What is the circumference of the circle?
21.18
100.17
18.21
9.11

The correct solution to the equation 3x = 11 is x = ln11 - ln3.

To solve the equation 3x = 11, we can use logarithmic properties to isolate the variable x. Taking the natural logarithm (ln) of both sides, we have ln(3x) = ln(11). Using the logarithmic rule for the product of terms, we can rewrite ln(3x) as ln(3) + ln(x).

Therefore, the equation becomes ln(3) + ln(x) = ln(11). Rearranging the terms, we have ln(x) = ln(11) - ln(3). By the logarithmic property of subtraction, we can combine the logarithms, resulting in ln(x) = ln(11/3). Finally, exponentiating both sides with base e, we find x = ln(11/3).

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The probability that the total baggage weight exceeds the limit is 0.1056.

The normal distribution is a continuous probability distribution with most values located close to the center peak and is symmetrical around its mean.

For example,  heights, measurement errors, blood pressure, and IQ scores are normally distributed because the majority of people have these values close to the standard value.

Here, the mean \(\mu\) is 22 lbs, the standard deviation \(\sigma\) is 4 lbs, and the sample size n is 100.

The total baggage weight of the passengers is represented as \(\sum x\).

Then,

\(\begin{aligned} P\left(\sum x > 2250\right) &= P\left(\frac{\sum x}{ n} > \frac{2250}{100}\right)\\& = P( \bar{X} > 22.5) \end{aligned}\)

We know, that \(z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}\)

So, representing in a normal distribution,

\(\begin{aligned}P\left[z > \frac{(22.5 - 22)}{\frac{4}{\sqrt100}}\right] &= P(z > 1.25) \\&= 0.1056\end{aligned}\)

From the z-distribution table, the value for z>1.25 is 0.1056.

Therefore, the answer is 0.1056.

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Answer:

The point

Step-by-step explanation:

I hope this helps. Have a good day!

Answer:

Part A and D: Cubic function, Part B and C: Quadratic function,

Step-by-step explanation:

Answer:

Pages ll Minutes

2 ll 5

3 ll 7.5

5 ll 12.5

Step-by-step explanation:

Answer:

63

Step-by-step explanation:

Answer:

(100/t) minutes

Step-by-step explanation:

Craig's rate can be written as (5 minutes/t pages).  This is a conversion factor.  This means we can also invert the factor to (t pages/5 minutes), if desired.  A conversion factor tells us the that top value is equal to the bottom value, such as 12 inches/1 foot.  This can be inverted to 1 foot/12 inches.

We want to know how many minutes Craig needs to type 20 pages.  Assuming no distractions, we can use the conversion factor.

We can write:  (20 pages)*(5 minutes/t pages)

(20 pages)*(5 minutes/t pages)

(20 )*(5 minutes/t ) [The pages unit cancels]

(100/t) minutes

====

We don't know the value of t, so the result must include t.  If t happens to be 2 pages, for example, it would take Craig (100/2) or 50 minutes, to type 20 pages.

Multiplying matrices is a mathematical operation used to find the total cost of ads for each target group.

The order in which the matrices are multiplied is important because matrix multiplication is not commutative, meaning the result can differ depending on the order of multiplication. In the context of the problem, the order of multiplication determines how the various factors, such as the costs and target groups, are combined to calculate the total cost for each group. In the context of finding the total cost of ads for each target group, matrices are used to represent the costs and the allocation of ads to different groups. Let's say we have a matrix representing the costs of ads and another matrix representing the allocation of ads to target groups. To find the total cost for each group, we multiply these matrices.

However, matrix multiplication is not commutative, meaning that changing the order of multiplication can yield different results. This is because the order of multiplication determines how the elements of the matrices are combined. In the given problem, the order of multiplication determines how the costs and the allocation of ads are multiplied and summed to obtain the total cost for each target group.

For example, if we multiply the matrix representing the costs by the matrix representing the allocation of ads, we would be multiplying the costs by the number of ads allocated to each group, resulting in the total cost for each group. If we reverse the order and multiply the matrix representing the allocation of ads by the matrix representing the costs, the result would be different because we would be multiplying the number of ads allocated to each group by the costs, which would not give us the desired total cost for each group.

Therefore, the order of multiplication is important in this context to ensure that the factors, such as the costs and the allocation of ads, are correctly combined to calculate the total cost for each target group.

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Answer: = -2/4x + -1/2

Step-by-step explanation:

hope this helped

The value for x in the given triangle is 7. The solution is obtained using triangle proportionality theorem.

What is triangle proportionality theorem?

The triangle proportionality theorem states that if a line drawn parallel to any of the triangle's sides contacts the other two sides twice, then the other two sides of the triangle are divided in the same proportion.

In the figure, we are given a pair of parallel lines.

So, by using the basic proportionality theorem, we get

⇒5 / 40 = 3 / (2x + 10)

⇒5 (2x + 10) = 3 * 40

⇒10x + 50 = 120

⇒10x = 70

⇒x = 7

Hence, the value for x in the given triangle is 7.

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You have the following inequality:

√x > 2

Consider that only positive values of x result in real solutions. Moreover, if you squared both sides of the inequality, you obtain:

x > 4

The graph of the inequality is shown below:

If the pattern continues, the value of y when x is 5 would be 35.

Based on the given pattern, we need to determine the value of y when x is 5.

Let's analyze the relationship between x and y:

When x = 0, y = 15

When x = 1, y = 19

When x = 2, y = 23

When x = 3, y = 27

By observing the pattern, we can see that the value of y increases by 4 as x increases by 1.

This indicates that there is a constant rate of change between x and y.

To find the value of y when x is 5, we can continue the pattern by adding 4 to the previous value of y:

When x = 4, y = 27 + 4 = 31

When x = 5, y = 31 + 4 = 35

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Geometry is a branch of mathematics that deals with the study of shapes, sizes, positions, and dimensions of objects in space. It includes the study of points, lines, angles, curves, surfaces, and solids, and the relationships between them.

Euclidean geometry is a type of geometry that is based on the work of the ancient Greek mathematician Euclid. It is a branch of mathematics that deals with the properties and relationships of points, lines, angles, and planes in two and three-dimensional space.

In the given question

The specific property of the given axiomatic system is the Euclidean geometry of two-dimensional space. The system specifies the basic properties of points and lines in this geometry, including how they intersect, and serves as a foundation for further geometric reasoning and deduction.

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Answer:

it is an isosceles triangle

so angle c is 50°

and you know the sum of angle of the triangle is 180° so 50° is already given and angle c is also 50° then 50° +50°+b= 180°

then b= 180° -100°

b= 80°

hence angle B is 80°and

angle c is 50°.

Answer:

angle c is 50°

Step-by-step explanation:

The given set equality (A - (C ∪ B)) ∪ (C ∪ (A - (C ∪ B))) = A holds true.

To prove the given set equality (A - (C ∪ B)) ∪ (C ∪ (A - (C ∪ B))) = A, we will show that both sides are subsets of each other.

Let's start with the left-hand side (LHS):

(LHS) = (A - (C ∪ B)) ∪ (C ∪ (A - (C ∪ B)))

Consider any element x in (LHS). This element can belong to either of the two sets within the union.

a) If x belongs to (A - (C ∪ B)), it means x is in A but not in (C ∪ B). Since x is not in (C ∪ B), it implies that x is not in C and not in B. Therefore, x is in A, but not in C or B.

b) If x belongs to (C ∪ (A - (C ∪ B))), it means x is in either C or (A - (C ∪ B)). If x is in C, then it is trivially in A. If x is in (A - (C ∪ B)), it means x is in A but not in (C ∪ B), which implies x is not in C or B. Hence, x is in A.

Therefore, any element x in (LHS) is also in A, which implies (LHS) is a subset of A.

Next, let's examine the right-hand side (RHS):

(RHS) = A

Consider any element y in (RHS), which is A. By definition, y is in A.

Since (RHS) is A itself, every element y in (RHS) is also in A.

Hence, (RHS) is a subset of A.

Since we have shown that (LHS) is a subset of A and (RHS) is a subset of A, and vice versa, we can conclude that (LHS) is equal to (RHS). Therefore, the given set equality (A - (C ∪ B)) ∪ (C ∪ (A - (C ∪ B))) = A holds true.

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Given

The table,

The sample size is 27.

To find:

The mean weight of these 27 babies.

Explanation:

It is given that,

That implies,

The mean weight of 27 babies is,

Hence, the mean weight of 27 babies is 6.1 pounds.

Answer:

------------------

Use the formula for the union of two sets:

In this case, we have:

Plugging these values into the formula:

Now, solve for |A ∩ B| (the number of elements in common):

So, sets A and B have 32 elements in common.

Answer:

9

Step-by-step explanation:

The given information provides a square thin plane lamina with side length 4 cm, which is earthed along three sides.

(i) Deriving expressions for the potential and electric field strength:

Electric Field Strength (E):

E = -∇V, where ∇ represents the gradient operator and V(x, y) = sin(πx/2a)sin(πy/2a).

Now, let's calculate the components of the electric field E using the partial derivatives:

E = -(∂V/∂x)î - (∂V/∂y)ĵ

= -[(πcos(πx/2a))/2a]î - [(πcos(πy/2a))/2a]ĵ

= -(π/2a)cos(πx/2a)î - (π/2a)cos(πy/2a)ĵ.

(ii) Calculating the values at the center of the plate:

Voltage at the center of the square:

V(x, y) = sin(πx/2a)sin(πy/2a)

V(0.02, 0.02) = sin(π/4)sin(π/4) = 0.5V.

Vector E field at the center of the square:

E = -(π/2a)cos(πx/2a)î - (π/2a)cos(πy/2a)ĵ

E(0.02, 0.02) = -(π/2(0.04))cos(π/4)î - (π/2(0.04))cos(π/4)ĵ

= -19.63î - 19.63ĵ V/m.

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Answer:

1, 2 +, 3 | 1, +, + | 1 +, 2 +, +

1, 2, 3, 4 | 2, 3, 5, 6 | 1, 3, 4, 5, 6

Step-by-step explanation:

"+" is the upbeat "and" (eighth notes)

The Probability that 2 or fewer will withdraw without completing the introductory statistics course is 0.4547  .

The Binomial  Distribution formula is

P(X=x) = C(n,x)*pˣ*qⁿ⁻ˣ

where ,

n is the number of trials

x is the number of times success occurs

p is the probability of success

q is the probability of failure .

In the given question ;

it is given that

students that are registered for the course = 20

so , n=20

Let x denote the number of students that withdraw without completing the course .

given that 14 % students  withdraw without completing the course ,

hence p = 14% = 0.14

So , q= 1-p = 1-0.14 = 0.86

the probability that 2 or fewer will withdraw from the course is denoted by P(X ≤ 2) and  is calculated using

the formula , P(X≤2)=P(X=0)+P(X=1)+P(X=2)        ...(i)

using Binomial Probability we get

P(X=x) = C(n,x)*pˣ*qⁿ⁻ˣ

P(X=0) = C(20,0)*(0.14)⁰*(0.86)²⁰⁻⁰

= C(20,0)*(0.14)⁰*(0.86)²⁰

= 1*1*(0.0489)

= 0.0489

So , P(X=0)=0.0489        ...(ii)

P(X=1) = C(20,1)*(0.14)¹*(0.86)¹⁹

= 20*0.14*0.0569

= 0.1593

So , P(X=1)=0.1593        ...(iii)

P(X=2) = C(20,2)*(0.14)²*(0.86)¹⁸

= 190*0.0196*0.0662

= 0.2465    

So , P(X=2)=0.2465        ...(iv)

Substituting the values of (ii) , (iii) and (iv) in (i) , we get

P(X≤2)=P(X=0)+P(X=1)+P(X=2)

P(X ≤ 2) = 0.0489 + 0.1593 + 0.2465

= 0.4547

Therefore , the Probability that 2 or fewer will withdraw without completing the introductory statistics course is 0.4547   .

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Hope you get the right answer

Step-by-step explanation:

Answer:

85 beats per minute

Step-by-step explanation:

khan academy

Start by setting up your two sets of parenthses.

X² breaks down into x and x.

What we are looking for is factors of the constant term

that add to the coefficient of the middle term.

The question is, what is the coefficient of the middle term

in this problem if there is nothing written in front of the x.

Well if there is nothing written there,

the coefficient is understood to be 1.

So what we are looking for are factors of -12 that add to -1.

Factors of -12

+12 · -1

-12 · +1

+6 · -2

-6 · +2

+4 · -3

-4 · + 3

We can see that -4 and +3 add to -1.

So they go in the second position of each binomial.

This gives us (x - 4)(x + 3) as our answer.

(a) The population proportion of success is given as 53%. This means that 53% of the population is expected to have a successful outcome from the flu shot.

To calculate the population proportion of success, we are given that the flu vaccine is effective for 53% of patients administered the shot. This means that 53% (or 0.53) of the entire population is expected to have a successful outcome from the flu shot.

(b) The mean of the sampling distribution of the sample proportion is also 53%.

The mean of the sampling distribution of the sample proportion can be calculated using the same population proportion of success, which is 53%. The sampling distribution represents the distribution of sample proportions if multiple samples of the same size are taken from the population. Since the mean of the sampling distribution is equal to the population proportion, the mean in this case is also 53%.

(c) The standard deviation of the sampling distribution of the sample proportion is approximately 0.017.

To calculate the standard deviation of the sampling distribution of the sample proportion, we use the formula:

\(\sigma = \sqrt{\frac{p \cdot q}{n}}\)

where σ represents the standard deviation, p is the population proportion of success (0.53), q is the complement of p (1 - p, which is 0.47), and n is the sample size (85).

Plugging in the values, we get:

\(\sigma = \sqrt{\frac{0.53 \cdot 0.47}{85}}\)

Calculating this expression, we find:

\(\sigma \approx \sqrt{\frac{0.0251}{85}} \approx \sqrt{0.000295} \approx 0.0171\)

Rounding this value to three decimal places, the standard deviation of the sampling distribution of the sample proportion is approximately 0.017.

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The probability of getting at least one nun in three spins of a dreidel is approximately 0.578

The probability is the ratio of number of favorable outcomes to the total number of outcomes

The probability of getting no nuns in a single spin is 3/4, since there are three non-nun letters (Gimel, Hei, Shin) and four total letters.

The probability of getting no nuns in three spins is then (3/4)^3, since the spins are independent and we can multiply probabilities of independent events.

So the probability of getting at least one nun in three spins is

= 1 - (3/4)^3

= 1 - 0.421875

= 0.578125

Therefore, the probability of getting at least one nun is 0.578

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The given question is incomplete, the complete question is:

A dreidel is a four-sided spinning top with the Hebrew letters nun, gimel, hei, and shin, one on each side. Each side is equally likely to come up in a single spin of the dreidel. Suppose you spin a dreidel three times. Calculate the probability of getting (a) at least one nun?

Answer:

yes that's possible for example -3-5=-8

Answer:

46

Step-by-step explanation:

It will help :)

Answer:

46

Step-by-step explanation:

RIGHT ON EDGE~