-by-step explanation: 10000(1+0.03/4)^36

First, convert R as a percent to r as a decimalr = R/100r = 3/100r = 0.03 rate per year,Then solve the equation for AA = P(1 + r/n)ntA = 10,000.00(1 + 0.03/4)^(4)(9) A = 10,000.00(1 + 0.0075)^(36) A = $13,086.45 Summary:The total amount accrued, principal plus interest, with compound interest on a principal of $10,000.00 at a rate of 3% per year compounded 4 times per year over 9 years is $13,086.45.

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.

Learn more about exponential function here:

brainly.com/question/11487261

#SPJ1

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 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

To learn more about function rule click :

https://brainly.com/question/3760195

#SPJ1

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.

Know more about pyramid perpendicular height,

https://brainly.com/question/27846538

#SPJ1

The value of length x is given by, x = 98 mm.

So in the figure we can see that it is a scalene triangle.

And the lengths are given by,

VT = 57 mm

YK = 68 mm

TK = 129.2 mm

and the length of VK = x mm.

So, YV = (x - 68) mm

We have to find the value of this 'x' here.

Also we can conclude that TY is the angle bisector for the angle VTK in the triangle KTV.

So by angle bisector theorem we get,

YK/TK = YV/VT

68/129.2 = (x - 68)/57 [Putting the values given]

x - 68 = (68*57)/129.2

x - 68 = 30

x = 30 + 68

x = 98

Hence the value of x is, x = 98 mm.

To know more about angle bisector theorem here

https://brainly.com/question/9742008

#SPJ1

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.

25 testers will require 40 days to complete 50 test cases.

Given that all the testers are equally productive i.e. they complete an equal number of tests in equal time.

According to the question, 50 testers can complete 25 test cases in 10 days

Number of tests completed in one day by 50 testers = 25 / 10

= 2.5

The number of tests completed in one day by a single tester = 2.5 / 50

= 0.05

The number of tests completed in one day by 25 testers = 0.05 X 25

= 1.25

The time taken to complete 50 tests by 25 testers = 50 / 1.25

= 40

Hence, 25 testers will require 40 days to complete 50 test cases.

Learn more about work and time click;

https://brainly.com/question/3854047

#SPJ1

The complete question is =

50 testers can complete 25 test cases in 10 days. All testers are equally productive. A project has 25 testers and 50 test cases. How much time will they take to complete?

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

Read more about inequality at

brainly.com/question/25275758

#SPJ1