match the quadratic equation with the easiest method that could be used to find the solutions.​

the parameter and obtain the standard form of the rectangular equation would be: [tex]\frac{y-k}{r} = sin\theta.................(2)\\\\[/tex]

[tex]x=h+rcos\theta ,y=k+rsin\theta\\x-h=rcos\theta\\\frac{x-h}{r}=cos\theta...................(1)y=k+rsin\thetay-k=rsin\theta[/tex]

[tex]\frac{y-k}{r} = sin\theta.................(2)\\\\[/tex]

square and add both the equations

[tex]\frac{(x-h)^2}{(r^2)} + \frac{(y-k)^2}{(r^2)} = sin^2\s\theta + cos^2\s\theta\\\\\frac{(x-h)^{2}}{r^{2}}+\frac{(y-k)^{2}}{r^{2}}=1\\\\ the value of (sin^{2}\theta+cos^{2}\theta=1)\\\\(x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

The overall rectangular (or standard) form of the perplexing numbers is a + b I. We can change over complex numbers in rectangular form, by tracking down r = a 2 + b 2 and θ = tan − 1 ⁡.

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Answer:

Step-by-step explanation:

We can use the formula for exponential growth to solve this problem:

N = N0 * 2^(t/T)

where N is the final number of bacteria, N0 is the initial number of bacteria, t is the time elapsed, and T is the doubling time.

We know that N0 = 80, and T = 5 hours. We want to find t when N = 136.

136 = 80 * 2^(t/5)

Dividing both sides by 80, we get:

1.7 = 2^(t/5)

Taking the logarithm of both sides (base 2), we get:

log2(1.7) = t/5

Solving for t, we get:

t = 5 * log2(1.7) ≈ 3.4 hours

Therefore, it would take approximately 3.4 hours, to the nearest tenth of an hour, until there are 136 bacteria present.

Therefore, since a movement is set to start at T minus 80, the move will be completed at T plus 10 seconds.

The amount of rotations a shape can undergo around its center before returning to its initial position is referred to as the order of rotation in mathematics and geometry. It is also referred to as a shape's circular symmetry. A circle, for instance, has an order of rotation of infinite because it can be rotated indefinitely around its center without changing how it appears. A cube has an order of rotation of four because it will remain the same in shape whether it is rotated 90, 180, 270, or 360 degrees around its center.

given

At T minus 80 seconds, or 80 seconds prior to liftoff, the move is slated to start.

We must multiply the duration of the maneuver by the beginning time to determine the time at which it will be finished.

The move is estimated to take 1 and a half minutes. Since there are 60 seconds in a minute, we can change this to seconds by multiplying it by 60:

1 and a half minutes is equal to 1.5 minutes, 1.5 minutes multiplied by 60 seconds is equal to 90 seconds.

The move lasts 90 seconds as a result.

We multiply the duration of the move (90 seconds) by the start time (T minus 80 seconds) to determine the time at which the maneuver will be finished:

The move will be finished in T minus 80 seconds plus 90 seconds.

By adding the integers, we can make this simpler:

When the move is finished, the time will be T minus 80 seconds + 90 seconds + T plus 10 seconds.

Therefore, since a movement is set to start at T minus 80, the move will be completed at T plus 10 seconds.

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If the cycle time is 2 minutes per customer, 30 customers can be served per hour.

The given cycle time is 2 minutes per customer. To calculate how many customers can be served per hour, we need to calculate the number of minutes in an hour as follows: 60 minutes = 1 hour.

The time taken for each customer is 2 minutes. Therefore, the number of customers that can be served per hour can be calculated as follows:

Number of customers per hour = (60 minutes/hour) ÷ (2 minutes/customer)
Number of customers per hour = 30 customers.

Therefore, the number of customers that can be served per hour is 30, according to the given cycle time of 2 minutes per customer.

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Answer:

The term 2x+4y-2 is a binomial equation.

Step-by-step explanation:

Factoring said equation: 2(x+2y-1)

x intercepts: (1,0)

y intercepts: (0, 1/2)

-12 will be the value of the variable x.

The given expression is:

-9 = (-6 +x)/2

Simplifying the expression,

-6+x = -18

x = -18 +6

x = -12

Therefore, the value of the variable x will be -12.

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Answer:

A. The initial height, h, in feet, of the object.

Answer:

A The initial height, h, in feet, of the object.

Step-by-step explanation:

Let t = 0

h(t) = -16t ² + 110t + 72

h(0) = -16(0)² + 110 × 0 + 72

h(0) = 72

The height at time zero is 72.

72 is the initial height.

Answer: A The initial height, h, in feet, of the object.

Check the picture below.

so the ball hits the ground when g(x) = 0

[tex]\stackrel{g(x)}{0}=-16t^2+30t\implies 0=-2t(8t-15) \\\\[-0.35em] ~\dotfill\\\\ 0=-2t\implies \boxed{0=t} \\\\[-0.35em] ~\dotfill\\\\ 0=8t-15\implies 15=8t\implies \cfrac{15}{8}=t\implies \stackrel{ seconds }{\boxed{1.9\approx t}}\qquad \textit{falls to the ground}[/tex]

we get two values for "t", once at 0, because that's when the ball was at rest before being kicked.

The list price of the gift basket is $65.20. This can be determined by taking the total charge of the gift basket ($45.20) and subtracting the shipping charge of $5.50. The remaining $39.70 is the discounted amount of the gift basket.

Since the gift basket was discounted by 30%, the original list price can be determined by dividing the discounted amount by 70%, which is 0.7. Then, the list price can be calculated by multiplying the discounted amount by 1.43 (the reciprocal of 0.7). Therefore, the list price of the gift basket is $65.20.

This method of calculating the list price of the gift basket is called reverse-discounting. The process of reverse-discounting involves subtracting the discounted amount from the total charge to get the original list price. This method is useful when the discount rate is known and the total charge is given. It allows for the original list price of the item to be determined quickly and accurately.

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The measure of angle DBC based on the information given will be 115°.

A circle is a geometric shape that consists of all the points in a plane that are equidistant from a fixed point called the center. The distance between any point on the circle and the center is called the radius. A circle can also be defined as the set of all points that are a fixed distance away from the center point.

The total circle is 360 degrees.  The sum of the arcs of the circle is 360

Arc DC = 360 - Arc CB - Arc BC

DC = 360 -30-100

DC =230

Inscribed Angle =1/2 Intercepted Arc

<DBC = 1/2 CD

<DBC = 1/2 (230)

          = 115

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The amount of the mark up is $66 and the selling price is $286.

The amount by which a product's cost is raised to determine its selling price is known as the markup percentage. Usually, it is represented as a percentage of the item's price. Markup percentage is determined by the following equation:

Markup percentage = (Selling price - Cost price) / Cost price x 100%

Given that, the mark up is 30%.

Thus,

Mark up = 0.3 x $220 = $66

The selling price is:

Selling price = $220 + $66 = $286

Hence, the amount of the mark up is $66 and the selling price is $286.

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the probability that there are at most 2 defective components in the box is approximately 0.9044 and the probability of having at most 3 defective components out of 250 boxes is very close to zero.

a) Let X be the number of defective components in a box of 10 components. Then X follows a binomial distribution with n=10 and p=0.01, since the probability of a component being defective is 0.01. We want to find the probability that there are at most 2 defective components in the box, i.e., P(X ≤ 2).

Using the binomial probability formula, we get:

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

= (10 choose 0) × 0.01⁰ × 0.99¹⁰ + (10 choose 1) × 0.01¹ × 0.99⁹ + (10 choose 2) × 0.01² × 0.99⁸

= 0.90438222

Therefore, the probability that there are at most 2 defective components in the box is approximately 0.9044 (rounded to four decimal places).

b) We want to find the probability of having at most 3 defective components out of 250 boxes, each containing 10 components. Since np = 100.01 = 0.1 < 5 and n × (1-p)=10 × 0.99=9.9 > 5, we can use the normal approximation to the binomial distribution, with mean μ = np = 2.5 and standard deviation σ = √np(1-p) = 1.577.

Let X be the number of boxes with at most 3 defective components. Then X follows an approximate normal distribution with mean μ' = np=2.5250 = 625 and standard deviation σ' = √np(1-p)) = 12.5 × 1.577 = 19.712.

We want to find P(X ≤ 250), which can be written as P(X < 251) since X is a discrete variable. Using the continuity correction, we can approximate this probability as P(X < 251.5). Then we standardize the variable:

z = (251.5 - μ')/σ' = (251.5 - 625)/19.712 = -18.919

Using a standard normal table or calculator, we find that P(Z < -18.919) is a very small number, practically zero. Therefore, the probability of having at most 3 defective components out of 250 boxes is very close to zero.

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Complete Question

factory produces components of which 1% are defective. The components are packed in boxes of 10. A box is selected by random a) Find the probability that there are at most 2 defective components in the box b) Use a suitable approximation to find the probability of having at most 3 defective (inclusive 3 cases) components out of 250.

The deposit amount need to be paid in option 1 with 20% of the cost is equal to R10,000.

Cost of a tv = R50,000

Option 1.

Deposit amount = 20% of the cost.

Balance to be paid in 36 months

Simple interest = 12% p.a.

Deposit amount

= 20% of R50,000

= 0.2 x R50,000

= R10,000

Now,

Let x be the balance amount that needs to be paid.

x = R50,000 - R10,000

⇒ x = R40,000

Simple Interest = ( Principal × Rate of interest × time ) / 100

Total amount to be paid = Principal + Simple Interest

= R40,000 + (R40,000 x 0.12 x 3)

= R40,000 + R14,400

= R54,400

Therefore, the deposit amount for option 1 as per the given details is equal to R10,000.

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The sales price of the two shirt with 30%off on original price and 7% sales tax is equal to $22.47.

Original price of one shirt = $15

Number of shirts bought = 2

Sale discount = 30% off on original price

Sale price of one shirt = Original price - 30% of the original price

Substitute the value we get,

⇒Sale price of one shirt = 15 - (0.30)(15)

⇒Sale price of one shirt = $10.50

The cost of two shirts is equal to,

2 x $10.50 = $21.00

Sales tax = 7% of the total cost.

Substitute the value we have,

⇒Sales tax = 0.07 x $21.00

                   = $1.47

Total cost of two shirts = Cost of two shirts + Sales tax

⇒ Total cost of two shirts = $21.00 + $1.47

⇒ Total cost of two shirts = $22.47

Therefore, the total cost of two shirts at the sale price including the 7% sales tax is $22.47.

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for the angle measures where cos(0) = 0, sin(x) equals 1 for π/2 radians and -1 for 3π/2 radians.

cos(0) = 0 when the angle is π/2 or 3π/2 radians.

To label the corresponding points on the unit circle, we can use the following conventions:

The angle 0 radians (or 0 degrees) starts at the positive x-axis and goes counterclockwise.

The angle π/2 radians (or 90 degrees) is at the positive y-axis.

The angle π radians (or 180 degrees) is at the negative x-axis.

The angle 3π/2 radians (or 270 degrees) is at the negative y-axis.

So, for cos(0) = 0, the corresponding angle measures are π/2 and 3π/2 radians. On the unit circle, these correspond to the points (0, 1) and (0, -1), respectively.

the values of sin(x) for these angle measures:

sin(π/2) = 1

sin(3π/2) = -1

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Answer:

  5 days

Step-by-step explanation:

You want to know the amount of time that is 1/3 of 2 weeks and 1 day.

There are 7 days in a week, so 2 weeks and 1 day will be a total of ...

  2·7 +1 = 14 +1 = 15 . . . . days

If this time is split into 3 equal parts, each part is 1/3 of the total.

  1/3 · 15 days = 5 days

Brandon spent 5 days with each of his 3 bro.

B. F(y) = 1, 2 ≤ y

C. P(8000 < Y < 12000) = 1 - 0.4 = 0.6

D. P(Y > 15000) = 1 - 1 = 0

A detailed explanation of the answer.

A. The graph of the probability density function, f(y), is shown below:

B. The cumulative probability distribution function, F(y), is given by:

F(y) = 0, 0 ≤ y < 1

F(y) = (y-1)/2, 1 ≤ y < 2

F(y) = 1, 2 ≤ y

The graph of F(y) is shown below:

C. The probability that the station will pump between 8000 and 12,000 gallons in a particular month is calculated by subtracting the cumulative probability at 8000 (0.4) from the cumulative probability at 12,000 (1):

P(8000 < Y < 12000) = 1 - 0.4 = 0.6

D. Given that the station pumped more than 10,000 gallons in a particular month, the probability that the station pumped more than 15,000 gallons during the month is calculated by subtracting the cumulative probability at 10,000 (1) from the cumulative probability at 15,000 (1):
P(Y > 15000) = 1 - 1 = 0

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Answer:

(-1,1)

Step-by-step explanation:

The two cars are 10 miles apart, measured in a straight line.

We can use the Pythagorean theorem to find the distance between the two cars. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Let's imagine that the cars have traveled for some time, forming a right triangle where the distance between them is the hypotenuse. The northbound car has traveled 6 miles, which corresponds to the length of one of the legs of the triangle. The eastbound car has traveled 8 miles, which corresponds to the length of the other leg of the triangle. Therefore, the distance between the two cars is

distance = √(6² + 8²) = √(36 + 64) = √100 = 10 miles

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Using equations, we can find that he purchased 6 footballs.

An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. As in 3x + 5 = 15, for example.

Here in the question,

Let the number of footballs purchased be f.

Let the number of basketballs purchased be b.

Cost of each football = $60.

Cost of each basketball = $30.

Total amount spent = $450

Now,

60f + 30b = 450

Given,

2b = f

⇒ b = f/2

Putting the value of b in the equation,

60f + 30(/2f) = 450

⇒ 60f + 15f = 450

⇒ 75f = 450

⇒ f = 6

Therefore, he purchased 6 footballs.

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On his journey to his room, Eugene first found a few pieces of paper before discovering three more. Let's assume that he began with x bits of paper. Eugene started with  [tex]3[/tex] pieces of paper.

Eugene started with some pieces of paper, and then he found 3 more on his way to his room. So, let's say he started with x pieces of paper.

After finding the 3 more pieces, he had a total of   [tex]x + 3[/tex] pieces of paper.

He then cut each piece of paper in half, which means he doubled the number of pieces of paper. So, he ended up with  [tex]2 \times (x + 3) = 2x + 6[/tex]  half-pieces of paper.

We're given that he had 12 half-pieces of paper in the end, so we can set up the equation:

[tex]2x + 6 = 12[/tex]

Solving for x, we get:

[tex]2x = 6[/tex]

[tex]x = 3[/tex]

Therefore, Eugene started with 3 pieces of paper.

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Answer:

To find the probability of the next customer ordering peanut butter cup, we need to determine the total number of ice cream cones and the number of cones that are peanut butter cup.

The total number of cones is:

4 + 5 + 2 + 3 + 2 = 16

The number of cones that are peanut butter cup is 2.

Therefore, the probability of the next customer ordering peanut butter cup is:

2/16 = 0.125

So, the probability of the next customer ordering peanut butter cup is 0.125 or 12.5%.

There are 1001 ways to assign 10 employees to the dayshift and 4 employees to the night shift out of a group of 14 employe

WHAT IS COMBINATION ?

Combination refers to a mathematical concept used to count the number of ways in which a specific number of objects can be selected from a larger set, without considering their order. In other words, it is a way to calculate the number of possible combinations that can be formed from a given set of objects, where the order in which the objects are chosen does not matter. Combinations are denoted by the symbol "nCr" or "C(n,r)" and can be calculated using the formula: nCr = n!/r!(n-r)!, where n represents the total number of objects, and r represents the number of objects being chosen.

To solve this problem, we can use the combination formula. The number of ways to select k items from a set of n items is given by:

C(n, k) = n! / (k! * (n - k)!)

where n! means n factorial (i.e. n multiplied by all the positive integers less than n).

In this case, we want to select 10 employees for the dayshift and 4 employees for the night shift, out of a total of 14 employees. So the number of ways to make this assignment is:

C(14, 10) * C(4, 4) = (14! / (10! * 4!)) * (4! / (4! * 0!))

Simplifying this expression, we get:

C(14, 10) * C(4, 4) = (14 * 13 * 12 * 11) / (4 * 3 * 2 * 1) * 1

C(14, 10) * C(4, 4) = 1001 * 1

C(14, 10) * C(4, 4) = 1001

So there are 1001 ways to assign 10 employees to the dayshift and 4 employees to the night shift out of a group of 14 employe

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If delta and united flights are not equally on time, then the chance that we see a sample statistic of not equally or any statistic (larger or smaller) is larger, 0.05.

This is because the probability of a sample statistic being either larger or smaller (relative to the population) is always greater than the probability of it being equal. The p-value of 0.05 indicates that there is a 5% probability that the difference in on-time performance between Delta and United flights is due to chance.

The p-value of 0.05 indicates that there is a 5% chance that the observed sample statistic (of being larger or smaller than expected) is due to chance alone.

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The complete question is:

Complete the interpretation for the p-value:

If delta and united flights are (equally, not equally) on time, then the chance that we see a sample statistic of ______ or any statistic (larger, smaller) is _______ .

The 90% confidence interval for the population proportion is (0.1171, 0.1829).

To calculate the confidence interval, we first need to find the point estimate of the population proportion. The point estimate is the sample proportion which is given by:

p-bar = x/n = 60/400 = 0.15

where x is the number of items that failed the test and n is the sample size.

Next, we need to find the margin of error, which is given by:

ME = z*√(p_bar(1-p_bar)/n)

where z is the z-score corresponding to the confidence level, p_bar is the sample proportion, and n is the sample size.

For a 90% confidence level, the z-score is 1.645 (using a standard normal distribution table). Substituting the values, we get:

ME = 1.645*√(0.15(1-0.15)/400) = 0.0329

Finally, we can construct the confidence interval by adding and subtracting the margin of error from the point estimate:

CI = p_bar ± ME = 0.15 ± 0.0329 = (0.1171, 0.1829)

Therefore, we are 90% confident that the true population proportion of items that will fail the test is between 0.1171 and 0.1829.

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Answer:

5

Step-by-step explanation:

Landing 7 times on blue and 7 times on other colors means it landed on blue half of the time.

I expect it will land on blue half of the next 10 spins.

Answer: 5

Answer:

x:5,x:7

x^2-12x+35

x^2-12x=-35

x^2-12x+6^2=-35+36

(x+6)^2=1

insert a radical anywhere

x+6=1

x=1-6

x=-5. x=5

x=-1-6

x=-7. x=7

Answer:

Let the maximum number of operations the computer can perform per second be x.

According to the problem, the computer is running at 65% of the maximum, so it is performing 0.65x operations per second. We also know that it is performing 30 operations per second. So we can write the equation:

0.65x = 30

Solving for x, we get:

x = 30/0.65

x ≈ 46.1538

Rounding to the nearest whole number, we get:

x ≈ 46

Therefore, the maximum number of operations the computer can perform per second is 46, which is option 2.