A particular strain of bacteria triples in population every 45 minutes. Assuming you start with 50 bacteria in a Petri dish, how many bacteria will there be after 4.5 hours? Possible answers:
A. 33,960
B. 36,450
C. 12,150
D. 7015

The ratio of the volume of the hemispherical tank to its surface area is, V/A = 2r/9.

A three-dimensional object's total surface area exists the whole area of all of its external surfaces.

Let r be the radius of the circle and h be the height

To find volume of the hemispherical tank and its surface area.

Here,

TSA = Total Surface Area

CSA = Curved Surface Area

Volume of a hemisphere (V) = (2/3) πr³

TSA of the hemispherical tank(A) = CSA of the tank + CSA of the base.

TSA(A)  = 2πr² + πr² = 3πr²

The ratio of the volume of the hemispherical tank to its surface area is,

V/A = (2/3)πr³ / 3πr²

V/A = 2r/9

Therefore, the ratio of the volume of the hemispherical tank to its surface area is, V/A = 2r/9.

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The correct option regarding the skewness of the distribution is given by:

This is a skewed-left distribution, because the mean is less than the median.

If the mean is greater than the median, the distribution is right-skewed, also called positively skewed. Otherwise, if the median is greater than the mean, the distribution is left-skewed, also called negatively skewed.

In this problem, we have that:

The median is greater than the mean, hence the correct option is given by:

This is a skewed-left distribution, because the mean is less than the median.

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Answer:

hike 2 = -62

hike 3= -38

hike 4 = -225

In the given normal distribution with a mean of 100 and standard distribution of 15, 95% of values will fall between 70 and 130 using the Empirical rule of 95%.

It states that in a normal distribution approximately 95% of observations fall within two standard deviations from the mean on both sides of the normal curve. The normal curve's centre corresponds to the mean in a normal distribution.

The distance between the mean and the necessary point on either side in a normal distribution is known as the standard deviation.

Given: Mean = 100

Standard deviation = 15

Apply the 95% rule we get,

The normal curve's right side

Mean + 2 x standard deviation

= 100 + 2x 15

= 100 + 30

= 130.

The normal curve's left side,

Mean - 2 x standard deviation  

= 100 - 2x15

= 100 - 30

= 70.

Thus, we see that by using the Empirical rule of 95%, 95% values will fall between 70 and 130.

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Answer:2.10971436E14

Step-by-step explanation:

Answer:

Step-by-step explanation:

1,747,544,165,078,382 is the answer.

The 95% confidence interval for the true proportion of all registered voters who feel the economy is the most important issue is 0.686 to 0.734. The margin of error for this estimate is 0.024. The minimum sample size required to estimate the proportion with 95% confidence and a margin of error of 2% is approximately 1663.

a) Using the sample data, the 95% confidence interval for the true proportion of all registered voters who feel the economy is the most important issue is approximately 0.686 to 0.734.

b) The margin of error for this estimate is approximately 0.024.

c) To estimate the proportion with 95% confidence and a margin of error of 2%, the minimum sample size required can be calculated using the formula:

n = (Z^2 * p * (1 - p)) / E^2

Plugging in the values, we have:

n = (1.96^2 * 0.71 * (1 - 0.71)) / (0.02^2) ≈ 1663

Therefore, the minimum sample size required would be 1663.

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Answer:

25

Step-by-step explanation:

Step-by-step explanation:

64/(1+1+2)

= 64/4

= 16

1 : 1 : 2

mark = 1×16 = 16

dave = 1×16 = 16

ralph = 2×16 = 32

Step-by-step explanation:

hope it helps

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Answer:

5 ft

Step-by-step explanation:

trapezoid area = ((base + base) / 2) height

25.5 = ((3.2+7)/2) height

25.5= 10.2/2height

25.5/5.1

height = 5

The value of s for the given value is 24.05.

Given is an equation v² = u²+2gs, we need to find the value of s if v = 25, u = 12 and g = 10,

So,

25² = 12² + 2(10)s

625 = 144 + 20s

20s = 481

s = 24.05

Hence the value of s for the given value is 24.05.

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The measure of the angles and arc length for the circle are:

a: m∠BAD = 40°; b. arc CE = 48°; c. m∠BCD = 40°; d. m∠ADC = 42°; e.  m∠ABE = 66°.

Hence, the distinction between chord length versus arc length is that the former provides the distance between two places, whilst the latter provides the entire area covered across two points.

The chord's length is equal to twice the angle's radius multiplied by its sine.

The arrow theorem and central angle theorem are other names for the inscribed angle arc  theorem. The measuring of the central angle equals equal to twice the value of the inscribed angle occupied by the same arc, according to this theorem.

arc BD = 80°

arc AC = 84°

∠CBE = 24°

Thus,

a: m∠BAD

m∠BAD = 1/2(arc BD)

m∠BAD = 1/2(80°)

m∠BAD = 40°

b: arc CE

m∠CBE = 1/2(arc CE)

24° = 1/2(arc CE)

24°*2 = arc CE

arc CE = 48°

c: m∠BCD

m∠BCD = 1/2(arc BD)

m∠BCD = 1/2(80°)

m∠BCD = 40°

d: m∠ADC

m∠ADC = 1/2(arc AC)

m∠ADC = 1/2*84°

m∠ADC = 42°

e: m∠ABE

m∠ABE = 1/2(arc AC + arc CE)

m∠ABE = 1/2(84° + 48°)

m∠ABE = 1/2(132°)

m∠ABE = 66°

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Answer:

93

Step-by-step explanation:

The sum of the three angles of any triangle is equal to 180 degrees

Therefore,

180-41-46=93

Answer:

21 in

Step-by-step explanation:

As we can see 3 is multiplied by 3 to get 9

5 is also multiplied by 3 to get 15

so 7 should be multiplied by 3 to get 21

The expected number of times that they will end up flipping the coin \(\boxed{N}$.\)

Let P be the probability that Alpha goes bankrupt before either player reaches 2N dollars. We can calculate this probability using a recursive approach. Let p_i be the probability that Alpha goes bankrupt given that Alpha has i dollars and Beta has 2N-i dollars. Then we have:

\($p_i = \frac{1}{2}p_{i-1} + \frac{1}{2}p_{i+1}$\)

The first term represents the probability that Alpha loses the next flip and ends up with i-1 dollars, while the second term represents the probability that Alpha wins the next flip and ends up with i+1 dollars. The boundary conditions are\(p_0 = 1\) (Alpha is already bankrupt) and \($p_{2N} = 0$\) (Alpha has reached 2N dollars). We can solve this system of equations to find:

\($p_i = \frac{i}{2N}$\)

This result can be verified by induction.

Now, let\($E_i$\)be the expected number of flips required to reach the endpoint of the game (either bankruptcy or 2N dollars) starting from the state where Alpha has i dollars and Beta has \($2N-i$\)dollars. Then we have:

\($E_i = 1 + \frac{1}{2}E_{i-1} + \frac{1}{2}E_{i+1}$\)

The first term represents the flip that is about to be made, while the second and third terms represent the expected number of flips required to reach the endpoint starting from the new state after the next flip. The boundary conditions are \($E_0 = E_{2N} = 0$\)(we have already reached an endpoint). We can solve this system of equations to find:

\($E_i = 2N\left(1 - \frac{i}{2N}\right)^2$\)

Therefore, the expected number of flips required to reach the endpoint of the game starting from the initial state where both players have N dollars is:

\($E = E_N = 2N\left(1 - \frac{1}{2}\right)^2 = \boxed{N}$\)

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Answer:

Yes

Step-by-step explanation:

The whole number in 3 1/2 is 3

the whole number in 1 1/15 is 1

Since 1 1/15 isn't an improper fraction, if it's whole number is smaller then the whole fraction is smaller

since 3>1, 3 1/2 is greater than 1 1/15

Answer:

31/2 > 11/15

Step-by-step explanation:

Question: Is 31/2 greater than 11/15 ?

To solve this let us convert the fractions to decimals.

31/2 = 15.5

11/15 = 0.733

With a look we can easily say that 31/2 is indeed greater than 11/15.

So, 31/2 > 11/15.

Answer:

.41 cents

Step-by-step explanation:

divide it by 6

Answer:

I think it is $0.41

Answer:

AB slope is 1/2

CD slope is 1/3

Since the slopes of the lines aren't the same, the lines aren't parallel.

Step-by-step explanation:

The statement "x ∈ {x}" is true. The statement "{x} ⊆ {x}" is true. The statement "{x} ∈ {x}" is false. The statement "{x} ∈ {{x}}" is true.

a) The statement is true because an element x can be a member of a set that contains only itself. In this case, the set {x} contains the element x.

b) The statement is true because every element in {x} is also in {x}. Since both sets are identical, {x} is a subset of itself.

c) The statement is false because a set cannot be an element of itself. In this case, {x} is a set, and it cannot be an element of the same set.

d) The statement is true because the set {{x}} contains the set {x} as its only element. Therefore, {x} is an element of the set {{x}}.

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Answer:

91. The probability that Caroline will be ready before Andrew is 0.25 (Option B). Since the service times are exponentially distributed with a mean 15 minutes, the remaining service time for Andrew when Caroline arrives is also exponentially distributed with the mean 15 minutes. The service time for Caroline is also exponentially distributed with mean 15 minutes. The probability that Caroline’s service time is less than Andrew’s remaining service time is given by the formula P(X < Y) = 1 / (1 + λY / λX), where λX and λY are the rates of the exponential distributions for X and Y respectively. Since both service times have the same rate (λ = 1/15), the formula simplifies to P(X < Y) = 1 / (1 + 1) = 0.5. Therefore, the probability that Caroline will be ready before Andrew is 0.25.

92. The probability that Caroline will be ready before Bob is 0.35 (Option A). Since Bob arrived 10 minutes after Andrew, his remaining service time when Caroline arrives is exponentially distributed with mean 15 minutes. Using the same formula as above, we get P(X < Y) = 1 / (1 + λY / λX) = 1 / (1 + 1) = 0.5. Therefore, the probability that Caroline will be ready before Bob is 0.35.

The probability of winning a certain lottery is p = 1/64,481. For a single play, the expected number of wins is E(X) = 1*p + 0*(1-p) = p.

The variance of the number of wins for a single play is\(Var(X) = p(1-p) = 1/64,481 * 64,480/64,481 = 64,480/64,481^2\).

For 669 plays, the expected number of wins is 669p and the variance of the number of wins is \(669Var(X) = 669(64,480/64,481^2) = 668.99/64,481\).

The standard deviation is the square root of the variance, so the answer is approximately sqrt(668.99/64,481) = 0.309.

Therefore, the closest answer choice is D) 0.3.

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Answer:

An equivalent expression to p - 0.20p is 0.8p Hope this helps :)

Answer:

The answer is A. 12%

Step-by-step explanation:

Answer:

yay thx for the points, hehe

The frequency of the clock signal will determine the rate at which the counter counts.

To design a counter with the counting sequence 4, 3, 2, 1, 0, 11, 12, 13, 14, 15, 4, 3 ..., we need a modulo-16 counter that counts from 4 to 15 and then wraps around to 4 again. We can use a 74x169 counter chip for this purpose. The 74x169 is a 4-bit synchronous, reversible, up/down counter that can count up or down depending on the state of its up/down input (U/D). We need to modify the counter to count down from 4 to 0 and then count up from 11 to 15.

To implement this, we can use three inverters to generate the complement of the U/D input. We can then connect the complemented U/D input to the carry input (CI) of the counter, which will cause the counter to count down when the complemented U/D input is high and count up when it is low. To make the counter count from 4 to 15 instead of 0 to 15, we can preset the counter to 4 using the preset input (P) of the counter.

The following is the schematic for the counter:

+-|P      CP    |------+

   | |             |      |

   | +------+------|------|-+

   |        |      |      | |

   |        |      |      | |

   |        |      |      | |

   | +------+      |      | |

   | |             |      | |

   +-|U/D    QD    |------+ |

     |             |        |

     +-------------+        |

   +-|U/D'   Qa    |--------+

   | +-------------+

   |

   |

   |       +--------+

   +-------|  INV1  |

           +--------+

           |

           |

           |       +--------+

           +-------|  INV2  |

                   +--------+

                   |

                   |

                   |       +--------+

                   +-------|  INV3  |

                           +--------+

where CP is the clock input, P is the preset input, QD is the output of the counter, Qa is the complemented output of the counter, U/D is the up/down input, and U/D' is the complemented up/down input.

The counting sequence will be as follows:

When the counter is preset to 4 and the complemented U/D input is low, the counter will count up from 4 to 15.

When the counter reaches 15, it will wrap around to 4 and continue counting up.

When the counter reaches 4 again, the complemented U/D input will be high and the counter will count down from 4 to 0.

When the counter reaches 0, it will wrap around to 15 and continue counting down.

When the counter reaches 11, it will wrap around to 4 and start counting up again.

Therefore, the counting sequence will be: 4, 3, 2, 1, 0, 15, 14, 13, 12, 11, 4, 3, 2, 1, 0, 15, 14, 13, 12, 11, ...

Note that this counter will require a clock signal to operate. The frequency of the clock signal will determine the rate at which the counter counts.

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Answer:

14

Step-by-step explanation:

Let's take it step-by-step

7x-1+6x-1=180

We move all terms to the left:

7x-1+6x-1-(180)=0

We add all the numbers together, and all the variables

13x-182=0

We move all terms containing x to the left, and all other terms to the right

13x=182

x=182/13

x=14

So remember, we move all terms to the left. We add all the numbers together, and all the variables. And we move all terms containing x to the left, and all other terms to the right.

The equation of g(x) is 24 (3)ˣ when the graph is stretched vertically by a factor of 3 to form the graph g(x).

What is function?

For the parent function f(x) and a constant k >0,

then, the function given by  

g(x) = kf(x) can be sketched by vertically stretching f(x) by a factor of k if k>1 (or)

if 0 < k < 1 , then it is vertically shrinking f(x) by a factor of k

As per the given statement that the graph of f(x) is stretched vertically by a factor of 3 i.e

k = 3 >1

so, by definition

g(x) = 3 f(x) = 3 . 8(3)ˣ

= 8(3)ˣ⁺¹

= 24 (3)ˣ

Hence, the equation of g(x) is 24 (3)ˣ when the graph is stretched vertically by a factor of 3 to form the graph g(x).

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Answer:

2

Step-by-step explanation:

area of a parallelogram : b x h (base x height)

since there are no measurements, we are looking at the squares

im assuming that the squares are 1x1 squares

hence, for the base of the parallelogram, we are counting the squares

i added the halves together and got the answer 2

then we need to take the height

which im also assuming is 1

b x h = 1 x 2

a = 2

sorry if this is wrong but the angle that it was taken at, is not very clear ; (

The value of z-score for a score that is three standard deviations above the mean is 3.

In this question,

A z-score measures exactly how many standard deviations a data point is above or below the mean. It allows us to calculate the probability of a score occurring within our normal distribution and enables us to compare two scores that are from different normal distributions.

Let x be the score

let μ be the mean and

let σ be the standard deviations

Now, x =  μ + 3σ

The formula of z-score is

\(z_{score} = \frac{x-\mu}{\sigma}\)

⇒ \(z_{score} = \frac{\mu + 3\sigma -\mu}{\sigma}\)

⇒ \(z_{score} = \frac{ 3\sigma }{\sigma}\)

⇒ \(z_{score} = 3\)

Hence we can conclude that the value of z-score for a score that is three standard deviations above the mean is 3.

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