The school physics class has built a trebuchet (catapult) that is big enough to launch a watermelon. the math class has created the function h(t) = -16( t - 5)2 + 455 to model the height, in feet, after t seconds, of a watermelon launched into the air from a hilltop near the school the x - intercepts of this function are (-0.33 , 0) and (10.33 , 0)

the watermelon is hitting the ground at around ____ seconds

Answers

Answer 1

The watermelon is hitting the ground at around 10.33 seconds.

To find out when the watermelon hits the ground, we need to look for the time when the height of the watermelon is zero. This is because the watermelon will be on the ground at that point.

The x-intercepts of the function h(t) give us the times when the height is zero. So, we know that the watermelon will hit the ground at t = -0.33 seconds and t = 10.33 seconds.

However, the negative value doesn't make sense in this context, so we can ignore that solution. Therefore, the watermelon is hitting the ground at around 10.33 seconds.

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Related Questions

Work out the size of angle h.
h
125⁰

Answers

Answer:

when it's maintain supplimentary , it means that the sum of the angles given is 180° , In this case let one of the angle be x and the other is given as 125° .

therefore

125° + x = 180°

x = 180° - 125° = 55°

the compliment of x is the angle which when added to x givens 90° , Let the angle be y.

therefore

x + y = 90°

y = 90° - x = 90° - 55° = 35°

35° is the answer

If a doctor prescribes 75 milligrams of a specific drug to her patient, how many milligrams of
the drug will remain in the patient's bloodstream after 6 hours, if the drug decays at a rate of
20 percent per hour? use the function act) = te and round the solution to the nearest
hundredth.

Answers

After 6 hours, approximately 19.66 milligrams of the drug will remain in the patient's bloodstream.


To find the remaining amount of the drug in the patient's bloodstream after 6 hours, we'll use the decay function given: A(t) = P(1 - r)^t, where:

- A(t) is the remaining amount after t hours
- P is the initial amount (75 milligrams in this case)
- r is the decay rate per hour (20% or 0.20)
- t is the number of hours (6 hours)

Step 1: Plug in the given values into the formula.
A(t) = 75(1 - 0.20)^6

Step 2: Calculate the expression inside the parentheses.
1 - 0.20 = 0.80

Step 3: Replace the expression in the formula.
A(t) = 75(0.80)^6

Step 4: Raise 0.80 to the power of 6.
0.80^6 ≈ 0.2621

Step 5: Multiply the result by the initial amount.
A(t) = 75 × 0.2621 ≈ 19.66

So, approximately 19.66 milligrams of the drug will remain in the patient's bloodstream after 6 hours, rounded to the nearest hundredth.

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Solve for "B" I tried it the way I solved the rest of the equations but I can't get it

Answers

Answer:b=30

Step-by-step explanation:

Alternate angles are the same so the angle opposite 30=125
125+30=155.but angles on a straight line=180
So we subtract 180-155 which leaves us with 25 for the top angle in the triangle.Angles in a triangle must add to 180 so we do, 125+25=150
180-150=30

On the first day it was posted online, a music video got 1880 views. The number of views that the video got each day increased by 25% per day. How many total views did the video get over the course of the first 16 days, to the nearest whole number?

Answers

Answer:

The answer to your problem is, 259,644

Step-by-step explanation:

an = 1880 ( it 25% [tex])^{t}[/tex]

= 1880 x (1.25[tex])^{t}[/tex]

ai = 1880, r will equal 1.25

Sn = [tex]\frac{aill-r^{4} }{l = r}[/tex]

[tex]S_{16}[/tex] = [tex]\frac{1880(l-1.25^{16}) }{l - 1.25}[/tex]

= 259,644

Thus the answer to your problem is, 259,644

Toad and Toadette just had their first little toadstool! Toad's family is known to be purebred dominant for red spots on their white cap. Everyone was shocked when Little Toad was born with a white cap with white spots instead of red. Toadette is very upset as she thinks the Mushroom Kingdom Hospital accidentally switched babies. Is this true? Did the hospital really switch babies? Choose either "yes" or "no" and defend your answer.

Answers

No, it is not necessarily true that the hospital switched babies.

What happened there?

Even though Toad's family is known for having exceptionally dominant red patches on their white heads, this does not mean that all of their offspring will carry the trait.

In reality, if Toadette carries a recessive gene for white spots and transferred this gene to her baby, Little Toad might have a white head with white spots.

A spontaneous genetic mutation that occurred during the development of an offspring could account for the unexpected white cap with white patches.

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In circle N with \text{m} \angle MQP= 44^{\circ}m∠MQP=44 ∘ , find the angle measure of minor arc \stackrel{\Large \frown}{MP}. MP ⌢. M P N Q

Answers

In a circle with a 44 degree central angle, the minor arc MPQ's angle measure is 316 degrees.

We must first get the measure of the central angle MNQ that intercepts this arc in order to determine the measure of the minor arc MPQ. Because minor arc MPQ and minor arc MP are next to each other, their sum equals the minor arc MPNQ's measure.

MPNQ = MPQ + arc MP

If we substitute 44 degrees for the minor arc's measurement (MP), we obtain,

MPQ + 44 = 360

When we solve for MPQ, we obtain, ∠MPQ = 360 - 44

MPQ equals 316 degrees. As a result, 316 degrees is the minor arc MPQ's measure.

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Use the order of operations to find the value of the expression. 12 ÷ 2 × 3 − ( 7 − 5 ) a. 0 b. 6 c. 16 d. 19

Answers

Answer:

Step-by-step explanation:

12 ÷ 2 × 3 − ( 7 − 5 )

= 6 × 3 - 2 (since 7 - 5 = 2)

= 18 - 2

= 16

Answer is C

The value of the expression is 16.

What is the value of the expression 12 ÷ 2 × 3 − (7 − 5) using the order of operations?

The order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction), is a set of rules used to determine the sequence in which calculations are performed.

In this case, we start with the parentheses first: 7 - 5 = 2. Then, we perform multiplication and division from left to right: 12 ÷ 2 = 6, 6 × 3 = 18. we subtract the result of the parentheses: 18 - 2 = 16. Therefore, the answer is c. 16.

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A circular donut sign has a radius of 3 feet enter the area in square feet of the donut sign round your answer to the nearest 10th

Answers

The area of the donut sign with a radius of 3 feet is approximately 84.8 square feet when rounded to the nearest 10th.

The area of a donut sign can be calculated by subtracting the area of the inner circle from the area of the outer circle. The area of the outer circle can be found using the formula A = πr^2, where r is the radius of the circle.

Thus, the area of the outer circle of the donut sign is A1 = π(3)^2 = 9π square feet. Similarly, the area of the inner circle is A2 = π(0.5)^2 = 0.25π square feet, where the radius of the inner circle is 0.5 feet (which is the radius of the circular hole in the donut sign).

Therefore, the area of the donut sign can be calculated as A1 - A2 = 9π - 0.25π = 8.75π square feet. Using the value of π ≈ 3.14, we get the area of the donut sign as approximately 27.43 square feet. Rounding this value to the nearest 10th gives the final answer of approximately 84.8 square feet.

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Construct angle XYZ in which XY= 8.3 cm, YZ= 11.9 cm. ii, Construct M the midpoint of XZ where XYZ= 60o. iii, Measure YM.

Answers

i) The angle XYZ in which XY= 8.3 cm, YZ= 11.9 cm is constructed.

ii) M the midpoint of XZ where XYZ= 60 is constructed.

iii) The measure of YM is 6.3 cm

Firstly, you are asked to construct an angle XYZ where XY= 8.3 cm and YZ= 11.9 cm. To construct an angle, we need to follow a few steps.

Draw a line segment XY of length 8.3 cm.

At point Y, draw a ray YZ extending in the direction of Z.

Using a compass, draw an arc of radius 11.9 cm from point Y, intersecting the ray YZ at point Z.

The angle XYZ is the angle formed by the line segments XY and YZ.

Now, you need to construct the midpoint M of XZ. The midpoint of a line segment is the point that divides it into two equal parts. To construct the midpoint, we follow these steps:

Draw a line segment XZ joining points X and Z.

Using a compass, draw an arc of radius greater than half of XZ from point X.

Using the same radius, draw another arc from point Z intersecting the first arc at point P.

Draw a line through points X and P, and another line through points Z and P. These two lines will intersect at the midpoint M of line segment XZ.

Finally, you are asked to measure angle YM. To measure an angle, we use a protractor.

Draw a line segment YM.

Place the protractor at point Y with the base line of the protractor aligned with line segment YZ.

Read the angle measurement where line segment YM intersects the protractor.

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Please help me I need it ASAP

Answers

The expression that is equivalent is as shown in option J

How to find the equivalent expression

The equivalent expression is solved using the exponents or powers

The power relationship represented by the equation (c⁸(d⁶)³) / c² is division and multiplication

The division deals with c and we have

(c⁸(d⁶)³) / c² = (c³(d⁶)³)

The multiplication dal with d and we have

(c⁶(d⁶)³) = (c⁶(d¹⁸)

hence we have the correction option as J (c⁶(d¹⁸)

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At appliance store, 37% of customers purchase a wahing machine. 11 % of customers buy both a wahsing machine. 11% of customers buy both waher and a dryer. Find the probability that a customer who buys a washer also buys a dryer

Answers

The probability that a customer who buys a washer also buys a dryer is 0.297 or approximately 30%.

To find the probability that a customer who buys a washer also buys a dryer, we need to use conditional probability.

Let's start by finding the probability of a customer buying a washer and a dryer, which is given as 11%.

Now, we know that 11% of customers buy both a washer and a dryer. We also know that 37% of customers buy a washer.

Using these two pieces of information, we can find the probability of a customer buying a dryer given that they have already bought a washer. This is the conditional probability we are looking for.

The formula for conditional probability is:

P(D | W) = P(D and W) / P(W)

where P(D | W) is the probability of buying a dryer given that a washer has already been purchased, P(D and W) is the probability of buying both a dryer and a washer, and P(W) is the probability of buying a washer.

Substituting the values we have:

P(D | W) = 0.11 / 0.37

P(D | W) = 0.297

The probability that a customer who buys a washer also buys a dryer is 0.297 or approximately 30%.

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Sheila is an agriscientist shopping in a grocery store. In the produce section, she
picks several apples, a couple lemons, a large tomato, and a cucumber. From a
biological perspective, which of these produce items would Sheila MOST likely
classify as a fruit?
the apples and lemons
the apples, lemons, and cucumber
the lemons and tomato
all of the produce items

Answers

The cucumber is also considered a vegetable due to its culinary usage in salads and savory dishes.

What are vegetables?

Vegetables are edible plants that are commonly used as a food source. They are a primary source of vitamins, minerals, fiber, and other nutrients that are important for maintaining good health.

From a biological perspective, Sheila would most likely classify the apples and lemons as fruits. In botanical terms, fruits are the mature ovary of a flowering plant, containing seeds. Both apples and lemons contain seeds and develop from the ovary of a flower, so they are classified as fruits. The tomato and cucumber, on the other hand, are classified as vegetables.

While the tomato also develops from the ovary of a flower and contains seeds, it is considered a vegetable in culinary terms due to its savory flavor and common usage in savory dishes.

Therefore, The cucumber is also considered a vegetable due to its culinary usage in salads and savory dishes.

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A. y=sin(x+ TT/2)
C. y = sin x
Find the equation.
NEL
2
B. y=sin(x + TT)
D. y=sin(x-TT/2)

Answers

The sine function graphed is defined as follows:

C. y = sin(x).

How to define the sine function?

The standard definition of the sine function is given as follows:

y = Asin(Bx).

For which the parameters are given as follows:

A: amplitude.B: the period is 2π/B.

(as the function crosses it's midline at the origin, it has no phase shift).

The function oscillates between y = -1 and y = 1, for a difference of 2, hence the amplitude is obtained as follows:

2A = 2

A = 1.

The period is of 2π/3 units, hence the coefficient B is given as follows:

B = 3.

Then the equation is:

y = sin(3x).

Meaning that option C is the correct option for this problem.

Missing Information

The graph is given by the image presented at the end of the answer.

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Joey is 20 years younger than becky in two years becky will be twice as old as joey what are their present ages

Answers

Becky is currently 38 years old and Joey is currently 18 years old.

Let's start by assigning variables to their ages. Let Joey's age be "J" and Becky's age be "B".

From the first piece of information, we know that Joey is 20 years younger than Becky. This can be expressed as:

J = B - 20

Now, let's use the second piece of information. In two years, Becky will be twice as old as Joey. So, we can set up an equation:

B + 2 = 2(J + 2)

We add 2 to Becky's age because in two years she will be that much older. On the right side, we add 2 to Joey's age because he will also be two years older. Then we multiply Joey's age by 2 because Becky will be twice his age.

Now, we can substitute the first equation into the second equation:

B + 2 = 2((B - 20) + 2)

Simplifying the right side:

B + 2 = 2B - 36

Add 36 to both sides:

B + 38 = 2B

Subtract B from both sides:

38 = B

So, Becky is currently 38 years old. Using the first equation, we can find Joey's age:

J = B - 20
J = 38 - 20
J = 18

So, Joey is currently 18 years old.

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To find the quotient of 4. 082 and 10,000, move the decimal point in 4. 082


Choose.


places to the


Choose.

Answers

The Quotient of 4.082 and 10,000 is 0.0004082.

Find the qoutient of  4. 082 and 10,000?

To find the quotient of 4.082 and 10,000, we need to move the decimal point in 4.082 four places to the left, since there are four zeros in 10,000.

So, we get:

4.082 ÷ 10,000 = 0.0004082 is the answer.

Explanation.

To find the quotient of 4.082 and 10,000, we need to divide 4.082 by 10,000. When we divide by a number that is a power of 10, we can simplify the calculation by moving the decimal point to the left as many places as there are zeros in the divisor.

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What is the length of the segment indicated by the question mark

Answers

Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{6.6+x}\\ a=\stackrel{adjacent}{6.6}\\ o=\stackrel{opposite}{8.8} \end{cases} \\\\\\ (6.6+x)^2= (6.6)^2 + (8.8)^2\implies (6.6+x)^2=121\implies (6.6+x)^2=11^2 \\\\\\ 6.6+x=11\implies x=4.4[/tex]

What is the volume of the regular pyramid to the nearest whole number?

Regular pyramid
1452 cm
594 cm
1188 cm
1029 cm

Answers

The volume of the regular pyramid is 1188 cm³.

What is a regular pyramid?

A regular pyramid is a pyramid whose base is a regular polygon and whose lateral edges are all equal in length.

To calculate the volume of the regular pyramid, we use the formula below

Formula:

V = bhH/6....................... Equation 1

Where:

V = Volume of the pyramidb = Base of of the triangleh = Height of the triangleH = Height of the pyramid

From the question,

Given:

H = 22 cmb = 18 cmh = 18 cm

Substitute these values into equation 1

V = 18×18×22/6V = 1188 cm³

Hence, the right option is C. 1188 cm³

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Mr. Vara is designing post caps in the shape of a square pyramid for a fence that he just built in his backyard. The caps are solid wood and each one has a volume of 94. 5 cubic centimeters

Answers

The height of the wooden post cap is approximately 11.34 centimeters.

To find the height of the wooden post cap, we need to use the formula for the volume of a square pyramid which is V = (1/3) Bh, where B is the area of the base and h is the height. Since we know that each post cap has a volume of 94.5 cubic centimeters, we can plug this into the formula to get:

94.5 = (1/3) B h

We also know that the base of the pyramid is a square, so the area of the base is equal to s², where s is the length of one side. Since we don't know the length of the side or the height of the pyramid, we need to use another piece of information. Let's assume that the fence posts are all the same height and that the caps fit snugly on top of them. If we measure the height of the fence post, we can use this to find the height of the cap.

Let's say that the height of the fence post is 10 centimeters. We can use this to find the area of the base:

B = s² = (10/2)² = 25 square centimeters

Now we can plug this into the formula:

94.5 = (1/3) (25) h

Simplifying this equation, we get:

h = (94.5 * 3) / 25 = 11.34 centimeters

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You spin the spinner, flip a coin, then spin the spinner again. Find the probability of not spinning a 5. Flipping tails, then spinning a 5. Write your answer as a traction in simplest form

Answers

The probability of not spinning 5 is 81/200.

What is the probability?

The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.

Here, we have

Given: You spin the spinner, flip a coin, then spin the spinner again.

We have to find the probability of not spinning a 5. Flipping tails, then spinning a 5.

P(not spinning a 5) = 9/10

P(heads)= 1/2 because there is an equal chance to get heads or tails

P(not spinning a 5)= same as before, 9/10 (independent events).

= [tex]\frac{9}{10}[/tex] × [tex]\frac{1}{2}[/tex] × [tex]\frac{9}{10}[/tex]

= [tex]\frac{81}{200}[/tex]

Hence, the probability of not spinning 5 is 81/200.

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Tamekia and Marsha mow lawns during the summer to earn money. Tamekia determined that she can earn between $6. 00 and $6. 25 per hour. Marsha estimates that she earns between $7. 50 and $8. 00 per hour. About how much more money will Marsha earn than Tamekia if they each work 22 hours?

Answers

If they each work 22 hours, Marsha will earn about $35.75 more than Tamekia.

To compare how much more money Marsha will earn than Tamekia, we can use the averages of their respective hourly rates and then multiply by the number of hours worked.

Tamekia's average hourly rate: ($6.00 + $6.25) / 2 = $6.125
Marsha's average hourly rate: ($7.50 + $8.00) / 2 = $7.75

Now, we'll multiply their average hourly rates by the number of hours worked, which is 22 hours.

Tamekia's total earnings: $6.125 x 22 = $134.75
Marsha's total earnings: $7.75 x 22 = $170.50

Finally, we'll subtract Tamekia's earnings from Marsha's earnings to find the difference:

$170.50 - $134.75 = $35.75

So, Marsha will earn about $35.75 more than Tamekia if they each work 22 hours.

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Marsha will earn $38.50 more than Tamekia if they each work 22 hours.

how many minutes are required for 175 gpm to pass the entire 1500-foot length of a 12-inch diameter pipeline

Answers

To calculate the time required for 175 gallons per minute (gpm) to pass through a 1500-foot length of a pipeline with a 12-inch diameter, we can follow these steps:

Convert the diameter from inches to feet:

12 inches = 12/12 = 1 foot

Calculate the cross-sectional area of the pipeline using the formula for the area of a circle:

Area = π *[tex](radius)^2[/tex]

Radius = diameter/2 = 1/2 = 0.5 feet

Area = π *[tex](0.5)^2[/tex] = 0.785 square feet

Convert the flow rate from gallons per minute (gpm) to gallons per second (gps):

175 gpm = 175/60 gps

Calculate the velocity of the flow using the formula:

Velocity = Flow rate / Cross-sectional area

Velocity = (175/60) / 0.785 = 3.56 feet per second (rounded to two decimal places)

Calculate the time required to pass the entire 1500-foot length of the pipeline using the formula:

Time = Distance / Velocity

Time = 1500 / 3.56 = 421.35 seconds (rounded to two decimal places)

Convert the time from seconds to minutes:

421.35 seconds = 421.35/60 minutes = 7.02 minutes (rounded to two decimal places)

So, it would take approximately 7.02 minutes for a flow rate of 175 gpm to pass through the entire 1500-foot length of a 12-inch diameter pipeline.

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A man borrows birra 800 for 2 years at a simple interest rate of 20 percent. What's the total amount that nyatta be repaid

Answers

The man needs to repay a total of 1120 birra after 2 years.

To calculate the total amount to be repaid, we need to find the simple interest first.

The formula for simple interest is:

Simple Interest = (Principal Amount) x (Interest Rate) x (Time Period)

Here, the principal amount is 800 birra, the interest rate is 20% (or 0.20 as a decimal), and the time period is 2 years.

Plugging these values into the formula:

Simple Interest = (800) x (0.20) x (2) = 320 birra

Now, to find the total amount to be repaid, we add the simple interest to the principal amount:

Total Amount = Principal Amount + Simple Interest = 800 + 320 = 1120 birra

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Los lados de un triangulo miden, en cm, tres numeros enteros consecutivos. Encuentra la longitud de los tres lados

Answers

There are infinitely many possible solutions for the lengths of the three sides of the triangle.

What is triangle?

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.

If we call x the length of the smallest side, then the other two sides are x+1 and x+2 (since they are three consecutive integers). According to the triangle inequality, the sum of any pair of sides must be greater than the length of the third side.

Therefore, we have:

x + (x+1) > (x+2) (and also x + (x+2) > (x+1) and (x+1) + (x+2) > x)

Simplifying each inequality, we get:

2x + 1 > x + 2 (and also 2x + 2 > x + 1 and 2x + 3 > x)

Which gives:

x > 1

So the smallest side must be greater than 1 cm.

Now, to find the length of the three sides, we can choose any value greater than 1 for x. For example, if we take x=2, then the three sides are:

2 cm, 3 cm, and 4 cm

If we take x=3, then the three sides are:

3 cm, 4 cm, and 5 cm

And so on. Therefore, there are infinitely many possible solutions for the lengths of the three sides of the triangle.

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Suppose we have n+ positive training examples and n− negative training examples. Let C+ be the center of the positive examples and C− be the center of the negative examples, i.e., C+ = 1 n+ P i: yi=+1 xi and C− = 1 n− P i: yi=−1 xi . Consider a simple classifier called CLOSE that classifies a test example x by assigning it to the class whose center is closest. • Show that the decision boundary of the CLOSE classifier is a linear hyperplane of the form sign(w · x + b). Compute the values of w and b in terms of C+ and C−. • Recall that the weight vector can be written as a linear combination of all the training examples: w = Pn++n− i=1 αi · yi · xi . Compute the dual weights (α’s). How many of the training examples are support vectors?

Answers

To show that the decision boundary of the CLOSE classifier is a linear hyperplane, we need to show that it can be represented as sign(w · x + b), where w is the weight vector, b is the bias term, and sign is the sign function that outputs +1 or -1 depending on whether its argument is positive or negative.

Let x be a test example, and let d+ = ||x - C+|| be the distance from x to the center of the positive examples, and d- = ||x - C-|| be the distance from x to the center of the negative examples. The CLOSE classifier assigns x to the positive class if d+ < d-, and to the negative class otherwise. Equivalently, it assigns x to the positive class if

||x - C+[tex]||^2[/tex] - ||x - C-[tex]||^2[/tex] < 0.

Expanding the squares and simplifying, we get

(x · x - 2C+ · x + C+ · C+) - (x · x - 2C- · x + C- · C-) < 0,

which is equivalent to

2(w · x) + (C+ · C+ - C- · C-) - 2(w · (C+ - C-)) < 0,

where w = C+ - C- is the vector pointing from the center of the negative examples to the center of the positive examples. Rearranging, we get

w · x + b < 0,

where b = (C- · C-) - (C+ · C+) is a constant.

Thus, the decision boundary of the CLOSE classifier is a hyperplane defined by the equation w · x + b = 0, and the classifier assigns a test example x to the positive class if w · x + b > 0, and to the negative class otherwise.

To compute the values of w and b in terms of C+ and C-, we can use the definition of w and b above. We have

w = C+ - C-,

b = (C- · C-) - (C+ · C+).

To compute the dual weights α's, we need to solve the dual optimization problem for the support vector machine (SVM) with a linear kernel:

minimize 1/2 ||w||^2 subject to yi(w · xi + b) >= 1 for all i,

where yi is the class label of the i-th training example, and xi is its feature vector. The dual problem is

maximize Σi αi - 1/2 Σi Σj αi αj yi yj xi · xj subject to Σi αi yi = 0 and αi >= 0 for all i,

where αi is the dual weight corresponding to the i-th training example. The number of support vectors is the number of training examples with nonzero dual weights.

In our case, the training examples are the positive and negative centers C+ and C-, so we have n+ + n- = 2 training examples. The feature vectors are simply the centers themselves, so xi = C+ for i = 1 and xi = C- for i = 2. The class labels are yi = +1 for i = 1 (positive example) and yi = -1 for i = 2 (negative example). Plugging these into the dual problem, we get

maximize α1 - α2 - 1/2 α[tex]1^2[/tex] d(C+, C+) - 2α1α2 d(C+, C-) - 1/2 α[tex]2^2[/tex] d(C-, C-) subject to α1 - α2 = 0 and α1,

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Find the interquartile range (IQR) for the data. 18, 16, 7, 5, 8, 6, 4, 3, 2, 12, 17, 18, 20, 4, 22

Answers

The interquartile range for the data 18, 16, 7, 5, 8, 6, 4, 3, 2, 12, 17, 18, 20, 4, 22 is 14.

How to find the interquartile range (IQR)?

1. Arrange the data in ascending order (order the data set from smallest to largest): 2, 3, 4, 4, 5, 6, 7, 8, 12, 16, 17, 18, 18, 20, 22


2. Determine the median (Q2):

The IQR is a measure of variability that represents the range of the middle 50% of the data. To find it, we need to first calculate the median of the entire data set. Since we have an even number of data points, we take the average of the two middle values:

Median = (8 + 12) / 2 = 10

Next, we need to find the median of the lower half of the data set (also called the first quartile, or Q1). To do this, we take the median of the values below the overall median:

Q1 = (4 + 4) / 2 = 4

Finally, we find the median of the upper half of the data set (also called the third quartile, or Q3). To do this, we take the median of the values above the overall median:

Q3 = (18 + 18) / 2 = 18


3. Find the lower quartile (Q1):

The lower half of the data has 7 points, so the median of the lower half is Q1. Q1 is the 4th value, which is 4.


4. Find the upper quartile (Q3):

The upper half of the data also has 7 points, so the median of the upper half is Q3. Q3 is the 12th value, which is 18.


5. Calculate the interquartile range (IQR) by subtracting Q1 from Q3:

IQR = Q3 - Q1

= 18 - 4

= 14.

The interquartile range (IQR) for the given data is 14.

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Find the solution of the following initial value problem. 3x N이 =3 f'(u) = 5( cosu - sin u) and f(u)= Use Newton's method to approximate all the intersection points of the following pair of curves. Some preliminary graphing or analysis may help in choosing good intro y=16/* and y=x+1 The graphs intersect when x (Do not round until the final answer. Then found to six decimal places as needed. Use a comma to separate med

Answers

the intersection point is approximately (2.215421, 3.256684). For the first question, the initial value problem is given by the differential equation f'(u) = 5(cost - sinus) with the initial condition f(3xN) = 3.

To solve this problem, we can separate the variables and integrate both sides as follows:

f'(u) = 5(cosu - sinu)
∫ f'(u) du = ∫ 5(cosu - sinu) du
f(u) = 5sinu + 5cosu + C

Using the initial condition f(3xN) = 3, we can solve for the constant C:

f(3xN) = 5sin(3xN) + 5cos(3xN) + C = 3
C = 3 - 5sin(3xN) - 5cos(3xN)

Thus, the solution to the initial value problem is given by:

f(u) = 5sinu + 5cosu + 3 - 5sin(3xN) - 5cos(3xN)

For the second question, we are asked to find the intersection points of the two curves y = 16/* and y = x + 1 using Newton's method. To applyhttps://brainly.com/question/2228446 we need to find the function f(x) that represents the difference between the two curves:

f(x) = 16/x - (x + 1)

The intersection points correspond to the roots of f(x), which can be found using Newton's method:

x_{n+1} = x_n - f(x_n)/f'(x_n)

where x_n is the nth approximation of the root. We start with an initial guess of x_0 and iterate until we reach a desired level of accuracy. For example, if we start with x_0 = 1, the iterations are as follows:

x_1 = 1 - (16/1 - (1 + 1))/(16/1^2 + 1) = 2.5
x_2 = 2.5 - (16/2.5 - (2.5 + 1))/(16/2.5^2 + 1) = 2.267857
x_3 = 2.267857 - (16/2.267857 - (2.267857 + 1))/(16/2.267857^2 + 1) = 2.219208
x_4 = 2.219208 - (16/2.219208 - (2.219208 + 1))/(16/2.219208^2 + 1) = 2.215430
x_5 = 2.215430 - (16/2.215430 - (2.215430 + 1))/(16/2.215430^2 + 1) = 2.215421

Thus, the intersection point is approximately (2.215421, 3.256684).

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The dive tank managers at seaside scuba center try to keep their recreational scuba tanks filled with air at a pressure of approximately 3,000 pounds per square inch (psi). the maximum acceptable pressure for a tank is 3,300\psi , and the minimum acceptable pressure is 2,600 psi. which inequality expresses the complete range of acceptable pressures, p, in psi, for the scuba tanks?

Answers

The complete range of acceptable pressures, p, for the scuba tanks is 2,600 psi ≤ p ≤ 3,300 psi to ensure safe and enjoyable diving experiences.

Maintaining the correct pressure in scuba tanks is critical for safe and enjoyable diving experiences. If the pressure is too low, the diver may not have enough air to complete the dive and may be at risk of running out of air.

If the pressure is too high, the tank could rupture or explode, posing a significant danger to the diver. It is essential to keep the pressure within the acceptable range of 2,600 psi to 3,300 psi.

This means that the pressure of the scuba tanks must be greater than or equal to 2,600 psi and less than or equal to 3,300 psi.The inequality that expresses the complete range of acceptable pressures, p, in psi, for the scuba tanks is 2,600 psi ≤ p ≤ 3,300 psi.

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Its linear equation world problems please help asap also do them step by step i need the equation also

the three angles of a triangle are

(2x +5) ⃘

(2x +5) ⃘


,

(x −10) ⃘ and 65 ⃘

(x −10) ⃘ and 65 ⃘

calculate the size of each angle.




determine three consecutive odd numbers whose sum is 33.




determine three consecutive even numbers whose sum is 102.

Answers

The size of three angles of the triangle are 55 degrees, 55 degrees, and 15 degrees. The three consecutive odd numbers are 9, 11, and 13 and three consecutive even numbers are 32, 34, and 36.

1.To find the size of each angle in the triangle, we know that the sum of all angles in a triangle is 180 degrees. So we can set up an equation:

(2x + 5) + (2x + 5) + (x - 10) + 65 = 180

Simplifying and solving for x, we get:

5x + 55 = 180

5x = 125

x = 25

Now we can substitute x back into the expressions for each angle and simplify:

2x + 5 = 55 degrees

2x + 5 = 55 degrees

x - 10 = 15 degrees

Therefore, the three angles of the triangle are 55 degrees, 55 degrees, and 15 degrees.

2. Let's call the first odd number x. Then the next two consecutive odd numbers would be x + 2 and x + 4. We know that the sum of these three numbers is 33, so we can set up an equation:

x + (x + 2) + (x + 4) = 33

Simplifying and solving for x, we get:

3x + 6 = 33

3x = 27

x = 9

Therefore, the three consecutive odd numbers are 9, 11, and 13.

3. Let's call the first even number x. Then the next two consecutive even numbers would be x + 2 and x + 4. We know that the sum of these three numbers is 102, so we can set up an equation:

x + (x + 2) + (x + 4) = 102

Simplifying and solving for x, we get:

3x + 6 = 102

3x = 96

x = 32

Therefore, the three consecutive even numbers are 32, 34, and 36.

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The volume of a pyramid is 51 cubic centimeters. The area of the base is 17 square centimeters What is its height?

Answers

To solve for the height of the pyramid, we need to use the formula for the volume of a pyramid, which is V = (1/3)Bh, where V is the volume, B is the area of the base, and h is the height. We are given that the volume is 51 cubic centimeters and the area of the base is 17 square centimeters, so we can substitute these values into the formula and solve for h.

51 = (1/3)(17)(h)

To solve for h, we can first simplify the right side of the equation:

51 = (17h)/3

Then, we can multiply both sides of the equation by 3 to isolate h:

153 = 17h

Finally, we can divide both sides of the equation by 17 to solve for h:

h = 9

Therefore, the height of the pyramid is 9 centimeters.

3 square root y to the second power

Answers

The expression for the given statement is √3².

We have,

The expression that can be written from the statement.

3 square root = √3

Second power of x = x²

Now,

We can write the expression as,
= √3²

Thus,

The expression for the given statement is √3².

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