A student shapes a piece of clay into a small cube. The students places the clay at the bottom of the ramp in Setup 2. The student rolls the 1-kilogram ball down the ramp and observes the collision between the ball and the clay cube.

Part(A),

The estimated area under the graph of f(x) over the interval [3, 5] using four rectangles and right endpoints is approximately 0.231 square units.

Part(B),

The estimated area under the graph of f(x) over the interval [3, 5] using four rectangles and left endpoints is approximately 0.2405 square units.

To estimate the area under the graph of f(x) = 1/(x²+1) over the interval [3, 5] using four rectangles and right endpoints, we can use the following formula:

[tex]R_n = \dfrac{(b-a)}{n} \times [f(x_1) + f(x_2) + ... + f(x_n)],[/tex]

where a = 3, b = 5, n = 4, and xi = a + i(b-a)/n for i = 0, 1, 2, ..., n.

Using this formula with the right endpoints, we get:

[tex]R_4 = \dfrac{(5-3)}{4 }\times [f(3.5) + f(4) + f(4.5) + f(5)][/tex]

R₄ = (1/2) x [0.361 + 0.250 + 0.178 + 0.132]

R₄ = 0.231

Hence, the estimated area under the f(x) graph utilizing four rectangles and the right endpoints over the range [3, 5] is about 0.231 square units.

To repeat the approximation using left endpoints, we can use the following formula:

[tex]L_n = \dfrac{(b-a)}{n} \times [f(x_0) + f(x_1) + ... + f(x_{n-1)],[/tex]

where [tex]x_i = a + i\dfrac{(b-a)}{n}[/tex] for i = 0, 1, 2, ..., n-1.

Using this formula with left endpoints, we get:

[tex]L_4 = \dfrac{(5-3)}{4} \times [f(3) + f(3.5) + f(4) + f(4.5)][/tex]

L₄ = (1/2) x [0.250 + 0.361 + 0.250 + 0.178]

L₄ = 0.2405

Therefore, the estimated area under the graph of f(x) over the interval [3, 5] using four rectangles and left endpoints is approximately 0.2405 square units.

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The solution of the each given equations:

(1) x = 9

(2) x = -2

(3) x = -2

(4) x = 26

(5) x = 3/5

(6) x = 13/12

(7) x = 15

(8) x = 26

(9) x = 7/3

(10) x = 5/8

We have to solve this given equation in on variable.

(1) Given equation is,

x - 7 = 2

x = 2 + 7 = 9

Hence, the solution is, x = 9

(2) Given equation is,

3x + 4 = -2

3x = -2 -4

3x = -6

x = -6/3 = -2

Hence, the solution is, x = -2

(3) Given equation is,

2x + 7 = x + 5

2x - x = 5 - 7

x = -2

Hence, the solution is, x = -2

(4) Given equation is,

x/2 = 13

x = 2*13 = 26

Hence, the solution is, x = 26

(5) Given equation is,

5(2 + x) = 13

10 + 5x = 13

5x = 13 - 10

5x = 3

x = 3/5

Hence, the solution is, x = 3/5

(6) Given equation is,

6(2x - 1) = 7

12x - 6 = 7

12x = 7 + 6 = 13

x = 13/12

Hence, the solution is, x = 13/12

(7) Given equation is,

2x/5 = 6

2x = 6*5 = 30

x = 30/2 = 15

Hence, the solution is, x = 15

(8) Given equation is,

x/2 = 13

x = 2*13 = 26

Hence, the solution is, x = 26

(9) Given equation is,

(x - 1)3 = 4

3x - 3 = 4

3x = 4 + 3 = 7

x = 7/3

Hence, the solution is, x = 7/3

(10) Given equation is,

(2x - 1)4 = 1

8x - 4 = 1

8x = 1 + 4

8x = 5

x = 5/8

Hence, the solution is, x = 5/8

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The sum of 150, 20 , and 20 is more than 180 degrees, therefore, it is not possible to draw a triangle.

A triangle is simply a three sided polygon that has three sides and three interior angles. When all three interior angles are added together, the sum is equal to 180 degrees according to the triangle sum theorem.

If we have a set of angles with the measure of 150, 20, and 20 degrees, respectively, the sum of these is more than 180 degrees.

150 + 20 + 20 = 190 degrees.

Therefore, it is not possible to draw a triangle with those set of angles.

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If a₁ = 9 and sequence aₙ = -3aₙ₋₁ , then the value of a₅ is approximately equal to 729.

To find the value of a₅, we need to use the recursive formula provided, which relates each term in the sequence to the previous one. The formula given is a bit unusual, as it defines each term in terms of the negative three times the previous term. However, we can use this information to work out the value of a₅.

Starting with a₁ = 9, we can use the recursive formula to find the next few terms of the sequence:

a₂ = -3a₁ = -3(9) = -27

a₃ = -3a₂ = -3(-27) = 81

a₄ = -3a₃ = -3(81) = -243

a₅ = -3a₄ = -3(-243) = 729

Therefore, the value of a₅ is 729. We can check that this is correct by verifying that it satisfies the given recursive formula:

a₄ = -3a₃ = -3(81) = -243

a₅ = -3a₄ = -3(-243) = 729

This confirms that our solution is correct.

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Answer:

We can see that the sequence is formed by multiplying each term by 2 to obtain the next term. Therefore, the fourth term is 12 x 2 = 24, the fifth term is 24 x 2 = 48, and so on.

To find the ninth term, we can multiply the third term by 2 six times:

3 x 2^6 = 3 x 64 = 192

Therefore, the ninth term of the sequence is 192.

The displacement of the particle at time t is 11t - t², and the total distance traveled by the particle in 2 seconds is 9 meters.

The displacement of a particle moving along a straight line can be calculated by finding the area under the velocity-time graph. In this case, the velocity function is v(t) = 11 - 2t for 0 ≤ t ≤ 2.

To find the displacement at time t, we need to find the area under the velocity-time from t = 0 to t = t. The formula for displacement is the integral of the velocity function with respect to time:

s(t) = ∫v(t) dt = ∫(11 - 2t) dt = 11t - t²

Therefore, the displacement of the particle at time t is given by s(t) = 11t - t².

To find the total distance traveled by the particle in 2 seconds, we need to consider both the forward and backward motion. Since the velocity is decreasing at a constant rate of 2 m/s², the particle will come to rest at t = 11/2 seconds.

The total distance traveled by the particle in 2 seconds is given by:

d(2) = ∫|v(t)| dt =  [tex]\int\limits^{11/2}_0[/tex] v(t) dt + [tex]\int\limits^2_{11/2}[/tex]|v(t)| dt from 11/2 to 2

= [[tex]\int\limits^{11/2}_0[/tex](11t - t²) ] + [[tex]\int\limits^2_{11/2}[/tex](-11t + t²) ]

= (121/2 - 121/4) + (4 - 121/2) = 9 meters

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Answer:

41 grams

Step-by-step explanation:

trust i jus took it

The mass of an American Eagle Silver Bullion Coin is about 41 grams.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

Each coin has a diameter of 40.6 millimeters and is 2.98 millimeters thick. The density of silver is 10.5 grams per cubic centimeter.

Hence, Volume is,

V = 3.14 x (40.6/2)² x 2.98

V = 3857.96 mm³

Since, 1000 mm³ = 1 cm³

Hence, The mass of an American Eagle Silver Bullion Coin is,

⇒ 33857.9 / 1000 x 10.5

⇒ 41 grams

Thus, The mass of an American Eagle Silver Bullion Coin is, 41 grams

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The verification of given segments in a triangle are parallel is as follow,

In triangle ABE, AC/ CE = BD/DE  are in proportion ⇒ CD || AB.

In triangle RVS, VT/TR = VU/US  are in proportion ⇒ UT || SR.

In the triangle ABE,

CD is the line segment divides AE and BE into equal parts.

AC = 1.5

CE = 1.5

BD = 1.5

DE = 1.5

AC/ CE = BD/DE

Line divides the two adjacent sides of a triangle are in proportion.

This implies ,

CD is parallel to AB.

In triangle RVS,

VT /TR = 90 /72

⇒VT /TR = 1.25

VU/US = 67.5/54

⇒VU/US = 1.25

This implies ,

VT/TR = VU/US are in proportion.

Hence , triangle proportionality theorem UT is parallel to RS.

Therefore, using triangle proportionality theorem in both the triangle that is,,

In triangle ABE , CD is parallel to  AB and in triangle RVS , UT || RS.

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Answer: .025

Step-by-step explanation: we first have to find the distance between each term we divide 12/5 by 6 you have to change it into multiplication so you invert is to 12/5 times 1/6 you then get 12/30 you reduce that to become 2/5 if you want to test this to make sure it is right then you can. you then use a formula but I can't remember it so then you can just multiply it several times to find the answer. you get the answer by round from the thousandths

Jenny is paying $334.82 per year on credit card interest.

We need to find his annual interest payment which is:

= $1100 * 2% * 12 month

= $264

So, we have an annual interest payment of $264

We must account for interest that accumulates on the interest itself. To calculate this, we can use the formula: A = P (1 + r/n)^(nt) when P is $264, r is 24%, n is 12 and t is 1.

A = $264 * (1 + 0.24/12)^(12*1)

A = $264 * 1.26824179456

A = $334.815833764

A = $334.82.

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The valid inference based on the information provided is:

Inferences cannot be made about all blood pressure patients, and the conclusion cannot be made that the new medication lowers blood pressure more effectively than the original medication for patients taking blood pressure medication.

The study involved only 200 volunteers who were already taking blood pressure medication. This is a relatively small sample size and may not be representative of all blood pressure patients. Inferences about all blood pressure patients cannot be made from this limited sample.

While the group taking the new medication showed a significantly lower overall blood pressure than the group taking the original medication, it was also mentioned that the new medication did not significantly lower cholesterol levels.

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From the pharmaceutical company's test, we can conclude that the new medication is more effective than the original in lowering blood pressure for patients already taking blood pressure medication. However, this conclusion doesn't apply to all blood pressure patients.

A valid conclusion from the scenario about the pharmaceutical company's testing of its new medication would be the following: Inferences cannot be made about all blood pressure patients, though the conclusion can be made that the new medication lowers blood pressure more effectively than the original medication for patients who are already taking blood pressure medication. The study has a specific sample population: people who are already taking blood pressure medication. We can't extrapolate this to all blood pressure patients, because the study didn't include those who don't take any medication. However, it was observed that the new medication was more effective in lowering blood pressure than the original one within this specific group.

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If the train travels at an average speed of 50 Km/h, it would be late by 10 minutes.

Speed is simply referred to as distance traveled per unit time.

It is expressed as:

Speed = distance / time

Given that the train running between two stations 50 Km apart arrives on time if it travels at an average speed of 60 km/h.

The time taken by the train to travel 50 km at an average speed of 60 km/h can be calculated using the formula:

Speed = distance / time

time = distance / speed

time = 50 km / 60 km/h

time = 5/6 hour

Next, if the train travels at an average speed of 50 km/h, the time taken to cover the same distance of 50 km would be:

Speed = distance / time

time = distance / speed

time = 50 km / 50 km/h

time = 1 hour

Now, the difference in time between the two scenarios would be:

time difference = 1 hour - 5/6 hour

time = 1/6 hour

Convert to minutes

time = 1/6 × 60

time = 10 minutes

Therefore, the train would be late by 10 minutes.

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Answer:

Step-by-step explanation: bot

The solution of the triangle have been shown below.

To solve a triangle means to find the values of all its angles and sides. The method for solving a triangle depends on the given information.

Given that;

a/Sin A = b/SinB

Sin B = bSin A/a

B = Sin-1(bSin A/a)

B = Sin-1 (23Sin 40/17)

B = 60.4 degrees

Then we have that

C = 180 - (40 + 60.4)

= 79.4 degrees

Then;

a/sinA = c/Sin C

c= aSin C/Sin A

c = 17 * Sin 79.4/Sin 40

c =   16.71/0.643

c = 25.9

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The solution is, simplification of  the expression 4√ 2 + 2√ 32 is 12√2 .

We know that,

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Here, given expression is,  

4√ 2 + 2√ 32

=4√ 2 + 2√ 16 × 2

we know that,

√16 = 4

so, we get,

=4√ 2 + 2√2 × 4

=4√ 2 + 8√2

=12√2

Hence, The solution is, simplification of  the expression 4√ 2 + 2√ 32 is 12√2 .

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Answer:

2 Dozen Chocolate, 3 Dozen Vanilla, 5 Dozen Sugar.

Explanation:

0.5 x 10 = 5.

0.3 x 10 = 3.

0.2 x 10 = 2.

An expression that represents the amount of Huang's change include the following: A. 100 – (12(3x)).

In this scenario and exercise, you are required to write and determine an expression that represents the amount of change which Huang should receive from the seller.

This ultimately implies that, an expression that models or represents the amount of Huang's change would have the form;

Huang's change = Money presented - Total cost of 3 shirts

Huang's change = 100 - (12(3x))

By simplifying further, we have the following expressions;

Huang's change = 100 - 36x

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The area of each square would be 36 square inch.

We have,

Area of sheet = 12 square inches

So, the area of square to be cut

= 12in × 12in

= 144 square in

Now, number of squares=4

So, area of each square =144÷4

                                        =36 square inches

Thus, the side of each square is

= 36/4

= 6 inch

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The required posterior mean prevalence is closest to 0.47.

We can use Bayes' theorem to find the posterior distribution of the prevalence parameter, given the data and the Beta prior:

posterior ∝ likelihood x prior

where the likelihood is given by the binomial distribution:

likelihood = P(observing 4 cases out of 10 | prevalence)

and the prior is a Beta distribution with parameters α = β = 10:

prior = Beta(α=10, β=10)

We can calculate the posterior distribution by multiplying the likelihood and prior, and then normalizing:

posterior = Beta(α=14, β=16)

where the posterior Beta distribution has parameters α=14 (10 + 4) and β=16 (10 + 10 - 4).

The posterior mean of a Beta distribution with parameters α and β is:

posterior mean = α / (α + β)

Plugging in the values of α and β from the posterior distribution, we get:

posterior mean = 14 / (14 + 16) = 0.467

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Answer:

Step-by-step explanation:

b. the length of the adjacent side :11

c. you want to know the x which is hypotenuse

d. SOH CAH TOA, you know a and wants to know h, so should use cos function

The percentage of the sodas that was served which were regular would be = 18%

The quantity of regular sodas served = 18

The quantity of diet soda served = 82

The total number of soda served = 18+82 = 100

Therefore the percentage of soda that were regular would be;

= 18/100 × 100/1

= 18%

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Answer:

7/25

Step-by-step explanation:

0.28 = 28/100 = 7/25

Answer:

The irrational numbers are:

368.5468432...

14.19274128...

√.156

Answer:

The correct answer is 98°.

Answer: 82

Step-by-step explanation: all the angles of the triangle have to add up to 180 you all up the other angles and you get 98. 98= angle A your trying to find the outside angle we know that a line equals 180 degrees therefore we subtract that angle from 180 and get 82 which is your answer

The value of x is 5.48 units

Let us assume that the left right triangle be ABC and the right triangle on the right side be ABD.

So, the larger right triangle would be DAC.

Consider thr outer right triangle DAC.

The length of the hypotenuse DC would be,

DC = CB + BD

DC  = 3 + 7

DC = 10 units

Also right triangle ABC and DAC are similar triangles.

We know that the sides of the smilar triangles are in proportion.

Using the definition of similar triangles for DAC and ABC,

DA/AB = AC/BC = DC/AC

Consider, AC/BC = DC/AC

x/3 = 10/x

this is the required proportion.

x² = 3 × 10

x² = 30

x = 5.48 units

Thus the value of x = 5.48 units

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The diameter of the circle is 16.04 cm.

The circumference is 50.39 cm

A = πr²

where A is the area of the circle and r is its radius.

square both sides

r = √(A/π) = √(201.06/π) = 8.02 cm

The diameter of the circle is twice the radius, so we can find it by multiplying the radius by 2:

d = 2r = 2(8.02) = 16.04 cm

Therefore, the diameter of the circle is 16.04 cm.

To find the circumference of the circle, we can use the formula:

C = 2πr

where C is the circumference and r is the radius. We already know the value of the radius, so we can substitute it into the formula:

C = 2π(8.02) = 50.39 cm

Therefore, the circumference of the circle is 50.39 cm.

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Answer:

-----------------

Given system:

Add up the two equations to get same coefficient on both variables:

As we see none of the choices match the answer. It means either question or answer choices are inaccurate.

[tex]g(x)=\sin^2(x)+3\cos(x) \\\\[-0.35em] ~\dotfill\\\\ g(\pi )=\sin^2(\pi )+3\cos(\pi )\implies g(\pi )=[\sin(\pi )]^2+3\cos(\pi ) \\\\\\ g(\pi )=(0)^2+3(-1)\implies g(\pi )=-3[/tex]

The series of transformations that would map polygon ABCDE onto polygon A'B'C'D'E' is given as follows:

A rotation followed by a translation.

Examples of transformations are given as follows:

For this problem, we have that the inclination of the figure changed, and the figure moved from the second quadrant to the first/fourth, hence the figure underwent a rotation of 90º counterclockwise about the origin.

The figure also had the vertices changed from the rotation, hence a translation was also applied.

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