What value is needed to complete the square x^2-6x+

Answer:

Well if perminder = 52ft that means x=5b8

Step-by-step explanation:

a) The 90% confidence interval for the population proportion is approximately (0.7777, 0.8423).

b) The 95% confidence interval for the population proportion is approximately (0.7737, 0.8463).

To calculate the confidence intervals for the population proportion, we can use the formula:

Confidence Interval = sample proportion ± margin of error

The margin of error can be calculated using the formula:

Margin of Error = critical value * standard error

where the critical value is determined based on the desired confidence level and the standard error is calculated as:

Standard Error = \(\sqrt{((p * (1 - p)) / n)}\)

Given that the sample proportion (p) is 0.81 and the sample size (n) is 500, we can calculate the confidence intervals.

a. 90% Confidence Interval:

To find the critical value for a 90% confidence interval, we need to determine the z-score associated with the desired confidence level. The z-score can be found using a standard normal distribution table or calculator. For a 90% confidence level, the critical value is approximately 1.645.

Margin of Error = \(1.645 * \sqrt{(0.81 * (1 - 0.81)) / 500)}\)

≈ 0.0323

Confidence Interval = 0.81 ± 0.0323

≈ (0.7777, 0.8423)

Therefore, the 90% confidence interval for the population proportion is approximately (0.7777, 0.8423).

b. 95% Confidence Interval:

For a 95% confidence level, the critical value is approximately 1.96.

Margin of Error = \(1.96 * \sqrt{(0.81 * (1 - 0.81)) / 500)}\)

≈ 0.0363

Confidence Interval = 0.81 ± 0.0363

≈ (0.7737, 0.8463)

Thus, the 95% confidence interval for the population proportion is approximately (0.7737, 0.8463).

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Step-by-step explanation:

a = 7

d = 14-7 = 7

s(50) = n/2*[a+(n-1)*d]

         = 50/2*[7+(50-1)*7]

         = 8750

The greatest common divisor of 6, 14, and 21 is 1, and it can be written as 6(0) 14(0) 21(1).

To find the greatest common divisor (GCD) of 6, 14, and 21 and write it in the form 6r 14s 21t, we can use the Euclidean algorithm.

Step 1: Find the GCD of 6 and 14.
- Divide 14 by 6: 14 ÷ 6 = 2 remainder 2
- Replace 14 with 6 and 6 with 2: Now we have 6 and 2.
- Divide 6 by 2: 6 ÷ 2 = 3 remainder 0
- Since the remainder is 0, the GCD of 6 and 14 is 2.

Step 2: Find the GCD of the result from step 1 (2) and 21.
- Divide 21 by 2: 21 ÷ 2 = 10 remainder 1
- Replace 21 with 2 and 2 with 1: Now we have 2 and 1.
- Divide 2 by 1: 2 ÷ 1 = 2 remainder 0
- Since the remainder is 0, the GCD of 2 and 21 is 1.

Therefore, the GCD of 6, 14, and 21 is 1. In the given form 6r 14s 21t, r would be 0, s would be 0, and t would be 1.

So, the GCD of 6, 14, and 21 is 1, and it can be written as 6(0) 14(0) 21(1).

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Answer:

We can assume that each one of the 15 sections has one of the animals. And because each one of the 15 sections is equal, the probability of landing in any animal must be the same, this means that the probability of landing on a given animal must be:

p = 1/15

Then the probability of landing on a pig is:

p1 = 1/15

The probability of landing on a giraffe is:

p2 = 1/15

The probability of landing on a pig, or a giraffe, will be equal to the sum of the two individual probabilities

P = p1 + p2 = 1/15 + 1/15 = 2/15.

So each spin has a probability of 2/15

This means that the probability of NOT landing on these animals must be 13/15.

Now, the probability of not landing on these animals in 234 different spins will be:

P´ = (13/15)^234 = 2.9*10^(-15)

Then the probability of landing on one of these animals, in at least one of the 234 different spins, will be:

prob = 1 - P´= 1 - 2.9*10^(-15) = 0.999999...

The number of simple events in this experiment is 16.

The correct answer to the given question is option c.

The probability of an event can be calculated by dividing the number of favorable outcomes by the number of possible outcomes. A simple event is one in which only one of the outcomes can occur. For example, if a coin is tossed, a simple event would be the outcome of the coin being heads or tails.

The total number of possible outcomes in the experiment of tossing 4 unbiased coins simultaneously is 2⁴, since there are two possible outcomes for each coin. Thus, the total number of possible outcomes is 16.

Each coin has two possible outcomes: heads or tails. If all four coins are flipped, there are two possible outcomes for the first coin, two possible outcomes for the second coin, two possible outcomes for the third coin, and two possible outcomes for the fourth coin. Therefore, the total number of possible outcomes is 2 × 2 × 2 × 2 = 16.

Therefore, the number of simple events in this experiment is 16, which is option (c).

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The rotation of the triangle ABC 360 degrees about the y-axis forms a cone

From the question, we understand that the triangle ABC is a right triangle

The vertical cross-section of a cone is a right triangle.

This means that a right triangle can be rotated 360 degrees on one of its legs (opposite or adjacent) to form a cone

Hence, the rotation of the triangle ABC forms a cone

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Answer:

UT= 24

Step-by-step explanation:

you use a^2+b^2=c^2

a is the straight long side (UT)

b is the base (UV)

c is the hypotenuse (UV)

a^2+7^2=25^2

a^2+49=625

a^2=576

to get a you square root

a=24

so UT = 24

Using differentials to estimate the relative error in the calculated area of the disk of disk with radius 15 cm is equals to the 3.192%.

We have, a disk with radius of 15 cm.

Maximum error = 0.25

We have to determine the area of the disk. Area is a two dimensional quantity. It is defined as the space occupied by figure or any two dimensional shape. Here, formula for area of disk, A = πr² --(1)

here, r = 15 cm , dr = 0.25

Relative error is defined as the ratio of absolute error in measurement to the oringnal measurement. Differentating the equation (1) with respect to r, dA = d( πr²)

=> dA = 2πr dr

Substitutes the known values, in above formula, dA = 2× π × 15 ×0.25

=> dA = 7.50 × π = 23.55

So, absoulte error in area = 22.55

Original value of area = π(15)² = 706.5 cm²

Now, relative error % = (∆A/A)×100

= (22.55/706.5)×100

= 0.031917 × 100

= 3.1917 ~ 3.192 %

Hence, required value is 3.192%.

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Complete question:

the radius of a disk is given 15 cm as with a maximum error of 0.25 . use differentials to estimate the relative error in the calculated area of the disk. please enter your answer in decimal format with three significant digits after the decimal point.

Answer:

$46.25

Step-by-step explanation:

If 2 cans are 18.50 then one can is 9.25.

9.25 x 5 is 46.25

Answer:

the rate which they sell a can is 9.25 which is 18.50 ÷ 2

so 9.25 multiplied by 5 will be 46.25

The profit-maximizing output level and the associated profit are both zero.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

To find the minimum value of SRATC, we need to first find the expression for SRATC:

SRATC = SRTC/q = (200 + 109 + 2q)/q = 309/q + 2

To minimize SRATC, we need to differentiate it with respect to q and set it equal to zero:

d(SRATC)/dq = -309/q² = 0

Solving for q, we get q = √(309).

Substituting q back into the expression for SRATC, we get the minimum value of SRATC:

\(SRATC_{min}\) = 309/√(309) + 2 ≈ 17.22

Therefore, the value of q that minimizes SRATC is √(309) and the minimum cost value of SRATC is approximately $17.22.

If the market price is $90, the profit-maximizing value of q can be found by setting marginal cost equal to price:

MC = d(SRTC)/dq = 109 + 4q/3 = 90

Solving for q, we get q = (3/4)(90 - 109) = -14.25, which is not a feasible value since q has to be non-negative.

Therefore, the firm would not produce any output at a price of $90.

If we assume that the firm can produce any positive amount of output, the profit-maximizing value of q would be where marginal cost equals marginal revenue, which is also equal to price under perfect competition.

Since marginal revenue equals price for a perfectly competitive firm, we have:

MR = price = $90

Setting MR = MC, we get:

90 = 109 + 4q/3

Solving for q, we get q = (3/4)(90 - 109) = -14.25, which is not a feasible value.

Therefore, the firm would not produce any output at a price of $90, regardless of the assumption of being able to produce any positive amount of output.

Hence, the profit-maximizing output level and the associated profit are both zero.

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First Dave picks his swimming day, then his running day, and then his biking day. Since each activity is different, the order in which he selects the days matters. Therefore the number of selections is P(7, 3).

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. The probability is calculated by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't. It is based on the likelihood that something will occur. The justification for probability serves as the main foundation for theoretical probability. For instance, the theoretical chance of getting a head when tossing a coin is 1/2.

Here,

He does 3 activities in 7 days,

P(7,3) is the ways to select the schedule.

Dave chooses his swimming, running, and biking days in that order. The sequence in which he chooses the days is important because each activity is distinct. Consequently, P is the number of choices (7, 3).

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Answer:

6.2x10^3

Step-by-step explanation:

I just used a scientific calculator

The gradient of the chord PQ is 2h + 8

Let's first find the coordinates of points P and Q on the curve y = 2x^2+1.

Point P has an abscissa of 2, so its coordinates are (2, 2(2)^2+1) = (2, 9).

Point Q has an abscissa of 2+h, so its coordinates are (2+h, 2(2+h)^2+1) = (2+h, 2(4+4h+h^2)+1) = (2+h, 8+8h+2h^2+1) = (2+h, 2h^2+8h+9).

The gradient of the chord PQ is given by:

(m) = Δy /Δx

(m) = (2h^2+8h+9 - 9) / (2+h - 2)

(m) = (2h^2+8h) / (h)

(m) = 2h + 8

As h approaches zero, the gradient of the chord PQ approaches 8, because the term 2h becomes negligible compared to 8 when h is small. Therefore, the gradient of the tangent to the curve at point P is 8.

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Answer:

A.) Two sides and the included angle of a triangle are congruent to the CP of another triangle

Step-by-step explanation:

So, SAS. The Side-Angle-Side congruence postulate.

To have SAS congruence, 2 adjacent sides of a triangle need to be congruent to another triangle's adjacent sides, AND the angles between (re: included angles) them need to be congruent as well.

The answer most similar to that would be A!

By the way, is that Savvas? We use that in our class too!

Anyhow, have a nice day fam. Spread The Love

Answer: Voila

Step-by-step explanation:

26. equal opposite sides

27. Alla angles must equal 360 so 101+101=202 360-202=158/2=79

28. Intersecting equal sides

29. Opposite sides p=5 and  since q-3=6 then q=9

30. Opposite equal angles 2m=70 so m=35 and n=110 because 360-140=220/2= 110

31. intersecting sides k+4=11 so k=7 and  m=8

If we simplify the quotient of algebraic expressions we get the following:

therefore, the restriction is x different of 0

At time t, the first pool contains 50+2.3t gal of water, while the second pool contains 102.2-3.5t gal.

They contain the same amount of water when these quantities are equal:

50 + 2.3t = 102.2 - 3.5t

5.8t = 52.2

t = 9

so the pools have the same amount of water after 9 min have passed.

The pools will contain same amount of water in 9 minutes

Let the number of minutes that the pools contain the same amount of water be represented by t.

Since the first pool contains 50 gallons of water and is filling at a rate of 2.3 gallons per minute, then this will be:

= 50 + (2.3 × t)

= 50 + 2.3t ......... equation i

The second pool contains 102.2 gallons of water and is draining at a rate of 3.5 gallons per minute. This will be:

= 102.2 - (3.5 × t)

= 102.2 - 3.5t ........ equation ii

Equate both equations and this will be:

50 + 2.3t = 102.2 - 3.5t

Collect like terms

2.3t + 3.5t = 102.2 - 50

5.8t = 52.2

Divide both side by 5.8

5.8t/5.8 = 52.2/5.8

t = 9

In conclusion, they'll have same amount of water in 9 minutes

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Answer:

Poli (muchas) edro (caras) luego sería muchas caras lo que representas las figuras poliédricas.

Step-by-step explanation:

La palabra poliedro viene del griego clásico πολύεδρον (polyedron), de la raíz πολύς (polys), «muchas» y de ἕδρα (hedra), «base», «asiento», «cara».

In the scenario described above, 5.2 is the population mean or parameter because it represents the mean of the entire population. The number 5.2 in this scenario is the population mean.A population refers to a complete group of objects, people, or other things that share common characteristics. Parameters are used to describe population attributes. The population mean (μ) is the average of all the values in a population.

A population mean may be determined using various statistical methods, including the simple random sampling technique.Simple random sampling is a probabilistic sampling method that ensures that each element in the population has an equal chance of being included in the sample. In other words, a simple random sample is one in which each member of the population has an equal chance of being chosen as part of the sample.

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The absolute maximum value of f(x) = \(x^3\) - 3x + 1 on the interval [0,3] is 19, which occurs at x = 3 and the absolute minimum value of f(x) =\(x^3\) - 3x + 1 on the interval [0,3] is -1, which occurs at x = 1.

To find the absolute maximum and absolute minimum values of f(x) = \(x^3\) - 3x + 1 on the interval [0,3], we need to first find the critical points of the function on this interval.
Taking the derivative of the function, we get:
f'(x) = \(3x^2\) - 3
Setting this equal to zero and solving for x, we get:
\(x^2\\\) - 1 = 0
(x - 1)(x + 1) = 0
So the critical points of the function on the interval [0,3] are x = 1 and x = -1.
Next, we evaluate the function at these critical points as well as at the endpoints of the interval:
f(0) = 1
f(1) = -1
f(3) = 19
f(-1) = 3
Thus, the absolute maximum value of the function on the interval [0,3] is 19, which occurs at x = 3, and the absolute minimum value of the function on the interval [0,3] is -1, which occurs at x = 1.
Therefore, we can summarize the answer as follows:
The absolute maximum value of f(x) = \(x^3\) - 3x + 1 on the interval [0,3] is 19, which occurs at x = 3.
The absolute minimum value of f(x) = \(x^3\) - 3x + 1 on the interval [0,3] is -1, which occurs at x = 1.

The complete question is:-

Find the absolute maximum and absolute minimum values of f on the given interval.f(x) =  \(x^3\) - 3x + 1[0,3](min)(max)

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Answer: I think the answer would be -4

There are 144 ways to form a five-digit number that is divisible by 5 using the numerals 0, 1, 2, 3, 4, and 5 without repetition.

For the number to be divisible by 5, its units digit must be either 0 or 5. Since we cannot repeat digits, we have two cases to consider:

Case 1: The units digit is 0.

In this case, we have 5 choices for the units digit (0, 1, 2, 3, or 4). For the remaining four digits, we can choose them in 4! ways (i.e., 4 choices for the first digit, 3 choices for the second digit, 2 choices for the third digit, and 1 choice for the fourth digit).

Therefore, the total number of five-digit numbers that are divisible by 5 and have a units digit of 0 is:

5 × 4! = 120

Case 2: The units digit is 5.

In this case, we have only one choice for the units digit, which is 5. For the remaining four digits, we can choose them in 4! ways as before.

Therefore, the total number of five-digit numbers that are divisible by 5 and have a units digit of 5 is:

1 × 4! = 24

The total number of ways to form a five-digit number that is divisible by 5 without repeating digits is the sum of the numbers from both cases:

120 + 24 = 144

Therefore, there are 144 ways to form a five-digit number that is divisible by 5 using the numerals 0, 1, 2, 3, 4, and 5 without repetition.

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Answer:

6 1/2 minutes per miles

2/13 miles per minutes

Step-by-step explanation:

Distance travelled = 2 1/2 miles

Time taken = 16 1/4 minutes

Average: minutes per mile

= 16 1/4 minutes / 2 1/2 miles

= 65/4 ÷ 5/2

= 65/4 × 2/5

= 13/2

= 6 1/2

Average time per mile in minutes

= 6 1/2 minutes per mile

Average (miles per minutes)

= 2 1/2 ÷ 16 1/4

= 5/2 ÷ 65/4

= 5/2 × 4/65

= 20 / 130

= 2/13 miles per minutes

Answer:

180,000 people

Step-by-step explanation:

2/5= 0.4

0.4x450,000=180,000

Answer:

180,000

Step-by-step explanation:

450,000/5 = 90,000

90,000 * 2 = 180,000

By using normal distribution of probability, it can be calculated that -

Probability that the height of a randomly chosen man is between 68 inches and 72 inches = 0.38296

What is normal distribution of probability?

Normal distribution of probability is a continuous type probability distribution whose probability density function is given by

f(x) = \(\frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{z^2}{2}}\)

Where z = \(\frac{x - \mu}{\sigma}\)

\(\mu\) is the mean and \(\sigma\) is the standard deviation

Here, normal distribution of probability is used

Mean = 70 inches

Standard deviation = 4 inches

For X = 68,

z = \(\frac{68 - 70}{4}\) = -0.5

For X = 72

z = \(\frac{72 - 70}{4}\) = 0.5

Probability the height of a randomly chosen man is between 68 inches and 72 inches = P(68 < X < 72)

                = P(X < 72) - P(X < 68)

                = P(z < 0.5) - P(z < -0.5)

                = 0.6915 - 0.30854

                = 0.38296

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The restaurant can make 992 pancakes in 2 hours

Given

The restaurant uses 124 cups every hour

Each cup can be used to make 4 pan cakes.

Since 1/4 cups of mix can make one pancake.

All the pancakes are in equal size

Since 4 pancakes can be made from one cup of mix

The restaurant uses 124 cups of mix which means

For an hour the restaurant produces 4 x 124 pancakes Which is equal to 496 pancakes

In two hours The restaurant can make double that of one hour

Hence 496 x 2

992

The restaurant can make 992 pancakes in two hours

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Answer:

y = -2x - 4

Step-by-step explanation:

We transform the line equation of L:

2x + y = 3 --(-2x)--> f(x) = y = -2x + 3

We now know that L intersects the y-axis at 3 and it has a slope of -2.

In order to construct a parallel line M, it needs to have an identical slope to L.

All we need to do now is to move one step from the given point (1,-6) towards 0 with the predetermined slope of -2, resulting in the point (0,-4).

Since we know slope and intersection with the y-axis (0,-4), we can construct the line equation:

f(x) = y = -2x - 4 for line M.

The appropriate values for the critical value, standard deviations, and sample sizes into the margin of error formula, you can calculate the margin of error for a 90% confidence interval estimate for the difference between the population means.

The margin of error for a 90% confidence interval estimate for the difference between the population means depends on the sample size, standard deviations of the populations, and the desired confidence level. To calculate the margin of error, you need the sample sizes of both populations (n1 and n2), the standard deviations of both populations (σ1 and σ2), and the critical value corresponding to the desired confidence level.

The formula to calculate the margin of error is:

Margin of Error = Z * √[(σ1^2 / n1) + (σ2^2 / n2)]

Where:

Z is the critical value based on the desired confidence level (e.g., for 90% confidence level, Z is approximately 1.645).

σ1 and σ2 are the standard deviations of the two populations.

n1 and n2 are the sample sizes of the two populations.

It's important to note that this formula assumes that the populations are normally distributed and that the samples are independent.

By plugging in the appropriate values, you can calculate the margin of error for your specific scenario.

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