Determine whether the conjecture is true or false. Give a counterexample for any false conjecture.
If you have three points A, B , and C , then A, B, C are noncollinear.

Answer: So the probability that both students have reaction times greater than or equal to 9 seconds is approximately 0.0251 or 2.51%.

Step-by-step explanation:

However, assuming that you are referring to a hypothetical scenario where two students are chosen at random from a larger population, and that their reaction times follow a normal distribution with a mean of μ and a standard deviation of σ, the probability that both students have reaction times greater than or equal to 9 seconds can be calculated as follows:

Let X1 and X2 be the reaction times of the first and second students, respectively. Then, we can write:

P(X1 ≥ 9 and X2 ≥ 9) = P(X1 ≥ 9) * P(X2 ≥ 9 | X1 ≥ 9)

Since the students are chosen at random, we can assume that their reaction times are independent, which means that:

P(X2 ≥ 9 | X1 ≥ 9) = P(X2 ≥ 9)

Now, if we assume that the reaction times follow a normal distribution, we can standardize them using the z-score:

z = (X - μ) / σ

where X is the reaction time, μ is the mean, and σ is the standard deviation. Then, we can use a standard normal distribution table to find the probability that a random variable Z is greater than or equal to a certain value z. In this case, we have:

P(X ≥ 9) = P(Z ≥ (9 - μ) / σ)

Assuming that μ = 8 seconds and σ = 1 second, we can calculate:

P(X ≥ 9) = P(Z ≥ 1)

Using a standard normal distribution table, we can find that P(Z ≥ 1) ≈ 0.1587.

Therefore:

P(X1 ≥ 9 and X2 ≥ 9) = P(X1 ≥ 9) * P(X2 ≥ 9 | X1 ≥ 9)

= P(X ≥ 9) * P(X ≥ 9)

= (0.1587) * (0.1587)

≈ 0.0251

So the probability that both students have reaction times greater than or equal to 9 seconds is approximately 0.0251 or 2.51%.

Answer:

-5m/2

Step-by-step explanation:

-m+ (-2m) +(-3m)+(-4m) +(-4m)+(-3m)+(-2m)+(-m)/8

-m-2m-3m-4m-4m-3m-2m-m/8

-20m/8

-5m/2

Answer:

2/5

Step-by-step explanation:

she can paint 2/5 of the fence

The probability of a randomly selected timber stand having more than 92 trees is 0.0744 or 7.44%.

Managed timber stands average 150 trees per acre with a standard deviation of 40. Assume acres are normally distributed.To find the probability of a randomly selected timber stand having more than 92 trees.We have to calculate the Z-Score using the formula,Z= (X-μ)/ σWhere X= 92 treesμ = 150 treesσ= 40Using the formulaZ= (X-μ)/ σZ= (92-150)/40= -1.45We know that the area under the normal distribution curve is 1. To find the probability of a random variable that falls between two points, we need to find the area between those points.A normal distribution curve is shown below:To find the probability of a randomly selected timber stand having more than 92 trees, we need to find the area to the right of Z= -1.45 using a normal distribution table. The probability is 0.0744 or 7.44%.Therefore, the probability of a randomly selected timber stand having more than 92 trees is 0.0744 or 7.44%.

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Answer:

6

Step-by-step explanation:

The atomic number of Carbon is 6, meaning it has 6 protons and 6 electrons

Answer:

6

Step-by-step explanation:

The atomic number is the number of protons in an atom. The atomic number of carbon is 6

Answer:

is 30 because 3 multiply by 10 is 30

Answer:

30 wpm

Step-by-step explanation:

1 hour=60min

1800/60=30

in 1min he can type 30 words

Answer:

the perimeter is

104/5 feet or 20 4/5 ft

Step-by-step explanation:

The perimeter is a loop that surrounds, circumscribes, nor defines a two-dimensional shape and a one length.

A park's sandbox measures \(20 \ \text ft\) in diameter at its base.

Todd's sandbox has a \(4 \ \text ft\) base.

Now \(\frac{4}{20}=\frac{1}{5}\\\\\)

As a result, the scale factor for smaller sandboxes is \(\ \frac{1}{5}\\\\\)

\(\to 14 \times \frac{1}{5} = 2.8\\\\\to 18 \times \frac{1}{5}= 3.6\\\\\)

As a result, in Todd's sandbox, the missing lengths (in feet) are 2.8 and 3.6.

Todd's sandbox has a perimeter of \(4 + 2.8 + 3.6 = 10.4\) feet.

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Answer:

I believe that your answer is a

Step-by-step explanation:

I remember that the exponent would be multiplied by both sides.

Answer: A

Step-by-step explanation:

the answer is b because if you

multiply it inside and get the exponents the answer

so the answer is A

Hope this helps :)

Answer:

8.8

Step-by-step explanation:

To find mean, add all of the numbers together, then divide that sum by how many numbers there are.

3 + 5 + 10 + 11 + 15 = 44

44 ÷ 5 = 8.8

hope this helps!

Step-by-step explanation:

3+5+10+11+15÷5=

44 divided by 5 which gives 8.4

therefore that is the mean hope this helps

To maximize profits, the firm should produce a quantity of goods x = 5 and y = 10, based on the cost function and price constraints.

To maximize profits, the firm needs to find the quantities of goods x and y that will yield the highest profit. The profit function can be defined as the revenue minus the cost. Revenue is calculated by multiplying the quantity of each good produced with their respective prices, while the cost function is given as C(x, y) = 10x + xy + 10y.

The firm is committed to delivering a total of 15 units, which can be expressed as x + y = 15. To determine the optimal production quantities, we need to maximize the profit function subject to this constraint.

By substituting the price expressions Ps = 50 - x + y and Py = 50 - x + y into the profit function, we obtain the profit equation. To find the maximum profit, we can take the partial derivatives of the profit equation with respect to x and y, set them equal to zero, and solve the resulting system of equations.

Solving the equations, we find that the optimal production quantities are x = 5 and y = 10, which maximize the firm's profits.

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Answer:

a) $1961

b) $710

c) $2671

Step-by-step explanation:

Bi-weekly mortgage & taxes: 718/2 weeks = 2 x 718 = $1436/month

Condo fees: $525/month

Electricity bill bi-monthly $320/2 weeks = 2 x 320 = $640/month

Water bill is quarterly, so 210/3 months. 210/3 = $70/month

a) housing expenses = mortgage, taxes, condo fees

1436 + 525 = $1961

b) utilities = electricity and water

640 + 70 = $710

c) all expenses listed

1961 + 710 = $2671

Answer:

1,440

Step-by-step explanation:

Because 360*4=1,440

Answer:

$1440

Step-by-step explanation:

What you're going to want to do is multiply 4 by 36 at first. This is going to get you to 144. If you really wanted to break it down, you can multiply 4 by 3, place a zero at the end, multiply 4 by 6, and add the totals. Next, since the question is 4x360 and not 36, we will need to place a zero at the end of the product. This will get you 1440. And so, the answer is $1440.

Answer:

B). ∠BAC and ∠CAD

C). ∠BAE and ∠EAD

D). ∠EAD and ∠DAC

Step-by-step explanation:

As we know, a linear pair consisting of angles at a single point of the line has a sum of 180° in total. In other words, two supplementary angles together comprise a linear pair. In the given figure, the pair of supplementary angles ∠BAC and ∠CAD, ∠BAE and ∠EAD, and ∠EAD and ∠DAC are the linear pairs as their sum is 180°. Thus, options B, C, and D are the correct answers.

Step-by-step explanation:

EAD ∠BAC and ∠CAD ∠BAE

Answer:

120 $12 tickets and 180 $15 tickets

Step-by-step explanation:

Given the 2 equations

12x + 15y = 4140 → (1)

x + y = 300 ( subtract y from both sides )

x = 300 - y → (2)

Substitute x = 300 - y into (1)

12(300 - y) + 15y = 4140 ← distribute and simplify left side

3600 - 12y + 15y = 4140

3600 + 3y = 4140 ( subtract 3600 from both sides )

3y = 540 ( divide both sides by 3 )

y = 180

Substitute y = 180 into (2)

x = 300 - 180 = 120

Number of $12 tickets : 120 ; Number of $15 tickets : 180

Step-by-step explanation:

<c =90 °

So, Pythagoras theorem can be used,

Hypotenuse ² = base ² + altitude ²

AB²=AC²+BC²

11²=AC²+4²

11²-4²=AC²

121-16=AC²

Root 105=AC

AC=10.2 cm

The length of AC is 10.25 cm

If ΔABC is a right angle triangle, then

AB² = BC²+AC²

where AB = Hypotenuse, BC & AC are adjacent sides of the right angle

Given, hypotenuse = AB = 11 cm

One of adjacent sides = BC = 4 cm

We have to find the length of AC.

Using pythagorean theorem,

AB² = BC²+AC²

⇒ AC² = AB² - BC²

⇒ AC² = 11²-4²

⇒ AC² = 121-16

⇒ AC = √105

⇒ AC = 10.25

So the length of AC = 10.25 cm

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Answer:

Step-by-step explanation:

\(Mean = \frac{Sum \ of \ all \ the \ data}{number \ of \ data}\\\\= \frac{3.8+5.1+4.1+3.8+3.3+3.6}{6}\\\\=\frac{23.7}{6}\\\\= 3.95\)

Mean = 3.95

B) To find the median, arrange the data in ascending order

3.3 ;  3.6 , 3.8  ; 3.8  ; 4.1  ; 5.1

As number of data is even, median = Average of (n/2)th term and (n/2)th term +1

= Average of 3 and 4th term

\(= \frac{3.8+3.8}{2}\\\\= 3.8\\\)

Median  = 3.8

C) 3.8 occurs two times.

So, Mode = 3.8

d) 14.6 is above the mean. So, if we add a data above the mean, then the mean will increase

e) If April (3.8)  is deleted from chart, Mean will increase. If we remove a data below the mean, then mean will increase

If April is deleted from chart,  there will be no change in median.

Still median will be 3.8 only

Answer:

2/7

Step-by-step explanation:

\(slope = \frac{1 - 3}{2 - 9} \\ = \frac{ - 2}{ - 7} \\ = \frac{2}{7} \)

The population size (in millions of cells) after 3 hours is approximately 11.9 million cells.

The population of a yeast cell grows with a constant relative growth rate of 0.4279 per hour. The initial population is 3.3 million cells. We need to calculate the population size after 3 hours.

The population size can be calculated using the formula for exponential growth:

P(t) = P₀ * e^(rt)

Where:

P(t) is the population size at time t,

P₀ is the initial population size,

r is the relative growth rate, and

t is the time in hours.

Given that the initial population (P₀) is 3.3 million cells and the relative growth rate (r) is 0.4279 per hour, we can substitute these values into the formula:

P(3) = 3.3 * e^(0.4279 * 3)

Using a calculator, we can evaluate the exponential term:

P(3) ≈ 3.3 * e^(0.4279 * 3)

      ≈ 3.3 * e^(1.2837)

      ≈ 3.3 * 3.6121

      ≈ 11.9187

Rounding to one decimal place, the population size after 3 hours is approximately 11.9 million cells.

Therefore, the population size (in millions of cells) after 3 hours is approximately 11.9 million cells.

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Answer:

Whats ur quetsion?

Answer:

i is probably 1.

Step-by-step explanation:

1^3 is equal to 1

1^47 is equal to 1

At 9:00, the distance between the tips of the hands is changing at a rate of 0.00 m/min (rounded to two decimal places).

To solve this problem, we can use the law of cosines to relate the angle between the two clock hands, e, and the distance between the tips of the two hands, c. The law of cosines states that:

\(c^2 = a^2 + b^2 - 2abcos(e)\)

Where a and b are the lengths of the clock hands and c is the distance between the tips of the hands.

At 9:00, the hour hand is pointing directly at the 9 and the minute hand is pointing directly at the 12. This means that the angle between the hands is:

e = 90 degrees

Substituting this into the law of cosines, we get:

\(c^2 = 2.5^2 + 2^2 - 2(2.5)(2)cos(90)\\c^2 = 6.25 + 4 - 0\\c^2 = 10.25\)

c = sqrt(10.25)
c = 3.2 meters (approximately)

Now we can differentiate both sides of the equation with respect to time, t:

2c(dc/dt) = 2a(da/dt) + 2b(db/dt) - 2ab(sin(e))(de/dt)

At 9:00, we know that da/dt = 0 and db/dt = 0, since the lengths of the clock hands are not changing. We also know that sin(90) = 1. Substituting these values and solving for dc/dt, we get:

2(3.2)(dc/dt) = 2(2.5)(0) + 2(2)(0) - 2(2.5)(2)(1)(de/dt)
6.4(dc/dt) = -10(de/dt)
dc/dt = -10/6.4
dc/dt = -1.56 meters per hour (approximately)

Therefore, the distance between the tips of the clock hands is changing at a rate of approximately -1.56 meters per hour (or about 1.56 meters per hour in the opposite direction).
At 9:00, the hour hand is at the 9 on the clock face, and the minute hand is at the 12. Let the length of the hour hand be 2.5m (A) and the length of the minute hand be 2m (B). We want to find the rate at which the distance between the tips of the hands (C) is changing with respect to time (t).

Using the Law of Cosines, we can write an equation relating the angle between the clock hands (θ) and the distance between the tips of the hands (C):

C² = A² + B² - 2AB * cos(θ)

At 9:00, the angle θ is 90 degrees, so cos(θ) = 0.

C² = (2.5)² + (2)² - 2(2.5)(2)(0) = 6.25 + 4

Now we differentiate both sides of the equation with respect to t:

2C * dC/dt = 0

Since we want to find dC/dt at 9:00, we need to calculate C first:

C = √(6.25 + 4) = √10.25 ≈ 3.20m

Now, using the derived equation:

2(3.20) * dC/dt = 0

dC/dt = 0 m/min

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Answer:

Ans

Confidentiality promotes respect and value for individuals because sensitive information about their personal life is not shared with others.

Answer:

its just 50 points

Step-by-step explanation:

Answer:

15 cm

Step-by-step explanation:

i had this question before

Nadia has constructed a pentagonal prism

We know that, a pentagonal prism has two pentagonal bases like top and bottom and five rectangular sides.

If we consider the bottom view of  pentagonal prism then it would be pentagon in shape.

If we consider the side view of  pentagonal prism then it would be rectangular in shape.

If we consider the front view of  pentagonal prism then it would be rectangle.

Therefore, Nadia has constructed a pentagonal prism

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The expression for A is P / B.

To solve the formula A = 21(a + b) for b, we need to isolate b on one side of the equation.

1. Start by distributing 21 to both terms inside the parentheses: A = 21a + 21b.
2. Next, subtract 21a from both sides of the equation to move all the terms containing b to one side: A - 21a = 21b.
3. Simplify the equation: A - 21a = 21b.
4. Divide both sides of the equation by 21 to solve for b: (A - 21a) / 21 = b.

So, the expression for b is (A - 21a) / 21.

Now let's solve the formula Ax + By = C for y.

1. Start by subtracting Ax from both sides of the equation to isolate the term containing y: By = C - Ax.
2. Next, divide both sides of the equation by B to solve for y: By / B = (C - Ax) / B.

So, the expression for y is (C - Ax) / B.

Lastly, let's solve the formula P = BA for A.

1. Divide both sides of the equation by B to isolate the term containing A: P / B = A.

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Answer:

98172

Step-by-step explanation:

I really hope this helps

Answer: the answer is -32

Step-by-step explanation: multiply -2 by itself 5 separate times.

Answer:

-32

Step-by-step explanation:

-2×-2×-2×-2×-2=4×4×-2

=-32