5) Find the LCM of 12 and 32​

The probability that a biased coin that lands on heads 60% of the time will be mistakenly declared fair according to the original criterion is 29.259%.

The original criterion for declaring a coin fair is that the probability of landing on heads is between 40% and 60%. A coin that lands on heads 60% of the time will fall within this range, so it is possible that it could be mistakenly declared fair.

The probability that this will happen can be calculated using the following formula:

P(mistake) = P(heads > 40%) × P(heads < 60%)

The probability that the coin will land on heads more than 40% of the time is 1 - 0.4 = 0.6. The probability that the coin will land on heads less than 60% of the time is 1 - 0.6 = 0.4.

Plugging these values into the formula, we get:

P(mistake) = 0.6 × 0.4 = 0.24

This is equal to 29.259%.

Therefore, the probability that a biased coin that lands on heads 60% of the time will be mistakenly declared fair is 29.259%.

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The value of following limit is zero which is less than one so the series is convergent.

What is convergent or divergent series?

The term "convergent series" refers to a series whose partial sums tend to a limit. A divergent series is one whose partial sums, in contrast, do not approach a limit. The Divergent series often reach, reach, or don't reach a particular number.

As given,

Infinity ∑ (k = 1) (9/K!)

Suppose that ak = 9/K!

Apply ratio test:

I (ak + 1)/ak I = I 9/(K + 1)! (K!/9) I

Simplify values,

I (ak + 1)/ak I = I K!/(K + 1)K! I

                    = I 1/(K + 1) I

So, that Left hand limit is,

Lim (n⇒∞) I (ak + 1)/ak I = Lim (n⇒∞) I 1/(K + 1) I

                                     = 1/(∞ + 1)

                                     = 0

Since Right hand limit is,

Lim (n⇒∞) I (ak + 1)/ak I = 0

Which is less than one.

So, the given series is Convergent series.

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The standard error of the sample mean is approximately 8.9 pounds.

What is standard error of the sample mean?

Simple division of the standard deviation by the square root of the sample size yields the SEM. By evaluating the sample-to-sample variability of the sample means, standard error determines the accuracy of a sample mean.

To find the standard error of the sample mean, we need to first find the sample mean weight of the students. To do this, we add up the weights of all the students and divide by the number of students:

(128 + 193 + 166 + 147 + 202 + 183 + 181 + 158) / 8 = 171.5

Next, we need to find the variance of the sample. The variance is a measure of the spread of the data around the mean, and is calculated as follows:

       \(variance = ((weight - mean)^2) / (n-1)\)

where weight is the weight of each student, mean is the sample mean weight, and n is the number of students.

Plugging in the values from our data, we get:

variance = (128 - 171.5)^2 + (193 - 171.5)^2 + (166 - 171.5)^2 + (147 - 171.5)^2 + (202 - 171.5)^2 + (183 - 171.5)^2 + (181 - 171.5)^2 + (158 - 171.5)^2 / 7

= 1096.5

Finally, we can find the standard error of the sample mean by taking the square root of the variance and dividing by the square root of the number of students:

                \(standard\ error = \sqrt{(variance / n)} \\\\= \sqrt{1096.5 / 8 )\\\\=8.9\)

So, The standard error of the sample mean is approximately 8.9 pounds.

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There are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

The multiplication principle states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.

To find the number of ways to choose 3 men from the 12 men, we can use the formula for combination, which is: ⁿCᵣ = n! / (r! (n-r)!).

where n is the total number of men and r is the number of men chosen

so, the number of ways to choose 3 men from the 12 men = ¹²C₃ = 1.

Similarly, we evaluate the number of ways to choose 2 women from the 8 women

as = ⁸C₂ = 14

Now, using the multiplication principle, we can find the total number of ways 3 men and 2 women be chosen if they are equally considered.

220 x 14 = 3080

Therefore, there are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

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Answer:

£12 per hour

Step-by-step explanation:

7 × 5 = 35 hours

35 h : 420

1 h : x

x = 420×1 / 35

= £12 per hour

Answer:

Concept: Numerical Analysis

Answer:

700,000

Step-by-step explanation:

x*0.80=560000

560000/0.80=x

x=700,000

Answer:

54cm, which is one side length

Step-by-step explanation:

The sum of all of the sides are 6, it's a regular hexagon the perimemter is just six times one side 36cm

Hope It Helps!

Step-by-step explanation:

In a parallelogram, opposite sides are equal and parallel. Therefore,

QT = PS = 3y ...(1)

PT + TR = PS

y + 2x + 1 = 3x + 9

2x - y = 4 .....(2)

PR = QT = 3y

PR = SQ = 3x + 9 ....(3)

From equations (1) and (3), we can see that:

3y = 3x + 9

y = x + 3

Substitute this value of y in equation (2):

2x - (x + 3) = 4

x = 7

To find the value of y, we can substitute x = 7 in equation (2):

2(7) - y = 4

y = 10

Therefore, x = 7 and y = 10.

Step-by-step explanation:

I=(pxRxt)/100

I=(1250×5.25×10)/100

I=656.25

amount to be paid is $1906.25 pls give me brainliest

the expression is "2 + 8." To find the quotient of 12 and 6, divide 12 by 6. The result is 2.

Step 1: Add 8 to the quotient.

Now, add 8 to the quotient found. The expression is "quotient + 8."

Step 2: Write the final expression.

The final expression that represents "8 more than quotient of 12 and 6" is "quotient + 8."

So, the expression is "2 + 8."

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The sample of 25 people interviewed by the sportswriter is not a Random sample. The correct answer is Option C. No, because not all residents of Columbus, Ohio have an equal chance of being selected.  

In statistics, sampling is the process of selecting a subset of individuals or units from a larger population to estimate or infer information about the population.

A random sample is a subset of individuals or units from a larger population that is selected in a way that every member of the population has an equal chance of being selected. In other words, a random sample is unbiased and represents the population as a whole.

In the given scenario, the sportswriter interviews the first 25 people who enter the stadium before a game in Columbus, Ohio to determine how strongly Columbus residents support building a new stadium for the local minor league baseball team.

Now, the question is whether this sample is a random sample or not.

The answer is "No, because not all residents of Columbus, Ohio have an equal chance of being selected," which is option C.

The reason is that the sportswriter only interviews the first 25 people who enter the stadium before the game. This means that the sample is not selected randomly from the entire population of Columbus residents, but only from the people who happened to be at the stadium at that particular time.

Moreover, people who attend minor league baseball games may not be representative of the entire population of Columbus residents. For example, people who attend baseball games may be more likely to support building a new stadium than those who do not attend such games.

Therefore, the sample of 25 people interviewed by the sportswriter is not a random sample and may not be representative of the entire population of Columbus, Ohio. The results of the survey based on this sample may not accurately reflect the opinions of all Columbus residents.

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Complete Question

A sportswriter wants to know how strongly Columbus, Ohio residents support building a new stadium for the local minor league baseball team. She stands outside the stadium before a game and interviews the first 25 people who enter the stadium. Is this a random sample?

A. Yes, because it gives very accurate results.

B. Yes, because all fans had a chance to be asked.

C. No, because not all residents of Columbus, Ohio have an equal chance of being selected.

D. No, because the sample size is not right.

The surface with the given vector equation, r(s, t) = (s cos(t), s sin(t), s), is a circular cone.

The vector equation r(s, t) = (s cos(t), s sin(t), s) represents a surface in three-dimensional space. Let's analyze the equation to determine the nature of the surface.

In the equation, we have three components: s, cos(t), and sin(t). The presence of s indicates that the surface expands or contracts radially from a central point. The trigonometric functions cos(t) and sin(t) determine the angle at which the surface extends in the x and y directions.

By observing the equation closely, we can see that as s increases, the radius of the surface expands uniformly in all directions, while the height remains constant. This behavior is characteristic of a circular cone. The circular base of the cone is defined by s cos(t) and s sin(t), and the vertical component is determined by s.

Therefore, the surface described by the vector equation r(s, t) = (s cos(t), s sin(t), s) is a circular cone.

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The integer that matches the situation I go for a hike in Colorado. The top of the mountain is feet above sea level is 14000.

A number system is defined as a system of writing to express numbers.

Given,

I go for a hike in Colorado. The top of the mountain is ___ feet above sea level.

We need to find the suitable integer in the blank.

The top of a mountain would be a high number above sea level, 144 is around ground level above sea level therefore the top of the mountain would be 14,000 feet above sea level

Hence, the integer that matches the situation I go for a hike in Colorado. The top of the mountain is feet above sea level is 14000.

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Answer:

The answer for this is B 15/36

it will take 6 cleaners working at the same rate to clean all the rooms in the hotel in 5 hours.

If 4 cleaners can clean all the rooms in a hotel in 7 1/2 hours, we can start by using the concept of work rate. Work rate is a measure of how much work is completed in a certain amount of time. If we assume that the work rate of each cleaner is constant, we can set up a proportion to find how long it will take 6 cleaners to clean the same amount of rooms:

4 cleaners can clean all the rooms in 7 1/2 hours.

Therefore, 1 cleaner can clean all the rooms in (4 x 7 1/2) hours = 30 hours.

So, if 1 cleaner takes 30 hours to clean all the rooms, then 6 cleaners working at the same rate will take:

(time for 1 cleaner) / (number of cleaners) = (30 hours) / (6 cleaners) = 5 hours

Therefore, it will take 6 cleaners working at the same rate to clean all the rooms in the hotel in 5 hours.

It is important to note that this assumes that the work rate of each cleaner is constant and that there are no factors that may affect the cleaning time, such as interruptions or changes in the number of rooms to be cleaned. Additionally, the optimal number of cleaners may vary depending on the size of the hotel and the specific cleaning needs.

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Answer:

x = -3

Step-by-step explanation:

See steps of solution:

Answer is -3

Answer:

x = -3

Step-by-step explanation:

5(5x+3) - 4(2x-9) = 0     Multiply out.

5*5x + 5*3 - 4*2x + 36 = 0

25x + 15 - 8x + 36 = 0 Combine like terms.

25x - 8x + 15 + 36 = 0

17x + 51 = 0 Subtract 51 from both sides.

17x = - 51   Divide each side by 17.

17x/17 = -51/17

x = - 3

Answer:

wachu wachu wa

Step-by-step explanation:

To calculate the work done to move a charge from one location to another, we can use the equation:

Work = (Change in Potential Energy) = q * (Change in Electric Potential)

where q is the charge and the change in electric potential is the difference in potential between the initial and final positions.

Given that the charge Q₁ = +2.0 μC is fixed at the origin, we need to calculate the change in potential energy for the moving charge Q₂ = +4.0 μC.

(a) Moving from (-3 cm, 4 cm) to (-1.5 cm, 2 cm):

The change in electric potential, ΔV = V(final) - V(initial), can be calculated using the equation for electric potential due to a point charge:

V = k * (Q / r)

where k is the Coulomb's constant (8.99 × 10^9 N·m²/C²), Q is the charge, and r is the distance between the charges.

Initial electric potential, V(initial) = k * (Q₁ / r₁)

Final electric potential, V(final) = k * (Q₁ / r₂)

Change in electric potential, ΔV = V(final) - V(initial)

Next, we can calculate the work done:

Work = q * ΔV

Given that q = Q₂ = +4.0 μC, we can substitute the values into the equation to find the work done.

To calculate the power, we can use the formula:

Power = Work / Time

Given that the time to make the change is 10 ms (0.01 s), we can calculate the power by dividing the work done by the time.

You can repeat this process for parts (b) and (c) by substituting the respective coordinates and following the same calculations.

Please note that the distances should be converted to meters before performing the calculations.

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Answer:

16

8

36

Step-by-step explanation:

Answer:

  x    y

\(\left[\begin{array}{ccc}16&4\\8&2\\36&9\end{array}\right]\)

Step-by-step explanation:

\(y = \frac{x}{4}\)

take the number on the y and substitute it on the equation:

1st one :

⇒ \(4 = \frac{x}{4}\)

(then multiply 4 on both sides)

⇒ 4 x 4 =  \(\frac{x}{4}\) x 4

⇒ 16 = x

2nd one :

⇒ 2 = \(\frac{x}{4}\)

( then multiply 4 on both sides)

⇒ 2 x 4 = \(\frac{x}{4}\) x 4

⇒ 8 = x

3rd one :

⇒ 9 = \(\frac{x}{4}\)

(then multiply 4 on both sides)

⇒ 9 x 4 = \(\frac{x}{4}\) x 4

⇒ 36 = 4

Your missing the diagram. Thus, I will try my best to help

Answer/Step-by-step explanation:

Given;

The diagram below shows how much time Antoine spends doing different activities each day.

How many hours does Antoine sleep in a day?

Solve;

To find how many hours does Antoine sleep in a day;

24 hour × percent of hour sleep = Hours sleep in a day

The sleeping hours = 24h × % = Hour

If you still do not understand please shown the diagram!

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a. The probability P(X < 10) is U(0, 50) is 0.20.

b. The probability P(X > 595) is U(0, 1,000) is 0.405.

c. The probability P(21 < X < 49) is U(19, 68) is 0.4762.

a. For a uniform continuous distribution U(0, 50), the probability of an event X < 10 can be calculated by dividing the length of the interval [0, 10] by the length of the entire interval [0, 50]. Since the lengths of both intervals are equal, the probability is 10/50 = 0.20.

b. Similarly, for a uniform continuous distribution U(0, 1,000), the probability of an event X > 595 can be calculated by dividing the length of the interval [595, 1,000] by the length of the entire interval [0, 1,000]. The length of the interval [595, 1,000] is 1,000 - 595 = 405, and the length of the entire interval is 1,000 - 0 = 1,000. Thus, the probability is 405/1,000 = 0.405.

c. For a uniform continuous distribution U(19, 68), the probability of an event 21 < X < 49 can be calculated by dividing the length of the interval [21, 49] by the length of the entire interval [19, 68]. The length of the interval [21, 49] is 49 - 21 = 28, and the length of the entire interval is 68 - 19 = 49. Therefore, the probability is 28/49 = 0.5714.

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53 inches is the mean height of the students in the group.

Given data: \(54,48,52,56,55\)

We know that mean of the heights =  \(\frac{Sum of all the heights}{No. of students}\)

                                                         \(= \frac{54+48+52+56+55}{5}\)

                                                         \(= \frac{265}{5}\)

                                                         \(= 53\) inches

Thus, the mean height of the students is 53 inches

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Answer:

10

Step-by-step explanation:

27-\(3x^{3}\)+(4 x \(2x^{2}\)) - 6

= 27 - 27 + (4 x 4) - 6

= 0 + 16 - 6

= 10

Answer: 10

Step-by-step explanation:

27 - 3^3 + 4 × 2^2 - 6

= 27 - 27 + 4 × 4 - 6 (since 3^3 = 27 and 2^2 = 4)

= 0 + 16 - 6= 10

Therefore, the simplified value of the expression is 10.

Answer:

1. 2

2. 2

Step-by-step explanation:

1.

2x+1 = x+3

-x -x

x+1 = 3

-1 -1

x=2

2.

3x-4 = x-8

-x -x

2x-4 = -8

+4 +4

2x = -4

/2 /2

x = 2

Answer:

1) x=2

2) x=-2

Step-by-step explanation:

2x+1=x+3

2x=x+2

2x-x=2

x=2

3x-4=x-8​

2x-4=-8

2x=-8+4

2x=-4

2x/2=-4/2

x=-4/2

x=-2

Hope it helps!

The value of the subtraction 4 kg 575 g from 8 kg 008 g is equal to

3 kilograms 433 grams.

First value of the expression is equal to

4 kilograms 575 grams

Second value of the expression is equal to

8 kilograms 008 grams

Subtract first expression from the second expression we have,

8 kilograms 008 grams

4 kilograms 575 grams

Now here 8 grams is smaller than 575 grams.

Borrow 1 kg from 8 kg

Convert kg into grams

1 kilograms = 1000 grams

Now,

 7 kilograms 1008 grams

- 4 kilograms   575 grams

3 kilograms 433 grams

Therefore, the value when we subtract  4 kg 575 g from 8 kg 008 g is equal to 3 kilograms 433 grams.

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Step-by-step explanation:

180(n-2)/n=90 ( this is the solution for the 90)

cross multiplying

180n-360=90n

180n-90n=360

90n=360

90n/90=360/90

n=4, the number of sides for the polygon with 90° is 4 sides

Solution for 100°

180(n-2)/n=100

180n-360=100n

180n-100n=360

80n=360

80n/80=360/80

n=4.5

Same applies to the rest 110°,125° ,150°,175°

The total area of the figure can be written as -

A{T} = {L x B} + {πR²/2}.

Area is a collection of two dimensional points on a plane enclosed by a one - dimensional line. Mathematically -

A = ∫∫F(x, y) dx dy

Given is that the area of figure a can be found by determining the sum of the area of the rectangle and of a semicircle.

We can write the total area as -

A{T} = A{Rectangle} + A{Semicircle}

A{T} = {L x B} + {πR²/2}

Therefore, the total area of the figure can be written as -

A{T} = {L x B} + {πR²/2}.

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The critical numbers of the function h(p) = (p - 1) / (p^2 - 5) are "dne" (does not exist).

To find the derivative of h(p), we can apply the quotient rule. Taking the derivative, we have:

h'(p) = \([(p^2 - 5)(1) - (p - 1)(2p)] / (p^2 - 5)^2\)

Simplifying this expression, we get:

h'(p) = \((p^2 - 5 - 2p^2 + 2p) / (p^2 - 5)^2\)

= \((-p^2 + 2p - 5) / (p^2 - 5)^2\)

To find the critical numbers, we set h'(p) equal to zero and solve for p:

\(-p^2 + 2p - 5 = 0\)

However, this quadratic equation does not factor easily. We can use the quadratic formula to find the solutions:

p = (-2 ± √\((2^2 - 4(-1)(-5))) / (-1)\)

p = (-2 ± √(4 - 20)) / (-1)

p = (-2 ± √(-16)) / (-1)

Since the discriminant is negative, the equation has no real solutions. Therefore, the critical numbers of the function h(p) = (p - 1) / (\(p^2\) - 5) are "dne" (does not exist).

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